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1、Modeling ignition phenomena

Modeling ignition phenomena in spray-guided

spark-ignited engines

R.Dahms a,*,T.D.Fansler b ,M.C.Drake b ,T.-W.Kuo b ,

A.M.Lippert b ,N.Peters a

Institute of Combustion Technology,RWTH Aachen University,Templergraben 64,D-52056Aachen,Germany

General Motors Research and Development Center,Warren,MI 48090-9055,USA

Abstract

An ignition model for spray-guided (SG)direct-injection gasoline engines called SparkCIMM—Spark Channel Ignition Monitoring Model—is presented in this paper.The model concept is motivated by high-speed imaging data showing complex processes for spark (formation,turbulent stretching and wrinkling,and multiple restrikes)and ignition (localized ?ame kernel formation and growth).Turbulent ?uctuations occurring on the scale of turbulent spark-channel wrinkling ($0.05–0.1mm)and local ignition ($0.1–0.5mm)are analyzed using expressions for the sub-grid turbulent kinetic energy,eddy turnover velocity and mixture-fraction https://www.wendangku.net/doc/ca19030506.html,putational particles are introduced along the spark channel to monitor its motion and ignitability.Ignition is determined by a local Karlovitz-number criterion that incorporates e?ects of turbulence,detailed chemical kinetics,and continuous energy deposition from the spark.Wher-ever suitable ignition conditions are found along the elongated spark channel,a small ?ame kernel is launched and tracked as it grows and merges with other ?ame kernels to form the turbulent ?ame surface.When the ?ame surface is su?ciently large,a G-equation ?amelet combustion model tracks the turbulent ?ame front.Both the early ?ame-kernel-growth and G-equation combustion models include e?ects of local mixture-fraction variance.Results from the SparkCIMM ignition model and G-equation combustion model are compared with experiments in an SG direct-injection engine.The model reproduces the general experimental features of spark-channel stretching,corrugation,and localized ignition;and ?ame front location probabilities are in good agreement.

Keywords:Engine;Direct-injection;Ignition;Imaging

1.Introduction

Spray-guided (SG)spark-ignition direct-injec-tion (SIDI)engines o?er substantially improved fuel economy and performance by injecting fuel directly into the cylinder and by igniting and com-busting the resulting highly strati?ed fuel cloud [1].The closeness of the fuel spray and spark elec-trodes can cause unfavorable conditions for igni-tion,including steep gradients in local velocities and equivalence ratios with substantial cyclic vari-ability [4].The narrow,high-velocity spray plumes from multihole fuel injectors exacerbate the situation.Optimizing ignition in SG engines with multihole injectors requires a more fundamental understanding of the ignition process,which has

Corresponding author.Fax:+492418092923.

E-mail address:rainer.dahms@itv.rwth-aachen.de (R.

Dahms).

Proceedings of the Combustion Institute 32(2009)

2743–2750

https://www.wendangku.net/doc/ca19030506.html,/locate/proci

Proceedings of the

Combustion Institute

been obtained here through experiments(high-speed imaging of the fuel spray,spark channel,igni-tion and?ame-kernel development in an optically accessible engine)and modeling described in this paper.This is a signi?cant advance over extensive experimental/computational studies of an earlier SG engine,which employed relatively coarse igni-tion submodels[2–5].

Two ignition models of greater complexity than[2–5]are the arc-and-kernel tracking ignition model(AKTIM)[6,7]and the discrete-particle ignition kernel(DPIK)model[8].In the DPIK model a single?ame kernel is initialized(and remains)centered on the spark gap while its sur-face is tracked by computational particles as it grows by spark-energy input and?ame propaga-tion until it is large enough for a G-equation sim-ulation.The AKTIM model introduces marker particles to represent both the spark and?ame kernels that advect and di?use in response to the turbulent?ow?eld.

In this paper,ignition measurements of an improved SG engine[9]provide more detail on spark and early?ame kernel processes.A new ignition model is presented that includes sub-grid scale turbulent velocity and mixture-fraction?uc-tuations and that represents the experimentally observed phenomena of spark stretching and tur-bulent wrinkling,localized ignition along the spark channel,and development of the early?ame kernel into a propagating turbulent?ame.Finally, experiment and model are compared.

2.Experimental investigation

The single-cylinder SG-SIDI engine(Fig.1) has a four-valve pent-roof head and a contoured combustion bowl in the piston.Gasoline is temperature and minimize NOx production.Opti-cal access is obtained through a quartz window in the bottom of the piston bowl and through a win-dow in the cylinder head and a side cutout in the piston.Table1summarizes engine speci?cations and operating conditions for a warmed-up,highly strati?ed part-load condition;more details are available elsewhere[9].

Figure2a shows selected high-speed(24,000 frames/s)images of CN*-radical emission[10] from the spark-ignition process.The initial spark (not shown)occurs across the 1.25-mm spark gap.Local turbulent?ow moves the spark attach-ment points along the ground and center elec-trodes,and stretches and wrinkles the thin ($0.05–0.1mm)spark channel.The spark channel can stretch up to$10mm before a restrike occurs. Restrikes are frequent because of the high veloci-ties and the long spark duration(1–3ms).Under the conditions here,CN*is generated only from carbon in the fuel by the spark and not by com-bustion[10].CN*intensities have been calibrated under homogeneous conditions and used for quantitative fuel-concentration measurements in other strati?ed SIDI engines[3,4,10].The widely varying CN*intensities in Fig.2a,although not calibrated,suggest widely varying fuel concentra-tions along the spark channels.

Reliable ignition requires optimum conditions (approximately,equivalence ratio0.6–2,velocity <15m/s,and minimum liquid fuel)[4]anywhere along the spark channel.For example,the broad-band visible-wavelength(350–800nm)images in Fig.2b show locally rich ignition regions which generate intense soot luminosity.Despite the large cyclic variability in the spark and ignition events, these general experimental features are consis-tently observed in this engine over a range of operating conditions.

Soot luminosity from fuel-rich regions (Fig.2b)does not adequately represent the growth of the spark kernel into a turbulent premixed

Fig.1.Single-cylinder optical SG engine.Table1

Engine speci?cations and operating conditions

Stroke95mm

Bore86mm Compression ratio12.0

BMEP 2.0bar

MAP95kPa

Intake air temperature95°C

IVCà114°CA aTDC Engine speed2000r/min Spark advanceà29°CA aTDC Spark duration2ms

Spark energy100mJ

Swirl index 2.0

Start of Injectionà43°CA aTDC End of Injectionà35°CA aTDC Injected fuel mass9.3mg

Mean air/fuel ratio26.61

Mean EGR45.87%

2744R.Dahms et al./Proceedings of the Combustion Institute32(2009)2743–2750

High-speed(24000frames/s)individual-cycle imaging of spark and combustion luminosity in an is outlined in color.Images(height$15mm)are labeled with time after spark breakdown.(a)CN

from the spark showing stretching and wrinkling by the local turbulent velocity?eld and suggesting

fuel concentration along the spark channel.(b)Broadband visible(rich combustion)luminosity showing rich zones along the spark channel which persist after the spark restrikes back to the spark-gap between

third and third and fourth images.[Di?erent engine cycle from(a)].

?ame.As illustrated in Fig.3a,partially

?ame kernels,irrespective of local equivalence

ratio,have been visualized here using a

tition-rate copper-vapor laser sheet and

speed(24,000frame/s)camera to record

tering from$1l m silicone-oil droplets

(a).High-speed laser-sheet Mie-scattering

combustion from one engine cycle.Dark

burned gas zones where silicone-oil droplets

vaporized.(b)Enlarged,contrast-enhanced Mie-scatter-

showing localized ignition of a?ame

point along a stretched spark channel.

are strongly a?ected by turbulent curvature, wrinkling,and mixture-fraction?uctuations. Third,the?ame kernels develop into a turbulent ?ame whose laminar preheat zone is perturbed by the smallest turbulence https://www.wendangku.net/doc/ca19030506.html,bustion continues by turbulent?ame propagation through rich and lean regions,followed by rich-zone burnout by slower mixing-dominated com-bustion[4].

3.1.Spark-channel evolution

The spark channel is too thin to resolve by conventional computational grids.The model for-mulation therefore begins by analyzing the mix-ture fraction Z and turbulent kinetic energy (TKE)k on the scale of the spark channel.The well known transport equation for the mixture fraction variance g Z002[11](whose solution in this work gives the evolution of local equivalence ratio ?uctuations on the integral length scale)is also

assumed to be valid in sub-grid space.Further assuming equilibrium between production and dissipation yields[12]:

g Z002?2:0

c v k

D ter e ZT2

The turbulent di?usivity of the

variance scales with the eddy turnover

and the integral length scale:D t$v0áthis in Eq.(1)and assuming only

yields the mixture-fraction variance on a

within the inertial range:

g Z002 sub $

2:0

c v

sub

e v0subá‘suber e ZT2

sub

For the sub-grid TKE,the used to derive a turnover velocity length scale‘sub[13]

~v sub$~v0

‘sub

‘t

1=3

;‘sub6‘t

The TKE then scales as

~k sub $~ká

‘sub

2=3

;‘sub6‘t

The scaling law for the sub-grid mixture-frac-

tion variance is derived from the ratio of g

Z002

sub

and g Z002at the integral scale,assuming that

e?const in the inertial range and using Eq.(4):

Z002

sub

g Z002$

‘sub

‘t

er e ZT2sub

er e ZT2

‘sub

‘t

2=3

;‘sub6‘t

e5T

The spark channel is modeled by computa-

tional particles(size50l m[14])that de?ne its

shape and track its local mixture composition,

motion and turbulent wrinkling.As the local?ow

?eld elongates the spark channel,new particles are

introduced to maintain a uniform distribution

along the channel.

For each particle,the local mixture fraction is

computed as the sum of the interpolated local

mean mixture fraction and a random sub-grid tur-

bulent?uctuation that is derived from Eq.(5)on

the characteristic scale of the spark channel‘spk

with the?uctuation time scale taken as the sub-grid

turbulent time scale:D s H?s$~k sub=e.Particle

Z p?e Z celltr e Z celláD~x p;cell |?????????????????{z?????????????????}

local mean mixture fraction t

áeg Z002celltr g Z002celláD~x p;cellT

1=2

‘spk

1=3

ásigne1;randeD s HTT

|??????????????????????????????????????????????????????????????????{z??????????????????????????????????????????????????????????????????}

superimposed turbulent fluctuation

e6T

Fig. 4.Procedure for evaluating the spark channel

mixture strati?cation based on computational cell quan-

tities.The cross indicates the center of gravity of the

computational cell where all CFD quantities are de?ned.

Gradients are interpolated from neighboring cells(not

shown here).Solid circles indicate particle positions.

Enlargement illustrates the characteristic turbulent eddy

size active on the spark channel scale.

2746R.Dahms et al./Proceedings of the Combustion Institute32(2009)2743–2750

The mixture ignitability(considering the local charge strati?cation,dilution,and temperature, which is particularly important near the spark plug) is computed at each particle location.For every particle encountering ignitable mixture,a small ?ame kernel is launched,as described in the next section.The ignitability criterion is based on the local Karlovitz number:Ka=(v g/s L)2

The e?ect of restrikes on ignition are included in the model by resetting the spark marker parti-cles to their original locations when the spark channel exceeds a prede?ned length(10mm) determined from experiments.Several restrikes may occur during the assumed2-ms spark dura-tion,with additional small?ame kernels initiated as local conditions permit.

3.2.Early?ame-kernel development

When local conditions permit ignition at a par-ticle position,a small(0.5-mm[14])?ame kernel is initiated,and its growth on the sub-grid scale is modeled using an extension of[5]which includes mixture-fraction?uctuations.Multiple?ame ker-nels grow spherically due to the turbulent?ame speed,advect at the local?ow velocity,and merge until they form a turbulent?ame surface that can be resolved on the computational grid.Merging of di?erent?ame kernels is modeled by the envelop-ing?ame surface of intersecting kernels.

Flame-kernel advection is evaluated from Eq.

(6)but with the mixture fraction and its variance replaced by the velocity and turbulent kinetic energy,respectively,and with the kernel diameter taken as the length scale for evaluating the sub-grid turbulent turnover velocity.

The radius of each?ame kernel is evaluated from

r K?

??????????

3m K

4p.

e7T

with m K as the?ame-kernel mass and R b as the density of the burnt gas.From the continuity equation d m K

d t

?4p r2

s T;j:e8TThe density in the burned gas can be signi?cantly lower than the density of adiabatically burned gas at temperature T ad due to the increased kernel temperature T K caused by electrical energy depo-sition at rate_Q spk.This e?ect is modeled following

[15]:

d T K

d t

?à

_m K

m K

eT KàT adTt

spk

g eff

m K c p

c p

d p

d t

;e9T

where g e?%0.3is the e?ciency of electrical energy transfer to the gas,c p is the speci?c heat,and p is the pressure.

The turbulent burning velocity including the mixture-fraction variance is

~s T;j?

s LeZTáe1te r teZTTe PeZ;e Z;g

Z002

sub

Td Z

àjeD0tD t;pTe10TThe?ame surface area ratio~r is the ratio be-tween the areas of a smooth and an instanta-neous wrinkled?ame front:~r?jr~G jt~r t.The turbulent?ame surface area ratio~r t,which is de?ned as the increase of the?ame surface area ratio~r caused by turbulence beyond the laminar value~r?jr e G j for v0?0,expresses the increase of turbulent over laminar?ame speed: ~r t?e~s Tà~s LT=~s L.The turbulent di?usivity D t scales with the local curvature j,the sub-grid turbulent kinetic energy~k and the?ame-front position variance g G002as

D t$

e~k subág G002T1=2e11TEarly?ame wrinkling is modeled by locally solv-ing a sub-grid equation for the mean?ame surface variance:

d g G002

d t

?2:0áe D tàc s~e~

ág G002e12T3.3.Turbulent?ame propagation

As soon as the?ame can be resolved on the computational grid,the G-equation approach is used to transport the mean turbulent?ame sur-face[11,16].The kinematic equation valid on the iso-surface is

h.i

o e G

o t

th.i~~vár e G?fh.~s T iàh.i~j D t gjr e G je13TOutside of this iso-surface,the scalar is required to be a signed distance function:jr e G j?1.

By analogy with the variance equation for a passive scalar,the variance e G002as the second moment of e G is[13,15,17]

R.Dahms et al./Proceedings of the Combustion Institute32(2009)2743–27502747

h.i o g G002

o t

th.i e~v flameár g G002

?r káeh.i D t r k g G002Tt

2h.i D ter e GT2àh.i c s g G002e~e14T

4.Results

CFD calculations using the new ignition model

were performed for the SG-SIDI engine(Fig.1

and Table1)using ACFluX(formerly GMTec

[20]).The code solves ensemble-averaged equa-

https://www.wendangku.net/doc/ca19030506.html,puted3D visualization of(a)equivalence ratio[–],(b)turbulence energy(m2/s2)and(c)velocity magnitude(m/s)along the spark channel at220,330and 500l s after spark onset.Ignition is locally detected $490l s after spark onset at the bottom of the spark channel and a spherical?ame kernel is initialized.Fig. https://www.wendangku.net/doc/ca19030506.html,parison of probabilities of?nding instantaneous?ame front between a simpler?ame kernel model[5](left),experiments[9](middle)and the new ignition model presented here(right)at three times after spark breakdown.Equation(18)is used to calcu-late the?ame-location probability from both G-equa-tion simulations.

Fig.7.3D visualization of the evolution of the simu-lated mean turbulent?ame front using the same G-equation combustion model with a simpler?ame kernel model(left)and with new ignition model presented here (right).

2748R.Dahms et al./Proceedings of the Combustion Institute32(2009)2743–2750

fuel spray is modeled with25,000stochastic Lagrangian spray parcels coupled to the gas phase via source terms.An initial droplet size distribu-tion(SMD=15l m)is assumed instead of model-ing the primary breakup.Vaporization is captured using a continuous multi-component mixture approach[21].Spray model parameters(e.g., spray-plume mass distribution at the injector exit; initial drop size and velocity)were optimized by comparison to spray-rig experiments.

Figure5shows that the computed displace-ment,stretching and wrinkling of the simulated spark channel are quite similar to those in the experiments(Fig.2).The turbulent turnover velocity is clearly su?cient to corrugate the spark channel.The color coding of the spark channels in Fig.5illustrates the high velocities and TKE in the spark-gap region as well as the strong gradi-ents in velocity,TKE and equivalence ratio.Fig-ure5also shows a small?ame kernel initialized at the?rst location along the spark channel at which the Karlovitz-number ignition criterion is satis?ed,which occurs at490l s after spark initia-tion.This ignition delay re?ects the combined e?ects of mixture strati?cation and intense turbu-lence(via the role of the Kolmogorov-scale eddies in the ignition criterion).Delays on this scale before the?rst detectable?ame are typical of the Mie-scattering experiments.

The importance of including the new ignition model is demonstrated by the planar images in Fig.6and the3D renderings in Fig.7.The center column of Fig.6shows experimental measure-ments of the probability of instantaneous?ame location at three times after spark breakdown evaluated from200consecutive engine cycles[9]. The left and right columns of Figs.6and7show results of calculations with the same3D G-equa-tion code at comparable times after spark,but with di?erent ignition models.The left column is with a simpler ignition model[5]that neglects spark stretching,lacks a local ignition criterion, and ignores e?ects of?uctuations in equivalence ratio and velocity on early?ame-kernel-growth. The right column shows results with the present ignition model that includes all these e?ects.The elongated shape and growth of the early?ame kernel seen in the experiment are predicted reasonably well by the present approach,whereas at the earliest times the simpler model fails com-pletely to predict these characteristic features of spray-guided ignition and early combustion.

5.Discussion

The ignition model introduced here includes several physical processes that have been shown experimentally to be important for ignition under the highly strati?ed and diluted charge condi-tions that characterize part-load spray-guided gasoline engine operation.Prior approaches such as[5,22]and the DPIK[8]and AKTIM[6]mod-els do not include these physical processes.In the DPIK model,the spark channel structure is neglected entirely;the mixture is not monitored locally for ignitability;and a single?ame kernel grows spherically by spark-energy input and ?ame propagation without advection until it is large enough to be followed by a G-equation simulation.In the AKTIM model,both the spark channel and early?ame kernels are repre-sented by marker particles that are advected with the?ow,but the spark channel itself is una?ected by turbulence.Following Adelman[23],the AKTIM ignition criterion excludes turbulence e?ects on ignition.Both the DPIK and AKTIM approaches ignore the e?ects of turbulent equiv-alence-ratio?uctuations on early?ame-kernel development.

The present model also makes signi?cant sim-pli?cations.E?ects of liquid droplets on the spark channel and energy transfer from the spark to liquid fuel are neglected,although heat transfer from the?ame to liquid fuel is included.Energy deposited by the spark into the mixture is treated as constant in time,whereas the DPIK and AKTIM approaches use time-dependent energy deposition based on experiment.The restrike cri-terion here is also simpler than that in AKTIM, which initiates a restrike when the voltage across the spark gap(from an ignition-system model) exceeds the gas breakdown voltage.These features could be added to the present model.

The spark-channel modeling in the present approach explicitly includes turbulence/spark-channel and turbulence/?ame-kernel interactions. Ignition is triggered locally along the spark chan-nel depending on the local equivalence ratio and turbulence intensity.The ignition criterion is based on a modi?ed second Karlovitz number [11]and incorporates e?ects of continuous energy deposition from the spark,detailed chemical kinetics,and turbulence.Scaling laws for turbu-lent?uctuating quantities describe the e?ects of turbulence on each sub-model considering its characteristic length scales.Experimentally,the earliest detectable?ame kernels(Fig.3b)are already comparable to the$1mm integral length scale that results from the intense turbulence induced by the fuel spray.It is therefore impera-tive to include turbulent velocity and mixture-fraction?uctuations when modeling?ame-kernel growth before the?ame can be fully resolved on the computational grid.

6.Summary and conclusions

High-speed imaging experiments have shown the distinctive advection and corrugation of the spark channel by the local turbulent?ow?eld in

R.Dahms et al./Proceedings of the Combustion Institute32(2009)2743–27502749

SG-SIDI engines,as well as the transition from a spark to a wrinkled?ame kernel and?nally to a turbulent?ame.Analysis of the turbulent?uctua-tions on the scale of the spark channel found that, despite its thin topology,turbulent velocity?uctu-ations cannot be neglected,and indeed are respon-sible for the spark-channel corrugations observed experimentally.The local mixture ignitability, determined by a local Karlovitz-number criterion, varies strongly along the spark channel due to the strong gradients in mean mixture composition and to the sub-grid turbulent composition varia-tions and intense velocity?uctuations induced by the fuel spray.

A new ignition model has been introduced that monitors local mixture ignitability along the spark channel over the duration of a typical spark ($2ms),even after a?ame kernel has been initi-ated.Whenever local conditions along the spark channel permit ignition,a?ame kernel is launched and tracked as it grows and merges with other kernels to form the turbulent?ame surface.The local mixture-fraction variance is incorporated into both the early-kernel-growth model and the G-equation?amelet model that takes over once the?ame surface can be resolved on the computa-tional grid.This approach yields early?ame-loca-tion probabilities in much better agreement with experiment than simpler ignition models that do not monitor the mixture composition along the extended,moving spark channel or that ignore the e?ect of the mixture-fraction variance on the propagating?ame.

Acknowledgments

The authors are grateful to D.L.Reuss,A.S. Solomon,R.O.Grover and X.Yang(GM R&D)for helpful discussions and to Mark Hue-bler(GM R&D)for generating the computational mesh.This work has been funded by General Motors.References

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