Large-eddy simulations of turbulent flows in internal combustion

International Journal of Heat and Mass Transfer 60 (2013) 781–796

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International Journal of Heat and Mass Transfer

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Large-eddy simulations of turbulent flows in internal combustion engines

A. Banaeizadeh ⇑, A. Afshari, H. Schock, F. JaberiDepartment of Mechanical Engineering, Michigan State University, East Lansing, MI 48824, United States

a r t i c l e i n f o

Article history:Received 15 May 2012Received in revised form 7 December 2012Accepted 27 December 2012

Keywords:Large-eddy simulationsFiltered mass density functionTwo-phase flowCombustionInternal combustion engines

0017-9310/$ - see front matter � 2013 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.ijheatmasstransfer.2012.12

⇑ Corresponding author. Current address: Altair Eng94043.

E-mail addresses: [email protected] (A. BanaeAfshari), [email protected] (H. Schock), jaberi@egr

a b s t r a c t

Large-eddy simulations (LES) of turbulent spray combustion in internal combustion engines are con-ducted with a new hybrid Eulerian–Lagrangian methodology. In this methodology, the Eulerian filteredcompressible gas equations are solved in a generalized curvilinear coordinate system with high-orderfinite difference schemes for the turbulent velocity and pressure. However, turbulent mixing and com-bustion are simulated with the two-phase compressible scalar filtered mass density function (FMDF)and Lagrangian spray models. The LES/FMDF model is used for simulation of in-cylinder turbulent flowand spray mixing and combustion in three flow configurations: (1) a poppet valve in a sudden expansion,(2) a simple piston–cylinder assembly with a stationary valve, and (3) a realistic single-cylinder, direct-injection spark–ignition (DISI) engine. The flow statistics predicted by the LES model are shown to com-pare well with the available experimental data for (1) and (2). The computed in-cylinder flow for the thirdconfiguration shows significant cycle-to-cycle variations. The flow in the DISI engine is also highly inho-mogeneous and turbulent during the intake stroke, but becomes much more homogeneous and less tur-bulent in the compression stroke. Simulations of spray, mixing and combustion in the DISI engineindicate the applicability of the LES/FMDF model to internal combustion engines and other complex com-bustion systems.

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1. Introduction

Accurate numerical simulation of the complicated in-cylinderflow in an internal combustion (IC) engine requires robust modelsand numerical methods capable of simulating turbulence, dropletdispersion, evaporation and chemical reactions in complex geome-tries. Computational models employed for the in-cylinder flowsimulations have traditionally been based on the Reynolds-aver-aged Navier–Stokes (RANS) method. RANS models predict themean flow only and do not account for the unsteady three-dimen-sional (3D) fluid motions and the cycle-to-cycle variations (CCV) inIC engines [1]. In contrast, models developed based on the large-eddy simulation (LES) method can capture the CCV and large-scaleflow structures in these engines [2,3]. Naitoh et al. [4] conductedone of the earliest LES of in-cylinder flow with a first-order time-differencing and a third-order upwind space-differencing methodover a relatively coarse grid. As a result, they found that the sub-grid-scale (SGS) turbulent energy to be about 50 percent of the to-tal energy which is too significant for LES [5]. Nevertheless, Naitohet al. were able to capture the dynamics of large coherent struc-tures in the cylinder in their simulations. Haworth et al. [6] also

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ineering, Mountain View, CA

izadeh), [email protected] (A..msu.edu (F. Jaberi).

simulated the in-cylinder flow in an IC engine with LES using astandard Smagorinsky model [7,8] and a numerical method whichwas second-order accurate in time and space at best. Comparisonwas made with the Laser Doppler Anemometry (LDA) experimen-tal data of Morse et al. [9] for a relatively simple ‘‘engine’’,composed of an axisymmetric piston-cylinder assembly with a non-moving central valve and a low speed (200 rpm) moving piston.Haworth [10] and Verzicco et al. [11] used LES and the boundarybody force method [12] to simulate the flow in Morse et al. exper-iment [9] and in a two-valve Pancake-Chamber four stroke engine.The reported LES results were shown to be comparable to theexperimental data. Thobois et al. [13] performed LES of flowaround a poppet valve [14] and that in a real engine by a finite-vol-ume method. In other studies, Sone et al. [15] and Lee et al. [16,17]used the linear-eddy model [18] and KIVA-3 V flow solver [19] forthe simulation of in-cylinder flow, fuel mixing and combustionin IC engines. The model was reportedly able to predict the mainfeatures of the flow in these engines. Dugue et al. [20] used Star-CD software [21] to study the CCV in an IC engine. They simulatedseveral cycles via RANS and LES, and showed that the predictedvolume-averaged turbulent kinetic energy is significant in LES,but it is close to zero in RANS. Jhavar et al. [22] simulated turbulentcombustion in a CAT 3351 IC engine with the KIVA code, a one-equation SGS stress model [18], and a CHEMKIN-based combustionmodel. Their simulations indicate that in contrast to RANS, LES isable to predict the CCV. More recent studies involving LES and

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in-cylinder flows [23–27], confirm the reliability and applicabilityof LES models to IC engines.

In this paper, the in-cylinder flow in various engine-related con-figurations are simulated with our new two-phase compressiblescalar filtered mass density function (FMDF) model. FMDF repre-sents the joint probability density function (PDF) of SGS variablesand is obtained by the solution of its transport equation with aLagrangian Monte-Carlo method. The chemical reaction term inthe FMDF formulation appears in a closed form, regardless of thetype of reaction (slow, fast, premixed, nonpremixed, etc.). Thisand other features of the LES/FMDF make it very attractive for tur-bulent combustion simulations. The FMDF model has indeed pro-ven to be very effective for LES of various turbulent reactingflows [28–44]. Moreover, the model was recently extended to com-pressible flows [45] and multiphase flows [46–48]. However, it hasnot yet been applied to complex flows of the type seen in ICengines.

The main objective of this study is to develop/evaluate high-or-der consistent LES/FMDF models for turbulent mixing and combus-tion in IC engines. The LES data will also be used for betterunderstanding of flow in IC engines. For these, LES of turbulentflows with spray and combustion in three different configurationsare considered. The first configuration involves the flow around apoppet valve in an axisymmetric sudden expansion [14] which issimilar to the flow around and behind the intake valves in IC en-gines. The second configuration is that of Morse et al. [9],consistingof a fixed open valve and a slowly moving flat piston. The last con-figuration is the most complicated one, involving the in-cylinderflow, mixing and combustion in a 3-valve direct-injection spark-ignition (DISI) laboratory engine, built at Michigan State University(MSU) [49].

2. Mathematical formulation

The two-phase compressible LES/FMDF model is based on threemain mathematical components: (1) the filtered gas dynamicsequations, (2) the FMDF and its equivalent stochastic equations,and (3) the Lagrangian spray equations. These equations are pre-sented in the following sections.

2.1. Filtered gas dynamic equations

The compressible forms of Favre-filtered [50] continuity,momentum, energy and scalar equations in curvilinear coordinatesystem can be written in the following compact form [41,51–53]:

@ðJUÞ@sþ @ðF � FvÞ

@nþ @ðG� GvÞ

@gþ @ðH � HvÞ

@f¼ JSo; ð1Þ

where J ¼ @ðx;y;z;tÞ@ðn;g;f;sÞ is the Jacobian of transformation and

U ¼ ð�q; �q~u; �q~v ; �q ~w; �q~E; �q~/Þ is the solution vector. The primary vari-ables in Eq. (1) are the filtered density, �q, the Favre filtered veloci-ties, ~u; ~v; ~w, the Favre filtered total energy, ~E ¼ ~eþ 1

2~ui~ui, and the

Favre filtered scalar mass fraction, ~/. The inviscid fluxes in Eq. (1),F, G and H are defined as:

F ¼

�qU

�q~uU þ �pnx

�q~vU þ �pny

�q ~wU þ �pnz

ð�q~Eþ �pÞU � nt

�q~/U

266666666664

377777777775; G ¼

�qV

�q~uV þ �pgx

�q~vV þ �pgy

�q ~wV þ �pgz

ð�q~Eþ �pÞV � gt

�q~/V

266666666664

377777777775; H ¼

�qW

�q~uW þ �pfx

�q~vW þ �pfy

�q ~wW þ �pfz

ð�q~Eþ �pÞW � ft

�q~/W

266666666664

377777777775;

U ¼ nt þ nx ~uþ ny ~v þ nz ~w; V ¼ gt þ gx ~uþ gy ~v þ gz ~w; W ¼ ft þ fx ~uþ fy ~v þ fz ~w;

ð2Þ

with nx ¼ J@n=@x,. . ., etc., being the metric coefficients [51]. Thesefluxes are calculated based on the relative velocity of flow and grids

by adding the time derivative of metrics nt ; gt and ft to U; V and W .In Eqs. (1) and (2), �p is the filtered pressure and So represents thesource term. The viscous fluxes, Fv ; Gv and Hv are defined in Ref.[41]. The subgrid stress terms [54,55] are closed here via gradi-ent-type closures and different models for the turbulent kinematicviscosity, mt. In the Smagorinsky model [7,8], the SGS turbulent vis-cosity is modeled as:

mt ¼ ðCdDÞ2j~Sj; ð3Þ

where j~Sj is the magnitude of the rate-of-strain tensor, D = (vol-ume)1/3 represents the characteristic size of the filter function, andCd is the model coefficient which can be either fixed or obtainedby the dynamic procedure [56–58]. The SGS velocity correlationsin the energy and scalar equations are also modeled with the fol-lowing closures [59,60]:

�qðguiE � ~ui~EÞ þ ðgpui � ~p~uiÞ ¼ ��q

mt

Prt

@ ~H@xi

; ð4Þ

�qðgui/ � ~ui~/Þ ¼ ��q

mt

Sct

@~/@xi

; ð5Þ

where ~H ¼ ~Eþ �p�q, is the total filtered enthalpy and Prt and Sct are the

SGS turbulent Prandtl and Schmidt numbers, respectively. The con-vection of the SGS kinetic energy by the SGS velocity is assumed tobe negligible.

The first term on the left hand side of Eq. (1), the temporal term,is decomposed into two terms as:

@ðJUÞ@s

¼ J@U@sþ U

@J@s: ð6Þ

The time derivative of Jacobian is zero for a fixed grid system. In amoving grid system, it is calculated based on the geometric conser-vation law (GCL) [51,61]:

@J@s¼ � ðntÞn þ ðgtÞg þ ðftÞf

h i; ð7Þ

where

nt ¼ � xxðnxÞ þ yxðnyÞ þ zxðnzÞh i

;

gt ¼ � xxðgxÞ þ yxðgyÞ þ zxðgzÞ� �

;

ft ¼ � xxðfxÞ þ yxðfyÞ þ zxðfzÞh i

:

The vector (xx,yy,zz) is the grid speed vector which is computedbased on the piston and intake/exhaust valve speeds.

2.2. Compressible two-phase FMDF equations

The scalar FMDF represents the joint SGS PDF of the scalar vec-tor and is defined as:

PLðW; x; tÞ ¼Z þ1

�1qðx0; tÞr W;Uðx0; tÞ½ �Gðx0 � xÞdx0; ð8Þ

r W;Uðx0; tÞ½ � ¼ PNsþ1a¼1 dðwa � /aðx; tÞÞ; ð9Þ

where G denotes the filter function, W is the scalar vector in thesample space and r is the ‘‘fine-grained’’ density [28], defined basedon a set of delta functions, d. The scalar vector, U � /a,(a = 1,. . .,Ns + 1), includes the species mass fractions and the specificenthalpy (/a�Nsþ1). The transport equation for the FMDF is derivedfrom the following unfiltered scalar equations:

q@/a

@tþ qui

@/a

@xi¼ @

@xiC@/a

@xi

� �þ Srea

a þ Scmpa þ Sspy

a � /aSm: ð10Þ

Here, for simplicity, we consider the Cartesian form of the scalarequation. For the species mass fraction, Srea

a represents theproduction or consumption of species a due to reaction and Sspy

a is

A. Banaeizadeh et al. / International Journal of Heat and Mass Transfer 60 (2013) 781–796 783

the production of species a due to droplet evaporation. For the en-ergy or enthalpy, Srea

a , Scmpa and Sspy

a represent the effects of heat ofcombustion, compressibility and droplet evaporation, respectively.The FMDF transport equation is obtained by inserting the instanta-neous unfiltered scalar equation (Eq. (10)) into the time-derivativeof fine-grained density and filtering that,

@PL

@tþ @ huijWilPL½ �

@xi� 1

q@q@tþ @ðquiÞ

@xi

� �� w l

PL

¼ @

@wa� 1

q@

@xiC@/a

@xi

� �� W l

PL

� �� @

@wa

Sreaa

q

��W l

PL

� �� @

@wa

Scmpa

q

��W l

PL

� �� @

@wa

Sspya

q

��W l

PL �waSm

q

��W l

PL

� �; ð11Þ

where

Sreaa ¼ q _xa; Scmp

a ¼ 0; Sspya ¼ Sm a � 1; . . . ;Ns

Sreaa ¼ q _Q ; Scmp

a ¼ @p@t þ ui

@p@xiþ sij

@ui@xj; Sspy

a ¼ Sh a � Nsþ1

(:

In Eq. (11), hfjWil denotes the conditional filtered value of variable‘‘f’’. Also, in this equation, _xa represents rate of production or con-sumption of species a and _Q represents the heat release rate. ThePrandtl (Pr) and Schmidt (Sc) numbers are assumed to be the same.The mass/thermal diffusion coefficients are defined as, C = l/Sc,where l is the molecular viscosity. The second term on the right-hand side (RHS) of Eq. (11) is the chemical reaction term and isclosed when the effect of SGS pressure fluctuations are ignoredand Srea

a

��W� �l ¼ Srea

a ðwÞ. This term is not closed in the filtered scalarequation and ‘‘conventional’’ LES methods.

The FMDF equation (Eq. (11)) cannot be solved due to presenceof three unclosed terms. The first one is the convection term (thesecond term on the LHS of Eq. (11)) which can be decomposed intolarge-scale convection by the filtered velocity and the SGS convec-tion as [29]:

huijWilPL ¼ huiiLPL þ ðhuijWilPL � huiiLPLÞ: ð12Þ

The SGS convection is modeled here with a gradient type closure:

huijWilPL � huiiLPL ¼ �Ct@ðPL=hqilÞ

@xi; ð13Þ

where Ct = hqilmt/Prt is the turbulent diffusivity. (Notations hiL andhil are used for the Favre filtering and filtering, respectively, i.e.,hf iL ¼ ~f and hf il ¼ �f for variable f.)

The second unclosed term in the FMDF transport equation (thefirst term on the RHS of Eq. (11)) is also decomposed into twoparts: the molecular transport and the SGS dissipation. The SGSdissipation is modeled with the linear mean–square estimation(LMSE) model [70,71] or the interaction by exchange with themean (IEM) model [72]:

@

@wa� 1

q@

@xiC@/a

@xi

� �� W l

PL

� �¼ @

@xiC@ PL=hqilð Þ

@xi

� �þ @

@wa½Xmðwa � h/aiLÞPL�; ð14Þ

where the SGS mixing frequency, Xm ¼ CxðCþ CtÞ= D2Ghqil

�is ob-

tained from the molecular and SGS turbulent diffusivities (C andCt) and the filter length (DG).

In the scalar FMDF model, considered in this study, the pressureis not directly included in the FMDF formulation, and only the ef-fect of filtered pressure on the scalar FMDF is considered [45].The last term on the RHS of Eq. (11) represents the effect of pres-sure and viscosity on the scalar. The part due to temporal deriva-tive of pressure is approximated here as:

1q@p@t

� ��W l

PL ¼1hqil

@hpil@t

� �PL a � Nsþ1: ð15Þ

However, the spatial derivative of the pressure term and theviscous dissipation term are decomposed into the resolved andSGS parts as:

1q

ui@p@xi

� ��W l

PL ¼1hqilhuiiL

@hpil@xi

PL

þ 1q

ui@p@xi

� ��W l

PL �1hqilhuiiL

@hpil@xi

PL

� �a � Nsþ1; ð16Þ

1q

sij@ui

@xj

� ��W l

PL ¼1hqilhsijiL

@huiiL@xj

PL

þ 1q

sij@ui

@xj

� ��W l

PL �1hqilhsijtiL

@huiil@xj

PL

� �a � Nsþ1: ð17Þ

Here, we ignore the SGS pressure term in Eq. (16) and the SGS vis-cous term in Eq. (17).

There are three terms in the FMDF equation (Eq. (11)) due tospray/droplets; the third term on the LHS of this equation is dueto the mass addition of the evaporated gas and the last two termson the RHS are due to other droplet-gas interactions. Here, theseterms are approximated as:

� @

@wa

Sspya

q

��W l

PL �waSm

q

��W l

PL

� �þ hSmjwilPL

hqil

¼ � @

@wa

Sspya

� �lPL

hqil� wahSmilPL

hqil

" #þ hSmilPL

hqil: ð18Þ

By inserting Eqs. (12)–(18) into Eq. (11), the final form of the FMDFtransport equation for a two-phase compressible reacting systembecomes:

@PL

@tþ @ huiiLPL½ �

@xi¼ @

@xiðCþ CtÞ

@ðPL=hqilÞ@xi

� �þ @

@wa½Xmðwa

� h/aiLÞPL� �@

@wa

Sreaa PL

hqil

� �� @

@wa

~Scmpa PL

hqil

" #

� @

@wa

Sspya

� �lPL

hqil� wahSmilPL

hqil

" #þ hSmilPL

hqil; ð19Þ

where

Sreaa ¼ hqil _xa; ~Scmp

a ¼ 0; Sspya

� �l ¼ hSmil a � 1; . . . ;Ns

Sreaa ¼ hqil _Q ; ~Scmp

a ¼ @hpil@t þ huiiL

@hpil@xiþ hsijiL

@huiiL@xj

; Sspya

� �l ¼ hShil a � Nsþ1

8<: :

Eq. (19) will reduce to the scalar FMDF transport equation for sin-gle-phase, constant pressure reacting flows [29] whenScmpa ¼ 0; Sm ¼ 0 and Sh = 0.

2.3. Lagrangian droplet equations

As mentioned before, the spray (droplet) field is simulated herewith a Lagrangian model. In this model, the evolution of the drop-let displacement vector, velocity vector, temperature, and mass arebased on a set of non-equilibrium Lagrangian equations [62–69]:

dXi

dt¼ Vi; ð20Þ

dVi

dt¼ Fi

md¼ f1

sdð~ui � ViÞ; ð21Þ

dTd

dt¼ Q d þ _mdLv

mdCL¼ Nu

3PrCp;G

CL

f2

sdðTG � TdÞ þ

_md

md

Lv

CL; ð22Þ

dmd

dt¼ _m ¼ � Sh

3ScG

md

sdlnð1þ BMÞ; ð23Þ


where sd = qLD2/(18 lG) is the droplet time constant, D is the

droplet diameter, CL is the heat capacity of liquid,Lv ¼ h0

v � ðCL � Cp;V ÞTd is the latent heat of evaporation and h0v

and Cp,V are the enthalpy of formation and specific heat of theevaporated fuel vapor at constant pressure, respectively. Thedroplet drag force is empirically corrected by the f1 correlationfunction, and f2 is the correction function for the evaporative heattransfer [64]. The Nusselt, Sherwood, Prandtl and Schmidt num-bers are respectively denoted by Nu,Sh,Pr, ScG and TG is the gastemperature. Finally, BM is the mass transfer number, calculatedusing the non-equilibrium surface vapor function. Eqs. (20)–(23)yield the position, Xi, velocity, Vi, temperature, Td, and mass, md,of a single droplet at different times.

The effects of droplets on the carrier gas mass, momentum, en-ergy and species mass fractions are expressed with several source/sink terms in Eq. (1) as a vector So = (Sm,Su1,Su2,Su3,Se,Sm). Theseterms model the two-way coupling between the Lagrangian (drop-let) and the Eulerian (gas) phases. Here, the mass term, Sm repre-sents the mass contribution of droplets due to evaporation. Themomentum term, Sui

represents the momentum transfer betweentwo phases due to drag force and the heat term, Se represents theinternal and kinetic energy exchange by the convective heat trans-fer and particle drag. The droplet source/sink terms are evaluatedby volumetric averaging and interpolation of the Lagrangian drop-let variables with the weighting of wa within a computational cellwith the volume dV as:

Sm ¼ �Xa2dV

wa

dV½ _md�a

�; ð24Þ

Sui¼ �

Xa2dV

wa

dV½Fi þ _mdVi�a

�; ð25Þ

Se ¼ �Xa2dV

wa

dVViFi þ Q d þ _md

ViVi

2þ hv ;s

� �� a

� �: ð26Þ

In Eq. (26), hv;s ¼ h0v þ Cp;V Td is the evaporated vapor enthalpy at

droplet surface. Se represents the source term for the total internalenergy equation (Eq. (1)). The source term in the enthalpy equationis:

Sh ¼ Se � ~uiSuiþ

~ui~ui

2Sm: ð27Þ

3. Numerical solution procedure

In the modeled scalar FMDF equation (Eq. (19)), the carrier-gas velocity and pressure fields and spray terms are not knownand should be obtained by other means. Here, the filtered veloc-ity and pressure are obtained by solving Eq. (1) with the ‘‘con-ventional’’ finite difference (FD) methods. The Lagrangian fueldroplet equations are solved explicitly by using the filtered gasvelocity and temperature obtained from Eqs. (1) and (19). Spraysource terms are computed by local interpolation and averagingover the FD grid points. With the known velocity and pressurefields and spray terms, the modeled FMDF equation are solvedby the well-developed Lagrangian Monte Carlo (MC) procedure[75]. In this procedure, each MC particle undergoes motion inphysical space due to filtered velocity and molecular and subgriddiffusivities. Effectively, the particle motion represents the spa-tial transport of the FMDF and is modeled by the following sto-chastic differential equation (SDE) [76]:

dXþi ¼ huiiL þ1hqil

@ðCþ CtÞ@xi

� �dt þ

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2ðCþ CtÞhqil

s" #dWiðtÞ; ð28Þ

where Wi denotes the Wiener process [77]. The compositional valueof each particle is changed due to mixing, reaction, droplet evapora-

tion, viscous dissipation and pressure variations in time and space.The change in composition is described by the following SDEs:

d/þa ¼ �Xm /þa � h/aiL� �

dt

þ 1hqil

Sreaa þ eScmp

a þ Sspya

� �l � /þa hSmil

h idt a

� 1; . . . ;Nsþ1: ð29Þ

When combined, the diffusion processes described by Eqs. (28) and(29) have a corresponding Fokker–Planck equation which is identi-cal to the FMDF transport equation (Eq. (19)). In this work, the sprayterms in the FMDF equation are weighted averaged from FD gridpoints to the MC particle locations. To include the ‘‘compressibility’’in the FMDF formulation, the term ~Scmp

a , as computed from the Eule-rian grid points are interpolated and added to the corresponding MCparticles. Consistency of the Favre filtered temperatures obtainedfrom the Lagrangian MC and Eulerian FD data might become depen-dent on the inclusion of the pressure effect in the FMDF equation[45].

To manage the number of MC particles and to reduce the com-putational cost, a procedure involving the use of nonuniformweights is also considered. This procedure allows a smaller numberof particles in regions where a low degree of variation is expected.Conversely, in regions of high variation, a larger number of parti-cles is allowed. The variable weighting for particles allow the par-ticle number density to remain above a certain minimum numberregardless of density variations [75]. To calculate the Favre-filteredvalues of any variable at a given point, the MC particles areweighted averaged over a box of size DE centered at the point ofinterest [29]. It has been shown [29,75] that the sum of weightswithin the ensemble averaging domain, DE, is related to the filteredfluid density as:

hqil �DmVE

Xn2DE

wðnÞ; ð30Þ

where VE is the volume of the domain and Dm is the mass of a MCparticle with a unit weight. For the spray simulation, particleweights should be modified due to added mass to the carrier gasby the evaporating droplets. Here, we adjust the particle weight

as dwðnÞ ¼ VEDm hSmildt. The Favre-filtered value of any function of sca-

lars like Q(/) is obtained from the following weighted averagingoperation:

hQiL �P

n2DEwðnÞQð/ÞP

n2DEwðnÞ

: ð31Þ

Fig. 1(a) shows some of the main features of our hybrid two-phasecompressible scalar LES/FMDF methodology. For the solution of fil-tered Eulerian carrier gas equations (Eq. (1)) any high order numer-ical method may be used. The discretization procedure for thisequation in this work is based on the fourth order compact FDscheme [74] and the third order low storage Runge–Kutta method.The FD equations are solved with ‘‘standard’’ closures for the SGSstress and scalar flux terms. For the moving boundary case, at thebeginning of every time step, grids are moved to their new locations(using the new piston/valve locations as inputs), and then the gridspeed vector, Jacobian and metrics are calculated based on thenew grid locations. Computations are performed with multi-blockstructured grid on parallel machines using MPI library. The filteredvelocity and the derivatives of filtered pressure and velocity arecomputed over the FD grid points and then interpolated from theFD grid points to the MC particle locations. The Lagrangian sprayequations are solved with numerical methods similar to that usedfor the FMDF [47] and coupling terms are then calculated by volu-metric averaging of droplet variables.

(a) (b)Fig. 1. (a) Elements of the hybrid two-phase LES/FMDF methodology. (b) A two-dimensional view of a portion of the LES/FMDF computational domain; thick black lines showan ensemble domain, FD cells are specified by the thin blue lines, the smaller circles denote MC particles, and the larger circles are liquid droplets. (For interpretation of thereferences to colour in this figure legend, the reader is referred to the web version of this article.)


Fig. 1(b) shows a segment of the FD grid, some of the MC parti-cles and spray droplets and the boundary of a typical ensembleaveraging box used for the particle averaging. In the present hybridmethodology, the filtered values of variables like temperature maybe calculated from both FD grids and MC particles. This provides aunique opportunity for the assessment of LES-FD and FMDF-MCparts of the LES/FMDF method. Mathematically, LES-FD andFMDF-MC results should be identical. Consistency of MC and FDdata implies the numerical accuracy of both solvers. For establish-ing the consistency between the FD and MC methods in reactingflows, the chemical source/sink terms in the FD equations, whichare closed in the FMDF formulation, are calculated from the MCparticles. This is only possible in the hybrid LES/FMDF method.

4. Results and discussions

In this section the results obtained by LES for non-reacting andreacting flows are discussed. Three different flows are considered:(1) the flow around a fixed valve, (2) the flow in a simple piston-cylinder assembly with fixed open valve, and (3) the flow and com-bustion in a three-valve DISI engine. We start with non-reacting re-sults. Reacting results with spray are presented next.

4.1. Non-reacting flows

Among the three non-reacting flows considered in this section,the flow around a fixed valve is the simplest one as it does not in-volve any moving component. The second flow is more compli-cated and involves a fixed open valve and a moving piston. Thelast non-reacting flow considered in this study mimics the mainfeatures of in-cylinder flows in DISI engines.

4.1.1. Sudden expansion with a poppet valveDuring the intake stroke in a typical IC engine, large-scale vortical

fluid motions are developed behind the intake valves. These motionshave a significant effect on the fuel–air mixing and combustion inthe cylinder at later stages of engine operation. The ability of LESand SGS models to capture the complex motions behind the valveis assessed here by simulating the non-reacting flow in a suddenexpansion geometry with a fixed poppet valve [14] (Fig. 2(a)). Thesimulated flow is statistically stationary or steady with a constantmass flow rate of 0.05 kg/s and Reynolds number of 30000.Fig. 2(b) shows three-dimensional (3D) and two-dimensional (2D)

views of the 5-block grid system used in our simulations. To avoidsingularity at the centerline, a rectangular H-H block was employedin the central zone, coupled with an O-H grid outside. The predicted3D and 2D vorticity contours and streamlines for the poppet valveflow are shown in Fig. 2(c) and (d), respectively. The results in thisfigure confirm the generation of large-scale vortical fluid motionsbehind the valve and in the corner of the ‘‘cylinder’’ head and cylin-der wall. As ’’fluid particles’’ accelerates around the valve and entersthe cylinder, they separate into three parts. The part that reaches thewall is partly reflected away from the valve toward the outlet bound-ary and is partly returned to the region behind the valve, generatinga wake-like flow structure. A fraction of the incoming flow recircu-lates back toward the corner of cylinder head.

To make a quantitative comparison between LES and experi-ment, the predicted mean and root mean square (rms) values ofthe axial velocity at two locations from the cylinder head are com-pared with the experimental data in Fig. 3(a) and (b). The meanvelocity is calculated by time-averaging of the filtered velocityfor about 0.03 s. Fig. 3(a) shows that the mean axial velocity, pre-dicted with the dynamic SGS Smagorinsky model, is in good agree-ment with the LDA laboratory data. Fig. 3(b) shows that the rms ofaxial velocity, also compares reasonably well with the experimentin the middle of the cylinder and behind the poppet valve (see re-sults from r/R = 0 to r/R = 0.5). The discrepancy between the exper-imental and numerical results in the region close to the cylinderwall can be attributed to the wall model or to the uncertainty inthe inlet flow condition. With constant coefficient Smagorinskymodel (Cd = 0.1), the predicted mean and rms values are more ‘‘dif-fused’’ in comparison with the experimental data, as expected.

4.1.2. Piston–cylinder assembly with a fixed valveThe second non-reacting flow is that in a simple piston–cylinder

assembly with a fixed open valve and is considered in this paperfor better understanding of the in-cylinder flow physics and valida-tion of LES solver and its SGS stress model. The geometrical fea-tures of this idealized ‘‘engine’’ are shown in Fig. 4(a). The valveis fixed but the piston moves with a simple harmonic motionand a low RPM of 200. The average piston speed, Vp is 0.4 m/sand the flow Reynolds number based on the cylinder diameterand average piston speed is 2000. Using the LDA method, Morseet al. [9] measured the velocity in the cylinder and reported the ra-dial profiles of the phase-averaged mean and rms of axial velocityat different locations and crank angles. The 2D and 3D views of the

(b)

0.001 0.01 0.1 0.5 1

vorticitymagnitude

(c)

Fig. 2. (a) Geometrical details of the sudden expansion configuration with a simple valve (dimensions in mm). There is no piston and the valve is fixed. (b) Two-dimensional(cross sectional) and three-dimensional view of the 5-block LES grid. (c) Two-dimensional and (d) three-dimensional contour plots of the vorticity magnitude and thestreamlines as predicted by LES for the sudden-expansion with fixed valve.

mean

r/R

0 100

0.2

0.4

0.6

0.8

1X=20 mm

(a) velocity-4 0 4

X=70 mm

rms

r/R

0 3 6

0.2

0.4

0.6

0.8

X=20 mm

(b) velocity1 2 3

X=70 mm

Fig. 3. (a) Mean axial velocity and (b) rms of axial velocity, normalized with the inlet velocity, at two different distances from the cylinder head (20 and 70 mm). Solid anddashed lines represent the LES results with the dynamic and constant coefficient (Cd = 0.1) Smagorinsky models, respectively. Symbols represent the experimental (LDA) data.


4-block grid system employed for simulating the flow field in thisengine are shown in Fig. 4(b). The simulated flow during the intakestroke shows some similarities to the sudden expansion flow overa poppet valve considered in the previous section, even though it is

unsteady due to harmonic motion of the piston. Devesa et al. [78]conducted their LES of jet-tumble with a specific non-zero initialvelocity condition to reduce the computational time. The LES cal-culations presented in this paper are all initiated with zero velocity

Fig. 4. (a) Geometrical details of the simulated piston–cylinder assembly with a fixed valve and a moving piston (dimensions in mm). (b) Two-dimensional and three-dimensional views of the 4-block LES grid.


and constant pressure and temperature. We then allow the turbu-lence to be naturally generated and grown by the governing equa-tions during the first few cycles. The in-cylinder flow becomeshighly unsteady, 3D and turbulent after the first cycle, as expected.

The instantaneous contours of the axial velocity, normalizedwith the mean piston speed, are shown in Fig. 5(a), (b), (c) and(d) at crank angles of 24 �,48 �,108 � and 180 �. By acceleratingthe piston away from its reference position at top dead center

CA=24 /Vp98764321-1-2-3

(a)

C

(

CA=108/Vp

22181410620

-4-8-12-15

(c)

C

(

Fig. 5. Instantaneous contours of the axial velocity normalized by the mean pi

(TDC), the fluid around the fixed valve accelerates and enters thecylinder like a coannular jet flow. As the accelerated flow entersthe cylinder, a major part of it moves straight toward the pistonbut a portion of it turns back toward the cylinder head, generatinga large-scale wake-like structure behind the valve. A smaller recir-culating flow zone also appears at the upper corner of the cylinder,with the direction of rotation being the opposite of the flow behindthe valve (see Fig. 5(a)). Later at the crank angle of 48 �, large-scale

A=48 /Vp1614108642

-2-4-6-8

b)

A=180/Vp

865420

-2-4-6-8-10

d)

ston speed at crank angles (CA) of (a) 24 �, (b) 48 �, (c) 108 � and (d) 180 �.


vortices are generated close to the piston where the main jet ro-tates from the piston toward the cylinder wall (see Fig. 5(b)).Around crank angle of 80 �, the small corner vortex disappearsbut it reappears again around 108 � crank angle when the intakejet flow reaches the cylinder wall. Also at this crank angle, thewake behind the valve moves toward the cylinder wall and theflow induced by the piston becomes smaller as it rotates awayfrom the piston (see Fig. 5(c)). Fig. 5(d) shows that just beforethe bottom dead center (BDC) the generated large-scale vorticesbecome unstable and break down into smaller structures.

The axisymmetric geometry of the cylinder permits averagingin the azimuthal direction. The data gathered by azimuthal averag-ing for any piston position or crank angle may also be further aver-aged over different cycles, (excluding the first cycle) to get thephase-averaged mean and rms values. Our results (not shown)indicate that there is a significant CCV in the flow quantities. Theradial profiles of the mean axial velocity and the rms of axial veloc-ity calculated by azimuthal and phase-averaging at crank angle of36� and at locations of 10, 20 and 30 mm from the cylinder headare shown in Fig. 6(a) and (b). The reported mean axial velocities,computed with both constant-coefficient and dynamic Smagorin-sky models, are in good agreement with the experimental data.However, the dynamic model is shown to predict the rms valuesbetter than the constant-coefficient model. The predicted meanand rms values of the axial velocity at crank angle of 144 � and dif-ferent locations are also in good agreement with the experimental

radi

aldi

stan

cefr

omax

is(m

m)

-3 0 3 6 9

10

20

30

X=10

(a) mean velocity-3 0 3 6

X=20

0 3

X=30

radi

aldi

stan

cefr

omax

is(m

m)

-5 0 5 10

10

20

30

X=10

(c)

X=20 X=30

/Vp

X=40 X=50 X=60 X=70

Fig. 6. (a) Mean axial velocity and (b) rms of axial velocity, normalized by the mean pistnormalized by the mean piston speed, at crank angle of 144 �. Solid lines and dashedSmagorinsky models, respectively, and symbols are experimental (LDA) data.

data (Fig. 6(c) and (d)). These results indicate that the LES is able tocapture the spatial variations of the velocity within the cylinder atdifferent crank angles.

4.1.3. Three-valve DISI engineThe two flow configurations described in the previous sections

have some geometrical and flow features of realistic engines andare considered here for better understanding of in-cylinder flowand validation of LES model. However, our high order LES modelis applicable to flows in more complex and more realistic ‘‘en-gines’’. In this section, we consider the flow in MSU’s 3-valve, opti-cally accessible DISI engine [49] (see Fig. 7(a) for schematic viewsof the engine). The engine has two intake valves and one bigger ex-haust valve, with valves being tilted with respect to the piston. Themaximum valve lifts for the intake and exhaust valves are 11 and12 mm, respectively. Simulations for this engine are conductedwith a constant RPM of 2500 and mean piston speed of 12.5 m/s.To have a high quality grid for the moving piston, complicated cyl-inder head and moving valves, a 9-block grid system is generatedout of 32 initial blocks. In addition to these blocks, separate gridblocks are generated for each of the three intake/exhaust valvesand the corresponding manifold sections. By adding the valveand manifold grids to the cylinder grids, a total of 18-block gridis generated (Fig. 7(b)). As valves move up and down, their corre-sponding grids move with different velocities than the surroundinggrids in the cylinder, which move with the piston speed. Therefore,

radi

aldi

stan

cefr

omax

is(m

m)

0 2 4

10

20

30

X=10

(b) rms velocity0 2 4

X=20

0 2

X=30

radi

aldi

stan

cefr

omax

is(m

m)

0 50

10

20

30

X=10

(d)

X=20 X=30

rms/Vp

X=40 X=50 X=60 X=70

on speed, at crank angle of 36 �. (c) Mean axial velocity and (d) rms of axial velocitylines are LES results obtained by the dynamic and constant coefficient (Cd = 0.1)

stroke = 106 mmbore = 90 mmRPM = 2500compression ratio = 11 : 1Intake valve diameter = 33 mmIntake valve Max. lift = 11 mmIntake valve tilt angle = 5.6Exhaust valve diameter = 37 mmExhaust valve Max. lift = 12 mmExhaust valve tilt angle =5.1o

o

(a)

Fig. 7. (a) Schematic of the Michigan State Universitys 3-valve DISI engine. (b)Three-dimensional and two-dimensional (cross sectional) views of the 18-blockgrid system used for LES of the 3-valve DISI engine.


the grids that cover the overlap regions between the moving blockscan no longer be kept aligned and some interpolation for transfer-ring the data between the blocks is needed. The flow field insidethe cylinder, around the valves and in the port sections are simu-lated by our LES model using the 18-block grid system. Several cy-cles are simulated with an efficient parallel algorithm. The gridresolution and time stepping are selected to fully resolve large-scale turbulent motions in space and time [20,79,80].

Figs. 8(a), (b) and (c) show the volume-averaged temperature,vorticity and SGS turbulent viscosity predicted by LES with theconstant coefficient Smagorinsky model (Cd = 0.17) at differentcrank angles. Experimental data did not indicate considerableCCV in the thermodynamic variables, but the CCV in the velocityfield was found to be significant. Consistent with the experimentalobservations, the LES results in Fig. 8(a) indicate insignificant CCV

crank angle

tem

pera

ture

0 180 360 540 720

300

400

500

600

7001st cycle2nd cycle3rd cycle4th cycle5th cycle6th cycle7th cycle

(a) cran

vort

icity

mag

nitu

de

0 180

5000

10000

15000

(b)

Fig. 8. Volumetric averaged values of (a) filtered temperature, (b) vorticity m

in the averaged temperature but the CCV in the vorticity and SGSturbulent viscosity are shown to be significant. During the intakestroke period, as the incoming air accelerates around the valves,the volume-averaged values of the vorticity and SGS turbulent vis-cosity increase and reach to their maximum values at mid-intakestroke, and then decrease as piston decelerates. During the com-pression stroke, the average temperature increases and reachesto its maximum value at TDC as expected, while the vorticity andSGS turbulent viscosity continue to decrease with significantCCV. At the beginning of the expansion stroke, the initial accelera-tion of piston causes a slight increase in the vorticity and SGS tur-bulent viscosity, but the gas temperature starts to decrease. Withthe opening of the exhaust valve, 90 � after the TDC, the vorticityand SGS turbulent viscosity both increase.

Fig. 9(a) shows the volumetric average values of the SGS turbu-lent viscosity, vorticity magnitude and velocity magnitude, nor-malized by their minimum and maximum values. These variablesfollow trends consistent with the piston and valve movement.First, they increase and reach to their peak values with acceleratingpiston then decrease again as piston speed decreases. Accelerationof piston during the early phase of the intake stroke draws themanifold air into the cylinder with such a high speed that strongvorticity, velocity gradients and SGS turbulent viscosity are gener-ated. Later in the intake stroke, the piston decelerates as it ap-proaches the BDC and the intake flow speed starts to decrease,leading to lower values of vorticity and SGS turbulent viscosity.During the compression stroke, although the piston accelerates to-ward the TDC, the volumetric average values of turbulent variablesdecrease (Fig. 9(a)) since intake values are closed. The temperatureand velocity rms values at different crank angles, as calculated byaveraging over six cycles after the first cycle, are shown in Fig. 9(b).Similar to the vorticity, the rms values of all velocity componentsincrease during the intake stroke, reaching to their maximum val-ues in the middle of the intake stroke, then decrease continuouslytill the end of compression stroke. They again increase at thebeginning of expansion stroke and at the opening of the exhaustvalve. The rms of temperature remains fairly small during the in-take stroke but increases during the compression stroke andreaches to its maximum value at TDC before decreasing again dur-ing the expansion stroke.

To quantify the flow inhomogeneity and the level of turbulencein the cylinder, the volumetric average values of turbulent inten-sity are calculated at nine different zones or areas inside the cylin-der. These zones, as shown in Fig. 10(a), have equal volumes andcover different regions of the flow near the cylinder head. The cal-culated turbulent intensity at each zone at crank angles of 90 �,180 �,270 �, and 360 � are shown in Fig. 10(b). Based on the resultsin this figure, one may conclude that the in-cylinder flow is highlyinhomogeneous at mid-intake stroke (CA = 90 �). After that time,

k angle360 540 720

1st cycle2nd cycle3rd cycle4th cycle5th cycle6th cycle7st cycle

crank angle

turb

ulen

tvis

cosi

ty

0 180 360 540 720

0.0005

0.001

0.0015

1st cycle2nd cycle3rd cycle4th cycle5th cycle6th cycle7st cycle

(c)

agnitude and (c) turbulent viscosity at different crank angles and cycles.

crank angle0 90 180 270 360

0

0.5

1

piston speedturbulent viscosityvorticity magnitudevelocity magnitude

(a) crank angle

rms

0 180 360 540 720

10

20

30

40 u’v’w’T’

(b)

Fig. 9. Comparison of in-cylinder flow statistics at different crank angles computed by volume averaging of the instantaneous data. (a) Piston speed, turbulent viscosity,vorticity magnitude and velocity magnitude. (b) rms of the three velocity components and temperature.

zone number

turb

ulen

tint

ensi

ty

1 2 3 4 5 6 7 8 90

200

400

600

800

1000

1200

1400 CA=90CA=180CA=270CA=360

(b)

Fig. 10. (a) Nine different zones or sections inside the cylinder for calculating the ‘‘local’’ turbulent intensity, (b) turbulent intensity at different zones and crank angles (CA).


the in-cylinder turbulence starts to decay and becomes relativelyhomogeneous at the end of compression stroke (CA = 360 �).

For a better understanding of the flow dynamics during the in-take stroke, the evolution of various flow variables for a set of 40Lagrangian fluid particles were monitored. These particles wereoriginally located around one of the intake valves at crank angleof 30 �, but they move into the cylinder along various paths bythe filtered velocity and molecular and subgrid dispersion. Thefluid variables like velocity and temperature for each particle were

crank angle

tem

pera

ture

50 100 150 200 250

280

300

320

340

360

380

400 in-cylinder avg.particle # 3particle # 9particle # 15particle # 24particle # 31particle # 37

(a) cra

vort

icity

mag

nitu

de

50 100

10000

20000

30000

40000

50000

(b)

Fig. 11. Lagrangian values of fluid particles traveling within the cylinder during the intak(c) kinetic energy.

interpolated from the surrounding Eulerian grid points at everytime step. Fig. 11(a), (b) and (c) show the temperature, the vortic-ity, and the kinetic energy of 6 sample particles at different crankangles. During the intake stroke, the particles have very differenttemperatures, vorticities and kinetic energies as they undergo dif-ferent paths and experience different flow conditions. However,during the compression stroke, the particle values become closerto the (volume) averaged in-cylinder values. The variation in tem-perature is less than those in the vorticity and kinetic energy. These

nk angle150 200 250

in-cylinder avg.particle # 3particle # 9particle # 15particle # 24particle # 31particle # 37

crank angle

kine

ticen

ergy

50 100 150 200 250

500

1000

1500

2000

in-cylinder avg.particle # 3particle # 9particle # 15particle # 24particle # 31particle # 37

(c)

e stroke and beginning of the compression stroke. (a) Temperature, (b) vorticity and


findings are consistent with the results shown in Fig. 10(b), indi-cating that the flow is highly inhomogeneous during the intakestroke but becomes relatively homogeneous in the compressionstroke.

During the intake stroke, the flow in the 3-valve engine hassome similarities with those in previous section (Figs. 4–6). Forexample, the recirculation zones between the valve and the cylin-der wall or the wake flow behind the valves are somewhat similar.There are, however, some noticeable differences between theseflows. For instance, in the 3-valve engine, as the incoming flowfrom the intake ports enter the cylinder and merge, they form astronger flow with different spatial structure and turbulent fea-tures than those shown for simpler single, stationary valve. Also,in the 3-valve engine, part of the flow recirculates back towardthe cylinder head generating large-scale vortices in the corners ofthe cylinder head. As the incoming flow reaches the cylinder wall,a significant portion of it moves toward the piston, but a fraction ofit returns back toward the exhaust valve. These fluid movementsare captured with 40 (sample) Lagrangian particles (Fig. 11). Thepath-lines of these sample particles together with 3D contour plotsof the pressure during the intake stroke at crank angles of 60, 90,and 180 � are shown in Fig. 12(a), (b) and (c), respectively. Closeexaminations of various particle path-lines indicate that some ofthe particles are initially trapped at the recirculation zone betweenone of the intake valves and the cylinder wall at corner regions be-fore entering the center portion of the cylinder. In contrast, some ofthe fluid particles circulate for some time in the vortex formed be-tween the two valves, and then move into the cylinder in the wake

Fig. 12. Three-dimensional contours of the filtered pressure and path of several Lagrangi

flow behind the intake valves. There are also some particles mov-ing directly into the central section of the cylinder in the regionjust under the exhaust valve. Some of these particles reach to thepiston, but some return back toward the exhaust valve. The pres-sure contours in Fig. 12(a), (b) and (c) indicate that during the in-take stroke, the in-cylinder pressure is smaller than the manifoldpressure on average. This is expected and is attributed to the vac-uum generated by the piston. However, at the end of intake stroke,when the piston decelerates, and the manifold air enters the en-gine with high momentum, the in-cylinder pressure becomesslightly higher than the manifold pressure.

Fig. 13(a), (b) and (c) show the 2D contours of axial velocity at acenter plane over the intake valve at crank angles of 60 �,90 � and180 �, respectively. The results in these figures are consistent withthose shown before. At 60 � (Fig. 13(a)), the piston velocity andvalve lift are 8.5 m/s and 8 mm, respectively. At this crank angle,a strong voticity field is generated at the upper corner of the cylin-der close to the intake valves. At 90 � (Fig. 13(b)), the piston is at itsmaximum velocity of 14 m/s and the valve lift is 11 mm. At thiscrank angle, there exist a vorticity at the cylinder corner, a wakeflow behind the valve, and a recirculation zone under the exhaustvalve, all interacting with each other and with the cylinder and pis-ton wall. With the deceleration of piston the in-cylinder vorticityand the turbulence are weakened to such an extent that at BDC(Fig. 13(c)) the recirculation zones almost disappear. At crank angleof 220 � during the compression stroke, the intake valves areclosed. From this point on, the main source of turbulent productionis absent and the piston motion compresses the in-cylinder flow to

an particles during the intake stroke at crank angles of (a) 60 �, (b) 90 � and (c) 180 �.

Fig. 13. Two-dimensional contours of the axial filtered velocity during the intake stroke at crank angles of (a) 60 �, (b) 90 � and (c) 180 �.


higher pressures and temperatures while the in-cylinder turbu-lence decays and becomes somewhat homogeneous.

4.2. Reacting flows

In this section, the results obtained by the LES/FMDF model forreacting flows in the 3-valve DISI engine are presented. The goal isto show the applicability of the compressible two-phase LES/FMDFmodel to complex flows involving turbulence, spray and combus-tion and to establish the numerical accuracy and reliability of themodel for these flows. The LES/FMDF model is recently extendedand numerically tested for simulations of relatively simple two-phase and compressible flows [46–48].

In a typical spark ignition engine, the combustion is initiated byan electrical spark some time before TDC. Advance ignition givessufficient time for the initiation and flame propagation before thepiston reaches to TDC. Normally, spark energy is deposited in anarea smaller than the LES filter size and the SGS model has to cap-ture the spark effect on gas mixture. In the LES/FMDF methodology,the Lagrangian MC particles can well capture the local effectsincluding the ignition. Here, the spark plug is modeled by addingan energy deposition source term [81],

_Q ig ¼ �q�

4p2D3igsig

exp �12

Xþi � Xig� �2

D2ig

!exp �1

2ðt � tmÞ2

s2ig

!; ð32Þ

to the FMDF and its MC particles. In Eq. (32), Xþi and Xig are the po-sition of MC particles and location of the spark plug, respectively,while tm is the time of maximum input power. By adding _Qig to

the stochastic MC equation for the enthalpy (Eq. (29) with a � Ns+1),� amount of energy is deposited on MC particles located in thevicinity of the spark plug within the sphere with the diameter Dig

and for the time period sig (about 1 crank angle for the simulatedDISI engine). The temperature profile generated by the spark sourceterm is Gaussian in space and time. Also, the spark model parame-ters are set in such a way that the temperature does not increase be-yond a specific value [81]. Although the energy deposition modeldescribed by Eq. (32) does not simulate the plasma and detailedthermodynamics of ignition, it can capture the initial flame kernelcaused by the ignition. Using Eq. (31), the source term in Eq. (32)is weighted averaged and added to the LES-FD energy equation atevery time step.

After establishing the reliability of LES/FMDF and the consis-tency of its LES-FD and FMDF-MC subcomponents for single-phasereacting flows, the new two-phase compressible scalar LES/FMDFmodel is employed here for studying the spray and combustionof iso-octane in the DISI engine [82–85]. For the iso-octane reac-tion, a one-step global mechanism is employed [86]. We allowthe flow in the cylinder to be developed for several cycles beforespraying the fuel and studying the combustion. Fuel injector has8 nozzles and is located between the intake valves in the cylinderhead. The injection starts when the crank angle is 79 � and stops atcrank angle of 148 �. Here, the liquid iso-octane is injected withaverage initial velocity of 50 m/s and a Rosin–Rammler distribu-tion with Sauter mean diameter (SMD) of 30 lm to represent theinitial droplet distribution before they undergo secondary break-up. The droplet break-up is implemented by the Rayleigh–Taylor(RT) model [87–89]. Those droplets which reach the piston and

Fig. 14. Vorticity iso-levels and fuel droplet distribution during intake stroke at crank angles of (a) 84 �, (b) 100 � and (c) 148 �.


cylinder wall are modeled to randomly bounce back or to stick towalls as a liquid film. The spray and LES/FMDF models are usedfor the simulation of flow in Fig. 14(a), (b) and (c) which showthe iso-levels of vorticity together with the injected fuel dropletsat crank angles of 84 �, 100 � and 148 �, respectively. The initialspray pattern and the impingement of droplets to the cylinder wallunder the exhaust valve are clearly illustrated in Fig. 14(a), (b).Some of the droplets which were reflected back from the wall be-low the exhaust valve are also shown in Fig. 14(c). Due to strongrotational motion in the cylinder above the open intake valvessome fuel droplets enter the intake manifold (Fig. 14(c)). Secondarybreak-up of particles are found to be not also very important as ini-tial injected droplet’s were small. Similar patterns for the fueldroplets were observed in the experiment [82,83]. During the in-take and early compression stroke (between crank angles of79 � � 270 �), droplets are strongly dispersed by the in-cylinderturbulent flow but the fuel evaporation remains to be insignificant.High level of fuel evaporation starts in the middle of compressionstroke as the temperature increases.

The combustion is initiated by activating the spark plug inthe cylinder head, when the crank angle is 335 �. The iso-levelsof temperature as predicted by LES/FMDF at crank angles of345 �, 355 � and 365 � are shown in Fig. 15(a), (b) and (c),respectively. As explained before, the spark is modeled by addingthe energy deposition source term (Eq. (32)) to the FMDF energyequation which increases the energy content of MC particles thatare within the spark plug area. This source term is weighted

Fig. 15. Iso-levels of temperatures predicted by LES/FMDF in the D

averaged and added to the filtered FD energy equation as well.Due to inhomogeneity of fuel mass fraction and temperature atthe time of ignition, the flame does not propagate radially. How-ever, consistent with the experimental observations [83], flamestarts from the spark plug location and propagates towards leftintake valve and the exhaust valve and ultimately the cylinderwall at that location.

To assess the performance of compressible two-phase LES/FMDF model, the spatial variations of the gas temperature andevaporated fuel mass fraction as predicted by LES-FD and FMDF-MC parts of the hybrid model along three arbitrary axial lines arecompared in Fig. 16. These lines are chosen to be the ones connect-ing the center of the exhaust and the two intake valves to the pis-ton face. The comparison between the LES-FD and the FMDF-MCresults are made during the compression at three different crankangles of 250 �,290 � and 330 �. Evidently, the rate of evaporationand the corresponding changes in temperature during the com-pression stroke is well captured by the compressible two-phaseFMDF model. Furthermore, the LES-FD and FMDF-MC predictionsare shown be consistent at this crank angles. Consistency of thetwo parts of the hybrid two-phase LES/FMDF model is importantand establishes the numerical accuracy of both LES-FD andFMDF-MC solvers for the simulated flows.

Scatter plots of LES-FD and FMDF-MC temperatures at crank an-gle of 365 � in Fig. 17(a) show the overall consistency of FD and MCmethods after the ignition and during the flame propagation. Thevolume-averaged values of the temperature and fuel mass fraction

ISI engine at crank angles of (a) 345 �, (b) 355 � and (c) 365 �.

LES-FD

FM

DF

-MC

600 1200 1800 2400

600

1200

1800

2400temperature (K)

R=0.96

(a)

1.2

0.9

0.6

0.3

LES-FDFMDF-MCLES-FDFMDF-MCLES-FD

330 340 350 360

crank angle(b)

Fig. 17. (a) Scatter plots of temperatures predicted by LES-FD and FMDF-MC in the DISI engine at crank angles of 365 �. (b) Volume-averaged values of the filteredtemperature, equivalence ratio and pressure as predicted by the LES-FD and FMDF-MC parts of the hybrid LES/FMDF model. Temperature and pressure values are multipliedby 2500 and 80 for including all plots in one figure.

0 0.004

0.02

0.04

0.06X

CA=250

(a) fuel mass0 0.004

X/2

.65

CA=290

fraction0.04 0.08 0.12

X/5

.0

(Ex)

(In2)

(In1)FDMC

FD

FDMC

MC

CA=330

360 365

0.02

0.04

0.06

X

CA=250

(b) temperature515 520

X/2

.65

CA=290

640 650 660

X/5

.0

(Ex)

(In2)

(In1)FDMC

FD

FDMC

MC

CA=330

Fig. 16. Comparison of LES-FD and FMDF-MC results for (a) evaporated fuel mass fraction and (b) temperature during the compression stroke at crank angles of 250 �, 290 �and 330 � along the lines connecting the exhaust (Ex), and intake (In1, In2) valves to the piston.


as predicted by the FMDF-MC are shown in Fig. 17(b) to be also ingood agreement with the LES-FD predictions. Good consistency ofLES-FD and FMDF-MC results in Figs. 16 and 17 indicates thenumerical accuracy and the reliability of the two-phase LES/FMDFmodel for spray combustion simulations. The volume-averagedvalues of filtered pressure and temperature in Fig. 17(b) indicatethat the flame propagation in the cylinder takes about 30 crank an-gles after the ignition, which is in good agreement with the exper-imental observation [83]. Furthermore, the volume-averagedpressure reaches a pick value few degrees after the TDC which isalso in good agreement with the experimental data [83].

5. Summary and conclusions

The compressible two-phase scalar filtered mass density func-tion (FMDF) model is employed for large-eddy simulation (LES)of turbulent flow, spray and combustion in internal combustion(IC) engine. Three flow configurations relevant to IC engines areconsidered: (1) non-reacting flow around a fixed poppet valve ina sudden expansion, (2) non-reacting flow in a simple piston cylin-der assembly with a stationary valve and harmonically moving flatpiston, (3) non-reacting and reacting flows with spray in a single-cylinder, 3-valve direct-injection spark-ignition (DISI) engine with

moving valves and piston. The first two flows are relatively simplein comparison to those seen in real IC engines, and are consideredhere for better understanding of the in-cylinder flow dynamics andvalidation of LES model. The third flow mimics the one in a realisticDISI engine. Comparison of the mean and rms of axial velocity forthe sudden expansion flow, predicted by with the constant coeffi-cient and dynamic Smagorinsky models, with the experimentaldata indicates that the LES with dynamic Smagorinsky model cancapture the main features of this flow. The predicted unsteadyand turbulent flow over the valve and in the cylinder in the secondsimulated flow as generated by the harmonic movement of the pis-ton are also shown to compare well with the experimental data.The LES results for the flow in the DISI engine indicate substantialcycle-to-cycle variations (CCV) in the velocity field but the CCV inthermodynamic variables are found to be not significant. This isconsistent with the experimental observation. The flow drawn intothe cylinder through the open intake values during the intakestroke is highly inhomogeneous and turbulent but it becomesnearly homogeneous and less turbulent at the end of the compres-sion stroke.

Reacting flow simulations in the DISI engine with the two-phase compressible LES/FMDF model indicate the applicability ofthe model to IC engines. Our results indicate that the fuel massfraction and temperature statistics obtained by the LES-FD and


FMDF-MC parts of the hybrid LES/FMDF model are in good agree-ment with each other despite complexities of the grid, spray, evap-oration, mixing and combustion in the DISI engine. This indicatesthe numerical accuracy and reliability of the two-phase LES/FMDFmodel and its ability to compute the three way coupling betweenthe flow, spray and combustion in IC engines.

Acknowledgement

This work is supported by the US Department of Energy underAgreement Number DE-FC26-07NT43278. Additional support wasprovided by the Michigan Economic Development Corporation.Computational resources were provided by the High PerformanceComputing Center at Michigan State University.

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Large-eddy simulations of turbulent flows in internal combustion