Applied Thermal Engineering 106 (2016) 925–937

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate /apthermeng

Research Paper

On ignition mechanisms of premixed CH4/air and H2/air using a hotturbulent jet generated by pre-chamber combustion

http://dx.doi.org/10.1016/j.applthermaleng.2016.06.0701359-4311/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: lqiao@purdue.edu (L. Qiao).

Sayan Biswas, Saad Tanvir, Haifeng Wang, Li Qiao ⇑School of Aeronautics & Astronautics, Purdue University, West Lafayette, IN 47906, United States

h i g h l i g h t s

� Different types of pre-chamber generated hot jet ignition mechanisms are proposed.� Lean premixed CH4/air and H2/air ignition behavior by hot jet is investigated.� Two ignition mechanisms exist – jet ignition and flame ignition.� Damköhler number separates non-ignition, flame ignition and jet ignition regimes.

a r t i c l e i n f o

Article history:Received 23 March 2016Revised 9 June 2016Accepted 11 June 2016Available online 13 June 2016

Keywords:Turbulent jet ignitionFlame ignitionPre-chamber combustionDamköhler number

a b s t r a c t

An experiment was developed to investigate the ignition mechanisms of premixed CH4/air and H2/airmixtures using a turbulent hot jet generated by pre-chamber combustion. Simultaneous high-speedSchlieren and OH⁄ chemiluminescence imaging were applied to visualize the jet penetration and ignitionprocess inside the main combustion chamber. Results illustrate the existence of two ignition mecha-nisms: jet ignition and flame ignition. The former produced a jet comprising of only hot combustion prod-ucts from pre-chamber combustion. The latter produced a jet full of wrinkled turbulent flames and activeradicals. A parametric study was performed to understand the effects of pressure, temperature, equiva-lence ratio along with geometric factors such as orifice diameter and spark position on the ignition mech-anisms and probability. A global Damköhler number was defined to remove parametric dependency. Thelimiting Damköhler number, below which ignition probability is nearly zero, was found to be 140 for CH4/air and 40 for H2/air. Lastly, the ignition outcomes were plotted on the turbulent premixed combustionregime diagram. All non-ignition cases fell within the broken reaction zone regime, whereas flame and jetignition mostly fell within the thin reaction zone regime. These results can provide useful guidelines forfuture pre-chamber design and optimization.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Stringent emission regulations for oxides of nitrogen (NOx)require engine manufacturers to move towards ultra-lean opera-tion to reduce the peak combustion temperature and thereby min-imizing NOx formation [1,2]. Ultra-lean operation, however, givesrise to some serious challenges. As the fuel/air mixture becomesleaner, ignition becomes more difficult. Poor ignition or failure toignite the lean mixture can lead to misfires, which can lead toundesirable effects such as cycle-to-cycle variability, rough opera-tion, and reduction in efficiency and increased unburned hydrocar-bon emissions [3–5]. An approach that can potentially solve theseproblems is to use a hot turbulent jet to ignite the ultra-lean mix-

ture. The ignition of fuel/air mixtures by a hot jet is a processutilized in various applications ranging from pulse detonationengines, wave rotor combustor explosions, to supersonic combus-tors and natural gas engines [6]. Length scales of the combustorused in the current study is more appropriate for the land basedlarge-bore natural gas engines that offer efficient power produc-tion for the purposes of generating electricity and compressinggases. A small quantity of stoichiometric fuel/air was burned in aseparate combustion chamber called the pre-chamber. The com-bustion products were then discharged into the main chamberfilled with ultra-lean premixed fuel/air through a small diameterorifice in the form of a hot turbulent jet. Compared to a conven-tional spark plug, the hot jet has a much larger surface area leadingto multiple ignition sites on its surface which can enhance theprobability of successful ignition and cause faster flame propaga-tion and heat release.

Nomenclature

Da Damköhler numberdq quenching distancep pressureN overall reaction ordert time/ equivalence ratioq densityX mole fractiond orifice diameterD prechamber diameterb d=DCd discharge coefficientY expansion factorc specific heat ratioU0 centerline jet velocity

u0 velocity fluctuationI turbulent intensityM mach numbersL laminar burning speedl integral length scalelf flame thickness

Subscriptspre prechambermain main chamberi ith speciesmix mixturecrit criticaltran transition

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The physics behind ultra-lean jet ignition is rather complicated.The complex coupling between turbulence and chemistry needs tobe understood. Ignition mechanism heavily depended on the mix-ing characteristics and the composition of the hot jet. The compe-tition between thermal and mass diffusivity between the hotexhaust gases and the cold fresh lean mixtures and presence ofactive radicals such as H, O, HO2, and OH all affect the ignition pro-cess [7]. Till date, several computational and experimental studieshave been conducted to explore the fundamental mechanisms ofhot jet ignition.

Chen et al. [8] was one of the earliest investigators to studyturbulent jet ignition. He found that the formation of the large-scale eddy structures of the turbulent jet were first generatedby vortex couples. The external features of the jet were domi-nated by these eddy structures. The flame shape, speed, and prop-agation processes had a strong dependence on the number andthe locations of the ignition sources deposited onto turbulentjet. Pitt et al. [9] showed the jet ignition system exhibits shorterdelay times and increased burn rates when compared to a con-ventional spark system. Yamaguchi et al. [10] investigated theeffect of orifice diameter on turbulent jet ignition in a dividedspherical combustion chamber. Their results showed that a smal-ler orifice diameter resulted in ‘well-dispersed burning’, the largerorifice diameter resulted in ‘flame kernel torch ignition’, and thelargest orifice diameter enabled laminar flame to pass throughthe orifice. Wallesten et al. [11] explored the effect of spark posi-tion in the pre-chamber in relation to orifice on the combustionefficiency of the main chamber. They found that the spark posi-tion farther away from the orifice showed higher combustion ratethan the positions close to the orifice. Elhsnawi and Teodorczyk[12] explored ignition of near stoichiometric H2/O2 mixture by ahot inert gas jet (argon and nitrogen) in a detonation tube withan orifice size ranging from 8 to 11.2 mm. It was observed thatthe main chamber ignition initiates from jet side surfaces in theturbulent mixing zone. Sadanandan et al. [13,14] investigatedignition of H2/air mixtures by a hot jet using simultaneoushigh-speed laser Schlieren and OH Planar Laser Induced Fluores-cence (PLIF) techniques. They did not observe any noticeableamount of OH radicals at the orifice exit and speculated that pos-sible heat loss through the orifice walls had a strong influence onquenching the pre-chamber flame. Additionally, they found thatignition in the main chamber occurs near the jet tip and not atthe lateral sides of the jet.

Studies recently conducted by Toulson et al. [15–18] werefocused on the effect of different pre-chamber fuels (H2, C3H8, nat-

ural gas, CO) on combustion stability, extension of lean limit andemission control in an optically accessible engine. The lean opera-tion enabled by the turbulent jet ignition system resulted in nearelimination of in-cylinder NOx emissions; significant improve-ments in efficiency and fuel economy were observed. Pereraet al. [19] investigated the ignitability and ignition delay time forethylene/air ignited by a hot jet and found a lean equivalence ratiolimit of 0.4 for the main-chamber mixture. Carpio et al. [20]numerically studied the critical radius of an axisymmetric jet com-prising combustion products for ignition of H2/air using detailedchemistry. For a given equivalence ratio, the critical radius wasfound to increase with increasing injection velocities. On the otherhand, for a given injection velocity, the smallest critical radius isfound at stoichiometric conditions. Karimi et al. [21] numericallystudied ignition of ethylene/air and CH4/air in a long constant-volume combustor using a traversing hot jet. They found that ahigher traverse rate of the hot jet increases delay time and loweredthe entrainment rate and in turn jet-vortex interaction. Shah et al.[22,23] studied the effect of pre-chamber volume and orifice diam-eter for heavy duty natural gas engines. They found that increasingthe pre-chamber to main chamber volume ratio does not signifi-cantly increase the effectiveness of the pre-chamber as an ignitiondevice. Orifice diameter was not found to have an effect on the leanlimit except for the largest pre-chamber volume cases. Wang et al.[24] studied three different ignition methods including spark plug,hot jet and pre-detonator on a pulse detonation engine. They foundthe detonation initiation time and deflagration to detonation tran-sition distance became shorter for hot jet ignition compared tospark ignition. Biswas and Qiao [25] explored the ultra-leanflammability limit of H2/air using supersonic hot jet ignition. Theyfound the ultra-lean limit of H2/air extends to / ¼ 0:22 using asupersonic nozzle. However, thermo-acoustic combustion instabil-ity triggered at ultra-lean limit.

Many of the studies mentioned above, especially those con-ducted using an optically-accessible engine or a real engine, showgreat potential of hot jet ignition for extra-lean combustion. Ourfundamental understanding, however, is far from complete. Forexample, there are contradictions in literature on the ignitionlocations. Sadanandan et al. [13] observed ignition occurring nearthe tip of the jet, whereas Elhsnawi et al. [12] observed ignitionoccurring on the lateral sides of the jet. Furthermore, dependingon pre-chamber geometry and operating conditions, main-chamber ignition can be caused by either a flame jet containingactive radicals or a hot jet containing combustion products with-out any radicals. For example, Toulson et al. [15–18] found a jet

S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937 927

torch is responsible for ignition although it was not clear whetherthe torch contained active radicals.

Motivated by this, an apparatus that uses a dual combustionchamber design (a small pre-chamber resided within the big mainchamber) was developed to explore the fundamental mechanismsof turbulent hot jet ignition. Two fuels, CH4 and H2 were studied.Simultaneous high-speed Schlieren and OH⁄ chemiluminescenceimaging was applied to visualize the jet penetration and ignitionprocesses. It was found there exist two ignition mechanisms: flameignition (ignition by a reacting jet) and jet ignition (ignition by areacted jet). A parametric study was conducted to understandthe effects of a number of parameters on the ignition mechanismand probability, including orifice diameter, initial temperatureand pressure, fuel/air equivalence ratios in both chambers, andpre-chamber spark position. The mean and fluctuation velocitiesof the transient hot jet were calculated according to the measuredpressure histories in the two chambers. A limiting global Damköh-ler Number was found for each fuel, under which the ignition prob-ability was nearly zero. Lastly, the ignition outcome of all tests (noignition, flame ignition and jet ignition) were marked on the clas-sical turbulent combustion regime diagram. These results provideimportant guidelines for design and optimization of efficient andreliable pre-chambers for natural gas engines.

2. Experimental method

2.1. Apparatus

The schematic of the experimental setup is shown inFig. 1a and b. A small volume, 100 cc cylindrical stainless steel(SS316) pre-chamber was attached to the rectangular(30.48 cm � 15.24 cm � 15.24 cm) carbon steel (C-1144) mainchamber. The main chamber to pre-chamber volume ratio waskept at 100. A stainless steel orifice plate with a diameter rangingfrom 1.5 to 4.5 mm (d = 1.5, 2.5, 3, 4.5 mm) with a fixed orificelength to diameter ratio at L=d ¼ 5, separated both chambers. Athin, 25-lm thick aluminum diaphragm isolated both chamberswith dissimilar equivalence ratios from mixing. The fuel/air mix-ture in both chambers was heated up to 600 K using built-in heat-ing cartridges (Thermal Devices, FR-E4A30TD) inserted into the

Fig. 1. Schematic of (a) experimental setup for ignition of premixed CH4/air and H2

(b) pre-chamber and main chamber assembly.

main chamber walls. The mixture in the pre-chamber was ignitedby an electric spark created by a 0–20 kV capacitor discharge igni-tion (CDI) system. An industrial grade double Iridium Bosch sparkplug was attached at the top of the pre-chamber. Spark locationwas varied using spark plugs with longer electrodes from Auburnigniters (Model I-3, I-31, I-31-2, I-32, OJ-21-5). The transient pres-sure histories of both chambers were recorded using high fre-quency Kulite (XTEL-190) pressure transducers combined with aNational Instrument’s compact data acquisition chassis (cDAQ-9178) with NI-9237 signal conditioning and pressure acquisitionmodule via LabVIEW software. Two K-type thermocouples werepositioned at the top and bottom of the main chamber to ensureuniform temperature lengthwise thus minimizing natural convec-tion or buoyancy effect. A 25 mm thick polymer insulation jacketwas wrapped around the pre-chamber and main chamber to min-imize heat loss. Fuel (industrial grade CH4 and H2) and air wereintroduced separately to the main chamber using the partial pres-sure method. Unlike the main chamber where fuel and air mixed inthe chamber, fuel/air for pre-chamber was premixed in a smallstainless steel mixing chamber (2.54 cm diameter, 10 cm long)prior going into the pre-chamber.

2.2. Diaphragm rupture assessment

While the fuel/air mixture in the pre-chamber was always keptstoichiometric, the equivalence ratio in the main chamber variedfrom / = 0.45–1.0. To separate two chambers with different equiv-alence ratios, a diaphragm was necessary. A lightweight,25 ± 1.25 lm thick aluminum sheet (aluminum alloy1100) wasused as diaphragm material. A ‘+’ shaped scoring was made atthe diaphragm center to provide stress concentration and easy rup-ture. The ruptured diaphragm was replaced after each test. Whenthe pressure difference between the two chambers reached athreshold, the diaphragm ruptured, resulting in a transient hotjet. The characterization of the threshold pressure and diaphragmrupture time were essential in order to accurately determine igni-tion delay in main chamber. Ignition delay is defined as the timebetween the diaphragm rupture and the onset of ignition inmain chamber. A series of tests were conducted and the pressurethreshold was found to be 0.21 MPa which depends on the

/air mixtures using a hot turbulent jet generated by pre-chamber combustion,

Fig. 2. (a) Rupture time and rupture pressure shown on a typical H2/air pre-chamber pressure profile, (b) rupture time for various orifice sizes.

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diaphragm thickness and material only. The rupture time, which islargely influenced by how fast the pressure of the pre-chamberrises, depends on the type of fuel used and the fuel/air equivalenceratio in the pre-chamber (which was fixed) only, regardless of theorifice size. Fig. 2a shows the rupture time and rupture pressure fora typical pre-chamber pressure profile for H2/air mixture. Fig. 2bshows rupture times for various orifice sizes for both CH4/air andH2/air mixtures. The CH4/air mixture was observed to have a longerrupture time, 4.15 ± 0.2 ms, than the H2/air mixture, 2.6 ± 0.1 ms.

2.3. High-speed Schlieren and OH⁄ chemiluminescence imaging

A customized trigger box synchronized with the CDI sparkignition system sent a master trigger to two high-speed camerasfor simultaneous Schlieren and OH⁄ chemiluminescence imaging.The main chamber was installed with four rectangular(14 cm � 8.9 cm � 1.9 cm) quartz windows (type GE124) on itssides for optical access. One pair of the windows was used forthe z-type Schlieren system. Another pair was selected for simulta-neous OH⁄ chemiluminescence measurements.

The high-speed Schlieren technique was utilized to visualize theevolution of the hot jet as well as the ignition process in the mainchamber. The system consisted of a 100W (ARC HAS-150 HP)mercury lamp light source with a condensing lens, two concaveparabolic mirrors (15.24 cm diameter, focal length 1.2 m), and ahigh-speed digital camera (Vision Research Phantom v7). Schlierenimages were captured with a resolution of 800 � 720 pixels with aframe rate up to 12,000 fps.

The high-speed OH⁄ chemiluminescence measurement pro-vided a better view of the ignition and flame propagation pro-cesses. A high-speed camera (Vision Research Phantom v640),along with video-scope gated image intensifier (VS4-1845HS) with105 mm UV lens, were utilized to detect OH⁄ signals at a very nar-row band 386 ± 10 nm detection limit. The intensifier was exter-nally synced with the camera via high-speed relay and acquiredimages at the same frame rate (up to 12,000 fps) with the Phantomcamera. A fixed intensifier setting (gain 65,000 and gate width20 ls, aperture f8) was used all through.

3. Results and discussion

As described earlier, the high-speed Schlieren techniqueenabled visualization of the jet penetration, ignition and the subse-

quent turbulent flame propagation processes in the main chamber.High-speed OH⁄ chemiluminescence was used to identify the pres-ence of OH radicals. It also facilitated in determining whether thehot jet coming out from the pre-chamber contains hot combustionproducts only or also contains active radicals such as OH. A numberof experiments were carried out for various initial pressures, orificediameters, and spark locations at varying equivalence ratio, / inmain chamber for CH4/air and H2/air, while keeping pre-chamberequivalence ratio stoichiometric.

Tables 1 and 2 summarize the experimental conditions alongwith ignition mechanism outcomes and the ignition delay timesfor CH4/air and H2/air mixtures, respectively. Many test conditionsdid not result in main chamber ignition. Only the test conditionsthat resulted in successful main chamber ignition were includedin Tables 1 and 2. For successful ignition, two distinct mechanismswere observed: (a) flame ignition (ignition by a reacting jet) - whenthe pre-chamber flame survived the high stretch rate and heat lossthrough the orifice and resulted in a jet containing many flame ker-nels which ignite the main chamber mixture; and (b) jet ignition(ignition by a reacted jet) - when the pre-chamber flame quenchedwhile passing through the orifice and resulted in a jet containinghot combustion products only which then ignited the main cham-ber mixture. These are discussed in detail in subsequent sections.

3.1. Flame ignition (ignition by a reacting jet) mechanism

In flame ignition, the hot jet contains remnants of the pre-chamber flame. This occurs if the pre-chamber flame is notquenched by wall heat loss and high stretch rate through the ori-fice. Depending on the pre-chamber pressure, temperature, equiv-alence ratio and the orifice diameter, the flame that passes throughthe orifice can be either laminar or turbulent. The Reynolds Num-ber at the jet exit was used to determine if the flow was laminar,transient or turbulent. We used the criteria that for the Reynoldsnumber above 4000 the flow is fully turbulent. Calculated Reynoldsnumbers for all the test conditions were between 4200 and 12,000.So for all of our test conditions the flame jet was turbulent. The hotjet contains many small turbulent flames penetrating into the mainchamber causing almost instantaneous ignition of the main cham-ber mixture.

Figs. 3 and 4 show a time sequence of the simultaneous Sch-lieren and OH⁄ chemiluminescence images of the flame ignitionprocesses for CH4/air (test condition 20 in Table 1) and H2/air (test

Table 1Test conditions for CH4/air ignition.

Test no. Orifice diameter (mm) T (K) P (MPa) Spark location Pre-chamber, / Main chamber, / Ignition mechanism Ignition delay, ms

Effect of spark location1 4.5 500 0.1 Top 1.0 0.8 Jet ignition 7.822 4.5 500 0.1 1/3 from top 1.0 0.8 Jet ignition 7.643 4.5 500 0.1 Middle 1.0 0.8 Jet ignition 7.584 4.5 500 0.1 Bottom 1.0 0.8 Jet ignition 7.10

Effect of orifice diameter5 2.5 500 0.1 Top 1.0 1.0 Jet ignition 18.326 2.5 500 0.4 Top 1.0 1.0 Jet ignition 16.217 3 500 0.1 Top 1.0 1.0 Jet ignition 15.438 3 500 0.4 Top 1.0 1.0 Jet ignition 12.219 4.5 500 0.1 Top 1.0 1.0 Jet ignition 6.72

10 4.5 500 0.4 Top 1.0 1.0 Flame ignition 2.27

Effect of initial pressure11 4.5 500 0.1 Top 1.0 1.0 Jet ignition 6.7212 4.5 500 0.3 Top 1.0 1.0 Flame Ignition 3.0813 4.5 500 0.4 Top 1.0 1.0 Flame ignition 2.27

Effect of main chamber equivalence ratio14 3 500 0.1 Top 1.0 1.0 Jet ignition 15.4315 3 500 0.4 Top 1.0 0.9 Jet ignition 14.4816 3 500 0.4 Top 1.0 0.8 Jet ignition 16.2217 3 500 0.4 Top 1.0 0.7 Jet ignition 17.8618 3 500 0.4 Top 1.0 0.5 Jet ignition 19.1519 4.5 500 0.4 Top 1.0 1.0 Flame ignition 2.2720 4.5 500 0.4 Top 1.0 0.9 Flame ignition 2.8021 4.5 500 0.4 Top 1.0 0.7 Flame ignition 4.1222 4.5 500 0.4 Top 1.0 0.6 Flame ignition 5.3623 4.5 500 0.4 Top 1.0 0.5 Flame ignition 7.76

Table 2Test conditions for H2/air ignition.

Test no. Orifice diameter (mm) T (K) P (MPa) Spark location Pre-chamber, / Main chamber, / Ignition mechanism Ignition delay, ms

Effect of spark location1 4.5 300 0.4 Top 1.0 1.0 Flame ignition 1.282 4.5 300 0.4 1/3 from top 1.0 1.0 Flame ignition 1.223 4.5 300 0.4 Middle 1.0 1.0 Flame ignition 1.164 4.5 300 0.4 Bottom 1.0 1.0 Flame ignition 1.06

Effect of orifice diameter5 2.5 300 0.1 Top 1.0 1.0 Jet ignition 9.586 2.5 300 0.5 Top 1.0 1.0 Jet ignition 4.327 3 300 0.1 Top 1.0 1.0 Jet ignition 8.788 3 300 0.5 Top 1.0 1.0 Flame ignition 2.159 4.5 300 0.1 Top 1.0 1.0 Flame ignition 2.7710 4.5 300 0.5 Top 1.0 1.0 Flame ignition 1.13

Effect of initial pressure11 3 300 0.1 Top 1.0 0.9 Jet ignition 9.0612 3 300 0.3 Top 1.0 0.9 Flame ignition 3.6013 3 300 0.5 Top 1.0 0.9 Flame ignition 2.42

Effect of main chamber equivalence ratio14 2.5 300 0.1 Top 1.0 1.0 Jet ignition 9.5815 2.5 300 0.1 Top 1.0 0.9 Jet ignition 9.0116 2.5 300 0.1 Top 1.0 0.7 Jet ignition 8.3117 2.5 300 0.1 Top 1.0 0.6 Jet ignition 10.5118 2.5 300 0.1 Top 1.0 0.5 Jet ignition 12.8519 4.5 300 0.1 Top 1.0 1.0 Flame ignition 2.7720 4.5 300 0.1 Top 1.0 0.9 Flame ignition 3.2421 4.5 300 0.1 Top 1.0 0.7 Flame ignition 4.0122 4.5 300 0.1 Top 1.0 0.5 Flame ignition 5.2223 4.5 300 0.1 Top 1.0 0.45 Flame ignition 5.78

S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937 929

condition 1 in Table 2), respectively. As shown in Fig. 3, shortlyafter (about 0.67 ms) the diaphragm had ruptured, noticeableOH⁄ signal was detected in the jet just coming out of the orificefrom the pre-chamber. This indicates the flame in the pre-chamber did not extinguish after passing through the orifice.Rather, it developed into a turbulent flame jet. The OH⁄ signal grewin time; a jet containing ample OH⁄ radicals appeared at 1.67 ms.The onset of the main chamber ignition occurred at 2.8 ms. Ignition

of the main-chamber mixture was initiated from the entire surfaceof the jet and then propagated outwardly. Similar behavior wasobserved for H2/air as shown in Fig. 4. Noticeable amount of OH⁄

signal was detected in the jet just coming out of the orifice, whichgrew over time and eventually caused ignition of the main cham-ber mixture at 1.28 ms. For the same initial conditions and geomet-ric configurations, H2/air mixtures exhibit approximately half theignition delay time compared to CH4/air mixtures.

t=0.67 t=1.17 t=1.67 t =2.80 t =3.42 t=4.67

Fig. 3. Time sequence of simultaneous Schlieren (top) and OH⁄ chemiluminescence (bottom) images showing flame ignition process for CH4, test condition 20 in Table 1(Vprechamber ¼ 100cc, orifice diameter = 4.5 mm, Pinitial ¼ 0:4 MPa, Tinitial ¼ 500 K, /prechamber ¼ 1:0, /main chamber ¼ 0:9). The ignition delay, signition is 2.80 ms.

t=0.95 t=1.08 t=1.28 t =1.34 t =1.45 t=1.70

Fig. 4. Time sequence of simultaneous Schlieren (top) and OH⁄ chemiluminescence (bottom) images showing flame ignition process for H2, test condition 1 in Table 2(Vprechamber ¼ 100cc; orifice diameter = 4.5 mm, Pinitial ¼ 0:4 MPa, Tinitial ¼ 300 K, /prechamber ¼ 1:0, /main chamber ¼ 1:0). The ignition delay, signition is 1.28 ms.

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The pressure profiles in the pre-chamber and main chamber areshown in Fig. 5a and b for the CH4/air and H2/air cases discussedabove. The trends are similar for both fuels, although H2/air hasshorter ignition delay. The pre-chamber pressure first raised andthen reached a maximum indicating combustion in the pre-chamberwas completed. Shortly after that, the pressure in themainchamber started to rise as a result of ignition in the main-chamber.The main-chamber pressure reached a maximum at 12.6 ms for

CH4/air and 8.9 ms for H2/air, indicating that the reactants in themain chamber were completely consumed by these times. Shortlyafter, the main-chamber pressure started to decrease because ofcooling through chamber walls. During the combustion process ofthe main-chamber mixture, some burned gases were pushed intothe pre-chamber as the pressure in the main chamber had becomehigher than that of the pre-chamber. As a result, the pre-chamberpressure profile showed a second peak.

Fig. 5. Typical pressure profiles for flame ignition. Pressure profiles in pre-chamber and main chamber for (a) CH4/air flame ignition, test condition 20 in Table 1, (b) H2/airflame ignition, test condition 1 in Table 2.

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3.2. Jet ignition (ignition by a reacted jet) mechanism

For jet ignition mechanism, the hot jet coming from the pre-chamber contained hot combustion products only. This meansthe pre-chamber flame had extinguished while passing throughthe orifice due to heat loss and/or high stretch rate. Because thejet contained very little or no radicals, OH⁄ signal could not bedetected at the orifice exit. Ignition by a jet of combustion prod-ucts had several definite characteristics in comparison to theflame ignition mechanism and will be discussed in followingsection.

Figs. 6 and 7 show time sequence of simultaneous Schlieren andOH⁄ chemiluminescence images of the jet penetration and ignitionprocesses for CH4/air (test condition 1 in Table 1) and H2/air (testcondition 16 in Table 2), respectively.

As soon as the aluminum diaphragm ruptured, the jet startedflowing into the main chamber. However, unlike flame ignitionmechanism, no appreciable OH⁄ chemiluminescence signal wasdetected in the jet coming out of the orifice during this period. This

t =1.48 t=6.43 t =7.82 t = 8.43

Fig. 6. Time sequence of simultaneous Schlieren (top) and OH⁄ chemiluminescence ((Vprechamber ¼ 100cc;orifice diameter = 4.5 mm, Pinitial ¼ 0:1 MPa, Tinitial ¼ 500 K, /prechamber

indicates the pre-chamber flame had been quenched when passingthrough the orifice. After some time, OH⁄ signal was first detectedat a location a few centimeters downstream of the orifice and themain-chamber pressure started to rise. The jet lasted about7.82 ms for CH4/air and 8.31 ms for H2/air before it ignited themain chamber mixture. These ignition delay times are longer incomparison to the typical ignition delays observed in flame igni-tion (H2/air � 1–6 ms, CH4/air � 1–8 ms). Additionally, we foundthat ignition started from the side surface of the jet. Ignition atthe jet tip was not observed for any of our test conditions wherethe jet ignition mechanism holds. This is consistent with the obser-vations of Elhsnawi et al. [12] but conflicts with Sadanandan et al.[13] who observed ignition starting at the jet tip. Furthermore,both the Schlieren and OH⁄ chemiluminescence images showedthat ignition started in a region that was 2–3 cm downstream ofthe orifice exit for CH4/air and 4–5 cm downstream of orifice exitfor H2/air. The reason why ignition took place in these regions/locations is explained by examining the jet velocities and theDamköhler Numbers in the following sections.

t=9.80 t=11.18 t = 13.8

bottom) images showing jet ignition process for CH4, test condition 1 in Table 1¼ 1:0, /mainchamber ¼ 0:8). The ignition delay, signition is 7.82 ms.

t =2.50 t =8.31 t=9.63 t= 10.76 t = 10.88 t=11.13 t = 11.75

Fig. 7. Time sequence of simultaneous Schlieren (top) and OH⁄ chemiluminescence (bottom) images showing jet ignition process for H2, test condition 16 in Table 2(Vprechamber ¼ 100cc;orifice diameter = 2.5 mm, Pinitial ¼ 0:1 MPa, Tinitial ¼ 300 K, /prechamber ¼ 1:0, /mainchamber ¼ 0:7). The ignition delay, signition is 8.31 ms.

Fig. 8. Typical pressure profiles for jet ignition. Pressure profiles in pre-chamber and main chamber for (a) CH4 jet ignition, test condition 1 in Table 1, (b) H2 jet ignition, testcondition 16 in Table 2.

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Fig. 8a and b shows the typical pressure histories in the pre-chamber and the main chamber for the CH4/air and H2/air casesdiscussed above. The ignition delay for CH4/air was similar to thatof H2/air. After the onset of spark ignition in the pre-chamber, itspressure started to rise. This increased pressure in the pre-chamber and created a transient pressure difference responsiblefor driving the hot combustion products through the orifice inthe form of a turbulent hot jet. At the end of main chambercombustion, which is marked by the peak of the main-chamberpressure profile, part of the main chamber combustionproducts entered into the pre-chamber. Therefore, the pre-chamber pressure increased again following the main chamberpressure profile.

3.3. Parametric effects on ignition mechanisms and ignition probability

The two ignition mechanisms discussed in preceding sectionshave certain identifiable characteristics. The ignition delay time

for flame ignition is rather short as compared to jet ignition. Thisis because the flame jet contains key radicals and intermediate spe-cies that promote chain-branching reactions. Whereas, jet ignitiontakes longer time because the quenched flames need time to mixwith the cold unburned ambient gases in the main chamber. Fur-thermore, flame ignition was normally initiated from the entiresurface of the jet, whereas jet ignition was always observed start-ing from the lateral sides of jet at a location a few centimetersdownstream of the orifice. Lastly, for jet ignition, OH⁄ signal wasabsent in the jet coming out of the pre-chamber through the ori-fice, while it can be detected in the jet for flame ignition. Forinstance, both Figs. 6 and 7 suggest that the pre-chamber flamehad quenched in the orifice and the hot jet consisted of combustionproducts only. The occurrence of flame or jet ignition mechanismdepends on a number of parameters such as orifice diameter, initialpressure, fuel type, and equivalence ratios. In the following, we willdiscuss the effects of these parameters on ignition mechanismsand ignition probability.

Fig. 9. The mean centerline jet velocity, U0 and the Mach number at the orifice exitas a function of time for various CH4/air test conditions.

S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937 933

The results presented in Tables 1 and 2 show that keeping allother variables unchanged, a decreasing orifice diameter switchesthe ignition mechanism from flame ignition to jet ignition. A smal-ler orifice imposes a higher stretch rate to the pre-chamber flame,hence flame extinction becomes more likely in a smaller orificeleading to jet ignition. This observation is consistent with theresults of Iida et al. [26] who studied the transient behavior ofCH4/air flame flowing into a narrow channel at atmospheric pres-sure. They found that the flame can either pass, standstill, or extin-guish depending on the mixture equivalence ratio, the channelwidth, and the flame inflow velocity. They also found a criticalchannel width of 2–3.5 mm, below which the flame could not sur-vive and would extinguish due to high stretch rate which conse-quently resulted in high mixing rate between the flame front andthe cold unburned ambient gases.

The results in the tables also suggest that as pressure increasesflame ignition mechanism becomes more prevalent. This attributecan well be explained by flame quenching behavior as a function ofpressure. As defined in [27], the quenching distance, dq is the min-imum separation distance between two cold, flat plates, beyondwhich a flame cannot pass. Quenching distance is expected to beon the same order as flame thickness. This is because the quench-ing distance is the characteristic length through which heat is con-ducted from the hot flame to the cold wall. It is reasonable toassume that quenching distance is proportional to laminar flamethickness, dq � lf [27]. With the increase in pressure, CH4/air andH2/air flame thicknesses decrease. As a result, a higher pressureresulted in a shorter quenching distance. This means that at highpressures, prechamber flame can pass through a smaller diameterorifice without quenching. Thus ignition mechanism shifted toflame ignition at higher pressures.

For all test conditions, the pre-chamber mixture was kept atstoichiometry, / ¼ 1, whereas the main chamber mixture was var-ied from stoichiometric to lean conditions. Decreasing the main-chamber equivalence ratio will reduce ignition probability,although it does not affect the ignition mechanism. Lastly, tounderstand the effect of spark location in the pre-chamber onthe ignition mechanism and probability, three locations weretested (one very close to the top of the pre-chamber, one in themiddle, and the third one very close to the bottom of thepre-chamber and near the orifice). The results showed that sparklocation had little effect on ignition mechanism and probability.However, depending on the spark plug position the ignition delaytime varied slightly. The spark plug location closest to the orificeresulted in marginally shorter (10–15% lower) ignition delay timesas compared to the farthest spark location.

3.4. Jet characteristics and the global Damköhler number

To understand the jet ignition mechanism and the complexinteractions between chemistry and turbulent mixing, knowledgeof the hot transient jet produced by pre-chamber combustion isrequired. For a given orifice diameter, d, the mean jet velocity atthe orifice exit, U0, was calculated based on the experimentallymeasured pressure drop between the pre-chamber and the mainchamber, DPðtÞ ¼ PpreðtÞ � PmainðtÞ, and the gas properties. Due tothe low viscosity of pre-chamber combustion products (order of�O[10�5]), the boundary layer thickness is negligible comparedto orifice diameter, d. Thus the velocity profile at the orifice exitcan be assumed to be flat-topped (plug flow). Then the mean jetvelocity of the compressible gas flow at the orifice exit, U0ðtÞ canbe expressed as [28],

U0ðtÞ ¼ CY

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2DPðtÞqmixðtÞ

sð1Þ

where qmixðtÞ ¼P

iXiqi is the density of the pre-chamber gas mix-

ture, C ¼ Cd=

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� b4

q, Y is the expansion factor to account for the

compressibility effect and it is a function of c;b and ppre=pmain. Thevalue of Cd was 0.97, and b, the ratio of orifice to prechamber diam-eter, varied from 0:02 to 0:15. Y was then calculated using tabulateddata presented in [28]. The values of Y ranged from 0:65 to 0:82depending on ppre=pmain and b. Mixture density and specific heatratio were calculated using ChemkinPro [30] Equilibrium module.Heat loss through the orifice wall was neglected. Even though theorifice diameters were small, the transient jet lasted for 1–20 msonly. This short period of time coupled with the high velocity ofthe jet while passing through the orifice, did not result in significantheat conduction to the orifice wall. The jet exit temperatures weremeasured using hot wire pyrometry technique and showed 2.5%variation of the hot jet temperature from calculated temperatureswithout considering heat loss. Additionally, the Kulite pressuretransducer had an uncertainty ±0.1% of its full scale value. Thisresulted in an uncertainty of 2.51% in density and 2.92% in velocitycalculations due to uncertainty in pressure and temperature.

Fig. 9 shows time evolution of the mean centerline jet velocityat the orifice exit, U0, for three different CH4/air test conditions(test number 1, 7 and 8 in Table 1 respectively). All of theminvolved the jet ignition mechanism. The purpose was to showthe effect of orifice diameter, d and the initial pressure, p on thejet velocities, and subsequently on the ignition mechanism. Asexpected, for a given pressure, a smaller orifice resulted in higherjet velocities than a larger orifice. For a fixed orifice size, as pres-sure goes up, the density increased significantly. However, athigher pressure the pressure difference, DP increased as well. Thusfor a fixed-diameter orifice, the centerline mean jet velocity variesonly slightly in the pressure range of 0.1–0.4 MPa, as shown inFig. 9. For all cases, the hot jet started to flow into the main cham-ber after the diaphragm ruptured 4.15 ms after spark ignition inthe pre-chamber. As the pre-chamber pressure went up, the jetaccelerated, reached a maximum, and then started decelerating.We marked the instant at which ignition of the main chambermixture took place in Fig. 9. The results show that main-chamberignition did not take place during the jet acceleration process.Rather, it always occurred when the jet was decelerating. The cor-responding centerline velocity U0 at the orifice exit for these threecases ranges from 109 m/s to 187 m/s. These velocities were lessthan half of their respective maximums.

Table 3Global Damköhler number calculation for CH4/air at 1 atm and 300 K, d = 2.5 mm.

/ sL (cm/s) lF (lm) u0 (m/s) Da

0.6 10.52 27 1.24 390.7 19.34 21 1.62 700.8 27.91 17 1.78 1110.9 32.65 14 1.93 1451.0 37.41 12 2.42 155

Table 4Global Damköhler number calculation for H2/air at 1 atm and 300 K, d = 2.5 mm.

/ sL (cm/s) lF (lm) u0 (m/s) Da

0.5 54.45 16 5.12 430.6 90.32 12.5 7.63 560.7 121.1 10 11.21 580.8 148.94 8 16.25 590.9 175.32 6 20.18 721.0 201.53 4.5 22.72 93

934 S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937

To evaluate the compressibility effect, the Mach numbers of theCH4/air jets were plotted in the same Fig. 9. Fig. 9 shows the Machnumber as a function of time corresponding to the transient veloc-ity profiles discussed above. Only for a short period of time duringits lifetime, the hot jet became chocked. Although for the majorityof its lifetime, it remained subsonic. We observed that the mainchamber ignition started at a Mach number that was much lowerthan the maximum Mach number of the jet during its lifetime.Although the maximum Mach number for CH4/air was rangingfrom 1.4 to 0.41, for majority of the test conditions the flowremained subsonic. The jet exit Mach number, at the momentwhen ignition in the main chamber just started, remained less than0.3 for all test conditions.

As the hot jet penetrates into the main chamber, the jet surfacecontains many small eddies. These eddies help mixing the hot jetwith the cold, unburned fuel/air mixture in the main chamber.As turbulent eddies dissipate energy, the temperature of the hotjet drops during the penetrating process. If jet temperature dropstoo rapidly, it may not be able to ignite the main chamber mixture.The competition between the turbulent mixing timescale and thechemical timescale, characterized by the Damköhler number, hasa deterministic effect of the ignition outcome (successful or failed).The maximum initial pressure and temperature in the presentexperiments were limited to 0.5 MPa and 500 K. However, theprior-ignition pressure and temperature in natural gas enginescan be as high as 10–25 MPa and 800–900 K. Thus it was importantto remove the parametric dependency of current data so theknowledge developed here can be applied to engine relevant con-ditions. To make the results more useful, we generated a diagramto illustrate the range of the Damköhler numbers that likely resultsin successful ignition (high ignition probability) based on the manytests we had performed. This diagram could be used as a tool toevaluate ignition probability at various operating and design con-ditions such as different pressures, temperatures, equivalenceratios and pre-chamber designs.

The Damköhler number, Dawas defined as the ratio of the char-acteristic flow timescale, sF to the characteristic chemical reactiontimescale, sC .

Da ¼ sFsC

ð2Þ

Here the characteristic flow timescale is the turbulent mixingtimescale, which largely depends on the turbulent mean and fluc-tuation velocities (or the turbulent Reynolds number). The charac-teristic chemical timescale is the ignition timescale, which mainlydepends on the chemistry of the reactions and the temperature atwhich the reactions take place. The Damköhler number can furtherbe written in terms of the fuel/air thermo-physical properties andflow field information as [29],

Da ¼ sLlu0lf

ð3Þ

sL and lf were calculated using the PREMIX module of ChemkinPro[30]. lf was estimated as full width half maximum (FWHM) of thevolumetric heat release rate from the PREMIX calculations. Thelocal velocity fluctuations at the orifice exit were determined usingI and U0, u0 ¼ U0I. Turbulent intensity for internal flows can be esti-

mated using an empirical correlation [28], I ¼ u0=U0 ¼ 0:16Re�1=8d .

The integral length scale was estimated along the orifice lip lineusing the correlation for compressible round jets [31,32],l=d ¼ 0:052x=dþ 0:0145; where x is distance downstream of orificeexit. Tables 3 and 4 provide values for turbulent intensity, laminarflame speed and the flame thickness to calculate the globalDamköhler number for CH4/air and H2/air at 1 atm, 300 K and usingan orifice diameter of 2.5 mm.

Ignition is a highly localized phenomenon. Ideally, the Damköh-ler number near the ignition location i.e. ‘local’ Damköhler numbershould be calculated considering ‘local’ flow conditions. However,such information is very difficult to obtain experimentally becauseof the unsteady, highly transient nature of the hot jet. So wedefined a ‘‘global” Damköhler number using the orifice exit asthe location and at the time just prior to the main chamber igni-tion. For each test condition that results in a successful ignition(either by flame ignition or by jet ignition), we calculated the glo-bal Damköhler number based on the jet mean and fluctuationvelocity at the orifice exit at the time of main-chamber ignition,as well as the laminar flame speed and the flame thickness, bothof which were obtained from PREMIX calculations. This ‘‘global”Damköhler number would give us insights on the competitionbetween turbulent mixing and ignition chemistry as well as under-standing the effect of a number of parameters such as orifice diam-eter on ignition probability.

We plotted the ignition delay time as a function of the globalDamköhler number for all test conditions summarized in Tables1 and 2, as shown in Fig. 10a for CH4/air and in Fig. 10b for H2/air. The range of Damköhler numbers under which successful igni-tion takes place is Da = 140–500 for CH4/air and Da = 40–380 forH2/air. The lower limit (Dacrit = 140 for CH4/air and Dacrit ¼ 40 forH2/air) separating no ignition and ignition regimes was referredas the critical Damköhler number, Dacrit . Below Dacrit , turbulentmixing timescale was too small as compared to the chemical time-scale, indicating rapid mixing and heat loss and thus extinction ofthe ignition kernels. Moreover, the flame ignition cases had lowerignition delay time and higher Damköhler numbers than jet igni-tion cases. Flame and jet ignition mechanisms were divided by aDamköhler number of 300–350 for CH4/air and 120–130 for H2/air. These are referred to as transition Damköhler numbers, Datran.

Critical conditions necessary for ignition were considerablyinfluenced by the Lewis number of the reactant mixture. Lewisnumber, Le, is defined as thermal diffusivity of the mixture to themass diffusivity of the deficient reactant. Lewas smaller than unity(0:2 < Le < 0:6Þ for fuel-lean H2/air mixtures and near unity forCH4/air mixtures. Our results showed that the effect of higher reac-tant diffusivity of H2 lowered the critical Damköhler number(Dcrtical ¼ 40 for H2 as compared to Dcrtical ¼ 140 for CH4). This obser-vation was consistent with the Iglesias et al.’s numerical study onthe effect of Lewis number on initiation of deflagration by a hotjet [33]. As reflected by smaller values of the fuel Lewis numberfor H2, the cold unburned H2/air rapidly diffused into the hotjet before the jet loses much of its heat to the cold surroundings.

Fig. 10. Ignition delay, signition as a function of the global Damköhler number, Da for all test conditions involving (a) CH4/air and (b) H2/air.

S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937 935

This preheated H2/air facilitates favorable combustion conditionsand combustion becomes possible at lower Damköhler numberthan for CH4/air, as has been explained in [33].

3.5. Turbulent premixed combustion regimes for hot jet ignition

Diagrams defining regimes of premixed turbulent combustionin terms of velocity and length scale ratios have been proposedby Borghi [34] and later modified by Peters [35], Abdel-Gayedet al. [36], Poinsot et al. [37], Williams [38,39] and others. Asshown in Fig. 11a and b, several regimes exist including laminarflames, turbulent flamelets, thin reaction zones and broken reac-tion zones based on the logarithm of velocity ratio, u0=sL, andlength scale ratio, l=lf . They indicate different interactions betweenturbulence and chemistry. It would be interesting to see how theno-ignition, jet ignition and flame ignition cases fitted in the pre-mixed turbulent combustion regime diagram. Motivated by this,the ignition outcome for each test condition in Tables 1 and 2 along

Fig. 11. The ignition outcome of all test conditions involving (a) CH4/air and (b) H2/air arbased on Peters [29].

with no-ignition cases were plotted in the turbulent premixedcombustion diagram, as shown in Fig. 11a for CH4/air and inFig. 11b for H2/air.

Most non-ignition cases fall into the broken reaction zones forboth CH4/air and H2/air. Mansour and Chen thoroughly investi-gated the stretched premixed flames on a Bunsen burner that weresurrounded by a large pilot flame in a series of studies [40–42].Their results show that in the broken reaction zone regime, apremixed flame is unable to survive. The present experimentalobservations are consistent with this conclusion; as local extinc-tion events would appear more frequently when flames enter intothe broken reaction zones regime. The non-ignition cases corre-sponded to pre-chambers with smaller orifice diameters, at lowerinitial temperatures, higher initial pressures, and at fuel-leanconditions. The fundamental reason for non-ignition is that theturbulent jet is very strong with relatively high mean velocityand fluctuations. This results in rapid mixing between the hotjet and the cold unburned main chamber mixture. The initial

e presented in the premixed turbulent combustion regime diagram. The diagram is

936 S. Biswas et al. / Applied Thermal Engineering 106 (2016) 925–937

temperature of the unburned mixture, however, was limited to amaximum of 500 K in the present experiments. These result in rel-atively large chemical time scales and thicker preheat zones andreaction zones in flame. As a result, the smallest turbulent eddiesare smaller than the inner reaction zone thickness. Turbulenteddies can penetrate into the inner reaction zone perturbing itand causing local chemistry to break down because of increasedheat loss to the preheat zone [29].

Most ignition cases fall within the thin reaction zones regimefor both CH4/air and H2/air, with a few at the boundary betweenthe thin reaction zones regimes and the broken reaction zonesregime. None of them fall within the corrugate flamelets regime.In general, flame ignition cases correspond to a larger l=lf ratio.As we increase orifice diameter and pressure, the ignition mecha-nism tends to switch from jet ignition to flame ignition. The flamejet coming out the pre-chamber orifice contains key radicals suchas H, O and OH, which initiate chain-branching reactions andenhance ignition probability. Compared to CH4/air, H2/air flameshave higher burning velocities and thinner preheat and reactionzones. In other words, the chemical time scale for H2/air flameswas shorter than CH4/air flames. As a result, under the same levelof turbulence, H2/air has a better chance for ignition than CH4/air,even at lower initial temperatures.

4. Conclusions

We investigated the ignition characteristics of CH4/air and H2/air mixtures using a turbulent hot jet generated by pre-chambercombustion using simultaneous high-speed Schlieren and OH⁄

chemiluminescence. The vital finding was the existence of two dif-ferent ignition mechanisms namely, jet ignition and flame ignition.The former produced a jet of hot combustion products (whichmeans the pre-chamber flame is quenched when passing throughthe orifice); the latter produced a jet of wrinkled turbulent flames(the composition of the jet is incomplete combustion products con-taining flames). As the orifice diameter increased, the ignitionmechanism tends to switch to flame ignition, from jet ignition.With the increase in pressure, flame ignition became more preva-lent. The ignition took place at the side surface of the hot jet duringthe jet deceleration process for both mixtures. A critical globalDamköhler number, Dacrit; defined as the limiting parameter thatseparated ignition from no-ignition, was found to be 140 forCH4/air and 40 for H2/air. All possible ignition outcomes wereplotted on the turbulent combustion regime diagram. Nearly allno-ignition cases fell into the broken reaction zone, and jet andflame ignition cases mostly fell within the thin reaction zones.

Appendix A. Uncertainty analysis

An uncertainty analysis was carried out to estimate the uncer-tainty of pressure and temperature on the contribution of theuncertainty of density and the jet velocity. GRI3.0 [43] (53 species,325 reactions) was used for CH4/air and a comprehensive model byWestbrook [44] (10 species, 19 reactions) was used for H2/air in thesimulations. However, only stable species in the products withsignificant mole fractions (> 10�5) were considered to calculatethe mixture density. The species mole fractions and densities wereevaluated at the adiabatic flame temperatures of respectivemixtures. An analysis was performed to estimate the contributionof temperature uncertainty and pressure uncertainty in calculatingdensity and velocity.

Hot wire pyrometry technique was performed to measure jetexit temperature. We found that the measured jet exit temperaturewas within 2.5% of adiabatic flame temperature. Additionally, theKulite pressure transducer had an uncertainty ±0.1% of its full scale

value. Thus the relative error for density, q ¼ P=RT can be writtenas,

Dqq

¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiDPP

� �2

þ DTT

� �2s

ðA1Þ

This results in an uncertainty of 2.51% in density calculationsdue to uncertainty in pressure and temperature.

At any instance of time, jet exit velocity can be written as,

U0 ¼ CYffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðP1 � P2Þ=qmix

qðA2Þ

where prechamber pressure is P1 and main chamber pressure is P2.Using functional form of C and Y [45], the exit velocity can be writ-ten as,

U0 ¼ Cdffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� b4

q 1� f ðbÞ 1� P2

P1

� �1c

( )" # ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

qmix

sðA3Þ

where C ¼ Cdffiffiffiffiffiffiffiffi1�b4

p , Y ¼ 1� f ðbÞ 1� P2P1

� �1c

� �and b ¼ d=D.

All variables except pressures (P1, P2) and density, q can betreated as a constant and the exit velocity can be rearranged as,

U0 ¼ C1 1� C2 þ C2P2

P1

� �C3" #

1ffiffiffiffiqpffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

pðA4Þ

where C1;C2; C3 are constants. The error in velocity then can beexpressed as,

DU0ð Þ2 ¼ @U0

@P1DP1

� �2

þ @U0

@P2DP2

� �2

þ @U0

@qDq

� �2

ðA5Þ

ðDU0Þ2 ¼C1 C2

P2P1

� �C3 �C2 þ1 2

ffiffiffiffiqp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

p �C1C2C3P2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

p P2P1

� �C3�1

P21

ffiffiffiffiqp

2664

3775ðDP1Þ2

þC1C2C3

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

p ðP2P1ÞC3�1

P1ffiffiffiffiqp �

C1 C2P2P1

� �C3 �C2 þ1 2

ffiffiffiffiqp ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

p

2664

3775ðDP2Þ2

þ C1 C2P2

P1

� �C3

�C2 þ1

" #1

2q32

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP1 � P2

p" #ðDqÞ2

ðA6ÞDP ¼ 0:1% and Dq ¼ 2:51%. Then the relative error of the calculatedvelocities, U0=U0 is within ±2.92%. In Section 3.4 we have addedestimated uncertainties in density and velocity calculations.

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