International Journal of Engine Research-2011-Rutland-1468087411407248

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Large-eddy simulations for internal combustionengines a reviewC J Rutland

Engine Research Center, University of Wisconsin - Madison, Madison, WI, USA.

email: [email protected]

The manuscript was received on 12 August 2010 and was accepted after revision for publication on 16 March 2011.

DOI: 10.1177/1468087411407248

Abstract:A review of using large-eddy simulation (LES) in computational fluid dynamic stud-ies of internal combustion engines is presented. Background material on turbulence model-ling, LES approaches, specifically for engines, and the expectations of LES results arediscussed. The major modelling approaches for turbulence, combustion, scalars, and liquidsprays are discussed. In each of these areas, a taxonomy is presented for the various types ofmodels appropriate for engines. Advantages, disadvantages, and examples of use in the litera-ture are described for the various types of models. Several recent examples of engine studiesusing LES are discussed. Recommendations and future prospects are included.

Keywords:LES, engines, CFD, turbulence, combustion, sprays

1 INTRODUCTION

It is generally agreed that the next generation of tur-

bulence modelling in computational fluid dynamics

(CFD) for many applications will be some form of

large-eddy simulation (LES). For the appropriate

applications, LES can offer significant advantages

over traditional Reynolds Averaged Navier Stokes

(RANS) modelling approaches. For example, in

internal combustion (IC) reciprocating engines, LES

can be used to study cycle-to-cycle variability, pro-

vide more design sensitivity for investigating bothgeometrical and operational changes, and produce

more detailed and accurate results. There are also

characteristics of IC engines, such as inherent

unsteadiness and a moderately sized domain, that

are well suited to LES. This is not to say that LES will

replace RANS. There are pluses and minuses for

both methods and users should pick the appropriate

tool for the topics being studied. However, as inex-

pensive computing power increases, the ability to

use LES in IC engine simulations is increasing.As LES gains in capability, there is the potential for

a larger set of people using the models and a broaderapplication of LES to engines. In addition, LES in IC

engines is new, and there are potential uncertainties

and ambiguities since a generally accepted best

practice is still developing. This motivates the objec-

tive of this paper, which is to describe and categorize

the current LES models that could have application

to engines and to evaluate their suitability and poten-

tial predictive capability for use in engine CFD. This

is meant to help users of engine CFD be better

informed about LES so that it can be used wisely.In several important ways, IC engines are a good

application for LES. The flow physics are well suited

to LES in that: (a) the flows are inherently unsteady

due to moving piston and valves, (b) large-scale flowstructures are usually important, (c) the Reynolds

numbers of engine flows are modest, commonly of

the order of 10 000 to 30 000, and (d) the domain of

interest is primarily confined and moderate in size.

The last two points result in grid requirements that

are more limited than other applications such as

aeronautical flows. This has even tempted some

researchers to claim that they are approaching

direct numerical simulation (DNS) engine simula-

tions [1], although this is probably overstating the

situation. In addition, the low Reynolds numbers in

engines and the reduced, or even missing, inertialrange indicate that traditional LES models may not

work as well in these applications.

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In contrast, the complex physical processes that

occur in engines increase the difficulty for any CFD

modelling, including LES. Models (sometimes called

submodels) are required, not only for turbulence,

but also for liquid sprays, combustion, and variousscalar processes. This means that LES modelling for

engines should be more than just using a turbulence

model, such as the dynamic Smagorinsky model,

and leaving all of the other submodels the same as

RANS models. Unfortunately, this approach is fairly

common, as shown in a later section, and is another

motivation for this report. Proper use of LES in

engines requires potential modification of many

submodels to make them consistent within the LES

context.

The evaluation of LES models in this review is

focused on IC engine cylinder flows, including thegas exchange, spray, and combustion processes.

This is because of their primary importance in

determining engine fuel efficiency and emissions.

The review contains three major sections. First, a

general discussion of LES is provided. This includes

specific IC engine issues and uses RANS to provide

a context for understanding LES. Second, the vari-

ous types of LES models that might be applied to

engine simulations are listed and categorized. This

includes lists and discussions for basic turbulence

models, combustion models, scalar mixing models,

and fuel-spray models. Next, there is a section that

presents several recent studies that use LES to

simulate IC engines. This section uses the model

taxonomy from the previous section to help cate-

gorize the types of LES models being used in the

various studies. The review concludes with a sec-

tion that discusses future prospects of LES of

engines.

In this article, it is assumed that the reader is

familiar with basic turbulence modelling in engine

CFD applications and has some familiarity with the

concepts underlying the LES approach. While somebackground information is provided, the emphasis

in this paper is on describing and evaluating current

LES approaches as they pertain to IC engines. The

report does not include a tutorial on LES modelling

or detailed descriptive equations of the models dis-

cussed. Some details are provided in the

Appendices, but readers seeking detailed model

descriptions or a basic primer on LES are encour-

aged to consult excellent resources of general LES

theory and modelling presented by Ferziger [2],

Fureby et al. [3, 4], Geurts [5], Piomelli [6], and

Pope [7]. While there are interesting advanced LESmodels in the literature, they are not addressed here

since the focus is on approaches that are mature

enough to show promise for near-term successful

use in real engine simulations.

2 GENERAL LES BACKGROUND

The word LES is becoming very common as a way

to describe a variety of turbulent flow simulations.

Some researchers working on CFD turbulence mod-

els may describe their models as LES, even if they

may not follow traditional approaches. Generally,

most people use the term LES to mean fairlysimple, dissipative models for single phase, non-

reacting turbulence. Large-eddy simulation models

for scalar mixing, combustion, and liquid sprays have

not received much attention, but are very important

for engine applications. However, even in the engineCFD community, LES is still often used to indicate a

model for the turbulence only. The remaining mod-

els, such as combustion, are essentially RANS-based

models. This is a type of hybrid approach that can be

useful and is discussed in section 2.2.Formally, LES means solving equations that have

been spatially filtered (see appendix 2). This is in

contrast to RANS approaches in which ensemble

averaging has been used. Reynolds Averaged Navier

Stokes is better known than LES and is used here toprovide a context for understanding LES. Note that

in the IC engine community, RANS refers to unstea-dy RANS (also known as URANS). An important dif-

ference in LES and RANS is in the interpretation of

the results and the reasoning used to build the mod-

els. Both LES filtering and RANS averaging processes

result in similar equations with similar terms that

must be modelled. Yet, the physical meaning ofthese terms and their required modelling can be

very different, and this will impact the proper for-

mulation of models.The averaging process in both LES and RANS

results in separation of velocity components into

two parts

ui= ~ui+ u00i (1)

Here, the overbar symbol represents the spatial fil-

tering in LES or the ensemble averaging in RANS.For engines, density varies significantly and the

overbar represents a mass weighted (or Favre) filter-

ing or averaging [8]. Then, ui is usually called the

mean velocity, although more formally it is the fil-

tered velocity in LES. In both LES and RANS, the

overbar represents an averaging process designed to

reduce the range of eddy sizes or length scalesin the flow so that u ican be represented on a com-

putational grid appropriate for engines. An

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important point to understand is that this averaging

process is never performed in either an LES or aRANS code. From an applications point of view, the

operation that produces the overbar is purely con-

ceptual. This means the distinction between LESand RANS occurs primarily in the choice of modelsas described below. This choice is influenced by the

desired meaning of the overbar and the objective ofthe simulation.

The third term in equation (1), u00i, is either the

subgrid velocity in LES or the fluctuating velocity in

RANS. However, like the mean or filtered velocity,

ui, the distinct meaning of u00i, is not explicitly for-

mulated in CFD codes. Again, it is conceptual anddepends on the choice of the approach used, either

LES or RANS, and on the model formulations. The

models should have the correct characteristics forRANS or LES. For example, in RANS, the average ofthe fluctuating velocity is zero, but in LES, the fil-

tered subgrid velocity is not zero. In LES, both uiand u

00iare dependent on the filter size and the

impact of modelling in LES should decrease as the

filter size decreases.

The introduction of the velocity decomposition,equation (1), into the differential momentum equa-tion results in the following equation

r~ui

t

+ r~ui~uj

xj=

r

xi+

Gij

xj rtij

xj(2)

whereGijis the viscous stress tensor. As stated, thisequation is foruiand is used in both LES and RANS.The tij term represents the subgrid stresses in LES

or the Reynolds stresses in RANS. However, once

again, this distinction is primarily conceptual andthe actual subgrid stresses or Reynolds stresses arenever calculated in a CFD code. Only a model fortijis calculated and the specific model used is a pri-

mary distinction between LES and RANS.There are other aspects of a calculation that sepa-

rate LES and RANS that are discussed later.However, at the equation level, the similarity is clearand it is probably best to view LES as an evolving

development of turbulence modelling rather than acompletely new approach distinct from RANS. The

equations also point out the importance of thechoice one makes for modelling the termtij.

Turbulence modelling for the term tij meansthat it must be represented in terms of quantities

that are known through their own equation, pri-marily ui. The most common form of turbulence

modelling involves the use a quantity called the

turbulent viscosity, nT. Using a Boussinesq ormean-gradient assumption gives the followingtraditional model

trij=2nT ~Sij (3)where trij is the anisotropic portion of tij (see, for

example, Pope [9]) and ~Sijis the strain rate

~Sij=1

2

~uixj

+ ~uj

xi

(4)

Once again, we arrive at an important observation

that equation (3) is used in both LES and RANScodes. Until a model fornT is specified, the LES and

RANS equations are still the same. This means that

LES models based on equation (3) can have the

same difficulties and limitations as RANS models. If

LES is to offer an improvement over RANS, it seems

that there should be distinct differences in the char-

acteristics of the turbulence model. This discussioncontinues in more detail in section 2.2, after explor-

ing the expectations of LES, so that a more informed

evaluation can be made.

2.1 Expectations of LES

There is a broad perception that LES is an improve-

ment over RANS modelling for engines that is based

on several general expectations about LES simulations

and results. These expectations are consis-tent withthe general characteristics of the two approaches, and

can be important because they help to distinguishbetween LES and RANS simulations beyond a theore-

tically based distinction. They also offer a useful

method for evaluating LES results that is less formalthan full validation against experimental data. These

expectations can be grouped into several major cate-

gories that are discussed in the following subsection.

2.1.1 More flow structures

One of the primary expectations is that there will be

more flow structures, eddies, and vortices repre-

sented on the computational grid. Figure 1 shows acomparison of RANS and LES results that illustrates

this defining characteristic of LES results. This only

serves to demonstrate the difference in results since

a proper comparison would require simulating sev-

eral LES cycles and ensemble averaging the results.The eddies and vortices resolved on the LES grid

could be described as turbulence, but in this paper,

they will be referred to as flow structures to avoid

confusion. The increased flow structures are due

primarily to the lower dissipation in an LES turbu-

lence model compared to a RANS model. In terms

of equation (3), LES models use a smaller value forthe turbulent viscosity,nT. Correspondingly, there is

usually more kinetic energy in the LES flow

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structures. Increased grid resolution can also play arole in permitting more flow structures on the grid,

but as discussed below, this is not always required.

2.1.2 Better predictive capability

Another expectation of LES is that it will provide bet-

ter predictive capability. This is based on the argu-

ment that the CFD solver for the resolved scales, ui,

is doing more of the turbulence calculation using the

momentum equation itself, as evidenced by the

increase in flow structures. Thus, the turbulence

model is required to do less. Since there is moreuncertainty in the turbulence model than in the basic

equations, the simulations have the potential to be

more predictive. However, this assumption is not

universally true and can be hard to substantiate and

fully validate for LES. Problems and uncertainties in

boundary conditions, initial conditions, turbulence

models, and grid resolution can contribute to LES

results that are not as good as RANS results, even

though there is more resolved flow structures.

2.1.3 Interpretation of results is different

The LES framework of spatially averaged terms means

that results do not represent ensemble averages. This

is advantageous in the sense that new phenomenon

can be studied with LES. However, it can be a disad-

vantage if one is trying to compare to experimental

results that are often averaged over many cycles.

Proper comparison with experiments requires multi-ple cycle LES simulations and the related increase incomputational time. Users should match the CFD

modelling tool to the problem at hand and use LES

appropriately.

2.1.4 Easier models

Another possible expectation of LES simulations is

that the models involved will use fewer adjustablecoefficients and thus be easier to use. This can

occur because some LES models are designed to

automatically adjust coefficients according to the

local flow conditions. This is typically called thedynamic approach and was one of the major

advances in LES modelling in the 1990s (see [11]and appendix 3). However, another way to under-

stand the reduced number of coefficients is to real-ize that LES turbulence models are often simpler

than the models commonly used in RANS in partbecause they do not have to account for ensemble

average statistics.

2.1.5 More CPU time

A final expectation of LES simulations is that theywill require more computer time than RANS mod-

els. This expectation is true, but not always to theextent that one may expect. The increase in CPU

time reported in many LES studies is due to thegreatly increased number of grid points compared

to standard RANS grids. This increase is due in large

part to the simple and sometimes crude LES modelsbeing used. The simple models often require denser

grids so that more energy is in the resolved scales

and the models play only a minor role. However, agood LES model does not necessarily require a

major increase in the number of grid points. Forcomparable grids, good LES models themselves

often require only a modest increase in computer

times, typically of the order of 20 per cent longer.

The issue of grid resolution and turbulence model-ling is important and discussed in more detail in the

following section.

2.2 Turbulence modelling

Flow structures and turbulence in general arise fromthe non-linear terms, r~ui~uj=xj, in the momentum

equation (equation (2)). Thus, the expected increasein resolved scale flow structures in LES must comefrom these terms. The flow structures do not come

Fig. 1 Comparison of (a) RNG RANS and (b) LESvelocity vectors to demonstrate more flowstructures appearing in the LES on the samecomputational grid (from [10], reprinted withpermission from SAE paper 2003-01-1069, 2003, SAE International)

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from the turbulence model. To achieve the

increased flow structures, the non-linear terms mustbe allowed to function sufficiently. This can be

achieved through less dissipative turbulence models

and/or a denser grid. Both of these increase thekinetic energy in the resolved scales so that non-linear interactions are stronger and flow structures

are more likely to develop.To achieve flow structures in LES, one can choose

between crude turbulence models with more grid

cells or better turbulence models with reduced gridrequirements. The choice of denser grids with

simple models is the traditional way to achieveflow structures. However, it comes at the price of

increased computational time. The denser grid pro-vides more resolution so that a wider range of

resolved length scales are maintained and non-linear interactions are more likely to occur. In thiscase, it is often acceptable to use simple turbulence

models since they are not required to do muchother than provide dissipation at the small scales.

As shown below, the problem is that often the mod-els are so simple that they provide dissipation over a

wide range of length scales, and one is forced toprovide even more grid resolution to counteract thiseffect.

In many situations, the number of cells in a gridcould be reduced and the grid would still be suffi-

cient for maintaining a range of length scales andallowing non-linear interactions. However, the tur-

bulence model must allow this to happen. Simplychoosing a less dissipative but crude model oftenwill not work because of numerical instability. In

addition, reduced dissipation is counter to the con-cept of LES spatial filtering in which more subgrid

dissipation should occur as the number of cells inthe grid decreases. Instead, the turbulence model

needs to improve as the number of grid cells isreduced. An important characteristic of better LESturbulence models are ones that let the non-linear

interactions occur while still maintaining numericalstability.

An example of one such turbulence model isshown in Fig. 2. The model is one of a class known

as dynamic structure models described in appendix4. Several of the dynamic structure models are com-

pared to the two most common LES models used inengines: the Smagorinsky model based on equation(3) and the viscosity-based one-equation model to

be described later. The figure shows the power spec-tra of the transfer term between the resolved flow

kinetic energy and the subgrid kinetic energy. This

is the energy that is removed from the large scales.The dynamic structure models follow the spectra

from the DNS result much better. It is characterized

by higher values at higher wave numbers (smaller

scales) and lower values at lower wave numbers. In

contrast, the Smagorinsky and viscosity-based one-

equation models show high values at all wave num-

bers. This indicates that these models take energyout of the resolved scales (low wave numbers) and

reduce the possibility that non-linear interactions

will occur and result in flow structures. Thus, a den-

ser grid is required with these types of model to

counteract the overly dissipative effect. The dyna-

mic structure model reduces resolved scale energy

primarily in the small scales and lets the resolved

scale non-linear actions occur.

The use of dense grids and simple models goes

back to the early work on LES [13]. The initial argu-

ment for LES was that the filtering size and hence

the grid size should be well into the inertial sub-range of an isotropic turbulence spectrum. This also

justifies a simpler turbulence model. However, look-

ing more closely, one sees that the inertial subrange

requirement was not part of the original LES defini-

tion. Originally, LES meant only that spatial filtering

rather than ensemble averaging was being used

[14]. The requirement for dense grids and inertial

range inclusion grew out of the common use of sim-

ple, overly dissipative models such as Smagorinsky.

This type of approach is still common when LES is

used to study more basic or fundamental aspects

of turbulence. In those situations, the flow is oftenfor a simple configuration such as homogeneous

turbulence. This also allows the use of higher order

Fig. 2 Power spectra of the subgrid kinetic energyproduction term as a function of wave numberfor rotating turbulence. DNS is direct numericalsimulation, SM is a Smagorinsky model (T2,described in Table 2), KEM is a viscosity-basedkinetic energy equation model (T5), SSM is a

scale-similarity model, and the rest are all var-iations of the dynamic structure model (T7)(from [12])





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numerical methods that avoided numerical

dissipation.However, the use of very dense grids in simple

flow configurations is a more scientific use of LESand is distinctly different from using LES in applica-

tions such as IC engines. Flows are almost neverhomogeneous in applications. Traditional concepts,

such as the inertial subrange, rely on a sufficient

statistical population that often does not exist at thesmaller scale subgrid level in a complex evolving

flow. In engine applications, it is not practical to use

extremely dense grids or higher order numerical

methods. The domain size and configuration do notallow it. In addition, the more complex physical

processes, such as combustion and sprays in

engines, require their own modelling and computa-

tional time. Thus, most practical LES applications

for engines must use coarser grids and lower ordernumerics.

To account for the different types of LES, the

notation scientific LES and engineering LES isintroduced. Some of the characteristics of these two

types are listed in Table 1. Since the motivation and

objectives of the two types of LES are different, each

should be evaluated within their own context. For

example, engineering LES must contend with errorsand added dissipation arising from lower order

numerical methods. This is somewhat countered by

the higher values of subgrid kinetic energy in engine

LES. This is indicated by the fourth item in Table 1,and is similar to the LES quality index introduced by

Pope [7]. Larger values of subgrid kinetic energy

mean that numerical dissipation is a smaller frac-

tion of the subgrid values and the relative impact of

numerical errors in engineering LES is potentiallyless significant. However, this places more reliance

on the subgrid models. Generally, knowledgeable

users are able to incorporate these characteristics of

engineering LES into their interpretation of resultsand analysis.

An example of how LES can be used in a CFD

code designed for engine applications is shown inFig. 3. This shows experimental, RANS, and LESsimulations of the Sandia Cummins direct injection

diesel engine. The RANS and LES simulations dupli-

cate the region of the experimental images using the

same coarse grid of a simple sector mesh common

in diesel engine simulations. The RANS results show

a broadened or smeared region for the higher tem-

perature, while the LES results show the same typeof jet large-scale structures seen in the experimental

images. Thus, with only a change to LES turbulence

and scalar mixing models that are appropriate for

applications, the simulation results pick up flow

processes that occur in the experiments that were

not previously available in the RANS simulations.

2.3 Expectations of LES for IC engines

In addition to the general expectations of LES listed

above, there are additional expectations related to

IC engine simulations. Generally, these can bedescribed as the ability to study new physical phe-

nomena in engines and an increased sensitivity to

design changes. These are discussed in more detail

in the following subsection.

2.3.1 Study new phenomena

A very important aspect of using LES for engines is

that it will allow studies of new phenomenon. There

are important aspects of engine flows and combus-

tion that are difficult, if not impossible, to address

with RANS but which are more amenable to LESapproaches. One of the primary features is cycle-to-

cycle variability. Reynolds Average Navier Stokes

uses models designed to capture the ensemble

averages. This results in higher turbulent viscosity

that almost always removes, or at least smears out,

the variation of in-cylinder flows and combustion

that coincide with cycle-to-cycle variability. Since

LES models are designed to filter out the smaller

scales and retain the larger scales, they are less dis-

sipative. The remaining large scales respond to the

non-linearities inherent in the Navier Stokes equa-

tions, and at least some aspects of cycle-to-cyclevariability can occur in the simulations. As dis-

cussed in section 4, several research groups are

Table 1 Characteristics of the primary types of LES studies

Scientific LES Engineering LES

Emphasis Study of fundamental topics Study of applications and practical devicesNumber of grid cells Very large; governed by access to very large

computing systems

Moderate; governed by reasonable turnaround

Numerical methods High accuracy, typically spectral or at leasteighth-order finite difference

Engineering accuracy, typically first or second order

Fraction of kinetic energyresolved on grid

Very high; typically 95% or more Moderate; typically 60% to 80%

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already making use of LES to study cycle-to-cycle

variations.

2.3.2 Increased design sensitivity

In addition, there are other flow-based processes in

engines that are best addressed with LES rather thanRANS. For example, LES should be better at captur-

ing the impact of relatively small changes in geome-

try (combustion chamber shape, pistons bowls, port

design, valve curtain regions, etc.), small changes in

fuel injection angles for direct injection applica-

tions, and small changes in operation (spark timing,

injection timing, valve timing, etc.). These types of

applications could be classified as design sensitiv-

ity studies. Similar to cycle-to-cycle variability

applications, LES is a necessary tool for these stud-

ies due to its increased sensitivity.

Even though LES represents the next generationof turbulence modelling, it is not always the best

choice for engine applications. The primary and

very common situation in which RANS is still the

best choice is when the desired output is a cycle-averaged result. Obtaining a cycle-averaged result

with LES requires running several consecutive full

720 crank-angle degree cycles and averaging theresults. This can be expensive since additional gridpreparation is required for the open portions of the

cycles and computer run times are long for the tenor more cycles required. Several research groups arepursuing this approach (see section 4). One justifi-

cation for this more computationally expensiveapproach is that LES results are more accurate so

that the average is better than a RANS result. Still,users should evaluate their objectives and choose

the best approach, either RANS or LES.The other significant reason that LES is at a dis-

advantage for engine applications is that many addi-tional complex physical processes occur.Combustion and fuel injection are probably the pri-

mary complicating processes, and these are not tri-vial. The use of LES for turbulent combusting flows

is still a very active area of fundamental researchwith many basic issues still being investigated [16].

There has been even less work in LES for liquidsprays where one could easily argue that the physi-cal processes are even more complex. Beyond

sprays and combustion there are complex processesin ignition, gas phase and solid phase emissions,

boundary layers and wall heat transfer, and movingboundaries. All of these require some sort of model-

ling that should be adapted, or at least understood,for the LES approach.

In many situations, researchers use LES for turbu-

lence (e.g. subgrid stresses that appear in themomentum equation) and maybe for scalar flux

modelling, but then rely on existing RANS-type sub-models for the other physical processes. This type of

hybrid approach is very common and a very reason-able way to proceed. Waiting until all engine sub-models have been adapted to LES is unreasonable

and disregards the advantages that can come fromintelligent use of hybrid approaches. Since turbu-

lence is the background for most aspects of engineflows, using LES turbulence submodels can improve

the context for the other models. The turbulencemodels provide flow fields with more large-scale

structures and greater sensitivity so that manyadvantages of LES can be realized, even when com-bined with RANS models for other processes. One

could argue that there is some justification in thisapproach since RANS models for combustion and

sprays should respond correctly to the resolved

large-scale flow field [17]. However, the correctresponse of RANS models to the LES flow field

is not guaranteed. A user should understand the

Fig. 3 Comparison of LES (middle row) and RANS(bottom row) with experimentally imaged (toprow) ignition chemiluminescence, showing liq-

uid fuel in blue and temperature in green (seescale) (from [15], reprinted with permissionfrom SAE paper 2007-01-0163, 2007, SAEInternational)





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specifics of the hybrid situation being used so that

they can better evaluate the appropriateness of thetools for the specific study and the validity of

the results. An even better approach is to examine

the various submodels and determine if they areconsistent with the LES spatial filtering conceptsand the resulting scaling.

This brings us to the main objective of this

review, which is to report on, evaluate, and categor-ize the use of various LES turbulence, combustion,spray, etc., models for IC engines. Since there are

many physical processes that need modelling, thereis a wide variety of hybrid approaches in the litera-

ture that may mix-and-match various models from

these lists. Examples from the literature will be usedto illustrate some of the main categories. Then,

these categories are used to describe and classifysome of the recent uses of LES to study engines.

3 LES MODELS IN IC ENGINES

There are many complex physical processes in IC

engines, and each of these requires some sort ofmodelling. These processes occur in a turbulent gas

phase flow so turbulence models, also called turbu-lence submodels, provide the context for the other

physical processes. In addition, LES submodelsshould also be used for scalar mixing, combustion,

and fuel sprays since all of these can be significan-tly impacted by the turbulent flows. Large-eddy

simulation modelling for turbulence and theseother engine processes are discussed in the sections

below. In each case, the major modelling app-roaches are described and classified with an empha-

sis on their suitability for engine CFD. A table isprovided in each subsection to summarize the

descriptions.

3.1 Turbulence modelling

For a quick background on turbulence modelling,one can start from the gradient assumption used inequation (3), although as explained below, this is

not necessarily the best approach. From equation(3), the turbulence model is based on a turbulenceviscosity, nT, and an expression for this term isrequired. As a context for the LES approach, the

most common RANS-based models use thekepsi-lon (ke) approach so that

nT= Cmk2

e

(5)

The terms k and e are interpreted to be the turbu-lent kinetic energy (TKE) and the turbulent kinetic

energy dissipation rate (or just dissipation). In mod-

ern approaches, these terms are obtained from indi-

vidual transport equations. Thus, the RANS (ke)

model is a two-equation turbulence model.

To provide additional understanding, it is usefulto rewrite the model based on a physical interpreta-tion using a velocity and length scale

nT= u00 (6)

Then, k and e provide a turbulent velocity scale

u00e ffiffiffikp and a turbulent length scale of ek1.5/e. Inthis interpretation, the length scale is thought of asthe integral scale of the turbulence even though the

flow is not homogeneous.

If equation (3) is used for LES models, there are

several approaches for obtaining expressions fornT.One of the more common models is based on the

ideas of Smagorinsky [18] and results in

nT= CSD 2 ~S (7)

where |~s| measures the magnitude of the resolved

strain rate and D is a measure of the grid cell size.

Using the same physical interpretation as above,

the Smagorinsky model velocity scale is u00~D|~s| andthe length scale is the numerical grid size, D. Using

the grid size for the length scale in LES is consistentwith the LES filtering using a grid cell scale (seeappendix 2). However, it is not guaranteed that grid

size times the strain rate gives the correct velocity

scale for the LES subgrid turbulence since this is

a crude model. Usually, there are no additional

transport equations in Smagorinsky-type models so

they are zero-equation models. Variations on theSmagorinsky model are common, and these are

described in Table 2.

Within the turbulent viscosity approach to mod-

elling, the LES model length scale is related to the

grid cell size. This means that fundamentally LES isnot grid independent. As the grid cell size becomessmaller, an LES solution should approach a DNS

solution. This limit is well accepted and usually rea-

lized by most LES models. In contrast, as the grid

cell sizes become larger, the limit is not well estab-

lished. One possible interpretation is that the LESmodel length scale should approach a RANS model

integral scale. However, this is not observed in prac-

tice and, pragmatically, it is inadvisable to use LES

models on grids coarser than ones used in RANS.

Even though most turbulence models use some

form of equation (3), it can be argued that it is notthe best type of model for LES for three important

reasons.

8 C J Rutland




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1. Overly dissipative. As discussed in the previoussections, this approach can be overly dissipative.

2. No subgrid kinetic energy. In equation (3) typemodels for LES, the subgrid TKE is arbitrary. Thisis because the trace of the subgrid stress tensor,

tii, is twice the kinetic energy, but the trace of thestrain rate tensor is zero in incompressible flows.

This is why equation (3) uses the anisotropic partof the subgrid stress tensor, trij. In engine flows,

the subgrid kinetic energy is a very importantvariable for additional models in combustion,

scalar mixing, and sprays. Thus, an additionalmodel must be formulated for the subgrid kineticenergy. These models are commonly very simple,

ad hoc, and poorly justified [19].3. Incorrect tensor relationship. Fundamentally,

equation (3) assumes the tensor relationshipbet-ween trij and is valid. Specifically, equation

(3) assumes the principle directions oftrij and ~sijalign. This is known to be incorrect [14], and

indicates a basic problem with the Boussinesqassumption embodied by equation (3). Thereare LES models that do not use equation (3),

and these may offer advantages for LES inengine applications. These are described in

appendix 4 and Table 2.

Table 2 classifies the major approaches to LES tur-

bulence models and briefly states advantages and

disadvantages. This is followed by more detailed dis-

cussions of each type of model. This table does not

list more esoteric or academic models, but includes

only modelling approaches that are likely to find use

in engine applications. Note that this table is only

for simple turbulence (e.g. no scalars, sprays, com-bustion, etc.).

T1.The simplest turbulence model is no model at

all. This approach relies on very dissipative numeri-

cal methods to replace the turbulence model (see,

for example, [20]). Somewhat surprisingly, this

approach can give realistic results, mainly because

the characteristics of numerical dissipation are simi-

lar to those of viscosity. However, it is generally

viewed that one should explicitly represent the sub-

grid effects rather than relying completely on

numerical properties. This is particularly true in

flows with complex physics such as engines. Thus,

this approach is not recommended.

T2. The Smagorinsky approach was the first LES

turbulence model and has already been described

previously in equations (3) and (7). It is an algebraic

(e.g. zero-equation) turbulent viscosity model.

There is a model coefficient, CS, in the turbulent

viscosity term of equation (7) that must be specified.

In simple Smagorinsky, the coefficient must be

adjusted for each simulation situation. The model is

very dissipative and requires fine grids to obtain

good results. Since the model is easy to program, it

often appears as an option in commercial CFDcodes. The Smagorinsky model is fairly common in

engine simulations, but the dense grid requirement

is usually too restrictive and better models exist.Celik et al. were some of the first researchers to

explore LES in engines [21]. Their work used the T2

turbulence model in the KIVA code [22] and simu-

lated intake and compression flows in diesel-type

cylinders. Despite being originally developed for

RANS models, results from KIVA demonstrated that

it was capable of capturing large-scale flow struc-

tures. A review of the early work in engine LES

helped to increase awareness of using LES inengines [23].

Table 2 Classification of the major LES turbulence modelling approaches

Model type Turbulent viscosity Transport equations Advantages Disadvantages

T1 None Numerical viscosity only

0 No model required Depends on grid and numericaldissipation; hard to control

T2 Smagorinsky Yes 0 Simple to implement Requires adjusting a viscosity coefficient for each case

T3 Scale similarity No 0 Accurately models spatialdistribution of subgrid stresses

Requires additional viscositymodel to remain stable

T4 Dynamic Smagorinsky Yes 0 Dynamically determines theviscosity coefficient

Requires additional averaging toremain numerically stable

T5 k-equation LES Yes 1 Uses additional transportequation for more physics

Requires adjusting a viscositycoefficient for each case

T6 Dynamick-equation LES Yes 1 Contains more physics anddynamically adjusts theviscosity coefficient

Still based on turbulent viscosity

T7 Dynamic structure Non-viscosity 1 Contains more physics anddirectly models stress tensorwithout a turbulent viscosity

Difficult to make implicit intime integration scheme





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An additional variation associated with T2 type

models was developed by Nicoud and Ducros [24]and called wall adapting local eddy (WALE) viscos-

ity. This replaces the strain rate magnitude in the

turbulent viscosity in equation (7) by a more com-plex tensor contraction of the strain rate and velo-city gradient tensor. There is some indication WALE

has better near-wall performance so that gridrequirements can be reduced, but this needs furtherinvestigation. Poinsot, with a variety of other

researchers, has used WALE with non-engine flowsin the development of a new code for engine appli-

cations [25, 26]. Bianchi et al. have shown goodresults with WALE in engine flows with a detailed

analysis of flow around the intake valves [27,28].

T3. The scale-similarity modelling approach was

originally proposed by Bardina et al. [29], and isexplained in more depth by Meneveau and Katz[30]. The concept is that unresolved subgrid scales

can be approximated by the smallest resolvedscales. In other words, the best way to represent

subgrid scales is with the next largest scales. Thisapproach is implemented by using an additional

spatial filtering operation on the already filteredscales. The additional filtering may be called a testfilter in some approaches and is indicated by an

additional overbar-type symbol (see appendix 3).Scale-similarity is an important concept in LES

and does not occur in RANS modelling. The originalapproach is usually unstable, mainly because it is

not a viscosity model and does not use an energybudget to track the subgrid kinetic energy. Thus, thescale-similarity model is usually augmented by the

addition of a Smagorinsky term in what is termed ahybrid model.

The Lund University group has been exploringLES for engines for several years using a scale-simi-

larity model for turbulence. A lot of their work isfocused on homogeneous charge compression igni-tion (HCCI) combustion, and is reviewed in section

4. They worked with Paul Miles from theCombustion Research Facility at Sandia National

Labs to make detailed comparisons of motored in-cylinder velocity fields [31]. They used dense grids,

and the comparisons between the LES and the PIVare reasonable. Interestingly, the work demonstrates

the difficulty in validating the LES.T4. A major improvement in the Smagorinsky

approach occurred when the dynamic approach

was developed by Germano et al. [11]. In thisapproach, the adjustable coefficient,Cs, in equation

(7) is obtained using the dynamic procedure. The

dynamic procedure uses the scale-similarity con-cept of T3 that requires an additional spatial filter-ing step. The dynamic coefficient is found from the

difference between these additionally filtered quan-

tities and the base quantities calculated on the CFD

grid (see appendix 3). This additional filtering oper-

ation is a modest increase in computational cost,

resulting in an increase of ~20 per cent for a simpleturbulent flow.An interesting variation of the dynamic procedure

was developed by Meneveau et al. [32], in which a

Lagrangian concept was used to develop the model

coefficient. The idea was to average over fluid parti-

cle pathlines to improve accuracy. In practice, two

additional transport equations were used to repre-

sent the Lagrangian average of terms used to evalu-

ate the dynamic coefficient.Haworth et al. were also some of the early

explorers in using LES for IC engines [33]. They

mostly used T2 and T4 type models in several differ-ent codes. They carried out extensive studies on a

simple, engine type flow with a stationary valve [34].

This configuration, sometimes called the Imperial

College engine, has a large experimental dataset and

is useful for validating valve flows. Haworth et al.

have shown good comparison between ensemble

averaged LES models and experimental data for

both mean and fluctuating velocity profiles at differ-

ent locations and different crank angles.The dynamic procedure is very powerful and can

be used in many situations to find modelling coeffi-

cients. When used with the Smagorinsky model, theresults are reasonably good for non-reacting flows.

However, dense grids are required and often an

additional averaging must be used to avoid instabil-

ities that arise from negative viscosities. Despite the

improvements found in T4, it still retains the draw-

backs of the equation (3) viscosity models discussed

in the previous section. No matter how good a

model is formulated for the turbulent viscosity, the

fundamentals of T2 and T4 are very weak.

T5.The k-equation approach is a practical viscos-

ity-based, one-equation LES model. It was originally

developed for atmospheric flows [35], and is stillcommon in that field. Some of the first useful

k-equation models for engineering flows were devel-

oped by Kim and Menon [36]. This model was still

viscosity based (equation (3)), but now the turbulent

viscosity was formed from the subgrid TKE,ksgs, and

a grid length scale, D, resulting in the following

expression

nT= CkDffiffiffiffiffiffiffiffi

ksgs

q (8)

The subgrid TKE was obtained from an additionaltransport equation that was readily derived from the

basic equations. The use of thektransport equation

10 C J Rutland




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has several distinct advantages. First, it incorpo-

rates more physical processes, such as the convec-tion, production, and dissipation of subgrid kinetic

energy. Second, the subgrid kinetic energy provides

a velocity scaling that can be used in other models,such as combustion, scalar transport, and sprays.Third, models that use a subgridk-equation provide

a better model for the subgrid stresses and thuswork better on the coarser grids commonly found in

engine CFD [37,38].Menon et al. have applied the T5 turbulence

model to engine flows with good results [39].Bianchiet al. have performed careful studies of LES

models for engine type flows in simple configura-tions. For example, they have compared T2 and T5

turbulence models with RANS results for a station-

ary valve, steady flow bench configuration [28].The subgrid kinetic energy equation is fairly sim-

ple to implement. It requires only one additionalmajor modelled term, which is for the dissipation of

subgrid kinetic energy. Fortunately, this term plays

its proper role in LES, which at the subgrid scale isto remove kinetic energy. The dissipation term is

not required to provide the mean value for all scales,nor is it used to obtain length scales or time scales

as it is in RANS modelling. Thus, dissipation model-ling is much less critical, and simple models seem

to work well.

T6. The k-equation LES models have also beenimplemented using the dynamic procedure to

obtain a better, local value for the coefficient inequation (8) [36]. This method is a logical extension

of T5; however, additional implementation details

must be observed to maintain stability. At this time,it is not clear if this additional complexity beyond

the basic T5 model is useful in engine simulations.

T7.A recent development in LES turbulence mod-

els is the dynamic structure approach developed byPomraning and Rutland [40] and Chumakov and

Rutland [41]. In this approach, a turbulent viscosity

is not used. Instead, a tensor coefficient is obtaineddirectly from the dynamic procedure. This tensor

coefficient is multiplied by the TKE that is obtainedfrom a transport equation (see appendix 4 for more

details). The resulting dynamic structure model is

tij= Cijksgs (9)

An important major aspect of the dynamic structureapproach is that there is no turbulent viscosity.

Thus, it is not a purely dissipative model. Instead, abudget of TKE is maintained between the grid scale

velocity field and the subgrid k-equation. In otherwords, energy removed from the grid scalesgoes into the subgrid kinetic energy. Then, within

the k-equation, a viscous dissipation term removes

the energy through molecular viscosity. Detailed a

priori and a posteriori testing of the model has

shown it performs well in rotating turbulence in

which energy is transferred accurately from small tolarge scales, a process that is similar to that occur-

ring in sprays and combustion systems [12,42].

The model was developed for practical applica-tions, especially IC engines, in which the number of

grid cells must remain reasonable. The model works

very well in engine applications, and provides a

good model for the subgrid TKE for use in combus-

tion, scalar mixing, and spray models. The T7

approach has been used for diesel engine simula-

tions with good results [15,43,44].

3.1.1 Turbulence: additional considerations

Wall boundary conditions. Wall boundary condi-

tions for LES submodels are not very well devel-

oped. There has been continued effort is this area

for several years (e.g. Kannepalli and Piomelli [45]

and Chang et al. [46]), but, to date, no significant

progress has been made on practical models for

CFD applications. Some promising advanced work

by Cabot and Moin [47] used RANS models with

additional consideration for unsteadiness and ejec-tion events. However, these have only been used on

simple channel flows and will probably requiremuch more additional testing before they can be

used with confidence in applications. More recently

Piomelli [48] has reviewed the status of wall model-

ling for LES, and Frohlich and von Terzi [49] dis-

cussed combining LES with RANS wall models.Thus, most LES simulations use one of two

approaches for wall boundary conditions: (a) no

special treatment of the wall, except for additional

grid points (Kannepalli and Piomelli [45]), and (b)

wall-layer models essentially the same as used in

RANS that have been shown, by Rodi et al. [50], to

give reasonably good results. For engine applica-tions, the use of wall functions is probably the best

approach for the near future. This is especially true

when one considers wall heat transfer for whichthere has been essentially no work on engines for

LES specific wall models.

Higher order numerics. In simulations that are

less focused on applications and more focused ongeneric flows, such as channels and isotropic turbu-

lence, numerical accuracy is an important issue

[51]. The concern is that numerical errors could be

of the same order as the LES modelled terms. The

generic flows commonly use higher order spatialnumerics, typically fourth order or higher. In addi-

tion to being higher order, the methods have low





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dispersion and dissipation errors. This is possible

because the computational domains are simple andthe grids allow easy implementation of higher order

numerics. In contrast, applications such as IC

engines commonly have complex grids and it is verydifficult to achieve anything higher than second-order spatial accuracy. This should not and has not

deterred the use of LES to achieve better results inengine applications.

There has been encouraging work by the group at

Doshisha University to improve the numerical accu-racy in the KIVA engine applications code [52, 53].

This work correctly focuses on the advection or con-vection term in the momentum equation and has

compared several numerical methods, includingone that is up to third-order accurate. The results

are encouraging, but have only been demonstratedon simple grids in the engine code and have notbeen demonstrated on grids for actual engine

configurations.Another tactic for higher order accuracy is being

used by Poinsotet al. at IFP and CERFACS, in whichan existing LES code developed for aeronautical

applications is being adapted for IC engines [25,54]. The code is known as AVBP, and has second-order time accuracy and third-order spatial accu-

racy on the convection terms. The time integrationscheme is explicit, which offers higher accuracy

than an implicit scheme since the time step isrestricted to smaller values. Adaption for engines is

not straightforward, but moving mesh algorithmshave been implemented; however, grid removaldoes not seem to be included yet. The code is being

carefully tested and is showing good results forengine applications [55].

Compressibility effects. Even though the gas den-sity varies significantly in engines, they are generally

considered low Mach number regimes [56]. Thus,pressure wave effects on turbulence modelling arealmost never considered. The exception is when

engine knock or extremely rapid ignition occurs.While some HCCI operation is similar to knock, it

can be considered a different mechanism that isprobably not a consequence of pressure waves in

most cases. There are many RANS-based studies ofknock (see, for example, [57]) but there does not

appear to be any LES studies yet. This will probablychange before long as mega knock in downsized[58] or direct injection gasoline engines is studied.

Open boundary conditions. Many engine studiesare focused on the closed portion of the cycle and

thus avoid open boundaries. However, as multicycle

simulations become more common to study topicssuch as cycle-to-cycle variability, inflow and outflow

boundary conditions must be considered. It is not

always clear what information should be specified

on the boundaries to achieve accurate simulations.

One LES study found that boundary flow perturba-

tions can have a significant impact on combustion

[59]. This topic needs additional study, and it islikely that the type of engine, the specific models

being used, and the focus of the investigation will

have an impact on what boundary conditions are

required.

3.1.2 Turbulence: recommendations

1. The use of LES for basic turbulence modelling in

applications is becoming better established andcan be used for engine CFD with the appropriate

models.2. The most common LES models use simple visc-

osity formulations (T2, T4) and do not take

advantage of LES concepts. They require highgrid resolution, which can be achieved usinghighly parallel codes.

3. The more advanced differential LES turbulencemodels (T5T7) should be used. These do not

require extremely fine grids and work well onthe grids commonly found in engineapplications.

4. Models that use a subgrid TKE,ksgs, are well sui-

ted to engines because this term can be used inmodelling combustion, scalar mixing, andsprays.

3.2 Combustion modelling

The phrase combustion modelling refers to model-

ling the chemical reaction rate terms in the energy

and species conversation equations. Often, these

models incorporate additional transport equations

for mixture fraction or flame surface expressions.

These additional equations may require additionalmodels for terms such as scalar dissipation or tur-

bulent flame speeds. Combustion modelling is a

complex and evolving field. Readers should consult

reviews by Pitsch [16], Menon [60], Veynante and

Vervish [61], Hilbert et al. [62], and the book by

Poinsot and Veynante [8] for detailed background

information. In this section, the major combustion

models that are used or have potential application

for IC engine CFD are classified and briefly

described.In almost all cases, the combustion models are

essentially RANS models that have been or could beadapted for use in LES. This approach clearly treats

LES as an evolution of RANS modelling and seems

12 C J Rutland




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to work well. The combustion models benefit from

the LES flow field and scalar mixing models. In

addition, as noted by Kempf et al. [17], the RANS

formulations, though originally based on ensemble

averaging, may still be appropriate for LES-based

spatial averaging and respond correctly to the

LES flow field. However, the best approach is to re-

evaluate the models and make appropriate modifi-

cations to be consistent with the LES approach. This

adaptation may be as simple as adjusting coeffi-

cients within the original RANS model. Or they may

be more complex and require reformulation of the

expressions to be consistent with the time scales

that are available from the LES turbulence and mix-

ing models. For example, specific LES formulations

of scalar dissipation models may be required in

mixture-fraction-based combustion models (see, for

example, [63]).Table 3 classifies and briefly describes the major

approaches to combustion modelling that have

either been used or could be used for engine CFD.

Some of the models have been grouped into families

with specific approaches listed as subcategories.

C1. The direct integration approach is also called

the mean-flow approach since reaction terms are

evaluated using the grid scale (e.g. filtered) tempera-

ture and species. These do not account for subgrid

mixing effects, so they are best suited for more

homogeneous flows and detailed chemical kinetic

schemes. Alternatively, direct integration is suitable

for dense grids when the subgrid values are

Gaussian with small variance. This approach has

proven to be very successful for studying low-

temperature combustion (LTC) approaches such as

HCCI. For example, Reitz and his group have suc-

cessfully applied C1 modelling for RANS modelling

in direct injection and homogeneous charged LTC

diesel engine studies [64], gasoline direct injectionengines [65], and in similar dual-fuel combustion

strategies [66]. The approach has also been used

Table 3 List of major combustion modelling approaches that have potential for use in LES.

Original or primary type of combustion for each model is indicated by Mode in column

2: H for homogeneous, P for premixed, D for diffusion

Model type Mode Advantages Disadvantages

C1 Direct IntegrationCHEMKIN or other stiff ODE integrators H Uses detailed kinetic mechanisms;

no special modelling requiredIgnores subgrid turbulence effects.

Better suited for homogeneouscombustion. Computationallyexpensive

C2 Blended modelsRIF D Better computational efficiency for

detailed chemistry. Uses flameletconcepts to model subgrid mixing(method C4d)

Not really a CFD method since themodel is not applied to each grid cell

C3 Time-scale models(a) Magnusson D Simple; uses both kinetic and

turbulent time scalesRequires using same time scales for all

reactions within individual grid cells(b) CTC D Improves on Magnusson by

integrating towards currentequilibrium state

Still requires same time scales

C4 Transport-equation models Flamelet approaches. Soundmathematical descriptions

Transport equations require modellingof scalar flux, source terms, and sinkterms

(a) Progress variable C P, D Sound modelling of turbulenceeffects on flame front

No detailed chemistry. Better suited forhigh Reynolds number flows.Requires high grid resolution toresolve flame

(b) Level set G-equation P, D Similar to C4a for premixed flames.Diminishes grid resolutionrequirements

Not suited for detailed chemistry.Requires model for turbulent flamespeed

(c) Flame surface area density S P, D Similar to G-equation approach(C4b) but uses the flame area for amore physical description

(similar to C4b)

(d) Mixture fraction Z D Can incorporate detailed chemistrythrough flamelet library. Usesprescribed PDF to model subgrid

mixing effects

Requires flows with fast chemical timesscales (high Da number) unlessunsteady effects are incorporated

(e) Conditional moment closure D Tries to improve on mixturefraction models (C5d) by usingvalues from the reaction zone

Increased complexity due to moreterms that require modelling

C5 PDF transport all Provides direct closure withoutmodels for reaction terms

Complex; Monte Carlo method;requires phase space mixing model





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successfully in LES applications using the T7 turbu-

lence model for direct injection diesel LTC studiesby Rutland and his group [15,43,44].

The C1 approach requires detailed chemical

kinetic mechanisms to be successful in engines, andthis usually results in very large computational runtimes. Progress in improving run times is being

achieved by improved load balancing in parallelcomputing environments [67]. Additional run-timeimprovements are being achieved by applying

advanced numerical techniques such as cell cluster-ing and analytical Jacobians [68] or precomputed,

tabulated results from detailed chemistry calcula-tions [69, 70]. These methods are computationally

efficient, but may require close monitoring ofapproximation errors, especially for ignition and

other situations where results are sensitive to kineticdetails.

C2. In an attempt to incorporate more detailed

chemical kinetics but without the computationalpenalty, Peters group have developed the represen-

tative interactive flamelet (RIF) model [7174].Individual flamelets that represent the main com-

bustion process are tracked using a Lagrangianmethod through the domain. The approach can becalibrated to work with conventional diesel combus-

tion and provide detailed chemistry for emissions.However, the approach has difficulty with more

homogeneous flows, wall heat transfer, multiple fuelinjection operation, and spatially non-uniform

mixing that can occur in different regions of thecombustion chamber. Additional flamelets aresometimes added to help address these issues, and

the method begins to resemble the cell clusteringapproach used in C1 models. Combustion is tracked

by the Lagrangian flamelets rather than the pro-cesses within each CFD grid cell. The approach is

more of a blending between a CFD flow model anda system level heat-release model. Since it is notclear how a representative flamelet concept is con-

sistent with the LES spatial filtering approach, theRIF approach is not recommended for LES.

C3. For RANS applications, the time-scaleapproach was originally developed for spark ignition

engines (Abraham et al. [75]) and later adapted fordiesel engines (Kong and Reitz [76]). The character-

istic time-scale (CTC) model is a very practicalapproach that can give good results when experi-mental data are available to adjust coefficients. The

CTC model is an outgrowth of the less commonlyused Magnusson type approaches, but is more

advanced in that CTC drives species concentrations

to a specified value. This specified value is com-monly the local equilibrium value. However, in

some models this specified value is obtained from a

strained laminar flamelet solution (see, for example,

Rao and Rutland [77]). This effectively combines theflamelet-prescribed PDF approach (C4d) with the

time-scale approach and has been used successfully

with LES turbulence models in diesel engine simula-tions [78].C4a.The flame-sheet approximation for premixed

flames has been developed in two formulations: the

C-equation and the G-equation approaches origi-nally developed by Bray [79] and Kersteinet al. [80],

respectively. However, as shown by Zimont [81], theapproaches are very similar. In the C-equationapproach, the RANS flame brush is represented by

a progress variable C (commonly normalized

temperature). This flame-sheet approach has beenextended by Zimont et al . [82] for RANS

simulations.The group at the Lund University has publisheda series of papers using a progress variable

approach with a very highly resolved T2 turbulencemodel [31, 8385]. Their work was focused on

understanding HCCI and they achieved good com-parisons with experimental pressure traces.

Figure 4 shows an example from one of their LESsimulations. Additional discussion of their workappears in section 4.

The adaptation of the Cprogress variable modelfor LES has shifted away from the RANS moment-

based approaches towards a simpler formulationcalled the thickened flame model [86]. This is a sim-

ple concept that artificially increases the flamethickness and is motivated by reducing the com-putational time used in the combustion model.

This allows denser grids and more resolved scalemotions that work well with the thickened flame.

Researchers in France have made good use of thisapproach in LES and have simulated multiple cycles

of a spark ignited premixed charge compressionignition (PCCI) engine [55].

C4b.The G-equation approach uses a continuous

variable,G, but assumes that a specific line of con-stant Grepresents the flame front. It is a level-set,

kinematically based approach and is extended tocombustion only by the concept of a flame sheet.

The function G evolves by a standard transportequation that requires models for the subgrid sca-

lar flux. This approach is being developed for RANSsimulations (see summary in Peters [87]). It alsoshows some promise for use in LES simula-

tions of premixed flames [88]. More recently the

G-equation approach has been formulated for dif-

fusion flames and used in diesel engine simulations

by Yang and Reitz [65]. These simulations useRANS modelling, but the extension to LES shouldbe straightforward.

14 C J Rutland




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C4c. The flame area per unit volume approach

was originally developed for diffusion flames by

Marble and Broadwell [89]. It was later adapted for

premixed flames in RANS simulations by Candel

and Poinsot [90] and Ducros et al. [91], and is com-

monly called the coherent flamelet model (CFM).

The flame surface density,S, is used with a laminar

flamelet solution to obtain the total reaction rate in

a CFD cell. Commonly a transport equation is used

to obtain S. This requires modelling of the scalar

flux and additional source and sink terms specific to

flames sheets. These source and sink terms are key

components for accurate predictions.

For engine applications, the coherent flamelet

has been used in RANS simulations by Angelberger

et al. [92], Henriot et al. [93], Colin et al. [94], and

Colin and Benkenida [95]. More recently, the

approach has been expanded for RANS enginesimulations and called the ECFM and ECFM3z

methods [9698]. The CFM approach was adapted

specifically for LES by Welleret al. [99] for premixed

flames in non-engine applications. For LES engine

applications, the CFM model was adapted for diesel

combustion and used by Musculus and Rutland

[100] and the ECFM-LES method was developed by

the researchers at IFP, the EM2C laboratory at Ecole

Centrale Paris, and the CERFACS organization [59,

101] (see section 4 for additional discussion).C4d. The LES versions of the mixture fraction

approaches are very similar to RANS models themean and variance of a conserved scalar (usually

mixture fraction) are used to build an assumed PDF.

This PDF is then used to obtain mean quantities

from laminar flamelet solutions. In general, the

solutions are not very sensitive to the shape of the

PDF and beta functions are the most commonly

used PDF. The mean of the scalar is usually

obtained from a transport equation that requires

mixing models (e.g. scalar flux models; see following

section). The variance of the scalar can be obtained

from either another transport equation or from an

algebraic closure by equating scalar production and

scalar dissipation. Either method requires the scalar

dissipation. This approach has been used success-

fully by many people for non-engine LES combus-

tion models [69, 102106]. The mixture fraction

approach also works well with LES in engine appli-

cations (see, for example, [15,78,107,108]).

C4e. The conditional moment closure (CMC) is a

variation of C4d in which many terms are supposedto be evaluated at the reaction zone (e.g. a condi-

tional evaluation). The objective is to resolve local

mixing conditioned on the mixture fraction. The

model was originally developed for non-premixed

flames independently by Klimenko [109] and Bilger

[110]. The approach expands the mixture fraction

models by using a conditional averaging approach

so that many terms in the transport equation use

values at the reaction front. Most of these condi-

tional terms require additional assumptions and

modelling, so CMC can be more complex and com-

putationally expensive than conventional mixture-fraction models. The CMC approach has been used

in RANS simulations of engine-like flows [111, 112]

Fig. 4 Instantaneous temperature fields from an HCCI test engine with a square bowl designedto increase turbulence levels (from [85], reprinted with permission from SAE paper 2008-01-1656, 2008, SAE International)





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and in diesel engines [113]. The CMC approach has

been adapted to LES for non-engine flows (see, for

example, Steiner and Bushe [114]), but it is not

straightforward, as shown by Triantafyllidis and

Mastorakos [115]. Generally, results with CMC areusually slightly better than a typical C4d model.

However, the CMC complexity and lack of general

experience that comes from wider use indicate that

the approach still needs development for use in LES

of complex engine flows.

C5. An additional combustion modelling

approach is based on the PDF evolution equation

models. The approach is often referred to as the

transported PDF approach as opposed to the pre-

sumed PDF approach in C4d and C4e. The theorywas originally developed by Pope [116], primarily

for RANS environments. A recent review of thismethod by Haworth [117] provides detailed infor-

mation about the physics, mathematics, and

numerical details of this approach, including a sec-

tion on its use for engines. This is a complex

approach using Monte-Carlo methods to track the

evolution of the underlying PDFs that describe the

thermal and, in some cases, velocity fields. The pri-

mary advantage of the approach is that it does not

require any additional models for the chemical reac-

tion terms. However, it does require models for sub-grid turbulence and phase space mixing. The

method is so different from the other approachesdiscussed here that some users find it difficult to

use. Since it is a statistical approach, the method

can require long CPU run times. However,

Subramaniam and Haworth [118] and Kung and

Haworth [119] are actively developing the method

for IC engine application and are achieving goodresults in RANS simulations. There is little LES work

with the transported PDF approach and there does

not appear to be any published applications of the

models to LES engine simulations to date.

3.2.1 Combustion: additional considerations

Time scales. Combustion models in LES require

good models for mixing of species and/or thermal

energy. Large-eddy simulation is well suited to pro-

vide better mixing information in support of com-

bustion models, especially at the grid scale. At the

subgrid scale, combustion models require time-

scale information in one form or another (mixingtimes, scalar dissipation, kinetic times, etc.).

Currently, LES models are less well suited to this

task because there has been less development on

models that provide this information. Often, subgridtime-scale information is obtained from turbulent

viscosity and local mean gradients, but this is based

on RANS concepts. The newer one-equation turbu-

lence models (T5, T6, T7) are better at providing

time-scale information because they track the sub-

grid kinetic energy ksgs using a transport equation.

This can be combined with length scales (gradientsor filter length scales) to provide time scales to com-

bustion models.

Multimode combustion. In some engine appli-

cations, combustion does not easily fall into the

traditional classifications of premixed mode or

non-premixed mode. Or combustion may occur in

multiple modes within a cycle. Examples are direct

injection gasoline technologies and some of the

newer LTC technologies such as partially PCCI.

These types of combustion processes are probably

best described by combinations of direct integration

for ignition (C1), premixed and partially premixedcombustion for early, more highly mixed processes

(C3, C4ac), and mixing controlled combustion for

later processes (C4de). These multimode opera-

tions can occur in a time sequence, or simultane-

ously, but in different regions in the combustion

chamber, or some combination of these two situa-

tions. A combination C4a and C4d model for non-

engine LES was reported by Ihme and Pitsch [120].

For engine applications, hybrid approaches have

been explored for RANS diesel applications [107]

and premixed/diffusion combustion in the ECFM3Z

model [95]. More recent work has demonstratedLES simulations of diesel engine simulations using a

combination of C1, C3b, and C4d combustion mod-

els with a T7 turbulence model [15,44].

The difficulty with multimode approaches is des-

ignating and accurately evaluating the best para-

meters for switching between the modes.

Commonly, these parameters measure a mixing

state (for example scalar dissipation rate), relative

timescales (Damkohler or Karlovitz numbers), or

reaction progress (for example, reaction products or

normalized temperature). Currently, there is not a

good theoretical framework for determining theswitching parameters, so they are often developed

based on physical arguments. In addition, the

switching procedure and the value at which

the switch occurs may have a greater impact on the

results than the details of the individual combustion

models. Clearly, much more work needs to be done

in this area for both RANS and LES modelling.

3.2.2 Combustion: recommendations

1. Use transport-based combustion models (C4).

The transport equations in these models benefit

16 C J Rutland




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from the large-scale flow structures that occur inLES simulations.

2. Use LES specific modification for major termswithin the models such as mixing time scales,scalar dissipation rate, turbulent flame speeds,

scalar flux, etc.3. Use a k-equation-based turbulence model (T5,

T6, T7) that can provide a subgrid TKE to thecombustion model.

3.3 Scalar transport and mixing

Reacting flows require simulation and modelling of

scalars such as species concentrations and thermal

energy. Since it is becoming more common to use

larger, more detailed chemical kinetic mechanisms,

there can be a large number of species, and eachone requires its own transport equation (see, for

example, Tamagnaet al. [121, 122]). There are usu-

ally source terms in these equations from the chem-

ical reactions, but these are modelled by the

combustion models described in the previous sec-

tion. Beyond this, the primary modelling require-

ment is the subgrid scalar flux term that comes

from spatial filtering the non-linear convection term

in the transport equations (see equation (14)). In the

future, as fine grids and detailed kinetic mechan-

isms become more common, complex molecular

transport and Lewis number effects may need to beconsidered.

Subgrid scalar flux or turbulent scalar mixing is

physically and mathematically similar to turbulent

subgrid stresses (equation (12)). As a result, models

for scalar mixing are often extensions of turbulence

models. In addition, turbulent flow structures

enhance scalar mixing, both directly at larger scalesand indirectly at subgrid scales through larger gradi-

ents. So models for scalar mixing usually play a sec-

ondary role in engine applications. The primary LES

approaches for scalars are listed in Table 4 and

described in more detail below.SC1. As with the T1 turbulence model, one can

rely on numerical dissipation to provide mixing

[20]. This does not work well for reacting flows and

is rarely used even for passive mixing.

SC2a. The viscosity and mean-gradient approach

is essentially the traditional RANS model with the

turbulent viscosity provided by the LES model (seeequations (7) or (8)). As in RANS modelling, LES tur-

bulent viscosity is combined with a turbulent

Schmidt or Prandtl number. These numbers may be

assumed constant or evaluated through dynamic

procedures (see, for example, Moin et al. [123]).

Probably, this is the most common scalar mixing

model used in LES simulations, even for reacting

flows [104]. The model relies heavily on the turbu-

lence model.

SC2b. An important extension of the viscosity

approach is to combine it with the one-equation

turbulence models (T5T7). In this case, the turbu-

lent viscosity is formulated with the subgrid kinetic

Table 4 Classification of the major LES scalar mixing model approaches

Model type Transport equations Advantages Disadvantages

SC1 None 0 Simple; uses numerical dissipationfor mixing

Poor results

SC2 Viscosity based(a) Simple turbulent viscosity 0 Inexpensive, works well in simple

flowsUses lower level turbulence model;

requires high grid resolution; usestraditional RANS approach

(b)ksgsbased viscosity 1 Combined with advancedturbulence models (T5T7);inexpensive; good results inengine flows

Still relies on a viscosity meangradient approach

SC3 Self-similarity 0 Uses additional filtering that hasproven successful in dynamicapproaches

Not fully dynamic, may be unstableand requires estimating a modelcoefficient

SC4 Subgrid transport equation 1 A higher level of modelling thanalgebraic closures; uses additionaltransport equation for subgridscalar fluctuations

Each transport equation requires amodel for its own scalardissipation rate. Expensive whenused with many species thatoccur in detailed kinetics models

SC5 Dynamic structure 1 Extension of SC4 using concepts of T7

Can be computationally expensiveunless used with a mixturefraction approach (C5d)

SC6 Linear eddy model many Uses a simple one-dimensionalsubgrid mixing model

Requires many subgrid elements(~1000) per CFD cell





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energy (equation (8)) and combined with a turbu-

lent Schmidt or Prandtl number. This approach isused with LES in IC engine applications [15]. It pro-

vides good results at reasonable computational

expense. This is primarily because it is combinedwith advanced turbulence models T5T7.

SC3. Scale-similarity models are based on the

same concepts that underlie many of the turbulencemode

International Journal of Engine Research-2011-Rutland-1468087411407248

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