(c)2001 American Institute of Aeronautics & Astronautics ... · Kazuo Sone, Nayan Patel and Suresh Menon School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia

(c)2001 American Institute of Aeronautics & Astronautics or Published with Permission of Author(s) and/or Author(s)' Sponsoring Organization.

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AIAA 2001-0635Large-Eddy Simulation of Fuel-AirMixing in an Internal CombustionEngineKazuo Sone, Nayan Patel and Suresh MenonSchool of Aerospace EngineeringGeorgia Institute of TechnologyAtlanta, Georgia 30332-0150

39th AIAA Aerospace Sciences Meeting2001 / Reno, NV

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Large-Eddy Simulation of Fuel-Air Mixing inan Internal Combustion Engine

Kazuo Sone* Nayan Patel* and Suresh Menon*School of Aerospace EngineeringGeorgia Institute of TechnologyAtlanta, Georgia 30332-0150

In this study, a Large-Eddy Simulation (LES) methodology has been implementedinto the well-known Internal Combustion (1C) engine simulation code KIVA-3V andused to study unsteady fuel-air mixing process in a Direct-Injection Spark-Ignitiontype 1C engine. This new code incorporates a LES approach (called henceforthKIVALES) using the fc-equation SGS model (Menon et a/., 1996) and a modifiedversion of the Linear-Eddy Mixing (LEM) model. To evaluate the accuracy of KI-VALES, comparisons between KIVALES, original KIVA-3V, and another high-orderLES code (well-validated elsewhere) are first carried out using flow over backward-facing step and temporally growing mixing layers. These types of flows are wellknown and therefore, sufficient data is available for comparison. Good agreementis obtained with earlier DNS/LES or experimental study using the new KIVALES,whereas the original KIVA-3V shows poor agreement. Next, both KIVALES andKIVA-3V are used to study fuel-air mixing process with direct spray injection intothe cylinder. The comparisons between KIVALES with and without LEM and theoriginal KIVA-3V are also made. A qualitative comparison (since no experimentaldata is available) suggests that KIVALES predicts significantly more unsteady mixingregions than KIVA-3V. The implications of the non-homogeneous mixed region oncombustion are discussed.

1 IntroductionRecent progress in spray combustion has made

it possible to produce direct injection gasoline en-gine that is expected to have advantages of bothconventional diesel and gasoline engines. Since cur-rent port fuel injection type gasoline engine is atthe state-of-the-art and is less likely to experiencegreat progresses in the next decade, gasoline directinjection technology is a promising technology, capa-ble of achieving very severe emission standards andrestrictions such as EURO IV or SULEV. The crit-ical issue associated with direct injection engine oreven other types of spray combustion system is thatwe have to understand the liquid fuel evaporationprocess and the subsequent mixing of the vaporizedfuel with air in the cylinder. This process is verysensitive to the type of fuel injectors, its operatingparameters and so on, and it is apparent that thesuccessful control of spray dispersion and turbulentfuel-air mixing process will imply an efficient direct

* Graduate Research Assistant, Student Member AIAA;Current address, Hitachi America, Ltd., R &; D Division,34500 Grand River Avenue, Farmington Hills, MI 48335

t Undergraduate Research Assistant, Student MemberAIAA

* Professor, Associate Fellow AIAACopyright © 2001 by Kazuo Sone, Nayan Patel and Suresh Menon.

Published by the American Institute of Aeronautics and Astronautics, Inc.with permission.

injection engine.To achieve this goal, the efficient use of compu-

tational tools is inevitable since the in-cylinder flowfield with spray is quite hard to visualize or to mea-sure accurately even with up-to-date experimentaltechniques. Numerical studies of direct injectionengine has been carried out by many authors,1'2and they are comprehensively reviewed by Zhao.3However, most of the Internal Combustion enginesimulations are performed using Reynolds-AveragedNavier-Stokes (RANS) equations with turbulencemodel such as the well known k — e model, whichthe KIVA code4 used in this study, also employs.It is recognized, however, that steady-state modelsdo not have the ability to capture unsteady mixingprocess inside the cylinder accurately since all turbu-lence effects are modeled (therefore, the model is alsocalled a full-field model5). There is another tech-nique called Large-Eddy Simulation (LES), in whichlarger eddies are calculated explicitly in a space- andtime-accurate manner while smaller eddies that areof the scale of the computational grid or smaller aremodeled using subgrid scale (SGS) models. Appli-cation of LES to 1C engines is relatively new and lesscommon while application of LES in other flow fieldsis rapidly growing.6 LES studies of 1C engine flowshave been recently reported by several authors.7"9

American Institute of Aeronautics and Astronautics Paper 2001-0635


A recent attempt by Celik et a/.10 actually imple-mented LES models into an earlier version of theKIVA code. Nearly all these earlier LES attemptsemployed the Smagorinsky's algebraic eddy viscos-ity SGS model and no study so far has addressedsubgrid scalar mixing.

Here, LES with well-validated Adequation SGSmodel11 is implemented into the most recent com-mercial 1C engine simulation code (KIVA-3V), whichoriginally solves the RANS equations with the k — emodel. The new code is denoted here as KIVALES,and the accuracy of the code is evaluated with thesimulations of temporal mixing layer and flow overrearward-facing step. The new code is, then, ap-plied to direct injection engine simulations to studyspray dispersion and fuel-air mixing process associ-ated with fuel spray evaporation.

To investigate scalar mixing at the small scales, asubgrid scalar mixing model called the Linear-EddyMixing (LEM) model is also implemented. LEM wasoriginally developed by Kerstein12 for stand-aloneturbulent mixing, but later, it was found to be effec-tive as a SGS scalar mixing model for LES.13 LEMis particularly attractive for turbulent reacting flowssince all the relevant scales are resolved in a 1-DLEM domain inside each LES computational cell.Thus, the reaction-rate and molecular diffusion ef-fects can be computed in an exact manner withoutrequiring any closure model.

2 Governing EquationsThe conservative equations for compressible flow

are filtered with a density-weighted box filter to ob-tain equations for LES, and they are described asfollows.

dt (1)(2)

plte + "i

dpY0*9*

m=i hmYmVj,m- Throughout this study, Fickiandiffusion is used to model species diffusion velocity

j> m -

Following original KIVA code, we employ the spe-cific internal energy equation rather than the totalenergy equation.14 To the authors' best knowledge,specific energy equation has never been publishedelsewhere in a context of LES except by Celik et at.However, in that work, the details of the closure ofspecific internal energy equation was not described.Therefore, for completeness we describe the deriva-tion and filtering of the internal energy equation inthe Appendix.

In the above equations, the following subgrid re-lated terms are unclosed and have to be modeled:

= p[UiUj - UiUjl

= p(eui - eui] + \pv~ -

dp _ dp

and

(5)(6)

(7)

(8)

(9)(10)

These terms represent subgrid stress tensor, sub-grid heat flux, subgrid viscous work, subgrid velocitypressure gradient correlation, subgrid species massflux and diffusive mass flux, respectively. The clo-sure of these terms are considered in the followingsection.

3 Subgrid ModelingThe small scale effects on a resolved scale is ap-

proximated by SGS models in LES. Even thoughLES is less model dependent than RANS, the se-lection of SGS models is of great importance and achallenging part of research in LES. In this study,^-equation model developed by Menon et a/.11 isadopted. In this model, subgrid stress tensor r^s

is modeled as T*°S = -2pvt(Sij - (1/3)5**^) +(2/3)pkS9$6ij, with eddy viscosity given by i/t =CJ//cS5sl/2A using subgrid turbulent kinetic energykS9S, which is provided by solving the following equa-tion.

dpk ,sgs

dt(11)

_— / .xwhere the production term, PS9S is closed by(4)

where stress tensor r^ = —pSij + cr^ = -p$ij -f*ij)> and heat flux 0j =

—T*?s(dui/dxj), and the subgrid energy dissipationrate term DS9S is closed by C£pkS9s3/2/A. Thetransport term TS9S = V-{(pvt/Prt)VkS9S}. For the



present study, Cv and C£ are constant and chosenas 0.067 and 0.916, respectively.15 A more expen-sive dynamics version is also available,16'17 but isnot used at present. The last term Ws is the sub-grid turbulence effects due to spray, and this termfollows the original KIVA model.14

The species mass flux $S9S is modeled by gradientdiffusion closure,

9YmSet

(12)

in the conventional approach and the present studyalso uses this closure (KIVALES). The diffusive massflux O*9^ is ignored in this study since this term issmall compared to $^.18

The velocity pressure gradient correlation termUS9S is ignored, and h*9S term is modeled by gra-dient diffusion hS9S = -pvtCp/Prt(df / d x j ) , by theanalogy from HS9S term closure.18 Finally, 9^s

stands for subgrid viscous work, and following orig-inal KIVA-3V, is modeled by SGS turbulent energydissipation rate QS9S - DS9S = C£pkS9s3/2/^, Thisterm has been neglected in the earlier LES stud-ies.18'19 The implications of this term in terms ofSGS model is discussed elsewhere.20

4 Linear-Eddy Mixing ModelAn alternate approach to study scalar mixing is

based on the LEM model. In this model, the scalarconservation equations are not filtered. Instead,these scalar equations are implemented in a sub-grid simulation model within the LES grid. Thismodel was originally developed by Kerstein12 forstand-alone simulation of turbulent mixing, and wasextended into a subgrid model of LES.13 LEM mod-els subgrid scale mixing process in a one-dimensionalcomputational domain within each LES cell. There-fore, each LES cell has a 1-D LEM domain withinit and this 1-D domain is resolved with a gridfine enough to resolve the smallest turbulent eddy(e.g., Kolmogorov eddy). The key advantage of thismodel is that the two inherently different mixingprocesses, turbulent stirring and reaction-diffusion,can be treated separately but concurrently. Also,due to the 1-D nature of the LEM, the computa-tional cost of subgrid simulation is also reasonable.

To implement LEM, the species conservationequation is re- written in the following form:

dYm _at

„, dYm i d

where HJ is the Favre-filtered velocity and u" = Uj -Uj is unresolved velocity. Note that this equation is

not filtered unlike Eqn.(4). Therefore, no additionalclosure is required. This equation is solved in threephases employed in KIVA as follows:

yB _*

At_ r)" pdx/

flym

dxj— u4

yn+1 _ yB1 m______ rn

At

dYn

(14)

(15)

Superscripts n, A, B denote respectively time level,phase A, in which spray and chemistry is solved,and phase B, in which Lagrangian fluid motionsare solved.14 At present, we have not implementedsubgrid combustion, but this extension can be ac-complished within LEM subgrid model. Equation(15) is solved on the resolved scale while equation(14) is implemented in the 1-D LEM domain in thefollowing form.

dY^

dt1 d

ds<8tir (16)

where 5 is a coordinate along the LEM domain. Inthese equations, the molecular diffusion is imple-mented in the first term of the RHS and is solvedexplicitly as in a DNS while the subgrid scale advec-tion (turbulent stirring) denoted as F^IT is modeledby a stochastic process. This is briefly discussed be-low, and more details can be found elsewhere.13'15'21

Turbulent stirring is implemented as random re-arrangements of the scalar field along the 1-D do-main. This random rearrangement physically repre-sents eddyjnotion smaller than-the computationalgrid size, A and is governed by two parameters: adistribution of eddy size I in the subgrid domain/(/) = (5/3)(/-8/3)/(rT5/3 - A~5/S) in the range77 < / < A and an event frequency per unit lengthA:12

•" (A/^)5/3 - 1A = ^3A l-(,/A)4/3>

(17)

where subgrid Reynolds number is defined asReS9S = u'A/i/, and u' = y/(2/S)k*3*. The as-sumption of statistical isotropy in 1-D domain isimplemented by choosing the location of the eventsrandomly from a uniform distribution. The randomrearrangement events occur every stirring time inter-val. The stirring interval is given by Atstir = I/A A,and in each event, segment that is affected by thisrandom event is chosen according to the distribu-tion described above and the rearrangement followsa triplet map procedure.12

To implement LEM into LES and to allow for ad-vection of the subgrid scalar fields across LES cells



due to the large-scale resolved motion, a Lagrangianadvection process is employed to model the processin equation (15). This concept suits ALE (ArbitraryLagrangian-Eulerian) method, which is used in theKIVA code. In ALE method, Lagrangian phase andadvection phase are treated respectively. There havebeen various attempts to address this issue.18'19

In this study, linear superposition of subgrid fieldaccording to the local cell-face volume flux is im-plemented based on the recent work of Pannala22

since this method suits phase C (advection phase)of KIVA. In this method, each upwind side subgridscalar field is superimposed onto the adjacent down-wind side subgrid field, and its ratio is determinedby the local volume-flux ratio (u • AAt/V).

5 Results and Discussion5.1 Temporal Mixing Layer

First, the ability to simulate scalar mixing pro-cess of the new KIVALES code is examined usingtemporal mixing layers. The flow is initialized by amean streamwise velocity with a tangent hyperbolicprofile and with the fundamental instability modewith a non-dimensional wave number a = 0.446,which is the most unstable wave number mode pre-dicted by Michalke.23 This initialization of veloc-ity profile follows earlier DNS study by Metcalfe eta/.24 Another study by Riley and Metcalfe25 showedthat it takes a non-dimensional time of around 8for the fundamental mode to grow and saturate.They non-dimensionalized time by J;/A£/o, and thepresent study also follows this approach. The com-putational domain is non-dimensionalized by <5t-, theinitial vorticity thickness and the Reynolds num-ber based on initial vorticity thickness is 400. Thepresent results are compared to these earlier DNSresults. The study by Metcalfe et al. used spanwiseand streamwise periodic boundary conditions. Inthe present effort, however, we use periodic bound-ary conditions only in the streamwise direction anduse symmetric conditions in the spanwise direction.This modification was required due to some inher-ent limitation of the KIVA code. However, thisdifference is believed to result in negligible effectssince the initial fundamental mode disturbance isinherently two-dimensional. It should be noted thatthe original code can handle axi-symmetric periodicboundary but can not handle periodic boundaries inthe streamwise direction, and therefore, minor mod-ifications were implemented in both KIVA-3V andKIVALES so that we can simulate this flow field.

Here, 323 and a 643 grid simulations were carriedout using both KIVALES and LESLIE3D (a fourth-order accurate finite-volume code used extensively in

the past26). At this particular low Reynolds numberand without any random turbulence initialization,the SGS models should not contribute any dissipa-tion. This is confirmed in this study.

Figure 1 shows the growth of fundamental energymode as a function of time. KIVALES shows a sim-ilar trend as in Fig. 1 of Metcalfe et al. (1987).Although KIVALES is more dissipative than theDNS or the 4th order LES and eventually is not ableto maintain a saturated state of vortex-rollup, thenumerical dissipation is significantly reduced (rela-tive to the KIVA-3V code) and shows the correctphysical behavior of the vortex rollup. The initiallinear energy growth rate a = (dE/dt)/2E predictedby KIVALES is 0.19, which matches to the value of0.19 predicted by linear instability analysis23 andpredicted by DNS. In contrast, KIVA-3V shows animmediate energy decay right after the initialization,and this is the case even for a higher grid reso-lution (643) case while KIVALES using the higherresolution shows an even better resolution of the fun-damental mode energy saturation.

These differences can clearly be seen in the snap-shots of the mixing layer at a certain time as shownin Fig. 2. KIVALES shows vortex roll-up at the non-dimensional time of 8 as predicted by DNS and LES(not shown here), and this prediction becomes moreaccurate as the number of grid points is increased.The "braid" region is more clearly captured in thehigher grid resolution case. On the contrary, KIVA-3V shows high dissipation due to turbulence modelby a time of 2 even when the higher grid resolutionis used. It is clear that the RANS based KIVA-3Vcode does not simulate vortex rollup correctly.

This study, therefore, shows the importance of nu-merical and turbulence model dissipation, and itsimpact in the RANS code. The results demonstratethat the RANS based KIVA-3V is inappropriate tosimulate unsteady mixing problem whereas the mod-ified KIVALES resolves energy containing motion.

5.2 Flow over Backward-Facing Step

Even though the simulations of mixing layeryielded a significant difference between KIVALESand the original KIVA-3V, accurate prediction of theevolution of coherent vortices is not sufficient enoughto evaluate the effect of turbulence subgrid model.To examine the LES implementation in KIVA codein more detail, flow over a backward-facing step issimulated and the results are compared with theearlier DNS study by Le and Moin27 and the ex-periments cited therein.

Computational geometry used in this study isshown in Fig. 3, which is similar to that used by Ak-



selvoll and Moin28 with the same Expansion Ratio(ER) of 1.2 (also used by Le and Moin for their DNSstudy). Our geometry incorporates 96 x 64 x 32 instreamwise, wall-normal, and spanwise direction, re-spectively, which is somewhat finer than the LES ofAkselvoll and Moin's study, but this is inevitable dueto the lower spatial order of accuracy of KIVA-3V,and subsequently, KIVALES. The geometry incor-porates periodic boundary conditions in spanwisedirection, and no-slip wall condition is applied tothe other boundaries except inlet and outlet. In-let condition employs a fixed inlet velocity UQ of10,000 cm/s with small random fluctuations, and theReynolds number is 5100 based on the step height.

Figure 4 shows the spanwise- and temporal-averaged spanwise vorticity field. Since RANS solvesthe time-averaged equations, it is more appropriateto make direct comparison on the averaged quantityrather than the instantaneous quantity. It shouldbe pointed out that there is not much difference be-tween the instantaneous snapshots of KIVA-3V andits temporal averaged snapshots, which is due tothe time-averaged nature of the RANS code. Thetemporal average flow field for the LES is obtainedover several flow-through time after around 5 flow-through time after the initialization to obtain statis-tically stationary state. (1 flow-through time is thetotal length of geometry divided by inlet mean veloc-ity and represents an approximate travel time for afluid element to pass through the computational do-main.) KIVALES predicts the re-attachment length(XR — x/h) of 6.0, which is also predicted by Leand Moin27 whereas KIVA-3V predicts an earlier re-attachment length of 4.0. The re-attachment lengthis calculated from the temporal and spanwise av-eraged data as the location where the wall-normalvelocity gradient is zero. From these snapshots, italso should be realized that KIVALES captures re-circulation region clearly, which is characteristic ofthis type of flow field while KIVA-3V does not.

Mean velocity profile and root mean squarestreamwise velocity are plotted in Fig. 5. KIVALESfollows the earlier DNS study and experimentalstudy reasonably well.

5.3 Internal Combustion Engines

The simulations of mixing layer and backward-facing step have shown that KIVALES has thepotential for capturing unsteady flow accurately.Therefore, KIVALES should be able predict moreaccurately the in-cylinder mixing process. The ge-ometry employed here (Fig. 6) incorporates twomoving valves, one of which is used for intake andthe other for exhaust. The spray injector is located

at the top center of the cylinder. No experimen-tal data for this configuration is currently availablebut is used here to show that KIVALES is capa-ble of handling more complex engine configurations.Although no combustion is currently investigated itwill be the focus of a future study.

As droplet evaporation and subsequent fuel-airmixing process is of interest, we are going to dis-cuss the in-cylinder mixing process with fuel sprayhere. The geometry used for this study is shownin Fig 6. For comparison purpose, three differentfuel injection cases are studied: no injection case,Start-Of-Injection (SOI)=90, and SOI=180 degreeCrank Angle (CA). Only SOI=180 case is reportedhere, although a comparative study of these threecases has been reported elsewhere.29 In these sim-ulations, the cycle is assumed to be the middle ofengine operation at a fixed revolution (1500 RPM).Therefore, initially moderate high temperature (900K) and some gaseous fuel and combustion productsare assumed to remain in the combustion chamber.These conditions are primarily obtained from Hanet a/.30 Fuel used is gasoline (CgHiy) as a 'sin-gle' species and injected directly into combustionchamber in a conical spray, and the spray vaporizesimmediately after injection because of the high tem-perature in the cylinder. The fuel injector is locatedat the middle of the cylinder top looking verticallydownward. Wall boundary condition used is the tur-bulent 'law-of-the-wall', which is the default KIVAboundary condition. The use of this wall functionwith LES is still an open question, but it is not fea-sible to resolve wall layer for in-cylinder turbulentflow with a LES grid. However, its validity might bea topic of future studies using KIVALES.

Shown in Fig. 7 is the comparison between KI-VALES and KIVA-3V of the droplet 'parcels' insidethe cylinder and the stoichiometric surface due tospray evaporation at 90 degrees after SOL Obvi-ously, KIVALES shows a more wrinkled stoichio-metric surface due to the resolved scale turbulentmotion. This effect can also be seen in Fig. 8, inwhich the spatially averaged modeled-part turbu-lent kinetic energy is plotted. Obviously, KFVA-3Vshows a larger value of the turbulent kinetic energythan KIVALES. This is understandable since in theLES, the subgrid kinetic energy represents only theenergy unresolved on the grid whereas in the RANSapproach, all turbulent kinetic energy is consideredunresolved and hence, modeled.

Particle dispersion by turbulence is studied bothnumerically and experimentally.31"33 In this study,we study particle dispersion in terms of the secondinvariance of deformation tensor following Hunt et



a/.34 The second invariant of deformation tensor isdefined as

lid = -~ —- — - —~ ~ +

(18)Squires and Eaton35'36 have found this quantityand the particle concentration are weakly correlated,and, on the other hand, the invariant and enstrophyis negatively correlated. It can be intuitively under-stood that since droplets have higher density thanthe surrounding liquid, droplet particles are moreand more pushed outward by the centrifugal forcein strongly rotating region. The evolution of thenumber density of particles in terms of the invari-ant is shown in Fig. 9. The distribution is widelyspread for both positive and negative value at theearly CA after SOI, however, the distribution evolveswith CA and showrs a strong preference at CA of 260.This tendency is not confirmed by KIVA-3V, whichlacks the ability to capture shear regions and vor-tical structures. Our correlation with KIVALES isstill very weak, and this is probably because particleresponse time is much larger than the characteris-tic flow time, which is the engine piston speed in1C engine case. It is interesting to note that pos-itive correlation between the invariant and particleconcentration occurs even in a relatively short time.However, the effects of droplet evaporation cannotbe determined from this data.

Another interesting observation is that KIVA-3V,KIVALES, and KIVALES-LEM all predicts nearlysame spatial mean evaporated fuel mass fractionprofile. However, KIVALES-LEM predicts largerscalar variance compared to the other two code(Fig. 10). This wrould be the consequence of sub-grid turbulent motion. It is interesting to mentionthat, at each CA, KIVALES and KIVALES-LEMshowed qualitatively almost similar scalar distribu-tion in the cylinder. However, it is known that theconventional gradient-diffusion closure fails in reac-tive flow field,37 therefore, these two closures shouldbe compared in a reactive flow field. Our futurestudy will address this issue. As piston approachesTDC and turbulence decays, the three curves con-verge close to each other, however, the actual PDFof fuel mass fraction is different in each case (notshown here).

6 ConclusionThe new KIVA code with LES capability has been

validated using several different flow fields, and inevery study, the LES version of KIVA code yieldedpromising results. In contrast, the original KIVA-3V code completely failed to predict the unsteady

turbulent flows. It is clear from the present studythat in order to capture the dynamics of in-cylinderanisotropic turbulent mixing LES appears to be theonly feasible approach. However, there are severalissues that remain to be resolved. For example, al-though the subgrid scalar mixing model based onLEM has shown significant promise in earlier LESstudies, the applicability of LEM in the study of1C engine fuel-air mixing flows remains to be estab-lished. In particular, in the direct injection sparkignition type engine different combustion regimes(non-premixed, premixed and partially premixed)occurs depending upon the engine operation condi-tion and for this type of flow, the LEM subgrid scalarmixing model may prove to be particularly useful.Another unresolved issue is the application of thewall boundary condition. Currently, a law-of-the-wall condition as in the original KIVA is employed.However, wall boundary condition is of particularimportance in the LES of wall-bounded flows andtherefore, its effect will have to be investigated. Fi-nally, for practical application to realistic engines,chemical reactions and effect of heat release has to bestudied. Again, for such studies, the subgrid LEMprovides an unique capability to close the reactionrate in an exact manner and may prove to be a vi-able SGS approach. These issues will be addressedin the near future.

7 AcknowledgmentWe thank Ford Motor Company for their support

and acknowledge additional support by a Connec-tivity Grant from Engineering Research Center atMississippi State University.

A Filtered Specific Internal EnergyEquation

The total energy equation of gas phase for reactingcompressible flow with spray is38

(19)

in which internal energy is defined as e — h — p/p,where h = £m Ym(Ah°f>m + ̂ Cp,mdT>).

Subtracting kinetic energy contributions (Usingmomentum equation given as Eqn.(2)) from the totalenergy equation, yields the following internal energyequation:

ate = _ + +(^spray_

j oxj oxj(20)

The last two terms represent spray effects and de-noted as Qs.



Filter equation (20) to obtain specific internal en-ergy equation for LES (3):

where = p(euj -£-, and e«

+ - pv,j,= ± - o T . Note

that stress tensor is decomposed into pressure workand viscous work.

It should be pointed out that chemical source termQc in the original equation14 is included in our def-inition of internal energy.

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21 Chakravarthy, V. K. and Menon, S. SubgridModeling of Premixed Flames in the FlameletRegime. Flow, Turbulence and Combustion,2000. (to appear).

22 Pannala, S. On Large eddy Simulations of Re-acting Two-Phase Flows. PhD thesis, GeorgiaInstitute of Technology, Atlanta, GA, May 2000.

23 Michalke, A. On the Inviscid Instability of theHyperbolic-tangent Velocity Profile. Journal ofFluid Mechanics, 19:543-556, 1964.

24 Metcalfe, R. W., Orszag, S. A., Brachet, M. E.,Menon, S., and Riley, J. J. Secondary Instabilityof a Temporally Growing Mixing Layer. Journalof Fluid Mechanics, 184:207-243, 1987.

25 Riley, J. J. and Metcalfe, R. W. Direct Numeri-cal simulation of a Perturbed, Turbulent MixingLayer. AIAA Paper, 80-0274, 1980.

26 Nelson, C. and Menon, S. Unsteady Simulationsof Compressible Spatial Mixing Layers. AIAAPaper, 98-0786, 1998.

27 Le, H. and Moin, P. Direct Numerical Simula-tion of Turbulent Flow over a Backward-FacingStep. CTR Annual Research Briefs, pages 161-173, 1992.

28 Akselvoll, K. and Moin, P. Large Eddy Sim-ulation of Turbulent Confined Coannular Jetsand Turbulent Flow Over a Backward FacingStep. Technical Report TF-63, Stanford Univer-sity, 1995.

29 Sone, K. and Menon, S. The Effect of SubgridModeling on the In-Cylinder Unsteady MixingProcess in a Direct Injection Engine. Manuscriptsubmitted to the ASME Spring Technical Confer-ence, 2001.

30 Han, Z. and Reitz, R. D. Turbulence Modelingof Internal Combustion Engines Using RNG A: -e Models. Combustion Science and Technology,106:267-295, 1995.

31 Kobayashi, H., Masutani, S. M., Azuhata, S., andArashi, N. Dispersed Phase Transport in a PlaneMixing Layer. In Hirata, M. and Kasagi, N.,editors, Transport phenomena in turbulent flows,pages 433-466. Hemisphere Publishing Corpora-tion, 1988.

32 Longmire, E. K. and Eaton, J. K. Structure andControl of a Particle-Laden Round Jet. In FluidsEngineering: Korea - U.S.Progress, pages 465-484. Hemisphere Publishing Corporation, 1989.

33 Elghobashi, S. and Truesdell, G. C. On the two-way interaction between bomogeneous turbulenceand dispersed solid particles. I. Turbulence mod-ification. Physics of Fluids A, 5(7):1790-1801,1993.

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35 Squires, K. D. and Eaton, J. K. Particle responseand turbulence modification in isotropic turbu-lence. Physics of Fluids A, 2(7):1191-1203, 1990.

36 Squires, K. D. and Eaton, J. K. Preferential con-centration of particles by turbulence. Physics ofFluids A, 3(5): 1169-1178, 1991.

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38 Oefelein, J. C. and Yang, V. Analysis of Tran-scritical Spray Phenomena in Turbulent MixingLayers. AIAA Paper, 96-0085, 1996.

102

10

10°

10"1

0.0 8.0 16.0 24.0 32.0Non-dimensional time I15/2UJ

40.0

Fig. 1 Resolved scale fundamental mode energygrowth. The linear growth rate of KIVALES is0.19, which is also predicted by Michalke.23 Incontrast, KIVA-3V rapidly dissipates the energy.



a) KIVA-3V at T = 2

Fig. 3 Geometry used for the simulation of flowover backward-facing step. Number of cells is96 x 64 x 32. Only an area closed by a bold line isshown in the next figure.

b) KIVALES at T = 8

c) KIVALES at 7 = 8 with 643 grid

Fig. 2 Spanwise vorticity field in the temporalmixing layer. The figures are drawn using thesame contour interval of Au = 500(5ec~1).

a) KIVALES b) KIVA-3V

Fig. 4 Spanwise and temporal averaged span-wise vorticity.



00 0.4 O.S 0.0 0.4 0.8 0.0 0.4 0.8

Fig. 6 Geometry used for the simulations of 1Cengine. It incorporates around 80,000 cells atBDC.

0.0 0.1 0.0 O.I O.O O.I 0.2

a) KIVALES

b) urms

Fig. 5 Spanwise and temporal averagedmean streamwise-velocity and root mean squarestreamwise-velocity

b} K1VA-3V

Fig. 7 Stoichiometric surface at CA=270, whichis 90 degrees after SOI.

10American Institute of Aeronautics and Astronautics Paper 2001-0635


90 180 270

Crank .ajte [degree]

Fig. 8 Comparison between the turbulent ki-netic energy of KIVA-3V and SGS turbulent ki-netic energy of KIVALES. Both of them showthe modeled turbulent energy, and the former issignificantly larger than the latter.

270.0Crank angle [degree]

0.20

0.10

0.00 '

Fig. 10 Temporal evolution of scalar (fuelmass fraction) mean (p) and variance (a2) (stan-dard deviation (a) is shown) for comparison be-tween gradient diffusion closure KIVALES andKIVALES-LEM. Light lines denote mean whileblack lines denote standard deviation. Notethat LEM predicts larger scalar variance betweenBDC and TDC.

"-100.0 -50.0 0.0 50.0 100.0The second Invariant of deformation tensor [lld, 10s sec"2}

Fig. 9 Correlation between the second invariantof deformation tensor and particle concentration.

11American Institute of Aeronautics and Astronautics Paper 2001-0635

Documents

(c)2001 American Institute of Aeronautics & Astronautics ... · Kazuo Sone, Nayan Patel and Suresh Menon School of Aerospace Engineering Georgia Institute of Technology Atlanta, Georgia