study on the laminair burning velocity of light alcohols and their mixtures with gasoline using an

Lander Buffel, Jelle Bauwens

GUCCI setupLaminar burning velocity measurements using the

Academic year 2013-2014Faculty of Engineering and ArchitectureChairman: Prof. dr. ir. Jan VierendeelsDepartment of Flow, Heat and Combustion Mechanics

Master of Science in Electromechanical EngineeringMaster's dissertation submitted in order to obtain the academic degree of

Counsellors: Louis Sileghem, Dr. ir. Jeroen VancoillieSupervisor: Prof. dr. ir. Sebastian Verhelst

�On a deux vies et la deuxième

commence le jour où l'on se

rend compte qu'on n'en a

qu'une.�

� Confucius, Sur Le Destin

ii

Voorwoord

Ik wil dit voorwoord gebruiken om enkele mensen te bedanken. Allereerst prof. dr. ir. Sebastian

Verhelst en ir. Louis Sileghem voor de uitstekende begeleiding van ons werk gedurende het hele

jaar. Jullie hebben ons altijd bijgestaan waar dat nodig was en gaven voldoende input om

steeds te kunnen blijven gaan voor deze thesis hoewel dat soms niet gemakkelijk was. Ook als

we vragen hadden konden we steeds bij jullie terecht.

Verder zou ik graag alle mensen bedanken die in het verleden hebben bijgedragen tot het re-

aliseren van de GUCCI opstelling zoals deze er nu uitziet. Ik wil ook ABC in het bijzonder

danken voor de sponsoring die zij aangeboden hebben om het onderzoek aan deze universiteit te

steunen. Bij het realiseren van deze thesis werden we vaak met praktische problemen geconfron-

teerd die enkel opgelost konden worden indien goed vakmanschap toegepast werd. Vandaar ook

speciale dank aan Koen voor het installeren, construeren en repareren van onderdelen, de vele

nuttige tips en zoveel meer. In het bijzonder wil ik ook ir. Roel Verschaeren danken voor zijn

hulp en goede raad bij onze thesis. Zijn GUCCI expertise en ervaring was een grote hulp bij het

realiseren van onze thesis. Ik wil ook de andere GUCCI thesisgroep, Tom Van Laere en Wesley

Elegeert, bedanken. Dankzij hun begrip en het wederzijdse respect konden we een goede en

correcte planning opzetten en werd het voor beide groepen een aangenaam laatste jaar. Ik wil

ook in het bijzonder Louis Descheemaecker bedanken voor het nauwkeurig en kritisch nalezen

van deze thesis. Tevens wil ik mijn vriendin bedanken voor het begrip wanneer een groot deel

van mijn tijd naar mijn thesis ging en ik vaak tot ’s avonds laat doorwerkte. In het kader van

het afsluiten van mijn studie dank ik ook mijn ouders voor het financieren van mijn studies en

kotleven, alsook het vertrouwen dat ze me altijd gegeven hebben.

Tot slot wil ik mijn thesispartner Jelle bedanken voor de vele plezante en minder plezante uren

die we samen doorbrachten aan de GUCCI opstelling. Zonder zijn aanwezigheid, motivatie en

inspiratie was deze thesis niet wat hij nu is. Verder wil ik je ook bedanken voor de vele hilarische

momenten. Jelle, het was een leuk thesisjaar met jou. Ik wens je veel succes met je verdere

carriere en toekomst.

Lander Buffel, juni 2014

Ik wil graag prof. dr. ir. Sebastian Verhelst, ir. Louis Sileghem en ir. Roel Verschaeren

bedanken om ons gedurende het hele jaar te steunen met onze thesis en te luisteren naar al onze

vragen. We konden steeds bij jullie terecht, een begeleiding als deze is zonder enige twijfel een

voorrecht voor elke thesisstudent. Ik zou in het bijzonder ook Koen Chielens willen bedanken,

die steeds voor ons klaar stond wanneer we praktische problemen hadden, wat zeker niet evident

is. Onze thesis liep niet altijd van een leien dakje, maar dankzij de vele vergaderingen met de

professor en Louis, de praktische tips en ervaring van Roel en het vakmanschap van Koen, zijn

we er in geslaagd deze tot een goed einde te brengen. Ook de feedback die we telkens kregen van

onze begeleiders was zeer bruikbaar en liet ons toe om progressie te blijven maken. Ik wil ook de

andere thesisgroep die de GUCCI-opstelling dit jaar gebruikte, Tom en Wesley, bedanken. Er

werden steeds goeie afspraken gemaakt en er was wederzijds respect. Het was een aangenaam

jaar.

Tot slot wil ik mijn thesispartner Lander Buffel bedanken voor de vlotte en aangename samen-

werking. Je was een toonbeeld van inzet, en een aangenaam persoon om mee samen te werken.

Ik ben er ook zeker van dat deze eigenschappen jou een prachtige carriere zullen bezorgen. Ook

ik zal de vele hilarische momenten nooit vergeten, zonder een flinke dosis humor zou dit jaar er

volledig anders uitgezien hebben. Veel succes met je verdere carriere en toekomst!

Jelle Bauwens, juni 2014

iv

Permission

“The authors give permission to make this master dissertation available for consultation and

to copy parts of this master dissertation for personal use. In the case of any other use, the

limitations of the copyright have to be respected, in particular with regard to the obligation to

state expressly the source when quoting results from this master dissertation.”

Lander Buffel and Jelle Bauwens, june 2014

Laminar burning velocity measurements

using the GUCCI setup

by

Lander Buffel and Jelle Bauwens

Scriptie ingediend tot het behalen van de academische graad van burgerlijk ingenieur

werktuigkunde-elektrotechniek

Academic year 2013–2014

Promotor: Prof. dr. ir. S. Verhelst

Mentor: Ir. L. Sileghem

Faculty of Engineering and Architecture

Ghent University

Department of Flow, Heat and Combustion Mechanics

Head of department: Prof. dr. ir. J. Vierendeels

Abstract

This text starts with a general introduction followed by the two main parts. Part I is a liter-ature study on the basics and current knowledge of laminar burning velocity. Part II focuseson the results of the measurements, obtained by performing experiments with the GUCCI setup.

Chapter 1 is a general introduction, describing the context and importance of the study onlaminar burning velocity of alcohols and their mixtures with gasoline.

Part I: literature review

Chapter 2 gives the reader the necessary theoretical knowledge of laminar burning velocityin order to easily understand the experimental part of the thesis. This chapter is part of theliterature study but it is actually meant as an introduction to chapter 3.Chapter 3 provides an overview of the most important laminar burning velocity data on alco-hols. Some important physical effects on laminar burning velocity are studied. This is the mainliterature study part.

Part II: LBV experiments with the GUCCI setup

Chapter 4 gives a complete overview of the used experimental GUCCI setup. The criticalaspects are clarified.Chapter 5 contains all the LBV results. The results are compared with literature in order toset up a validation study wherein the GUCCI is validated for laminar burning velocity measure-ments.Chapter 6 summarizes the complete work and gives suggestions for future laminar burningvelocity research on the GUCCI.

In Appendix A, B, C, D and E some more practical issues that were covered in the maintext are further explained in detail. Appendix F gives a complete overview of the LBV resultsthat were obtained during this work.

Keywords

Laminar burning velocity, GUCCI (optically accessible combustion chamber), schlieren tech-

nique, alcohol as fuel, fuel properties

Measurements of laminar burning velocity using theGUCCI setup

Jelle Bauwens, Lander BuffelDepartment of Flow, Heat and Combustion Mechanics

Ghent University, Belgium

Supervisor(s): Sebastian Verhelst, Louis Sileghem

Abstract— This article reports the results of the authors’ experimentalstudy on laminar burning velocity.

Keywords— Laminar burning velocity (LBV), alcohols, GUCCI, valida-tion, methane

I. INTRODUCTION

DE pletion of fossil energy sources, climate change and en-vironmental pollution have led to a continuous search for

alternative fuels. In this context light alcohols, ethanol andmethanol in particular, are of great interest from a productionpoint of view but also regarding storage and intrinsic properties.The present study describes LBV measurements of methane-airmixtures performed with the GUCCI, which was validated us-ing the results of these measurements. This validation is veryimportant in view of future work, which will be aimed primarilyat obtaining LBV data of light alcohols and their mixtures withgasoline.

II. EXPERIMENTAL METHOD

A. The GUCCI setup

The experiments were performed using the GUCCI setup, aconstant volume combustion vessel at Ghent University. Upto today there have not been any experiments with the GUCCIyielding peak pressures higher than 150 bar. Therefore, in thiswork it was decided not to exceed this value. For measure-ments at high initial pressures, the peak pressure was first cal-culated using the GASEQ software. A schematic overview ofthe GUCCI setup is given in Fig. 1. It is equipped with two or-thogonal quartz windows of diameter 150 mm, which have beentested up to 150 bar. Close to the wall of the bomb an electri-cally driven fan was installed to properly mix the reactants. Gastemperatures were obtained with a type K thermocouple. Partialpressures of the reactants were measured using the UNIK5000absolute pressure sensor from the manufacturer Druck. Pressureprofiles during the explosions were obtained with an AVL typerelative pressure sensor. Two opposite electrodes were mounteddiagonally in order to provide central ignition. The gap widthbetween both electrodes was set at 1 mm.

B. Schlieren technique

The growth rate of the spherically expanding flames wasmeasured by high speed schlieren cine photography. A highspeed PCO camera was used to capture flame propagation. Forthe methane-air measurements in the present work, the cameraspeed was set at 3000 frames/s with 1152 x 1428 pixels; theresolution was 0.16 mm/pixel.

C. Mixture preparation

It was of high importance to properly flush the combustionchamber after each explosion. This was done by using a step-wise flushing procedure, in which two fixed sequences of com-

Fig. 1. Schematic overview of the GUCCI setup.

pression with dry air and evacuation to 0.1 bar were performed.At 2 bar initial pressure it was required to repeat the last se-quence in order to remove 99.99% of the residuals. After flush-ing, a series of actions was completed by the LabVIEW programin order to fill the chamber with the different gaseous compo-nents. Cumulative pressures were measured. From these valuesthe partial pressure of each component was derived, from whichthe equivalence ratio was calculated.

III. REPEATABILITY

To obtain a measure for the repeatability, at least three explo-sions were performed at each condition. After processing theimages, the standard deviation of the LBV values was calcu-lated. The principal uncertainty was in making up the mixture.Therefore the following factors affecting mixture stoichiometrywere accurately controlled:• The consistency of pressure and temperature just prior to ig-nition was important. The authors aimed at a tolerance of ±0.03bar and ±5 K, respectively.• Residuals were kept at a minimum through adequate flushingof the vessel after each explosion.• The vessel sealing could not entirely exclude leakages. Theinfluence on mixture composition was particularly important atelevated pressures.

IV. ERROR ASSESSMENT

This part of the validation was crucial since the GUCCI setuphad never been used for LBV measurements before. The per-formed error analysis is based on previous work in the contextof LBV experiments of Vancoillie [1], Verhelst [2] and Vanthillo[3]. The analysis can be subdivided into two main parts. Thefirst part comprises the error on the directly measured quanti-ties: initial pressure and temperature, and schlieren image qual-

ity. For the measurements at 2, 5 and 10 bar the errors on thestarting pressure were 5, 2 and 1 %, respectively. The maximumabsolute error on the initial temperature was estimated at 2.5 C.During the image processing, two different errors were made:an error on the flame radius and a calibration error. Since thehorizontal resolution was set to 0.16 mm/pixel for all measure-ments, an absolute error of 0.16 mm was made. Regarding thecalibration error it was concluded that the variation in diameterwas less than 0.15 %, which was negligible.

The second part treats the error on mixture composition. Ananalysis for three different filling procedures was done. The re-sults are indicated in table I.

The relative error decreases with pressure and is larger forlean mixtures. It is important to mention that this part of the er-ror analysis was highly conservative, and provides rather a qual-itative insight in the mixture composition variation. The resultsindicate that, for low partial pressures, the gas filling system isnot accurate.

V. RESULTS AND DISCUSSION

LBV values of methane-air flames were measured at three dif-ferent initial pressures: 2, 5 and 10 bar. The initial temperaturewas 298 K. The equivalence ratio was varied from 0.7 to 1.3with a step size of 0.5. In agreement with literature, ul varieslinearly with 1√

p . This is shown in Fig. 2. LBV values are lowerfor mixtures that are lean or rich of stoichiometric.

Fig. 2. Mean values of LBV ul as a function of equivalence ratio φ, at p = 2, 5and 10 bar. Values were obtained by measurements using the GUCCI setup.Standard deviations on both burning velocity and corrected equivalence ratioare indicated by vertical and horizontal error bars, respectively.

Due to the poor accuracy at low pressures, the spreading ofthe results at 2 bar is significant. However, the quality of themeasurements appears to increase with pressure. This is de-picted by the vertical error bars in Fig. 3, which also shows anoverall decrease in burning velocity for increasing pressure.

The present LBV data for methane-air mixtures at 2 bar, 298K were compared against three data sets from reliable literature.It was observed that the data of Goswami et al. [5] were themost comparable with the present results. Excluding a deviatingvalue at φ = 1, the present data are considered acceptable.

Fig. 3. Mean values of LBV ul as a function of equivalence ratio φ, at p = 2, 5and 10 bar. Values were obtained by measurements using the GUCCI setup.Standard deviations on both burning velocity and corrected equivalence ratioare indicated by vertical and horizontal error bars, respectively.

At 5 bar, 298 K it was observed that the data of Rozenchan etal. [6] agreed best with the present data. Mixtures that were richof stoichiometric showed slightly higher values of ul. However,the present results are still considered acceptable as variabilityin literature is high.

At 10 bar, 298 K it was observed that the data from literaturehad a low variability and present data agreed very well with li-terature. The absolute deviation was 1 cm/s for all equivalenceratios except φ = 1.2, for which the deviation was 2 cm/s. It isconcluded that the GUCCI setup provides qualitative results atan initial pressure of 10 bar.

VI. CONCLUSION

Based on the present discussion and comparison of the ob-tained LBV data with literature, it can be stated that the GUCCIsetup has been validated for LBV measurements of methane-airmixtures at pressures up to 10 bar. The deviation from mean li-terature data is generally below 15%, excluding some very leanand very rich conditions.

REFERENCES

[1] J. Vancoillie, Modeling the combustion of light alcohols in spark-ignitionengines, ph.d. thesis, Ghent University, 2013.

[2] S. Verhelst, A study of the combustion in hydrogen-fueled internal combus-tion engines, ph.d. thesis, Ghent University, 2005.

[3] J. Van Thillo, Metingen van de laminaire verbrandingssnelheid van brand-stofarme en verdunde methaan-lucht mengsels met behulp van de ehpe,ph.d. thesis, Eindhoven: Technische Universiteit, 2008.

[4] P. Logghe and W. Roose, Flowbench- en vlamsnelheidsmetingen als inputvoor simulaties voor vonkontstekingsmotoren, master thesis, Ghent Univer-sity, 2012.

[5] M. Goswami, S. Derks, K. Coumans, W. Slikker, M. Oliveira, R. Bastiaans,C. Luijten, L. de Goey, and A. Konnov, The effect of elevated pressures onthe laminar burning velocity of methane + air mixtures, Fuel, vol. 160, pp.1627-1635, 2013.

[6] D. L. Rozenchan, G. and Zhu, C. K. Law, and T. S. D., Outward propaga-tion, burning velocities and chemical effects of methane flames up to 60 atm,Proceedings of the combustion institute, vol. 160, pp. 1627-1635, 2013.

[7] F. Egolfopoulos, D. Du, and C. Law, Twenty-fourth symposium on combus-tion, The combustion institute Pittsburgh, 1992.

[8] M. Hassan, K. Aung, and G. Faeth, Measured and predicted properties oflaminar premixed methane/air flames at various pressures, Combustion andFlame, vol. 115, pp. 539-550, 1998.

[9] X. J. Gu, M. Z. Haq, M. Lawes, and R. Woolley, Laminar burning velocityand markstein lengths of methane-air mixtures, Combustion and Flame,vol. 121, pp. 41-58, 2000.

CONTENTS ix

Contents

1 Introduction 11.1 The potential of alcohols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 GUEST code . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Goal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.4 SI engine research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41.5 Overview dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2 Theory 82.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.1.1 Definition for spherical flames . . . . . . . . . . . . . . . . . . . . . . . . . 102.2 Flame front . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Flame speed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 Flame stretch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5 Flame front instabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.6 Premixed turbulent combustion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.6.1 Regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.6.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3 Literature review 283.1 Measurement methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.1.2 Combustion bomb vessel method . . . . . . . . . . . . . . . . . . . . . . . 29

3.2 Available LBV data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.1 Methanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.2 Ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383.2.3 Effects of high pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.4 Effects of high temperature . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.5 Effects of dilution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.3 LBV correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.4 Conclusion literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4 Experimental setup 514.1 The GUCCI setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4.1.1 Gas filling system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534.1.2 Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.2 Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.2.1 Flushing and filling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.2 Filling tool for liquid fuels . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.3 Lens positioning: schlieren technique . . . . . . . . . . . . . . . . . . . . . 624.2.4 High speed camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 674.2.5 Ignition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.3 Post-processing methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

CONTENTS x

4.3.1 Optical post-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734.3.2 Pressure based . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.4 Error analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764.4.1 Directly measured quantities . . . . . . . . . . . . . . . . . . . . . . . . . 774.4.2 Equivalence ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.5 Repeatability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

5 LBV measurements 885.1 Measurement matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.2 CH4-air LBV up to 10 bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2.1 General analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.2.2 Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 985.2.3 Pressure derived results . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102

5.3 Validation of the GUCCI setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1045.4 CH4-air LBV at 15 bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1125.5 Physical phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1155.6 Ethanol LBV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

5.6.1 Results and comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6 Summary and possible future research on the GUCCI setup 1226.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1226.2 Possible future research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

Appendices 126

A Alcohols as a fuel: properties 126

B Optical based post-processing: MATLAB script 128B.1 Image processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128B.2 Linear extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143B.3 Independent functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151B.4 Practical example of the post-processing method . . . . . . . . . . . . . . . . . . 151

C Pressure based post-processing: MATLAB script 153

D Datasheets and equipment information 155D.1 Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155D.2 pco.dimax camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156D.3 Ignition coil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158

E Determination of the φ-value of a mixture in the GUCCI 160E.1 Gaseous fuel: methane . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160E.2 Liquid fuel: methanol, ethanol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162

F Constant volume bomb measurements 165

Bibliography 177

CONTENTS xi

List of Abbreviations

LBV laminar burning velocity

GUEST Ghent University Engine Simulation Tool

CVB constant volume bomb

CVCC constant volume combustion chamber

HFM heat flux method

EHPC Eindhoven High Pressure Cell

LDA laser-doppler anemometry

AFR air to fuel ratio

RON research octane number

HoV heat of vaporization

BMEP break mean effective pressure

fps frames per second

CONTENTS xii

List of Symbols

ul laminar burning velocity

Sn flame speed

Ss flame speed at zero stretch

T0 standard temperature (25◦C)

p0 atmospheric pressure

ρu density of unburned mixture

ρb density of burned mixture σ = ρuρb

DT thermal diffusivity

λ thermal conductivity

cp heat capacity

lF thermal flame thickness

ν kinematic viscosity

ru cold flame front radius

rsch highest density gradient radius (schlieren)

α stretch rate

Lb burned gas Markstein length

Ma Markstein number

Ka Karlovitz number

Pr Prandtl number

Le Lewis number

Sc Schmidt number

INTRODUCTION 1

Chapter 1

Introduction

These days climate change, environmental pollution and public health constitute very important

topics. Both on a local and global scale the massive usage of fossil fuels as an energy source

has led to harmful results. Our transportation options, especially those driven by internal

combustion engines, are huge and flexible, but also have a strong environmental impact. As our

present energy supply for these kind of vehicles is based on fossil fuels, which are depletable,

they are regulated by very strict standards. The emissions and fuel consumption of modern

engines must be as low as possible with no significant loss of power. The current fossil energy

sources are rapidly decreasing, which leads to a continuous search for alternative fuels. Up to

today there has been much research and development into vehicles powered by fuel cells and

electric motors. The fuel cell and in particular hydrogen have the advantage of not producing

harmful emissions. The only waste product is water. However, the poor storage and distribution

infrastructure possibilities and the low energy density can count as big disadvantages. Electric

vehicles could be the solution for city transport. However, when the distance to travel is long,

these vehicles will not meet the requirements. Other promising alternative fuels for fossil fuel

replacement are alcohols, methanol and ethanol in particular.

1.1 The potential of alcohols

At the moment gasoline is widely used as a fuel for transportation. The most important char-

acteristics of gasoline are its volatility and octane number. Next to gasoline, alcohols have also

certain advantages as fuels, particularly in countries without oil resources, or where there are

1.1 The potential of alcohols 2

sources of the renewable raw materials for producing methanol (CH3OH) or ethanol (C2H5OH).

Car manufacturers have extensive programs for developing alcohol-fueled vehicles. Alcohols can

also be blended with oil-derived fuels which improves the octane ratings. Both ethanol and

methanol have high octane numbers (the RON of ethanol/methanol is 109 compared to 91-

92 for gasoline) and high heat of vaporization (HoV). This improves volumetric efficiency but

can cause starting problems. For cold ambient conditions it may thus be necessary to start

engines with gasoline. Increasing the ethanol content in an ethanol-gasoline blend also results

in an increase in knock resistance, due to ethanol’s high values of RON, sensitivity, and HoV.

Improved knock resistance enables increased knock-limited BMEP, particularly with boosted,

direct injection engines, and/or increased compression ratio. A disadvantage of alcohols is the

lower energy density, which is - on a volumetric basis - about half that of gasoline for methanol

and two-thirds for ethanol. This is illustrated in figure 1.1. Due to this lower energy content

compared to gasoline, volumetric fuel economy (mpg) decreases with increasing ethanol content

of the fuel as does the driving range for a given fuel tank size. This degradation can be partially

offset (or perhaps completely offset for E20 - E30) by the improved fuel efficiency. Further-

more, particulate matter emissions, emissions of toxic compounds, and off-cycle emissions due

to enrichment are expected to decrease significantly [1].

Figure 1.1: Net volumetric and gravimetric energy densities for various on-board energy carriers pro-

vided by Pearson and Turner (2012) [2]. A drawback of alcohols as a fuel is the lower

volumetric energy density compared to gasoline. For E20 and E30 this is almost fully com-

pensated by the better fuel efficiency. For higher E levels a bigger amount of fuel is needed

on board of the vehicle to travel the same distance as with a gasoline fueled vehicle.

1.2 GUEST code 3

1.2 GUEST code

The GUEST (Ghent University Engine Simulation Tool) code is a quasi-dimensional engine

simulation code developed within the Department of Flow, Heat and Combustion Mechanics at

Ghent University. This code was integrated within the commercial engine simulation tool GT-

Power, which greatly extends its functionality. Several LBV correlations and turbulent burning

velocity models were implemented in the GUEST code. These correlations make use of and can

be validated with LBV data of alcohol blends. The lack of qualitative data is currently a big

problem. From a survey of published literature by Vancoillie (2013) [3], a lack of LBV data at

engine-like conditions became apparent for ethanol and methanol.

LBV gives basic information about ignition delay, diffusion, minimum ignition energy, emissions

and the exothermic nature of a given fuel composition and is also used for the verification of

turbulent modeling. Furthermore, LBV values can be used as a validation for reaction kinetics

models, which are extensively used in the chemical industry. In fact, work of this nature is

appearing at an increasing rate because of the correspondingly increasing interest in accurate

values of laminar flame speeds for studies of fuel chemistry.

The GUEST code has already been tested for hydrogen, and recent doctoral research performed

by Vancoillie [3] aimed at extending the software to work with alcohol blended fuels. The

gathering of correct data on LBV is very important for the validation of the correlations used

in the GUEST code. Although the mixture burning in the cylinder is always fully turbulent

in nature - except in the very beginning of the combustion - measurements of LBV are highly

important for input into turbulent models. These models require ‘stretched’ burning velocity

data of the mixture at instantaneous pressure and temperature. Stretch is an essential concept

in the context of the LBV of a mixture. The details in this regard will be discussed further

in this text. So a library of stretched flamelets or a model for the effect of stretch is needed.

However a stretch-free LBV database is always required.

1.3 Goal

At the moment there are insufficient data on LBV at engine conditions, for any fuel and especially

for alcohols. Stretch and instabilities, which will be explained further in chapter 2, hamper the

1.4 SI engine research 4

experimental determination of stretch-free data at higher (engine-like) pressures. In the present

work a first research experience on the GUCCI (in the context of LBV) was realized.

The main goal of this master dissertation can be subdivided into 4 ideas:

� Determine a robust and systematic methodology in order to use the GUCCI setup for

measuring the LBV of methane-air mixtures at different conditions.

� Create a powerful ‘post-processing’ MATLAB tool in order to easily obtain the LBV values

from a series of experiments.

� Successfully complete a large set of LBV measurements on methane-air mixtures.

� Validate the GUCCI setup using an extensive database of methane-air measurements. The

goal is to prove that the GUCCI setup enables LBV measurements which are meaningful

and suitable for international publication.

In future research the goal will be to use the GUCCI to measure the laminar (stretch-free)

burning rates of alcohols and mixtures of alcohols with gasoline at a variety of conditions (start

pressure, start temperature, mixture composition,...). The range in boundary conditions will

cover engine-like conditions as much as possible. The results will be validated with existing

experimental results presented in literature. The newly developed database will provide a way

to validate the correlations that are currently used in the GUEST code.

1.4 SI engine research

This introduction is used to explain the authors’ view on the positioning of the present study

in the broader view of spark-ignition engine research. As already mentioned in section 1.3 it is

the authors’ goal to provide an accurate methodology for performing LBV measurements with

the GUCCI. In future work, obtained LBV data on alcohols will be used to validate existing

correlations that provide LBV values in the simulation tools created by Vancoillie et al. (2011)

[4]. The range and accuracy of the data is of paramount importance. In this research, the

outwardly propagating spherical flame is adopted as the model flame for the determination of

LBV. Fundamentally, the propagating spherical flame is relatively easy to generate and its global

configuration and dynamics are also well defined. It is very important that the method used to

1.4 SI engine research 5

calculate the LBV is as accurate as possible. The present literature study is meant to provide

a broad overview of all the different factors affecting spherical flame propagation and thus also

the calculated LBV values. Furthermore, it is the authors’ purpose to analyze the critical parts

of the measurement methodology using the most recent literature available.

Both thermodynamic and CFD type engine codes require a turbulent combustion model to track

the progress of the flame front through the cylinder. These combustion models generally assume

fast chemistry (flamelet regime, see section 2.6). The influence of turbulence is then limited to

flame stretch and the increase in flame front area. The contribution of chemical reactions

is grouped in the LBV. Thus, these models need data on the stretched burning velocity at

instantaneous cylinder pressure, unburned mixture temperature and composition. This velocity

can be calculated from the LBV at the local conditions. This is a physicochemical property of

the fuel-air-residuals mixture and thus a fundamental building block of any engine model.

A convenient way to implement LBV data in an engine cycle code is by using a correlation

which gives the LBV in terms of pressure, temperature and unburned mixture composition.

The work of Vancoillie et al. [4] extended the validity of the GUEST code (originally validated

for hydrogen) to methanol and ethanol. Two new correlations were formulated. Unfortunately,

the validity of these and other previous correlations is doubtful, since most of them are based

on simulations and validated with outdated measurements. Another fundamental flaw is that

these measurements provided LBV data from flames that were highly unstable. These unstable

spherical flames show cellular structures at the flame front and the flame speed is much higher

than for stable flames.

Figure 1.2 illustrates the purpose of present and future research.

1.5 Overview dissertation 6

Figure 1.2: Positioning of present and future research in the broader view of spark-ignition engine

research.

1.5 Overview dissertation

The literature study for the present work is bundled in chapters 2 and 3. In chapter 2, a

brief but exhaustive overview on the theoretical background of LBV is given. The purpose of

this chapter is to give the reader the necessary knowledge on LBV, so that almost no external

theoretical literature needs to be consulted. The concept of stretch is explained. Instabilities

and their causes and consequences are also discussed. This theoretical part is based on research

by Bradley et al. (1998), Verhelst (2005), Van Thillo (2008) and insights from the (unpublished)

course ‘Modelling of Turbulence and Combustion’ by Merci (2013).

Chapter 3 contains the main part of this literature study. First the measurement methodology

is presented. The different methods are outlined: tube method, burner method and combustion

bomb vessel method (CBV). The main advantages of the CBV are discussed. A disadvantage of

the method is the influence of the finite volume of the combustion bomb on the measurements.

In literature some solutions were found that cope with this constraint. This first part is closed

with a discussion on linear and nonlinear extrapolation. An explanation of the two methods is

1.5 Overview dissertation 7

given based on Kelley and Law (2009). This published study gives the general extrapolation

rule for both linear and nonlinear extrapolation. By further literature review one method was

selected that was deemed appropriate considering the available measurement equipment.

Next, the available data on LBV is reviewed based on Vancoillie (2013) and extended with more

recent work. A lack of data at high pressures is noticed. In comparison to the more classic fuels,

there is not much data available for ethanol and methanol. After composing an exhaustive

database of LBV of methanol-air and ethanol-air mixtures, it is the authors’ objective to take

a look at the effects of higher pressures and temperatures. In this section an overview of the

available high pressure data is given, based on Gulder (1982), Egolfopoulos et al. (1992), Liao

et al. (2007) and Bradley et al. (2009). The main limitations (evaporation of fuel, shift of onset

of cellularity, technical issues) for measurements at high pressure are summarized. The major

part deals with the experimental results and general conclusions of Bradley et al. (2009) and

Beeckmann et al. (2009). Furthermore, influences of pressure and temperature on burning veloc-

ity and Markstein length are discussed based on Bradley et al. (2009), Galmiche et al. (2012),

Beeckmann et al. (2009), Vancoillie et al. (2013)and Sileghem et al. (2014). The final part

comprises an overview of the effects of diluent gases (EGR), based on the work of Vancoillie

et al. (2013).

Chapter 4 provides the details about the experimental setup (GUCCI) that was used. First,

a complete overview on the hardware components is given. Next the measurement procedure

and post-processing methodology are explained. The chapter is closed by the error analysis and

some issues concerning the repeatability of the experiments.

Chapter 5 provides a complete overview of all the LBV results. This includes all the results for

methane-air mixtures and the few data obtained for ethanol-air mixtures. The most important

part of this chapter comprises the validation of the GUCCI setup. Chapter 6 combines the

conclusions made in the foregoing chapters by giving a complete summary. The authors are

proud to present this master dissertation and hope it helps the reader to gain a profound insight

in the fascinating world of LBV.

THEORY 8

Chapter 2

Theory

This chapter contains a concise overview of the theoretical aspects of LBV the reader needs

to understand completely in order to be able to understand new experimental results. The

combustion process in an engine cylinder generates a certain pressure rise in the cylinder. It

is by this pressure rise that the piston is pushed and work is delivered on the crankshaft. In

computer models these burning processes are simulated using turbulent combustion models. The

models, that are using correlations that need the LBV data, cover both laminar and turbulent

burning of the mixture in the cylinder. Combustion in alcohol-fueled engines mostly occurs in

the flamelet regime, where the only influence of turbulence is flame front wrinkling and the effect

of chemistry is grouped in the LBV. The LBV value of the in-cylinder mixture is therefore a

crucial building block for most turbulent combustion models.

2.1 Definition

In general, most of the energy is released during the combustion of near-stoichiometric mixtures

(equivalence ratio near unity). Since the reaction rate of a chemical reaction increases with

temperature, the reaction rate will be the highest at stoichiometric conditions (highest possible

temperature). This gives already a notion towards the fact that the LBV will be growing towards

its maximum value in the vicinity of this condition. The maximum LBV is mostly reached at

slightly rich conditions.

A quantity for the reaction rate (the speed at which the concentration of a substance changes

during a certain time interval) of an oxidation reaction is the burning velocity. The laminar

2.1 Definition 9

burning velocity, ul, is a physicochemical property of the air-fuel-residual gas mixture, and is

defined as the speed at which a steady planar flame front propagates in a premixed, quiescent

mixture in front of the flame (laminar flow condition), in a direction normal to the plane. This

is illustrated in figure 2.1.

Figure 2.1: Definition of laminar burning velocity.

It is only defined for premixed flames and depends on the unburned mixture composition,

temperature and pressure. The mixture composition is quantitatively given by the equivalence

ratio, which is the result of the combination of different components: fuel, air and potential

diluent gas. The symbol that is used in general is ul (the stretch-free burning velocity). Equation

2.1 gives the general definition of LBV (for an unstretched, laminar one-dimensional flame;

stretch is defined in section 2.4).

ul =dmbdt

Af · ρu(2.1)

Experimentally it is impossible to generate a truly one-dimensionally propagating, planar and

adiabatic flame. There will always be effects of flame stretch and non-planar geometry will also

play a role. These effects should be considered and are discussed below. The LBV is often given

at a standard pressure and temperature. Most of the available data in literature is presented

at T0 (25°C) and atmospheric pressure p0. A lot of correlations are presented in literature

that calculate the LBV within certain boundary conditions of temperature and pressure. The

following power law form is generally used:

ul(φ, T, p) = ul0(φ)

(TuT0

)α( p

p0

)β(2.2)

The most recent correlations are discussed in section 3.3. In equation 2.2 ul0 is the LBV value

2.1 Definition 10

of a mixture with a certain equivalence ratio φ, at standard conditions T0 and p0. When other

values of Tu and p are introduced, new values of LBV are calculated. The basic correlation form

2.2 already provides an insight into the different influencing factors on LBV. Temperature and

pressure are very important quantities in the context of LBV.

2.1.1 Definition for spherical flames

When studying outwardly propagating spherical flames, two types of (stretched) burning veloc-

ities can be defined. These burning velocities are intrinsically stretched because of the strain

and curvature of the moving flame front. First, the reason for the usage of two definitions is

explained.

Although there is, of course, always conservation of mass globally, locally the mass flow rate of

the unburned gases does not match with the mass flow rate of the burned gases (leaving the

flame front). The difference in mass flow rate between burned and unburned is due to the finite

thickness of the flame front. This is called the flame thickness effect [5]. For a quasi perfect

one-dimensional, planar, adiabatic flame this flame thickness is determined. The ‘thermal’ flame

thickness lF has typical values of 0.1 - 1 mm at atmospheric pressure. This total flame thickness

(which is, in fact, the flame front thickness) consists of a pre-heat zone and a reaction zone (inner

layer). The inner layer is the zone where fuel is consumed together with oxygen by chemical

reactions; the thickness is δlF , with typically δ = 0.1. So the inner layer has a thickness of the

order 0.1 mm at atmospheric pressure, which is extremely thin. At higher pressures this value

will be even smaller. This flame front is further discussed in more detail in section 2.2 and also

shown in figure 2.2.

Because there is a local difference in mass flow rate between burned and unburned gases, two

possible definitions of burning velocity exist, each legitimate and of practical significance. The

first, unr, is based on the rate of appearance of burned gas. In equation 2.3, ρu is the density of

the unburned mixture, A is the surface of the flame front and mb is the rate of appearance of

burned gas.

unr =1

ρu

(mb

A

)(2.3)

The second definition is based on the rate of disappearance of cold, unburned gas.

un =1

ρu

(mu

A

)(2.4)

2.2 Flame front 11

With an outwardly propagating spherical flame the flame thickness effect is dependent on the

radius of the flame. At smaller radii the flame thickness effect is important, but it is less so

at larger radii. As the radius tends to infinity, both un and unr tend towards ul. Because unr

governs the pressure development in engines and, probably, the quenching of turbulent flamelets

it is the more pertinent in such contexts. In [6] it is shown that, in the context of propagating

spherical flames, un and unr are related as follows:

unr =ρb

ρb − ρu(un − Sn) (2.5)

Here, ρu is the density of the unburned mixture, ρb is the density of the burned mixture and Sn

is the flame speed, which is defined in section 2.3.

2.2 Flame front

Figure 2.2 shows a one-dimensional unstretched laminar flame structure. The temperature

increases from the unburned to the burned zone due to heat and mass transfer, as well as

chemical reaction. Four zones can be discerned: cold reactants, the pre-heat zone, the reaction

zone (inner layer) and the hot products. The inner layer is much smaller than the pre-heat zone.

The pre-heat zone is dominated by heat conduction and mass diffusion of reactants. Chemical

reaction and mass diffusion dominate the reaction zone. As the reactants pass through the

preheat zone, they are heated by conductive heat transfer from the reaction zone. The mixture

is preheated to the ignition temperature of the mixture. The ignition temperature is defined

as the temperature separating preheat zone and reaction zone. The heating of the reactants

eventually leads to their reaction at an increasing rate. In the reaction zone the ‘visible flame

zone’ or ‘luminous zone’ is also found. In this zone light is emitted.

2.2 Flame front 12

Figure 2.2: Concentration and temperature profiles of a one-dimensional unstretched laminar flame

structure.

When a spherical flame is expanding (see figure 2.3) two regions can be discerned: one comprising

the unburned mixture and one comprising burned flue gases. In between these two regions a

small zone (flame front) is found, where a continuous chemical reaction turns reactants (fuel,

air and diluent gas) into products.

Figure 2.3: Flame front of an outwardly propagating spherical flame.

2.2 Flame front 13

As mentioned previously, the inner layer is the zone where fuel is consumed due to chemical

reaction. The thermal diffusivity DT is defines as follows:

DT =(λ/cp)

ρu(2.6)

In this equation λ is the thermal conductivity of the unburned mixture, cp is the heat capacity.

Based on equation 2.6 the characteristic length scale lF (the ‘thermal’ flame thickness, or thick-

ness of the flame front) is defined:

lF =DT

ul=

(λ/cp)

(ρul)u(2.7)

The definition for lF presented in the work of Bradley et al. [5] is based on the kinematic

viscosity ν of the unburned mixture. There it is defined as:

lF =ν

ul(2.8)

This definition is used to relate rsch to ru, as explained in the next paragraph.

When an outwardly propagating spherical flame is studied, the instantaneous position of the

flame front is given by ru, which stands for the cold flame front radius. It is defined using the

isotherm that is 5 K above the reactant temperature and is also the radius used in the data

processing. The radius measured with schlieren imaging (see section 4.2.3) is different from

the cold front radius. This radius is the location of the highest density gradient, and thus the

largest refraction, within the flame front. Bradley et al. [5] related both radii with the following

relation constructed from computations for methane-air mixtures:

ru = rsch + 1.95lF

(ρuρb

)0.5

(2.9)

This equation has been applied in unaltered form for different fuels such as hydrogen, iso-octane,

ethanol and methanol. The spatial temporal development of the flame then yields the (stretched)

flame speed Sn, using the following assumption:

Sn =drschdt

=drudt

(2.10)

2.3 Flame speed 14

2.3 Flame speed

It is important to note the different notations. LBV and flame speed are not the same. The

flame speed is the propagation speed of a flame with respect to a certain static reference system.

The flame speed differs from the burning velocity because of the expansion effect of the burned

gases and is given by [5]:

Sn =drudt

(2.11)

ru is the cold flame front radius, which is expanding in the case of an outwardly propagating

spherical flame (ru is related to the schlieren radius, see equation 2.9).

The flame speed has no unique value for a certain mixture. It is the sum of un, the stretched

LBV based on the propagation of the spherical flame front, and ug, the gas velocity resulting

from the flame expansion at ru. This gas velocity ug is the velocity of the gas that is situated

immediately adjacent to the flame front. The following equation can be written:

Sn = ug + un (2.12)

As a result of the conservation of mass, flame speed and burning velocity are related as:

un · ρu = S · Sn · ρb (2.13)

With S a generalized function that depends on the flame radius and the density ratio, and

accounts for the effect of the flame thickness on the mean density of the burned gases. In [5]

the generalized expression for S is:

S = 1 + 1.2

[δl

ru(ρuρb

)2.2]− 0.15

[δl

ru(ρuρb

)2.2]2

(2.14)

This equation was modeled from methane-air flames at 1 bar over a range of equivalence ratios.

2.4 Flame stretch

There are different mechanisms that lead to instability of a laminar flame. Realistic flames

can be wrinkled and become unsteady. They can exist in flow fields that are non-uniform and

2.4 Flame stretch 15

unsteady. The flame front can deform continuously during its expansion (see figure 2.4). A

propagating flame front is subjected to a strain and curvature effect, which together constitute

flame stretch and change the frontal area. Both effects are explained intuitively.

Figure 2.4: Deformed flame front.

Flow field aerodynamic strain or elongation is caused by velocity gradients in the plane of the

flame front. Velocity gradients occur because the flow is not perpendicular to the flame front

in combination with a gradient in the flow field. They can also occur because of a curved flame

front. In this way, the velocity gradients provide a locally stretched or compressed flame front.

Curvature is the effect of a moving flame front, as shown in figure 2.5, left. The local curvature

changes when a curved flame front moves, especially when a spherical outwardly propagating

flame front is examined. If a gas mixture is ignited in the center of a closed vessel, the radius of

the spherical flame front increases evenly. Initially the surface of the flame is small, causing the

curvature to be big. During the growth of the flame front, the curvature of the sphere decreases.

Further in this text these mechanisms are explained. In reality the different mechanisms work

simultaneously. When a flame is ‘stretched’, the diffusion processes on the surface of that flame

are disturbed. Flame stretch rate is defined as the normalized change of an infinitesimal surface


on the flame front. For a spherical outwardly propagating flame this becomes:

α =1

A

dA

dt=

2

ru

drudt

=2

ruSn (2.15)

Equation 2.15 states that when α > 0 the (infinitesimal) surface grows and when α < 0 the

(infinitesimal) surface decreases.

Flame stretch can increase or decrease the burning velocity significantly since the stretch has an

effect on the flame temperature of a fuel-air mixture, whereby also the combustion velocity of

the mixture changes. As mentioned previously, this ‘total’ flame stretch rate is the result of two

effects - strain and curvature. The stretch due to the curvature at the cold front of a spherical

outwardly propagating flame is given by [6]:

αc =2unru

(2.16)

The stretch due to the flow field aerodynamic strain is given by [6]:

αs =2ugru

(2.17)

The total stretch rate is thus given by:

α = αc + αs (2.18)

An example of a flame in which the flame stretch rate is only determined by the strain effect is

a stagnating flame, while a perfectly growing spherical flame is an example of a flame in which

the flame stretch rate is completely determined by the curvature effect. Thus, a flame with a

stretch rate equal to zero is a stationary flame surface in combination with a flow field that

stands perpendicular to the flame front. This is the case with a static spherical flame or with a

flat flame in combination with a uniform flow field along the flame surface. An overview of the

different cases is shown in figure 2.5. The continuous and dotted arrows represent the flow field

and the moving flame front, respectively.


Figure 2.5: Overview of the different causes of stretch.

Markstein lengths express the dependence of burning velocity on stretch. A positive Markstein

length means a reduction in burning velocity for increasing stretch. If ul is the (unstretched)

LBV then:

ul − unr = Lcrαc + Lsrαs (2.19)

ul − un = Lcαc + Lsαs (2.20)

Two different Markstein length types are defined according to the preferred definition of burning

velocity. There is a relation between Lc and Lcr, and between Ls and Lsr.

Lsr =1

ρuρb− 1

(Lb − Ls) (2.21)

Lcr =1

ρuρb− 1

(Lb − Lc) (2.22)

Here, Lb is the burned gas Markstein length expressing the influence of stretch on the flame

speed.

The authors have decided to continue working with unr because it is the more important def-

inition in the context of spherical propagating flames. Lcr and Lsr are the Markstein lengths

2.5 Flame front instabilities 18

associated with curvature and strain, respectively. Lb is used in the following, strongly simplified

expression, which gives the difference between unstretched (Ss) and stretched (Sn) flame speed:

Ss − Sn = Lbα (2.23)

Obviously equation 2.15 shows that α is inversely proportional with ru. The gradient of the best

straight line-fit for the plot of Sn against α yields the burned gas Markstein length, Lb, which

expresses the influence of stretch on the flame speed (see equation 2.23).

When ru tends to ∞, α tends to zero and Sn to Ss. This yields Ss as the intercept value of

Sn at α = 0. The gradient of the best straight line fit to the experimental data gives Lb. The

unstretched LBV is deduced from Ss since, for constant pressure flame propagation, ul and Ss

are related by:

ul = Ssρbρu

(2.24)

The Markstein length L is often normalized by the flame thickness in order to obtain a dimen-

sionless Markstein number Ma:

Ma =L

lF=Lulν

(2.25)

Similarly, the stretch rate can be normalized by multiplying by a chemical lifetime in order to

obtain a dimensionless Karlovitz stretch factor Ka:

Ka =αlFul

(2.26)

Hence equation 2.15 becomes (for small to moderate stretch rates (<1000-1)):

ul − unrul

= KaMa (2.27)

The bigger a positive Ka (stretch) and a positive Ma (Markstein length) are, the lower is the

burning velocity unr (unr < ul).

2.5 Flame front instabilities

The different instability mechanisms have been expounded by Verhelst [7]. For completeness,

part of the discussion is literally repeated here (Vancoillie [3]). Furthermore, a few other mech-

anisms are discussed that were explored by Kwon et al. [8]. The focus will be on hydrodynamic


and diffusional-thermal cellular instabilities in premixed flames. According to Kwon et al. [8]

there are four parameters influencing these instabilities: thermal expansion, flame thickness,

non-unity Lewis number, and global activation energy.

When a flame front is regarded as a passive, infinitely thin interface between unburned and

burned gases, a wave-like perturbation will increase the volumetric burning rate through in-

creased flame area and will have the following additional effects.

The discontinuity of density across the flame front (ρu → ρb) causes a hydrodynamic instability.

The hydrodynamic theory of Darrieus and Landau shows that, in the limit of an infinitely thin

flame propagating with a constant velocity, the flame is unstable in the event of disturbances of

all wavelengths. The growth rate is proportional to the density jump across the flame (σ = ρuρb ).

σ is probably the most sensitive parameter controlling the onset of hydrodynamic instability. If

σ is quite big, then the flame will be more unstable. As illustrated in figure 2.6 below, a wrinkle

of the flame front will cause a widening of the streamtube to the protrusion of the flame front

into the unburned gases, resulting in a locally decreased gas velocity. This will cause a further

protrusion of this flame segment, since the flame speed remains unaffected if the effect of stretch

on the structure of the flame is neglected. So when only the hydrodynamic effect is considered,

the flame is unconditionally unstable.


Figure 2.6: Structure of a wrinkled flame front showing the hydrodynamic streamlines and the diffusive

fluxes of heat and mass.

An important parameter is the Karlovitz number (see equation 2.26). It was shown in literature

(Istratov and Librovich and Bechtold and Matalon [9]) that a positive stretch tends to be

stabilizing. Conceptually, cells cannot form if their growth rate is smaller than that of flame

expansion. Since the expanding flame suffers the strongest stretch during the initial phase of its

propagation when its radius is small, the tendency for cell development is expected to increase as

the flame propagates outwardly. Stretch is thus stabilizing for the flame. When stretch becomes

too small the flame will exhibit hydrodynamic instability and develop cellularity.

The lower density of burned gases compared to unburned gases produces a second instability

arising from gravitational effects. This buoyant instability, known as the Rayleigh-Taylor insta-

bility, arises when a less-dense fluid is present beneath a more-dense fluid, which is the case in

e.g. an upwardly propagating flame.

Next to σ, the flame thickness lF is also expected to have a strong influence on the hydrodynamic

instability, for two reasons:

� First, it shows the influence of curvature which, being positive for the outwardly propa-

gating flame, has a stabilizing effect on the cellular development. The thinner the flame,


the weaker the influence of curvature and, consequently, the stronger the destabilizing

propensity.

� The second influence is that it controls the intensity of the baroclinic torque developed

over a slightly wrinkled flame surface, which depends on the density gradient across the

flame and the pressure gradient along the flame. Since the density gradient increases with

decreasing flame thickness, development of the hydrodynamic instability is correspondingly

enhanced due to the increased intensity of the induced baroclinic torque.

Flame instability can also be triggered through unequal diffusivities (diffusional-thermal insta-

bilities). The flame propagation rate is largely influenced by the flame temperature, and this is

in turn influenced by the conduction of heat from the flame front to the unburned gases (full

arrows in figure 2.6). On the other hand, flame propagation is also influenced by the diffusion of

reactants from the unburned gases to the flame front (dashed arrows). The result is a perturba-

tion of the balance between diffusivities, which will have important effects. Three diffusivities

are of importance: the thermal diffusivity of the unburned mixture (DT ), the mass diffusivity of

the deficient reactant (DM,lim), also called the ‘bottleneck’ component, and the mass diffusivity

of the excess reactant (DM,exc). In a lean flame the deficient reactant is the fuel or one of the

components in the fuel mixture, while in a rich flame it is oxygen. The ratio of two diffusivities

can be used to judge the stability of a flame when subject to a perturbation or flame stretch.

For the development of diffusional-thermal instability, an appropriate parameter representing

the effect of non-equidiffusion is the flame Lewis number, Le. It gives the ratio of heat to mass

diffusivity. It is also the ratio of two non-dimensional numbers: the Schmidt (Sc = µρD ) and

Prandtl (Pr =µcpλ ) number.

Le =Sc

Pr=

λcp

ρuD=

λ

ρucpD(2.28)

In this equation D is the mass diffusivity and λ is the heat conductivity. In a normal situation

every component of a fuel-air mixture has a certain Lewis number. As already mentioned the

Lewis number of the ‘bottleneck’ component will be the most critical one and is chosen as the

Lewis number of the total mixture. The ratio of the thermal diffusivity of the unburned mixture

to the mass diffusivity of the deficient reactant thus gives the Lewis number of the mixture:

Le =DT

DM,lim(2.29)


It is well established and understood theoretically that unstretched flames are diffusionally

unstable (stable) for Le’s that are smaller (greater) than a value slightly less than unity. If the

Lewis number of the mixture is for instance greater than unity, the thermal diffusivity exceeds

the mass diffusivity of the limiting reactant. The conductivity of heat to the preheat zone in

the flame front is bigger than the diffusion of mass. The generated heat coming from the inner

layer will easily diffuse to the cold unburned gases. Contrary to this easy diffusion, the mass

diffusion of unburned gases to the reaction zone will go more difficult. This results in a lower

flame temperature to close the energy balance. When this is the case, a wrinkled flame front will

see its parts that are bulging towards the unburned gases lose heat more rapidly than diffusing

reactants can compensate for. The parts that recede in the burned gases, on the contrary, will

increase in temperature more rapidly than they are depleted of reactants. A lower temperature

implies a lower mass burning rate and thus a lower burning velocity. As a result, the flame speed

of the ‘crests’ will decrease and the flame speed of the ’troughs’ will increase, which counteracts

the wrinkling and promotes a smooth flame front. The mixture is then thermo-diffusively stable.

Similar reasoning shows that a Lewis number smaller than unity indicates unstable behavior.

The diffusional-thermal instability mechanism is a very powerful destabilizing influence. This

influence is much stronger than the influence of flame thickness.

Another mechanism involving unequal diffusivities is the following: when the limiting reactant

diffuses more rapidly than the excess reactant (DM,lim > DM,exc), it will reach a bulge of the

flame front into the unburned gases more quickly and cause a local shift in mixture ratio towards

stoichiometry, which will increase the local flame speed. Thus, a perturbation is amplified and

the resulting instability is termed preferential diffusional instability. The selective diffusion of

reactants can be viewed as a stratification of the mixture. Both mechanisms involving unequal

diffusivities are sometimes called differential diffusional instabilities, or instabilities due to non-

equidiffusion.

A final mechanism is dependent on the global activation energy Ea. Since development of

diffusional-thermal instability involves modification of the flame structure, the global activation

energy should also affect the cell development. In particular, it is reasonable to expect that a

large (small) Ea will facilitate (suppress) the cell development of a diffusionally unstable (stable)

flame.

A spherically expanding flame is subject to positive stretch (indicated by a positive Markstein

2.6 Premixed turbulent combustion 23

length), so a thermo-diffusively stable mixture will start out smoothly as wrinkles tend to be

smoothed out. When the stretch rate becomes too small to stabilize hydrodynamic instability,

cellular structures will develop. It can be stated that, in general, non-equidiffusivity and thus

the Lewis number is dominant compared to σ, δT and Ea. The combined effect of instability

mechanisms (illustrated in figure 2.6) can lead to the fact that a spherical growing flame is ini-

tially stable up to a specific flame radius, after which the flame becomes unstable and develops

cellular structures. As a consequence the flame speed increases fast as a result of the addi-

tional flame surface. This phenomenon complicates the determination of fundamental burning

velocities because there is no linear relationship anymore between flame speed and stretch.

The development of cells over the flame surface can be delayed by the expansion of the flame

front. The recent theory of Bechtold and Matalon [10] shows that the critical flame radius Rcr

at which cells start to grow is given by the relation Rcr v δTEa (Le− Le∗) /σ2. Here, Le∗ is a

corresponding critical Lewis number. Self-accelerating motion of the spherical cells is still under

study. It is not generally understood.

2.6 Premixed turbulent combustion

The main aspects of a premixed laminar propagating flame are now understood. The combustion

of a mixture in a spark ignition engine is definitely not laminar. The flow field is highly turbulent

and this leads to a turbulent combustion. In this section a short introduction to turbulent

combustion is given. The goal is not to perform turbulent burning velocity measurements, so

there will not be gone too much into detail.

Turbulent combustion is characterized by the large-scale velocity fluctuations (u′, rms turbulent

velocity) and the characteristic length scales of the flow field of the unburned gas mixture. These

length scales are, from large to small, the integral length scale (lI), the length scale boundaries

(lEI and lDI), and the Kolmogorov length scale (η). Heywood et al. [11] gives an indication

of the length scales in a spark-ignition engine. The integral length scale is proportional to the

lift of the intake valve (< 10 mm for car engines). The turbulent energy is generated by these

large scale flow irregularities. The energy is transferred to the successively smaller scales, until

the smallest scales dissipate the energy. The dissipation is due to the kinematic viscosity ν.

Due to viscosity, the kinematic energy of the turbulence is transferred into heat at the smallest


(Kolmogorov) scales. This transfer of energy is called the energy cascade.

Figure 2.7: Scales in a turbulent flow, the energy cascade.

There are different non-dimensional numbers that are important when premixed turbulent com-

bustion is studied. The first non-dimensional factor is the turbulent Reynolds number.

Ret =ρu′lIµ

=u′lIν

(2.30)

If this number exceeds a predetermined value, the flow becomes turbulent. Transition numbers

are defined for a variety of applications. When the transition number is reached the behavior

of the flow changes dramatically. Large eddies are then generated. These large eddies break up

into smaller eddies as explained above.

A second important number is the Damkohler number:

Da =τtτc

(2.31)

This number expresses the ratio of the turbulence integral and the characteristic chemical time

scales. The turbulent integral time scale is associated with the time an eddy of dimension lI

needs to rotate once. When Da is large, the chemical time scale is very small in comparison

to the turbulent time scale, which leads to fast chemistry. This is then expressed by a thin

reaction zone, distorted and convected by the flow field. On the other hand slow chemistry is

seen when Da is small. The reactants and products are then well mixed by turbulent structures


before reaction takes place. Analogously, the Karlovitz number can be defined, based on the

Kolmogorov time scale:

Ka =τcτη

(2.32)

This Karlovitz number is the ratio of chemical and Kolmogorov turbulence time scales and

is not equal to the Karlovitz stretch factor that was introduced in the context of flame front

instabilities. When Ka is large it expresses slow chemistry. Another notation for the Karlovitz

number, based on the thickness of the ‘inner layer’, is given below (δ = 0.1, the fraction of the

flame thickness that represents the inner layer):

Kaδ =(δlF )2

η2= δ2Ka (2.33)

In literature [12] it is shown that:

Ret = Da2Ka2 (2.34)

The turbulent fluctuations in the flow have important implications for the phenomena in flames.

In a turbulent flow, the flame front is highly disturbed and co-dragged by the vortices in the

flow. The instantaneous flame front of a premixed turbulent flame is therefore much larger

in area than the surface envelope of the time-averaged turbulent flame. As a consequence, a

turbulent flame burns a lot more mass than a laminar one. In comparison to a laminar flame,

the flame front is highly irregular and thick.

2.6.1 Regimes

After defining the above dimensionless parameters, the so-called Borghi diagram can be ana-

lyzed. This diagram represents the different regimes of turbulent premixed combustion. The

Borghi diagram is explained using figure 2.8.


Figure 2.8: Borghi diagram for premixed turbulent combustion. [13]

The abscis of the log-log diagram represents the ratio of the turbulent integral length scale to

the flame thickness. The ordinate represents the ratio of the turbulent velocity fluctuations to

the LBV. The line Ret = 1 is the separation line between laminar and turbulent combustion.

In this context the authors are only interested in the right part of the diagram.

The ‘wrinkled flamelets’ zone is also not very important. In this regime, where u′ < ul, the

rotation speed of even the largest eddies is not big enough to withstand the propagation of the

flame front.

Ka < 1 corresponds with the ‘corrugated flamelet’ regime. Because Ka < 1 the chemical time

scale is smaller than all the turbulent time scales, so there is very fast chemistry. Furthermore,

the flame thickness is much thinner than the smallest turbulent length scales, so the inner

structure is not affected by turbulent motions (and can thus be approximated by a laminar

structure). The flame front is only wrinkled by the turbulence. The wrinkled and the corrugated


flamelet regime together are called the laminar flamelet regime. The flame front has the structure

of a laminar flame and is deformed by the turbulent motion.

The line where Ka equals 1 is the ‘Klimov-Williams’ line. Ka > 1 corresponds with the ‘thin

reaction’ or ‘thickened-wrinkled flames’ zone. The turbulent motions affect and thicken the

pre-heat zone, but not the inner (reaction) zone. The smallest eddies are much larger than the

reaction zone thickness. In this zone the laminar flamelet structure for the reaction zone is still

valid.

Values of Ka > 100 or Kaδ > 1 correspond with the ‘broken reaction zone’. The turbulent

motions affect and thicken the pre-heat zone and affect and break-up the inner reaction zone.

The smallest eddies are comparable to the reaction zone thickness: they can affect the inner

zone. No laminar flame structure is found anymore.

2.6.2 Conclusion

In general, Borghi diagrams give an order of magnitude indication of what kind of premixed

combustion occurs. Naturally, there are many other available representations of the Borghi

diagram. There is still a lot of research on turbulent combustion in spark-ignition engines. A

clear answer to where each ‘mode’ of turbulent combustion can be placed in a spark-ignition

engine is still under consideration. Researchers state that the kind of turbulence is situated in

the laminar flamelet regime [13]. It is useful to know this, but during this master dissertation

there will be no investigation of turbulent combustion. It is, however, very important to know

the LBV of a mixture undergoing turbulent combustion. The inner structure of a premixed

flamelet in a turbulent flow consists of several layers embedded within each other [13]. The

main principle is that when this flamelet propagates, this occurs with a speed equal to the

LBV and an added effect of stretch due to curvature. This demonstrates the importance of the

knowledge of LBV data.

LITERATURE REVIEW 28

Chapter 3

Literature review

3.1 Measurement methodologies

3.1.1 Introduction

Throughout the years several methods have been developed to measure LBV, each with their

strengths and weaknesses. A number of these methods are briefly discussed here. This section

relies on the work of Vancoillie [3], which is a summary of the review paper by Andrews and

Bradley [15]. In the present experimental study a CBV is used. First, two alternative methods

are explained.

The tube method involves igniting the mixture at one end of a tube and photographing the flame

front propagation towards the other end. This method typically underestimates the burning

velocity due to flame area overestimation and the wall quench effect.

Burner methods involve a stationary flame. They are limited to the conditions that produce a

stable, laminar flame. Different types of burners can be employed, including nozzle, slot and flat

flame burners. Mostly used are Bunsen burners. The burning velocity can be derived from the

mean gas velocity in the nozzle and the cone angle of the flame. Errors may arise from the flame

front curvature, stretch effects, deviations from conical shape, uneven velocity distributions,

etc. These factors are less of an issue when a flat flame burner is used. An interesting, recently

developed method using a flat flame burner is the heat flux method (HFM). In this method

a non-stretched flame is stabilized on a perforated plate burner and its burning velocity is

determined under conditions where the net heat loss from the flame to the burner is zero. The

3.1 Measurement methodologies 29

stagnation point flat flame burner and counterflow twin-flame burner are variations in which a

stationary flat flame is stabilized using a nozzle burner with respectively a flat plate on top or

an opposed flow. Laser-Doppler anemometry (LDA) is used to characterize flame stretch.

3.1.2 Combustion bomb vessel method

Combustion bomb vessel methods involve ignition of the mixture inside a constant volume vessel

(for example the GUCCI). Originally, the LBV was calculated from the recorded pressure rise

after central ignition of the mixture. Typical assumptions included spherical flame propagation

and negligible flame thickness. As this method allowed to obtain the burning velocity over a

range of pressures and temperatures from a single experiment, it was often used to develop

LBV correlations valid at engine conditions. However, when only considering the pressure, it is

difficult to take stretch effects and flame instabilities such as cellularity into account [16]. The

method has not been used as extensively as many of the others, although it has been described

by Linnett as ‘... potentially a powerful method for determining burning velocities’. If its full

potentialities are used it can yield considerably more information from a single experiment than

any other method.

A more recent method relies on photographic observation of the pre-pressure period of the com-

bustion, where stretch is uniform and well defined. This method also allows determination of

Markstein lengths. To obtain data closer to the safe working pressure of the combustion vessel

two igniters have been used in order to produce two spherically expanding flame fronts simulta-

neously [17]. The burning velocity is then determined from the photographic observation of the

last moments of flame propagation, when the imploding flames are nearly flat. Unfortunately,

Markstein numbers are not obtained appropriately at these low stretch rate conditions. Also,

allowance must be made for the higher burning velocities due to instabilities at these conditions.

To visualize the flame front a special optical technique is used: the (high-speed) schlieren tech-

nique. From the resulting images LBV values can be calculated using post-processing software.

The specific aspects of the schlieren technique will not be discussed in the present literature

study, but the authors refer to a paper of Sulaiman et al. [18]. In this paper it is shown

that a digitized image processing technique is more effective as the processing time has been

reduced and human-related errors have been minimized. In section 4.2.3 the schlieren setup in-

stalled at the GUCCI setup is explained in detail. In contrast to this optical technique, another


methodology exists. This methodology is solely based on pressure measurements as a function of

time [19]. In comparison with other results, corresponding results using this method are 5-10%

higher. It is concluded that this methodology should only be used under circumstances where

more accurate methods cannot be applied.

Based on qualitative experiments and data analysis, the flame propagation in a CBV consists of

three distinctive periods. The first period is the one where the flame is dominated and influenced

by the ignition energy input. The subsequent period is a quasi-steady period of stretched flame

propagation suitable for the extraction of the laminar flame speed. The final period is, in

most cases, influenced by instabilities and chamber confinement. The first and last period are

explained in more detail in subsequent sections. The different periods are visualized in figure

3.1. In this figure the flame speed sb is given as a function of the stretch rate κ. When the flame

is generated, the stretch rate is very high and the flame speed is still quite low. As the flame

expands the flame speed increases and the stretch rate decreases continuously. It is common to

‘read’ this kind of graphs from right to left. When extrapolating towards zero-stretch, one tries

to select only the steady part of the graph, as that part is not disturbed by chamber confinement

or ignition energy. Figure 3.2 shows the flame speed as a function of flame radius. This figure

is easier to understand. As the flame expands the flame speed first drops but then gradually

increases towards a steady value.


Figure 3.1: Different periods of a propagating n-butane-air flame within a CBV. Influences of ignition

and wall confinements can be seen (φ = 0.8, 1 bar). [20]

Figure 3.2: Development of a methanol-air flame (φ = 1.2, 5 bar, 358 K). [3]

3.1.2.1 Ignition energy

When ignition of the mixture occurs, an initial period of decreasing flame speed as a function

of stretch rate is observed [3]. This is caused by the transition of the spark-driven (thermal

conduction from the ignition kernel to the reaction front) to normal flame chemistry. After


the effects of ignition have decayed, a linear relation is observed between Sn and α. This

linear relation has been suggested in theoretical analysis and numerical computation and has

been confirmed experimentally. The unstretched flame speed Ss can thus be obtained as the

intercept value of Sn at α = 0 and the dependence of the flame speed on stretch can be expressed

by a burned gas Markstein length Lb. The initial region of spark affected flame speed will not

be taken into account because otherwise a false LBV value would be calculated. To avoid the

effects of spark overdrive, Vancoillie [3] only considered radii larger than 15 mm in the linear fit.

Bradley [5] considered radii larger than 6 mm. The radius choice depends on the dimensions of

the closed vessel and the spark energy that is used to ignite the mixture. By discarding the data

up to and slightly after these radii, the influence from the initial conditions and transient effects

are eliminated. Kelley and Law [20] did several experiments with varying spark energy. Figure

3.3 shows two typical experiments ignited with different ignition energies. It is observed that,

after an initial, transient period during which results of the two experiments differ substantially

as a result of different ignition energies, with the lower curve having a smaller ignition energy,

the two flame trajectories eventually align as the influence of the ignition kernel is dissipated.

Figure 3.3: Two experiments with different ignition energies. The region where the two experiments

disagree is affected by the ignition energy (n-butane/air, φ = 0.8, 1 bar). [20]


3.1.2.2 Finite volume

When a CBV is used it is important to take into account its finite volume. When the flame

front grows towards the periphery of the vessel, the unburned gases are compressed (due to the

restriction of the flow of the unreacted gas) and the pressure increases. Due to this increasing

pressure the flame speed decreases, which - together with the increasing flame radius - causes

the stretch rate to decrease. At this stage the flame is still sufficiently far away from the wall in

terms of its thermal thickness, so there will not be conductive heat loss at this point [20]. When

the flame propagates beyond this point, the conductive heat loss will lead to a further decrease

in flame speed.

Kelley and Law [20] indicate that chamber confinement significantly decreases the flame speed

when the flame radius becomes larger than 40% of the inner chamber radius. For cylindrical

chambers, Burke et al. [21] calculated the influence on flame speed by chamber confinement and

stated that the effect is less than 1%, thus negligible, for flames at less than 40% of their way

to the chamber wall.

Kelley and Law [20] proposed a dual-chamber CBV to minimize effects of chamber confinement.

Two chambers are initially partitioned from one another by two sleeves with holes that are off-

set from each other. The mixture is then spark-ignited. Simultaneous to the spark ignition, the

holes on the two sleeves are aligned. The resulting outwardly propagating spherical flame is sub-

sequently quenched upon reaching the partitioning wall and coming into contact with the inert

gas through the aligned holes. Since the volume of the inner chamber is 25 times smaller than

the volume of the outer chamber, the pressure rise during flame propagation is small, rendering

its propagation to be at essentially constant pressure. By this method the limitation of chamber

confinement is more or less circumvented. Next to this combustion chamber adjustment, Kelley

and Law also did experiments in each combustion chamber separately. The result is given in

figure 3.4. The larger chamber provides a flame with a larger quasi-steady period.


Figure 3.4: Two experiments with different confinement. Disagreement at high stretch rates and low

flame speed occurs due to the ignition energy (n-butane/air, φ = 0.8, 1 bar). [20]

3.1.2.3 Linear vs nonlinear extrapolation

The present section discusses the differences between the usage of a linear and a nonlinear

extrapolation method. These two methods are nearly always used in CBV experiments. The

most popular one is the linear extrapolation method. Next to these two basic methods, new

extrapolation methods based on Halter et al. [22] are discussed. It is the authors’ purpose to

select one of these methods and use it as a basis to develop a new post-processing routine, based

on arguments found in several papers.

Linear extrapolation In equation 2.23 a linear relation between Sn and the stretch rate α

was presented. This linear relation has been extensively adopted for flame speed determinations

using counterflow flames and outwardly propagating flames [20]. It is possible to write equation

2.23 in a different way. A more simplified relation is then generated:

s = 1− σ (3.1)

where s = SnSs

, σ = LbαSs

is a non-dimensional stretch parameter, Sn is the stretched flame speed,

α is the stretch rate and Lb the burned Markstein length that measures the mixture’s sensitivity

to stretch.

From the equation above it can be seen that Sn = Ss if σ = 0, which is at the zero-stretch point.

The stretch is never zero in an experiment, so it is necessary to extrapolate up to that zero-


stretch point. In a situation where higher-order effects could be important (high stretch rates,

strong mixture non-equidiffusion expressed by a high Lewis number) the linear approximation

is not only inaccurate, but the act of performing a linear extrapolation with a dataset exhibiting

curvature could also impart substantial uncertainty in the extrapolated value. If this is the case

a more reliable method is required: the nonlinear extrapolation method. It is therefore useful

to perform an error analysis on the linear extrapolation method in order to get more insight in

the accuracy of the LBV results.

Nonlinear extrapolation According to Kelley et al. [20] it is advantageous to choose non-

linear extrapolation when the fuel mixture is composed of higher hydrocarbon fuels. These

fuels intrinsically have higher Lewis numbers and thus non-equidiffusivity levels. Kelley et al.

suggested a non-linear relation between stretch rate and flame speed:(SnSs

)2

ln

(SnSs

)2

= −2Lbα

Ss(3.2)

This relationship was reported to lead to less error when fitting the Sn vs. α results obtained

in their 82 mm diameter cylindrical vessel.

Other extrapolation methods Some researchers have developed their own extrapolation

method, trying to minimize the fitting error by making use of smallest error methods and

optimization theory. Halter et al. [22] proposed three different methodologies for the extraction

of LBV information. These methodologies rely on polynomial fitting. Starting from a linear

method, improvements were made to minimize the error of the linear fit. Close to stoichiometric

conditions, the three methodologies provide similar results in terms of LBV and Markstein

length. For lean and rich mixtures, the relative difference between the results obtained by the

different methodologies is bigger. The new methodology proves to be the most robust and

provides more accurate results.

Conclusions The following conclusions can be made based on Kelley and Law [20]:

� Linear extrapolation is adequate for mixtures that are not so strongly affected by stretch.

� Strong mixture non-equidiffusivity needs nonlinear extrapolation. Nonlinear behavior is

mainly a consequence of small diffusivity of the fuel.

3.2 Available LBV data 36

� Near-stoichiometric mixtures show very little sensitivity to linear-versus-nonlinear extra-

polation.

� Linear extrapolation needs a quite large useful range of measurement points (quasi-steady

part) in the flame speed vs stretch rate curve. Chamber confinement, high pressure and

ignition energy are the limiting factors as they affect this useful range in a negative way.

Based on the statements above, the mathematical difficulties coming in to play when nonlinear

extrapolation is done and the fact that the biggest part of previous investigation is performed

with linear extrapolation, a linear methodology will be used in the present work. Furthermore,

in most cases the error between the two methods is so small that it is of the same order as the

measurement errors, so one could say that the efforts of nonlinear extrapolation are not really

necessary. However, it must be noted that these mathematical ‘efforts’ only occur during the

implementation of the method. Once the formulas are written into a clear MATLAB program

or put into an Excel-file, mathematical difficulties are no longer an issue.

3.2 Available LBV data

3.2.1 Methanol

Vancoillie [3] already presented an overview of available experimental data up to the year 2010.

The latest experiments will be added to this list. The findings of Vancoillie will not be explicitly

repeated in this text, but a more general conclusion will be derived. Only the most recent

experiments will be discussed in a detailed way. In table 3.2.1 an overview of the measurements

on methanol-air is given. There is a lack of data at elevated pressures and for diluted mixtures.

For the references of the measurements up to 2010, the authors refer to the work of Vancoillie

[3]. References of the more recent data are provided.


Year Author Ref. Technique Tu[K] p[bar] φ f[vol%]

1955 Wiser & Hill - Horizontal tube 298 0.85 0.7-1.4 0

1959 Gibbs & Calcote - Bunsen burner 298 1 0.8-1.4 0

1980 Ryan &Lestz - CVB, pressure derived 470-600 0.4-18 1 0-30

1981 Hirano et al. - bunsen burner 343-414 1 0.6-2.2 0-20

1982 Metghalchi & Keck - CVB, pressure-derived 298-700 0.4-40 0.8-1.5 0-20

1983 Gulder - CVB, flame ionization 298-800 1.0-8.0 0.7-1.4 0

1992 Egolfopoulos et al. - Counterflow 318-368 1 0.5-2 0

1997 Wang et al. - Counterflow 323-413 1 0.7-1.4 0

2004 Saeed & Stone - CVB, pressure-derived 295-650 0.5-13.5 0.7-1.5 0

2006 Liao et al. - CVB, schlieren 385-480 1 0.7-1.4 0

2008 Zhang et al. [23] CVB, schlieren 373-473 1-7.5 0.7-1.8 0-15

2009 Beeckmann et al. [24] CVB, schlieren 373 10 0.8-1.2 0

2010 Veloo et al. [25] Counterflow 343 1 0.7-1.5 0

2013 Vancoillie et al. [26] heat flux method 298-358 1 0.7-1.5 10-20

2013 Goswami et al. [27] heat flux method - 1-5 0.8-1.4 0

2014 Sileghem et al. [28] heat flux method 298-358 1 0.7-1.5 0

2014 Beeckmann et al. [29] CVB, schlieren 373 10 - 0

2014 Vancoillie et al. [30] CVB, schlieren 303-383 1-10 0.8-1.6 0

Table 3.1: Overview of the methanol-air burning velocity measurements in literature.

The experimental work on tube and burner methods will not be discussed in detail. The tube

method provides LBV values for a range of equivalence ratios. A horizontal tube method was

used, which typically leads to a burning velocity underestimation. The burner method performs

burning velocity measurements at atmospheric conditions. The complex flame geometry of those

burners makes it difficult to estimate the flame area and also causes substantial negative stretch

effects. This often results in an overestimation of the burning velocity. CVB methods provide

more reliable results.

Combustion bomb methods using the recorded pressure history during explosion in combination

with a two-zone thermodynamic burning model give a wrong prediction of the true burning

velocities. These ‘closed vessel’ studies do not take flame stretch and instabilities into account.

Failing to perform stretch corrections for the spherical flames inside these closed vessels can lead

to over- or underestimation of the true LBV, depending on the sign of the Markstein number.

Spherical flames are also sensitive to instabilities and may develop cellular structures. This


is especially the case at elevated pressures and can lead to overestimation of the true LBV

values at these conditions. It is of high importance not to take into account the data points

corresponding to these instabilities when performing the extrapolation towards zero-stretch.

More recently, Saeed and Stone employed a multiple-zone thermodynamic burning model to

find the relationship between the mass fraction burned and the recorded pressure rise during

contained explosions in a spherical vessel. They performed no stretch correction, but analyzed

the data only after the flame radii exceeded 50 mm, claiming that the effect of stretch on

burning velocity is smaller than 1% at these conditions. They studied the burning velocity for

pressures up to 13.5 bar, but observed cellular flame structures at pressures beyond 6 bar and

consequently removed these cellular flame points from their dataset. As a result, the validation of

their proposed ul correlation is quite limited at elevated pressures and temperatures. Transition

to cellularity was detected based on a sudden rise in burning velocity, which is less reliable

than photographic observation. Liao et al. used a high speed camera and schlieren optical

system to investigate LBV at atmospheric pressure. A linear extrapolation method was used.

An uncertainty of 8% was reported. Zhang et al. [23] used the same method for pressures up

to 7.5 bar. Residual gases were simulated using N2. Beeckmann et al. also employed the same

technique. In the present work no residual effects will be examined. Most recently, Sileghem

et al. [28] performed heat flux measurements on mixtures of methanol, ethanol, iso-octane

and n-heptane. The experiments were done at atmospheric pressure and for a wide range of

temperatures. As expected, the LBV values of the fuel blends were in between the burning

velocities of the pure fuels, with ethanol having the highest LBV values and iso-octane the

lowest.

3.2.2 Ethanol

In this section the relevant literature on ethanol LBV measurements is presented.

Table 3.2.2 illustrates that most of the experimental work on the LBV of ethanol-air mixtures

was published quite recently. This is due to the growing interest in ethanol from biomass during

the last decade. As for methanol-air mixtures data at elevated pressures and different dilution

ratios are scarce. Egolfopoulos et al. and Veloo et al. investigated the LBV for ethanol-

air mixtures using the burner method. The accuracy on the measured burning velocities was

estimated to be better than 1 cm/s. Some researchers used the CVB method. Kimitoshi et


Year Author Ref. Technique Tu[K] p[bar] φ f[m%]

1982 Gulder - CVB, flame ionization 298-800 1-8 0.7-1.4 0

1992 Egolfopoulos et al. - Conterflow 363-453 1 0.55-1.8 0

2006 Liao et al. - CVB, schlieren 385-480 1 0.8-1.2 0

2006 Kimitoshi et al. - CVB, schlieren 325 1 0.8-1.4 0

2009 Bradley et al. - CVB, schlieren 300-393 1-14 0.7-1.5 0

2009 Ohara et al. - CVB, schlieren 298 1-5 0.8-1.4 0

2009 Beeckmann et al. - CVB, schlieren 373 10 0.8-1.2 0

2010 Veloo et al. - Counterflow 343 1 0.7-1.5 0

2010 Konnov et al. [36] Flat flame, heat flux method 298-358 1 0.65-1.55 0

2011 Eisazadeh-Far et al. - CVB, pressure derived 300-650 1-5 0.8-1.1 0-10

2011 Broustail et al. - CVB, schlieren 393 1 0.8-1.4 0

2011 Varea et al. - CVB, schlieren 373 1-5 0.8-1.5 0

2011 Marshall et al. - CVB, pressure derived 400-650 0.5-4 0.7-1.4 0-30

2014 Glaude et al. [31] heat flux method 298-398 1 0.6-1.6 0

2014 Sileghem et al. [28] heat flux method 298-358 1 0.7-1.5 0

2014 Beeckmann et al. [29] CVB, schlieren 373 10 - 0

Table 3.2: Overview of the ethanol-air burning velocity measurements in literature.

al. used the optical schlieren technique but did not extrapolate to zero-stretch. They averaged

the stretched burning velocity over a range of flame radii between 27 mm and 40 mm, with the

assumption that the effects of flame stretch are small in that region. It can be concluded that

the range of measurement conditions is quite limited in general. It is definitely useful to expand

this range for ethanol and methanol in future research.

3.2.3 Effects of high pressure

At a fixed temperature an increase in initial pressure leads to a decrease in LBV. At high

pressures, the recombination reaction reduces the H atom concentration and thus competes

with the initiation reaction producing free radicals O and OH. This process tends to reduce

the overall oxidation rate and to inhibit the combustion reaction. It is quite logic that when

the combustion reaction rate decreases, ρuul decreases also. The expected value for ul is thus

lower than the ul value under normal pressure conditions, as ρu will increase because of a higher

pressure. The flame ‘speed’, and thus also the LBV value calculated from this flame speed, will

decrease according to [32].


Most recently, Bradley et al. [16] reported and discussed spherical explosion bomb measurements

for ethanol-air mixtures. These measurements were performed with central ignition, in the

regime of developed stable flame. Pressures ranged from 0.1 to 1.4 MPa, temperatures from 300

to 393 K and equivalence ratios from 0.7 to 1.5. Bradley et al. validated their experimental data

using [33], [34], [35] and numerous chemical kinetic models predicting ul. Because the spherical

explosion technique was used, moreover with central ignition, the results of Bradley et al. will

be very useful to validate LBV results measured with the GUCCI. Furthermore, the inevitable

limitations of elevating the pressure, which were also encountered in [16], will have to be taken

into account. These limitations are discussed in a proceeding paragraph.

In 1998, Bradley et al. [5] did similar measurements on iso-octane - air mixtures at initial

temperatures between 358 K and 450 K, pressures between 1 and 10 bar and equivalence ratios

of 0.8 and 1.0. Measured values of ul for ethanol were compared to corresponding values for iso-

octane. At atmospheric pressure and an unburned mixture temperature of 358 K the maximum

LBV value was significantly higher for ethanol than for iso-octane. An empirical expression

(power law) was assumed in [5] for the variation of ul with pressure:

ul = ul0

(p

p0

)β(3.3)

with T0 and p0 the reference values for temperature and pressure at which ul0 is determined.

Bradley et al. concluded that LBV curves for ethanol-air mixtures were clearly more sensitive

to pressure variations - i.e. a more distinct decrease of ul with increasing pressure, especially

for lean mixtures - than for iso-octane - air.

Initial pressure of 10 bar Recently, Beeckmann et al. [24] performed LBV experiments in

a spherical combustion vessel at an unburned mixture temperature of 373 K and a pressure of

10 bar. Tested fuels were methanol, ethanol, n-propanol and n-butanol. The propagation of the

flames was captured using the schlieren technique. After validating the setup, the experimental

conditions prior to ignition were set to a temperature of 373 K and a pressure of 10 bar.

Experiments were performed with equivalence ratios ranging from 0.7 to 1.3. A nonlinear model

was chosen to extract the LBV. In order to discard ignition effects, only flames with a diameter

above 5 mm were used. In case of hydrodynamic instabilities, the available amount of flame

images used for post-processing is reduced significantly. Also, the richer the mixture the earlier

the onset of cellular structure formation, corresponding to higher stretch rates. This leads to


a smaller number of useful images for post-processing and thereby less accurate LBV values.

Therefore the range of equivalence ratios was limited with a maximum value of 1.3. For validating

their measurements on methanol-air mixtures, Beeckmann et al. used three kinetic models and

an approximation formula for LBV values for lean to stoichiometric conditions.

Although the authors are especially interested in light alcohols, i.e. methanol and ethanol,

heavier alcohols like n-propanol and n-butanol can be used as a supplement to the former two

in spark-ignition engines. Beeckmann et al. compared the different alcohol components for two

experimental conditions, the first being their own combustion vessel method using technical air

as an oxidizer. They verified their results against published experimental data from a premixed

counter flow configuration at atmospheric pressure and an elevated temperature of 343 K, in

which ambient air was used as an oxidizer. Similar trends were observed.

It can be seen in figure 3.5 that methanol burns significantly faster than the other alcohols for

equivalence ratios higher than 1. Ethanol has the lowest maximum LBV of all four alcohols

at an equivalence ratio of 1.1. For equivalence ratios between 0.8 and 1.1, ethanol, n-butanol

and n-propanol LBV values are within a range of merely 5%. The maximum difference between

methanol and the other alcohols is around 15% for rich mixtures [24]. The measurements were

validated using three kinetic models and an approximation formula for the LBV. Trends were

also verified by comparison with the experimental data from the above-mentioned counter flow

measurements. It was concluded that all the models, including the approximation formula, were

lacking a correct sensitivity to pressure variations for the premixed combustion of methanol.

Figure 3.5: Measured LBV values for alcohol/air flames as function of equivalence ratio, pi = 10 bar

and Ti = 373 K, XO2 in air = 0.205. [24]


For ethanol, the same models and approximation formula were used to compare the experimental

data with. These data suggest that the maximum ul value is at an equivalence ratio between

φ=1 and φ=1.1.

Limitations Elevating the initial pressure of an experimental setup cannot be fulfilled without

taking into account the consequences. Before starting any measurements it is important to have

a good understanding of the accompanying limitations.

When φ is increased at higher pressures, more time is required to evaporate the fuel. In [16]

a maximum evaporation time of three minutes was recorded for the following conditions: T =

300K, φ=1.4, p = 1.0 MPa.

At higher pressures the range of stable flame measurements becomes more restricted since the

increase in initial pressure enhances flame instabilities and shifts the onset of cellularity to higher

stretch rates. This increases the uncertainty in LBV and Markstein numbers: flame cellularity

effects limit the number of shadowgraph images that can be used for the fitting of the flame

front radius temporal evolution ([32], p. 3297). Two ‘stretch rate limits’ can be discerned when

observing flame speed as a function of stretch rate: a higher limit, excluding ignition effects,

and a lower limit, excluding cellularity effects. When φ is increased, both stretch rate limits

are shifted towards higher values. This means that the onset of stable flame propagation is at

a higher stretch rate, though the same effect applies to the onset of cellularity. The increase

in φ is associated with a decreasing Lewis number (for example ethanol, which has a lower

diffusivity relative to the mixture than oxygen and consequently a decreasing Lewis number

when φ increases). It can be concluded that rich mixtures are easier to ignite than lean mixtures

but instability develops earlier, limiting the extrapolation range.

In figure 3.6 values of ul measured by Bradley et al. [16] at 358 K and different pressures between

0.1 and 1.4 MPa are shown. The curves for p = 1.2 and 1.4 MPa did not cover the whole range

of equivalence ratios. Near stoichiometry (φ = 1) of the ethanol-air mixture, measurements

could not be performed at initial pressures higher than 1.2 MPa due to the associated peak

pressure. At 1.2 MPa the peak pressure was 8.5 MPa, close to the maximum safe working

pressure (9 MPa). As expected, at 1.4 MPa initial pressure the maximum value of φ permitting

measurements was even lower. Both limiting values of φ are indicated by the points B in the

figure.


Figure 3.6: Measured LBV values by Bradley et al. [16] at 358 K and pressures from 0.1 to 1.4 MPa.

[16]

3.2.4 Effects of high temperature

For a fixed pressure, LBV increases with temperature since high temperatures boost the dissoci-

ation reactions that produce free radicals. These radicals initiate the combustion reaction, which

is why the velocity of flame propagation increases. Moreover, when the initial temperature is

increased, the density of unburned gases is lower, thereby reducing the density ratio ρuρb

.

Sileghem et al. [28] investigated the LBV of both methanol and ethanol using the heat flux

method. The temperature was varied from 298K to 358K. The obtained LBV data were com-

pared with the datasets of Bradley et al. [16]. The correspondence was reasonable although in

[16] a completely different measurement method was used.

To look at the effect of the unburned mixture temperature on the LBV, the following correlation

was used (reference conditions: 298 K and 1 bar):

ul = ul0

(TuTu0

)α(3.4)

Here, α represents the power exponent of the temperature dependence. Sileghem et al. derived

the temperature exponent α for each mixture composition of both methanol- and ethanol-air


mixtures. The resulting curves reached a minimum value around the equivalence ratio corre-

sponding with peak burning velocity, which implies that for slightly rich mixtures the tempera-

ture dependence is the lowest. This observation was consistent with results from previous work.

However, by comparison with the power exponents found by Vancoillie et al. [26] for methanol,

and those derived from the data of Konnov et al. [36] for ethanol, it was seen that there were

some important deviations.

For methanol, there was only a good agreement with the power exponents from [26] around

stoichiometry. Additionally, the power exponents derived from modeling results using the mech-

anism of Li et al. [37] were compared to the experimentally determined exponents. The mech-

anism of Li et al. also produces a minimum for slightly rich mixtures and there is excellent

agreement with the measurements of Vancoillie et al. [26], especially for lean mixtures.

For ethanol, the power exponents derived from the measurements in [36] tended to level off

with increasing equivalence ratio. Although this effect was also predicted for methane-air flames

[38], it was not seen in the measurements of Sileghem et al. Therefore, further experimental

data of the LBV of rich mixtures remains desirable. Also, the power exponents derived from

the measurements on ethanol in [28] were compared to the data of Dirrenberger et al. [31]. The

shape of the curve derived from these data is very different and the temperature dependence is

minimal for φ = 0.8 instead of at peak burning velocity. The cause of this deviation is probably

a lack of accuracy: the power exponent of Dirrenberger et al. was derived from measurements

at only three different temperatures [28]. Finally, calculated power exponents using the Konnov

mechanism [39] were added in [28]. These power exponents agreed well with the experimental

data, especially for rich mixtures.

3.2.5 Effects of dilution

Finally, the effects of dilution on the LBV are discussed. This will be done mainly on the basis

of the study of Vancoillie et al. [26] on diluted methanol-air mixtures at room and elevated

temperatures. LBV measurements on these mixtures were done using the heat flux method.

The pressure was kept atmospheric and the unburned mixture temperature was varied from 298

K to 358 K. The equivalence ratio ranged from φ = 0.7 to 1.5. Molar water vapor contents up

to 20% and molar excess nitrogen contents of almost 10% were used.


Dilution of combustible mixtures is important for combustion in automotive engines, especially

for EGR (Exhaust Gas Recirculation). The most important reason for diluting a combustible

mixture is the reduction of burned gas (or flame) temperatures, thereby reducing harmful NOx

emissions. Other advantages are the reduction of throttle losses in gasoline engines and the

suppression of knock. Dilution affects the burning velocity, which can lead to combustion in-

stabilities. Therefore it is of high importance to understand the impact of dilution on the

combustion process, especially since EGR has been applied in methanol engines in considerably

higher concentrations than what is common in gasoline engines [26].

Apart from EGR, dilution with water has also been applied to reduce NOx emissions and to

suppress knock phenomena in SI engines [26]. Vancoillie et al. investigated the influence of

nitrogen and steam dilution on the LBV of methanol.

In earlier work it was shown that the effect of nitrogen and water vapor dilution on chemical

kinetics is negligible, regardless of the dilution rate. The predominant effect of these dilution

components on the LBV is thermal, through a reduction of flame temperature. For carbon

dioxide, however, the chemical effect was found to be non-negligible, leading to a non-linear

decrease of the LBV in terms of molar CO2 content. As CO2 is an important constituent of

exhaust gases, this nonlinear behavior can also be expected for EGR dilution. This was con-

firmed by chemical kinetics calculations of methanol flames diluted with burned gases. Burned

methanol-air was used as a diluent to represent the residual gases as it might appear in a real

engine [26].

Nitrogen dilution Experimental and modeling results for methanol, burned with an oxidizer

containing 19 mol% O2 in (N2 + O2), were compared by Vancoillie et al. For rich mixtures

the values of ul were overpredicted by the mechanism of Li et al., which is in agreement with

the observations in [40]. It was concluded that these deviations at higher equivalence ratios

are due to an incorrect representation of the chemistry of rich mixtures. The nitrogen dilution

of methanol flames results in an almost linear decrease of the LBV (the global deviation from

linearity is less than 5% [26]), in line with earlier studies on methane-air flames.

Water vapor dilution Figure 3.7 shows burning velocities for methanol-air mixtures as a

function of water vapor percentage, obtained by both modeling and measuring. The dash-

3.3 LBV correlations 46

dotted lines (model with real H2O) do not coincide with the dotted lines (model with non-

reactive FH2O), although both lines are very close to each other. This implies that the chemical

contribution to the decrease of ul is practically negligible. The deviations from a linear decrease

are bigger than for nitrogen (see higher), but still limited to about 10% as the water vapor

content approaches 20%.

Figure 3.7: Measured (symbols) and calculated (lines) burning velocities for methanol-air mixtures as a

function of water vapor percentage (Tu = 338K). Dash-dotted lines: model with real H2O;

Dotted lines: model with non-reactive FH2O; Diamonds: φ = 0.7; triangles: φ = 1.5; and

circles: φ = 1.0. [26]

An explicit correlation between the properties of the fuel-air-diluent mixture and LBV decrease

due to dilution was derived [26], whereby a dilution coefficient F was defined:

ulul (f = 0)

= 1− F (φ, Tu, diluent)f (3.5)

3.3 LBV correlations

Most of the published LBV correlations for methanol- and ethanol-air mixtures use the correla-

tion form originally proposed by Metghalchi and Keck [41]:

SL = SL0

(TuT0

)α( p

p0

)β(1− 2.1f) (3.6)

3.3 LBV correlations 47

This form assumes the effects of equivalence ratio, pressure, unburned mixture temperature

and residual gas content (dilution level) to be independent of each other. Vancoillie et al. [26]

analyzed Chem1D calculation data and the result supported the exponential trends in pressure

and unburned mixture temperature, but also revealed that there can be a strong interaction

between the effects of φ, p and Tu. The temperature exponent α increases with pressure at lean

equivalence ratios and decreases with pressure at rich equivalence ratios. Similar interactions

were observed when the pressure exponent β was plotted as a function of equivalence ratio and

unburned mixture temperature.

Verhelst et al. [42] noted the same interaction effects in their calculation results for the LBV of

hydrogen-air mixtures. To cover these effects, the following functional form was proposed:

SL (φ, p, Tu, f) = SL0 (φ, p)

(TuT0

)α(φ,p)F (φ, p, Tu, f) (3.7)

In order to make both temperature and pressure non-dimensional, the standard reference con-

ditions were used, i.e. (p0 = 1 bar, T0 = 300K).

Both α (φ, p) and SL0 (φ, p) are polynomial functions of φ and p with cross terms due to the

interaction between these variables. The correction term F accounts for the residual gases and

is a complex function of φ, p, Tu and f , with f representing the diluent volume fraction. The

calculation results obtained by Vancoillie et al. already showed that the linear decrease in ul

with increasing diluents is only valid for very low diluent fractions (< 10%). Inspection of the

correction factor F as a function of φ, p, Tu and f shows that the dominating factor is the

diluent volume fraction, but there are also important effects of Tu, p and φ. For example, the

tolerance for dilution increases with temperature. As mentioned before, this effect of Tu on the

correction factor F is more pronounced for rich mixtures and at elevated pressures. Similar

interaction effects were reported by Verhelst et al. for the LBV of hydrogen-air mixtures [42].

It can be concluded that the LBV of the fuel-air-residuals mixture at instantaneous pressure

and temperature is an important building block for predictive engine codes. This building block

is conveniently implemented in engine codes by using correlations which give the LBV in terms

of pressure, temperature and composition of the unburned mixture. Both for methanol and

ethanol, it was shown by Vancoillie et al. [26] that there is a lack of burning velocity correlations

suitable for use in engine codes. Also, experimental LBV data at engine-like conditions are very

3.4 Conclusion literature review 48

scarce, especially at elevated pressures and for diluted mixtures. In future work, the developed

correlations will be further validated by comparison with experimental LBV data at engine-

like conditions. The reason for this is that the validity of these correlations depends on the

ability of the employed oxidation mechanisms to predict accurate burning velocities at elevated

temperatures, pressures and dilutions. Further experimental work on the burning velocity at

these conditions thus remains of critical importance.

3.4 Conclusion literature review

This final section relates the most important observations from previous sections of this chapter

to the present and future experimental work. The following topics are discussed concisely, from

on the experimental point of view:

1. Region of interest

2. Pressure limitations

3. Scatter and repeatability

Region of interest The database of LBV should cover a large part of the range of in-cylinder

conditions as appearing in alcohol-fueled engines. A good knowledge of this operating range is

required to identify the areas the database should cover in terms of initial chamber pressure,

temperature and mixture composition. In recent work of Vancoillie [3] the unburned mixture

conditions in alcohol-fueled engines were determined. These are shown in table 3.3.

engine type p [bar] T [K] φ EGR [m%]

flex-fuel 1-100 300-1000 0-2.5 0-20

dedicated 1-150 300-1400 0-2.5 0-50

Table 3.3: Overview of the unburned mixture conditions in alcohol-fueled engines. [3])

It is observed that the peak pressures and temperatures are quite high. With the GUCCI it

is not possible to measure the LBV at such high pressures and temperatures due to technical

constraints. When the initial pressure is high, the peak pressure reached during the explosion can

become too high and therefore not tolerable. The initial pressure and temperature ranges that


will be aimed at in the present work are, respectively, 1-10 bar and 300-400 K. The mentioned

pressure range is only a first indication; if the GUCCI setup works properly up to a pressure of

10 bar, which means peak pressures do not exceed the limiting value of 150 bar, measurements

at higher pressures may be performed (the peak pressure can be calculated theoretically using

the GASEQ software, but for safety reasons this will also be checked experimentally). Note:

this literature study was done before the experiments were performed. Eventually, the highest

initial pressure that was used for the LBV measurements in the present work was 15 bar..

Figure 3.8: Region of interest compared to known measurements up to 2013. Temperature ranges from

300 to 1400 K in alcohol-fueled ICEs, the measurement range up to today is only 300-400

K.

In figure 3.8 it can be observed very clearly that, up to today, measurements did not cover

the complete region of interest. Measurements at higher pressures will lead to improvements

of the known area, but at these conditions researchers have to cope with technical and other

constraints (see next paragraph). It is the authors’ main purpose to perform a large part of

the measurements within the ‘known’ zone, and potentially extend the data range to higher

pressures.

Pressure limitations At high initial pressures there are important limitations to take into

account. More time is required to evaporate the fuel (methanol or ethanol) for rich mixtures.

Beyond a certain equivalence ratio, the fuel will not be able to evaporate completely before

ignition. The same effect may occur due to an insufficient initial temperature (e.g. 300 K or

less). The measured partial pressures are then an indication of (in)complete evaporation.


A second limitation is the maximum allowable peak pressure in the combustion chamber. The

GASEQ program enables to calculate this peak pressure for a single explosion. This value must

not exceed 150 bar to ensure a safe operation of the GUCCI setup. Furthermore, at higher

values of φ instabilities develop earlier. Therefore, along with increasing the initial pressure, the

range of equivalence ratios will decrease towards leaner mixtures.

Scatter and repeatability At least three explosions should be performed at each condition

to obtain a measure for the repeatability of the experiments and to capture the stochastic

variation. In between experiments, the recorded pressure traces can be used to quickly assess

the repeatability. After the image processing, the standard deviation on the burning velocity

and Markstein length can be calculated for each condition.

Some important factors affecting mixture stoichiometry have to be accurately controlled.

� One important factor is the vessel sealing. Although the seals were replaced during the

initial stages of the present work, still some degree of leakage was present.

� The consistency of pressure and temperature just prior to ignition is of high importance.

The tolerance for these parameters is set at 0.03 bar and 3 K, respectively.

� Residuals are considered as another factor affecting mixture composition, but are kept

at a minimum through adequate ‘flushing’ of the vessel after each explosion. The exact

flushing procedure will be explained in the next chapter.

� Another factor is the uncertainty of the full scale deflection of the syringe used to inject

liquid fuels. The manufacturer tolerance was given as 0.5% at full scale.

� Finally, the sensitivity of the pressure and temperature sensors is crucial in order to attain

accurate results.

To properly account for the influencing factors listed above, a profound error analysis is required.

This analysis is provided in the next chapter.

EXPERIMENTAL SETUP 51

Chapter 4

Experimental setup

In the previous part, the background theory required to understand the experimental results

and the measurement principles was discussed. The following sections cover the experimental

part of the dissertation. This ‘introduction to the measurements’ starts with a discussion of

the experimental setup. By gradually guiding the reader through the different parts of the

GUCCI setup, a profound insight into the hardware of this setup is provided. After this,

the measurement procedure is clarified. Then the post-processing methodology and the error

analysis are discussed. The final section discusses the repeatability of the measurements.

4.1 The GUCCI setup

This section describes the experimental setup in more detail. During the dissertation a lot of time

was spent with the setup and different improvements led to more accurate LBV measurements.

Due to the versatility of a bomb and the ability to do basic research into the combustion pattern

of different fuels, Ghent University decided to build this setup. It is the authors’ intention to

provide a detailed strategy to perform LBV measurements using this setup.

The GUCCI (Ghent University Combustion Chamber I) setup is a constant volume bomb (CVB)

or constant volume combustion chamber (CVCC) with an internal volume of about 4.1 liters.

In figure 4.1 the setup is shown. It was developed at Ghent University some years ago (2008)

and initially used to study diesel injection in the context of marine diesel engines. During this

work some adaptations were done, which made it possible to also do flame speed measurements.

In all likelihood, further adaptations will be necessary in the future.

4.1 The GUCCI setup 52

Figure 4.1: An interior view of the closed vessel. Both electrodes are visible.

Basically, the GUCCI is a closed vessel wherein a certain fuel-air mixture is introduced and

eventually ignited. Apart from the mixture composition, the initial pressure and temperature

can also be set to certain values. In this work the GUCCI is used in a ‘static’ way. This means

that the different components of a certain mixture are filled sequentially, while a stirring element

or ‘fan’ causes an intense mixing.

The chamber is optically accessible in different directions (X, Y, Z). In this work, only one

optical measurement technique (schlieren technique) is used to capture flame propagation images

during a single combustion. In the nearby future, more equipment could be installed in order

to simultaneously use multiple types of optical image capturing techniques. The quartz glasses

(manufactured by LSP-Quartz, Wijchen, Netherlands), providing the optical accessibility, are

very thick and can withstand pressures up to 150 bar. The windows have a diameter of 150 mm.

To introduce the gaseous mixture a gas filling system is available. This system is able to do a

fully automated filling of the combustion bomb. The initial pressure is equal to the sum of the

partial pressures of the different gaseous components. Electric heaters at the wall provide up

to 6 kW for preheating the vessel and mixture up to 473 K. Images are captured using a high

speed imaging tool (high speed camera). The most important hardware parts of the setup are

discussed below.

The following scheme gives a general overview of the GUCCI setup.


Figure 4.2: General overview of the GUCCI setup.

4.1.1 Gas filling system

In order to perform meaningful measurements with the GUCCI it is of importance to know

exactly how the mixture is introduced in the closed vessel. Gaseous fuel and dry air are subse-

quently supplied by the gas filling system, which was designed to fill the chamber automatically.

When a mixture composition is calculated and the partial pressures are known, these values can

be entered into the LabVIEW program. The valves, controllers and absolute pressure sensor are

indicated in figure 4.3.


Figure 4.3: Scheme of the gas filling system.

In figure 4.3 the valves are marked yellow. The vacuum valve connects the tubing of the gas

filling system with the vacuum pump. The exhaust valve connects the tubing with the ambient

air and thus with atmospheric pressure. The gas valve is essential since it connects the tubes of

the gas filling system with the closed vessel. The air valve enables the introduction of compressed

air, e.g. for flushing the chamber.

To evacuate the chamber, the exhaust valve must be closed and the gas valve opened. The

vacuum pump needs to be turned on and the vacuum valve must be opened. To pressurize the

vessel, the air valve needs to be opened and the gas valve closed. The flushing procedure (see

section 4.2.1) is a sequence of evacuating and pressurizing the vessel.

After flushing the chamber to make sure most of the residual gases are extracted, the program

completes a series of actions to fill the chamber with the different gaseous components of which

the desired partial pressures were set in LabVIEW. These actions are a sequence of filling

the tubes of the gas supply with a gaseous component and opening a valve to introduce this

component into the chamber. For each gaseous component the ‘actual’ filled cumulative pressure

value is measured. Thereby the ‘actual’ filled partial pressure of each component is known.

The equivalence ratio of the mixture present in the chamber is then calculated from the actual

partial pressure values. This method always provides the opportunity to know the exact mixture


composition. Of course it is also needed to take into account the errors on the pressure sensor.

The real pressures can deviate from the measured ones.

4.1.2 Sensors

The GUCCI is equipped with pressure and temperature sensors in order to easily track a variety

of processes. In this section a short overview of these sensors is given. First a scheme is provided

showing the different sensor locations. Then the purpose of these sensors is explained. This

discussion provides the vital information for performing the error analysis.

Figure 4.4: Schematic overview of the different relevant sensors.

There are two pressure sensors present. The first one is the AVL QC34D, a water-cooled

piezoelectric relative pressure sensor especially designed for combustion analysis. This sensor is

mounted inside the closed vessel and is used to measure internal chamber pressure. Its mea-

surement range is very large (0-250 bar). On the one hand it is used to measure the low partial

pressures inside the chamber while filling and on the other hand it is used to measure the com-

bustion pressure profiles. This sensor is thus exposed to very high pressures and temperatures.

In case of a failure in the cooling system, the QC34D is designed in such a way that it can

survive temperatures up to 350 ◦C. As it is a relative pressure sensor, the pressure is referred

to a certain reference value.


Figure 4.5: Picture of the piezoelectric AVL QC34D relative pressure sensor. The mounting method

for this sensor is also represented.

The signal generated by this relative pressure sensor is transferred to a charge amplifier (Kistler

5011B). The working principle is as follows: the electrical charge yielded by piezoelectric sen-

sors is converted into a proportional voltage signal. This amplifier serves mainly to measure

mechanical quantities, e.g. pressure, force or acceleration. The maximum error is equal to

±0.05%FS.

Figure 4.6: Picture of the UNIK5000 absolute pressure sensor. The sensor is mounted on the tubing of

the gas filling system as shown in figure 4.4.

The second pressure sensor measures the pressure inside the tubes of the gas filling system.

The UNIK5000 from manufacturer Druck was installed. It is used to measure the pressures of

the individual components passing the corresponding tubes of the gas supply during the filling

procedure. The main features of this sensor are its good linearity and short reaction time. The

absolute pressure is measured, i.e. the pressure is referred to a vacuum and not to atmospheric

pressure. Table 4.1 below provides technical data concerning both sensors.

4.2 Measurement procedure 57

Pressure sensor 1 2

type AVL QC34D Druck UNIK5000

Range [bar] 0-250 0-70

Sensitivity 19 mC/bar /

Accuracy ±0.2% FS ±0.05% FS

Table 4.1: Characteristics of the pressure sensors.

In order to measure the temperature inside the combustion chamber, a type K thermocouple

is used. The PID chamber temperature control is based on the temperature measured with

this kind of sensor placed inside the chamber. The chamber temperature Tc is measured at

one location only, thus it is not clear to what extent the temperature inside the chamber is

uniform at the start of an ignition. By excessive use of the fan, and thus creation of turbulence,

an attempt was made to get the most uniform temperature profile inside the chamber. It is

clear that the temperature is the highest in the corners of the chamber, where contact with the

chamber walls is the most intense. In the centre of the chamber a slightly lower temperature is

expected. Based on previous work [43] an estimated error of δT = 2.5 ◦C is chosen.

4.2 Measurement procedure

The measurement procedure is now explained, comprising three major actions: positioning of

lenses and camera, flushing and filling, and finally ignition. The result is a sequence of schlieren

images of a single explosion.

After flushing the chamber it is desired to get a perfectly stirred mixture into the combustion

chamber. This is done using the automatic gas filling system. The components are then stirred

by a small fan. When the fan is turned off, a small period of rest is implemented in order to

avoid any influence from the created turbulence. Then ignition of the mixture occurs using two

opposite electrodes, mounted diagonally in order to provide central ignition. With an optical

technique, called schlieren technique, images of the propagating flame at different time steps are

obtained. Then the radius ru = f (t) is determined as a function of time. From this the stretch

rate α can be derived as a function of time. A graph of the ‘stretched’ flame speed Sn can now

be plotted against the stretch rate. Generally the influences of ignition energy and the finite


volume of the chamber are excluded by selecting the best possible range of stretch rate values.

These values generate a linear profile of ‘stretched’ flame speed values. By linearly extrapolating

up to the y-axis, the zero-stretch flame speed Ss can easily be determined. Finally, the LBV

of the mixture is calculated by multiplying the flame speed by the ratio of burned to unburned

mixture density, ρbρu

. Both densities are determined using the GASEQ program.

4.2.1 Flushing and filling

The filling procedure for gaseous fuels is now explained. The associated flushing procedure,

also discussed in this paragraph, is valid for both gaseous and liquid fuels. In the present work,

most of the gaseous fuel-air LBV measurements were performed with methane. Before the actual

measurements a series of experiments with acetylene-air mixtures was performed, but these were

of less importance as they served primarily to test the proper working of the GUCCI setup and

to become familiar with the setup. After calculating the partial pressures of CH4 and air using

MATLAB, these values are entered into the LabVIEW program. Details about the methodology

for calculating these partial pressures are provided in appendix E.1. Then the filling procedure

starts.

Flushing The flushing step comprises the first series of actions in the filling process. To

provide a stepwise ‘manual’ on how to properly flush the chamber, the different steps are given

below:

1. One minute of flushing (air valve + gas valve + exhaust valve open) with compressed air

to remove most of the burned components and thereby protecting the vacuum pump from

unnecessary soot pollution and potential damage. If combustion gases from previous ex-

plosions are still present inside the vessel, a flushing period of one minute with compressed

air is certainly required to be sure the burned components will not damage the vacuum

pump in the next step.

2. Evacuation to 0.1 bar (vacuum valve + gas valve open, start vacuum pump). Theoretically

the vacuum pump can evacuate down to 0.01 bar. In reality this is, however, not possible

due to pressure losses along the tubing. In order to make the connection of the vacuum

pump with the closed vessel both the vacuum and gas valve have to be opened. Then


the vacuum pump is started. The absolute pressure sensor measures the pressure in front

of the filter; the pressure inside the vessel is thus slightly higher due to the associated

pressure drop. The flow rate towards the vacuum pump is theoretically equal to 50 litersminute .

After reaching the set point of 0.1 bar, both valves are closed and the vacuum pump is

stopped.

3. 30 seconds of flushing, the pressure rises to a steady state value of ≈8-9 bar. After flushing

the air valve is closed. When the pressure drops again to 1.5 bar, the exhaust and gas

valve are closed.

4. Evacuation to 0.1 bar.

Steps 3 and 4 may be repeated once, depending on their importance relative to the initial

pressure. By flushing the chamber, most of the residuals from the previous measurement are

extracted. In order to provide some more quantitative information, the flushing procedure for a

methane-air mixture at 2 bar and stoichiometry is used as an example. It is assumed that the

maximum possible total pressure of the residual gases is equal to the initial pressure. Following

this approximation, 5% of the residuals is still present in the combustion chamber after the first

evacuation, or 95% is removed. Evacuating a second time to 0.1 bar makes that 0.25% of the

residuals is still present or 99.75% of the residual gases is effectively removed. In this simple

calculation, it was also assumed that the flushing steps 1 and 3 did not have any effect on the

actual residual content of the combustion reaction (and was only important to remove excessive

dirt), which is a rather conservative approach. After repeating steps 3 and 4 almost 99.99% of

the residuals is removed from the chamber. Because the difference between 99.75% and 99.99%

was still significant, steps 3 and 4 of the procedure were repeated for mixtures at 2 bar. When

measuring at an initial pressure of 5 bar, an acceptable amount of 99.96% was already removed

after the second evacuation (step 4). Therefore, no repetition was performed at this pressure.

At 10 bar, 99.99% of the residuals was removed without repetition.

Filling Now the filling procedure starts. This procedure is programmed in LabVIEW and

works completely automatically. First, the air valve is opened for a very short period of time.

The pressure inside the closed vessel then rises to 4 bar. Next, the pressure is reduced by opening

the gas and exhaust valve. When the pressure drops below 1.5 bar absolute, the exhaust and gas


valve are closed. An important remark is that the pressure inside the chamber is slightly higher

then, approximately 1.6 bar. This is a consequence of the gas flow over the particulate filter -

a small pressure drop is created. Next, the piping and the chamber are evacuated to 0.3 bar by

turning on the vacuum pump. Thereafter the first gas, which is the fuel, is filled respectively into

the tubing and closed vessel by opening the corresponding proportional pressure valve and the

gas valve - this happens automatically. When the target partial pressure is reached inside the

tubing, the gas valve opens instantaneously, permitting the gas to flow into the chamber. This

happens quite fast since the chamber was evacuated to approximately 0.3 bar. It is seen that

when the gas valve opens suddenly the pressure in the tubing drops, which is logical because

the pressure in the chamber is much lower than in the tubing. The proportional pressure valve

is now controlled by a PID controlled feedback system which uses as input the absolute pressure

value measured by the UNIK5000 pressure sensor. This valve provides the mass flow towards

the chamber and ensures that the absolute pressure in the tubing does not exceed the target

partial pressure value. When the partial pressure is reached, the gas valve is closed. Then the

tubing is evacuated and the next gas, which is normally air, is filled using the same procedure.

When liquid fuels have to be introduced, a special tool must be used as discussed next.

4.2.2 Filling tool for liquid fuels

Liquid fuels like methanol, ethanol and gasoline are supplied using a special filling tool (syringe

+ special nozzle), developed during a previous master dissertation. The amount of fuel to be

introduced into the GUCCI must be known as accurately as possible in order to be able to

perform measurements at a correct fuel-air ratio. Using the pressure and temperature inside

the bomb, the volume of air and the desired fuel-air ratio, the amount of fuel to be injected can

be calculated. The volume of the bomb was determined in an initial stage of the present work

by consulting the 3D-plots provided by SolidWorks. This volume was 3.954 liter. The volume

of the fan, determined by volume displacement of water and equal to 8.33 ml, was subtracted

from this volume. The real volume of the closed vessel, taking into account the fan and the two

electrodes, is thus 3.945 liter. In order to inject the liquid volume into the GUCCI a syringe was

used in which the correct amount of fuel was introduced. Before filling the syringe with fuel,

the bomb should be evacuated down to 0.1 bar. When this is done the fuel is injected using

the syringe (by means of a Luer Lock connection, this is a standardized system of small-scale

fluid fittings used for making leak-free connections between a male taper fitting and its mating


female part). By opening the needle valve of the filling tool the fuel is sucked into the bomb

as a consequence of the pressure exerted on the fuel by the syringe and the near-vacuum inside

the vessel. When all the fuel is introduced and the needle valve is closed, the bomb can be put

on the desired pressure by adding the appropriate amount of air. Now, ignition and combustion

can take place.

Figure 4.7: Picture of the syringe and filling equipment.

The liquid fuels that were intended to be used in this work are methanol and ethanol. First a few

measurements with gasoline were performed. Due to very bad evaporation of the gasoline due

to additives in the fuel, no meaningful results were realized. The methodology of determining

the volume to be injected is explained in appendix E.2.

Starting pressure and temperature As already mentioned in previous sections, the initial

temperature and pressure of the unburned mixture are essential due to their important influence

on the LBV value. When temperature increases, the LBV and mass burning rate rise. ul varies

approximately with Tu squared. An increase of initial pressure has a negative effect on LBV

(p−0.5) but due to the associated linear density increase, a positive effect on the mass burning

rate is provided (p0.5).

Temperature can be set due to heating elements in the side panels of the GUCCI. Pressure,

on the other hand, is determined by filling the chamber with the desired partial pressures of

the different components. The maximum starting pressure in this work was chosen to be 15

bar. Calculations with the GASEQ program indicated that this was a safe value taking into

account a safety working peak pressure limit of 150 bar. The GUCCI is equipped with a rupture

disc, which collapses when a pressure peak is too high. This element avoids damage to other

components such as the quartz glasses, which are quite expensive. The few measurements with

ethanol-air mixtures were performed at a starting temperature of 398 K.


4.2.3 Lens positioning: schlieren technique

In addition to the sensors and components, the measurement setup also includes a light source,

mirrors, lenses and a high speed camera so that schlieren visualization can be applied. The

schlieren visualization technique is based on the deflection of a light beam when it passes

through a medium with an inhomogeneous refractive index. The term ‘schlieren’ is derived

from the German noun ‘Schliere’, meaning ‘streak’. Most generally spoken, schlieren are op-

tical inhomogeneities in transparent material, not necessarily visible to the human eye. These

inhomogeneities are local differences in optical path length that cause light deviation, which in

turn can produce local brightening, darkening, or even colour changes in an image, depending

on which way the ray deviates.

Figure 4.8: Deflection of light rays.

In the conventional schlieren system, a point source is used to illuminate the test section con-

taining the schliere, meaning the combustion chamber. An image is formed by focusing the

(collimated) light using a converging lens. This image is located at the following distance to the

lens (thin lens equation):1

f=

1

d0+

1

di(4.1)

In the thin lens equation, f is the ‘focal length’ of the lens. The focal length is a measure of how

strongly the system converges or diverges light. For an optical system in air, it is the distance


over which initially collimated rays are brought to a focus. A system with a shorter focal length

has a greater optical power than one with a long focal length, that is, it bends the rays more

strongly, bringing them to a focus in a shorter distance. Furthermore, do is the distance from

the object to the lens and di is the distance from the image of the object to the lens. A knife

edge is placed at the focal point, positioned to block about half the light.

Because for gases there is a direct relationship between refractive index and density according

to equation 4.2 below, this technique can be used to visualize differences in density [44].

n− 1 = Kρ (4.2)

In this equation n is the refractive index and K is the Gladstone-Dale constant (K = δnδρ which

is a gas dependent constant). In Figure 4.9 the principle of the schlieren method is shown.

Figure 4.9: General overview of the schlieren visualization technique.

The optical setup used in the present work starts with an LED source containing 3 LEDs. The

light from this source is first diffused in order to provide a very homogeneous light intensity.

Then a condenser lens converges the light bundle towards a field lens and slit section. The


slit creates a perfect point source. The light arrays leaving this slit are diverging and bended

to a parallel bundle of light by two successive lenses. In picture 4.10 and 4.11 the practical

implementation is shown. In figure 4.13 an example image is shown that was recorded with the

schlieren visualization technique.

Figure 4.10: Schlieren visualization technique: creating a parallel light bundle. (picture 1)

Figure 4.11: Schlieren visualization technique: creating a parallel light bundle. (picture 2)


Figure 4.12: Schlieren visualization technique: creating a parallel light bundle. Overview of the first

part of the schlieren setup.

Figure 4.13: Schlieren visualization technique: schlieren image of a methane-air mixture with an equiv-

alence ratio of 0.9, at 2 bar and 298 K.

Now, the parallel light bundle is reflected by the first mirror and sent through the cube-shaped


combustion chamber. After passing the chamber, the light is reflected by a second mirror and

focused by a big lens. By two smaller successive lenses the light is focused to a point source

prior to ending up at the high speed camera. If no difference in density is present, this allows

the insertion of a knife or pinhole (diaphragm) at the focal point, just before the light enters the

camera. This way, the light intensity on the camera - thus on the screen - decreases. In flows

with uniform density, the knife edge will simply make the photograph half as bright. However,

in flow with density variations, as is the case here, the distorted beam focuses imperfectly, and

parts which have been focused in an area covered by the knife-edge are blocked. The result is a

set of lighter and darker patches corresponding to positive and negative fluid density gradients.

If a knife edge is not used, the system is generally referred to as a shadowgraph system, which

measures the second derivative of the density. Since the schlieren technique is used to image the

distribution of density gradients transverse to the incident beam, the irradiance of a schlieren

image is expected to change even when the density gradient is uniform. This is in contrast to

the shadowgraph technique, where no detectable change is expected in the illumination intensity

when the density gradient is uniform.

In the present work, a diaphragm was used instead of a knife edge. In practice, however, the

corresponding focal point does not entirely resemble the ideal of a point. This is the result of a

variety of effects, which are thoroughly discussed in [45] and shortly recited below:

� It is impossible to achieve an ideal point source; in the GUCCI setup, the point source is

approximated by placing a slit. Thereby it is inevitable that part of the light is lost.

� Diffusion of the light bundle yields a lower density of the light. As a consequence, the

bundle is more sensitive to influences from the environment. Furthermore, important

details may not be visible.

� In fact, an ideal point source is not desired; this would merely lead to black shades on the

one hand and exposed shades on the other hand.

� The phenomenon known as ‘astigmatism’ spreads the focal point over a certain distance.

� The phenomenon called ‘coma’ appears when the incident light of a lens is not parallel

with the optical axis. Instead of bringing the rays together in one point (focal point), a

comet-like image is generated.


� White light is composed of different wavelengths, thus different refractive indexes. This

results in deviations of focal distance.

Other possible causes of a non-ideal focal point are impurities and dirt on the lenses, incorrect

alignment of the lenses and ‘oblique’ placement of optical components. However, the sensitivity

and contrast of the setup are mainly determined by the knife-edge/diaphragm and the light

source. On the other hand, the quality of the schlieren image is inevitably affected by above-like

phenomena. It can be concluded that it is impossible to achieve theoretical results in practice;

there will always be a deviation from the expected result.

Thus, there is a neat visual distinction between the burned and unburned mixture during com-

bustion of a fuel-air mixture in the GUCCI. This allows to capture the growth of a spherical

flame during an explosion. In this short introduction on schlieren only some basic principles

were mentioned. For a complete discussion the book of G.S. Settles can be consulted [46]. As

already mentioned in chapter 3, the work of Sulaiman et al. [18] is also an interesting literature

source in this context. To end the discussion of schlieren implementation, a final picture with

the total schlieren setup is shown.

Figure 4.14: Complete overview of the schlieren setup.

4.2.4 High speed camera

For capturing the images a PCO high speed camera (pco.dimax camera) was used. It has a 12 bit

CMOS camera system, perfectly suited for high speed camera applications. Common examples

are material testing, off-board crashes or impact tests, or super slow-motion movie clips. The

system features also a variety of trigger options to cover all off-board applications that are


required by the automotive industry. The amount of frames per second (fps) can be regulated

between 1200 and 153000, depending on the desired pixel resolution. In order to perform proper

measurements it is necessary to take a somewhat lower resolution and by this increasing the

amount of frames per second. In appendix D.3 an overview of the possible resolutions and

frame rates is given. Furthermore, this camera system is typically used for spray analysis or fuel

injection tests. The camera driver is provided by PCO (Camware). This software is easy to use

and provides high quality images.

For the methane-air LBV measurements performed with the GUCCI, the camera speed was set

to 3000 fps. With this value a good resolution could still be chosen (1152 x 1428 pixels, the

resolution was 0.16 mmpixel ) and a detailed flame evolution was still captured. The resolution was

determined by placing a grid section at the position where the light array entered the vessel.

The dimensions of this grid (1 cm by 1 cm) were known.

Figure 4.15: Example of the calibration image. By counting the number of pixels in a single square

(Photoshop), the resolution [ mmpixel ] can be determined.

By capturing a single image, the amount of mm per pixel was easily determined. At low flame

radii the measured flame speed is very sensitive to the determination of the flame radius from

the digital images. The camera control was set in such a way that the images were captured in


synchronization with the pulsation of the light (LED) source. By also tuning the exposure, the

image quality and the amount of frames per second were adjusted in a positive way. In case a

higher frame rate is desired a smaller resolution needs to be chosen. It was possible to achieve

a camera speed of 10000 fps with loss of the visual chamber area; the ‘region of interest’ in this

case was only 464 x 720 pixels. For a small series of ethanol-air measurements this frame rate

was configured. Appendix D.3, which can be used as a manual for future work, provides the

complete camera configuration explained in detail.

4.2.5 Ignition

Of course, ignition is required in order to visualize the combustion of a certain mixture. Because

central ignition is needed to obtain a spherical flame, two electrodes were mounted into two

opposite diagonal parts of the combustion chamber.

Figure 4.16: Ignition with a visible spark. A dwell time of 0.7 ms was chosen.

These two electrodes (neutral mass electrode and positive electrode) were designed and man-

ufactured in a previous work [43]. At the end of each electrode a needle is mounted. Both

needles are facing each other, leaving a small gap between them. The electrodes are placed as

described in order to provide symmetrical flame images, which is useful considering the post-

processing. In picture 4.17 an electrode is shown. To generate the very high voltage peak and

consequently the spark, an automotive ignition coil was used (see also paragraph 4.2.5 about

dwell time). Such coils have the advantage that the amount of energy can easily be adjusted.

The principle is the same as with a spark plug. In both systems a spark is generated by a very

large potential difference between an electrode and a ground/mass electrode. The power supply

- a 24 V voltage source - provides the energy needed to generate the spark. It is very important

that the voltage delivered by this source is as stable as possible. When generating a spark, a


large amount of energy is required and a weak source could have the tendency to decrease in

voltage output, which in turn leads to a less intense spark. The source that was used was very

stable. The electrode distance should be small so that the initial flame front is also as small as

possible. Generating a spark after injecting a flammable mixture results in a flame ‘nucleus’,

which initiates spherical flame propagation.

An important trade-off has to be taken into account. On the one hand, the distance between

both electrodes has to be sufficiently small to avoid ‘spark boost’ or ‘ignition effect’. However,

on the other hand, the spark must be able to develop properly so that ignition is always assured.

In the present work a gap width of 1 mm was chosen. This choice is explained more thoroughly

below.

Figure 4.17: Picture of an electrode. The parts 1 are the needle and 2 bolts. The bolts are used to

fix the needle inside the electrode head part. Part 2 is a dummy piece with the main

component of the electrode inside. Part 3 is the covering for the dummy part, which fixes

the dummy inside the closed vessel. Part 4 is an electrode regulator for adjusting the

gap width. The voltage is supplied through this long cylindrical piece by a spring system

connected to the ignition coil.

Dwell time The dwell time is, in essence, the charge time of the ignition coil, corresponding to

the energy required to generate the spark. The ignition coil is constructed for primary currents

that not exceed 7.5 A. This is indicated in appendix D.3. In the GUCCI LabVIEW program

the dwell time can be adapted directly. There were some stubborn ignition problems during the


initial phase of the validation of the setup. A possible solution was to increase the gap width

between both electrodes in order to facilitate spark formation, but the small spacing showed not

to be the cause for the failure. Another idea was that there was a problem with the 24 V power

supply; it was indeed observed that it did not provide a continuous voltage to the ignition coil.

A new 24 V power supply was ordered and installed.

To enhance spark formation, the dwell time of the ignition coil may be increased to a maximum

value slightly lower than the primary current limit. It is clear that increasing the primary current

implies a corresponding increase in spark characteristics and high voltage. Due to the problem

encountered with the power supply it was necessary to work with a 12 V car battery for some

time. Because by using this battery the voltage was not fully continuous during ignition, the

dwell time was temporarily increased to 3 ms, corresponding to a current slightly lower than 7

A. This is also shown in appendix D.3. When the new 24 V voltage source was installed, a dwell

time of 0.7 ms turned out to be sufficient. This corresponds with a 4 A primary current, a spark

energy of 18 mJ and a peak voltage of 22 kV. For more information the complete datasheet of

the ignition coil can be found in appendix D.3.

Ignition timing An important factor is the waiting time between shutting down the fan when

the filling process is completed, and ignition of the obtained mixture. The mixture is given some

time to settle to a quiescent condition before ignition. In the present work this waiting period

was set at 30 seconds in order to have a uniform temperature and equal distribution of the

mixture in the combustion chamber. This period was calculated by applying the following

reasoning. The DC fan motor provides about 50 Watt at around 3000 rpm. The diameter of

the fan is about 4 cm. This gives a tip speed of the fan of about 6.3 ms . If we assume a very

conservative gas density value which is equal to 24 kgm3 (air at 20 ◦C, 20 bar) we find that the

kinetic energy of the flow at the fan tip is about 500 Jkg (= 1

2ρv2). Because the power of the

motor is equal to 50 Watt (= Js ) it takes 10 seconds to ‘energize’ 1 kg of mixture. The volume

of the closed vessel and the density of the mixture are known. The mass inside the chamber

can thus be calculated and is equal to 0.096 kg. This means that in 0.96 seconds the complete

mixture is ‘energized’. It can therefore be assumed that if the fan is working for a relatively long

time, a steady state energy level is reached due to production and dissipation energy rates. By

assuming that this level is reached after 15 seconds (15 times the time needed to energize the

4.3 Post-processing methodology 72

mixture, which is a good estimation ) it is understood that if the fan is turned off, it will take

15 seconds or less to have a zero energy mixture. In the present experimental work, 30 seconds

of rest time was chosen to be sure all the energy was dissipated prior to ignition.

Spark energy and gap width Upon ignition of the mixture an initial disturbance is created

by the spark. Localized deformations arise from the movement of the flame over the elec-

trodes. These deformations persist and create cracks that propagate along the surface. Based

on published literature, the resulting transient in the initial - ignition affected - stage of flame

propagation was already discussed in chapter 3. To minimize this effect the ignition energy must

be as low as possible. Therefore, the dwell time of the ignition coil was kept as low as possible

(0.7 ms).

In different studies ([20], [8]) however, it was found that the results were minimally affected

by variations in spark energy and gap width, i.e. the separation of the electrodes. In [20] the

authors assessed the influence of the ignition kernel on subsequent flame propagation by varying

the ignition energy. An initial, transient period was observed, during which results differed

substantially. However, the influence of ignition energy eventually dissipated, resulting in two

aligned flame trajectories.

For extrapolation of the flame speed to zero-stretch, a certain range of data points was selected

in the present work for each measurement, excluding data affected by ignition. In order to

obtain enough data points for this extrapolation, it was important to have minimal ignition

effect. This was obtained by setting the gap width at 1 mm, which was still large enough for

efficient ignition under lean conditions.

4.3 Post-processing methodology

The determination of the LBV from an explosion in a constant volume vessel can be performed in

different ways, either by using the measured pressure trace inside the vessel during combustion

or by using the expansion rate of the burned products, as obtained by high speed schlieren

cine photography of the combustion process. In the present work the focus was on the optical

technique. The pressure based technique is explained but was not applied. As mentioned before,

the schlieren technique was used in order to extract useful information from the combustion


process. This technique can only be applied when the vessel is relatively large, as is the case

with the GUCCI. For smaller vessels, the pressure based technique has always been used in

previous studies as it is, in that case, the most reliable method.

4.3.1 Optical post-processing

Regarding the post-processing method, a brief discussion is presented in this section. A more

detailed discussion can be found in appendix B, in which the entire method is explained with

the focus on important parts of the MATLAB code. In order to determine the LBV and

Markstein length a new image processing technique was created and, after excessive testing,

applied to generate data. The MATLAB script ‘imageprocessing.m’ is able to automatically

and robustly detect and reconstruct the flame front, based on the maximum grayness gradient

in the schlieren images combined with a circle fit method. First the acquired pictures of the

different experiments have to be stored in the appropriate subfolders, which are in turn stored

within a main folder. Details about the nomenclature of these folders are provided in appendix

B. The directory of the main folder, the applied camera speed (which must be the same for all

experiments) and the calibration factor (or resolution, in mmpixel ) need to be introduced in the

MATLAB script. Then the actual image processing can start. For every new series of images

of a single experiment, a new ‘central’ point is defined by a circle fit method. In order to create

the circle, the edge of the spherical flame needs to be determined. Therefore a method was

developed in which a calibration picture, i.e. the first picture in a series of captured images,

is required to create a single ‘background’ image. This image is then used for determining the

flame edge in every other picture of the series. The final result for each experiment (subfolder)

is an Excel-file containing the flame radius as a function of time. This file is further used in

a second MATLAB script ‘LinearExtrapolation.m’. This script is used to plot the flame speed

(Sn given by dr/dt) as a function of the flame stretch rate (given by α = (2/r) · Sn). A linear

extrapolation to zero-stretch rate can now be performed. The script is able to process a series of

subfolders fully automatically. Another possible approach is by using the GUI ‘LBV plotting.m’

to manually extrapolate to zero-stretch. This GUI also provides the possibility to perform a

non-linear extrapolation. In the present work only the linear extrapolation method was used.

In future research it might be useful to also perform the non-linear extrapolation as this may

lead to better results.


4.3.2 Pressure based

Several methods have been proposed to calculate the burning velocity from the pressure rise in

a closed vessel. The basic idea of the pressure based processing methodology is that the mass

burning rate mb can be calculated using conservation of mass and energy. The actual burning

velocity ul is then obtained by using this mass burning rate, together with the density of the

unburned mixture ρu and the assumption of a predefined flame shape.

Some researchers have used the two-zone model [44] in order to determine the LBV. The pres-

sure rise in the GUCCI, measured by the AVL sensor, would then be the input for the two-zone

model. The model can easily be implemented in MATLAB. The total volume inside the vessel

is considered as divided into two regions (two-zone model) - an unburned region and a burned

region. These two regions are separated by the flame front, having an infinitely small thick-

ness. During combustion the unburned mixture is transferred into burned mixture through the

outwardly propagating spherical flame front.

Rallis et al. [47] did an excessive study on the determination of LBV using the measured

pressure evolution. The idea was to determine LBV values using the two-zone model in which

the mass fraction burned is related to the pressure rise in the bomb. This pressure rise is

caused by compression of the fresh mixture by the burned flame front towards the walls of the

closed vessel. In earlier work by Lewis and Elbe [48] this principle was already used to develop

an approximate expression for the mass fraction burned in terms of pressures. The problem,

however, was that it was only valid during the early stages of combustion, when the pressure rise

is very small. Later on, an equation for the mass fraction burned was derived which was valid

throughout the entire combustion process. Subsequently, Rallis et al. derived a complete set

of burning velocity equations [47]. An important drawback of this method is its computational

complexity.

To determine the LBV, the two-zone model makes use of the following assumptions:

� Each zone in the GUCCI has a uniform temperature and composition. In reality, however,

temperature will never be completely uniform, resulting in a first error on the result. The

composition variation is quite limited because of the intense stirring by the fan.

� There are no pressure differences in the internal volume of the GUCCI, so pressure is


completely uniform and only a function of time. There are no pressure gradients or time

lag effects on the pressure measurements.

� The mixture in the GUCCI always consists of a mass fraction burned gas (x) and a mass

fraction unburned gas (1-x).

� Density of burned and unburned gas regions is uniform, which means that the density right

behind the flame front is a good approximation of the instantaneous spatially-averaged

density of the burned gas. The same assumption yields for the density in front of the flame

front.

� The thermal conductivity of the burned towards the unburned mixture is negligible. Both

burned and unburned gas regions are adiabatic systems - i.e. there is no heat loss or gain

from these regions.

� The heat loss towards the chamber walls is negligible, which was also the case in the work

of Rallis et al.

� The spherical flame front is smooth and propagates from the centre to the walls, where it

decays. Experiments with cellular effects are not considered.

� As a result of the increasing burned gas zone, the unburned gas undergoes a polytropic

compression.

The method that was proposed during the present work was the one introduced by Lewis and

von Elbe. As mentioned above this method is only applicable to the early stages of the

process, when the pressure rise is small. The windows of the GUCCI provide optical access

up to a flame radius of 70 mm. A radius up to 60 mm was considered. The time duration

upon reaching this radius can easily be determined by consulting the post-processing results of

a single experiment. Using this information the proper data can be selected from the pressure

data file. A MATLAB script (see appendix C) implements the methodology given below.

The unburned flame propagation velocity Su is obtained by the following equation:

Su =dridt

(rirb

)2(p0p

) 1γu

(4.3)

with ri and rb given by:

4.4 Error analysis 76

ri = rbomb

(p− p0pe − p0

) 13

(4.4)

rb = rbomb

[1−

(p0p

) 1γu p− p0pe − p0

] 13

(4.5)

p0 is the initial pressure obtained by the pressure sensor for mixture preparation, pe is the

maximum theoretical pressure in the vessel during combustion, γu is the ratio of specific heats

in the unburned mixture and rbomb is the ‘radius’ of the vessel. As the GUCCI is not spherical

but rather cube-shaped, a ‘pseudo’ radius was chosen, i.e. the radius of a sphere having the exact

same volume. γu and pe can be determined from a thermodynamic database such as GASEQ.

pe is computed for adiabatic constant volume combustion. These equations are derived using

the assumption that the fraction of burned gases is equal to the fraction undergoing the total

pressure rise. ri is the radius of the sphere occupied by the fraction of unburned gas that gives

rise to a pressure p during combustion, rb is the radius of the sphere occupied by this fraction

when burned. In equations 4.4 and 4.5 the quantities ri and rb are expressed explicitly as a

function of the captured pressure history. Next, the unburned flame speed Su is determined from

equation 4.3 and the stretch rate α is obtained by differentiating equation 4.4. More detailed

information concerning this method can be found in Lewis and Elbe’s book [48].

As already mentioned this method was implemented in MATLAB. The script can be found in

appendix C.

4.4 Error analysis

In this section, potential errors and their influence on the measurements are discussed. It is

important to note that the GUCCI setup has never been used before for this kind of measure-

ments. Therefore it is very useful to provide an extensive error analysis which can also be used

in proceeding work. The following discussion is based on the work of Vancoillie [3], Verhelst [7]

and Van Thillo [44]. The error analysis can be subdivided into two major parts:

� The first part comprises the error on the directly measured quantities, which are

initial pressure, initial temperature and schlieren image quality (resolution). Pressure and

temperature sensor accuracy information is of great importance.


� The second part comprises the error on starting composition and thus the equivalence

ratio φ. This includes the error due to the filling procedure (e.g. valve timing, gas leak-

age,...) and the error due to a limited pressure sensor accuracy and DAQ resolution.

Since most of the measurements were performed on gaseous fuels (methane and acetylene), the

error analysis focuses on the specific aspects related to these fuels. In order to provide a complete

error analysis some attention is also paid to liquid fuels, e.g. alcohols. First, some assumptions

are made concerning the error on the different sensors and filling tools. The different sensors

have already been discussed above. The following list contains an overview of important data

and specific errors of each item affecting the final mixture composition.

� Pressure sensor: UNIK5000, ±0.05%FS, so δp1 = 0.05100 · 70 = 0.035 bar

� Temperature: δT = 2.5 ◦C (value based on a previous master thesis [43])

� Syringe δVinj = 0.01 ml (liquid fuel filling tool)

Note that a measurement range of 70 bar is assumed for the pressure sensor and DAQ. Thereby

the ‘worst case scenario’ is fulfilled.

4.4.1 Directly measured quantities

The directly measured quantities leading to potential errors on LBV measurements are listed

below.

� Pressure: the maximum absolute error on the initial pressure prior to an explosion is

estimated at 100 mbar (10000 Pa). This includes the accuracy of the pressure sensor (35

mbar or 3500 Pa) as well as the occurrence of a pressure drop, with an estimated value of

60 mbar, over the particulate filter at the end of each filling procedure. The value of this

pressure drop was not exactly known and therefore a pragmatic analysis was done. In this

analysis, the variations in final total pressure for a series of ‘equal’ filling procedures, i.e.

filling procedures with the same desired partial pressures and thus the same desired total

pressure, were checked. If the variations were big this meant a large statistical error on

the pressure sensor. For the 2, 5 and 10 bar LBV measurements on methane-air mixtures

this resulted in table 4.2.


Ptarget [bar] Pmean [bar] Max. abs. dev. [bar] Stdv. [bar]

2 2.021 0.083 0.03

5 5.009 0.070 0.03

10 10.024 0.177 0.06

Table 4.2: Statistical information on the final pressure values filled in the GUCCI for a series of methane-air

experiments (2 bar: 68 fillings, 5 bar: 57 fillings, 10 bar: 52 fillings).

It is seen that the maximum absolute deviation from the target pressure was 180 mbar.

It must be mentioned that almost all the absolute deviations found were much smaller

than this value. The more appropriate information is found when checking the absolute

standard deviation values. Here the maximum value is 60 mbar. It is known from statistics

theory that 99.7 % of the resulting pressure values lay in the mean± 3 · Stdv. range, if a

normal distribution of the results is assumed. For 2, 5 and 10 bar the ranges of pressure

values are thus respectively 1.931 → 2.111, 4.919 → 5.099 and 9.844 → 10.204. The

relative standard deviation (3 ·Stdv.) is thus equal to 4.5 %, 1.8 % and 1.8 %, respectively.

The above reasoning only gives an idea about the measured pressure value variations; in

fact, it provides no information on the sensor error. However, it does provide information

on the variation in pressure drop value. The biggest pressure drop is expected when the

pressure inside the chamber is the highest, thus for 10 bar. The standard deviation is 0.06

bar or 60 mbar. It is assumed that this value is an indication for the size of the pressure

drop along the filter. The maximum absolute error then becomes 100 mbar (95 mbar to

be precise). For the measurements at 2, 5 and 10 bar this results in an error of 5 %, 2

% and 1 %, respectively. It is seen that these values are comparable with the relative

standard deviations given above. This is an indication that the defined error is properly

determined.

� Temperature: the maximum absolute error on the initial temperature prior to an explosion

is estimated at ± 2.5 ◦C.

� Schlieren image: the error on the radii of the flames determined from a schlieren image

arises from the resolution of the digital camera. For all the measurements the horizontal

resolution of the camera was set to 0.16 mmpixel . As the flame radius is determined from

the digital image, the absolute error on the flame radius thus amounts 0.16 mm. An


additional error is caused by the calibration. However, as the calibration was performed

using both a physical grid and by doing a thorough study in Photoshop, no excessive error

was expected. The Photoshop study was a stepwise (every 10 degrees) circular check on

the amount of pixels within the corresponding diameter of the image. It was concluded

that the variation in diameter was less than 0.15 %. This means the image was almost

perfectly circular and the mean pixel diameter was chosen to calculate the resolution with.

The obtained resolution was 0.16 mmpixel .

� Schlieren time: the error on the time is assumed to be negligible.

The accuracy of the image processing method is also very important since it directly affects the

final LBV value. Apart from resolution, other image quality aspects such as details, sharpness,...

are all of great importance. Fuzzy parts on the edge of the circular flame inhibit accurate flame

edge determination. Non-circular flames and non-uniformly expanding flames also result in

non-usable information, because the circle fit cannot be realized appropriately.

The error on the extrapolation methodology is quite difficult to determine. The range of mea-

surement points that is selected for extrapolation to zero-stretch flame speed has a large effect on

the resulting LBV value. An extrapolation plot as illustrated in figure 4.18 is normally created.

Figure 4.18: Variation of flame speed Sn with α, for a methane-air flame at 5 bar and 298K, φ = 1.

In order to obtain a structural way of extrapolation a systematical extrapolation route was

followed for each measurement. In the MATLAB script ‘Linear Extrapolation’ this system


was embedded. When flame speed is plotted versus stretch rate the operator needs to assign

the minimum and maximum stretch rate he/she wants to use for linear extrapolation to zero-

stretch. The minimum value must be the stretch rate at which the operator assumes initiation

of cellularity and thus a fast increase in flame speed. The maximum stretch rate is simply a

boundary condition given to the program. The operator can either search for a steep climb

in flame speed or simply look at the schlieren images in order to find the stretch rate where

initiation of cellularity occurs. The program performs the linear extrapolation using a variable

series of points starting at the minimum stretch rate and evolving to the total range of points

between minimum and maximum. All the obtained Markstein lengths are stored in a list. The

Markstein length that dominates the list is then assumed to be the ‘real’ Markstein length.

After extrapolating to zero-stretch flame speed, the LBV value is determined by scaling with

σ = ρuρb . Thus the program actually determines the linear extrapolation line for the series of

points corresponding with the dominating Markstein length. In most cases, these points form

the longest possible arrangement.

4.4.2 Equivalence ratio

Since it is very desired to know the accuracy of the composition of a fuel-air mixture, a lot of

attention is devoted to this part of the error analysis. In this section an error estimation on the

equivalence ratio φ is performed. Furthermore, it will be examined to what extent this error

can be reduced. It is, of course, the intention that measurements of laminar burning velocity

using the GUCCI setup are carried out with the highest possible accuracy.

The actual mixture equivalence ratio is influenced by the error on the bomb pressure as the

mixture is prepared using the partial pressure method. Temperature variations during the filling

procedure could also play a role, but for the present measurements on methane-air mixtures

this was not very important: atmospheric temperature was chosen for all the measurements.

However, for the few ethanol measurements that were performed, this certainly had an important

influence since the initial temperature was much higher. This was needed to ensure complete

evaporation of the liquid fuel.

The GUCCI is filled with a certain fuel-air mixture by successively adding a quantity of fuel

and an amount of synthetic air (79.1 % N2 and 20.9 % O2). Because every time a component is

introduced into the chamber the cumulative pressure is measured, the φ-value can be determined


for the total mixture. Appendix E.1 provides an example of the determination of the φ-value for

a stoichiometric methane-air mixture at an initial pressure of 2 bar and an initial temperature

of 298 K. Because the φ-value of a mixture is based on the partial pressures, the error on these

partial pressures must be calculated. Thus, the error on the φ-value is caused by the error on the

partial pressures, which are measured by the absolute pressure sensor of the arrangement. The

partial pressures are processed by a DAQ module before they are presented in the LabVIEW

interface. The determination of the error on the partial pressures is given below.

δp = 2 · δp1 = 70mbar (4.6)

� δp is the error on the measured partial pressures [bar]

� δp1 is the error of the static pressure sensor [bar]

Equation 4.6 shows that the error on the static pressure sensor is entrained twice. The reason is

that a measured partial pressure corresponds to the difference of two pressure measurements: the

partial pressure of a component is actually determined on the basis of the difference between the

pressure before and after a pressure measurement. Since in this study the ‘worst case scenario’

is assumed, the error of the absolute pressure sensor is thus included twice. In appendix E.1

it is shown that the masses of the various mixture components are determined by using the

measured partial pressures and the ideal gas law. The same principle is applied to calculate the

error on these masses, (δm), and the error on the measured partial pressures, (δp). The relative

error on the air-to-fuel ratio (AFR) errAF can then be calculated according to the fundamental

rules of error theory.

∆mi =δp · V ·Mi

R · T (4.7)

In equation 4.7, V is the volume of the closed vessel taking into account the two electrodes and

the fan (3.945 liters, as mentioned before), Mi is the molar mass of component i [ gmol ], R is the

universal gas constant [8.31441 JmolK ], and T is the temperature in Kelvin. The relative error

on the air-to-fuel ratio can now be calculated.

errAF =∆mair

mair+

∆mCH4

mCH4(4.8)


And:

errλ = errAF + errAF st (4.9)

The relative error of a constant value is equal to zero, thus the factor errAF st can be set to zero.

This means that the relative error on the λ-value of an air-fuel mixture is equal to the relative

error of the mixture’s AFR. An analysis for 3 different filling procedures is done in order to

determine the worst case errors.

The first example provides the error associated with the filling procedure for a methane-air

mixture at 2 bar, with an equivalence ratio of 0.7. This mixture composition contains the

smallest absolute mass of fuel. Therefore it is most interesting to look at the relative error on

this composition.

In the table below, the first line contains the maximum calculated absolute deviations in filled

gas masses. Therefore equation 4.7 is used with a δp of 70 mbar. The second line contains the

masses that theoretically need to be filled in order to obtain the specified mixture. In this case,

0.07 bar of methane and 1.93 bar of air need to be filled.

Air (vacuum, 1) CH4 Air (2)

∆ m [mg] 322.1 178.7 322.1

m [mg] 1380.5 178.7 7500.0

errAF =∆mair

mair+

∆mCH4

mCH4= 107.25% (4.10)

errλ = 107.25% (4.11)

It is observed that, due to the limited amount of methane that needs to be filled, the error on

the corresponding mass equals the value that needs to be filled. This is an indication that,

for very low partial pressures, the system will not be accurate enough to properly

perform the filling. The error on the UNIK5000 sensor is simply too big. It was

almost impossible to get proper ignition when the initial pressure was chosen 1 bar. Due to the

big expected error on the equivalence ratio and the narrowness of the flammability range (5 %


- 15 %) of methane-air mixtures, the probability of having a non-ignitable mixture was quite

high. Moreover, the system was not able to fill partial pressures below 0.13 bar. Therefore, in

the present work the lowest initial pressure used for the ignition of methane-air mixtures was

2 bar. In table F the results of these measurements are presented. The next example gives

the error associated with the filling procedure for a methane-air mixture at 5 bar, φ equal to 1

and an unburned mixture temperature of 298K (ambient temperature). The following result is

obtained:


∆ m [mg] 322.1 178.7 322.1

m [mg] 1380.5 633.7 20486.1

errAF =∆mair

mair+

∆mCH4

mCH4= 31.14% (4.12)

errλ = 31.14% (4.13)

The error is clearly smaller at 5 bar, but still not very satisfying. The final example

provides the error for a methane-air mixture at 10 bar, with an equivalence ratio of 1.3. This

mixture composition contains the highest amount of fuel.


∆ m [mg] 322.1 178.7 322.1

m [mg] 1380.5 1623.7 41710.8

errAF =∆mair

mair+

∆mCH4

mCH4= 12.5% (4.14)

errλ = 12.5% (4.15)

It can be concluded that the relative error decreases with pressure and is larger

for lean mixtures, when the amount of fuel is small. In the worst case scenario (2 bar,

φ = 0.7) the relative error is excessively big, even exceeding unity. However, it must be noted


that the analysis is done with the maximum possible error on the pressure sensor UNIK5000.

In reality, this error will - in most cases - be lower than this value. At an initial pressure of 2

bar poor LBV results are expected due to the considerable error on the equivalence ratio. In

chapter 5, which is devoted to the discussion of the results on methane-air mixtures, it is seen

that the spreading on the results is indeed much bigger at 2 bar. However, when the average

LBV values are compared to literature, very good agreement is observed.

Reduction of φ-error To reduce the error on φ some actions were taken. A first measure

was the usage of a synthetic air bottle (79.1% N2 and 20.9% O2, according to the manufacturers

datasheet) instead of the separated nitrogen, oxygen and argon bottles that were initially present.

By using dry air no error in oxidizer composition could be made.

Liquid fuels: error on equivalence ratio For liquid fuels the analysis is slightly different

than the error analysis for gaseous fuels. The biggest error is likely to be the error on the amount

of fuel injected in the closed vessel. This leads to a high uncertainty on the actual equivalence

ratio. Moreover, it is also possible that part of the fuel is not vaporized, which is detrimental for

the desired mixture composition. The analysis hereafter is based on a preceding GUCCI thesis

[43].

In section 4.2.2 the method to calculate the amount of fuel that needs to be injected in order to

obtain a certain equivalence ratio was explained. Here, some formulas are repeated:

Vol. of fuel to inject = Vinj =n ·M ·mf

ρ(4.16)

with:

n = number of molecules in the bomb =p · VbombRR · T · 1000 (4.17)

M = mole fraction of fuel =φ ·mole fraction fuel (stoich)

1− φ ·mole fraction fuel (stoich)(4.18)

mf = mass of fuel[g

mol] (4.19)


For ethanol, mf is equal to 46 gmol . For methanol, mf is equal to 32 g

mol . Now the actual error

can be calculated. An equation for φ can be formulated:

φ =1

mff·

ρmf· Vinj · 1

p·VbombR·T ·1000

1− ρmf· Vinj · 1

p·VbombR·T ·1000

(4.20)

From the equation above we are able to calculate δφδVinj

, δφδp and δφ

δT . Finally, the total error is

given by:

δφ =

√(δφ

δVinj)2 + (

δφ

δp)2 + (

δφ

δT)2 (4.21)

At 100 ◦C and for an equivalence ratio of 1.0 at 1 bar initial mixture pressure, the

relative error is slightly higher than 2%. This error is much lower than the errors

that were found for the gaseous fuel-air mixtures.

Figure 4.19: Error on φ for a 1 ml syringe. [43]

To end this section an overview of the results calculated in this error analysis is given in table

4.3.

4.5 Repeatability 86

Type Absolute error Relative error

Initial pressure 0.1 bar pressure dependent

Initial temperature 2.5 ◦C temperature dependent

Schlieren image 0.16 mmpixel

-

Initial φ gaseous fuels - 107 % (2 bar, φ = 0.7), 31 % (5 bar, φ =

1.0), 12 % (10 bar, φ = 1.3)

Initial φ liquid fuels - ≤ 2 %

Table 4.3: Overview of the GUCCI measurement errors.

4.5 Repeatability

To obtain a measure for the repeatability of the experiments, at least 3 explosions were performed

at each condition. After processing the images, the standard deviation on the mean LBV and

Markstein length was calculated. The standard deviation on ul was below 2 cms for most of the

2, 5 and 10 bar mixture compositions (see table F.11). The uncertainty on the Markstein length

was far higher, since the derivation of Lb is very sensitive to the selected range of data points

for the linear fit.

The principal uncertainty was in making up the mixture. Therefore, the following factors af-

fecting mixture stoichiometry were accurately controlled:

� Important was the consistency of pressure and temperature just prior to ignition. The

authors aimed at a tolerance of ±0.03 bar and ±5 K, respectively. However, because

of the poor accuracy of the gas filling system, deviations of these tolerances occurred

frequently. These deviations were especially important at 2 bar because of the significant

relative error. The main problem while filling at low pressures (1 - 2 bar) was that the gas

system was not able to measure (fill) partial pressures lower than 0.13 bar. This was mainly

important for the partial pressures of methane, due to its high air-to-fuel ratio (17.2). A

second problem concerning the filling process was the inconsistency of the evacuation of

the chamber prior to the actual filling.

� Residuals were kept at a minimum through adequate flushing of the closed vessel after

each explosion.

4.5 Repeatability 87

� A final factor was the vessel sealing, which could not entirely exclude leakages. This was

tested experimentally using a leakage spray and by filling the chamber with compressed

air up to 9 bar, leaving the gas valve open. This influence on mixture composition was

particularly important at elevated pressures (10 bar and higher). At these conditions a

small part of the methane-air mixture was leaking during the addition of dry air, again

affecting mixture stoichiometry.

In future work, when measurements on methanol-air mixtures will be performed using the

GUCCI setup, some important additional factors will come into play. The first problem arises

from the applied filling method for the liquid fuel. The methanol or ethanol has to be injected

using a syringe, so there will be an uncertainty on the full scale deflection of the syringe.

This in turn corresponds with an average uncertainty on the equivalence ratio. The mixture

stoichiometry should be controlled by injecting a calculated amount of fuel. The correctness

of the mixture composition should then be cross-checked by comparing the measured partial

pressures to the corresponding theoretical values, assuming ideal gas behavior. The partial

pressure of the fuel can be calculated by subtracting the vessel pressure before injection of the

fuel (pvacuum) from the pressure after injection.

LBV MEASUREMENTS 88

Chapter 5

LBV measurements

In this chapter the experimental results of a large amount of methane-air mixtures performed

with the GUCCI setup are presented. In these experiments the focus was on the accuracy and

repeatability of the mixture composition and on the schlieren technique implementation. First

the results of the GUCCI measurements are presented, then a comparison with literature data

is made with the aim to check the validity of the GUCCI setup for these kind of measurements.

Finally, some methane-air experiments at 15 bar and some ethanol-air experiments were done

in order to provide a starting point for future GUCCI LBV research. The experimental study

of LBV values of hydrocarbon-air mixtures at engine pressure conditions plays a major role

in premixed combustion research. LBV is, as already explained, a fundamental quantity that

is widely used in CFD combustion models in order to scale the turbulent burning velocity in

premixed turbulent reacting flows, as in spark-ignited engines. The turbulent burning velocity

dominates the mixture formation and, therefore, the development of emissions like NOx, CO

and soot (particulate matter). Therefore, accurate experimental measurements of LBV values

of hydrocarbon-air mixtures are needed to predict and improve the combustion process. Earlier

studies examined LBV values at atmospheric conditions and pressures up to 10 bar. In many

cases no assessment was made regarding flame stretch, flame cellularity or buoyancy effects.

Therefore, the reliability of these data may be significantly compromised. In this respect the

present experiments, based on the optical schlieren technique, will provide valuable data.

5.1 Measurement matrix 89

5.1 Measurement matrix

In table 5.1 an overview of the measurement conditions is given. The pressure range has a

minimum value of 2 bar and goes up to 10 bar. The measurements at 15 bar were done with the

intention to obtain more insight in pressure influence. Due to some practical problems and a

lack of time only few measurements were completed at this condition. At least 3 repetitions were

performed at each condition. Only at an initial pressure of 4 bar no repeatability was introduced.

The temperature was always set at 298 K with a maximal deviation of ±3 K, caused by the

heat release of a previous explosion and ambient temperature variations. The equivalence ratios

were varied from 0.7 to 1.3 with a step size of 0.5, except for the measurements at 4 and 15 bar.

p [bar] φ

2 0.7 - 1.3

4 0.8; 0.9; 1.0; 1.1; 1.3

5 0.7 - 1.3

10 0.7 - 1.3

15 0.85; 0.9

Table 5.1: Overview of the measurement conditions for methane-air mixtures used to validate the GUCCI

setup. The temperature was set at 298 ±3 K for all the measurements.

As concluded in chapter 3, the unburned mixture conditions in alcohol-fueled engines comprise

pressure ranges up to 100 bar and temperature ranges up to 1400 K. These conditions are very

high and cannot be used with the GUCCI. However, extrapolation could be used in order to

attain valuable information at these conditions. Regarding the measurements on methane-air

mixtures, it is highly valuable to obtain an extensive database in the range up to 10 bar in order

to validate the setup. Optical information and LBV values at the 15 bar condition are

valuable for new insights and future research.

5.2 CH4-air LBV up to 10 bar

In this section the results of the measurements on methane-air mixtures up to 10 bar are pre-

sented and discussed. A detailed list of the LBV results can be found in appendix F. The

conclusions made in this chapter are based on these results.

5.2 CH4-air LBV up to 10 bar 90

5.2.1 General analysis

First, it is important to know the influence of starting pressure on the LBV of methane-air flames.

As the temperature influence was not measured in this work, the only valuable information

comprises variable starting pressure results. Figure 5.1 shows a graph in which ul for φ equal

to 0.8, 1 and 1.3 is plotted as a function of pressure (2, 4, 5 and 10 bar). From this graph the

following conclusions can be made:

Figure 5.1: Plot of the LBV values of methane-air mixtures at an equivalence ratio of 0.8, 1 and 1.3 as

a function of pressure (2, 4, 5 and 10 bar).

� The LBV, ul, decreases with pressure. This decrease diminishes (becomes less steep) when

pressure is increased. As found in literature, ul varies linearly with 1√p . The present results

are thus acceptable.

� The LBV, ul, decreases when the mixture is rich or lean of stoichiometric.

These conclusions were to be expected, as the results were in line with the consulted literature

data.

In figure 5.1 it is observed that, at 5 bar for φ equal to 1.3, a deviating LBV value was calculated.

The deviation from the expected trend is probably due to a wrong mixture composition at this

relatively high equivalence ratio. It was found that when the GUCCI was used to measure LBV

of very lean or very rich mixtures, in some cases no ideal spherical flame resulted or the filling


procedure was not accurate enough. As a consequence, wrong LBV information was captured.

In section 5.3, wherein the GUCCI is validated, this observation will be examined in more detail.

In the next series of pictures (figures 5.2, 5.3 and 5.4), an overview of the resulting schlieren

images for different measurement conditions is given. The selection of the images was quality-

based.

Figure 5.2: Overview of the spherically propagating flame fronts of methane-air mixtures at a series of

time steps. The equivalence ratio is φ = 0.7 and the pressures are given.

For an equivalence ratio of 0.7 the different propagating flame front images are given in figure

5.2. It is observed that, for a starting pressure of 5 and 10 bar, the propagating flame speed

is much lower than for 2 bar. Also, a rather unstable flame front is seen at 10 bar. However,

the image processing method can still be applied on this flame since the circular shape is still

present, which enables circle fitting. For larger deviations from the desired circular form, this

is no longer possible. The development of a wrinkled cellular structure is already observed at

quite high stretch rates. This is due to the increasing Darrieus-Landau and thermodiffusive

instabilities. Moreover, the higher the pressure, the slower the flame front and hence the lower

the stretch rates that stabilize the flame. The quality of the circular edge at 2 and 5 bar is quite

good, without any pronounced irregularities. However, some smaller cracks caused by density

gradients are present on the surface.



time steps. The equivalence ratio is 1 and the pressures are given.

For an equivalence ratio of 1 the different propagating flame front images are given in figure

5.3. It is seen that, for a starting pressure of 5 and 10 bar, cellular structures develop at the

flame front surface. For 5 bar this occurs at 35 ms when the flame has a radius of 40 mm; for

the 10 bar starting pressure this already occurs in the initial phase of flame propagation, when

the flame radius is about 10 mm. As pressure increases, the useful region for extrapolation to

zero-stretch flame speed diminishes and the uncertainty on the calculated results increases. The

difference with an equivalence ratio of 0.7 is also remarkable. The flame speed, and thus the

LBV, is generally higher.



time steps. The equivalence ratio is φ = 1.3 and the pressures are given.

In figure 5.4 results for an equivalence ratio of 1.3 are provided. For 5 bar a deviating result

is seen, explaining the higher LBV value that was calculated at this condition. The flame is

propagating rather fast in comparison with the 2 bar measurement. It is important to note that

figure 5.1 plots the mean LBV values over a series of experiments at the same conditions. Figure

5.4 only shows a single experiment.

The physical explanation for the decreasing LBV with increasing starting pressure is found in the

fact that an increase in starting pressure causes a more important effect of the so-called ‘chain

breaking-reactions’ than the ‘chain initiation-reactions’. This leads to less free radicals and a

lower reaction temperature, which in turn leads to a decrease in flame temperature and thereby

ul. The physical explanation for the lower burning velocity for lean and rich mixtures is found

in the lower energy generation when reaction occurs. By this the resulting flame temperature

is lower and, as a consequence, ul.

It is convenient to have a graphical overview of the obtained LBV values at all conditions.

Therefore the figures 5.5, 5.6, 5.7 and 5.8 are given.


Figure 5.5: Graph of the LBV values at 2 bar for the total measured range of equivalence ratios. The

triangles represent the LBV values of single experiments, the circles represent the averaged

values.

At a starting pressure of 2 bar a lot of scatter is seen on the results. A maximum absolute

standard deviation of 5.84 cm/s on the LBV values is found. The maximum relative standard

deviation is 11 %. An explanation for these statistical values is provided in a following paragraph.


circles represent the LBV results of the single experiments (no repetitions were performed

at this starting pressure condition).


At a starting pressure of 4 bar no repetitions were performed. The obtained results are certainly

tolerable. At starting pressure conditions of 5 and 10 bar the results were very good as the

spreading was rather small.



values.

Figure 5.8: Graph of the LBV values at 10 bar for the total measured range of equivalence ratios.The


values.


The results at 5 and 10 bar are good compared to those at 2 bar since less scatter is present.

For 5 and 10 bar, the maximum absolute standard deviations are, respectively, 1.78 cm/s and

0.88 cm/s. The maximum relative standard deviations are, respectively, 10.7 % and 7.3 %.

To end this section, the summarizing table 5.2 is given, providing an overview of quantitative

information on the spreading (maximum absolute and relative standard deviation). In section 5.3

this information is further used to compare the obtained LBV values with data from literature.

Max. abs. Stdv. φ Max. rel. Stdv. φ [%] rel. Stdv. P [%] Max. abs.

Stdv. un

Max. rel.

Stdv. un

[%]

P = 2 bar 0.02 at φ= 1.15 1.74 at φ= 1.00 1.6 2.93 at φ=

0.90

11.78 at

φ= 0.90

P = 5 bar 0.02 at φ= 0.95 2.00 at φ= 0.95 0.6 1.78 at φ=

1.20

10.68 at

φ= 1.20

P = 10 bar 0.02 at φ=1.00;1.10 1.77 at φ= 0.9 0.6 0.88 at φ=

1.20

7.27 at φ=

1.20

Table 5.2: Overview of the maximum absolute and relative standard deviations on φ and ul. Values at φ equal

to 0.70, 0.75, 1.25 and 1.3 are neglected. The table is a complete summary of table F.11 in appendix

F.

At 4 bar no statistics were made because no experimental repeatability was introduced, although

a comparison with literature was done. The results can be found in section 5.3.

Some explanation is required to understand the numbers in the tables F.11 (see appendix)

and 5.2. The first two columns represent the maximum deviation from the mean mixture

equivalence ratio. The mean equivalence ratio was always aimed at a standard value (rounded

numbers like 0.8, 0.9, etc.). In absolute terms, the deviation of the mean value from this

standard value was 0.01, which is negligible. It is therefore appropriate to use the standard

equivalence ratio value instead of the mean value in order to present the data. The maximum

absolute and relative deviation are reached at different equivalence ratios for the different starting

pressures. These values are indicated in table 5.2. The relative standard deviation is defined as

the ratio of the standard deviation to the mean equivalence ratio. The third column contains

the relative standard deviation on the starting pressure. The fourth and last column contain

results concerning LBV, analogous to the results for the equivalence ratio.


It is important to analyze the spreading on the initial mixture conditions which are the equiva-

lence ratio and the starting pressure. It is observed that the spreading on the equivalence ratio

is limited; a maximum relative spreading of 2 % was calculated. Also, the relative spreading

on initial pressure was very limited, with a maximum value of 1.6 % for a 2 bar initial pressure

condition. This already provides an indication that it is legitimate to assume that the mean

mixture condition for a set of repeated measurements is equal to the intended condition. The

mean LBV value is than the average of the set LBV values corresponding with every single

experiment aimed to have the intended mixture condition. When the mean LBV value at a

particular mixture condition is taken, it can thus be assumed that this value is suitable for a

comparative study with literature data.

The maximum absolute standard deviation on the LBV values is equal to 2.93 cm/s and is

acceptable. The maximum relative standard deviation is equal to 11.78 %. These maximum

values are both found at a 2 bar starting pressure condition. It can thus be assumed that, at

this particular condition, the highest amount of spreading emerges. This is a confirmation of

figure 5.5, in which a lot of scatter on the results was observed. When the normalized relative

standard deviations on the LBV values in table F.11 (column Stdv. LBV [%]*) are observed,

it is seen that the maximum relative standard deviation is equal to 11 %, which is slightly

lower than 11.78 % as it is scaled to the largest LBV value at that starting pressure (2 bar).

Because the difference with the other values is quite big, it is assumed that these maximum

values are caused by irregularities (uncontrollable flaws) in the measurement process. When

these maximum values (marked in green) are neglected for each column, the average normalized

relative standard deviations are equal to:

� 5.0 % for 2 bar

� 4.5 % for 5 bar

� 2.6 % for 10 bar

In general, the spreading on the LBV values is in the range of 2.5 - 5 % for pressures

up to 10 bar. In combination with a maximum relative spreading on equivalence

ratio and initial pressure of, respectively, 2 % and 1.6 %, it can be concluded that

the database for pressures up to 10 bar is of good quality and therefore useful for

comparison with literature data.


5.2.2 Regression analysis

In the previous section, the influence of pressure on the LBV results was discussed. In the

present section it is examined to what extent it is possible to fit the LBV measurements to a

power law (functional form). To have a better understanding of the general relationship between

LBV, pressure and equivalence ratio, this power law is of great importance. It is also useful

when generating LBV values at other (higher pressure) conditions. From an engineering point

of view, it is very convenient to have this kind of relationship since it enables the researcher

to calculate LBV values fast at different conditions of starting pressure and equivalence ratio.

Finally, this power law will also be useful for the validation of the GUCCI setup. The power

law is based on 3 conditions of initial pressure (2, 4 and 10 bar). The 5 bar condition was

excluded because a deviating result was observed at an equivalence ratio of 1.3 (see higher). For

each pressure condition, the equivalence ratios between 0.8 and 1.3 were used in the regression

analysis. In figure 5.9 all the LBV values that were used are plotted as a function of pressure.

Figure 5.9: Plot of the LBV values of methane-air mixtures at equivalence ratios of 0.8; 0.9; 1; 1.1 and

1.3 as a function of pressure (2, 4 and 10 bar).

In section 3.3 the power law was already discussed for alcohol mixtures. In this section this law

is slightly simplified. The resulting correlation is given below.


ul(φ, T, p) = ul0

[p

p0

]β(5.1)

� ul0: LBV for a one-dimensional, laminar flame at p0 and a certain φ value [ms ]

� β: exponent of the pressure [-]

By using this functional form, the results of the GUCCI experiments can be extensively compared

with literature data. The exponent β was determined for different equivalence ratios and is given

in table 5.3. Unity was chosen as a reference value for pressure in order to obtain the standard

non-dimensional form between brackets. This further simplified the equation.

ul0[cms

]β ¯err [%] errmax R2

φ = 0.8 26.6 -0.50 2.63 3.88 0.9927

φ = 0.9 32.7 - 0.43 3.16 4.68 0.9861

φ = 1.0 34.8 -0.33 2.38 4.33 0.9959

φ = 1.1 33.3 -0.36 2.66 3.94 0.9858

φ = 1.3 26.9 -0.60 2.74 4.19 0.9947

Table 5.3: Overview of the β exponent and ul0 value of the different power laws, together with the mean and

maximum error at different equivalence ratios.

The exponent β and the value ul0 were determined using a linear ‘least squares method’. With

these exponents available and with the functional form as in equation 5.1, the LBV value can

be determined for the equivalence ratios ranging from 0.7 to 1.3 and for the total pressure range

starting at 1 bar up to 10 bar. The formulas used to determine the mean and maximum error

on the values obtained by means of the power law are given by equations 5.2 and 5.3 below.

¯err =

∑ √((uli )GUCCI−(uli )PL)2

(uli )GUCCI

N(5.2)

errmax = max

(√((uli)GUCCI − (uli)PL)2

(uli)GUCCI

)(5.3)

¯err is the mean error according to the least squares method. The maximum error is given by

errmax. N is the number of measurement points used to determine the β exponent and ul0 value


of the power law for each equivalence ratio. This value was 3 since the measurements at 2, 4

and 10 bar were used to determine the power law, which now can be used in order to provide

LBV information on a larger scale of pressures.

Figure 5.10: Plot of the LBV values as a function of pressure for different equivalence ratios.

The present experimental data could be compared graphically with these power laws. At 2, 4,

5 and 10 bar the experimental results can be plotted together with the power law functions.

The power laws were constructed from the mean LBV value at each set of conditions (pressure

and equivalence ratio). Of course, scatter is expected around the power law function. The

correspondence of these laws with the individual measured values will not be examined. It is

though interesting to look at the variation of ul0 as a function of equivalence ratio since it is the

LBV value at 1 bar: it was not possible to measure accurately at such a low pressure. In figure

5.11 the ul0 values are compared with literature [52]. A good agreement with literature data is

observed, especially for equivalence ratios up to 1. For richer mixtures the calculated values for


ul0 are slightly lower. In general, the obtained values are in the same order of magnitude as the

experimental data from literature. This provides another indication that the LBV results will

be trustworthy for comparison with the literature. It can be concluded that it is very interesting

to perform a regression analysis on the results, since it provides useful information for a large

range of pressures.

Figure 5.11: Plot of the ul0 values resulting from the regression analysis as a function of equivalence

ratio. The LBV results presented in the work of Egolfopoulos et al. [52] at 1 bar and 298

K are also shown.

To end this discussion a final 3D picture is given in which the different power laws are shown.

When a surface function were created, comprising these different lines, one could easily attain

an LBV value at a specific condition.


Figure 5.12: 3D-plot of the LBV values as a function of pressure for different equivalence ratios.

5.2.3 Pressure derived results

As already mentioned, it is possible to determine the LBV value of a certain mixture composition

using the pressure evolution inside the closed vessel. An example of such a pressure curve is

shown in figure 5.13. This curve corresponds with a methane-air mixture at 300 K, an initial

pressure of 5 bar and an equivalence ratio equal to 1.1. During combustion, the pressure inside

the closed vessel rises very fast upon reaching a peak value, then gradually decreases. The

pressure decrease is caused by cooling of the reaction products when reaching the ‘cold’ walls.

Only a limited part of the pressure trace can be used in the processing. This usable part

is located between the two red lines indicated in figure 5.13. Due to the cubic shape of the

closed vessel, the useful part of the pressure signal is limited to the period before the expanding

spherical flame reaches the chamber walls. In the present work, this radius was chosen to be

60 mm, as discussed previously. From the schlieren images it is known that, for the present

example, this radius is reached at 46 ms. The pressure at that point (≈ 7.3 bar) is much lower

than the attained peak pressure (≈ 36 bar). Besides that, the first part of the graph is not

useful either to determine the LBV. The reason is that the corresponding pressure increase is


too small with respect to the amount of noise on the signal. This noise contaminates the signal

too much to deliver useful data for processing. As a quantitative rule, the mass fraction burned

was used to determine this limit. By taking 3 % volumetric fraction burned as the lower limit,

almost all the noise was eliminated from the pressure trace. As the exact volume of the cubic

vessel is known, which is 3.945 liters, a 3 % volume fraction burned corresponds to a flame

radius of 30 mm. This radius was reached after 23 ms. By examining the processed result of

the schlieren image it was found that the linear range for extrapolation started around 23 ms.

This was an extra check to approve the chosen limit. In some cases it was needed to change

the 3% volumetric fraction limit to lower values when the extrapolation range appeared to start

from a lower value. By optimization of the signal using a polynomial fit this action caused no

problems.

Figure 5.13: Pressure trace during combustion of a methane-air mixture at T0=300 K, p0 = 5 bar and

φ = 1.1.

The signal that was used was further optimized by performing a third grade polynomial fit along

the data points. The results were not affected by this kind of fitting procedure. The processing

calculates a series of unburned flame propagation velocities Su.

5.3 Validation of the GUCCI setup 104

Figure 5.14: The third grade polynomial fit used to filter noise on the measured data points is shown.

The blue line is the fit, the red line shows the evolution of the raw pressure data points.

The result after extrapolating the range of Su towards zero-stretch appeared 18 cm/s. This

value is exactly equal to the value derived with the optical image processing technique. For

this example the two methods thus provided the same result, which is quite remarkable and

reassuring at the same time. To further test and check the accuracy of the pressure derived

method, a study could be completed in which different mixture conditions are postprocessed

using this method. In the present work this was not done due to a lack of time. In future work

it might be useful to further optimize the script that was made during this master dissertation

and to use it for post-processing. With the optical technique however, a very powerful tool

providing good results is available.

5.3 Validation of the GUCCI setup

As mentioned before, the validation of the GUCCI setup is essential in this work. The intention

is to provide a study which delivers the proof that the setup provides meaningful experimental

LBV results. To test the functionality and validity of the setup, the results on methane are used.

In the previous section these results were already presented. In literature, LBV data concerning

methane-air mixtures are widely available. To provide an overview of the literature used to

validate the setup, a summarizing table is given below. This literature and the data which it

provides is believed to be quite reliable and state of the art in the context of methane-air LBV.


Year Author Ref. Technique Tu[K] p[bar] φ

1998 Hassan et al. [49] CVB 298 1-5 0.6-1.3

2000 Lawes et al. [50] CVB 300-400 1-10 0.8-1.0

and 1.2

2002 Rozenchan et al. [51] CVB - up to 60 0.6-1.4

2008 Van Thillo [44] EHPC 300-400 up to 20 0.6-1.4

2010 Egolfopoulos et al. [25] - 343 1 0.7-1.4

2011 Egolfopoulos et al. [52] - 298 1-4 0.7-1.3

2013 Goswami et al. [27] HFM 298 1-5 0.8-1.4

Table 5.4: Overview of the methane-air burning velocity measurements in literature.

The published studies indicated in table 5.4 are believed to be the the more reliable on methane-

air mixtures. To provide a structured insight in the comparative study that was done, the next

analysis is partitioned in sections discussing the 2, 4, 5 and 10 bar results, respectively. In

each section the deviation from literature is analyzed and some main conclusions are derived.

LBV data at the same conditions, but found in different literature sources, vary slightly. The

challenge was how to set up a strategy to compare the data obtained in the present work to

the various data found in literature. First of all, the authors’ interest goes to the spreading

on the results obtained by other researchers. If the present measured results are within the

boundaries of a prescribed spreading range, this is a first indication that the data are acceptable.

The next step is to look at the absolute and relative deviation of the present results from

the calculated mean LBV values found in different literature sources. The final purpose is to

prove that the GUCCI setup is valid for the performance of LBV measurements.

In section 5.2.1 the fundamental arguments for stating that the present database is acceptable

for further comparison with literature data, were given. These arguments are summarized below.

� The spreading on the LBV values is in the range of 2.5-5 % for pressures up to 10 bar. Very

lean (φ equal to 0.7) and very rich (φ equal to 1.3) measurement conditions result in less

reliable results because the spreading on the LBV values is higher. However, for the range

of φ from 0.8 up to 1.2 the spreading lays within the above mentioned boundaries. As was

found in section 5.2.1 a measurement error (caused by unknown reason) at some particular

conditions caused a large deviation in LBV values. The above mentioned spreading range

was defined by excluding this condition.


� The maximum relative spreading on the equivalence ratio and initial pressure for the com-

plete database are respectively 2 % and 1.6 %.

� The regression analysis provides trustworthy results when comparison with literature data

is done.

� The error analysis stated an absolute error of 0.1 bar on the initial pressure measurements

and a relative error of 107 %, 31 % and 12 % on the equivalence ratios at, respectively, 2,

5 and 10 bar. Qualitatively, lean mixtures will have the highest spreading on equivalence

ratio. As these values are all very conservative, the real absolute pressure and equivalence

ratio error will be smaller in most cases. The errors obtained with this analysis are accepted

by the authors.

The aforementioned quite low relative spreading on the LBV results, in combination

with the acceptable errors found in the error analysis, gave the authors a well-

founded basis to start a comparative study of the obtained average LBV values

with literature.

Results at 2 bar Table 5.5 shows recent LBV results of Egolfopoulos et al. [52], Goswami

et al. [27] and Hassan et al. [49] and the mean results obtained in the present work. The last

column presents the relative deviation of the mean LBV value found in this work, from the

corresponding averaged LBV values found in literature, at that specific condition.

φ LBV [52] LBV[27] LBV [49] LBV present work Dev. [%]

0.7 13.5 - 10.9 13.5 9.7

0.8 20.0 17.8 21.0 19.3 1.6

0.9 25.6 21.6 - 24.9 6.2

1.0 28.5 27.7 28.1 24.0 17.3

1.1 29.0 27.7 28.1 26.6 2.8

1.2 25.0 23.0 25.2 22.7 5.8

1.3 18.1 17.0 - 17.3 1.5

Table 5.5: Overview of the LBV [cm/s] results in literature and obtained in the present work. The mixture

conditions are 2 bar, 298 K.


The last column gives an indication that the deviation is quite acceptable for all mixture com-

positions. It is observed that the database of Goswami et al.[27] (2013) is the most comparable

with the present results. The main conclusion is that the results at 2 bar are generally in line

with the data from literature. Only at an equivalence ratio of 1, a large deviation from literature

results is seen. The reason could be that the filling procedure was not working properly at this

particular condition. As a consequence, the assumed mixture composition is likely to be wrong.

The flame speed calculated from the recorded images is correct, but it corresponds with the

wrong mixture composition.

Figure 5.15: Present values of ul at 2 bar, compared against data from literature.

On the right graph in figure 5.15 it is seen that the LBV results are within the experimental

variability of the different literature data. The error bars give the standard deviation of the

literature LBV values around the average of these values. As already mentioned, a deviating

LBV value is found at an equivalence ratio of 1. This can also be seen on the right graph of

figure 5.15. It can be concluded that, for an initial pressure of 2 bar, the resulting LBV data

are quite acceptable. At least 3 measurements need to be done at a single condition to obtain

a meaningful average value.

Results at 4 bar Table 5.6 presents recent LBV results of Lawes et al. [50], Goswami et al.

[27] and Rozenchan et al. [51], and the mean results obtained in the present work. The last

column contains results analogous to these in table 5.5.



0.7 9.1 - 8.9 - -

0.8 15.2 14.3 14.9 12.9 15.1

0.9 20.0 18.6 18.9 17.1 12.3

1.0 22.0 21.4 24.0 19.5 15.2

1.1 21.5 21.5 21.0 19.4 9.8

1.2 16.7 17.4 17.1 12.2 40.2

1.3 - 11.6 11.0 10.5 7.5



In the last column it is seen that the deviation is not acceptable. It is observed that the database

of Goswami et al.[27] (dated from 2013) is the most comparable with the present results.

Figure 5.16: Present values of ul at 4 bar, compared against results from literature.

When examining the right graph in figure 5.16, it is seen that the LBV results are, in general,

approximately 2 cm/s lower than the mean LBV values resulting from literature. This could be

an indication that a wrong initial pressure was assumed. The results at 4 bar are not used in

this study, since no repeatability was introduced.

Results at 5 bar Table 5.7 presents LBV results of recent authors Lawes et al. [50], Goswami

et al. [27], Rozenchan et al. [51] and the mean results obtained in the present work. The last

column contains results analogous to these in table 5.5.



0.7 - - 6.0 6.1 1.9

0.8 11.6 13.1 10.9 11.4 4.3

0.9 - 17.5 15 14.6 11.1

1.0 19.0 - 18.5 18.1 4.9

1.1 - 19.5 18 17.8 6.4

1.2 16.6 15.3 16.2 16.7 13.6

1.3 - 10.3 10.8 14.3 24.5



In the last column it is seen that the deviation is quite acceptable. It is observed that the

database of Rozenchan et al. (dated from 2002) is the most comparable with the present

results.


When examining the right graph in figure 5.17 it is seen that the LBV results from literature

have rather high variability. By comparing the present results with the mean value of the

corresponding literature data, it is seen that for equivalence ratios below 1 the results are in line

with this mean value, but above 1 the results are higher. This could be an indication of wrong

mixture composition for the richer mixtures. However, as variability in literature is quite high,

these results can still be accepted.


Results at 10 bar Table 5.8 presents recent LBV results of Lawes et al. [50] and Rozenchan et

al. [51], and the mean results obtained in this work. The last column contains results analogous

to these in table 5.5.

φ LBV [50] LBV[51] LBV present work Dev. [%]

0.7 - 4.1 3.0 36.7

0.8 8.0 7.3 8.6 6.8

0.9 - 11.0 12.3 10.5

1.0 15.0 13.5 14.8 3.7

1.1 - 14.0 14.8 5.4

1.2 11.0 10.7 12.0 13.8

1.3 - 7.5 6.6 13.4

Table 5.8: Overview of the LBV [cm/s] results in literature and obtained in present work. The mixture condi-

tions are 10 bar, 298 K.


When examining the right graph in figure 5.18 it is seen that the LBV results in literature have

low variability. The present work delivers results that are highly comparable with literature

data. For all the equivalence ratios the absolute deviation is 1 cm/s, excluding φ = 1.2 for

which the deviation is 2 cm/s. It can be concluded that the GUCCI setup provides qualitative

results at an initial pressure of 10 bar.

For the pressures 2, 5 and 10 bar an overview of the absolute standard deviation is given in

order to support the graphical representations.


Pressure [bar] φ Abs. Stdv. Abs. Dev.

2 0.7 1.32 1.3

0.8 1.36 0.3

0.9 1.21 1.5

1 0.32 4.2

1.1 1.58 0.7

1.2 0.99 1.3

1.3 0.55 0.3

5 0.7 - 0.11

0.8 0.92 0.49

0.9 1.25 1.62

1 0.41 0.90

1.1 1.35 1.15

1.2 2.88 2.26

1.3 - 3.50

10 0.7 - 1.10

0.8 0.75 0.59

0.9 - 1.29

1 0.75 0.55

1.1 - 0.79

1.2 0.3 1.67

1.3 - 0.88

Table 5.9: Overview of the absolute standard deviations of mean literature LBV [cm/s] values, compared

against the absolute deviations of the present experimental results. The values marked in blue

exceed the standard deviation.

The above discussion and presentation of the obtained experimental LBV data and correspond-

ing data from literature provides enough fundamental information to state that the GUCCI

setup is valid for performing LBV measurements. When the complete pressure range (2

- 10 bar) is considered, the deviation from mean literature data is generally below

15 % (excluding some very lean and very rich conditions). In table 5.9 it is observed that, in

absolute terms, the deviations are acceptable. To end this section a summarizing figure 5.19 is

given. It could also be clarifying for the interested reader to analyze the extrapolation figures

(last pages of the appendix).

It is concluded that if one wants to execute LBV measurements with the GUCCI,

5.4 CH4-air LBV at 15 bar 112

it is designated to make sure that at least 3 experiments at the same mixture

conditions are performed. By taking the average of the LBV values of each single

experiment, a reliable result is obtained. If more than 3 experiments are performed

the reliability of the result increases.

Figure 5.19: Overview of the LBV results up to 10 bar.

5.4 CH4-air LBV at 15 bar

The results of the measurements at 15 bar are quite limited; only 4 measurements were com-

pleted. In table 5.10 these results are shown.


file p [bar] Tu [K] φ φcorr ul

[cm/s]

Lb [mm]

M15phi085e01 15.02 300 0.85 0.83 10.16 -0.5152

M15phi085e02 15.12 302 0.85 0.84 7.23 -0.2879

M15phi085e03 14.82 303 0.85 0.85 7.10 -0.8953

M15phi090e01 15.14 302 0.90 0.91 12.06 -0.0181

M15phi090e02 15.01 300 0.90 0.90 10.55 0.4778

Table 5.10: Laminar burning velocities [cm/s] of methane-air flames at 15 bar, 300 K.

Constant volume bomb measurements at pressures higher than 10 bar are not present in large

numbers in literature. Rozenchan et al. studied the LBV of methane-air flames up to 60 atm

[51]. The results from this study will be compared with the values for ul obtained in the present

work. Next, the results from the present study will be compared to power law calculations.

Comparison with literature In this section a comparison is made with the results obtained

by Rozenchan [51] for methane-air flames at 10 and 20 atm. Because no results at 15 bar

were found in the consulted literature, data of Rozenchan et al. at pressures below and above

the present results were used. For a given equivalence ratio, results from the present work are

expected to be in between the corresponding values for ul at 10 and 20 atm. For clarity it is

assumed that 1 bar is equal to 1 atm. The results are represented in table 5.11.

φ LBV 10 bar[51] LBV 20 bar[51]

0.7 4.1 2.1

0.8 7.3 4.7

0.9 11 7.9

1.0 13.5 9.2

1.1 14 9.0

1.2 10.7 6.7

1.3 7.5 4.9

Table 5.11: Overview of the LBV [cm/s] results at 298 K found in literature.

The mean LBV value at an equivalence ratio of 0.8 and 0.9 is, respectively, 6 cm/s and 9.45

cm/s. The experiment M15phi085e01 is not taken into account when doing this comparison


study. As the equivalence ratio for the files M15phi085e02 and M15phi085e03 is 0.85, the mean

of the values at equivalence ratios 0.8 and 0.9 is taken, which is 7.7 cm/s. Note that this way

of thinking is not perfectly correct but it provides a good indication of the order of magnitude.

By comparison of these data with the present results it is seen that they agree well. In figure

5.20 this is shown.


Power law calculations and comparison In the present work, the functional form known

as the power law was already introduced (see equation 5.1). As LBV values were measured at

15 bar at equivalence ratios 0.85 and 0.9, the power law can be used at equivalence ratios 0.8

and 0.9 to make a comparison. The values calculated with the power law are indicated in table

5.12.

ul powerlaw [cm/s] ul mean [cm/s] ul best [cm/s]

φ=0.8 6.86 7.17 7.10

φ=0.9 10.20 11.3 10.55

Table 5.12: Laminar burning velocities [cm/s] of methane-air flames at 15 bar and 300 K, calculated with the

power law and real experimental values (ul mean and ul value closest to the calculated power law

value).

5.5 Physical phenomena 115

The experimental results at 15 bar are certainly in line with expectations regarding the power

law. The result of the file M15phi085e01 was not used in this comparative study because the

two other values were more realistic. Attention has to be paid to the fact that the results

M15phi085e02 and M15phi085e03 are actually realized with an equivalence ratio of 0.85, thus

0.05 higher than 0.8. It is seen that the present LBV values are also slightly higher, as expected.

It can be concluded that it is certainly possible to complete a large amount of measurements

at 15 bar with the GUCCI setup. Since the complete post-processing (image processing and

extrapolation script) is now fully available and properly working, future research is definitely

able to provide a valuable database at pressures starting at 10 bar and going up to 15 bar.

Because of safety reasons it was not allowed to measure at pressures exceeding 15 bar. This was

also confirmed by calculations in the GASEQ program. In reality, however, the actual measured

peak pressures at this condition (15 bar and 298 K) were still below 150 bar. Therefore, it

should be possible to go up to higher pressures in the future.

5.5 Physical phenomena

During the measurements some physical phenomena were observed. In this section a short

overview of the various physical phenomena is given, comprising flame cellularity, buoyancy

effects and influence of ignition electrodes. Today, these phenomena are still not entirely under-

stood. Therefore the authors believe that it is useful to provide some important observations

that were encountered in the present work.

Cellularity The cellularity effect was observed when doing measurements at 5, 10 and 15 bar.

In figure 5.21 this phenomenon is shown. At 5 bar the evolution towards an unstable flame front

is perfectly visible. At 10 and 15 bar the cellularity is already present short after ignition. It

was still possible to postprocess the images because the circular flame shape was retained.


Figure 5.21: Combustion event: propagating flame at mixture conditions 5 bar, φ = 1, and T = 298

K; the pictures are recorded every 5 ms. Cellularity becomes visible after approximately

25-30 ms.

Buoyancy effect The Buoyancy effect was observed when the mixture was lean (equivalence

ratios 0.7 and 0.8). In figure 5.22 this phenomenon is clearly visible. In this sequence, a

fundamental problem of measuring the burning velocity of lean mixtures occurs. Due to the

slow combustion, the sphere of combustion products has time to rise to the top of the vessel. this

effectively shortens the part of the event that can be used, as heat loss becomes too severe when

the flame touches the wall. Also, the post-processing model assumes a spherical flame-shape,

whereas this flame is somewhat flattened and has a different volume-to-surface ratio.


Figure 5.22: Combustion event: propagating flame at mixture conditions 10 bar, φ = 0.7, and T = 298

K; the pictures are recorded every 10 ms.

Ignition electrodes influence In figure 5.23 the influence of the electrodes on the spherical

flame is seen. The tips of the electrodes give a first deformation of the flame front. At the

sudden change in electrode diameter a second impact on the flame front takes place. The

corresponding deformation was not of great importance when determining the LBV values. The

physical phenomenon is shown in figure 5.24.

Figure 5.23: Combustion event: propagating flame at mixture conditions 2 bar, φ = 1.15, and T = 298

K.

5.6 Ethanol LBV 118

Figure 5.24: Detail picture of ignition influence.

5.6 Ethanol LBV

The initial purpose of this work was to perform LBV measurements on light alcohols, ethanol

and methanol in particular. During the measurements a lot of practical problems were met

regarding ignition of these kind of mixtures. Therefore the purpose of the present work was

redefined to the goal which was stated in the introduction of this text. Only few measurements

on ethanol-air mixtures were performed. The results are given in this section.

5.6.1 Results and comparison

The results of the measurements on ethanol-air mixtures in the present work are indicated in

table 5.13. To make sure all the ethanol was evaporated prior to ignition, the initial temperature

5.6 Ethanol LBV 119

was set at 400 K using the electrical heater.

file p [bar] Tu [K] φ φcorr ul

[cm/s]

Lb

[mm]

E1phi090e01 1 399 0.90 0.91 46.0 0.7918

E1phi100e01 1 396 1.00 1.02 36.2 1.71735

E1phi100e02 1 397 1.00 1.01 52.2 1.79834

E1phi100e03 1 400 1.00 1.01 41.1 1.0325

E1phi110e01 1 396 1.10 1.12 41.0 1.1292

Table 5.13: Laminar burning velocities [cm/s] and Markstein lengths of ethanol-air flames at 1 bar and 3

different equivalence ratios: 0.9, 1 and 1.1. The initial temperature was set to 400 K.

In a study of Liao et al. [35] laminar burning velocities and Markstein lengths for mixtures

of ethanol and air were determined using the constant volume bomb method at atmospheric

pressure and an initial temperature of 358 K. The results of this study are shown in table 5.14.

φ ul

[cm/s]

Lb

[mm]

0.7 27.2 5.74

0.8 35.5 4.09

0.9 42.3 3.98

1.0 54.3 3.28

1.1 58.4 2.65

1.2 53.4 2.18

1.3 46.3 1.75

1.4 32.7 1.63

Table 5.14: Laminar burning velocities and Markstein lengths measured in [35] using the constant volume

bomb method for ethanol-air flames at 1 bar and 358 K.

The same experimental method was used in the work of Bradley et al. who performed measure-

ments at pressures ranging from 0.1 to 1.4 MPa [16]. In this study temperatures were varied

from 300 to 393 K and equivalence ratios were between 0.7 and 1.5. The results from [16] that

are relevant for comparison with the measurements performed in the present work, i.e. the

results at 0.1 MPa or 1 bar, are summarized in table 5.15.

5.6 Ethanol LBV 120

φ ul

[cm/s]

Lb

[mm]

0.7 27.8 2.11

0.8 37.5 1.36

0.9 43.8 1.18

1.0 51.9 1.10

1.1 56.4 0.92

1.2 55.0 0.67

1.3 49.8 0.45

1.4 43.0 0.19

1.5 35.5 -0.14

Table 5.15: Laminar burning velocities and Markstein lengths measured in [16] using the constant volume

bomb method for ethanol-air flames at 358 K and 0.1 MPa.

LBV values When the present values for ul (see table 5.13) are compared with the corre-

sponding values in tables 5.14 and 5.15, it is seen that the values at φ equal to 1 and 1.1 strongly

disagree with literature. Also, the sudden decrease in burning velocity from φ = 1 to φ = 1.1

was not expected according to results from literature. At an equivalence ratio of 0.9, on the

other hand, the corresponding values are comparable.

Markstein lengths Measurements in [16] and [35] were performed at 358 K instead of 400 K.

However, it was observed in [16] that varying temperature conditions has little effect on values

of Lb.

The values of Lb indicated in tables 5.14 and 5.15 show a clear decreasing trend with φ. This

decrease with φ can be explained by the lower diffusivity of ethanol relative to the mixture than

oxygen. The richer the mixture, the easier ignition takes place and the smaller the influence of

stretch on the burning velocity. Moreover, in table 5.15 Lb eventually becomes negative; this

means that for an equivalence ratio of 1.5 the flames burn even faster when stretched.

Comparing the obtained values of Markstein length Lb from the present work with the values in

table 5.14 and table 5.15, the decreasing trend was not observed for the present data. Moreover,

the measurements at φ = 1 are not consistent.

5.6 Ethanol LBV 121

Conclusion The bad agreement of the present results with literature is likely to be an indi-

cation of poor quality measurements, due to ignition of mixtures with incorrect partial pressure

ratios of the two components - ethanol and air. Leakages, inadequate working of the syringe

and bad evaporation of the ethanol are factors to be taken into account for future research. The

poor accuracy of the PID controller is another important factor, especially at pressures as low

as 1 bar. This issue is also discussed in the next chapter.

SUMMARY AND POSSIBLE FUTURE RESEARCH ON THE GUCCI SETUP 122

Chapter 6

Summary and possible future

research on the GUCCI setup

To end the experimental part of this thesis, the authors would like to give a short overview of

potential further research using the GUCCI setup. Of course, when it will be possible in the

near future to perform LBV measurements on liquid fuels such as methanol and ethanol, there

will be opportunities for many new research topics. However, based on the scope of the present

study, already some new ideas and points of attention can be addressed. In this final chapter a

short summary of the present work is given first. Thereafter some possibilities to improve the

accuracy and to extend the scope of the experiments using the current features of the setup are

listed.

6.1 Summary

A first LBV research experience on the GUCCI was realized. The setup was used to perform

a large amount (≈ 200) of methane-air LBV measurements. The temperature for the complete

database was equal to 298± 5K. Consistency of pressure and temperature just prior to ignition

was a crucial factor. The mixture conditions for the complete database are represented in

table 5.1. A high quality LBV database was obtained by using the optical schlieren technique

in combination with powerful and time-efficient post-processing software. In section 5.3 this

database was utilized to validate the correct working of the setup, and guarantee that the LBV

results obtained with the GUCCI setup are meaningful and suitable for international publication.

6.1 Summary 123

The spreading on the LBV results for a single measurement condition (pressures ≤ 10 bar and

0.8 ≤ φ ≤ 1.2) was not bigger than 5 %. The spreading on mixture equivalence ratio and initial

pressure was respectively 2 % and 1.6 %. The low spreading values for initial pressure were

obtained by choosing a tolerance of ±0.03 bar on the measured pressure value. Apart from this

the equivalence ratio was checked by using the measured partial pressure values. A tolerance of

±0.02 was chosen for the equivalence ratio. A regression analysis resulted in a set of power law

expressions. These were useful to get an insight into the evolution of ul as a function of pressure

and provided LBV information at 1 bar, which was successfully compared with literature. The

error analysis stated an absolute error of 0.1 bar on the initial pressure measurements. A relative

error of 107 %, 31 % and 12 % on the equivalence ratios at, respectively, 2, 5 and 10 bar was

calculated. These values are very conservative and only provide a qualitative insight into the

spreading on the equivalence ratio, which will be the highest for very lean mixtures at low

pressures. The aforementioned quite low relative spreading on the LBV results, in combination

with the acceptable error calculated in the error analysis, gave the authors a well-founded basis

to start a comparative study. The obtained mean LBV values were compared with data from

literature. First, the spreading on the results obtained by different researchers was determined.

Next, the absolute and relative deviation from the calculated average of the different literature

LBV data was studied. The present LBV data for methane-air mixtures at 2 bar were compared

against 3 other databases from literature. It was observed that the data of Goswami et al. [27]

were the most comparable with the present results. For the measurements at 5 bar it was

observed that the data of Rozenchan et al. [51] agreed best with the present data. In the

present study, mixtures that were rich of stoichiometric showed slightly higher values of ul.

This could be due to mixture leaking out of the vessel while dry air is added to reach the

desired initial pressure. The results are, however, considered acceptable since the variation in

literature was rather high. At 10 bar it was observed that the data from the literature had a

low variability. Moreover, the present data agreed very well. The absolute deviation from the

mean literature LBV value was around 1 cm/s for all equivalence ratios except for φ = 1.2, for

which the deviation was 1.67 cm/s. It can thus be concluded that the GUCCI setup provides

qualitative results at an initial pressure of 10 bar. The few results obtained at 15 bar proved

comparable with literature. However, further research will be needed to state fundamental

conclusions at this high pressure condition. Very few experiments were performed with ethanol-

air mixtures and the results were definitely not good. With this liquid fuel, ignition problems

6.2 Possible future research 124

were encountered. This was probably caused by a wrong mixture composition. Because of a

badly designed filling tool and in some cases incomplete vaporization of the fuel, the correctness

of the mixture composition was not sure. It is concluded that the GUCCI setup is validated for

methane-air mixtures, however, further studies are needed to identify potential problems and

solutions for liquid fuel (methanol, ethanol, gasoline, etc.) LBV measurements as well as the

design of a proper filling tool for these kind of fuels. In future research, the goal will be to use

the GUCCI setup to measure laminar burning velocities of alcohols and mixtures of alcohols

with gasoline at a variety of conditions.

6.2 Possible future research

In the above summary and thesis text some ideas and possible improvements were already

proposed. To give the future researcher some concrete ideas to start his/her work with, the

following list is provided. On the one hand, the entirety of items pinpoints problems encountered

during the present work that remain unsolved, on the other hand it provides some ideas on

improving the GUCCI setup.

� Due to the poor accuracy of the PID controller of the gas filling system, deviations from

the proposed tolerances occurred frequently. These deviations were especially important

at 2 bar because of the significant relative error. Measurements at 1 bar were not possible

because of too large deviations in fuel partial pressure at this low pressure condition.

The main problem while filling at low pressures (1 - 2 bar) was that the current filling

system did not seem to be able to measure (fill) partial pressures lower than 0.13 bar.

This was particularly important for the partial pressures of methane, because of its high

air-to-fuel ratio (17.2). It was indeed observed that the spreading on LBV values was

significantly lower at 5 and 10 bar, compared to the measurements at 2 bar. A solution for

this problem was already proposed during the present work and implies the installation of

a micro-controller instead of the current PID controller. This new controller will be much

more flexible and more accurate.

� A second problem concerning the filling process was the inconsistency of the evacuation

of the chamber prior to the actual filling. The deviation from 0.3 bar was significant for

many measurements. Both factors led to experimental errors. It could be an improvement

6.2 Possible future research 125

to install a better vacuum pump.

� Another factor was the vessel sealing, which could not entirely exclude leakages. This was

tested experimentally by using a leakage spray and filling the chamber with compressed

air up to 9 bar. This influence on the mixture composition was particularly important

at elevated pressures. At these conditions part of the methane-air mixture was leaking

during the addition of dry air, again affecting mixture stoichiometry.

� As already addressed, it would be convenient if a new filling tool were designed and

constructed. The current filling tool does not meet the requirements. After multiple tests

it was understood that the mixture composition was (almost always) completely wrong,

leading to mixtures that were not ignitable, and to wrong LBV results. Furthermore it

could also be useful to choose a more precise syringe in order to reduce the composition

error.

� Further improvements on the schlieren setup could be done. The quality of the images is

highly important. Investing in a better (higher frame rate, higher resolution) high speed

camera could be an option but is very expensive.

� Further optimizing a uniform chamber heating and thus temperature distribution.

� Due to a lack of time some important variables could not be investigated properly in this

master thesis. It would be very interesting to experimentally test the influence of the

flushing procedure on LBV, particularly with regard to the flushing time or the amount of

repetitions. Furthermore, the waiting time between shutting down the fan and the ignition

should be optimized. A possible way to do this is by tabulating different time periods for

a single mixture and examining the effect on the LBV.

� Although LBV measurements of methane-air mixtures were performed at pressures up to

15 bar, temperature dependence was not explicitly tested yet. The present study focused

primarily on the effect of increasing initial pressure. It would, however, also be interesting

to compare LBV data at higher temperatures with results from literature. This could be

done as a further validation of the GUCCI setup.

ALCOHOLS AS A FUEL: PROPERTIES 126

Appendix A

Alcohols as a fuel: properties

In the work of Vancoillie [3] a complete overview of the properties of alcohols is given. A short

summary is provided in this section. In figure A.1 the most important properties are listed for

methanol, ethanol and gasoline.

The most distinct feature of alcohol molecules is the polarity caused by the hydroxyl group.

This polarity is responsible for several interesting physico-chemical properties, most pronounced

in light alcohols. The strong inter-molecular forces caused by polarity, known as hydrogen

bonding, give rise to high boiling points, high heats of vaporization and good miscibility with

other substances having strong molecular polarity such as water. Polarity, however, also causes

the high corrosiveness of alcohols compared to other fuels.

Methanol and ethanol have the potential to increase engine performance and efficiency compared

to what is achievable with gasoline, thanks to a variety of interesting properties. Their high

heats of vaporization, combined with a low stoichiometric air-to-fuel ratio (AFR), lead to high

degrees of intake charge cooling as the fuel evaporates. This is especially true for engines with

direct injection. The charge cooling not only leads to increased charge density, and thus higher

volumetric efficiency, but also considerably reduces the propensity of the engine to knock.

The low propensity of alcohol to knock allows for most of the increase in power and efficiency

compared to gasoline engines. It permits the application of optimal values for spark advance,

high compression ratios and opens opportunities for aggressive downsizing without the need for

fuel enrichment at high loads. On the other hand, this property makes methanol and ethanol

unsuitable for use in conventional diesel engines.

ALCOHOLS AS A FUEL: PROPERTIES 127

Apart from the high knock resistance and volumetric efficiencies, there are some other properties

which bring about minor advantages. The burning velocity of alcohols is about 40% higher than

that of typical gasoline. This creates more isochoric combustion and also allows increased levels

of mixture dilution. Additionally, a higher burning velocity helps to mitigate knock concerns,

since it leaves the unburned gas less time to reach autoignition conditions.

The elevated heat capacity of the combustion products, due to a high ratio of triatomic to

diatomic molecules, combined with the lower combustion temperatures of alcohols, produce

lower heat losses and exhaust temperatures compared to gasoline.

The lower vapor pressures of alcohols and their high heat of vaporization raise cold start prob-

lems. When temperatures drop below the freezing point, insufficient alcohol evaporates to form

a combustible mixture. This is the main reason why methanol and ethanol are often used as

mixtures with gasoline. For example, in M85 or E85 15% (by volume) of highly volatile gasoline

is added to improve the cold start performance of the engine. Also, several cold start strategies

and devices have been proposed.

Figure A.1: Properties of typical gasoline, methanol and ethanol relevant to internal combustion engines.

OPTICAL BASED POST-PROCESSING: MATLAB SCRIPT 128

Appendix B

Optical based post-processing:

MATLAB script

B.1 Image processing

Some more information concerning the image processing method is provided here. It is important

to mention that two image processing methods were developed during this work. The first

method calculated the radius from the surface of a quarter piece of the circular flame. Because

this method was not accurate enough, a second method was developed. In this method, a

circelfit procedure was used to determine the radius. This last method was very accurate and

robust and was used to generate all results. The MATLAB script ‘imageprocessing.m’ is now

explained. The first important section in this MATLAB script is the part were the variables are

defined. There are 2 variables that need to be set manually:

� califact: calculation of the resolution in terms of pixelsmm ; this can be found by dividing the

number of pixels in between two opposite points on the window edge by 150 mm window

diameter size. The number of pixels can than be determined with Photoshop. Figure 4.15

shows a calibration grid placed in front of the first window. The grid spacing is known and

by counting the pixels between two points on the grid, the resolution can be determined.

This provides an alternative method to determine the califact, and to check te validity of

the first method.

� frame rate: the frame rate is the value that was set in the Camware software and the

LabVIEW program. This frame rate was set to 3000 fps for almost all the measurements.

B.1 Image processing 129

Only for ethanol a higher frame rate (10000 fps) was chosen.

Apart from these two variables also the main folder directory, in which all subfolders are located,

needs to be introduced in the script code. As an example the main folder named METHANE

298K contained all the image data of methane at 298 Kelvin. The MATLAB script will loop

over every single subfolder, which corresponds with a single experiment inside the directory, and

will do the image processing. It is important for the usage of the MATLAB sctipt that the same

folder structure is applied. The following structure needs to be used:

� METHANE 298K (main folder)

– M2phi090e01

* beelden (folder where the exported images from the pco.raw file are saved)

* rec file (contains information of camera settings used when recording the images,

this file is generated by the pco.camware software.)

* pco.raw file (This is the raw recorded file containing all images, it is generated

when a single explosion is recorded)

* Pressure history file (This is the pressure file containing the pressure evolution

inside the closed vessel)

– M2phi095e01

– M2phi095e02

– M2phi095e03

– ...

� METHANE 258K (main folder)

� ETHANOL 398K (main folder)

� ...

The script code section were the diretories are set is given below below.


%Give the directory where the script file is located

addpath(genpath(’C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing’));

directory1=’C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing’;

%Give the directory where the main folder is located

directory=’D:\Work\THESIS\LBV metingen\Methane 298K’;

%Define the variables

califact = 0.16;

frameRate = 3000;

The program has now all the information required to run completely by itself. By using a loop,

each subfolder is processed sequentially. In the following explanation it is assumed that the

program is processing a single subfolder. The first action which is performed by the script is

the creation of a calibration image. The first image in the total series of images, called the

starting image in this tutorial, is always used for calibration. By calibration is meant that, in

fact, a ‘universal background image’ is made. An example of a starting image (‘raw background

image’) is given in figure B.1.

Figure B.1: Example of the calibration image. This image is also called the ‘raw background image’.

This so-called ‘universal background image’ is further used in the processing method for pro-

cessing every single other image. To create this image the following steps are needed. First,

each pixel of the starting image is turned into a greyscale value of 0 or 150, depending if the

starting greyscale value is respectively higher or lower than 50. The resulting image is presented

in figure B.2.


Figure B.2: Example of the greyscale image.

Next a ‘mask’ image is made. This mask image is a black/white image with values 0 for black

and 1 for white. The command that is used is im2bw(name,0.3). 0.3 is a custom threshold to

start with, and not very important in this discussion. In this ‘mask’ image a sub-matrix system

is selected used to calculate an average intensity in the inverted starting image matrix I. This

average intensity is used to enhance the background in all other images. This inverted starting

image I is created B.3 by the following operation: I = 255− bgdata1.

Figure B.3: Example of the inverted background image ‘I’.

In the matrix I the average value of the sub-matrix (the boundary coordinates for this matrix

were calculated from picture ‘mask’) is calculated. This average value is then subtracted from


each value in the I matrix. So now the values of I range from 0 to 255 minus the average

value. The values in I are thus rescaled to values from 0 to 255 by multiplying each value with

255255−average . Finally the image I is converted back to the original ‘non-inverted’ starting image

by the operation: bgdata2 = 255− I. The image ‘bgdata2’ is now the ‘background’ image that

is further used in the process. There is a visible difference between the old and new background

image. The new background image is much lighter than the old one.

Figure B.4: Example of the resulting ‘universal background image’. The difference between the raw

and new background is clearly seen.

Before the processing can be done, the center of the image needs to be defined. This is completed

by performing a circle fit procedure for a series of flames at different quite late time steps. The

same procedure as for the normal image processing (see further in this text) is used. The only

difference is that the electrodes are not deleted from the flame image because the center is at

that point not known. However, this is not very important since the circle fit method is still

applicable. For the center determination only the flames in a later stage, which are quite big,

are used. Fundamentally, it is not really necessary to determine the center in order to be able

to delete the electrodes. The white edge of the flame is sufficient to fit the circle. However, in

some special cases the influence of the electrodes could lead to wrong results and are therefore

always deleted.

After the determination of the center, the actual processing starts. A loop procedure is used

to treat every single image at every timestep. Also for center determination this normal image

processing is used as already mentioned. First the same procedure as the one above is conducted.

By this the background of the image is improved. The MATLAB code is given below.


I=255-imdata1;

I1=imsubtract(I,average);

I4= immultiply(I1,255/(255-average));

imdata2=255-I4; %convert back the image

After these first series of operations the ‘imdata2’ image is subtracted from the background image

‘bgdata2’. The image resulting from this operation is given in figure B.5. In this discussion we

simply call the resulting image ‘imdata2’.

Figure B.5: Resulting image ‘imdata2’.

The ‘imdata2’ image is now converted to a binary image ‘imdata3’ with the values 0 and 255

only. The operation used in MATLAB is given below.

for x=1:w;

for y=1:h;

if imdata2(y,x)>50

imdata3(y,x)=255; % [Binary image 0-255]

else

imdata3(y,x)=0;

end

end

end


Figure B.6: The resulting image after converting ‘imdata2’ to a binary image.

By a filling operation, all holes in the binary grayscale image are filled. A hole is defined as an

area of dark pixels surrounded by lighter pixels. So the filling procedure converts these ‘black’

pixels surrounded by ‘white’ pixels into ‘white’ pixels. The values in this resulting image are

still 0 and 255. This resulting image is then converted to a black-white picture, with values of

0 and 1.

Now an important part in the processing methodology starts. In some cases some black pixels

are still visible inside the white space. These black spaces can’t be eliminated if there is still a

connection between the black pixels and the surrounding black space.

Figure B.7: The resulting image after the filling operation, not the total space is colored white because

of the connection with the surrounding black pixels.

A white square is created in a region around the center coordinates defined by the ‘cut’ param-

eter. This square is shown in figure B.8.


Figure B.8: The resulting image after drawing a white bar over the electrodes. The filling operation

will now be able to eliminate the black spot which is still visible.

This white bar is horizontally introduced and overwrites the black electrodes. By doing a filling

operation all black is turned into white. Finally, a black bar is drawn instead of a white bar and

the circlefit procedure can start.

Figure B.9: The filling operation is now completed.


Figure B.10: The white bar is now covered with a black bar.

This circlefit procedure needs the coordinates of the points located at the edge of the flame.

First the edge of the white flame must be determined. This is done by the following operation:

n=1;

for j=1:cimsize

for k=1:rimsize

if(-imdata8(k,j)<0);

circelx(n)=j;

circely(n)=k;

n = n+1;

break

end

end

end

for j=1:cimsize

for k=rimsize:-1:1

if(-imdata8(k,j)<0);

circelx(n)=j;

circely(n)=k;

n = n+1;

break

end


end

end

The first loop determines the upper edge of the circular flame. By running over each row element

in every single column until the specific value is 1 instead of 0, which is checked by the logical

expression −x < 0, the row number and column number are stored in a list of coordinates. The

second loop completes the same action, but by making the row loop coming from the lower side

of the picture only the lower edge coordinates are stored. The coordinates of the edge points

are then fitted by a circle and the radius in terms of ‘pixels’ is found. This fitting operation is

done by a function called ‘circfit’. This radius is then translated into a radius expressed in ‘mm’

by using the calibration factor. Finally all radii combined with their appropriate time step are

stored in an Excel-file. To give the reader the possibility to use the script for own work, the

complete code is provided below.

Listing B.1: The complete image processing MATLAB script.

1 %% ************************************************************************

2 % IMAGE PROCESSING

3 % Lander Buffel, based on Louis Sileghem

4 % *************************************************************************

5 disp('** Post−processing **')

6 display(' ')

7 clear all

8 close all

9 clear image array

10 %Give the correct directory for the script containing folder

11 addpath(genpath('C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing'));

12 directory1='C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing';

13 %Give the correct directory for the main folder

14 directory='D:\Work\THESIS\LBV metingen\METHANE 298K';

15 files=dir(directory);

16 cd(directory);


18 experiments=size(files,1);

19 %% DEFINE VARIABLES −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

20 califact = 0.16; %%mm/pixel

21 frameRate = 3000; %%fps


22 %% MAIN PROGRAM −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

23 for j=3:experiments %loop for processing every mainfolder

24 expdirectory=[directory,'\',files(j).name];

25 cd(expdirectory);

26 files2=dir(expdirectory);

27 expdirectory2=[expdirectory,'\',files2(6).name];

28 cd(expdirectory2);

29 files3=dir(expdirectory2);

30 last=max(strfind(expdirectory,'\'));

31 filename=expdirectory(last+1:length(expdirectory));

32 aantalfiles=size(files3,1)−1;

33 %delete all jpegs beginning with imdata, bgdata, moviedata

34 delete('imdata*.BMP');

35 delete('bgdata*.BMP');

36 disp(' ')

37 disp([' folder: ',filename] )

38 disp(j)

39 disp(' ')

40 %% CALIBRATION:

41 figure, bgdata1 = imread('image 0001.bmp');

42 [h,w,standaardwaarde] = size(bgdata1);

43 for x=1:w;

44 for y=1:h;

45 if bgdata1(y,x)>50

46 greycalidata(y,x)=0;

47 else

48 greycalidata(y,x)=150;

49 end

50 end

51 end

52 mask=im2bw(bgdata1,0.3);%0.3 is a custom threshold to start with (not very

important)

53 %invert image: background should be approaching black

54 I=255−bgdata1;

55 %select a row in the background in order to calculate the average intensity

56 Row=find(mask(size(mask,1)/2+20,:));

57 %determine the minimum collumn where the background starts

58 mincol=min(Row);

59 %determine the maximum collumn where the background starts

60 maxcol=max(Row);


61 %selection of part of I image

62 %+−10 makes more sure no influence from the boundaries of the window

63 matr=I(size(mask,1)/2+18:size(mask,1)/2+22,mincol+10:maxcol−10);

64 %averagevalue will be used to enhance the background in all the pictures of

folder j

65 average=mean(mean(matr));

66 I1=imsubtract(I,average);

67 %intensities of I1 are [0 − 255−average]. rescaling to [0 − 255]

68 %convert back the image

69 value=255/(255−average);

70 I4= immultiply(I1,value);

71 bgdata2=255−I4;

72 bgdata im=bgdata2;

73 %% CENTER DETERMINATION:

74 teller=0;

75 row=0;

76 col=0;

77 for Centr=70:10:aantalfiles−30

78 clear circelx;

79 clear circely;

80 mdata1 = imread(files3(Centr+3).name);

81 I=255−imdata1;


83 I4= immultiply(I1,255/(255−average));

84 imdata2=255−I4;

85 imdata3=imdata2;

86 imdata4=imsubtract(bgdata im,imdata3);

87 for x=1:w;

88 for y=1:h;

89 if imdata4(y,x)>50

90 %[Binary image 0−255]

91 imdata5(y,x)=255;

92 else

93 imdata5(y,x)=0;

94 end

95 end

96 end

97 % filtering and processing operations

98 imdata6=imfill(imdata5);

99 imdata7=im2bw(imdata6,0.5);


100 imdata8=bwlabel(imdata7);

101 flame=imdata8;

102 [rimsize,cimsize] = size(flame);


104 n=1;

105 for j=1:cimsize

106 for k=1:rimsize

107 if(−imdata8(k,j)<0);

108 circelx(n)=j;

109 circely(n)=k;

110 n = n+1;

111 break

112 end

113 end

114 end

115 for j=1:cimsize

116 for k=rimsize:−1:1

117 if(−imdata8(k,j)<0);

118 circelx(n)=j;

119 circely(n)=k;

120 n = n+1;

121 break

122 end

123 end

124 end

125 [xfit,yfit,Rfit] = circfit(circelx,circely);

126 row=row + round(yfit);

127 col=col + round(xfit);

128 teller = teller + 1;

129 end

130 Centerrow = round(row/teller);

131 Centercol = round(col/teller);

132 %% PROCESSING:

133 clear radius;

134 clear msec;

135 clear circelx;

136 clear circely;

137 cut=12;

138 time(1,1)=0;

139 radius(1,1)=0;


140 for i=1:aantalfiles−3

141 imdata1 = imread(files3(i+3).name);

142 I=255−imdata1;


144 I4= immultiply(I1,255/(255−average));

145 imdata2=255−I4;

146 imdata3=imdata2;

147 imdata4=imsubtract(bgdata im,imdata3);

148 for x=1:w;

149 for y=1:h;

150 if imdata4(y,x)>50

151 %[Binary image 0−255]

152 imdata5(y,x)=255;

153 else

154 imdata5(y,x)=0;

155 end

156 end

157 end

158 %filtering and processing operations


160 imdata7=im2bw(imdata6,0.5);

161 imdata8=bwlabel(imdata7);

162 flame=imdata8;

163 [rimsize,cimsize] = size(flame);


165 for f=Centerrow−cut:Centerrow+cut

166 for j=1:cimsize

167 imdata8(f,j)=1;

168 end

169 end


171 for f=Centerrow−cut:Centerrow+cut

172 for j=1:cimsize

173 imdata8(f,j)=0;

174 end

175 end

176 n=1;

177 for j=1:cimsize

178 for k=1:rimsize

179 if −imdata8(k,j)<0;


180 circelx(n)=j;

181 circely(n)=k;

182 n = n+1;

183 break

184 end

185 end

186 end

187 for j=1:cimsize

188 for k=rimsize:−1:1

189 if −imdata8(k,j)<0;

190 circelx(n)=j;

191 circely(n)=k;

192 n = n+1;

193 break

194 end

195 end

196 end

197 %list the different areas and their pixels

198 RegionAreas = regionprops(imdata8, 'area');

199 Area = cat(1, RegionAreas.Area);

200 max(Area);

201 if isempty(max(Area))

202 %no big flame is (yet detected, so skip calculation)

203 %very small radius, can't be zero for stretch calculation in excel

204 radius(i,1)=1e−10;

205 time(i+1,1)= time(i,1)+1/(frameRate*10ˆ(−3));

206 msec(i,1)=time(i,1);

207 else

208 [xfit,yfit,Rfit] = circfit(circelx,circely);

209 radius(i,1) = Rfit*califact;

210 time(i+1,1)= time(i,1)+1/(frameRate*10ˆ(−3));

211 %in msec;

212 msec(i,1)=time(i,1);

213 disp(['radius=', num2str(radius(i,1)),'mm']);

214 end

215 if radius(i,1)>70 && i>aantalfiles/2

216 break

217 end

218

219 if radius(i,1)>35 && i<aantalfiles/2

B.2 Linear extrapolation 143

220 cut=30;

221 end

222 end

223 %% STORE RESULTS−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

224 % access excel file Postprocessing.xlsx

225 cd(directory1);

226 xlswrite(['Postprocessing.xlsx'], radius,1,'A3');

227 xlswrite(['Postprocessing.xlsx'], msec,1,'B3');

228 [num1,txt1,raw1]=xlsread(['Postprocessing.xlsx'],'D:D');

229 [num2,txt2,raw2]=xlsread(['Postprocessing.xlsx'],'E:E');

230

231 % write to excel file Postprocessing filename.xlsx

232 cd(expdirectory)

233 d1={filename,'';'Radius[mm]','Time [msec]'};

234 xlswrite([filename '.xlsx'], d1,1,'A1');

235 xlswrite([filename '.xlsx'], radius,1,'A3');

236 xlswrite([filename '.xlsx'], msec,1,'B3');

237 d2={'Flame speed [m/s]','';'Av. of 5 adjcent points','Stretch [1/ms]'};

238 xlswrite([filename '.xlsx'], d2,1,'D1');

239 xlswrite([filename '.xlsx'], num1,1,'D3');

240 xlswrite([filename '.xlsx'], num2,1,'E3');

241

242 %clear data in Postprocessing.xlsx

243 cd(directory1);

244 emptycell=cell(size(radius,1),1);

245 xlswrite(['Postprocessing.xlsx'], emptycell,1,'A3');

246 xlswrite(['Postprocessing.xlsx'], emptycell,1,'B3');

247

248 end

B.2 Linear extrapolation

In this section the linear extrapolation method is explained. The MATLAB script is able to do

a semi-automated extrapolation with for each loop the requirement of some human interactions.

First the main folder, just as for the ‘imageprocessing’ script, needs to be introduced in the

script. It is essential that first the ‘imageprocessing’ is completed in order to acquire the proper

Excel-files. It is recommended to check the radius values manually, before feeding the Excel-files


to the linear extrapolation.

The MATLAB script will return to the user a folder located in the main folder in which all

extrapolation results of every single experiment in Excel format, together with the MATLAB

extrapolation figure, are stored. The big advantage of this script is that few human interactions

result in fast results. The working principle is now explained. It is important to mention that

an Excel database with σ values is located in the folder where this extrapolation software was

stored. This σ is the ratio of unburned density and burned density of the gaseous mixture.

First the radius and time evolution are read from the Excel-file which was generated by the

‘imageprocessing.m’ script and which was located in every subfolder. This data is first filtered

by a first loop in which all radii below 5 mm, which is in fact the initial phase of the propagating

spherical flame, are not taken into account in the proceeding operations. Then a correction is

done on the radius evolution in which the salient values are recalculated. If, for example, a

wrong circle fit was performed in the image processing it is appropriate to do this. The margin

to decide what can be tolerated can be set by adjusting a single value. The next step is the

calculation of Sn and α. After this the plot of Sn versus α is made and the operator is asked

to give the lower and upper stretch rate boundary value. In order to have a structural way

of extrapolation a systematical extrapolation route was followed for every single measurement.

The minimum value that needs to be introduced must be the stretch rate at which the operator

assumes the initiation of cellular effects, and thus a fast rise in flame speed. The maximum

stretch rate is simply a boundary condition that is given to the program. The program starts

with linear extrapolation using a variable series of points starting at the minimum stretch rate

and evolving to the total range of points between minimum and maximum. All Markstein

lengths are stored in a list. The Markstein length that dominates the list is then assumed as the

real Markstein length. The corresponding zero-stretch flame speed is then, after scaling with

σ, the LBV value. So the program actually determines the extrapolation line for the series of

points which give the dominating Markstein length. These points are almost always the longest

possible arrangement of stretch points giving a linear flame speed trace on the graph. It has to

be addressed that if the operator is not satisfied with the realized extrapolation figure, he/she

can always ask the program to reset the stretch boundaries. Finally all results are stored in a

single Excel-file, which is located in the main folder. The results are:

� Flame radius at which extrapolation starts


� Flame radius at which extrapolation ends

� Time at which extrapolation starts

� Time at which extrapolation stops

� Sigma value used to calculate LBV from zero-stretch flame speed

� LBV value

� Markstein length

More insight into the flame evolution can be obtained by checking starting and ending radii or

time. To give the reader the possibility to use the script for own work, the complete code is

provided below.

Listing B.2: The complete linear extrapolation MATLAB script.

1 %% ************************************************************************

2 % Linear Extrapolation to zero stretch (LBV)

3 % Lander Buffel

4 % *************************************************************************

5 disp('** Linear Extrapolation **')

6 display(' ')

7 clear all

8 close all

9 %Give the correct directory for the script containing folder

10 addpath(genpath('C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing'));

11 directory1='C:\Users\eigenaar\Documents\ugent\Thesis\Postprocessing';

12 %Give the correct directory for the main folder

13 directory='D:\Work\THESIS\LBV metingen\METHANE 298K';

14 %% MAIN PROGRAM−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

15 cd(directory);

16 last=max(strfind(directory,'\'));

17 proc=directory(last+1:length(directory));

18 mkdir(['z' proc ' Processed']);

19 %make a new folder


21 experiments=size(files,1)−1;

22 writingfolder=[directory,'\',files(experiments+1).name];


23 cd(writingfolder);

24 d1={'DATA','Start radius [mm]','Stop radius','Start Time [msec]','Stop Time','Sigma'

,'Flame speed [cm/s]','Markstein [mm]','phi','p'};

25 xlswrite(['Postprocessing ',proc,'.xlsx'],d1,1,'A1');

26 sigmadruk = cell(4,1);

27 sigmadruk{1,1} = '1';

28 sigmadruk{2,1} = '4';

29 sigmadruk{3,1} = '5';

30 sigmadruk{4,1} = '10';

31 sigmaphi = cell(15,1);

32 sigmaphi{1,1} = '060';

33 sigmaphi{2,1} = '065';

34 sigmaphi{3,1} = '070';

35 sigmaphi{4,1} = '075';

36 sigmaphi{5,1} = '080';

37 sigmaphi{6,1} = '085';

38 sigmaphi{7,1} = '090';

39 sigmaphi{8,1} = '095';

40 sigmaphi{9,1} = '100';

41 sigmaphi{10,1} = '105';

42 sigmaphi{11,1} = '110';

43 sigmaphi{12,1} = '115';

44 sigmaphi{13,1} = '120';

45 sigmaphi{14,1} = '125';

46 sigmaphi{15,1} = '130';

47 cd(directory1);

48 SigmaMatrix = xlsread('SigmaValues.xlsx',1,'A1:D15');

49 for j=3:experiments

50 clear X;

51 clear Y;

52 clear R;

53 clear T;

54 clear Sn;

55 clear alpha;

56 clear straal;

57 expdirectory=[directory,'\',files(j).name];

58 last=max(strfind(expdirectory,'\'));

59 filename=expdirectory(last+1:length(expdirectory));

60 cd(expdirectory);

61 disp(' ')


62 disp([' folder: ',filename] )

63 disp(' ')

64 phinummer=strfind(filename,'i');

65 phinummer2=strfind(filename,'e');

66 phiwaarde=filename(phinummer+1:phinummer2−1);

67 pnummer=strfind(filename,'M');

68 pnummer2=strfind(filename,'p');

69 pwaarde=filename(pnummer+1:pnummer2−1);

70 Rt=xlsread([filename,'.xlsx'],1,'A:A');

71 Tt=xlsread([filename,'.xlsx'],1,'B:B');

72 teller=1;

73 for i=1:length(Rt)

74 if Rt(i)>5

75 R(teller,1)=Rt(i);

76 T(teller,1)=Tt(i);

77 teller=teller+1;

78 end

79 end

80 for i=3:length(R)−1

81 if abs(R(i+1)−R(i))>1.2

82 a1 = linear regression(T(i−2:i),R(i−2:i));

83 R(i+1) = a1 * (T(i+1)−T(i)) + R(i);

84 end

85 end

86 for i=7:length(R)−6

87 Sn(i−6,1) = linear regression(T(i−6:i+6),R(i−6:i+6));

88 alpha(i−6,1) = Sn(i−6)*2/R(i);

89 straal(i−6,1) = R(i);

90 tijdmeting1(i−6,1) = T(i);

91 end

92 for i=1:length(Sn)

93 if alpha(i)>0

94 F(i,1)=Sn(i);

95 F(i,2)=alpha(i)*1000;

96 F(i,3)=straal(i);

97 tijdmeting2(i,1)=tijdmeting1(i,1);

98 end

99 end

100 %maximum number of extrapolation repeatments

101 einde=10;


102 for hoofdloop=1:einde

103 clear F2;

104 clear tijdmeting3;

105 clear boven;

106 clear onder;

107 clear a1;

108 clear a2;

109 clf

110 plot(F(:,2),F(:,1),'b.')

111 axis([0,max(F(:,2))*1.04,0,max(F(:,1))*1.2])

112 xlabel('alpha');

113 ylabel('Sn');

114 grid on;

115 prompt = {'Upper:','Lower:'};

116 dlg title = ['Define bounderies of',filename];

117 num lines = 1;

118 answer = inputdlg(prompt,dlg title,num lines);

119 a = answer{1};

120 b = answer{2};

121 boven = str2num(a);

122 onder = str2num(b);

123 clf

124 tel=1;

125 for i=1:length(F(:,1))

126 if F(i,2)>onder && F(i,2)<boven

127 F2(tel,1)=F(i,1);

128 F2(tel,2)=F(i,2);

129 F2(tel,3)=F(i,3);

130 tijdmeting3(tel,1) = tijdmeting2(i,1);

131 tel = tel+1;

132 end

133 end

134 l = length(F2(:,1));

135 for i=1:l−1

136 [a1(i,1),a1(i,2)] = linear regression(F2(l−i:l,2),F2(l−i:l,1));

137 end

138 for i=1:length(a1(:,1))

139 a2(i,1) = str2num(sprintf('%.4f',a1(i,1)));

140 end

141 A=unique(a2(:));


142 count=histc(a2(:),A);

143 positie = find(max(count)==count);

144 for i=1:length(positie)

145 Lbrow = a1(find(A(positie(i))==a2),1);

146 Flrow = a1(find(A(positie(i))==a2),2);

147 end

148 Lb = mean(Lbrow);

149 Fl = mean(Flrow)

150 Markstein = Lb*−1000

151 grootstestraal = max(F2(:,3));

152 positie2 = find(max(Lbrow)==a1);

153 kleinstestraal = F2(l−positie2,3);

154 start = tijdmeting3(l−positie2,1);

155 stop = max(tijdmeting3);

156 figure;

157 h = plot(F(:,2),F(:,1),'b.');

158 axis([0,max(F(:,2))*1.04,0,max(F(:,1))*1.2])

159 xlabel('alpha');

160 ylabel('Sn');

161 grid on;

162 hold on;

163 fplot(@(x)Lb*x+Fl, [0 max(F(:,2))*1.04]);

164 hold off;

165 w = waitforbuttonpress;

166 if w == 0

167 disp('Button click')

168 else

169 disp('Key press')

170 end

171 prompt={'OK?, 1=ja en 0=nee'};

172 title='Is deze extrapolatie...';

173 answer=inputdlg(prompt,title);

174 antwoord = str2num(answer{1});

175 if antwoord == 1

176 RowMark(j−2,1) = Markstein;

177 Rowgrootstestraal(j−2,1) = grootstestraal;

178 Rowkleinstestraal(j−2,1) = kleinstestraal;

179 Rowstart(j−2,1) = start;

180 Rowstop(j−2,1) = stop;

181 Rowdata{j−2,1} = filename;


182 Rowphi{j−2,1} = phiwaarde;

183 Rowp{j−2,1} = pwaarde;

184 for teller1=1:4

185 if sigmadruk{teller1,1} == pwaarde

186 break

187 end

188 end

189 for teller2=1:15

190 if sigmaphi{teller2,1} == phiwaarde

191 break

192 end

193 end

194 Sigma = SigmaMatrix(teller2,teller1);

195 RowLBV(j−2,1) = Fl*100/Sigma;

196 RowSigma(j−2,1) = Sigma;

197 break

198 end

199 end


201 mkdir(filename);

202 subfolder=[writingfolder,'\',filename];

203 cd(subfolder);

204 figure;

205 saveas(h,'figuur','fig')

206 clf;

207 cd(directory);

208 end

209 %% STORE RESULTS


211 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowdata,1,'A2');

212 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowkleinstestraal,1,'B2');

213 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowgrootstestraal,1,'C2');

214 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowstart,1,'D2');

215 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowstop,1,'E2');

216 xlswrite(['Postprocessing ',proc,'.xlsx'],RowSigma,1,'F2');

217 xlswrite(['Postprocessing ',proc,'.xlsx'],RowLBV,1,'G2');

218 xlswrite(['Postprocessing ',proc,'.xlsx'],RowMark,1,'H2');

219 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowphi,1,'I2');

220 xlswrite(['Postprocessing ',proc,'.xlsx'],Rowp,1,'J2');

B.3 Independent functions 151

B.3 Independent functions

The image processing and linear extrapolation scripts use 2 independent functions. These are

given below.

Listing B.3: The circlefit MATLAB script, used in the imageproocessing MATLAB script.

1 function [xc,yc,R,a] = circfit(x,y)

2 % [xc yx R] = circfit(x,y)

3 % fits a circle in x,y plane in a more accurate

4 % (less prone to ill condition )

5 % procedure than circfit2 but using more memory

6 % x,y are column vector where (x(i),y(i)) is a measured point

7 % result is center point (yc,xc) and radius R

8 % an optional output is the vector of coeficient a

9 % describing the circle's equation

10 % xˆ2+yˆ2+a(1)*x+a(2)*y+a(3)=0

11 % By: Izhak bucher 25/oct /1991,

12 x=x(:); y=y(:);

13 a=[x y ones(size(x))]\(−(x.ˆ2+y.ˆ2));

14 xc = −.5*a(1);

15 yc = −.5*a(2);

16 R = sqrt((a(1)ˆ2+a(2)ˆ2)/4−a(3));

17 end

Listing B.4: The linear regression MATLAB script used in the linear extrapolation MATLAB script.

1 function [a1,a0] = linear regression(x,y)

2 n=length(x);

3 a1 = (n*sum(x.*y)−sum(x)*sum(y))/(n*sum(x.ˆ2)−(sum(x))ˆ2);

4 a0 = mean(y)−a1*mean(x);

5 end

B.4 Practical example of the post-processing method

To give the reader a more practical insight in the procedure, the sequence of operating steps

is explained in this section. The first step in the procedure is to save all the image files corre-

B.4 Practical example of the post-processing method 152

sponding with every single experiment in the folder ‘beelden’. The recorded file is normally a

PCORAW file. The file is opened in this pco.camware software and via the tab File the option

‘Export Recorder Sequence (not re-loadable)’ is chosen. Now a sequence of frames can be se-

lected that will be exported to a specified folder on your PC. As already mentioned the folder

‘beelden’ was created within the experiment subfolder. The file format of the exported images is

.bmp, which is a bitmap image file, but also .jpg is a possible format (in that case line 41 in the

image processing script needs to be changed to ‘filename.jpg’). If all images are exported to the

‘beelden’ folders, the specific variables corresponding to the image file (framerate and calibra-

tionfactor) need to be introduced in the MATLAB file ‘imageprocessing’. When all this is done

it is important to check if the main directory that will be accessed is correct. The right directory

must also be introduced in the MATLAB script. After this the ‘imageprocessing’ script can be

started. The script returns for each experiment an Excel-file in which the time step combined

with the radius is given. Besides this also the stretch rate and flame speed are given to check the

correctness of the results. The next operation is the execution of the ‘Linear Extrapolation.m’

script. This script requires as an input the xls-file. The process described above can now be

repeated for every single series of measurements (for every main folder of experiments).

PRESSURE BASED POST-PROCESSING: MATLAB SCRIPT 153

Appendix C

Pressure based post-processing:

MATLAB script

The pressure based post-processing script is given below. It was not used extensive during this

work, only for a single experiment the script provided good results. In future work it might be

interesting to use this script to check the validity of the image processed results. A possible way

of doing this is by integrating the code below in the image processing script.

Listing C.1: The pressure based post-processing MATLAB script.

1 disp('**Two zone model**')

2 display(' ')

3 clear all

4 close all

5 %% VARIABLES

6 framerate = 10000;%frames per seconde

7 Pi = 5; %startdruk

8 Ti = 300; %starttemperatuur

9 Pe = 20.7105; %einddruk

10 % give region of interest in pressure data

11 start = 50;

12 eind = 40000;

13 time(1,1) = 50;

14 bereik = 'B50:B39999'; %eind min 1 nemen als rij

15 %% CONSTANTS

PRESSURE BASED POST-PROCESSING: MATLAB SCRIPT 154

16 gamma = 1.401;

17 rbomb = (3.945833*10ˆ6*0.75*(1/3.1415))ˆ(1/3); %% in mm

18 %% INITIALIZING

19 timestep = 1/framerate*1000;

20 p = xlsread('testje.xlsx',1,bereik);

21 for j = 1:eind−start

22 step(j,1) = j;

23 end

24 for j=2:eind−start

25 time(j,1) = time(j−1,1)+timestep;

26 end

27 %% linear filtering data (fit along data points)

28 [pc, gof] = fit(step, p,'poly3');

29 for j=1:eind−start

30 pn(j,1) = pc(j)+Pi;

31 Tu(j,1) = Ti * (pn(j,1)/Pi)ˆ((gamma−1)/gamma);

32 rb(j,1) = rbomb*(1−((Pi/pn(j,1))*(Tu(j,1)/Ti)*((Pe−pn(j,1))/(Pe−Pi))))ˆ(1/3);

33 ri(j,1) = rbomb*((pn(j,1)−Pi)/(Pe−Pi))ˆ(1/3);

34 end

35 teller = 1;

36 for j=10:eind−start−10

37 [a1,a0] = linear regression(time(j−2:j+2,1),ri(j−2:j+2,1));

38 un(teller,1) = a1*((ri(j,1)/rb(j,1))ˆ2)*(Pi/pn(j,1))ˆ(1/gamma);

39 teller = teller+1;

40 end

41 plot(step,pn)

42 hold on

43 plot(step,p+Pi)

The result from this script is the list of Su values. These values can be used for extrapolation

to zero stretch when they are combined with stretch rate values by differentiating ri.

DATASHEETS AND EQUIPMENT INFORMATION 155

Appendix D

Datasheets and equipment

information

D.1 Gases

Synthetic air and methane were used during this work, the datasheets provided by the manu-

facturer are given below.

Figure D.1: Synthetic air

D.2 pco.dimax camera 156

Figure D.2: Methane

D.2 pco.dimax camera

The pco.dimax gives us the possibility to capture images with a very high frame rate. In table

D.3 an overview of the possibilities is given.

For configuration of the high speed camera, two different options can be chosen: ‘ring buffer’

and ‘sequence’. The difference is that ‘ring buffer’ continuously captures images at a fixed

frame rate. After a certain delay, when a trigger is received from the LabVIEW program, the

camera stops capturing and the recording can be saved. This configuration was used for the first

measurement series on methane/air mixtures. But when the ring buffer configuration is used, a

problem occurs with the synchronization of the LED pulses and the exposure timing. Only the

trigger is synchronized; if the frame rate of the camera and the frequency of the LED pulses are

not exactly the same, problems occur in the recording. Therefore the configuration was changed

- after this first series of measurements - to ‘sequence’, which solves the recording problem:

each exposure is now synchronized with one LED pulse. Before starting measurements, certain

adaptations of the camera settings have to be made. Concerning the hardware, the BNC cable

has to be connected to ‘Exp. Trg.’ instead of ‘Acq. Enbl.’ Regarding the software, when clicking

‘Camera Control’, in the Timing tab one has to make sure that Trigger mode is set to Ext. Exp.

Start, Camera sync is turned off and FPS based is unchecked. Furthermore, Exposure has to be

D.2 pco.dimax camera 157

matched with the LabVIEW frame rate. In the tab Sensor (size), the Region of Interest (ROI)

depends on the chosen frame rate. One can check the frame rate limit for each possible ROI

in the table D.3. To achieve a frame rate of 10 kHz a resolution reduction to approximately

620x620 pixels is needed. The current maximum frame rate can be checked in the CamWare

software by clicking twice in the bottom information box. Then, when clicking the Recording

tab, Recorder mode is set to ‘Sequence’, Acquire mode to ‘Auto’, Sequence Trigger mode to

‘Software event’ and Delay to zero. Finally, in the tab I/O signals, Acquire Enable has to be

unchecked and Exposure Trigger checked with the following specs: TTL, off, rising. The high

speed camera is now fully ready for capturing qualitative images of flame propagation.

Figure D.3: Overview of the different possible resolutions combined with their highest possible frame rates.

D.3 Ignition coil 158

D.3 Ignition coil

Figure D.4: The ignition coil type is the P35-E/P35-TE from the manufacturer BOSCH. Some general data

are given above.

D.3 Ignition coil 159

Figure D.5: Dwell time as a function of primary current and battery voltage are represented in the upper

picture, spark characteristics and high voltage are represented in the lower picture.

DETERMINATION OF THE φ-VALUE OF A MIXTURE IN THE GUCCI 160

Appendix E

Determination of the φ-value of a

mixture in the GUCCI

E.1 Gaseous fuel: methane

The theoretical partial pressures for a stoichiometric methane-air mixture with a starting pres-

sure and temperature are calculated using a self-written MATLAB procedure. As in this work

a synthetic air mixture was used (the only components are oxygen and nitrogen), the real air-

to-fuel ratio was transformed into an oxygen-to-air ratio. By this we could calculate the exact

amount of synthetic air that needed to be introduced.

Listing E.1: MATLAB script for partial pressure calculations.

1 %% VARIABLES−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

2 Tu = 273+25; % [K], initial GUCCI temperature

3 P = 1; % [bar], initial pressure GUCCI

4 phi = 1.0; % equivalence ratio

5 AFR = 17.2; % AFR stoichiometric

6 Mfuel = 12.011+1.008*4; % [g/mol], molaire massa fuel

7 %% CONSTANTS−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

8 R = 8.3144621; % [J/mol*K], universele gasconstante

9 Mair = 28.97; % [g/mol], molaire massa air

10 V = 4.057 *10ˆ−3 ; % volume kamer (nog nauwkeuriger bepalen)

11 %% CALCULATION−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

12 n = P * 100000 * V/(R * Tu);

E.1 Gaseous fuel: methane 161

13 AFRreal = 1/(phi * (1/AFR ));

14 Nfuel = 1000/Mfuel; % calculate number of moles fuel

15 OFR = AFRreal*23.2/100; % oxy/fuel ratio

16 Noxy = OFR*1000/16; % calculate number off moles oxygen

17 % Depending on the oxygen volume fraction in the air bottle

18 Nair = Noxy/0.209;

19 fracfuel = Nfuel/(Nair+Nfuel);

20 Pfuel = P*fracfuel

21 Pair = P*(1−fracfuel)

22 som = Pfuel + Pair %Total pressure control

23 flammability = fracfuel*100;%flammability limits check

When the filling procedure was completed the following MATLAB script was used to calculate

the ‘real’ equivalence ratio present inside the closed vessel.

Listing E.2: MATLAB script for calculation of the effectively present equivalence ratio.

1 %% VARIABLES ((methane)−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

2 Mair=28.836; %= 0.209 * 16 * 2 + 0.791 * 2 * 14

3 Mmethaan=16;

4 AFRmethaan=17.2;

5 %% INPUT: give the LABview cumulative partial pressures−−−−−−−−−−−−−−−−−−−−

6 a=0.2866;

7 b=0.5286;

8 c=2.533;

9 %% CALCULATION−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

10 pvac=a;

11 pcum methaan=b;

12 pcum air=c;

13 p=pcum air

14 %Partial pressures

15 pCH4=pcum methaan−pvac

16 pair = p−pCH4

17 %molar fraction methane

18 molfrac methaan=pCH4/p;

19 %air to fuel ratio

20 AFR=Mair*((1/molfrac methaan)−1)/Mmethaan;

21 %% EQUIVALENCE RATIO−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

22 phi=AFRmethaan/AFR

E.2 Liquid fuel: methanol, ethanol 162

E.2 Liquid fuel: methanol, ethanol

The chemical formula of methanol is CH3OH and its molecular weight is 32.042 g/mole. The

stoichiometric burning reaction is written in equation E.1.

CH3OH +3

2(O2 + 3, 76N2)→ CO2 + 2H2O +

3

23, 76N2 (E.1)

The reactant side comprises a total amount of moles of air and fuel of 1 + 32(1 + 3, 76) being

the sum of the coefficients of the reactants. The stoichiometric mole fraction of methanol is

determined as n% = 11+3/2(1+3.76) . The stoichiometric mole fraction of air then equals this value

subtracted from 1. From now on a general approach can be followed. By using only the reactant

coefficients, as illustrated above for the case of methanol, one can easily determine stoichiometric

mole fractions of fuel and air. By dividing the fraction of the fuel by the fraction of air, the

stoichiometric fuel-air ratio (FAR)st is obtained. The equivalence ratio is presented in equation

E.2.

φ =FAR

(FAR)st(E.2)

FAR is the actual fuel-air ratio, which is the ratio of the mole fraction of fuel and the mole

fraction of the oxidizer - air. Now it becomes relatively easy to derive the actual mole fraction

of fuel. This is done by solving equation E.2. Once the molar fuel fraction is known, the

partial pressure of the fuel is simply obtained by multiplying the molar fuel fraction by the total

chamber pressure. The partial fuel pressure is needed to do calculations of flammability and to

check the equivalence ratio after filling. The actual amount of moles of the fuel at injection is

logically obtained by multiplying the actual molar fuel fraction by the total amount of moles

in the bomb. The latter can be derived from the ideal gas law: n = pVRT . In this well-known

equation p is the chamber pressure, V is the volume of the chamber (taking into account the

fan and other irregularities), T the chamber temperature in Kelvin and R is the universal gas

constant, which is used with the appropriate units: R = 0.08314 m3∗barkMol∗K . Finally, the volume of

fuel that has to be injected at the desired conditions (p, T,φ) can be determined.

Vfuel =Mfuel

ρfuel(E.3)

with Mfuel the fuel mass and ρfuel the liquid fuel density in g/ml (for methanol this is equal

to 0.792 g/ml). To calculate the fuel mass, the molecular mass of the fuel (32.04 g/mole) is

multiplied by the amount of moles at injection, as calculated previously.


The stoichiometric air to fuel ratio is a characteristic of the fuel. To check the calculation, one

can compare this tabulated value with the following ratio:

AFR =Mair

Mfuel(E.4)

with Mair the mass of air in the bomb, which is determined by multiplying the molecular mass

of air (28.97 g/mole) by the amount of moles present in the bomb, which is equal to

nair = n− nfuel (E.5)

To be sure the right amount of fuel is present in the chamber, the chamber pressure values before

and after filling are compared. The difference between these two values is the actual filled partial

pressure and is of the order of 0.06-0.08 bar. By using a MATLAB code one calculates the partial

pressures back to φ and so there is a possible way of error estimation.

The following MATLAB code is the implementation of the discussion above.

Listing E.3: MATLAB script to calculate liquid fuel volume.

1 %% CONSTANTS−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

2 %atomic weights

3 C=12.011;

4 H=1.008;

5 O=15.9994;

6 %% VARIABLES−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

7 AFR=9; %stoichiometric air−to−fuel ratio

8 MW=2*C+6*H+O; %molecular weight

9 d=0.79; %liquid fuel density in g/ml (at room temperature)

10 phi=1; %equivalence ratio

11 p=1; %pressure in bar

12 T=273+110; %temperature in K

13 V=0.004057; %volume of bomb

14 R=0.08314; %gas constant

15 nbom=p*V/(R*T)*1000; %amount of moles in bomb

16 %Coefficients from burning reaction (reactants)

17 a=1;

18 b=3;

19 %% CALCULATION−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−


20 %total moles air and fuel

21 ntot=a+b*(1+3.76);

22 %mole fractions air and fuel (stoichiometric)

23 fuelfrac=a/ntot;

24 airfrac=1−fuelfrac;

25 %(nfuel/nair) stoichiometric

26 st ratio=fuelfrac/airfrac;

27 %REAL mole fraction fuel

28 real fuelfrac=phi*st ratio/(1+phi*st ratio);

29 %check voor phi=1

30 Mair=28.97*(nbom−n fuel);

31 check AFR=Mair/Mfuel;

32

33 %humidity calculations (optional, only if humidity is quite high)

34 Tout=273+20;%dry bulb temperature (K)

35 b=77.345+0.0057*Tout−7235/Tout;

36 pws=exp(b)/(Toutˆ8.2);%saturation pressure of the water vapor

37 Patm = 101325;

38 RH = 0.55;

39 Pvapour = pws * RH;

40 SH = 0.622*Pvapour/(Patm−0.378*Pvapour);

41 Mvapour = SH * Mair;

42 Mdry = Mair − Mvapour;

43 Pdry = Mdry*10ˆ−3*287.058*T/V/100000;

44 Fracdry = Pdry/p;

45 %partial pressure fuel

46 p fuel=real fuelfrac*Pdry;

47 p air=Pdry;

48 %moles of fuel at injection

49 n fuel=real fuelfrac*nbom*Fracdry;

50 %volume of fuel to inject

51 Mfuel=MW*n fuel;

52 Vfuel=Mfuel/d

CONSTANT VOLUME BOMB MEASUREMENTS 165

Appendix F

Constant volume bomb

measurements

file p [bar] φ φcorr ρu/ρb ul

[m/s]

Lb

[mm]

M2phi060e01 2.016 0.60 0.60 5.55 0.634 -0.71

M2phi065e02 2.027 0.65 0.63 5.85 0.109 -0.08

M2phi070e01 2.020 0.70 0.70 6.13 0.136 -0.41

M2phi070e02 1.977 0.70 0.72 6.13 0.134 0.00

M2phi070e03 2.083 0.70 0.70 6.13 0.138 0.18

M2phi070e04 2.072 0.70 0.71 6.13 0.134 -0.29

M2phi070e05 1.999 0.70 0.68 6.13 0.134 0.09

M2phi075e01 2.035 0.75 0.74 6.41 0.145 0.02

M2phi075e02 2.032 0.75 0.75 6.41 0.159 -0.31

M2phi075e03 2.044 0.75 0.74 6.41 0.204 -0.91

M2phi080e01 1.982 0.80 0.81 6.67 0.149 0.10

M2phi080e02 1.977 0.80 0.81 6.67 0.214 -0.01

M2phi080e03 1.977 0.80 0.79 6.67 0.173 -0.10

M2phi080e04 2.024 0.80 0.80 6.67 0.181 0.00

M2phi085e01 2.033 0.85 0.85 6.92 0.226 0.17

M2phi085e02 2.031 0.85 0.84 6.92 0.238 -0.30

M2phi085e03 2.055 0.85 0.86 6.92 0.243 -0.19

Table F.1: Laminar burning velocities [m/s] of methane-air flames at 2 bar performed with the GUCCI. (part

1)



[m/s]

Lb

[mm]

M2phi090e01 2.022 0.90 0.89 7.15 0.275 0.52

M2phi090e02 1.989 0.90 0.88 7.15 0.271 -0.09

M2phi090e03 1.971 0.90 0.91 7.15 0.229 -0.19

M2phi090e04 1.983 0.90 0.91 7.15 0.225 -0.12

M2phi090e05 1.977 0.90 0.88 7.15 0.289 -0.20

M2phi090e06 2.022 0.90 0.88 7.15 0.210 -0.01

M2phi090e07 2.026 0.90 0.90 7.15 0.213 0.02

M2phi090e08 2.043 0.90 0.92 7.15 0.242 -0.26

M2phi090e09 2.014 0.90 0.91 7.15 0.282 0.10

M2phi095e01 1.999 0.95 0.97 7.36 0.285 0.33

M2phi095e02 1.996 0.95 0.96 7.36 0.261 0.32

M2phi095e03 2.009 0.95 0.95 7.36 0.268 0.30

M2phi095e04 2.060 0.95 0.96 7.36 0.239 0.18

M2phi095e05 2.048 0.95 0.94 7.36 0.243 0.22

M2phi100e01 2.042 1.00 1.01 7.52 0.255 0.30

M2phi100e02 2.059 1.00 1.02 7.52 0.249 0.31

M2phi100e03 2.061 1.00 0.99 7.52 0.236 0.20

M2phi100e04 2.082 1.00 0.98 7.52 0.232 0.30

M2phi100e05 2.047 1.00 0.98 7.52 0.227 0.10

M2phi105e01 1.970 1.05 1.06 7.57 0.272 0.71

M2phi105e02 2.015 1.05 1.04 7.57 0.263 0.31

M2phi105e03 2.006 1.05 1.05 7.57 0.266 0.40

M2phi105e04 2.027 1.05 1.03 7.57 0.269 0.42

M2phi105e05 2.060 1.05 1.05 7.57 0.262 0.32

M2phi105e06 2.077 1.05 1.04 7.57 0.256 0.43

M2phi105e07 1.987 1.05 1.07 7.57 0.270 0.51

M2phi110e01 2.000 1.10 1.11 7.54 0.277 0.82

M2phi110e02 2.013 1.10 1.09 7.54 0.269 0.70

M2phi110e03 2.071 1.10 1.11 7.54 0.258 0.40

M2phi110e04 2.063 1.10 1.08 7.54 0.255 0.38

M2phi110e05 2.068 1.10 1.10 7.54 0.253 0.39

M2phi110e06 2.044 1.10 1.08 7.54 0.277 0.38

M2phi110e07 2.044 1.10 1.08 7.54 0.263 0.57

M2phi110e08 2.004 1.10 1.12 7.54 0.273 0.21


2)



[m/s]

Lb

[mm]

M2phi115e01 2.002 1.15 1.09 7.48 0.227 0.69

M2phi115e02 2.047 1.15 1.14 7.48 0.258 0.30

M2phi115e03 2.023 1.15 1.13 7.48 0.262 0.30

M2phi115e04 2.017 1.15 1.15 7.48 0.266 -0.02

M2phi115e05 1.981 1.15 1.14 7.48 0.237 0.59

M2phi120e01 2.017 1.20 1.20 7.40 0.213 1.19

M2phi120e02 2.013 1.20 1.18 7.40 0.244 -0.70

M2phi120e03 1.980 1.20 1.20 7.40 0.215 0.71

M2phi120e04 2.079 1.20 1.21 7.40 0.244 0.12

M2phi120e05 2.025 1.20 1.18 7.40 0.260 0.13

M2phi120e06 1.988 1.20 1.20 7.40 0.183 1.30

M2phi125e01 1.977 1.25 1.23 7.32 0.197 0.59

M2phi125e02 1.992 1.25 1.27 7.32 0.110 -0.39

M2phi125e03 2.036 1.25 1.23 7.32 0.174 0.78

M2phi130e01 2.000 1.30 1.31 7.25 0.099 1.40

M2phi130e02 1.980 1.30 1.27 7.25 0.241 0.70

M2phi130e03 1.999 1.30 1.31 7.25 0.180 1.02


3)


[m/s]

Lb

[mm]

M4phi080e01 4.187 0.80 0.82 6.72 0.129 -0.09

M4phi090e01 4.216 0.90 0.91 7.22 0.171 -0.01

M4phi100e01 4.205 1.00 1.03 7.55 0.195 -0.52

M4phi110e01 4.200 1.10 1.13 7.55 0.194 0.32

M4phi130e01 4.189 1.30 1.29 7.29 0.122 0.51

M4phi130e02 4.160 1.30 1.32 7.29 0.105 1.30

Table F.4: Laminar burning velocities [m/s] of methane-air flames at 4 bar performed with the GUCCI.


file p [bar] φ φcorrρuρb

ul

[m/s]

Lb

[mm]

M5phi070e01 4.993 0.70 0.69 6.13 0.037 0.00

M5phi070e02 5.016 0.70 0.71 6.13 0.055 -1.41

M5phi070e03 5.000 0.70 0.68 6.13 0.062 -1.47

M5phi070e04 4.997 0.70 0.70 6.13 0.076 -0.21

M5phi070e05 5.016 0.70 0.70 6.13 0.066 -0.29

M5phi070e06 4.965 0.70 0.71 6.13 0.072 -0.30

M5phi075e01 4.979 0.75 0.76 6.41 0.101 0.11

M5phi075e02 4.951 0.75 0.76 6.41 0.107 -0.09

M5phi075e03 4.968 0.75 0.76 6.41 0.079 -0.51

M5phi080e01 4.985 0.80 0.79 6.68 0.106 -0.10

M5phi080e02 5.002 0.80 0.82 6.68 0.117 -0.11

M5phi080e03 4.994 0.80 0.79 6.68 0.119 -0.32

M5phi080e04 4.975 0.80 0.82 6.68 0.127 -0.09

M5phi080e05 5.012 0.80 0.81 6.68 0.100 -0.03

M5phi085e01 5.014 0.85 0.87 6.93 0.121 0.19

M5phi085e02 5.014 0.85 0.87 6.93 0.129 0.00

M5phi085e03 5.007 0.85 0.83 6.93 0.118 0.01

M5phi090e01 5.016 0.90 0.91 7.17 0.151 -0.11

M5phi090e02 5.029 0.90 0.90 7.17 0.126 0.21

M5phi090e03 4.987 0.90 0.91 7.17 0.162 0.09

M5phi095e01 5.014 0.95 0.94 7.40 0.161 -0.10

M5phi095e02 5.031 0.95 0.93 7.40 0.150 0.02

M5phi095e03 4.998 0.95 0.97 7.40 0.182 0.11

M5phi100e01 4.981 1.00 1.00 7.56 0.192 0.20

M5phi100e02 4.983 1.00 1.01 7.56 0.196 0.31

M5phi100e03 4.997 1.00 1.01 7.56 0.190 0.20

M5phi100e04 5.039 1.00 1.03 7.56 0.172 -0.58

M5phi100e05 5.024 1.00 1.00 7.56 0.182 -0.02

M5phi100e06 5.016 1.00 1.02 7.56 0.167 -0.78

M5phi100e07 4.999 1.00 0.99 7.56 0.169 -0.22

M5phi105e01 4.981 1.05 1.04 7.61 0.200 0.18

M5phi105e02 5.067 1.05 1.06 7.61 0.188 0.10

M5phi105e03 5.105 1.05 1.06 7.61 0.184 -0.18

M5phi105e04 5.102 1.05 1.05 7.61 0.188 0.19


1)



[m/s]

Lb

[mm]

M5phi110e01 5.019 1.10 1.09 7.56 0.189 0.20

M5phi110e02 4.968 1.10 1.09 7.56 0.168 -0.39

M5phi110e03 5.052 1.10 1.10 7.56 0.180 -0.32

M5phi110e04 5.054 1.10 1.12 7.56 0.179 -0.40

M5phi110e05 5.035 1.10 1.12 7.56 0.173 0.00

M5phi115e01 4.995 1.15 1.14 7.49 0.189 0.21

M5phi115e02 5.007 1.15 1.14 7.49 0.189 0.11

M5phi115e03 5.048 1.15 1.13 7.49 0.191 0.20

M5phi120e01 4.970 1.20 1.18 7.41 0.136 0.39

M5phi120e02 5.065 1.20 1.18 7.41 0.188 0.11

M5phi120e03 5.048 1.20 1.20 7.41 0.158 0.26

M5phi120e04 5.065 1.20 1.19 7.41 0.176 0.10

M5phi120e05 5.055 1.20 1.19 7.41 0.174 0.22

M5phi125e01 4.994 1.25 1.23 7.33 0.146 0.11

M5phi125e02 4.990 1.25 1.27 7.33 0.153 0.22

M5phi125e03 4.983 1.25 1.24 7.33 0.146 0.38

M5phi125e04 5.004 1.25 1.27 7.33 0.135 0.20

M5phi125e05 4.999 1.25 1.25 7.33 0.151 0.29

M5phi125e06 5.019 1.25 1.25 7.33 0.145 0.19

M5phi130e01 5.007 1.30 1.29 7.25 0.159 0.00

M5phi130e02 4.994 1.30 1.29 7.25 0.152 0.30

M5phi130e03 5.002 1.30 1.28 7.25 0.130 0.43

M5phi130e04 5.022 1.30 1.31 7.25 0.130 0.32


2)



[m/s]

Lb

[mm]

M10phi070e01 9.993 0.70 0.71 6.13 0.288 -1.89

M10phi070e02 10.007 0.70 0.71 6.13 0.025 -3.50

M10phi070e03 9.988 0.70 0.71 6.13 0.038 -0.81

M10phi070e04 10.013 0.70 0.72 6.13 0.028 -0.69

M10phi075e01 9.902 0.75 0.75 6.41 0.064 -1.50

M10phi075e02 10.024 0.75 0.76 6.41 0.063 -1.19

M10phi075e03 10.030 0.75 0.74 6.41 0.051 -1.18

M10phi080e01 9.968 0.80 0.82 6.68 0.088 -0.11

M10phi080e02 9.935 0.80 0.83 6.68 0.086 -0.51

M10phi080e03 9.986 0.80 0.81 6.68 0.081 -0.49

M10phi080e04 9.908 0.80 0.81 6.68 0.090 -0.49

M10phi080e05 9.923 0.80 0.81 6.68 0.088 -0.01

M10phi080e06 9.992 0.80 0.80 6.68 0.085 -0.33

M10phi085e01 10.017 0.85 0.85 6.94 0.099 -0.69

M10phi085e02 9.969 0.85 0.87 6.94 0.106 -0.41

M10phi085e03 9.968 0.85 0.87 6.94 0.105 -0.49

M10phi090e01 10.033 0.90 0.90 7.19 0.124 -0.30

M10phi090e02 10.054 0.90 0.93 7.19 0.124 0.49

M10phi090e03 10.046 0.90 0.93 7.19 0.124 -0.19

M10phi090e04 10.045 0.90 0.92 7.19 0.124 -0.22

M10phi090e05 10.095 0.90 0.91 7.19 0.124 -0.21

M10phi090e06 9.985 0.90 0.88 7.19 0.120 -0.21

M10phi090e07 10.039 0.90 0.91 7.19 0.121 -0.21

M10phi095e01 10.148 0.95 0.96 7.42 0.133 -0.39

M10phi095e02 10.061 0.95 0.94 7.42 0.135 -0.78

M10phi095e03 10.059 0.95 0.94 7.42 0.127 0.00

M10phi100e01 10.177 1.00 1.01 7.59 0.140 0.20

M10phi100e02 10.111 1.00 1.02 7.59 0.154 -0.17

M10phi100e03 10.132 1.00 1.04 7.59 0.159 0.59

M10phi100e04 10.158 1.00 0.98 7.59 0.150 0.41

M10phi100e06 10.019 1.00 1.01 7.59 0.146 0.00

M10phi100e07 10.006 1.00 1.01 7.59 0.145 0.27

M10phi100e08 9.990 1.00 0.99 7.59 0.143 0.10


1)



[m/s]

Lb

[mm]

M10phi105e01 10.016 1.05 1.06 7.63 0.155 0.09

M10phi105e02 9.965 1.05 1.06 7.63 0.152 0.01

M10phi105e03 9.979 1.05 1.04 7.63 0.160 0.32

M10phi105e04 10.096 1.05 1.05 7.63 0.146 0.11

M10phi110e01 10.085 1.10 1.13 7.57 0.142 -0.09

M10phi110e02 10.073 1.10 1.11 7.57 0.149 0.03

M10phi110e03 10.078 1.10 1.09 7.57 0.144 0.02

M10phi110e04 10.036 1.10 1.11 7.57 0.150 -0.22

M10phi110e05 9.984 1.10 1.08 7.57 0.154 0.00

M10phi115e01 10.001 1.15 1.16 7.49 0.132 -0.08

M10phi115e02 10.039 1.15 1.14 7.49 0.141 0.19

M10phi115e03 10.035 1.15 1.16 7.49 0.143 0.21

M10phi120e01 9.980 1.20 1.23 7.41 0.062 -0.40

M10phi120e02 10.003 1.20 1.20 7.41 0.108 0.02

M10phi120e03 9.972 1.20 1.22 7.41 0.123 0.01

M10phi120e04 10.049 1.20 1.19 7.41 0.119 -0.49

M10phi130e01 10.071 1.30 1.28 7.33 0.132 0.03

M10phi130e02 10.011 1.30 1.31 7.33 0.075 0.22

M10phi130e03 10.000 1.30 1.29 7.33 0.061 0.00


2)


[m/s]

Lb

[mm]

M15phi085e01 15.125 0.85 0.86 6.94 0.102 -0.52

M15phi085e02 15.0318 0.85 0.84 6.94 0.072 -0.29

M15phi085e03 15.0109 0.85 0.84 6.94 0.071 -0.90

M15phi090e01 15.0893 0.90 0.89 7.19 0.121 -0.02

M15phi090e02 14.8749 0.90 0.90 7.19 0.106 0.48

Table F.9: Laminar burning velocities [m/s] of methane-air flames at 15 bar performed with the GUCCI.



[m/s]

Lb

[mm]

E1phi090e01 1.000 0.90 0.89 7.14 0.450 0.79

E1phi100e01 1.022 1.00 1.01 7.46 0.362 1.72

1phi100e02 1.034 1.00 1.02 7.46 0.522 1.80

E1phi100e03 1.011 1.00 1.00 7.46 0.411 1.03

E1phi110e01 1.025 1.10 1.12 7.58 0.410 1.13

Table F.10: Laminar burning velocities [m/s] of ethanol-air flames at 1 bar performed with the GUCCI.


Filetype Mean LBV Stdv. LBV Mean φ stdv. φ Stdv. LBV [%] Stdv. LBV [%]* Stdv.φ [%]

M2phi070 13.54 0.12 0.70 0.0129 0.92 0.47 1.84

M2phi075 15.08 0.59 0.74 0.0036 3.89 2.21 0.48

M2phi080 19.29 1.68 0.80 0.0062 8.69 6.31 0.77

M2phi085 23.57 0.70 0.85 0.0082 2.99 2.65 0.96

M2phi090 24.85 2.93 0.90 0.0138 11.78 11.02 1.53

M2phi095 25.95 1.67 0.96 0.0089 6.44 6.29 0.93

M2phi100 23.97 1.06 1.00 0.0173 4.42 3.99 1.74

M2phi105 26.54 0.50 1.05 0.0103 1.88 1.88 0.98

M2phi110 26.56 0.92 1.10 0.0155 3.47 3.47 1.42

M2phi115 24.99 1.52 1.13 0.0192 6.09 5.73 1.70

M2phi120 22.68 2.56 1.20 0.0118 11.29 9.64 0.98

M2phi125 16.03 3.70 1.24 0.0192 23.07 13.92 1.54

M2phi130 17.32 5.84 1.30 0.0205 33.70 21.98 1.58

M5phi070 6.11 1.28 0.70 0.0117 21.00 6.73 1.67

M5phi075 9.57 1.20 0.76 0.0029 12.50 6.28 0.39

M5phi080 11.37 0.96 0.81 0.0132 8.46 5.04 1.63

M5phi085 12.26 0.44 0.86 0.0165 3.60 2.32 1.92

M5phi090 14.63 1.50 0.91 0.0068 10.24 7.85 0.75

M5phi095 16.43 1.29 0.95 0.0190 7.88 6.79 2.00

M5phi100 18.10 1.09 1.01 0.0119 6.04 5.73 1.18

M5phi105 19.07 0.69 1.05 0.0113 3.63 3.63 1.07

M5phi110 17.80 0.71 1.10 0.0136 4.00 3.73 1.23

M5phi115 18.99 0.09 1.14 0.0032 0.48 0.48 0.28

M5phi120 16.63 1.78 1.19 0.0082 10.68 9.31 0.69

M5phi125 14.61 0.57 1.25 0.0149 3.89 2.98 1.19

M5phi130 14.30 1.30 1.29 0.0117 9.12 6.84 0.90

M10phi070 3.00 0.47 0.71 0.0052 15.82 3.09 0.73

M10phi075 5.90 0.59 0.75 0.0070 9.99 3.84 0.93

M10phi080 8.64 0.30 0.81 0.0085 3.51 1.97 1.05

M10phi085 10.32 0.33 0.86 0.0089 3.17 2.13 1.03

M10phi090 12.29 0.17 0.91 0.0162 1.42 1.14 1.77

M10phi095 13.16 0.32 0.95 0.0082 2.45 2.10 0.86

M10phi100 14.80 0.62 1.01 0.0177 4.16 4.02 1.76

M10phi105 15.34 0.50 1.05 0.0086 3.28 3.28 0.81

M10phi110 14.79 0.43 1.10 0.0177 2.91 2.81 1.61

M10phi115 13.88 0.46 1.15 0.0080 3.34 3.03 0.69

M10phi120 12.07 0.88 1.21 0.0126 7.27 5.72 1.04

M10phi130 6.62 0.63 1.29 0.0090 9.48 4.09 0.70

Table F.11: Overview of the absolute and relative standard deviations on φ and LBV, ul [ cms

]. *The values

are scaled with the biggest LBV value, this gives a more normalized scaling which is better for a

comparative study.


Ф= 0

.7Ф

= 0.8

Ф = 0

.9Ф

= 1.0

Ф = 1

.1Ф

= 1.2

Ф = 1

.3

2 b

ar

ФU

l

[cm/s]

Lb

[mm

]

0.7

13

.50

.18

0.8

19

.30

.10

0.9

24

.90

.52

1.0

24

.00

.30

1.1

26

.60

.57

1.2

22

.70

.71

1.3

17

.31

.40


Ф = 0

.7Ф

= 0.8

Ф = 0

.9Ф

= 1.0

Ф = 1

.1Ф

= 1.2

Ф = 1

.3

5b

ar

ФU

l

[cm/s]

Lb

[mm

]

0.7

6.1

-0.2

1

0.8

11

.4-0

.09

0.9

14

.60

.09

1.0

18

.10

.31

1.1

17

.80

.20

1.2

16

.60

.10

1.3

14

.30

.43


Ф = 0

.7Ф

= 0.8

Ф = 0

.9Ф

= 1.0

Ф = 1

.1Ф

= 1.2

Ф = 1

.3

10

bar

ФU

l

[cm/s]

Lb

[mm

]

0.7

3.0

-1.8

9

0.8

8.6

-0.0

1

0.9

12

.3-0

.21

1.0

14

.80

.00

1.1

14

.80

.03

1.2

12

.10

.02

1.3

6.6

0.2

2

BIBLIOGRAPHY 177

Bibliography

[1] R.A. Stein, J.E. Anderson, and T.J. Wallington. An overview of the effects of ethanol-

gasoline blends on si engine performance, fuel efficiency, and emissions. SAE International,

2013.

[2] R. Pearson and J. Turner. Renewable fuels - an automotive perspective, volume Compre-

hensive Renewable Energy. Elsevier, Amsterdam, 2012.

[3] J. Vancoillie. Modeling the combustion of light alcohols in spark-ignition engines. Ph.d.

thesis, Ghent University, 2013.

[4] J. Vancoillie, S. Verhelst, and Demuynck J. Laminar burning velocity correlations for

methanol-air and ethanol-air mixtures valid at si engine conditions. SAE International,

2011.

[5] D. Bradley, R. A. Hicks, M. Lawes, C. G. W. Sheppard, and R. Woolley. The measurement

of laminar burning velocitie and markstein numbers for iso-octane-air and iso-octane-n-

heptane-air mixtures at elevated temperatures and pressures in an explosion bomb. Com-

bustion and Flame, 115(1):126–144, 1998.

[6] D. Bradley, P. H. Gaskell, and X. J. Gu. Burning velocities, markstein lenghths, and flame

quenching for spherical methane-air flames: a computational study. Combustion and Flame,

104(1):176–198, 1996.

[7] S Verhelst. A study of the combustion in hydrogen-fuelled internal combustion engines.

Ph.d. thesis, Ghent University, 2005.

[8] O.C. Kwon, G. Rozenchan, and C.K. Law. Cellular instabilities and self-acceleration of

outwardly propagating spherical flames. Proceedings of the combustion institute, 29(2):

1775–1783, 2002.

BIBLIOGRAPHY 178

[9] B.E. Gelfand, M.V. Silnikov, S.P. Medvedev, and S.V. Khomik. Thermo-gas dynamics of

hydrogen combustion and explosion. Springer, 2012.

[10] M. Matalon and J.K. Bechtold. A multi-scale approach to the propagation of non-adiabatic

premixed flames. Journal of engineering mathematics, 63:309–326, 2009.

[11] J.B. Heywood, editor. Internal combustion engine fundamentals. McGraw-Hill, inc., Sloan,

1998.

[12] B. Merci. Course on modelling of turbulence and combustion. 2013.

[13] N. Peters. Turbulent combustion. Cambridge University Press, 2000.

[14] N. Peters. Laminar flamelet concepts in turbulent combustion. Twenty-first symposium

(International) on Combustion, 21:1231–1250, 1988.

[15] G. Andrews and D. Bradley. Determination of burning velocities: A critical review. Com-

bustion and Flame, 18(1):133–153, 1972.

[16] D. Bradley, M. Lawes, and M. S. Mansour. Explosion bomb measurements of ethanol-air

laminar gaseous flame characteristics at pressures up to 1.4 mpa. Combustion and Flame,

156:1462–1470, 2009.

[17] D. Bradley, M. Lawes, Kexin L., and M.S. Mansour. Measurements and correlations of

turbulent burning velocities over wide ranges of fuels and elevated pressures. Proceedings

of the combustion institute, 34:1519–1526, 2013.

[18] S.A. Sulaiman and M. Lawes. High-speed schlieren imaging and post-processing for inves-

tigation of flame propagation within droplet-vapour-air fuel mixtures. The institution of

Engineers, Malaysia, 69(1), 2008.

[19] A.E. Dahoe and L.P.H. de Goey. On the determination of the laminar burning velocity

from closed vessel gas explosions. Journal of loss prevention in the process industries, 16:

457–478, 2013.

[20] A.P. Kelley and C.K. Law. Nonlinear effects in the extraction of laminar flame speeds from

expanding spherical flames. Combustion and Flame, 156:1844–1851, 2009.

BIBLIOGRAPHY 179

[21] Z. Chen, P. Burke, and Y. Ju. Effects of compression and stretch on the determination of

laminar flame speed using propagating spherical flames. Combustion Theory and modelling,

13:343–364, 2009.

[22] T. Tahtouh, F. Halter, and C. Mounaim-Rousselle. Measurement of laminar burning speeds

and markstein lengths using a novel methodology. Combustion and Flame, 156:1735–1743,

2009.

[23] Z. Zhang, Z. Huang, X. Wang, J. Xiang, and H. Miao. Measurements of laminar burning

velocity and markstein lengths for methanol-air-nitrogen mixtures at elevated pressures and

temperatures. Combustion and Flame, 155(3):358–368, 2008.

[24] J. Beeckmann, O. Rohl, and Peters N. Experimental and numerical investigation of iso-

octane, methanol and ethanol regarding laminar burning velocity at elevated pressure and

temperature. SAE international, 2009.

[25] P. S. Veloo, R. J. Wang, F. N. Egolfopoulos, and C. K. Westbrook. A comparative exper-

imental and computational study of methanol, ethanol and n-butanol flames. Combustion

and Flame, 33(1):1989–2004, 2010.

[26] J. Vancoillie, M. Christensen, E.J.K. Nilsson, S. Verhelst, and A.A. Konnov. The effects

of dilution with nitrogen and steam on the laminar burning velocity of methanol at room

and elevated temperatures. Fuel, 105:732–738, 2013.

[27] M. Goswami, S.C.R. Derks, K. Coumans, W.J. Slikker, M.H.A. Oliveira, R.J.M. Bastiaans,

C.C.M. Luijten, L.P.H. de Goey, and A.A. Konnov. The effect of elevated pressures on the

laminar burning velocity of methane + air mixtures. Fuel, 160:1627–1635, 2013.

[28] L. Sileghem, V.A. Alekseef, J. Vancoillie, E.J.K. Nilsson, Verhelst S., and A.A. Konnov.

Laminar burning velocities of primary reference fuels and simple alcohols. Fuel, 115:32–40,

2014.

[29] J. Beeckmann, L. Cai, and H. Pitsch. Experimental investigation of the laminar burning

velocities of methanol, ethanol, n-propanol, and n-butanol at high pressure. Fuel, 117:

340–350, 2014.

[30] J. Vancoillie, G. Sharpe, M. Lawes, and S. Verhelst. Laminar burning velocities and mark-

stein lengths of methanol-air mixtures at pressures up to 1.0 mpa.

BIBLIOGRAPHY 180

[31] P. Dirrenberger, P.A. Glaude, R. Bounaceur, H. Le Gall, A. Pires da Cruz, A.A. Konnov,

and F. Battin-Leclerc. Laminar burning velocity of gasolines with addition of ethanol. Fuel,

115:162–169, 2014.

[32] B. Galmiche, F. Halter, and F. Foucher. Combustion and Flame, 159:3286–3299, 2012.

[33] O.L. Gulder. Nineteenth symposium on combustion. The Combustion Institute, 1982.

[34] F.N. Egolfopoulos, D.X. Du, and C.K. Law. A comprehensive study of methanol kinetics in

freely-propagating and burner-stabilized flames, flow and static reactors, and shock tubes.

Combustion Science and Technology, pages 33–75, 1992.

[35] S.Y. Liao, D. M. Jiang, Zeng K. Huang Z. H., and Q. Cheng. Applications of thermal

engineering 27. 2007.

[36] A.A. Konnov, R.J. Meuwissen, and L.P.H. de Goey. The temperature dependence of the

laminar burning velocity of ethanol flames. 2011.

[37] J. Li, W. Zhao, A. Kazakov, M. Chaos, F.L. Dryer, and Scire J.J. A comprehensive kinetic

mechanism for co, ch2o, and ch3oh combustion. International Journal of Chemical Kinetics,

39(1):109–136, 2007.

[38] A.A. Konnov. The effect of temperature on the adiabatic laminar burning velocities of

ch4-air and h2-air flames. Fuel, 89, 2010.

[39] A.A. Konnov. Implementation of the ncn pathway of prompt-no formation in the detailed

reaction mechanism. Combustion and Flame, 156(11):2093–2105, 2009.

[40] J. Vancoillie, M. Christensen, E.J.K. Nilsson, S. Verhelst, and A.A. Konnov. Temperature

dependence of the laminar burning velocity of methanol flames. Energy fuels, 26, 2012.

[41] M. Metghalchi and J.C. Keck. Burning velocities of mixtures of air with methanol, isooc-

tane, and indolene at high pressure and temperature. Combustion and Flame, 48:191–210,

1982.

[42] S. Verhelst, C. T’Joen, J. Vancoillie, and Demuynck J. A correlation for the laminar burning

velocity for use in hydrogen spark ignition engine simulation. International Journal of

Hydrogen energy, 36(1):957–974, 2010.

BIBLIOGRAPHY 181

[43] P. Logghe and W. Roose. Flowbench- en vlamsnelheidsmetingen als input voor simulaties

van vonkontstekingsmotoren. Master thesis, Ghent University, 2012.

[44] J Van Thillo. Metingen van de laminaire verbrandingssnelheid van brandstofarme en ver-

dunde methaan-lucht mengsels met behulp van de ehpc. Master thesis, Eindhoven: Tech-

nische universiteit, 2008.

[45] J. Galle and M. Lagast. Design of the gucci-setup and study of the use of alternative fuels.

2009.

[46] A.F. Ibarreta, C. Sung, T. Hirasawa, and H. Wang. Burning velocity measurements of mi-

crogravity spherical sooting premixed flames using rainbow schlieren deflectometry. Com-

bust. and Flame, 2005.

[47] C.J. Rallis and A.M. Garforth. The determination of laminar burning velocity. 1980.

[48] Elbe and Lewis. Combustion, flames and explosions of gases. 3. sub edition. ED: Academic

Press; 1987:739.

[49] M.I. Hassan, K.T. Aung, and G.M. Faeth. Measured and predicted properties of laminar

premixed methane/air flames at various pressures. Combustion and Flame, 115:539–550,

1998.

[50] X. J. Gu, M. Z. Haq, M. Lawes, and R. Woolley. Laminar burning velocity and markstein

lengths of methane-air mixtures. Combustion and Flame, 121:41–58, 2000.

[51] G. Rozenchan, D. L. Zhu, C. K. Law, and Tse S. D. Outward propagation, burning velocities

and chemical effects of methane flames up to 60 atm. Proceedings of the combustion institute,

29:1461–1469, 2002.

[52] O. Park, P.S. Veloo, N. Liu, and F.N. Egolfopoulos. Combustion characteristics of alterna-

tive gaseous fuels. Proceedings of the Combustion Institute, 33:887–894, 2011.

[53] F.N. Egolfopoulos, D.X. Du, and C.K. Law. A study on ethanol oxidation kinetics in

laminar premixed flames, flow reactors, and shock tubes. Symposium (International) on

Combustion, 24(1):833–841, 1992.

[54] C.K. Westbrook and F.L. Dryer. Prediction of laminar flame properties of methanol-air

mixtures. Combust. flame, 37:171–192, 1980.

BIBLIOGRAPHY 182

[55] M.V. Petrova and F.A. Williams. A small detailed chemical-kinetic mechanism for hydro-

carbon combustion. Combustion and Flame, 144(3):526–544, 2006.

[56] P. Saxena and F.A. Williams. Numerical and experimental studies of ethanol flames. Pro-

ceedings of the Combustion Institute, 31:1149–1156, 2007.

[57] Sileghem L., V.A. Alekseev, J. Vancoillie, K.M. Van Geem, E.J.K. Nilsson, and S. Verhelst.

Laminar burning velocity of gasoline and the gasoline surrogate components iso-octane,

n-heptane and toluene. Fuel, 112:355–365, 2013.

Laminar burning velocity measurements using the GUCCIsetup

J. Bauwens, L. BuffelGhent University, Ghent

ABSTRACT

The GUCCI (Ghent University Combustion Chamber I)has been validated. This was done by laminar burningvelocity measurements on methane-air mixtures, whichwere compared with data from literature. Measurementswere done for an equivalence ratio range between 0.7and 1.3 and an unburned mixture temperature of 298K (ambient temperature). A linear extrapolation methodwas followed in order to obtain the LBV values. Pres-sures varied from 2 to 15 bar. It was initially intendedto also perform measurements of laminar burning velocityof gaseous methanol-air flames after validating the exper-imental setup. Due to practical problems it was not pos-sible to perform these measurements. From a survey ofpublished literature a lack of these data became apparent,especially at engine-like conditions. However, recent workhas been done for methanol-air mixtures using the spher-ically expanding flame technique by Vancoillie et al. [1]at elevated pressures and temperatures. In future work,these data can be used as a validation.

INTRODUCTION

Today, gasoline is widely used as a fuel for spark-ignitionengines. However, current fossil energy sources arerapidly decreasing and have an important effect on cli-mate change, environmental pollution and public health.This has led to a continuous search for alternative fuels.In this context light alcohols (ethanol and methanol in par-ticular) proved to be of great interest from two points ofview: firstly for production and secondly for storage andintrinsic properties. In the near future these alcohols canbe blended with oil-derived fuels to enhance engine per-formance and efficiency. Most of the recent experimentalwork has focused on ethanol, although methanol is moreversatile from a production point of view. A literature sur-

vey has shown that there is a lack of published experi-mental data at engine-like conditions. The present paperonly describes measurements of laminar burning veloc-ity of methane-air mixtures performed with the GUCCI,which was validated using the results of these measure-ments. However, these results will be highly important inview of future work, which will be aiming primarily at ob-taining laminar burning velocity data of light alcohols andtheir mixtures with gasoline.

EXPERIMENTAL METHOD

The experiments were performed using the GUCCI setup,a constant volume combustion vessel at Ghent Univer-sity. The corresponding experimental method is calledCVB (constant volume bomb method). To date there havenot been any experiments yielding peak pressures higherthan 150 bar. Therefore in this work it was decided notto exceed this value. For measurements at higher ini-tial pressures (10 bar and higher) the peak pressure wasfirst calculated using the GASEQ program. The vessel isequipped with two orthogonal quartz windows of diameter150 mm, which have been tested up to 150 bar. Close tothe wall of the bomb a fan was installed to properly mixthe reactants. This stirring element is driven by an elec-tric motor. Gas temperatures were obtained with a typeK thermocouple. Partial pressures of the reactants weremeasured using the UNIK5000 absolute pressure sensorfrom the manufacturer Druck. Pressure profiles during theexplosions were obtained with an AVL type relative pres-sure sensor. Two opposite electrodes were mounted diag-onally in order to provide central ignition. The gap widthbetween both electrodes was set at 1 mm.

The growth rate of the spherically expanding flames wasmeasured by high speed schlieren cine photography, aswas also the case in the study of J. Vancoillie at Leeds

1

Figure 1: Schematic overview of the GUCCI setup.

University [1]. A high speed PCO camera was used tocapture flame propagation. For the methane-air measure-ments in the present work, the camera speed was set at3000 frames/s with 1152 x 1428 pixels; the resolution was0.16 mm/pixel. It could also have been decided to sacri-fice the visibility of the entire vessel window area in favorof higher frame rate, but the authors have chosen not todo so in order to obtain a robust postprocessing method.

In between measurements it was of high importance toproperly flush the combustion chamber in order to makesure most of the residual gases from a previous explo-sion were removed. After 1 minute of flushing with com-pressed (dry) air, the chamber was evacuated down to 0.1bar. Next, the chamber was flushed for 30 seconds. Thechamber pressure reached a steady-state value of 8-9 barduring this action. Then as a final step the chamber wasevacuated for a second time, again to 0.1 bar. At an initialpressure of 2 bar, the last two steps were repeated oncein order to remove 99.99% of the residuals and thus avoidany influence on the composition of the next mixture to befilled. At the higher pressures (5 and 10 bar) this repetitionwas unnecessary.

After performing the flushing procedure, a series of ac-tions was completed by the LabVIEW program in orderto properly fill the chamber with the different gaseouscomponents. These actions were done automatically bythe software, while the desired partial pressures were setmanually. First, the chamber was evacuated down to ap-proximately 0.3 bar. Then methane was introduced intothe chamber by subsequently filling the correspondingtube with the desired partial pressure and opening theCOAX gas valve. Next, dry air was added in the sameway. The program measured the actual cumulative pres-sures after adding each component. From these valuesthe actual filled partial pressure of each component wasderived. The actual equivalence ratio was then calculatedfrom these partial pressure values.

REPEATABILITY

To obtain a measure for the repeatability of the experi-ments, at least three explosions were performed at eachcondition. After processing the images, the standard devi-

ation on the mean laminar burning velocity was calculatedfor each condition.

The principal uncertainty was in making up the mix-ture. Therefore the following factors affecting mixture sto-ichiometry were accurately controlled:

• Important was the consistency of pressure and tem-perature just prior to ignition. The authors aimed at atolerance of 0.03 bar and 5 K, respectively. However,due to the poor accuracy of the gas filling system,the PID controller in particular, deviations of these tol-erances occurred frequently. These deviations wereespecially important at 2 bar because of the signifi-cant relative error. The main problem while filling atlow pressures (1-2 bar) was that the gas system wasnot able to measure (fill) partial pressures lower than0.13 bar. This was particularly important for the par-tial pressures of methane, because of its high air-to-fuel ratio (17.2). A second problem concerning thefilling process was the inconsistency of the evacu-ation of the chamber before the actual filling. Thedeviation from 0.3 bar was significant for many mea-surements.

• Residuals were kept at a minimum through adequateflushing of the vessel after each explosion.

• A final factor was the vessel sealing, which could notentirely exclude leakages. This was tested using aleakage spray and by filling the chamber with com-pressed air, leaving the gas valve open. The influ-ence on mixture composition was particularly impor-tant at elevated pressures (10 bar and higher). Atthese conditions, a small part of the methane-air mix-ture was leaking during the addition of dry air, againaffecting mixture stoichiometry.

In future work, when measurements on methanol-air willbe performed with this experimental setup, some impor-tant additional factors will come into play. The first prob-lem arises from the applied filling method of the liquid fuel.The methanol has to be injected using a syringe, so therewill be an uncertainty on the full scale deflection of thesyringe. This in turn corresponds with an average uncer-tainty on the equivalence ratio. The mixture stoichiometryshould be controlled by injecting a calculated amount offuel. The correct composition of the mixture should thenbe cross-checked by comparing measured partial pres-sures to the corresponding theoretical values, assumingideal gas behavior. The partial pressure of the fuel canbe calculated by subtracting the vessel pressure beforeinjection (pvacuum) from the pressure after injection.

ERROR ASSESSMENT

The potential errors and their influence on the measure-ments results were calculated. This part of the validationwas of high importance because the GUCCI setup had

2

never been used for laminar burning velocity measure-ments before. The performed error analysis is based onprevious work of Vancoillie [2], Verhelst [3] and Vanthillo[4].

The error assessment can be subdivided into two mainparts. The first part comprises the error on directly mea-sured quantities: initial pressure and temperature, andschlieren image quality (resolution). The second parttreats the error on mixture composition, thus the erroron φ. This includes the error due to the filling procedure(valve timing, gas leakage,) and the error due to a limitedpressure sensor accuracy and DAQ resolution. The im-portance of the postprocessing (e.g. linear extrapolation)methodology and flame structure, which was not alwaysperfectly spherical, is also illustrated.

Some assumptions were made concerning the error onthe different sensors. The following list contains anoverview of the specific error and important data concern-ing the sensors.

• Pressure sensor: UNIK5000, ±0.08% FS, so δp1 =0.08/100 · 70 = 0.056 bar

• Temperature sensor: δT=2.5 ◦C (value based on aprevious master thesis [2])

A measurement range of 70 bar was assumed for thepressure sensor and DAQ unit in order to be as conserva-tive as possible.

DIRECTLY MEASURED QUANTITIES

The maximum absolute error on the initial pressureprior to ignition was estimated at 100 mbar (10000 Pa).This includes the accuracy of the pressure sensor (35mbar or 3500 Pa) as well as the occurrence of a pres-sure drop along the particulate filter at the end of eachfilling procedure. This pressure drop was estimated at 60mbar by analyzing variations in final total pressure for aseries of ‘equal’ filling procedures, i.e. filling procedureswith the same initial total pressure and the same desiredpartial pressures. This was done for each initial pressurecondition. For the measurements at 2, 5 and 10 bar, re-spectively, this resulted in a potential error of 5, 2 and 1%.

The maximum absolute error on the initial temperature,i.e. the temperature prior to ignition, was estimated at 2.5◦C.

During the image processing two different errors weremade: an error on the flame radius and a calibration er-ror. First, the error on the flame radius of a schlieren im-age is determined by the resolution of the digital camera.For all measurements the horizontal resolution was set to

0.16 mmpixel . This means an absolute error of 0.16 mm was

made. Second, the calibration of the circular schlieren im-age was performed using both a physical grid and a studyin Photoshop. It was concluded that the variation in diam-eter was less than 0.15 %.

The accuracy of the image processing method is also veryimportant since it directly affects the final LBV value. Im-age quality aspects such as details and sharpness are ofgreat importance. Fuzzy parts on the edge of the circularflame inhibited accurate flame edge determination. Non-circular flames and non-uniformly expanding flames alsoresulted in non-usable information, since the required cir-cle fit could not be realized appropriately.

ERROR ON MIXTURE COMPOSITION

Since it was very desired to know the accuracy of thefuel-air mixture composition, a lot of attention was de-voted to this part of the error analysis. The influence oftemperature (ambient) was considered negligible. The er-ror on φ resulted from the error on the partial pressures,which were measured by the UNIK5000 absolute pres-sure sensor. Then the measured partial pressures wereprocessed by the DAQ unit and presented in the LabVIEWinterface. It is important to note that the partial pressureof a gaseous mixture component was determined on thebasis of the difference between the pressure before andafter a pressure measurement during the filling process.Therefore the error of the static pressure sensor was in-cluded twice. The masses of the different componentswere determined by using the measured partial pressuresin combination with the ideal gas law. The very same prin-ciple was applied to calculate the error on these masses,m, on the one hand and the error on the measured partialpressures, δp, on the other hand. Finally, the relative erroron the air-to-fuel ratio, errAF , was calculated:

∆mi =δp · V ·Mi

R · T (1)

errAF =∆mair

mair+

∆mCH4

mCH4

(2)

In equation (1) δp is equal to 70 mbar, V is the vol-ume of the GUCCI (3.954 liters when taking into ac-count both electrodes and the fan), Mi is the molar massof component i ( g

mole ), R is the universal gas constant(8.31441 J

mole·K ) and T is the temperature of the GUCCIin Kelvin.

The relative error of the lambda-value of a certain air-fuelmixture, errλ , is equal to the relative error of the mixturesAFR, errAF .

An analysis for three different filling procedures was done.

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The results are indicated in the table 1.

Due to the small amount of methane that needed to befilled at an initial pressure of 2 bar (0.07 bar), the error onλ even exceeded its own value. This was a clear indica-tion that, for very low partial pressures, the system was farfrom accurate to properly perform the filling. Also, the er-ror on the UNIK5000 pressure sensor was simply too big.It was almost impossible to get proper ignition when theinitial pressure was chosen 1 bar. Due to the big expectederror on the equivalence ratio and the narrowness of theflammability range (5-15 %) of methane-air mixtures, theprobability of having a non-ignitable mixture was quite big.Moreover, the system was not able to fill/measure partialpressures below 0.13 bar. Therefore, in the present workthe lowest initial pressure used for the ignition of methane-air mixtures was chosen 2 bar.

At 5 bar, φ = 1 the error was already reduced consider-ably, although still not very satisfying. At 10 bar, φ = 1.3the amount of fuel was the highest of all measurements,providing the smallest possible error.

It can be concluded that the relative error decreases withpressure and is larger for lean mixtures, when the amountof fuel is small. It was observed that in the ‘worst casescenario’ (2 bar, φ = 0.7) the relative error was exces-sively big. However, it must be noted that the analysiswas done assuming the maximum possible error on thepressure sensor. In reality, this error will in most casesbe lower. At an initial pressure of 2 bar, poor LBV re-sults were expected due to the considerable error on φ.However, when the mean LBV values are compared to lit-erature, very good agreement is observed as illustratedbelow.

In the present work, some actions were taken in order toreduce the error on . A first measure was the usage ofsynthetic dry air (79.1% N2 and 20.9% O2 v/v) insteadof the separate nitrogen, oxygen and argon bottles thatwere initially present. By using dry air no error in oxidizercomposition could be made.

POSTPROCESSING AND FLAME STRUCTURE Therange of data points that was selected for extrapolationto zero-stretch flame speed was of great importance dueto its pronounced effect on the final laminar burning veloc-ity. The following extrapolation figure was typically madefor each measurement:

In order to obtain a structural way of extrapolation, a sys-

Figure 2: Variation of the flame speed Sn[m/s] with the stretch rate[s−1] for a methane-air flame at 5 bar and 298 K, φ = 1.

tematical extrapolation route was followed for each mea-surement. The flame speed was plotted as a function ofthe stretch rate. The minimum and maximum stretch rate,used for linear extrapolation to zero-stretch, were manu-ally selected. The minimum value must be the stretch rateat which the operator assumes initiation of cellularity, andthus a sudden increase in flame speed. The maximumstretch rate was simply a boundary condition for the ex-trapolation method, which was implemented in MATLAB.The program performed the extrapolation using a variableseries of data points, starting at the minimum stretch rateand gradually evolving to the total range of points be-tween minimum and maximum. All obtained Marksteinlengths were stored in a list, from which the dominatingvalue was determined. After extrapolating to zero-stretchflame speed, the laminar burning velocity was obtainedby scaling with σ, which is the ratio of burned to unburnedmixture density. Both densities were determined using theGASEQ program.

MEASUREMENT CONDITIONS

In order to validate the GUCCI setup, laminar burningvelocity values of methane-air flames were measured atthree different initial pressures (2, 5 and 10 bar). Theinitial temperature was always kept 298 K. The equiva-lence ratio of the mixture was varied from 0.7 to 1.3, witha step size of 0.5. This resulted in 39 different combina-tions of pressure and equivalence ratio. The measure-ments corresponding with each condition were repeatedat least three times. The measurement conditions withthe actual based on partial pressure together with the re-sulting values of ul for the individual measurements arelisted in Appendix A.

RESULTS AND DISCUSSION

First, the influence of starting pressure on laminar burningvelocity was investigated. In figure 3, LBV values are plot-ted as a function of pressure for 3 different equivalenceratios. Results at 4 bar are also included, although norepetitions were performed at this condition.

It is observed that laminar burning velocity decreases withpressure. This decrease becomes less steep when pres-

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Figure 3: Laminar burning velocities of methane-air mixtures at equiv-alence ratios 0.8, 1 and 1.3 as a function of pressure (2, 4, 5 and 10bar).

sure is increased. As found in literature, ul varies linearlywith 1√

p . LBV values also decrease when the mixture islean or rich of stoichiometric. Also, a deviating value isseen at 5 bar, φ equal to 1.3. This is probably due to awrong mixture composition. It was found that when theGUCCI was used to measure LBV of very lean or veryrich mixtures, in some cases no ideal spherical flame re-sulted or the filling procedure was not very accurate. As aconsequence, wrong LBV information was captured.

Due to the poor accuracy of the gas filling system at lowpressures, the spreading on the results of the measure-ments at 2 bar is significant. Although contra-intuitively,it was noticed that for increasing initial pressure the qual-ity of the measurements increased; the results at 5 and10 bar have, respectively, acceptable and small spreadingrates. This is shown by the error bars in figure 4, whichalso shows the expected overall decrease in burning ve-locity for increasing pressure.

Figure 4: Mean values of laminar burning velocity ul as a functionof equivalence ratio φ, at p = 2, 5 and 10 bar. Values were obtainedby measurements using the GUCCI setup. Standard deviations on bothburning velocity and corrected equivalence ratio are indicated by verticaland horizontal error bars, respectively.

Figure A.1 compares the present laminar burning velocitydata for methane-air mixtures at 2 bar and 298 K againstthree other datasets from literature, also obtained by theconstant volume bomb method. The vertical error barsindicate the standard deviation of ul between different ex-periments. The standard deviation on the corrected equiv-alence ratios is depicted by the horizontal error bars.

It is observed that the database of Goswami et al. [6] isthe most comparable with the present results. From theright graph in figure A.1, it can be concluded that the dataobtained by the present study are within the experimentalvariability of the different literature data. A deviating value,however, was found at an equivalence ratio of 1. It can beconcluded that, for an initial pressure of 2 bar, the presentdata are at least acceptable.

Results at 5 bar and 298 K are shown in Figure A.2. It isobserved that the database of Rozenchan et al. [7] is themost comparable with the present data. However, whenexamining the right graph, a rather high variability is seenfor the literature data. For mixtures that are lean of sto-ichiometric, the present results are in line with the meanvalue of the literature data. Mixtures that are rich of sto-ichiometric show higher values of ul. This could be anindication of wrong mixture composition for the richer mix-tures. However, the present results are still consideredacceptable as variability in literature is high.

Results obtained at 10 bar and 298 K are shown in FigureA.3. It is seen that the data from literature have a low vari-ability. The present data agree very well with literature.For all equivalence ratios the absolute standard deviationis 1 cm/s, excluding φ equal to 1.2, for which the devia-tion is 2 cm/s. It can be concluded that the GUCCI setupprovides qualitative results at an initial pressure of 10 bar.

CONCLUSION

Based on the present discussion and comparison of theobtained LBV data with literature, it can be stated thatthe GUCCI setup has been validated for LBV measure-ments of methane-air mixtures at pressures up to 10 bar.The deviation from mean literature data is generally below15%, excluding some very lean and very rich conditions.

REFERENCES

[1] J. Vancoillie, G. Sharpe, M. Lawes, S. Verhelst,Laminar burning velocities and Markstein lengths ofmethanol-air mixtures at pressures up to 1.0 MPa,University of Leeds, 2014.

[2] J. Vancoillie, Modeling the combustion of light alcoholsin spark-ignition engines, ph.d. thesis, Ghent Univer-sity, 2013.

[3] S. Verhelst, A study of the combustion in hydrogen-fueled internal combustion engines, ph.d. thesis,Ghent University, 2005.

[4] J. Van Thillo, Metingen van de laminaire ver-brandingssnelheid van brandstofarme en verdundemethaan-lucht mengsels met behulp van de ehpe,ph.d. thesis, Eindhoven: Technische Universiteit,2008.

[5] P. Logghe and W. Roose, Flowbench- en vlam-snelheidsmetingen als input voor simulaties voor

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vonkontstekingsmotoren, master thesis, Ghent Uni-versity, 2012.

[6] M. Goswami, S. Derks, K. Coumans, W. Slikker, M.Oliveira, R. Bastiaans, C. Luijten, L. de Goey, and A.Konnov, The effect of elevated pressures on the lam-inar burning velocity of methane + air mixtures, Fuel,vol. 160, pp. 1627-1635, 2013.

[7] D. L. Rozenchan, G. and Zhu, C. K. Law, and T. S. D.,Outward propagation, burning velocities and chemicaleffects of methane flames up to 60 atm, Proceedingsof the combustion institute, vol. 160, pp. 1627-1635,2013.

[8] F. Egolfopoulos, D. Du, and C. Law, Twenty-fourthsymposium on combustion, The combustion institutePittsburgh, 1992.

[9] M. Hassan, K. Aung, and G. Faeth, Measured andpredicted properties of laminar premixed methane/airflames at various pressures, Combustion and Flame,vol. 115, pp. 539-550, 1998.

[10] X. J. Gu, M. Z. Haq, M. Lawes, and R. Woolley,Laminar burning velocity and markstein lengths ofmethane-air mixtures, Combustion and Flame, vol.121, pp. 41-58, 2000.

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Figure A.1. Present results of 𝒖𝒍 at 2 bar and 298 K, compared against results from literature [43, 39, 67] (left) and the mean value of these literature data, calculated for each equivalence ratio 𝝓 (right).

Figure A.2. Present results of 𝒖𝒍 at 5 bar and 298 K, compared against results from literature [10, 6, 7] (left) and the mean value of these literature data, calculated for each equivalence ratio 𝝓 (right).

Figure A.3. Present results of 𝒖𝒍 at 10 bar and 298 K, compared against results from literature [10, 7] (left) and the mean value of these literature data, calculated for each equivalence ratio 𝝓 (right).

Figure A.4. Present results of 𝒖𝒍 at 15 bar and 298 K, compared against results from literature [7] at 10, respectively 20 bar.