research article numerical study of pollutant emissions in...

Research ArticleNumerical Study of Pollutant Emissions in a Jet StirredReactor under Elevated Pressure Lean Premixed Conditions

Karim Mazaheri and Alireza Shakeri

Center of Excellence of Aerospace Systems Sharif University of Technology Tehran 14588 33351 Iran

Correspondence should be addressed to Alireza Shakeri a shakeriaesharifedu

Received 5 August 2015 Revised 31 January 2016 Accepted 15 February 2016

Academic Editor Gerhard-WilhelmWeber

Copyright copy 2016 K Mazaheri and A Shakeri This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

Numerical study of pollutant emissions (NO and CO) in a Jet Stirred Reactor (JSR) combustor for methane oxidation underElevated Pressure Lean Premixed (EPLP) conditions is presented A Detailed Flow-field Simplified Chemistry (DFSC) methoda low computational cost method is employed for predicting NO and CO concentrations Reynolds Averaged Navier Stokes(RANS) equations with species transport equations are solved Improved-coefficient five-step global mechanisms derived froma new evolutionary-based approach were taken as combustion kinetics For modeling turbulent flow field Reynolds Stress Model(RSM) and for turbulence chemistry interactions finite rate-Eddy dissipation model are employed Effects of pressure (3 65 bars)and inlet temperature (408ndash573K) over a range of residence time (149ndash397ms) are numerically examined A good agreementbetween the numerical and experimental distribution of NO and CO was foundThe effect of decreasing the operating pressure onNO generation is much more than the effect of increase in the inlet temperature

1 Introduction

In recent decades natural-gas-fired turbine industries havebeen proceeded to lean premixed technology due to stringentenvironment regulations especially for NOx suppression andElevated Pressure Lean Premixed (hereinafter referred toas EPLP) has been recognized as the practical operatingcondition Numerical investigation of pollutant emissions ina combustor under such conditions relies on employing boththe suitable method of pollutant prediction and chemicalkinetics However due to high computational cost for a real-scale combustor the laboratory-scale combustors that is JetStirred Reactor (JSR) may be emphasized Issues mentionedabove are briefly reviewed in the following paragraphs

Generally four different numerical schemes can be foundin the literature for predicting of NO and CO emissionsDetailed Flow-field Detailed Chemistry (DFDC) DetailedFlow-field Simplified Chemistry (DFSC) Simplified Flow-field Detailed Chemistry (SFDC) and Simplified Flow-fieldSimplified Chemistry (SFSC) In the first 2D3D numericalsolutionmust be performed using a detailedmechanism anddespite very high accuracy of this method the computational

cost is huge therefore it is barely used for industrial appli-cations [1] In the 2nd a 2D3D numerical solution using areduced (or global) mechanism may be applied This schemeis used for predicting of NO and CO emissions for somecombustors under lean premixed conditions that is Hamerand Roby [2] Nicol et al [3] and Novosselov and Malte [4]In the 3rd a detailed mechanism is employed in a ChemicalReactor Network (CRN) created based on either analyzednumerical results or empirical data for example Glarborget al [5] Miller and Bowman [6] Drake and Blint [7]Michaud et al [8] and Nicol et al [9] In the last methodinstead of a detailed mechanism used in the third methoda simplified mechanism is replaced This scheme is used byNovosselov and Malte [4]

Mostly two different chemical kinetic mechanismsincluding detailed and simplified are available for methaneoxidation and NO formation Limited numbers of detailedmechanisms are available for instance GMK [5] MB [6] DB[7] GRI 211 GRI 30 Hughes et al [10] Petersen et al [11]and Pillier et al [12] However there are a large number ofstudies on simplified mechanisms for example Goussis andKelly 1990 [13] LamandGoussis 1994 [14]Mallampalli et al

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 4179638 10 pageshttpdxdoiorg10115520164179638

2 Mathematical Problems in Engineering

1998 [15] Massias et al [1] Sung et al 2001 [16] Belcadi et al2012 [17] andKaralus et al [18] Utilizing suchmechanisms incomputational fluid dynamics (CFD) problems needs a hugecomputational cost due to high number of species Further-more despite introducing a few numbers of global mecha-nismswith less number of species for example Nicol et al [3]andNovosselov [19] the rate coefficients of thesemechanismsare case dependent and of limited use for variety of operatingconditions especially for EPLP situations

There exist a lot of studies about lean premixed JSRcombustors First time Thornton et al [20] experimentallystudied this combustor to investigate the kinetic oxidationof the hydrocarbon fuels Corr et al [21] investigated theformation of NO and CO in JSR with the volume of 158 ccunder atmospheric pressure lean premixed conditions (120601 =06) using experiment and a PSR solver Steele et al [22] did asimilar work but over a range of equivalence ratio (041ndash067)and residence time (17ndash74ms) Furthermore Steele et al [23]examined effects of inlet temperature (300ndash600K) pressure(1ndash71 atm) volume (2 16 cc) and the ratio of area to volumeusing a solver consisting of a PSR and a plug flow reactor(PFR) Bengtsson et al [24] used alternative conditions in theexperiment that is pressure up to 20 bars equivalence ratioof 055 a range of temperature (1783ndash1823K) and three differ-ent residence times (10 15 and 20ms) Shuman [25] empir-ically inspected the formation of NO and CO over a widerrange for residence time (05ndash40ms) temperature (1815ndash1910 K) and different range for pressure (3ndash65 atm) and inlettemperature (344ndash573K)

The main objective of this study is to numerically inves-tigate effects of pressure and inlet temperature and a range ofresidence time onNOandCOemissions in a laboratory-scaleJSR combustor under EPLP operating conditions Nine oper-ating conditions from the experiment of Shuman [25] andgeneral form of the five-step global mechanism suggested byNicol et al [3] are considered as the base operating conditionsand base mechanism respectively However in this mech-anism the rate coefficients include analytical relationshipsbetween the reaction rate and the net rate of species Theyhave used regression analysis based on themechanism ofMBbut he did not present his model for high pressure conditionIn addition the effect of some parameters such as initialtemperature of the mixture on rate coefficients was notconsidered Here the optimization is improved by using theDE algorithm In this way we do not need any analytical rela-tionship and the optimal rate coefficients corresponding tothe desired operating conditions are determined So the newevolutionary-based approach is used to obtain the reactionrate coefficients of this mechanism under nine EPLP operat-ing conditions A DFSC scheme using CFD software (FLU-ENT) is employed to numerical simulation

2 Derivation of Chemical Kinetic Coefficients

A new evolutionary-based approach is implemented toobtain the reaction rate coefficients of the methane-aircombustion kinetics and the details are elaborately explainedin the following subsections The method consists of two

modules namely the simple Chemical Reactor Modeling(CRM) and the numerical optimizer For any given operatingcondition and a user defined detailed mechanism (as thetarget mechanism) the CRM gives the corresponding valuesof species concentrations that is NO and CO These arereserved as the target values for optimizer module With theaim of predicting NO and CO a global mechanism is speci-fied The unknown rate coefficients of this global mechanismare considered as the design variables used in the differentialevolution (DE) module Employing an interactive processthe CRM calculates the species concentrations through thecoefficients which are obtained by the DE The results arecompared with the detailed mechanism and this process iscontinued till the discrepancy between the predicted and thetarget values becomes as small as possible

21The Chemical Reactor Modeling (CRM) According to theprevious paragraph species concentrations are obtained fromthe CRM module Here a Perfectly Stirred Reactor (PSR)combined with a plug flow reactor (PFR) is addressed asthe CRM Possible detailed or predefined global mechanismsalong with a set of parameters that is operating pressureinitial mixture temperature residence time and equivalenceratio are the inputs Furthermore the length and diameterof the combustor are also added The CRM calculations havebeen carried out using the method described by Turns [26]It is noted that CHEMKIN [27] software is used for thecalculation of CRM The PSR-PFR output is distribution ofconcentrations along the reactor

22 Optimizer Module In this study the differential evolu-tion (DE) optimization algorithm [28] is employed to find therate coefficients for a predefined global mechanism throughthe procedure addressed in Section 2 Three key elementsshould be provided for the optimizer module (i) the designvariables (ii) the objective function and (iii) the constraintsThe design variables are the unknown rate coefficients of theglobal mechanism The cost function is intended to evaluatethe deviation of some species concentrations (ie NO andCO) predicted using the global mechanism from those cal-culated with the detailed mechanism Consequently the costfunction for the PSR-PFR is specified as

119868PFR =1

119883detmaxNO

int119871

0

10038161003816100381610038161003816119883detNO (119909) minus 119883

glbNO (119909)

10038161003816100381610038161003816 119889119909

+1

119883detmaxCO

int119871

0

10038161003816100381610038161003816119883detCO (119909) minus 119883

glbCO (119909)

10038161003816100381610038161003816 119889119909

(1)

where 119909119883 119871 are distance along the PFR mole fraction andlength of the reactor respectively Also det and glb denotedetailed and global mechanism respectively The optimiza-tion constraints are imposed by considering a finite intervalfor each design variable The intervals are assigned such thatthe best values lie between the lower and the upper boundsThe objective function is normalized based on the maximummole fraction of NO and CO It is obvious that one may addother target mole fractions to the above but then the modelaccuracy for predicting these two species will decrease

Mathematical Problems in Engineering 3

Table 1 Base operating conditions [25]

Case number 120591 (ms) 120601 (mdash) 1198791199050

(K) 119875 (atm) Fuel flow (grsec) PHNPHlowast

1 149 058 573 65 1219 PH2 209 061 573 65 0871 PH3 397 066 573 65 0460 PH4 165 064 573 3 0523 PH5 236 067 573 3 0366 PH6 333 074 573 3 0259 PH7 163 069 408 3 0526 NPH8 240 074 418 3 0360 NPH9 333 080 432 3 0260 NPHlowastPH preheated conditions NPH no preheated conditions

Table 2 General form of the five-step global mechanisms for CH4

air combustion [3]

Number Reaction description Reaction rate [molecm3s]1 CH

4

+ 15O2

rarrCO + 2H2

O 1198771

=1198601

[CH4

]1198611 [O2

]1198621 exp(minus1198631

119877119906

119879)

2 CO + 05O2

rarr CO2

1198772

= 1198602

[CO]1198612

[O2

]119862

2

exp(minus1198632

119877119906

119879)

3 CO2

rarr CO + 05O2

1198773

= 1198603

[CO2

]119861

3

exp(minus1198633

119877119906

119879)

4 N2

+ O2

+ COrarr 2NO + CO 1198774

= 1198604

[O2

]119861

4

[CO]1198624

exp(minus1198634

119877119906

119879)

5 N2

+ O2

rarr 2NO 1198775

= 1198605

119879minus05[N2

][O2

] exp(minus1198635

119877119906

119879)

23 Base Operating Conditions and Global Mechanism Theabove procedure has been applied to generate nine modelsbased on nine operating conditions These operating condi-tions are selected based on the studies of Shuman [25] Inall cases the combustion pressure is estimated from pressureloss in the premixed tube nozzle inlet and combustor Machnumber Similar estimates are used to deduce the residencetime based on the flow parameters and combustor volumeAll the flowparameters are given inTable 1 and the combustorvolume is assumed equal to 10 cm3

The general form of the five-step global mechanismproposed by Nicol et al [3] is considered as the base mecha-nism This mechanism and its unknown rate parameters arepresented in Table 2 According to Table 2 the five steps of themechanism are as follows oxidation of the methane fuel toCO andH

2

O oxidation of the CO to CO2

dissociation of theCO2

to CO flame-NO formation and post-flame-NO forma-tion

3 Numerical Solution Procedure

JSR combustor together with the relevant geometrical param-eters is schematically shown in Figure 1

This standard geometry is consisted of two truncatedcones one at the first and the other at the end of thecombustor and a cylinder in the middle Combustor inlet(with diameter of 119889

119894

) is located at the center of the lower basewhile four equally spaced holes (with individual diameter of1198890

) with elevation of ℎ0

from the base are positioned on thelateral surface of the first truncated cone Several researchersused a similar shape (but with different dimensions) for JSRin their experiments for example Corr et al [21] Steele et al[22] Steele et al [23] Steele et al [29] Shuman [25] and

h

hp

ho

h3

dh

dm

r

db

do

l2

l3

di

➀

➁

➂

Figure 1 JSR combustor geometry

Rutar and Malte [30] Some geometrical dimensions of thesecan be seen in Table 3

Here geometry of the JSR of Shumanrsquos work is consideredin our numerical study Since someof the reactors dimensionswere not clear in their references we have used ratio of apower of one-third of their volume to guess unknowndimensions

31 Governing Equations Here a brief description of con-servation equations for mass momentum chemical speciesenergy and turbulence is introduced These equations are


Table 3 Dimensions of different JSRs

119889119894

119889119900

119889119887

119889119898

ℎ1

ℎ119900

ℎ forall

mm cc440 400 160 250 2500 600 4500 158440 400 160 250 2500 600 4500 158074 950 mdash mdash mdash mdash mdash 495440 400 160 250 2500 600 4500 158100 240 mdash 127 1420 142 2220 200140 127 730 115 1346 mdash 2019 150

applicable for turbulent flow in a nonaccelerating referenceframe and details are available in certain reference [31]

(i) Conservation of Mass Continuity equation can be intro-duced as follows

120597120588

120597119905+ nabla sdot (120588V) = 0 (2)

where 120588 is the density and V is the velocity vector

(ii) Conservation of Momentum Conservation of momentumis described by

120597

120597119905(120588V) + nabla sdot (120588VV) = minusnabla119901 + nabla sdot (120591) + 120588 + (3)

where 119901 is static pressure 120591 is the stress tensor and 120588 and are the gravitational body force and external body forcerespectively The stress tensor is described by

120591 = 120583 [(nablaV + nablaV119879) minus2

3nabla sdot V119868] (4)

where 120583 is the molecular viscosity and 119868 is the unit tensor

(iii) Species Transport Equations The conservation equationsfor chemical species can be written as

120597

120597119905(120588119884119894

) + nabla sdot (120588V119884119894

) = minusnabla sdot997888rarr119869119894

+ 119877119894

(5)

where 119884119894

is the mass fraction of each species 119877119894

is the net rateof production of species 119894 by chemical reaction and 997888rarr119869

119894

is thediffusion flux of species 119894 and can be written as

997888rarr119869119894

= minus120588(119863119894119898

+120583119905

Sc119905

)nabla119884119894

(6)

where Sc119905

is the turbulent Schmidt number 120583119905

is turbulentviscosity and119863

119905

is the turbulent diffusivityHere the source terms 119877

119894

in (5) are computed by Eddydissipation model

(v) Turbulence Model The exact transport equations for thetransport of the Reynolds stresses (120588 119906

119894

119906119895

) are also solved asthe flow is turbulent These equations can be written as

120597

120597119905(120588 119906119894

119906119895

) +120597

120597119909119896

(120588119906119896

119906119894

119906119895

)

= 119863119879119894119895

+ 119863119871119894119895

+ 119875119894119895

+ 0119894119895

+ 120598119894119895

(7)

where119863119879119894119895

is turbulent diffusion119863119871119894119895

is molecular diffusion119875119894119895

is stress production 0119894119895

is pressure strain and 120598119894119895

is dissi-pation For details of modeling these terms it can be referredto Lien and Leschziner [32]

32 Grid and Boundary Conditions We use axisymmetricassumption to reduce the computational cost The outputholes are replaced with a slot with an area equivalent tothe area of all four holes A structured grid consisting of40000 cells is used for numerical solution Mass-flow-inletand pressure-outlet are considered for the inlet and outletboundaries respectively Mass fractions of the both reactantsand products are calculated in terms of equivalence ratio con-sidering one-step global mechanism for methane-air com-bustion Hydraulic diameter-turbulence intensity approachis used to calculate both kinetics and dissipation rate ofturbulence energy Inlet and outlet diameters are consideredas hydraulic diameter and turbulence intensities are deter-mined based on 119868 = 016Reminus0125

119863

33 Method of Numerical Solution The CFD software (FLU-ENT) is used for numerical simulation For faster con-vergence first a cold flow procedure is used and thenthe reactive-flow simulation is performed A pressure-basedmethod is employed to solve the RANS equations togetherwith species transport equations For modeling turbulentflow field Reynolds Stress Model (RSM) and for turbulencechemistry interactions finite rate-Eddy dissipationmodel areused To discretize the pressure the standard discretizationmethod of the software is used For other parameters (iedensity momentum turbulence kinetic energy dissipationrates and species concentrations) the upwind scheme is usedfor discretization For better convergence based on our expe-rience an under relaxation factor of 06 is used for the turbu-lence kinetic energy dissipation rate of energy and viscosityand a factor of 08 is used for density energy and chemicalspecies equations It is noted that here heat transfer is notmodeled

4 Validation and Results

Results are separately presented in three subsections InSection 41 validated results of the generated chemicalkinetics using the PSR-PFR module and evolutionary-basedmethod simultaneously are examined over different oper-ating pressures residence times and inlet temperatures InSection 42 the attention is confined to compare the numeri-cal predicted of NO and CO emissions with the experimentsAlso grid independency of the numerical solution is per-formed and results are presented for pollutant species (egNO and CO) In Section 43 we turn to investigate effectsof operating pressure and inlet temperature on NO and COemissions at different residence times

41 Validated Results of theObtained Kinetics Our algorithmis a very fast algorithm which produces a kinetic model foreach reactor at each operating condition (ie inlet tempera-ture pressure and the total equivalence ratio) As presented


in Table 1 nine different operating conditions (case numbers)are chosen six to investigate effects of the combustor pressureand three to examine impacts of the inlet temperature on NOand CO concentrations Mass flow is not a dependent param-eter in our analysis but is used in our CFD simulations as partof our boundary conditions Also as reported in Table 2 theglobal five-step mechanism of Nicol with unknown reactionrate coefficients is used as the base of our mechanism andthen the optimal values of these unknowns are obtained fromthe evolutionary-based procedure (explained in Sections 21and 22) The calculated coefficients are tabulated for eightcase numbers (Table 1) in Table 4 Comparison of the ratecoefficients obtained for the temperature and pressure con-ditions (Table 1) shows that these factors are more a functionof pressure and temperature changes have less effect on them

To compare the computational cost of this 5-step modelwith a full GRI-30 mechanism we use the PREMIXEDmodel of CHEMKIN software The computational cost forfullmechanismwas about 16 times the reduced 5-stepmecha-nism Since this is a one dimensionalmodel we expect signif-icant computational cost advantage for real three dimensionalcomputations

NO and CO concentrations and adiabatic flame temper-ature for nine cases are comparatively plotted in Figures 2ndash4 which show that there is a reasonable agreement betweenthe generated five-step mechanisms and the detailed GRI 30mechanism

42 Comparing the Predicted Emissions with ExperimentSome empirical data of Shuman is used for validation ofthe numerical study However the experiments were per-formed for three different pressures of premixed tube (3 47and 65 atm) residence time and inlet temperature rangedbetween 05ndash408ms and 323ndash573K respectively at leanequivalence ratios (058ndash080) here validations are presentedfor two different pressures (3 and 65 atm) and inlet tempera-tures (418 and 573K) and three different residence times (2125 and 4ms)

Comparison between predicted and empirical data forNO and CO versus radial coordinate inside the JSR com-bustor at fixed axial position of 1346mm are illustrated inFigures 5 and 6 for cases 2 and 8 (two different pressures andinlet temperatures)

As is obvious from these figures there is a reasonableagreement between the numerical and experimental data fordifferent case numbers

To investigate grid independency of the numerical solu-tion concentrations of NO and CO for the other case (egcase 3) based on two meshes with different cells (40000 and110000) are illustrated in Figure 7 and the distributions arecompared with the experiment

43 Effects of Inlet Temperature andOperating Pressure onNOIt is found that increasing residence time under a specifiedinlet temperature and operating pressure leads to increasingthe NO concentration at the exhaust of the JSR combustorFurthermore increasing both the inlet temperature and oper-ating pressure at a specified residence time leads to decreasing

Table 4 Calculated coefficients of five-step global mechanisms foreight case numbers given in Table 1

119868 Case number Derived coefficients119860 119861 119862 119863

1

1

1228119890 + 18 140034 0402908 5773532 4924119890 + 21 141719 1727700 3991373 2775119890 + 14 100304 mdash 1201894 1281119890 + 35 400016 0849971 1149895 2568119890 + 16 mdash mdash 1450001

2


3


4


5


6


7


8


levels of the exhausted NO It is quantitatively found thatincreasing the operating pressure about 116 may decreasethe NO level about 66 while for inlet temperature thevalues of 36 and 3 are obtained respectively Thereforethe impact of operating pressure on NO is about seven timesmore than the effects of inlet temperature Concentrations ofNO versus residence times at different pressures are illus-trated in Figure 8


0

20

40

60

80

100

120

GRI 3-case 15-step-case 1GRI 3-case 75-step-case 7GRI 3-case 3

5-step-case 3GRI 3-case 85-step-case 8GRI 3-case 95-step-case 9

Distance along the PFR (cm)0 02 04 06 08 1

NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140

GRI 3-case 25-step-case 2GRI 3-case 45-step-case 4


NO

(ppm

v)

(b)

Figure 2 NO concentration versus distance along the PFR using the PSR-PFR based on the generated five-step mechanism for methaneoxidation comparing with GRI 30 for different cases of 1 3 7 8 and 9 (a) and 2 4 5 and 6 (b)




0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)

Figure 3 CO concentration versus distance along the PFR using the PSR-PFR based on the generated five-step mechanism for methaneoxidation comparing with GRI 30 for different cases of 1 3 7 8 and 9 (a) and 2 4 5 and 6 (b)



1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)

Figure 4 Adiabatic flame temperature versus distance along the PFR using the PSR-PFR based on the generated five-step mechanism formethane oxidation comparing with GRI 30 for different cases of 1 3 7 8 and 9 (a) and 2 4 5 and 6 (b)

0 02 04 06 08 10

2

4

6

8

10

ExperimentalNumerical

NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)

Figure 5 NO (a) and CO (b) concentrations along the radial position between central line and sidewall of the JSR at fixed axial position(1346mm) using the generated five-step mechanism in PSR-PFR obtained fromCFD simulation for methane oxidation comparing with theexperimental data for case 2

5 Conclusion

In this paper numerical study of pollutant emissions (NOandCO) in a Jet Stirred Reactor (JSR) combustor for methaneoxidation under Elevated Pressure Lean Premixed (EPLP)conditions has been carried out A Detailed Flow-fieldSimplified Chemistry (DFSC) method a low computationalcost approach has been employed for predicting NO andCO concentrations Effects of pressure (3 65 bars) and inlet

temperature (408ndash573K) over a range of residence time(149ndash397ms) has been numerically examined A goodagreement between the numerical and experimental distribu-tions for NO and CO was found It was found that increasingboth the operating pressure and inlet temperature tendsto decrease the NO levels It was quantitatively found thatincreasing the operating pressure about 116 may decreasetheNO level about 66while for inlet temperature the valuesof 36 and 3 were obtained respectively


0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

Num-110000 cellsNum-40000 cells

(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)

Figure 7 NO (a) and CO (b) concentrations along the radial position between central line and sidewall of the JSR at fixed axial position(1346mm) using the generated five-step mechanism in PSR-PFR obtained from CFD simulations based on two meshes with 40000 and110000 cells for methane oxidation comparing with the experimental data for case 3

Mathematical Problems in Engineering 9N

O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)

Figure 8 NO concentrations versus residence times at differentEPLP conditions obtained from the CFD simulations based on thegenerated five-step global mechanisms using the DE evolutionary-based method

Competing Interests

The authors declare that they have no competing interests

References

[1] AMassias DDiamantis EMastorakos andDAGoussis ldquoAnalgorithm for the construction of global reduced mechanismswith CSP datardquo Combustion and Flame vol 117 no 4 pp 685ndash708 1999

[2] A JHamer andR J Roby ldquoCFDmodeling of a gas turbine com-bustor using reduced chemical kineticmechanismsrdquo inProceed-ings of the 33rd Joint Propulsion Conference and Exhibit Amer-ican Institute of Aeronautics and Astronautics Seattle WashUSA July 1997

[3] D G Nicol P C Malte A J Hamer R J Roby and R C SteeleldquoDevelopment of a five-step global methane oxidation-NO for-mationmechanism for lean-premixed gas turbine combustionrdquoJournal of Engineering for Gas Turbines and Power vol 121 no2 pp 272ndash280 1999

[4] I V Novosselov and P C Malte ldquoDevelopment and applicationof an eight-step global mechanism for CFD and CRN simula-tions of lean-premixed combustorsrdquo Journal of Engineering forGas Turbines and Power vol 130 no 2 Article ID 021502 2008

[5] P Glarborg J A Miller and R J Kee ldquoKinetic modeling andsensitivity analysis of nitrogen oxide formation in well-stirredreactorsrdquo Combustion and Flame vol 65 no 2 pp 177ndash2021986

[6] J A Miller and C T Bowman ldquoMechanism and modelingof nitrogen chemistry in combustionrdquo Progress in Energy andCombustion Science vol 15 no 4 pp 287ndash338 1989

[7] M C Drake and R J Blint ldquoCalculation of NOx forma-tion pathways in propagating laminar high pressure premixedCH4air flamesrdquo Combustion Science and Technology vol 75no 4ndash6 pp 261ndash285 1991

[8] M G Michaud P R Westnoreland and A S FeitelbergldquoChemical mechanisms of NO

119909

formation for gas turbine

conditionsrdquo Symposium (International) onCombustion Twenty-Fourth Symposium on Combustion vol 24 no 1 pp 879ndash8871992

[9] D G Nicol R C Steele N M Marinov and P C MalteldquoThe importance of the nitrous oxide pathway to NO

119909

in lean-premixed combustionrdquo Journal of Engineering for Gas Turbinesand Power vol 117 no 1 pp 100ndash111 1995

[10] K J Hughes T Turanyi A R Clague andM J Pilling ldquoDevel-opment and testing of a comprehensive chemical mechanismfor the oxidation of methanerdquo International Journal of ChemicalKinetics vol 33 no 9 pp 513ndash538 2001

[11] E L Petersen J M Hall S D Smith J de Vries A R AmadioandMW Crofton ldquoIgnition of leanmethane-based fuel blendsat gas turbine pressuresrdquo Journal of Engineering for Gas Turbinesand Power vol 129 no 4 pp 937ndash944 2007

[12] L Pillier M Idir J Molet A Matynia and S de Persis ldquoExperi-mental study andmodelling of NOx formation in high pressurecounter-flow premixed CH

4

air flamesrdquo Fuel vol 150 pp 394ndash407 2015

[13] D A Goussis and R E Kelly ldquoOn the thermocapillary Instabil-ities in a liquid layer heated from belowrdquo International Journalof Heat and Mass Transfer vol 33 no 10 pp 2237ndash2245 1990

[14] S H Lam and D A Goussis ldquoCSP method for simplifyingkineticsrdquo International Journal of Chemical Kinetics vol 26 no4 pp 461ndash486 1994

[15] H P Mallampalli T H Fletcher and J Y Chen ldquoEvaluationof CH4NOx reduced mechanisms used for modeling leanpremixed turbulent combustion of natural gasrdquo Journal ofEngineering for Gas Turbines and Power vol 120 no 4 pp 703ndash712 1998

[16] C J Sung C K Law and J-Y Chen ldquoAugmented reducedmechanisms for NO emission in methane oxidationrdquo Combus-tion and Flame vol 125 no 1-2 pp 906ndash919 2001

[17] A Belcadi M Assou E Affad and E Chatri ldquoCH4

NO119909

reducedmechanisms used formodeling premixed combustionrdquoEnergy and Power Engineering vol 4 no 4 pp 264ndash273 2012

[18] M F Karalus K B Fackler I V Novosselov J C Kramlich andP C Malte ldquoA skeletal mechanism for the reactive flow simula-tion of methane combustionrdquo in Proceedings of the ASME TurboExpo 2013 Turbine Technical Conference and Exposition (GTrsquo13) San Antonio Tex USA June 2013

[19] I V Novosselov Eight step global kinetic mechanism onmethaneoxidation with nitric oxide formation for lean premixed com-bustion turbine [MS thesis] University of Washington SeattleWash USA 2001

[20] M M Thornton P C Malte and A L Crittenden ldquoA well-stirred reactor for the study of pyrolysis and oxidation kineticscarbon monoxide and n-pentane oxidationrdquo Combustion Sci-ence and Technology vol 54 no 1ndash6 pp 275ndash297 1987

[21] R A Corr P C Malte and N M Marinov ldquoEvaluation of NO119909

mechanisms for lean premixed combustionrdquo Journal of Engi-neering for Gas Turbines and Power vol 114 no 2 pp 425ndash4341992

[22] R C Steele P C Malte D G Nicol and J C Kramlich ldquoNO119909

and N2

O in lean premixed jet stirred flamesrdquo Combustion andFlame vol 100 pp 440ndash449 1995

[23] R C Steele A C Jarrett P C Malte J H Tonouchi and DG Nicol ldquoVariables affecting NOx formation in lean-premixedcombustionrdquo Journal of Engineering for Gas Turbines and Powervol 119 no 1 pp 102ndash107 1997


[24] K U M Bengtsson P Benz R Scharen and C E FrouzakisldquoN119910

O119909

formation in lean premixed combustion of methane ina high-pressure jet-stirred reactorrdquo Symposium (International)on Combustion vol 27 no 1 pp 1393ndash1399 1998

[25] T R Shuman NOx and CO formation for lean premixedmethane-air combustion in a jet stirred reactor operated at ele-vated pressure [PhD thesis] University of Washington Wash-ington DC USA 2000

[26] S R Turns An Introduction to Combustion McGraw-Hill NewYork NY USA 3rd edition 2012

[27] R J Kee F M Rupley J A Miller et al CHEMKIN Release 40Reaction Design San Diego Calif USA 2004

[28] K V Price R M Storn and J A Lampine DifferentialEvolutionmdashA Practical Approach to Global Optimization Nat-ural Computing Series 2005

[29] R C Steele J H Tonouchi D G Nicol D C Horning P CMalte and D T Pratt ldquoCharacterization of NO

119909

N2

O andCO for lean-premixed combustion in a high-pressure jet-stirredreactorrdquo Journal of Engineering for Gas Turbines and Power vol120 no 2 pp 303ndash310 1998

[30] T Rutar and P C Malte ldquoNo119909

formation in high-pressure jet-stirred reactors with significance to lean-premixed combustionturbinesrdquo Journal of Engineering for Gas Turbines and Powervol 124 no 4 pp 776ndash783 2002

[31] G K Batchelor An Introduction to Fluid Dynamics CambridgeUniversity Press Cambridge UK 1967

[32] F S Lien and M A Leschziner ldquoAssessment of turbulence-transport models including non-linear rng eddy-viscosity for-mulation and second-moment closure for flow over a back-ward-facing steprdquo Computers and Fluids vol 23 no 8 pp 983ndash1004 1994

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


1998 [15] Massias et al [1] Sung et al 2001 [16] Belcadi et al2012 [17] andKaralus et al [18] Utilizing suchmechanisms incomputational fluid dynamics (CFD) problems needs a hugecomputational cost due to high number of species Further-more despite introducing a few numbers of global mecha-nismswith less number of species for example Nicol et al [3]andNovosselov [19] the rate coefficients of thesemechanismsare case dependent and of limited use for variety of operatingconditions especially for EPLP situations

There exist a lot of studies about lean premixed JSRcombustors First time Thornton et al [20] experimentallystudied this combustor to investigate the kinetic oxidationof the hydrocarbon fuels Corr et al [21] investigated theformation of NO and CO in JSR with the volume of 158 ccunder atmospheric pressure lean premixed conditions (120601 =06) using experiment and a PSR solver Steele et al [22] did asimilar work but over a range of equivalence ratio (041ndash067)and residence time (17ndash74ms) Furthermore Steele et al [23]examined effects of inlet temperature (300ndash600K) pressure(1ndash71 atm) volume (2 16 cc) and the ratio of area to volumeusing a solver consisting of a PSR and a plug flow reactor(PFR) Bengtsson et al [24] used alternative conditions in theexperiment that is pressure up to 20 bars equivalence ratioof 055 a range of temperature (1783ndash1823K) and three differ-ent residence times (10 15 and 20ms) Shuman [25] empir-ically inspected the formation of NO and CO over a widerrange for residence time (05ndash40ms) temperature (1815ndash1910 K) and different range for pressure (3ndash65 atm) and inlettemperature (344ndash573K)

The main objective of this study is to numerically inves-tigate effects of pressure and inlet temperature and a range ofresidence time onNOandCOemissions in a laboratory-scaleJSR combustor under EPLP operating conditions Nine oper-ating conditions from the experiment of Shuman [25] andgeneral form of the five-step global mechanism suggested byNicol et al [3] are considered as the base operating conditionsand base mechanism respectively However in this mech-anism the rate coefficients include analytical relationshipsbetween the reaction rate and the net rate of species Theyhave used regression analysis based on themechanism ofMBbut he did not present his model for high pressure conditionIn addition the effect of some parameters such as initialtemperature of the mixture on rate coefficients was notconsidered Here the optimization is improved by using theDE algorithm In this way we do not need any analytical rela-tionship and the optimal rate coefficients corresponding tothe desired operating conditions are determined So the newevolutionary-based approach is used to obtain the reactionrate coefficients of this mechanism under nine EPLP operat-ing conditions A DFSC scheme using CFD software (FLU-ENT) is employed to numerical simulation

2 Derivation of Chemical Kinetic Coefficients

A new evolutionary-based approach is implemented toobtain the reaction rate coefficients of the methane-aircombustion kinetics and the details are elaborately explainedin the following subsections The method consists of two

modules namely the simple Chemical Reactor Modeling(CRM) and the numerical optimizer For any given operatingcondition and a user defined detailed mechanism (as thetarget mechanism) the CRM gives the corresponding valuesof species concentrations that is NO and CO These arereserved as the target values for optimizer module With theaim of predicting NO and CO a global mechanism is speci-fied The unknown rate coefficients of this global mechanismare considered as the design variables used in the differentialevolution (DE) module Employing an interactive processthe CRM calculates the species concentrations through thecoefficients which are obtained by the DE The results arecompared with the detailed mechanism and this process iscontinued till the discrepancy between the predicted and thetarget values becomes as small as possible

21The Chemical Reactor Modeling (CRM) According to theprevious paragraph species concentrations are obtained fromthe CRM module Here a Perfectly Stirred Reactor (PSR)combined with a plug flow reactor (PFR) is addressed asthe CRM Possible detailed or predefined global mechanismsalong with a set of parameters that is operating pressureinitial mixture temperature residence time and equivalenceratio are the inputs Furthermore the length and diameterof the combustor are also added The CRM calculations havebeen carried out using the method described by Turns [26]It is noted that CHEMKIN [27] software is used for thecalculation of CRM The PSR-PFR output is distribution ofconcentrations along the reactor

22 Optimizer Module In this study the differential evolu-tion (DE) optimization algorithm [28] is employed to find therate coefficients for a predefined global mechanism throughthe procedure addressed in Section 2 Three key elementsshould be provided for the optimizer module (i) the designvariables (ii) the objective function and (iii) the constraintsThe design variables are the unknown rate coefficients of theglobal mechanism The cost function is intended to evaluatethe deviation of some species concentrations (ie NO andCO) predicted using the global mechanism from those cal-culated with the detailed mechanism Consequently the costfunction for the PSR-PFR is specified as

119868PFR =1

119883detmaxNO

int119871

0

10038161003816100381610038161003816119883detNO (119909) minus 119883

glbNO (119909)

10038161003816100381610038161003816 119889119909

+1

119883detmaxCO

int119871

0

10038161003816100381610038161003816119883detCO (119909) minus 119883

glbCO (119909)

10038161003816100381610038161003816 119889119909

(1)

where 119909119883 119871 are distance along the PFR mole fraction andlength of the reactor respectively Also det and glb denotedetailed and global mechanism respectively The optimiza-tion constraints are imposed by considering a finite intervalfor each design variable The intervals are assigned such thatthe best values lie between the lower and the upper boundsThe objective function is normalized based on the maximummole fraction of NO and CO It is obvious that one may addother target mole fractions to the above but then the modelaccuracy for predicting these two species will decrease







air combustion [3]


4

+ 15O2

rarrCO + 2H2

O 1198771

=1198601

[CH4

]1198611 [O2

]1198621 exp(minus1198631

119877119906

119879)

2 CO + 05O2

rarr CO2

1198772

= 1198602

[CO]1198612

[O2

]119862

2

exp(minus1198632

119877119906

119879)

3 CO2

rarr CO + 05O2

1198773

= 1198603

[CO2

]119861

3

exp(minus1198633

119877119906

119879)

4 N2

+ O2


= 1198604

[O2

]119861

4

[CO]1198624

exp(minus1198634

119877119906

119879)

5 N2

+ O2

rarr 2NO 1198775

= 1198605

119879minus05[N2

][O2

] exp(minus1198635

119877119906

119879)



2







119894




h

hp

ho

h3

dh

dm

r

db

do

l2

l3

di

➀

➁

➂







119889119894

119889119900

119889119887

119889119898

ℎ1

ℎ119900

ℎ forall




120597120588

120597119905+ nabla sdot (120588V) = 0 (2)



120597







120597

120597119905(120588119884119894

) + nabla sdot (120588V119884119894


+ 119877119894

(5)

where 119884119894



119894


997888rarr119869119894

= minus120588(119863119894119898

+120583119905

Sc119905

)nabla119884119894

(6)

where Sc119905



119905


119894



119894

119906119895


120597

120597119905(120588 119906119894

119906119895

) +120597

120597119909119896

(120588119906119896

119906119894

119906119895

)

= 119863119879119894119895

+ 119863119871119894119895

+ 119875119894119895

+ 0119894119895

+ 120598119894119895

(7)

where119863119879119894119895







119863
















1

1


2


3


4


5


6


7


8




0

20

40

60

80

100

120




NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140



NO

(ppm

v)

(b)





0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)




1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra















air combustion [3]


4

+ 15O2

rarrCO + 2H2

O 1198771

=1198601

[CH4

]1198611 [O2

]1198621 exp(minus1198631

119877119906

119879)

2 CO + 05O2

rarr CO2

1198772

= 1198602

[CO]1198612

[O2

]119862

2

exp(minus1198632

119877119906

119879)

3 CO2

rarr CO + 05O2

1198773

= 1198603

[CO2

]119861

3

exp(minus1198633

119877119906

119879)

4 N2

+ O2


= 1198604

[O2

]119861

4

[CO]1198624

exp(minus1198634

119877119906

119879)

5 N2

+ O2

rarr 2NO 1198775

= 1198605

119879minus05[N2

][O2

] exp(minus1198635

119877119906

119879)



2







119894




h

hp

ho

h3

dh

dm

r

db

do

l2

l3

di

➀

➁

➂







119889119894

119889119900

119889119887

119889119898

ℎ1

ℎ119900

ℎ forall




120597120588

120597119905+ nabla sdot (120588V) = 0 (2)



120597







120597

120597119905(120588119884119894

) + nabla sdot (120588V119884119894


+ 119877119894

(5)

where 119884119894



119894


997888rarr119869119894

= minus120588(119863119894119898

+120583119905

Sc119905

)nabla119884119894

(6)

where Sc119905



119905


119894



119894

119906119895


120597

120597119905(120588 119906119894

119906119895

) +120597

120597119909119896

(120588119906119896

119906119894

119906119895

)

= 119863119879119894119895

+ 119863119871119894119895

+ 119875119894119895

+ 0119894119895

+ 120598119894119895

(7)

where119863119879119894119895







119863
















1

1


2


3


4


5


6


7


8




0

20

40

60

80

100

120




NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140



NO

(ppm

v)

(b)





0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)




1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119889119894

119889119900

119889119887

119889119898

ℎ1

ℎ119900

ℎ forall




120597120588

120597119905+ nabla sdot (120588V) = 0 (2)



120597







120597

120597119905(120588119884119894

) + nabla sdot (120588V119884119894


+ 119877119894

(5)

where 119884119894



119894


997888rarr119869119894

= minus120588(119863119894119898

+120583119905

Sc119905

)nabla119884119894

(6)

where Sc119905



119905


119894



119894

119906119895


120597

120597119905(120588 119906119894

119906119895

) +120597

120597119909119896

(120588119906119896

119906119894

119906119895

)

= 119863119879119894119895

+ 119863119871119894119895

+ 119875119894119895

+ 0119894119895

+ 120598119894119895

(7)

where119863119879119894119895







119863
















1

1


2


3


4


5


6


7


8




0

20

40

60

80

100

120




NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140



NO

(ppm

v)

(b)





0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)




1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra




















1

1


2


3


4


5


6


7


8




0

20

40

60

80

100

120




NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140



NO

(ppm

v)

(b)





0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)




1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

20

40

60

80

100

120




NO

(ppm

v)

(a)


0

20

40

60

80

100

120

140



NO

(ppm

v)

(b)





0

01

02

03

04

CO (

mol

frac

tion)

(a)




0

01

02

03

04

CO (

mol

frac

tion)

(b)




1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1700

1800

1900

2000

2100

2200Ad

iaba

tic te

mpe

ratu

re (K

)

(a)


1850

1900

1950

2000

2050

2100

2150

Adia

batic

tem

pera

ture

(K)

(b)


0 02 04 06 08 10

2

4

6

8

10


NO

(ppm

v dr

y)

(rrmax

)2

(a)


0

03

06

09

12

15

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


5 Conclusion




0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0

5

10

15

20


NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2

(a)


0

03

06

09

12

15

18

21

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2

(b)


0

5

10

15

20

25

Experimental

NO

(ppm

v dr

y)

0 02 04 06 08 1(rrmax

)2


(a)

0

02

04

06

08

1

12

Experimental

CO (

mol

frac

tion

dry

)

0 02 04 06 08 1(rrmax

)2


(b)



O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra










O (p

pmv)

P = 3 atm

P = 65 atm

5

15

25

35

45

55

2 3 4 51

Residence time (ms)


Competing Interests


References









119909




119909





4







NO119909








and N2





O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra











O119909







119909

N2













Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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