Combustion and Flame 158 (2011) 401–415

Contents lists available at ScienceDirect

Combustion and Flame

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

A numerical study of vortex interactions with flames developingfrom ignition kernels in lean methane/air mixtures

Harinath Reddy ⇑, John AbrahamSchool of Mechanical Engineering, Purdue University, West Lafayette, IN, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 23 February 2010Received in revised form 13 April 2010Accepted 9 September 2010

Keywords:Ignition kernelFlame–vortex interactionsLean natural-gas enginesDeveloping flamesFlame surface area

0010-2180/$ - see front matter � 2010 The Combustdoi:10.1016/j.combustflame.2010.09.008

⇑ Corresponding author.E-mail address: reddyh@purdue.edu (H. Reddy).

In this work, the outcomes of interactions of counter-rotating vortex pairs with developing ignition ker-nels are studied. The conditions are selected to represent those in a lean-burn natural-gas engine withhot-jet ignition. The evolution of flame surface area during kernel–vortex interaction is quantitativelyand qualitatively examined. It is observed that flame development is accelerated and the net flame sur-face area growth rate, i.e. heat release rate, increased with increasing vortex velocity. In general, increas-ing the vortex length scale increases the surface growth rate, i.e. increases heat release rates, but for smalllength scales, i.e. when the ratio of vortex length scale to kernel diameter is small, high flame curvatureinduced during the interaction leads to flame weakening and slower growth rates. When the vortexvelocity is high relative to the flame speed and the length scale is comparable to the kernel diameter,the vortex breaks through the ignition kernel carrying with it hot products of combustion. This acceler-ates growth of the flame surface area and heat release rates compared to a kernel with no vortex inter-action. On decreasing the vortex velocity and increasing the length scale, the wrinkling of the kernelbecomes important. This also results in increased surface growth rates and higher heat release rates.

� 2010 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction carried out to provide useful insight into the processes, as opposed

Premixed natural gas combustion is employed as a means ofpower generation in reciprocating engines, for both stationaryand transportation applications [1–3]. In these engines, the mix-ture is typically burned lean to lower flame temperature and,hence, reduce nitric oxide emissions. Making the mixture lean alsoincreases thermal efficiency, up to a point [4]. When the mixture istoo lean, igniting the mixture can be a challenge, and misfire andslow combustion rates in the engine can result in a drastic reduc-tion in thermal efficiency. One means of enhancing ignition in leanpremixed mixtures is to use a hot-jet of burned products dis-charged from a pre-chamber [5]. The hot-jet generates turbulenceand increases the ignition surface area. The turbulent eddies gener-ated by the jet can act as individual ignition kernels. As the pre-mixed flame develops from the kernel, interaction of the flamewith the local turbulence field can have a significant influence onflame development and flame propagation. This study focuses onthis interaction. A simplified configuration of a counter-rotatingvortex pair interacting with a flame developing from a kernel ofhot combustion products will be employed for the studies. Suchsimple flow configurations are more amenable to analysis, andcomparisons with equally simple experimental setups can be

ion Institute. Published by Elsevier

to studies in engines. We will employ methane as a surrogate fornatural gas as its chemistry has been extensively studied.

Premixed methane flame–vortex interactions have been thesubject of prior studies [6–9]. A detailed review of the effect offlame–vortex interactions on flame structure, ignition and extinc-tion is provided by Renard et al. [10]. Since the focus of this studylies in interactions of vortices with developing ignition kernel, adiscussion of the relevant kernel–vortex studies is provided below.In an experimental study, conducted at 1 atm, Eichenberger andRoberts [11] explored the influence of vortices of different lengthand velocity scales on a spark-ignited kernel. They showed thatthe weaker vortices modified the local structure of the kernelflame. Increasing either velocity or length scale of the vortex leadsprogressively to global wrinkling, distributed combustion, andthen global quenching where there is no longer combustion. Localextinction can be observed during wrinkling and distributed com-bustion. They concluded that larger vortices are more effective incausing global quenching at lower vortex velocities. They observedglobal quenching for values of the ratio of vortex length scale (dv)to kernel diameter (dk) greater than about 4.

Xiong et al. [12] provide quantitative analysis of these resultsfocusing primarily on the regimes where flame propagation is en-hanced. They showed that vortex interactions with kernels duringthe early stages of flame development had maximum impact onenhancement of heat release rates. Xiong and Roberts [13] havecarried out kernel–vortex interaction studies in stratified mixtures

Inc. All rights reserved.

Fig. 1. Regime map for kernel–vortex interactions: (I) laminar kernel regime; (II)wrinkled kernel regime; (III) breakthrough regime; and (IV) global extinctionregime [13].

Fig. 2. Schematic of the problem setup.

Fig. 3. Time evolution of flame propagation speed with different chemical mechanis

402 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

where the equivalence ratio of the mixture was fixed at U = 0.6 andthat of the vortex was varied from zero (air alone) to infinity (fuelalone). Richer vortices were observed to have a higher burning ratethan stoichiometric or lean vortices. A possible reason suggested isthat the rich vortex attains a near stoichiometric equivalence ratiowhile it is propagating through the ambient mixture. It should benoted that the final equivalence ratio is dependent on the distancepropagated and hence different ignition kernel placement can pos-sibly influence the observations. The rich vortex is observed to beconsumed as a single pocket. On the other hand, the leaner vorticesbreak down into smaller pockets before being consumed.

Echekki and Kolera-Gokula [14] conducted numerical studies ofkernel–vortex interactions in an axisymmetric configuration usinga two-step global mechanism whose constants were adjusted tosimulate hydrocarbon flame propagation. The work was not spe-cific to methane, and mixture equivalence ratio was not directlyspecified. Vortex velocity, size, and kernel size were varied in theirstudy. They represented the kernel–vortex interactions on a spec-tral regime diagram. A schematic of the regime map showing thetrends is shown in Fig. 1. The characteristic scales that can be usedto form this regime map are the ratio of the vortex translationalvelocity ut to the laminar flame speed sL and the ratio of the kernelsize dk (diameter) to the vortex size dv (distance between centers ofcounter-rotating vortex pair). The laminar kernel regime wasobserved for weak vortices or small vortices dissipating into thekernel (dv/dk� 1). The wrinkling regime was observed for vorticeswhich were comparable in size with the ignition kernel (dv/dk � 1)or for very small vortices with large vortex strengths (ut/sL > 20).Global extinction was observed for vortices that were typically lar-ger than the ignition kernel (dv/dk > 1) and had very high vortexstrengths (ut/sL > 40). For the rest of vortex length and velocityscales, the breakthrough regime was observed. It is not possibleto conclude if the study is directly applicable to lean-burn enginesbecause the specific temperature and pressure conditions of theirwork, and equivalence ratio, were not provided. Nevertheless, thework is interesting and relevant to our study.

None of the studies above are under engine conditions. Highpressure and high unburned gas temperature in the engine caninfluence the outcomes of kernel–vortex interactions. Further-more, in the case of hot-jet ignition with products discharged froma pre-chamber, the ignition kernel conditions are established bythe conditions of the hot-jet as opposed to a spark-ignited kernel.In our work, the conditions employed are representative of

ms and grid resolutions for the baseline case with Tb = 1700 K and dK = 500 lm.

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 403

natural-gas premixed-charge engine chambers [15]. We considerthe interaction of a single counter-rotating vortex pair with a sin-gle ignition kernel. The vortex length and velocity scales are se-lected from an LES simulation of a 70,000 Re non-reacting jet,with the Re representative of the hot-gas jet. We isolate the inde-pendent effects of vortex length scales and velocity scales on netheat release rate.

In the section that follows, we discuss the computational setupand conditions employed. Results and discussion follow in Section3. The viability of using a one step global mechanism for studyingkernel–vortex interactions is investigated in Section 4. The papercloses with summary and conclusions in Section 5.

2. Computational setup and conditions

Note that our objective is not to compute the entire physicalsetup in the engine. We begin with the assumption that kernelsare formed by the hot-jet and ask: what is the influence of vorticeson the flame development and propagation from the kernel? Figure2 shows a schematic of the computational setup. The computa-tional domain is 2-D and measures 5 � 5 mm. The flame thickness

Fig. 4. Initial conditions: (a) temperature (K), and (b) velocity vectors.

dl estimated with a 2 lm resolution grid is about 50 lm. The com-puted thickness was estimated by measuring the width of the reac-tion zone where the chemical heat release is at least 20% of thepeak value. The computational domain in terms of flame thicknessis 100 dl � 100 dl. The domain size is selected so the flame canpropagate for a sufficient time to attain a steady flame speed beforeit is influenced by the boundaries. A uniform grid with 500 � 500points is employed resulting in a resolution of 10 lm. Since theflame thickness is 50 lm, it is resolved by five points.

The numerical code employed in this work [16,17] solves theconservation equations for multi-component gaseous mixtureswith chemical reactions. The sixth-order compact finite-differencescheme of Lele [18] is implemented for spatial discretization,whereas time integration is achieved through a compact-storagefourth-order Runge–Kutta scheme [19]. At the boundaries, non-reflective outflow conditions are implemented using the Navier–Stokes characteristic boundary conditions (NSCBC) method ofPoinsot and Lele [20], which is extended from its original formula-tion to account for multi-component transport. In the presentwork, the mass diffusivities Dk are computed using either thesimplified unity Lewis number model or the effective binarydiffusion coefficient model [21]. The code is written in Fortran 90and parallelized using the message passing interface (MPI). Theaccuracy of the code has been assessed in several prior studies[16,17,22–24].

The domain consists of lean premixed methane–air mixturewith an equivalence ratio U = 0.6. The kinetic mechanism em-ployed in this work is a 21-species 84-reaction reduced mechanism(RM) [25]. The RM has been tested against the 53 species 324 reac-tions Gri-Mech3.0 detailed mechanism [26] for flame speeds atpressures up to 20 atm and ignition delays at pressures up to10 atm [25]. Computed laminar flame speeds with the Gri-Mech3.0and the reduced mechanism (RM) for flames propagating from anignition kernel, in the absence of a vortex, are shown in Fig. 3. Thecomputations are carried out in the computational domain dis-cussed above for pressure and temperature conditions relevant tothis study. The flame speed is estimated by tracking the point ofpeak chemical heat release along y = 0.0025 m in Fig. 4a. An aver-age flame propagation speed is computed at discrete time intervalsof 0.05 ms and this is scaled with the ratio of burned and unburnedgas densities to obtain the flame speed. The flame propagationvelocity is initially low, but it increases with time until an approx-imately steady speed is achieved. The transient nature of this speedis on account of the unphysical initial conditions at the interface ofthe kernel. It is encouraging that Fig. 3 indicates that the twomechanisms show similar qualitative trends during this ‘‘unphysi-cal” transient period of flame and both mechanisms give a steadyspeed of approximately 0.9 ms. Figure 3 also shows results forflame speed, when the RM is employed, with 2, 5 and 10 lm gridresolution. The results for 2 and 5 lm resolutions are identical,while the 10 lm grid resolution has a maximum difference ofaround 4% during the ‘‘unphysical” transient, but the steady flamespeed is virtually identical. This difference is unlikely to influenceany of our conclusions; a 10 lm grid resolution will be used in thiswork as a compromise between accuracy and computationalspeed.

Table 1Length and velocity scales in a Re = 70,000 jet.

Vortex x/d LI (mm) u0 (m/s) Turbulent diffusivity(LI � u0) (cm2/s)

A 12 0.4584 8.72 40B 15 0.573 7.18 41.1C 20 0.764 5.56 42.5D 30 1.146 3.82 43.7

Fig. 5. Evolution of temperature (K) during the flame–vortex interaction of the baseline case with dv = 458 lm and u0 = 8.72 m/s at times (a) t = 0.05 ms, (b) t = 0.1 ms, (c)t = 0.15 ms, (d) t = 0.2 ms, (e) t = 0.25 ms and (f) t = 0.3 ms (RM).

404 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 405

As depicted in Fig. 2, the ignition kernel is initialized in the cen-ter of the domain with a diameter dK. The kernel is initialized witha temperature Tb, which relates to the temperature of the burnedproducts that are discharged into the combustion chamber fromthe pre-chamber. The composition of the ignition kernel is deter-mined by carrying out an equilibrium simulation of a premixedmethane–air mixture. The temperature in the kernel is selectedto be lower than the adiabatic flame temperature to account forheat losses that occur when the combustion products pass throughthe discharge-orifice. A mass-diffusion layer is initially set up usinglinear interpolation at the kernel interface. This layer is needed toavoid numerical instabilities arising from steep gradients in thecomputational domain in its absence. The width of this layer is lKand it is typically selected to be around 20% of the kernel diameter.Several computations were carried out to study the effect of thethickness of the layer on the flame development and flame propa-gation in the domain. It was observed that the transients during

Fig. 6. Evolution of (a) temperature (K), (b) v-velocity (m/s), (c) CHRR (ergs/cm3 s), and (dinteraction of the case with dv = 458 lm and u0 = 8.72 m/s (RM).

the flame development period are not affected by the thicknessof the layer provided it is in the range of 0–30% of the kernel diam-eter. If the thickness of this layer is selected to be greater than 30%of the kernel diameter, a longer transient is observed. The steadyflame speed is, as expected, not affected by the thickness of themass-diffusion layer.

To illustrate the magnitudes of the numerical parameters, con-sider the case illustrated in Fig. 4 with the initial setup of (a) temper-ature and (b) vortex. The unburned methane–air mixture has anequivalence ratio U = 0.6, temperature of 810 K, and the pressurein the domain is 70 atm. The ignition kernel has a diameterdK = 500 lm and temperature Tb = 1700 K. These conditions arechosen so that they are comparable to chamber conditions in typicalpre-chamber natural-gas engines [15]. The width of the mass-diffusion layer is 100 lm. The simulation employs a CFL number of0.9 which corresponds to a numerical time step of about5.78 � 10�9 s. The computations were carried out on an IBM

) strain rate (s�1) along the axis of symmetry of the vortex during the flame–vortex

Fig. 7. Evolution of (a) u-velocity (m/s) and (b) v-velocity (m/s) along the linejoining the centers of the vortex pair during the flame–vortex interaction of the casewith dv = 458 lm and u0 = 8.72 m/s (RM).

406 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

computing cluster with 64 2.5 GHz PowerPC 970MP processors. A10 lm resolution simulation with a single step mechanism for1 ms required 6 days of CPU time.

As shown in the figure, a counter-rotating pair of Oseen vortices[27] is superimposed on the initial flow field and allowed to self-propagate and interact with the initially cylindrical flame. Figure4a shows the initial velocity vectors for the vortex pair. The vortexpair shown in Fig. 4 and all the vortex pairs considered in this workare initialized at a distance of 700 lm from the center of the kernel.The vortex pair has a core to core diameter dv and a self-propagatingvelocity uv. It is possible that due to its proximity to the high temper-ature kernel, the strength of the vortex may be reduced by the en-hanced kinematic viscosity which results in viscous dissipationbefore interaction with the kernel. However, owing to the relativelylarge convective velocities (uv) of the vortices and the reduced kine-matic viscosity (m) at the high pressures simulated, i.e. due to the rel-atively high Reynolds number (>100) of the vortex, the dissipativetime-scales (d2

v=m, where dv is the vortex diameter) of the vortexare much longer than the convective time-scales (dv/uv). Hence,thermal expansion has a negligible effect in attenuating the vortexstrength prior to interaction with the flame.

The vortex length and velocity scales are selected from thelarge-eddy simulation of a 70,000 Re non-reacting jet [24]. ThisRe is representative of that of the jet of hot products in the naturalgas engine [15]. The vortex diameter (dv) is selected as the integralturbulent length scale (LI) and the vortex self-propagating velocity(uv) is set as the turbulent root-mean square velocity scale (u0)from the LES. Table 1 shows length and velocity scales employedcorresponding to four axial locations in the simulated jet. Table 1also shows the product of the length scale and velocity scale whichis a measure of turbulent diffusivity. As expected in turbulent jets,the diffusivity is approximately a constant [28].

3. Results and discussion

We will now consider a case where dv is 458 lm and u0 is 8.72 m/s(Vortex A in Table 1). Figure 5 shows the temperature contours in thedomain at different time instants. When the vortex pair interactswith the kernel, it causes deformation of the kernel into a crescentshape, see Fig. 5a and b. The hot combustion products are pushedoutwards into the crescent by the vortex and unburned methane–air mixture is gradually trapped within the evolving crescent, seeFig. 5b and c. The vortex causes local extinction of the flame as it pen-etrates through the ignition kernel and divides the kernel into twosymmetric halves. This observation is in agreement with the ‘‘break-through” regime proposed by Echekki and Kolera-Gokula [14]. It canbe seen in Fig. 5d that there is a temperature increase in the extin-guished region due to lateral diffusion of heat from the two halvesof the ignition kernel. This temperature rise can lead to ignition ofthe unburned mixture entrained between the two halves of the igni-tion kernel. It can be seen in Fig. 5e and f that this ignition process isgradual is nature. During the kernel–vortex interaction, the vortexpair also carries burned combustion products along its symmetryaxis as it penetrates through the kernel, see Fig. 5e and f. The temper-ature of the burned products is, however, unable to sustain flamedevelopment.

This process can be analyzed in greater detail by interrogatingparameters along the axis of symmetry of the vortex pair. Figure6a–d shows the variation of temperature, vortex centerline veloc-ity, heat release rate in the domain (CHRR), and strain rate, respec-tively, along the axis of symmetry of the vortex pair. The CHRR iscomputed as

CHRR ¼XN

i¼1

_wih0i ; ð1Þ

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.The strain rate is computed as

S ¼ @u@yþ @v@x

; ð2Þ

where S is the strain rate and u and v are velocity components in xand y directions, respectively.

At t = 0 ms, the vortex pair is located 700 lm from the kerneland does not noticeably influence the kernel. The temperature pro-file has an initial top-hat profile (Fig. 6a). As the vortex-pair prop-agates towards the kernel, it deforms the kernel, and the thicknessof the kernel along the axis of symmetry decreases (Fig. 6a). As aresult of the flame being subject to the strain from the vortex pair,the peak temperature decreases, see Fig. 6a time instants of 0, 0.1,and 0.15 ms. It is interesting to observe from Fig. 6b that the kernel(heat release) does not have a noticeable influence on the vortex

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 407

velocity along the centerline during this period. We observe inFig. 6c two distinct peaks, corresponding to the two flame frontsalong the centerline, in CHRR at 0.10 ms. Notice from Fig. 6d thatthe peak magnitude of the strain rate moves from a location belowthe flame at 0.1 ms to the flame at 0.15 ms as the vortex pairbreaks through the flame. As a result of the higher strain rate atthe flame location at 0.15 ms, the peak value of the CHRR reducesdrastically (by several orders of magnitude) and the flame is extin-guished. The temperature profile shows a similar trend as theCHRR along the axis of symmetry drops to nearly 1000 K. Thisextinction event occurs due to high strain rates which can beattributed to steep gradients associated with the v-velocity in thex direction. The local extinction along the axis of symmetry leadsto the formation of two distinct flame regions – on the left andright of the symmetry line (see Fig. 5d).

It is interesting to note that although the flame is extinguishedat the original location of y = 0.0033 m at 0.15 ms in Fig. 6c, we ob-serve that a region of low heat release is formed upstream of the

Fig. 8. Evolution of temperature (K) during the flame–vortex interaction dv = 1.15 mm an(RM).

vortex front at y = 0.0027 m. The extinction event is followed bysubsequent transport of burned gas by the vortex to this region(see Fig. 5d) which, coupled with heat transfer from the surround-ing gas to the symmetry plane, leads to ignition behind the vortexfront as shown by the increasing temperature and CHRR att = 0.20 ms. Notice that the strain rate at this location is reducedby an order of magnitude relative to the peak value at 0.15 ms be-cause the vortex has moved farther away. Comparing Fig. 6a and b,it is seen that prior to flame extinction, the vortex trails the flame.In other words, the kernel is advected by the vortex. Once ignitionoccurs a trailing flame is observed. It can be seen in Fig. 6b thatthere is a slight increase in the propagation velocity of the vortexcaused possibly by density changes.

Figure 7a and b shows the time evolution of u-velocity and v-velocity along the line joining the centers of the vortex pair. Itcan be observed that the magnitude of the u-velocity componentalong the vortex cores is negligible when compared to the v-veloc-ity component. It can also be seen in Fig. 7b that the kernel–vortex

d u0 = 3.82 m/s at times (a) t = 0.1 ms, (b) t = 0.2 ms, (c) t = 0.3 ms and (d) t = 0.4 ms

408 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

interaction leads to �5% decrease in the v-velocity componentfrom t = 0.10 ms to t = 0.15 ms. This implies that the expansion ef-fects, due to heat release rates, do not have a significant impact onthe vortex structure, i.e. the vortex itself is not influenced by thekernel–vortex interaction.

Results will now be presented from a simulation where the vor-tex length scale is 1.15 mm and velocity scale is 3.82 m/s (Vortex Din Table 1). The domain used for this simulation is 5 � 5 mm, i.e.500 � 500 uniformly-spaced cells, as before. Note that diffusivity,i.e. the product of the length and velocity scales, is comparable tothe previous case. Figure 8 shows the evolution of temperaturein the computational domain. In this case, there is greater defor-mation of the kernel and break through of the vortex pair is not ob-served. In the previous case, the original kernel was broken up. Thecombustion regime would correspond to ‘‘distributed” combustion[14,29]. The outcome from the interaction of Vortex D with thekernel lies in the ‘‘wrinkling” regime [14,29] where the vortex isunable to divide the kernel into two. The ignition kernel, in thiscase, is stretched in the lateral direction to a larger extent. The ker-

Fig. 9. Evolution of (a) temperature (K), (b) v-velocity (m/s), (c) CHRR (ergs/cm3 s) and (dinteraction of the baseline case with dv = 1.15 mm and u0 = 3.82 m/s (RM).

nel is also advected by the vortex pair. Note that the net effect is anincrease in area of the original kernel which can result in acceler-ated heat release rates. This is different from the previous case(Vortex A) where the increase in heat release rate is brought aboutby formation of multiple smaller ignition kernels.

Figure 9a–d shows the temperature, v-velocity, CHRR and strainrate, respectively, along the axis of symmetry. Recall that theseplots correspond to Fig. 6a–d for Vortex A. Similar to the previouscase, the initial kernel–vortex interaction results in the formationof a crescent shape and a reduction in the thickness of the kernelalong the symmetry plane, see Fig. 9a. However, in this case, thepeak temperature (see Fig. 9a) and CHRR (see Fig. 9c) continuouslyincrease with time and do not show evidence of extinction unlikethe previous case. The absence of extinction in this case can be ex-plained by comparing the spatial location of the peak vortex veloc-ity in Fig. 9b and the location of the flame as indicated by thetemperature and CHRR in Fig. 9a and c. It can be seen that the ker-nel is advected by the vortex pair. In other words, there is no breakthrough of the vortex. Comparing the strain rates in Figs. 9d and

) strain rate (s�1) along the axis of symmetry of the vortex during the flame–vortex

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 409

6d, it can be seen that although the peak strain value in the wrin-kling regime is nearly half of that in the breakthrough regime, thestrain rate at the flame location is an order of magnitude lowerthan that in breakthrough regime during the entire period of ker-nel–vortex interaction. Significantly lower strain rate at the flamelocation is consistent with the absence of extinction in the wrin-kling regime.

Figure 10a and b shows the time evolution of u-velocity and v-velocity along the line joining the centers of the vortex pair. Similarto the previous case, the magnitude of the u-velocity componentalong the vortex cores is negligible when compared to the v-veloc-ity component. Since, the vortex pair does not break through thekernel in this case and there is an absence of extinction, the v-velocity along the vortex core does not noticeably with time. Thus,the kernel–vortex interaction does not have a noticeable influenceon the vortex characteristics.

Fig. 10. Evolution of (a) u-velocity (m/s) and (b) v-velocity (m/s) along the linejoining the centers of the vortex pair during the flame–vortex interaction of the casewith dv = 1.15 mm and u0 = 3.82 m/s (RM).

In order to further characterize the influence of vortex lengthand velocity scales, we carried out simulations with Vortices Band C in Table 1. A Borghi-type regime map [14] can be constructedto characterize the outcomes. This regime map has non-dimen-sional length and velocity scales of the vortex as its characteristicscales. These scales are given by the ratio of the vortex transla-tional velocity ut to the laminar flame speed sL, and the ratio ofthe kernel size dk (diameter) to the vortex size dv (distance be-tween centers of counter-rotating vortex pair). Figure 11 showsthe outcomes of the interactions on a regime map. It can be ob-served in Fig. 11 that on increasing length scale ratio and velocityscale ratio simultaneously (as we move along the dotted line), wesuccessively move through laminar kernel, wrinkling, break-through and global extinction regimes on the regime map. Itshould be noted that all four vortices have comparable diffusivitiessince the length and velocity scales of these vortices have been se-lected at different axial locations of a jet. The vortex pairs havinglarger length scales have smaller turbulence intensities, i.e. smallerself-propagating velocities, and lie further from the orifice of thejet. In our work, Vortices A–C lie in the breakthrough regime whileVortex D lies in the wrinkling regime, i.e. vortices formed at down-stream locations in a jet will have a higher probability of lying inthe wrinkling regime. During kernel–vortex interactions, globalextinction depends on the characteristic length and velocity scalesof the interaction. An extinction event occurs when there is a rapidheat loss from the ignition kernel which leads to extinction of thekernel. This process is aided by vortices that are typically largerthan the ignition kernel and have very high (ut/sL > 40 at 1 atm)vortex velocities. Echekki and Kolera-Gokula [14] have reportedthat global extinction occurs when dv/dk > 1 and ut/sL > 40. How-ever, these limits are dependent on the equivalence ratio, kerneltemperature, unburned gas temperature, and pressure conditions.The vortices simulated in our work are smaller vortices with highvortex velocities or larger vortices with smaller vortex velocities.Thus, we do not encounter global extinction in our work.

We will now study these kernel–vortex interactions quantita-tively in order to compare the behavior in the wrinkling and break-through regimes. During kernel–vortex interactions, enhancementof the combustion process, which can be quantified by the totalheat release rate (THRR), is dependent on the flame surface areaand the speed of the reaction front. The THRR is computed as thesum over all the computational cells of the CHRR in each cell. Forexample, if the flame is highly strained, it can weaken and reducethe surface area of the flame which decreases the THRR. Thus, it ispossible to study the relative effect of different vortices on

Fig. 11. Kernel–vortex interaction regime map.

Fig. 12. Variation of flame surface area with time for different vortices (RM).

Fig. 13. Variation of net heat release with time for different vortices (RM).

Fig. 14. Time evolution of flame propagation speed with different chemical mechanisms for the baseline case with Tb = 1700 K and dK = 500 lm.

410 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 411

developing kernels by studying the evolution of flame surface areainside the computational domain.

We will now evaluate the results by considering the flame sur-face density R. It quantifies the surface area of the flame per unitvolume. Flame surface density-based transport models have beenformulated and utilized for Reynolds-averaged Navier–Stokes(RANS) and LES simulations [30]. The R can be estimated by firstdefining a reaction progress variable c, which measures the extentof the reaction, as

c ¼ T � Tu

Tad � Tu; ð3Þ

where T is the temperature of any point in the domain, Tu is un-burned gas temperature, and Tad is the adiabatic flame temperature.This reaction progress variable has a value of 0 in the unburned re-gion and 1 in the burned regions. The flame surface density R isthen computed as magnitude of the gradient of c [31], i.e.

R ¼ jrcj: ð4Þ

The flame surface area in any computational cell can be com-puted by multiplying the net R at any given time instant by thevolume of the cell. Figure 12 shows the time evolution of the total

Fig. 15. Evolution of temperature (K) during the flame–vortex interaction of the baselinet = 0.20 ms, and (d) t = 0.25 ms (SSM1).

flame area in the domain for the four different vortices (see Table1). Vortices in the breakthrough regime lead to local extinction ofthe flame along the axis of symmetry which leads to a decreasein the flame area. The start of the decrease in area can be seen at0.1, 0.15, and 0.3 ms for Vortices A, B, and C, respectively. Recallthat these three vortices lead to break through. It should also benoted that larger vortices have a greater tendency to deform theflame surface. Since the vortices in the wrinkling regime are largerin size, they lead to greater flame area compared to flames in thebreakthrough regime. The increase in the flame area is not, how-ever, proportional to the length scale.

Since the domain and kernel size and conditions are unchanged,the net heat release inside the domain provides a quantitativemeasure of the extent to which combustion is accelerated. Figure13 shows the variation of net heat release rate (THRR) inside thesimulation domain with time. It can be observed that the netamount of heat released is approximately the same for the fourcases until 0.15 ms. Beyond this time, the heat release rate in-creases with vortex size. Since large vortices lead to greater defor-mation of the kernel and subsequently lead to a larger interactionzone between the unburned and burned mixtures, it causes greaterenhancement of heat release rate. Also, local extinction occurs in

case with dv = 458 lm and u0 = 8.72 m/s at times (a) t = 0.10 ms, (b) t = 0.15 ms, (c)

412 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

the breakthrough regime at t = 0.15, 0.20, and 0.35 ms for VorticesA, B, and C, respectively. This leads to a drop in the THRR for thebreakthrough regime cases in Fig. 13. In principle, re-ignition ofthe extinguished flame region and formation of new kernels canoff-set the decrease in THRR due to local extinction. However, forthe given conditions, the re-ignition process is gradual and newpropagating kernels are unable to sustain flame development.Thus, it is possible to conclude that vortices in the wrinkling re-gime, i.e. those farther downstream in a jet, are more amenablefor flame development and lead to faster consumption of the pre-mixed charge.

Fig. 16. Evolution of (a) temperature (K), and (b) CHRR (ergs/cm3 s) along the axisof symmetry of the vortex during the flame–vortex interaction of the case withdv = 458 lm and u0 = 8.72 m/s (SSM1).

4. Predictions with a global mechanism

Engine computations are computationally intensive. Even theuse of the RM in three-dimensional Reynolds-averaged Navier–Stokes and large-eddy simulations is prohibitively expensive. It isworthwhile to evaluate the potential of global mechanisms to pre-dict the trends observed in the detailed simulations above. Wehave employed a simple single-step global mechanism (SSM) forthis evaluation, by calibrating its parameters against the flamespeed predicted by the RM.

The rate _wF (mol/cm3 s) for the SSM is given by the Arrheniusexpression:

_wF ¼ ATb½CH4�m½O2�ne�Ea=RuT ; ð5Þ

where A is the pre-exponential factor, b is the temperature expo-nent, set to zero in our work, m and n, set to unity, are reaction or-ders with respect to fuel and O2, respectively, Ea is the activationenergy, Ru is the universal gas constant, and [CH4] and [O2] arethe concentrations of CH4 and O2 in mol/cm3, respectively. Two val-ues of A have been employed to assess the sensitivity of the resultsto A. These two values have, in fact, been selected to give flamespeeds which are in good agreement with RM and Gri-Mech 3.0,respectively. The corresponding models will be referred to asSSM1 and SSM2. The pre-exponential factors for SSM1 and SSM2are 2.5 � 1011 and 5 � 1011 in cm mol s units. The activation energyis set to 104,500 J/mol for both the mechanisms. Laminar flamespeeds computed with the Gri-Mech3.0, the reduced mechanism(RM), and the SSM1 and SSM2 are shown in Fig. 14. We assessedthe grid dependence of the computed flame speed using the globalmechanism (SSM2) with 5 and 10 lm grid resolutions. There wereno noticeable differences in flame speeds. Recall that the grid inde-pendence of the RM results was shown earlier (see Fig. 3).

Consider the case where dv is 458 lm and u0 is 8.72 m/s (VortexA in Table 1). Figure 15 shows the temperature contours in the do-main at different time instants for SSM1. Figure 16 shows the var-iation of temperature and CHRR along the axis of symmetry of thevortex pair. It can be seen by comparing Fig. 5b and c (RM) andFig. 15a and b (SSM1) that the two sets of results are in good qual-itative agreement. In both of these cases, we successively observethe deformation of the ignition kernel into a crescent shape,entrapment of the hot combustion products within the deformedkernel, and extinction of the flame along the axis of symmetry.The extinction event is accompanied by a drop in the peak temper-ature to around 1000 K and a decrease in the CHRR by an order ofmagnitude (see Fig. 16a and b). The subsequent temperature risealong the axis of symmetry in Fig. 16a occurs at a similar rate asin Fig. 6a. Thus, SSM1 is able to capture both extinction and igni-tion phenomena.

Despite the similarities in the temperature profiles for SSM1and RM, there are several quantitative differences between thetwo mechanisms which are evident while comparing the CHRRprofiles for the two cases (see Figs. 6c and 16b). The peak CHRRfor the SSM1 case is about 30% lower than the RM. It can also be

seen in Fig. 16a and b that SSM1 predicts near-extinction of theflame as opposed to local extinction predicted by RM. This leadsto the formation of much more diffused CHRR region in theSSM1 case as opposed to a sharp thin trailing flame in RM case.Due to high strain rates, this heat release zone splits into two inthe SSM1 case. One of these zones leads to gradual ignition and atrailing flame similar to the RM case. The second CHRR peak att = 0.25 ms, which corresponds to re-ignition at the near-extin-guished flame location, moves along the vortex and favors flamedevelopment in the vortex region. The higher CHRR in this regionallows sustained flame development along the propagating vortexand leads to the formation of a propagating ignition kernel in theSSM1 case. On the other hand, the absence of a diffuse zone similarto the SSM1 case leads to slower flame development in the vortexregion for the RM. Consequently, the flame development cannot besustained and the ignition kernel formed in the vortex regionquenches.

Vortex D was also simulated with SSM1 and the results werecompared with the RM results. The differences between the two

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 413

mechanisms were negligible and SSM1 was able to capture the ex-tent of combustion accurately. Thus, it can be concluded that eventhough SSM1 leads to a more ‘‘stable” flame, as observed fromnear-extinction instead of extinction during the kernel–vortexinteraction, it is able to predict the onset of extinction and ignitionprocesses. However, this mechanism also over-predicts the CHRRis the vortex region which leads to development of propagatingignition kernels which are not observed with the RM.

We will now investigate kernel–vortex interaction for Vortex Ausing the SSM2 mechanism. It should be noted that this mecha-nism is calibrated against Gri-3.0 and thus has a faster transientcompared to the SSM1 and RM. This mechanism also providesus insight in how the pre-exponential factor in the global chem-istry model influences the outcome of the kernel–vortex interac-tion. Figure 17 shows the temperature contours in the domain atdifferent time instants for SSM1. Figure 18 shows the variation oftemperature and CHRR along the axis of symmetry of the vortexpair. It can be observed that SSM2 predicts the early interactionwell; i.e. deformation of the ignition kernel, entrapment of un-burned mixture, and the onset of extinction are resolved. How-ever, significant differences in the heat release rate profile are

Fig. 17. Evolution of temperature (K) during the flame–vortex interaction of the baselinet = 0.20 ms, and (d) t = 0.25 ms (SSM2).

observed at t = 0.15 ms for the two mechanisms. It was observedin Fig. 6d that the extinction event led to complete extinction ofthe flame at y = 0.0033 m in the RM. Figure 18b indicates that theSSM2 mechanism leads to near-extinction of the flame as op-posed to extinction observed with RM. It should be noted thatthough this behavior was also observed in the SSM1 case, themagnitude of CHRR was much lower. Consequently, significantdifferences are observed beyond this time instant. There is a rapidignition of the trailing flame and re-ignition of the near-extinctionflame along the symmetry axis for SSM2 as opposed to slower in-crease in the temperature and gradual ignition in the trailingflame for the RM case. The vortex pair also carries burned com-bustion products along its symmetry axis as it penetrates throughthe kernel, see Fig. 17c and d. These hot combustion productscause a new kernel to develop in the premixed charge beyondthe location of the original kernel. The higher CHRR, caused dueto rapid re-ignition of the near-extinguished flame, leads to fasterflame development in the vortex region and forms a stable prop-agating ignition kernel. The net effect is that the surface area ofthe flame increases dramatically and the combustion process isaccelerated.

case with dv = 458 lm and u0 = 8.72 m/s at times (a) t = 0.10 ms, (b) t = 0.15 ms, (c)

Fig. 18. Evolution of (a) temperature (K), and (b) CHRR (ergs/cm3 s) along the axisof symmetry of the vortex during the flame–vortex interaction of the case withdv = 458 lm and u0 = 8.72 m/s (SSM2).

414 H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415

Vortex D was also simulated with SSM2 and the results werecompared with the RM results. The differences between the twomechanisms are less evident for Vortex D where the vortex velocityis considerably lower than in the case above and extinction processis not observed. The difference between the two mechanisms lies inthe extent of consumption of the premixed mixture. It was observedthat the extent of consumption of the premixed charge (denoted bythe high temperature burned regions) is higher with the SSM2. Thisis not surprising since SSM2 has faster flame speeds compared to RMduring the transient flame development period. Hence, all theseresults point to a ‘‘faster” and ‘‘stronger” flame with the SSM2 whichimplies that increasing the pre-exponential factor in the globalmechanism increases the stability of the flame.

These three mechanisms discussed above can be comparedquantitatively by calculating the THRR in the computational do-main. Figure 19 shows the time evolution of the THRR for the dif-ferent cases. It can be observed that SSM2 seems to under-predictTHRR during the early interaction. However, once extinction, re-

ignition and ignition in the trailing flame occurs, the formationof an additional ignition kernel accelerates the rate of combustionfor SSM2 and it over-predicts the THRR in the later stages of theinteraction. SSM1 model shows good agreement in early interac-tion period and slightly under-predicts the HRR after the extinc-tion event. Sustained flame development in the propagatingignition kernel eventually increases the THRR for the SSM1 be-yond the RM.

While we have emphasized the differences between RM and thetwo global chemistry mechanisms, there are also striking similari-ties. SSM1 shows good agreement with RM for the extinction andignition processes but fails to capture the absence of re-ignitionof the extinguished flame and quenching of the additional ignitionkernel. Similarly, SSM2 is unable to resolve the re-ignition detailsaccurately in the breakthrough regime but captures the extinctionprocess. Also, it does a reasonable job at resolving the kernel–vor-tex interaction in the wrinkling regime. Based on the discussionabove, we can conclude that a well-tuned global mechanism isadequate for resolving kernel–vortex interactions. For the problemof interest, SSM1 model is suitable for studying early timescaleinteractions in the breakthrough regime and the complete interac-tion in the wrinkling regime. It might be possible to tune the modelparameters against other quantities of interest, such as ignitiondelay, instead of flame speeds to provide better agreement. Itsshortcomings, notwithstanding, SSM1 is adequate for large scalecomputations where reduced and detailed kinetics are not feasible.

5. Summary and conclusions

In this work, we investigate the influence of a counter-rotatingvortex pair on a flame-kernel developing in a lean methane–airmixture. The conditions considered are relevant to hot-jet ignitionof lean mixtures in homogeneous-charge natural-gas fueled recip-rocating engines. The vortex length and velocity scales are se-lected from a LES of a non-reacting jet with Reynolds numbercomparable to that of the hot-jet in such an engine. Two distinctcombustion regimes are observed. A kernel breakthrough regimeis observed for relatively smaller and faster vortices whereas akernel wrinkling regime occurs for larger and slower vortices.The flame surface area is computed by estimating the flame sur-face density. It is observed that the vortices increase the totalheat release rate by increasing the surface area of the originalflame. This surface area increase can result from wrinkling ofthe flame in the wrinkling regime and from the formation of dis-tributed ignition kernels in the breakthrough regime. It is ob-served that the increase in surface area is greater in thewrinkling regime than in the breakthrough regime, because of lo-cal extinction in the breakthrough regime and the greater defor-mation resulting from larger length scales in the wrinklingregime. From a practical viewpoint in lean-burn natural-gas en-gines, the wrinkling regime will result in higher heat release ratesand greater thermal efficiency.

A global mechanism was evaluated for its potential to repro-duce the physics observed with the reduced mechanism. The qual-itative behavior of kernel wrinkling and near-extinction due tostrain and ignition due to lateral transport of heat in the break-through regime are reproduced surprisingly well suggesting thatphysical effects rather than chemical effects are controlling theseoutcomes. In other words, the physical time scales are sufficientlyshort during this interaction that chemical time scales play a sec-ondary role, irrespective of the mechanism. However, the globalmechanism is unable to predict complete extinction of the flameand it shows re-ignition in the breakthrough regime unlike the re-duced mechanism. This implies that the kinetics are important inreproducing details of the interaction.

Fig. 19. Variation of net heat release with time for different mechanisms.

H. Reddy, J. Abraham / Combustion and Flame 158 (2011) 401–415 415

Acknowledgments

The numerical code employed in this work was developed byProfessor Vinicio Magi. The authors thank him for useful discus-sions during the course of this work. They also thank the RosenCenter for Advanced Computing at Purdue University and the Na-tional Center for Supercomputing Applications (NCSA) for provid-ing the computing resources. Financial support for this work wasprovided by Caterpillar, Inc. Discussions with Dr. Jonathan W.Anders, and valuable feedback from him, are gratefullyacknowledged.

References

[1] Natural gas overview. <http://www.naturalgas.org/>.[2] National Research Council, Fuels to Drive our Future, National Academy Press,

Washington, DC, 1990.[3] US Department of Energy, International Energy Outlook, Technical Report DOE/

EIA – 0484, US Department of Energy, September 2008.[4] J.B. Heywood, Internal Combustion Engine Fundamentals, McGraw-Hill Inc.,

New York, NY, 1988.[5] R.P. Roethlisberger, D. Favrat, Int. J. Therm. Sci. 42 (3) (2003) 223–237.[6] J.B. Bell, N.J. Brown, M.S. Day, M. Frenklach, J.F. Grcar, S.R. Tonse, Proc.

Combust. Inst. 28 (2000) 1933–1939.[7] Z. Shu, S.K. Aggarwal, V.R. Katta, I.K. Puri, Combust. Flame 111 (1997) 276–295.[8] G. Patnaik, K. Kailasanath, Proc. Combust. Inst. 27 (1998) 711–727.

[9] M. Hilka, D. Veynante, M. Baum, T. Poinsot, in: 10th Symposium on TurbulentShear Flows, vol. 2, 1995, pp. 19–24.

[10] P.H. Renard, D. Thevenin, J.C. Rolon, S. Candel, Prog. Energy Combust. Sci. 26(2000) 225–282.

[11] D.A. Eichenberger, W.L. Roberts, Combust. Flame 118 (1999) 469–478.[12] Y. Xiong, W.L. Roberts, M.C. Drake, T.D. Fansler, Combust. Flame 126 (2001)

1827–1844.[13] Y. Xiong, W.L. Roberts, Proc. Combust. Inst. 118 (1999) 469.[14] T. Echekki, H.K. Gokula, Phys. Fluids 19 (2007) 043604.[15] J.W. Anders., Caterpillar Inc., Peoria, IL, Private Communication, 2008.[16] J. Abraham, V. Magi, Int. J. Comput. Fluid Dyn. 8 (2007) 147–151.[17] A. Viggiano, V. Magi, Combust. Flame 137 (2004) 432–443.[18] S.K. Lele, J. Comput. Phys. 103 (1992) 16–42.[19] B. Carnahan, Applied Numerical Models, John Wiley & Sons, New York, 1969.[20] T.J. Poinsot, S.K. Lele, J. Comput. Phys. 103 (1992) 104–129.[21] R.B. Bird, W.E. Stewart, E.N. Lightfoot, Transport Phenomena, Wiley, New York,

1960.[22] J.W. Anders, V. Magi, J. Abraham, Comput. Fluids 36 (10) (2007) 1609–1620.[23] J.W. Anders, Turbulence and Residual Gas Effects in Pulsed Diesel Jets, PhD.

Thesis, Purdue University, August 2006.[24] R. Venugopal, J. Abraham, Combust. Flame 153 (3) (2008) 442–464.[25] A. Kazakov, M. Frenklach. <http://www.me.berkeley.edu/drm/>.[26] G.P. Smith, D.M. Golden, M. Frenklach, N.W. Moriarty, B. Eiteneer, M.

Goldenberg, C.T. Bowman, R.K. Hanson, S. Song, W.C. Gardiner Jr., V.V.Lissianski, Z. Qin. <http://www.me.berkeley.edu/gri_mech/>.

[27] T. Poinsot, D. Veynante, S. Candel, J. Fluid Mech. 228 (1991) 561–605.[28] H. Schlichting, K. Gersten, E. Krause, H. Oertel Jr., C. Mayes, Boundary-Layer

Theory, Springer, 2004 (Chapter 22).[29] F. Williams, Combustion Theory, Benjamin/Cummins, Menlo Park, C.A, 1985.[30] S.B. Pope, Int. J. Eng. Sci. 26 (1988) 445–469.[31] N. Peters, Turbulent Combustion, Cambridge University Press, UK, 2000.