Fuel 89 (2010) 3262–3271

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Fuel

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Ignition kernel development studies relevant to lean-burn natural-gas engines

Harinath Reddy *, John AbrahamSchool of Mechanical Engineering, Purdue University, West Lafayette, IN 47907-2014, United States

a r t i c l e i n f o

Article history:Received 27 January 2010Received in revised form 24 May 2010Accepted 26 May 2010Available online 8 June 2010

Keywords:Ignition kernelLean-burn natural-gas enginesDeveloping flamesHot-jet ignition

0016-2361/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.fuel.2010.05.040

* Corresponding author. Tel.: +1 765 426 0630.E-mail address: reddyh@purdue.edu (H. Reddy).

a b s t r a c t

In lean-burn premixed natural-gas engines, ignition and combustion can be accelerated by burning a smallfraction of the mixture in a pre-chamber. High pressure generated in the pre-chamber results in the dis-charge of burned products into the main chamber. This creates multiple ignition kernels along the surfaceof the resulting jet. In this work, lean-burn characteristics of methane under the high pressure and hightemperature conditions of a hot-jet ignited combustion chamber are investigated numerically by initializ-ing a kernel of specified composition, temperature and size in a lean premixed gas, and following the devel-opment of the flame. In the case of hot-jet ignition the kernel temperature is limited by the temperature ofthe hot products. The influence of variations in ignition energy, affected by both temperature and size, andequivalence ratio, on the flame development is studied in an initially quiescent gas. It is shown that as longas the available ignition energy is greater than a minimum, the duration in which a steady flame speed isachieved is a strong function of kernel temperature; it is not a function of kernel size.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Natural-gas is becoming increasingly important as an alterna-tive to petroleum-based fuels. Natural gas is one of the most abun-dant fossil fuels, and requires relatively little processing prior touse [1]. Currently, natural gas meets upward of 20% of the energydemand in the United States [2]. Increasing energy demand, cou-pled with diminishing reserves of petroleum-based fuels, makenatural gas an attractive alternate fuel [3]. Also, natural gas pro-duces 25–30% less CO2 emissions per unit energy than gasolineand diesel and therefore has a positive impact on the environment[4,5]. When using natural gas in engines, operating a lean fuel/airmixture has distinct benefits: nitric oxide emissions are lowerand thermal efficiency higher than when operating stoichiometric.However, lean operation also poses some challenges with regard toignition and flame stability, which, in turn, can increase cyclic var-iability and reduce thermal efficiency. In fact, if the mixture is toolean, misfire can occur.

The ignition characteristics of lean-burn premixed natural gas-air mixtures can be enhanced by injecting a jet of hot burned prod-ucts into the mixture [6]. A small fraction of the premixed fuel–airmixture is burned inside a pre-chamber and the combustion prod-ucts are then discharged into the main chamber. The resulting jet,comprising hot combustion products, can generate multiple igni-tion sites on its surface which can enhance the probability of suc-cessful ignition and lead to faster heat release rates in the lean

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mixture. The jet is turbulent and ignition kernels of a wide rangeof length and velocity scales are generated. The magnitudes ofthese scales are likely to influence ignition and flame propagation.Furthermore, when the hot products are discharged from the pre-chamber, heat loss in the orifice connecting the two chambers canlower the temperature of the products. If the temperature falls be-low a critical threshold, ignition may not occur. The ignition kernelsize and temperature will depend on the size of the orifice, Rey-nolds number of the jet, and gas and wall temperatures. Note thatthis method of ignition is distinctly different from spark ignition inthat during spark ignition, energy is deposited in a kernel. The tem-perature of the kernel can reach values as high as 4000–5000 K,whereas the temperature of the kernel in hot-jet ignition is limitedby the temperature of the hot jet. This temperature is typicallylower than the adiabatic flame temperature corresponding to themixture conditions, due to heat loss in the discharge orifice.

Hot-gas jet ignition has been investigated in several prior stud-ies. Cato and Kuchta [7] studied hot-gas jet ignition for varioushydrocarbon fuel–air mixtures using hot laminar air jets in a con-stant volume chamber. They observed that minimum ignition tem-perature, i.e. the temperature of the hot air jet below whichignition does not occur, can be reduced by increasing the jet diam-eter and thus increasing the contact area between the unburnedmixture and the hot-gas jet. More recently, Roethlisberger andFavrat [5,6] carried out experimental and numerical investigationsin a pre-chamber hot-jet ignited natural-gas engine. They observedthat the presence of a pre-chamber intensified and accelerated thecombustion process. They suggested that the injection of the hot-gas jets from the pre-chamber into the main chamber brings abouta significant increase in the initial flame front area.

H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271 3263

In addition to the studies in hydrocarbon–air mixtures, severalinvestigations have also been conducted on hot-jet ignition inhydrogen–air mixtures. Elhsnawi and Teodorczyk [8] experimen-tally studied the ignition process that occurs during the injectionof hot inert gas into a stoichiometric hydrogen–air mixture. Theystudied the mechanism of the ignition process through Schlierenphotography and reported that ignition occurs in the turbulentmixing zone at the edges of the jet. Sadanandan et al. [9], whostudied hot-jet ignition using optical diagnostics (OH-LIF, Schlie-ren) and Reynolds-averaged Navier–Stokes simulations, reportedquenching of the hydrogen flame in the discharge orifice, and sub-sequent re-ignition of the mixture in the tip of the hot jet. Theyconcluded that ignition does not occur at the lateral sides due tohigh shear stresses which result in strong mixing. On the otherhand, mixing at the tip is reduced and this favors ignition.

It can be inferred from prior studies that increasing pressure inthe pre-chamber results in faster ignition indicating that higherpressure differential between the pre- and main- chambers has apositive effect on ignition [8]. However, there is some conflict onthe effect of mixing rate on the ignition process as Sadanandanet al. [9] suggest that ignition does not occur at lateral edges dueto higher shear stresses while Elhsnawi and Teodorczyk [8] cometo the opposite conclusion. The effect of jet and chamber condi-tions on the ignition and flame development process is still notwell understood, and there is a need to study fundamental aspectsof hot-jet ignition in greater detail.

In hot-gas jet ignition, the characteristic kernel size is likely tobe dependent on the axial distance in the jet since it is known thatturbulent integral scales increase with axial distance. The temper-ature of the hot products in the kernel is likely dependent on theextent of reaction progress in the pre-chamber and wall heat lossthrough the discharge orifice. Our objective is to understand theinfluence of kernel size and temperature on ignition, flame devel-opment and flame propagation. To this end, we perform 2-Dnumerical simulations of combustion of lean mixtures initiatedby ignition kernels of hot combustion products. The ignition kernelis modeled as a circular hot-spot comprising combustion products.This idealized representation of the kernel enables us to isolate theindividual effects of kernel temperature and size.

In the section that follows, we provide a brief discussion of thenumerical method employed and a description of the simulationparameters and conditions. Laminar flame speed results are dis-cussed in Section 3. A discussion of ‘‘available ignition energy”and ‘‘minimum ignition energy” is also provided in this section.These definitions are used to analyze the combined effect of kerneltemperature and kernel size on the ignition delay. The paper closeswith summary and conclusions in Section 4.

2. Numerical model and parameters

2.1. Numerics

The numerical code employed in this work [10,11] directlysolves the conservation equations for multi-component gaseousmixtures with chemical reactions. The sixth-order compactfinite-difference scheme of Lele [12] is implemented for spatialdiscretization, and time integration is achieved through a com-pact-storage fourth-order Runge–Kutta scheme [13]. At the bound-aries, non-reflective outflow conditions are implemented using theNavier–Stokes characteristic boundary conditions (NSCBC) methodof Poinsot and Lele [14], which is extended from its original formu-lation to account for multi-component transport. The Courant–Friedrichs–Lewy (CFL) number selected for the computations inthis work is 0.9. In the present work, the mass diffusivities Dk arecomputed using either the simplified unity Lewis number modelor the effective binary diffusion coefficient model [15]. The code

is written in Fortran 90 and parallelized using the message passinginterface (MPI). The accuracy of the reacting fluid mechanics ele-ments of the code has been assessed in several prior studies forn-heptane and hydrogen chemistry [10,11,16–19]. We have usedthe ideal gas equation of state and the error in assuming that themixture is an ideal gas is less than 2% for the conditions of thiswork.

2.2. Chemical kinetic models

As stated earlier, we are primarily interested in conditions rep-resentative of lean-burn premixed natural-gas engine combustionchambers. Since methane is the primary constituent species of nat-ural gas, and the chemistry of methane has been studied exten-sively, and both reduced and detailed mechanisms have beendeveloped with applicability over a wide range of temperaturesand pressures, we choose methane as a surrogate fuel for naturalgas. The mechanisms employed are the 53-species 324-reactionGri-Mech 3.0 [20] detailed mechanism, a 21-species 84-reactionreduced mechanism (RM) [21], and a single-step irreversible reac-tion mechanism (SSM) for the oxidation of methane to CO2 andH2O [22]. The rate _wF (mol/cm3 s) for the single-step irreversiblereaction is given by the Arrhenius expression:

_wF ¼ ATb½CH4�m½O2�ne�Ea=RuT ; ð1Þwhere the pre-exponential factor is equal to 5.0 � 1011 cm–mol–sunits, b is the temperature exponent, set to zero in our work, m andn, set to unity, are reaction orders with respect to fuel and O2, respec-tively, Ea is the activation energy, equal to 104,500 J/mol, Ru is theuniversal gas constant, and [CH4] and [O2] are the concentrations ofCH4 and O2 in mol/cm3, respectively. The single-step model parame-ters have been calibrated by us to give flame speeds which are in goodagreement with reduced and detailed mechanisms.

In the present work, we employ these mechanisms at a rela-tively high pressure of 70 atm and unburned reactant temperatureof 810 K, both of which are representative of conditions in naturalgas-fueled premixed-charge engines [23]. Since the mechanismsare being employed at high temperature and pressure conditions,810 K and 70 bar, respectively, it is necessary to assess the accu-racy of these mechanisms under such conditions. The thermody-namic and transport properties for methane are reasonably wellknown, and we obtained these from the Gri-Mech3.0 reference.As for the kinetics, there lies the greatest uncertainty. The detailedmechanism has been evaluated in prior studies for ignition delaypredictions in lean mixtures at high pressures (3–450 atm) andtemperatures (1000–2000 K), and in stoichiometric mixtures athigh pressures (35–84 atm) [20,24,25]. While the mechanism hasnot been employed for the specific conditions in our study, priorstudies in high-pressure, high-temperature environments and inlean mixtures provide a measure of confidence. The reduced mech-anism has been tested, in prior work, against Gri-Mech for flamespeeds at pressures up to 20 atm and ignition delays at pressuresup to 10 atm [21]. This mechanism has not been tested for our con-ditions, but we will compare a limited set of our results with re-sults obtained with the Gri-Mech predictions to assess its accuracy.

While it is not possible to provide firm evidence of the validityof the mechanism for the conditions of interest here, it is interest-ing to estimate the flame speed using some correlations in the lit-erature. One correlation for the laminar flame speed SL onunburned gas temperature, Tu, and pressure, P, for hydrocarbonfuels [26] shows the following dependence:

SL ¼ SL;refTu

Tu;ref

� �c PPref

� �b

1� 2Ydilð Þ ð2Þ

where Ydil is the mass fraction of diluent present in the mixture, andc and b are temperature and pressure dependence exponents. At

3264 H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271

/=0.6, the value of c and b are 2.5 and 0.248, respectively. This cor-relation gives a flame speed of 21.5 cm/s for the conditions selectedin this work. The steady flame speed computed from the numericalsimulations is 18.5 cm/s which is within 20% of the estimated value.It should be noted, however, that this correlation was developed fora pressure range of 0.4–50 atm and 298–700 K temperature. Addi-tionally, this correlation was developed by curve-fitting data formethanol, iso-octane and indolene fuels. There is evidence thatthe pressure dependence of methane flame speed is stronger thanthose of these fuels [27].

2.3. Computational setup

Note that our objective is not to compute the entire physicalsetup in the engine. We begin with the assumption that kernelsare formed by the jet and ask: what is the influence of kernel tem-perature and size on the flame development and propagation fromthe kernel? Fig. 1 shows a schematic of the computational setup.The computational domain is 2-D and measures 2.5 � 2.5 mm.The flame thickness dl estimated with a 2 lm resolution grid isabout 50 lm. The computed thickness was estimated by measur-ing the width of the reaction zone where the chemical heat releaseis at least 20% of the peak value. This thickness is greater than thevalue of about 10 lm estimated by taking the ratio of the thermaldiffusivity in the unburned gas to the flame speed but about equalto the ratio of the thermal diffusivity in the burned gas to the flamespeed. The computational domain in terms of flame thickness is50 dl � 50 dl. The domain size is selected so the flame can propa-gate for a sufficient time to attain a steady flame speed before itis influenced by the boundaries. A uniform grid with 250 � 250points is employed resulting in a resolution of 10 lm. Since theflame thickness is 50 lm, it is resolved by five points. The pressurein the domain is 70 atm and the unburned gas temperature is810 K as indicated earlier.

The domain consists of lean premixed methane-air mixturewith equivalence ratio U = 0.6. A couple of cases with slightly high-er and lower U are also considered. As shown in Fig. 1, the ignitionkernel is initialized in the center of the domain with a diameter dK.The composition of the ignition kernel is determined by carryingout an equilibrium simulation of a premixed methane-air mixturefor the conditions in the chamber [28]. A mass-diffusion layer isinitially set up using linear interpolation at the kernel interface.This layer is needed to avoid numerical instabilities arising fromsteep gradients in the computational domain in its absence. Thewidth of this layer is lK and it is typically selected to be around

Fig. 1. Schematic of the problem setup.

20% of the kernel diameter. Several computations were carriedout to study the effect of the thickness of the layer on the flamedevelopment and flame propagation in the domain. It was ob-served that the transients during the flame development periodare not affected by the thickness of the layer provided it is in therange of 0–30% of the kernel diameter. If the thickness of this layeris selected to be greater than 30% of the kernel diameter, a longertransient is observed. The steady flame speed is, as expected, notaffected by the thickness of the mass-diffusion layer.

The kernel is initialized with a temperature Tb, which simulatesthe temperature of the burned products discharged into the maincombustion chamber from the pre-chamber. As the burned gasflows through the nozzle orifice, it undergoes cooling and thereis a temperature drop along the nozzle. Thus, the temperature inthe kernel is selected to be lower than the adiabatic flame temper-ature to account for heat losses that occur when the combustionproducts pass through the orifice [23]. A heuristic calculation todetermine this temperature drop is presented below. In fact, shortresidence time in the pre-chamber may result in partial combus-tion and lower temperature. This is not part of the estimate below.

During the transport of the burnt products from the pre-cham-ber to the main chamber, it loses heat to the surrounding metalprimarily through convective heat transfer expressed as follows:

_Q ¼ hAðTbulk � TwallÞ; ð3Þ

where h is the convective heat transfer coefficient, A is the surfacearea of the nozzle, and Tbulk and Twall are the temperatures of theburned gas and wall, respectively. The convective heat loss throughthe walls is proportional to the temperature drop in the passage, i.e.

hAðTbulk � TwallÞ ¼ _m cpDTdrop; ð4Þ

where _m is the mass flow rate of the burned gas, cp is the specificheat of the gas and DTdrop is the drop in temperature of the burnedgas as it flows through the passage. In order to determine DTdrop; anestimate of h is required. This can be estimated by calculating theNusselt number NuD of flow through a pipe, given by the followingSieder–Tate correlation [29]:

NuD ¼ 0:027Re4=5D Pr2=3 l

ls

� �0:14

; ð5Þ

where D is the diameter of the orifice, ReD is the Reynolds number,Pr is the Prandtl number, and l and ls are the viscosities at theburned gas and the wall surface temperatures. For the conditionsof this work, ReD � 100,000 and Pr � 0.73 which results in aNuD � 285. Thus, the convective heat transfer coefficient h is esti-mated to be 19,500 W/m2-K. The thermal conductivity for theburned gas is estimated, assuming the gas is air, at the mean tem-perature of the burned gas and the wall. The mass flow rate ofthe burned gas is given by

_m ¼ qp4

D2U; ð6Þ

where U is the velocity of the jet and q is the density of the burnedgas. Substituting _m in Eq. (4) and rearranging the equation, weobtain:

DTdrop ¼4hLðTbulk � TwallÞ

qDUcp; ð7Þ

where L is the length of the orifice. For the simulated conditions,cp = 1137 J/kg-K, q ¼ 10 kg/m3, D = 1 mm, L = 6 mm, U = 200 m/s,Tbulk = 2150 K (adiabatic flame temperature) and Twall = 400 K. Forthese conditions, DTdrop is estimated to be nearly 350 K. This impliesthat, if complete combustion is achieved in the pre-chamber, theexit temperature of the burned gas should be about 1800 K.

Fig. 2. Evolution of (a) temperature (K), and (b) HRR (ergs/cm3-s) along a linepassing through y = 1.25 mm in Fig. 1, for the baseline case with Tb = 1700 K anddK = 500 lm; single-step mechanism (dotted line), reduced mechanism (solid line),detailed mechanism (dashed line).

H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271 3265

The exit temperature of the burned gas will depend on severalparameters including orifice/pre-chamber geometry, completenessof combustion in the pre-chamber, heat loss from chamber, and cy-cle-to-cycle variability which can lead to temperature and compo-sitional changes through changes in trapped mass. Therefore, it isimportant to study the effect of variation of the kernel temperature(which represents the temperature of the burned has at the exit ofthe orifice) on flame development and flame propagation. A rangeof kernel temperatures (1500–1900 K) have been simulated with1700 K as a baseline.

Consider a case where the unburned methane-air mixture hasan equivalence ratio U = 0.6 and temperature of 810 K, and thepressure in the domain is 70 atm. For this case, the ignition kernelhas a diameter dK = 500 lm and temperature Tb varies from 1500–1900 K. These conditions are chosen so that they are comparable tochamber conditions in typical pre-chamber natural-gas engines[23]. The width of the mass-diffusion layer is 100 lm. The numer-ical time step obtained with the selected CFL number of 0.9 isabout 5.78 � 10�9 s. The computations were carried out on anIBM computing cluster with 64 2.5 GHz PowerPC 970 MP proces-sors. A 10 lm resolution (250 � 250 grid) simulation with a sin-gle-step mechanism for 1 ms (approximately 173,000 cycles)requires 2 days of CPU time, i.e. the equivalent of 128 days on a sin-gle processor. Note that the primary constraint here is the numer-ical time step. The chemical time scale sc for a single-stepmechanism can be estimated by [30]:

sc ¼_wF MWmix

q

� ��1

; ð8Þ

where _wF is the rate of reaction, q is the mixture density, andMWmix is the molecular weight of the mixture. sc is estimated tobe about 2.7 � 10�7 s using the adiabatic flame temperature andburned gas density in Eqs. (1) and (2). The reactant concentrationsare used in Eq. (1). The numerical time step is two orders of magni-tude lower than sc.

3. Laminar flame speed results

Laminar flame speed results will first be presented when theGri-Mech3.0, the reduced mechanism, and the single-step mecha-nism are employed for a baseline case whose parameters are givenabove. Fig. 2a and b show the evolution of the temperature and thechemical heat release rate (HRR), respectively, in the domain. HRRis computed as

HRR ¼XN

i¼1

_wih0i ; ð9Þ

where _wi is the production/destruction rate of species i, h0i is the en-

thalpy of formation of species i, and N is the total number of species.Results obtained by employing the three mechanisms are shown inthe figures. The results are extracted along the centerline of the do-main, i.e. they show temperature and chemical heat release rate(HRR) on a line passing through y = 1.25 mm (see Fig. 1). Initiallythe temperature at the edge of the kernel is relatively low (about1700 K) when compared with the adiabatic flame temperature.The adiabatic flame temperature for methane-air mixture with aninitial temperature of 810 K, pressure of 70 bar and equivalence ra-tio U = 0.6 is 2138 K. As time progresses, a flame front develops atthe edge of the kernel and starts propagating. There is a steady risein the peak temperature at the flame front. This peak temperatureeventually reaches a maximum value of about 2150 K at around0.8 ms. Notice that this temperature is slightly higher than the adi-abatic flame temperature. That temperature is obtained from thePREMIX code which is part of the CHEMKIN package. The PREMIXcode assumes constant pressure, i.e. the momentum equation is

not solved. In our calculations, the momentum equation is solved.Small differences in pressure and flame curvature probably ac-counts for the temperature difference. Recall that effective binarydiffusion coefficients [15] are employed. As expected, the peak heatrelease rate in the domain (see Fig. 2b) occurs at the flame front. Theheat release rate initially has a slightly increasing trend with time,but eventually reaches a steady value. We can conclude from theseresults that a flame will propagate from the kernel under these con-ditions. It can be observed from Fig. 2a and b that there is approx-imately 10–15% variation in the magnitude of the peak chemicalheat release (HRR) and 5% variation in the peak temperature be-tween the three mechanisms. It can be concluded that the threemechanisms are in reasonable qualitative and quantitativeagreement.

Fig. 3 shows the time evolution of the flame speed. The flamespeed is estimated by tracking the point of peak chemical heat re-lease along the center line (y = 1.25 mm) in time. An average flamepropagation velocity is computed at discrete time intervals of0.05 ms and this is scaled with the ratio of burned and unburnedgas densities to obtain the flame speed in the methane-air mixture.The flame propagation velocity is initially low, but it increases withtime until an approximately steady velocity is achieved. The timeperiod involving the rise in peak temperature and peak heat re-lease rate in the domain corresponds to the flame development

Fig. 3. Time evolution of flame propagation speed with different chemical mechanisms for the baseline case with Tb = 1700 K and dK = 500 lm.

3266 H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271

period. Once a steady flame is established, the temperature andheat release rate at the flame front are approximately constant.The flame development period for this case is around 0.9 ms.Fig. 3 indicates that the three mechanisms show similar qualitativetrends during the transient period of flame development and asteady speed is reached at around 0.9 ms. The SSM results, com-pared to the RM results, are in better agreement with the Gri-Mech3.0 results because the SSM model parameters have been adjusted(as indicated earlier) in this work to give good agreement with theGri-Mech 3.0 flame speed predictions.

A grid-independence study is also carried out to study the influ-ence of spatial resolution on the development of laminar flamespeed inside the computational domain. Recall that the resolutionin the studies above is 10 lm. The baseline case, employing RM, isrepeated with a grid resolution of 2 lm. It can be observed fromFig. 3 that the speed is practically independent of the resolutionof the grid when the resolution is 10 lm. The resolution is deter-mined by two factors: the diameter of the kernel and the flamethickness. The flame thickness was estimated earlier (see Section2.3) to be 50 lm. Typically, about five grid points, i.e. 10 lm reso-lution, is adequate to resolve the thermal structure of the flame.When the kernel diameter is 500 lm, 10 lm is also more than ade-quate to resolve the transport processes at the boundary of the ker-nel. When the kernel diameter is reduced to 100 lm, however, thecurvature at the boundary increases significantly relative to the500 lm diameter case, and a higher resolution is required,although the 10 lm is still adequate to resolve the flame. We havefound that 5 lm is sufficient in this case. We have ensured that thisresolution is adequate by re-computing the 100 lm case with a2 lm resolution so that the grid spacing is reduced in proportionto the reduction of the kernel diameter. The results (flame speed,temperature evolution, heat release rate evolution) have beenfound to be practically indistinguishable between the 5 and 2 lmresolutions. In subsequent discussion when the kernel diameteris reduced from 500 lm to 100 lm, 10 lm and 5 lm resolutionare used, respectively. Note that irrespective of the size of the ker-nel, the thickness of the fully-developed propagating flame will notchange. Hence, once fully developed, the 10 lm resolution is ade-quate irrespective of the kernel diameter. Our numerical code doesnot, however, allow for the grid to be dynamically changed.

We stated earlier that heat loss in the discharge orifice can varydepending on the orifice geometry, gas properties, and Reynolds

number. Differences in heat loss will lead to differences in ignitionkernel temperatures. In order to study the effect of the kernel tem-perature on the ignition process, simulations are carried out withTb = 1900 and 1500 K using the SSM. The simulation with kerneltemperature Tb = 1900 K showed similar trends as the Tb = 1700 Kcase. A gradual increase in the heat release rate and temperaturein the flame front with time is observed. Eventually, steady valuesare attained. The higher kernel temperature accelerates the flamedevelopment inside the domain and reduces the transient period.Fig. 4 shows the flame speed as a function of time. The transientis reduced from about 0.6 ms at 1700 K to about 0.3 ms at1900 K. The steady speeds for the two cases are about the same,i.e. 18.5 cm/s. This is consistent with the fact that the steady flamespeed should depend on the equivalence ratio and the temperatureand pressure of the unburned mixture.

When Tb is reduced to 1500 K, it can be observed from Fig. 4that the flame development period, i.e. time required for reachingthe steady flame speed, is substantially longer. In fact, the flamefront does not begin to propagate until 0.15 ms as opposed to0.05 ms in the 1700 and 1900 K cases. The time required to attainsteady flame speed is greater than 1 ms. The time required to at-tain the steady flame speed is of significance for the following rea-son: For an engine running at a speed of 1600 rpm, a 0.5 ms timeduration corresponds to approximately five crank-angle degrees.In an engine, where the piston is moving and the volume is chang-ing, the opportunity to ignite the mixture lies within a narrow timerange. Outside this range, misfire will occur. Since the time re-quired to attain steady flame speed is substantially higher for the1500 K kernel, it is likely that misfire or incomplete combustionwill occur. Thus, we categorize this case as a ‘‘no-ignition” case.These simulations were repeated with the reduced mechanism toassess the dependence of the conclusion on the mechanism se-lected in the simulation. Similar transient flame speed trends wereobserved for the reduced mechanism. We can conclude that theminimum ignition kernel temperature required to propagate aflame is above 1500 K in the initially quiescent mixture and thatthe higher the kernel temperatures the faster the flamedevelopment.

The ignition kernel size also plays an important role in the igni-tion process. In order to study this effect, two additional kernelswith Tb = 1700 K and dK of 100 and 50 lm are simulated usingthe SSM. Recall that the computations above were with dK =

Fig. 4. Flame speed for different kernel temperatures (Tb = 1500, 1700 and 1900 K) for an ignition kernel of diameter dK = 500 lm (SSM).

H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271 3267

500 lm. When dK is reduced, the mass-diffusion layer thickness isalso proportionately reduced. When dK is reduced to 100 lm from500 lm, the domain size is reduced by 1/5, i.e. 0.5 � 0.5 mm, andthe grid size decreased to 5 lm in order to resolve the higher gra-dients at the simulated interface. Fig. 5 shows the temperatureevolution for the 100 lm case. Comparing these results with thoseof Fig. 2a, it can be seen that there is a significant amount of ther-mal and species diffusion into the ignition kernel and out of it dur-ing the initial 0.1 ms because the diffusion length is the same orderas the radius of the kernel for the time period considered. Thisleads to the quenching of the kernel edges. At the same time thatthere is diffusion, there is heat release in the center of the kernelas the fuel and oxidizer mixed with the hotter products and react.This raises the temperature at the center of the kernel. Subse-quently, a flame propagates outwards. These transients are likelyto increase the time required to reach a steady flame speed, i.e.the ignition delay, and achieve adiabatic flame temperature inthe products.

Fig. 5. Evolution of temperature (K) along a line passing through y = 0.25 mm forthe case with Tb = 1700 K and dK = 100 lm (SSM).

Kernels smaller than 100 lm were observed to quench com-pletely. Fig. 6 shows the time evolution of temperature for an igni-tion kernel of 50 lm diameter. It can be seen that there is a rapidfall in the temperature and it approaches the reactant temperature.Similar decline in temperature was observed when the simulationwas conducted using the RM. As opposed to the Tb = 1500 K anddK = 500 lm case, where we concluded that the ignition delay istoo long to lead to sustained flame propagation under engine con-ditions, there is quenching of the ignition kernel due to rapid heatloss to the surroundings when Tb = 1700 K and dK = 50 lm, and thiskernel is incapable of igniting the mixture at all. We also carry outa simulation for the 50 lm kernel with an elevated ignition kerneltemperature of Tb = 1900 K. The quenching of the ignition kernelwas observed even at the elevated kernel temperature and noflame propagation was observed. If we assume that the kernelsoriginate from turbulent eddies, these results imply that larger ed-dies are likely to lead to ignition whereas smaller eddies willquench. This is not surprising.

Fig. 6. Evolution of temperature (K) along a line passing through y = 0.25 mm forthe case with Tb = 1700 K and dK = 50 lm (SSM).

3268 H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271

In addition to evaluating kernel conditions, simulations are alsocarried out to evaluate the effect on ignition of small variation inequivalence ratio of the unburned mixture. Such variations occurunder typical engine operating conditions. It is concluded that vari-ations of ±0.02 in equivalence ratio has no noticeable influence onthe findings reported above.

3.1. Ignition energy and ignition delay

It is possible that the influence of the two parameters, kerneltemperature and kernel size, studied above may not be indepen-dent of the other, i.e. the threshold temperature may be loweredby increasing the kernel size and vice versa. Additional insightcan be provided by computing the available ignition energy ofthe kernel (Eign). The available energy is dependent on the temper-ature difference between the unburned and the burned gas whichgoverns the amount of energy that can be transferred from theignition kernel to unburned gas. It is also dependent on the sizeand density of ignition kernel which determines the mass ofburned gas present inside the ignition kernel. Eign can be computedusing Eq. (4) [31,32].

Eign ¼ mkcpðTb � TuÞ; ð10Þ

where mk and cp are the mass and the specific heat of the burnedmixture inside the kernel, respectively, and Tb and Tu are the burned(kernel) and unburned (domain) temperatures, respectively. Eq.(10) can be expanded by substituting the mass per unit depth (re-call that these simulations are in a 2-D domain) mk ¼ qp d2

k4 and

using the ideal gas law to compute density q in terms of pressureP and temperature Tb of the ignition kernel to obtain

Eign ¼p d2

k

4cp 1� Tu

Tb

� �P

MWb

Ru; ð11Þ

where MWb is molecular weight of the burned mixture inside thekernel and dk is the diameter of the kernel.

The ignition kernel in hot-gas jet ignition can be consideredanalogous to the ignition kernels formed in spark ignition. In sparkignition, the minimum amount of energy needed to cause ignitionin a fuel–air mixture is called Minimum Ignition Energy (MIE).Applying the analogy to hot-gas jet ignition, the available kernelenergy should be greater than MIE for ignition to occur. The MIErequired to ignite the mixture can then be defined as the amountof energy required to heat up this critical spherical volume fromthe unburned gas temperature to the adiabatic flame temperature,i.e.

MIE ffi a3 43pd3qucpðTb � TuÞ; ð12Þ

where d is the laminar flame thickness and a is the constant of pro-portionality. An estimate of the proportionality constant a can beobtained by using MIE and d data available in literature. The MIEand d of a stoichiometric methane-air mixture at 300 K and 1 atmare 0.3 mJ [33] and 1 mm [31], respectively. On substituting therevalues in Eq. (12), we obtain a value of a = 0.32. Hence, the valueof a is the order of 1 in this expression for methane–air mixtures.

In a natural-gas engine, whether a certain value of Eign leads toignition or not will be determined by the duration of the ignitiondelay sid. As pointed out earlier, there is a limited window ofopportunity for combustion to take place inside the engine and ifthe ignition delay sid is too long, it results in incomplete combus-tion or misfire. Thus, in an engine, sid has to be below a certain va-lue in order for combustion to be complete [34]. In this work, wehave chosen this value to be 0.5 ms.

We will define ignition delay for premixed mixtures as the timerequired to reach the steady flame speed. It can be observed in

Fig. 4 that the transient profile of the flame speed asymptoticallyapproaches the steady flame speed. This makes it challenging todefine the ignition delay. Hence, we define ignition delay as thetime required for the flame speed to reach 70% of its steady value.This is an arbitrary definition, but will be employed consistently forall the cases considered. This choice results in ignition delays of 0.2and 0.35 ms for ignition kernels with Tb = 1900 and 1700 K. Chang-ing the percentage will change the quantitative value of the igni-tion delay. However, this criterion does not change the generaltrends observed in this section. This will be demonstrated laterin this section. Based on the definition of 0.5 ms as an ignition de-lay, the 1700 and 1900 K kernel temperature cases shown in Fig. 4will ignite.

We can change Eign by changing the temperature Tb or size dK ofthe ignition kernel (see Eq. (11)). Minimum ignition energy MIEcan be estimated from Eq. (12). Note that higher values of Eign

are likely to result in lower values of sid. Fig. 7 shows Eign as a func-tion of sid for several values of Tb when U = 1.0 and 0.6. This figureshows results for dK = 100 lm and the simulations are conductedusing the single-step mechanism (SSM). Also shown on the figureare MIE for the two values of U. MIE was calculated from Eq.(12) assuming a in Eq. (12) to be one. The flame thicknesses forU = 1.0 and 0.6 are estimated to be around 20 and 50 lm, respec-tively, by measuring the width of the reaction zone where thechemical heat release is at least 20% of the peak value. These valuesare comparable to the thickness estimated from literature [31]. Theunburned gas temperature is 810 K and the adiabatic flame tem-peratures for U = 1.0 and 0.6 are 2500 K and 2138 K, respectively.Hence, MIE required to ignite this mixture can be calculated usingEq. (12) and it is about 0.05 and 0.12 J/m for U = 1.0 and 0.6,respectively.

It can be observed that Eign > MIE for all temperatures consid-ered (1500–1900 K). When U = 1.0, however, temperatures lowerthan about 1300 K result in sid longer than 0.5 ms. Eign at this tem-perature is 0.1 J/m. The corresponding temperature and Eign whenU = 0.6 are 1550 K and 0.125 J/m, respectively. Also, note from thefigure that sid decreases with increase in Eign .

As stated above, Eign can be varied by changing either the tem-perature Tb or size dK of the ignition kernel. We have shown abovethat increasing Eign by increasing the Tb reduces sid. If the kernelsize also influences the flame development process, an increasein Eign due to an increase in dK should bring about a change insid. Fig. 8 shows sid as a function of Eign for dK = 100 and 250 lmfor kernel temperatures in the range of 1400–1900 K whenU = 0.6. We can see from this figure that increasing Eign by increas-ing the kernel size does not have any impact on the ignition delay.This observation leads us to conclude that ignition is not sensitiveto the size of the kernel, provided the size is greater than a criticalvalue. It is only sensitive to the temperature under these condi-tions. In the case where dK = 50 lm, the value of Eign is lower thanMIE for temperatures as high as 1900 K. This suggests that the ker-nel size has to be selected so that MIE is exceeded for ignition tooccur; but, beyond this size, the temperature is the controllingparameter.

It is interesting to assess the sensitivity of the quantitative re-sults to the choice of 70% flame speed to determine sid: Fig. 9 showsthe effect of available ignition energy on the ignition delay for igni-tion delay based on 70% and 90% flame speed definitions. In boththese cases, it can be observed sid increases with decrease in Tb.However, the minimum Eign required to attain sid of less than0.5 ms increases from 0.1 to 0.125 J/m from the 70% to the 90%flame speed definition, respectively, but the qualitative conclu-sions are unchanged.

The discussion above is based on the criterion that ‘‘ignition”occurs if ignition delay is less than 0.5 ms. As part of this work, alarge number of simulations were carried out varying kernel size

Fig. 7. Ignition energy required for a 100 lm diameter kernel to achieve specified ignition delay (sid) for two equivalence ratios; ignition delay is based on the 70% steadyflame speed criterion (SSM).

Fig. 8. Ignition delay as a function of initial energy in the ignition kernel for two kernel sizes (SSM). Initial energy is varied by varying kernel temperature.

H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271 3269

and temperature for fixed values of equivalence ratio, pressure,and unburned gas temperature, i.e. U = 0.6, P = 70 bar andTu = 810 K. The kernel temperature (Tb) was varied from 1500 to1900 K while the kernel diameter (dk) was varied from 50 to500 lm. It was observed that ignition is achieved for cases whereTb P 1550 K and dk P 50 lm. If the ignition delay criterion is re-laxed, i.e. increased to 1.0 ms, it is possible that the 1500 K casemight also fall into the ‘‘ignition” category. However, as long asthe temperature is less than 2150 K (the adiabatic flame tempera-ture), the 50 lm kernels will quench, irrespective of the ignitioncriterion, because their energy is less than the MIE. It may, ofcourse, be possible to ignite the 50 lm kernel by increasing itstemperature beyond 2150 K to a value such that Eign is greater thanthe MIE. A simulation was carried out with an ignition kernel ofdK = 50 lm and Tb = 3000 K. It was observed that this kernel ig-nited. However, note that in hot-gas jet ignition the kernel temper-ature is limited by the adiabatic flame temperature. Highertemperatures cannot be achieved unless an external heat source,

e.g. spark ignition, is provided. This is a disadvantage of hot-jetignition. The compensating effect is the increased surface area (ofthe jet) for ignition.

In hot-gas jet ignition, the presence of turbulent eddies can lo-cally distort the initially spherical ignition kernel and strain thedeveloping flame. There can also be interactions between flamesdeveloping from multiple ignition kernels which can then becomethe dominant feature of flame propagation. Since this work repre-sents an ignition kernel as an idealized circular hot-spot in a quies-cent mixture, it imposes a critical limitation on the directapplicability of these results of this work to a pre-chamber hot-jet ignited engine. In large natural-gas-fueled engines of interest,however, jet ignition is not the only method employed to ignitethe mixture. A more common approach is to use spark ignition.In this case, the kernel size is often smaller than the integral lengthscale of turbulence and the turbulence intensities are lower than injet-ignited engines; hence, the results of this study become morerelevant. The work provides fundamental insight into the key pro-

Fig. 9. Ignition energy vs. ignition delay (U = 1.0) where ignition delay is based on the 90% steady flame speed criterion (SSM).

3270 H. Reddy, J. Abraham / Fuel 89 (2010) 3262–3271

cesses which occur in flame development and propagation from anignition kernel. The limitation identified in this work on the kernelsize provides an estimate of the minimum size of ignition kernelsrequired for flames to develop whether it is from hot turbulent ed-dies or spark kernel. Also, since hotter ignition kernels lead toshorter ignition delays, i.e. faster attainment of steady flame speed,these flames would be less likely to quench as a result of localstrain induced by the turbulence. In fact, in spark-ignited engines,the kernel temperature is at least a factor of three greater than inthe jet-ignited kernels. As a result, flame quenching is less likely.On the other hand, the surface area is greater in jet-ignited enginessuggesting that if strain-induced quenching is not a limitation,burning rates will be significantly higher.

4. Summary and conclusions

In this work, a 2-D code was employed to study the influence ofignition kernel temperature and size on ignition of a lean premixedmethane–air mixture and subsequent flame development. Themixture was initially quiescent. The pressure and temperatureconditions of 70 bar and 810 K, respectively, represented those ina natural gas-fueled engine [23]. Kernel size and temperature werevaried. When the kernel diameter is comparable to the species dif-fusion length, the kernel temperature initially drops. If the reactiontime is sufficiently short, the temperature rises again. However, ifthe diffusion of heat and species is faster than the reaction rate,no flame development is observed. The smaller the diameter, thefaster the diffusion. These opposing physical effects establish aminimum (critical) kernel diameter for an initial kernel tempera-ture. When the kernel diameter is greater than this minimum (crit-ical) diameter, the kernel size does not play any role in ignition.The studies showed that the flame development process is acceler-ated with increasing initial kernel temperature unlike kernel size.Higher initial temperatures lead to shorter development time(ignition delay). In the case of natural-gas engines, where there isonly a finite time for the flame to develop from a kernel, a mini-mum kernel temperature is required.

For the specific conditions of this work where the peak kerneltemperature is limited by the adiabatic flame temperature of themixture, the critical kernel diameter is greater than 50 lm andthe minimum kernel temperature is 1550 K. Note that these valuesare obtained assuming a maximum ignition delay of 0.5 ms (5� CA

in an engine). The critical diameter will be smaller if the kerneltemperature is significantly higher. For example, in spark-ignitedengines where the kernel temperature is about a factor of twogreater than the adiabatic flame temperature of the mixture con-sidered here, the critical diameter will be smaller. In this sense,ignition in hot jet-ignited and spark-ignited engines is different.

Acknowledgements

The numerical code employed in this work was developed byProf. Vinicio Magi. We thank him for useful discussions duringthe course of this work. We also thank the Rosen Center for Ad-vanced Computing at Purdue University and the National Centerfor Supercomputing Applications (NCSA) for providing the comput-ing resources. Financial support for this work was partly providedby Caterpillar Inc. Discussions with Dr. Jonathan W. Anders, andvaluable feedback from him, are gratefully acknowledged.

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