large eddy simulation of turbulent combustion systems

Proceedings

Proceedings of the Combustion Institute 30 (2005) 537–547

www.elsevier.com/locate/proci

of the

CombustionInstitute

Large eddy simulation of turbulent combustion systems

J. Janicka*, A. Sadiki

Institute for Energy and Powerplant Technology, Darmstadt University of Technology, Germany

Abstract

This paper reviews recent and ongoing work on numerical models for turbulent combustion systemsbased on a classical LES approach. The work is confined to single-phase reacting flows. First, importantphysico-chemical features of combustion-LES are discussed along with several aspects of overall LES mod-els. Subsequently, some numerical issues, in particular questions associated with the reliability of LESresults, are outlined. The details of chemistry, its reduction, and tabulation are not addressed here. Second,two illustrative applications dealing with non-premixed and premixed flame configurations are presented.The results show that combustion-LES is able to provide predictions very close to measured data for con-figurations where the flow is governed by large turbulent structures. To meet the future demands, new keychallenges in specific modelling areas are suggested, and opportunities for advancements in combustion-LES techniques are highlighted. From a predictive point of view, the main target must be to provide a reli-able method to aid combustion safety studies and the design of combustion systems of practicalimportance.� 2004 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

Keywords: Combustion-LES; Overall-model; Reliability of LES results; Turbulent combustion systems

1. Introduction

With regard to both the environmental sustain-ability and operating efficiency demands, moderncombustion research has to face two major objec-tives, the optimization of combustion efficiencyand the reduction of pollutants. To achieve thesepurposes, an accurate prediction of the essentialphysical and chemical properties of the reactingflows is a prerequisite. In the case of conventionaland advanced gas turbine engines, for example,the design process includes nowadays carefuland deliberate trade-offs between often conflictingdesign requirements. These consist of high operat-

1540-7489/$ - see front matter � 2004 The Combustion Institdoi:10.1016/j.proci.2004.08.279

* Corresponding author. Fax: +49 0 6151 16 6555.E-mail address: [email protected] (J.

Janicka).

ing pressure and temperature, and low-emissionrequirements, low cost of ownership, and perfor-mance or efficiency, as well as durability and oper-ability. This task cannot be solved by the use of(empirical) design experience only. Today, almostevery industry that applies advanced design engi-neering uses CFD to predict and to optimize flowprocesses.

In fact, turbulent combustion systems involvemany phenomena and processes, such as turbu-lence, mixing, mass and heat transfer, radiation,and multiphase flow phenomena, which stronglyinteract. Their relative role is configuration depen-dent, and flows typically exhibit strong largecoherent structures and evolve in an unsteadymanner (see, e.g. [1]) making steady state compu-tations, at best, an approximation. Numericalmodels capable of providing the necessary infor-mation of the flow and scalar fields must be able

ute. Published by Elsevier Inc. All rights reserved.

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538 J. Janicka, A. Sadiki / Proceedings of the Combustion Institute 30 (2005) 537–547

to predict the highly unsteady behavior, in partic-ular that associated with turbulence-chemistryinteractions [2–48]. The final goal of these modelsmust be a reliable prediction of combustion sys-tems of practical and technical importance.

Direct numerical simulations (DNS) resolve allscale structures of scalar and velocity fluctuations.Although recent DNS of laboratory-jet flameexperiments have been reported with reduced orrealistic chemical kinetics [2,3], they are computa-tionally expensive and remain limited to low Rey-nolds numbers. For complex turbulent flows ofpractical importance, unsteady Reynolds averag-ing-based numerical simulations (U-RANS) andlarge eddy simulation (LES) have emerged as real-istic alternatives.

However, U-RANS models the turbulence andonly resolves unsteady mean flow structures.RANS-based turbulence models represent allscales of motion, so that more modelling effort isrequired. The determination of model coefficientsis often a problem, when new configurations arestudied. It is worth mentioning that numericalschemes are also frequently too dissipative. Re-cent innovative concepts have been reported in[5,6].

In this review, we focus on LES. There are sev-eral LES approaches. Recent critical reviews ofLES can be found in [7–16]. In the classical ap-proach, the governing equations (continuity,momentum, species mass fractions, and enthalpy)are filtered to separate the large-scale and small-scale turbulence (e.g. [7,10–17]). The large-scaleturbulence is solved for by the discretized equa-tions whereas the small-scale turbulence is mod-elled through the subgrid scales (SGS) models toreplace the information that has been lost. Thesimplest LES approach is to use no SGS model(e.g. [9]), and to let total numerical dissipationplay the role of the SGS-model for momentum.

Although some issues must still be clarified aspointed out in [7,10–16], LES for non-reacting

Fig. 1. Illustration of an overall mo

flow has reached a level of development makingits accepted advantages useful for reacting flowsimulations. Because chemical reactions and heatrelease in turbulent combustion occur essentiallyat the smallest scales of the sub-filter level, com-bustion processes in LES have to be modelled,as well as other unknown terms accounting forthe effect of unresolved scales in the filtered gov-erning equations. Nevertheless, the prediction ofcombustion processes using LES is expected tobe more reliable. First, LES handles transportprocesses affected by the resolved, large-scale mo-tions, and the modelling effort of turbulence is re-duced to the residual motion structures. Second,although LES experiences difficulties near the wall[5–10], important aspects of combustion processes(e.g. main reactions, heat release, pollution forma-tion, radiative heat transfer, etc.) frequently takeplace far away from walls. Third, because freshand burned gas zones, having different turbulencecharacteristics, are instantaneously identified atthe resolved grid level, a better description of tur-bulence-chemistry interactions can be expected[15]. A proper resolution of the spatio-temporalevolution of the unsteady mixing and combustionphenomena makes it possible for many other pro-cesses such as blowoff, combustion instabilities,and combustion control to find a reliable predic-tion by means of LES, see, e.g. [16,18].

An overall LES model formulation for turbu-lent combustion has then to contain physics-pre-serving turbulence/mixing closures, anappropriate combustion submodel able to capturefinite chemistry effects along with a submodelaccounting for turbulence-chemistry interactions,and possible submodels accounting for additionalphenomena, such as multiphase flow phenomena,radiative heat transfer and soot processes, etc.Figure 1 displays an illustration of an overallmodel for unsteady simulations.

To estimate the model performance, the preci-sion of LES results is often evaluated in compari-

del for unsteady simulations.

J. Janicka, A. Sadiki / Proceedings of the Combustion Institute 30 (2005) 537–547 539

son with experimental or DNS data. To providereliable and accurate predictions, the numericalalgorithm used must include a procedure capableof providing the numerical uncertainty of theLES along with the error in the solution arisingfrom modelling and numerical method.

In what follows, some issues related to the clas-sical LES approach for combustion systems arereviewed, with emphasis placed on important as-pects of an overall model. Some numerical issuesare outlined, whilst the details of chemistry, itsreduction, and tabulation are not considered.Two illustrative applications are presented. Thefirst application case is based on the conservedscalar method in connection with steady flameletand the concept of sub-grid scale probability den-sity function (PDF). It deals with non-premixedcombustion. The second focusses on a premixedflame configuration. Numerical simulation resultsfor both cases are presented by comparing statis-tically averaged LES and experimental data. Inconclusion, the performance and limitations ofcombustion-LES (CLES) for simulation of com-bustion systems are evaluated, and some openproblems for future research are suggested.

2. Features of CLES and closure issues

The equations mentioned above that governthe transport of a reacting Newtonian fluid are fil-tered to obtain the LES governing equations.They contain unknown terms (SGS-stress tensor,SGS-species, and heat transport due to turbu-lence, and filtered chemical source term) that mustbe closed with appropriate subgrid (sub)modelsbesides the temperature-species correlation termin the state equation. For recent reviews of filter-ing procedures, refer to [7,10,13]. The submodelsare then assembled in a combined model thatneeds to be validated. However, the evaluationof the combined model performance suffers fromdifficulties in identifying and quantifying thenumerical and modelling errors in the solution.In this section, emphasis is placed on the model-ling of physico-chemical processes and on somenumerical aspects.

2.1. Subgrid closures for momentum and scalarfluxes

Different SGS-models formulated for non-re-acting flows have been adapted to reactive cases.Most of the SGS-stress tensor models used inthe momentum equations are based on the gradi-ent assumption (linear eddy-viscosity models)with constant (e.g. [17,19–24]) or dynamicallydetermined model coefficient (e.g. [7,25]). Becauselarge-scale structures must be resolved, resolutionefforts are in some cases compelling, for example,near walls where even the largest scales are very

small. If attached boundary layers are important,LES will probably give poor predictions in theseregions, unless very fine grids are used [5,6]. Toincorporate history and non-local effects, trans-port equations of quantities related to the residualmotions, such as SGS turbulent kinetic energy orSGS-stress tensor, will then have to be consideredalong with algebraic, anisotropic eddy-viscosityapproaches. Advances in subgrid scale modellingcan be found in [7,10–16].

The gradient diffusion assumption is often usedto model the species transport terms due to turbu-lence [20–45]. Even setting aside the counter-gra-dient diffusion, a large-scale phenomenonoccurring in premixed cases [15,37], which cannotbe reproduced by this assumption, this type ofmodel for small-scale scalar turbulence and reac-tive species (with or without dynamic procedure)is recognized to be appropriate only for very spe-cialized cases [14]. However, in Priere et al. [19],predictions of mixing enhancement using thisassumption are close to experimental results. Seealso [24,25,29–35]. Alternative subgrid modellingapproaches, that avoid the gradient assumption,have been proposed in the form of transport equa-tions or non-linear assumptions [23,37] and of lin-ear eddy model (LEM) [46,47].

In addition to turbulent species transport, sub-grid models for the temperature-species correla-tions arising in the state equations need to beformulated. However, their modelling is eithertreated superficially or ignored [47].

2.2. Turbulent combustion and turbulence-chemis-try interaction

Notwithstanding an embryonic novel develop-ment of subgrid simulation based closures in [46],it appears that most recent works dealing withCLES focus on the applicability of RANS-likecombustion models to LES to provide the filteredchemical source term. Reaction models definerelations between thermochemical state variablesin combustion systems on the basis of chemicalmechanisms. The details of chemistry, its reduc-tion and tabulation using different detailed chem-istry or techniques (FPI, ILDM, QSSA, ISAT,ANN, etc.) will not be addressed here. In this sec-tion, we rather focus on the turbulence-chemistryinteraction description.

Apart from early LES of combustion systems[20,21], two main views of the flame have beenemerging (see [3,14,15]). The first view considersa statistical analysis, whereby scalar fields maybe collected and analyzed for any location withinthe flow. Filtered values and correlations areafterwards extracted via knowledge of filteredprobability density functions (FPDF) to be deter-mined either by a presumed assumption [21] orby solving a FPDF-transport equation [27,28].This statistical view is also close to the well-


known conditional moment closure (CMC)method and to the LEM or ODF (one-dimen-sional flame) approaches. The CMC modellingis based on conditional moments at a fixed loca-tion and time within the flow field. Uncondi-tional quantities are recovered from conditionalmeans by using the presumed PDF approach[29,30]. In the LEM, all relevant scales are re-solved in one dimension. Molecular diffusion istreated explicitly, and subgrid stirring is modelledby a stochastic rearrangement process applied toa scalar field along the linear domain [46,47].Like the FPDF-transport equation, these meth-ods are applicable to premixed as well as tonon-premixed combustion.

The second view treats the flame as a geometri-cal surface whereby the flame is assumed to be thincompared to integral length scales. Scalar fields(scalar progress variable, c, or mixture fraction, f)are studied in terms of dynamics and physical prop-erties of iso-level surfaces defined as flame surfaces.Following [3], the flame is then described as aninterface between fuel and oxidizer (for the non-premixed case) or between fresh and burned gases(for the premixed case). An iso-mixture fraction isconsequently used for non-premixed flames, andan iso-progress variable is applied for premixedflames. This geometrical view is usually linked toa flame surface density assumption or a c-equationas well as to theG-equation approach for premixedcombustion. Focussing the analysis on the struc-ture of the reacting flow along the normal to theflame surface leads to the flamelet modelling whenthis structure is compared to those of one-dimen-sional laminar flames. This results in a flameletmodel based on c- or G-equation for premixedflames (e.g. [42,43]) or in a steady flamelet modelbased on mixture fraction for non-premixed flames(e.g. [22–25,35]).

For non-premixed combustion, an extension tounsteady flamelets has been suggested in [31,32].The common idea behind flamelet models is todecouple the numerical simulation of the turbu-lent flow and mixture fields from the solution ofthe chemistry. To couple the chemistry and theturbulence, the presumed PDF method is usuallyapplied by specifying subgrid species mixing interms of an assumed PDF shape (b, c, d, etc.) thatis a function of, at minimum, second-order corre-lations. These correlations can be predicted fromtheir balance equations as it is the case for thesubgrid scale variance of the mixture fraction in[23]. However, simple gradient assumptions areoften used (e.g. [25,35]). The inadequacies in theprediction of the high order species correlationshave been pointed out as primary source of draw-backs of this method (e.g. [47]). For the filteredrate of scalar dissipation, an eddy-viscosity ap-proach is usually used (e.g. [33]). To account forprobable local inhomogenities of the scalar dissi-pation rate, the concept has been extended in

[44]. Promising new ideas, such as the flameletgenerated manifold (FGM) [48], have recentlyemerged as computationally efficient alternatives.

For premixed combustion simulations, besidesthe LEM and PDF approaches, the use of theflame surface density concept or c-equation (e.g.[36,38]) and of the G-equation (e.g. [39,42]) totrack the propagation of the thin flame front isstate-of-the-art. In this regard, the concept of anartificially thickened flame can be interpreted asa numerical technique to deal with steep gradientsat the flamefront [40]. As the filterwidth plays animportant role in LES, it has been recently in-cluded as an additional length-scale into the re-gime diagram of premixed combustion by Pitschand Duchamp de Lageneste [42]. Dusing [39] ex-tended this consideration by providing morenumerical requirements needed for DNS, LES,and RANS computations of premixed flames.Such a view gives guidance to properly chooseand combine strategies for modelling both thechemical reaction and the turbulent flow byprescribing for every situation whose physicalphenomena have to be resolved by a given simula-tion method or modelled (see also [49]).

Even though partially premixed combustionoccurs in many practical devices such as gas tur-bines or internal combustion engines, only fewstudies concentrate on partially premixed configu-rations. Existing investigations basically combinewell-known models for premixed and non-pre-mixed combustion (e.g. [43,45]). A comprehensivemodel classification is provided in Fig. 1.

Until now, most CLES works are conducted totest the feasibility of LES in combustion on labo-ratory-flame experiments well suited for modeldevelopment and validation [41]. Some applica-tions of LES to complex combustion configura-tions of engineering importance are reported in[5,18,46]. They require sufficient computer powerand accurate, robust numerical algorithms. There-fore, the progress of CLES would not depend onthe availability of appropriate SGS-models only.Serious difficulties come from the numerics andboundary conditions [11,13].

2.3. Some numerical aspects

In LES, the combination of accurate discreti-zation and integration schemes with large numer-ical efficiency plays a central role, in particular forcomplex flows in geometrically complicated flowdomains. These issues have already been reportedelsewhere [13,16] and will not be discussed here.Nevertheless, it is worth pointing out that theneed for reliable and accurate predictions requirescompromise on numerical accuracy, the range ofscales resolved, and testing for numerical andphysical accuracy, where computer power is lim-ited [11]. While this task is easy in RANS-context,this is more difficult for LES.


The most commonly used LES procedure is theimplicit (Schumann) filtering [20], in which thecomputational grid and the discretization opera-tors are considered as the filtering of the govern-ing equations. Because the implicit filter isdirectly connected to the grid spacing, the solutionconverges towards a DNS as the grid is refined[7,12], and not towards the solution of the filteredequations. As the grid is refined, more turbulencelength scales are resolved, and the influence fromthe SGS-models is reduced. A grid-independentsolution is therefore difficult to determine [25]. Aclassical error estimation or a separation betweennumerical and model error is consequently hardto achieve, even though the sum of numerical andmodel errors tends to be small. To outline someguidelines for LES, two tentative methods that al-low one to assess the quality of LES results usingimplicit filtering will be addressed in the nextsection.

Using explicit filtering, the filtering procedureis separated from the grid and discretization oper-ators. Thus, a grid-independent LES solution canbe expected by keeping the filter width constantwhile the computational grid is refined [7,12,13].A classical estimation of both numerical and mod-el errors is then feasible in principle.

To judge the overall model performance, LESresults are often compared with experimental (orDNS) data. As pointed out in [8], this is suggestiveif the errors arising from the numerics, themeasure-ments, and the discrepancies in the boundary con-ditions are relatively small. It is not judicious todraw conclusions about model performance oraccuracy from calculations containing large ornon-estimated numerical errors. To be able to as-sess the relative merits of different LES submodelcombinations (see Fig. 1), the criteria suggested in[8,11] can be applied. For the premixed combus-tion, the generalized regime diagram additionallyprovides numerical requirements and criteria thatallow a systematic appreciation of various modelsby restricting their applicability domains [49].

The final aspect of the numerical algorithm isthe enforcement of boundary conditions. A reli-able predictability using LES could be improvedwhen appropriate choice of boundary and inflowconditions is made. Besides immersed boundarymethods [16] and others [50], the use of the tech-nique of numerical inflow-generation, which

Table 1Different grids used for simulations

Flame Ujet (m/s) Uco. (m/s) nx n/ n

NRBB 61 20 300 32 6HM1e 108 35 200 32 4HM1e 108 35 400 32 6HM1e 108 35 400 64 6HM1 118 40 400 32 6

(k ” thousand nodes).

reproduces first- and second-order one-point-sta-tistics as well as a locally given autocorrelationfunction, appears to be very helpful [51].

In the following, two illustrative applicationsof LES are presented using feasible computationalcosts for predicting non-premixed and premixedflame configurations.

3. Illustrative applications

3.1. Large eddy simulation of non-premixed flames

To illustrate the performance of LES of turbu-lent non-premixed flames, the Sydney bluff-bodyflame investigated by Dally et al. [52] is discussed.It features a flame stabilized in the recirculationzone downstream of a bluff-body as encounteredin many technical applications.

The experimental configuration was discretizedusing a cylindrical computational domain of radius4.4D and 4D in length for the reactive cases(D = bluff-body diameter). For the iso-thermalcase, the domain was shortened to 3D. The lengthof the domainwas resolved by nx cells and its radiusby nr cells. The radius of the jet and the radius of thebluff-body were discretized by nr,j. and nr,b. nodes,respectively. In the circumferential direction, n/cells were used for three simulations performed ondifferent grids, respectively. On the fine grid, thisleads to a total of n = 1,536,000 cells. The temporaldevelopment was studied for nt time-steps. To as-sess the quality of the results, a number of simula-tions were performed on different staggeredcylindrical grids, as outlined in Table 1.

Transport of mass, momentum, and mixturefraction is described by solving the correspondingFavre filtered transport equations for density,momentum, and mixture fraction [24,25]. Thesgs-stresses were determined by the Smagorinskymodel with a dynamic Germano procedure [7],which leads to a turbulent eddy-viscosity. To-gether with the turbulent Schmidt-number(�0.45 [31]), this yields a turbulent diffusivity,which is required to model the subgrid scalarfluxes and the filtered scalar rate of dissipation(see, e.g. [24,25,31,32]).

The mixture fraction formulation [24] togetherwith a steady flamelet model [14] is used to projectthe mixture fraction field to density, viscosity,

r nr,j. nr,b. n nt Grid

0 4 32 576k 200k Normal5 3 18 288k 140k Coarse0 4 32 768k 200k Normal0 4 32 1536k 300k Fine0 4 32 768k 200k Normal


temperature, and species mass fractions. The sub-grid distribution of the mixture fraction is de-scribed by a presumed-shape b-PDF, whereasthe subgrid contribution of the scalar rate ofdissipation is modelled by a simple Dirac-func-tion. The chemical state is therefore a functionof the filtered mixture fraction ef , the modelledsubgrid variance ff 002 , and the filtered scalar rate

of dissipation ev. The flamelet libraries were deter-mined through the use of comprehensive detailedchemistry provided by the Lindstedt group [53].

Convective transport of steep gradients resultsin numerical oscillations if diffusivity is low.To avoid numerical oscillations, a nonlineartotal variation diminishing scheme (TVD, here:CHARM limiter) was applied for mass and mix-ture fraction transport. A similar approach wasused in [31,35], where a TVD-scheme was appliedto the mixture fraction only. The transport equa-tions are integrated in time by an explicit Runge–Kutta method. A predictor–corrector schemeaccounts for the non-linearities in the combustionmodels [25]. This scheme is conservative for bothmass and mixture fractions. The LES code usedis based on an incompressible formulation. Thisimproves the efficiency by an order of magnitude

Fig. 2. Resolved part of the turbulent kinetic energy.

Fig. 3. Comparison of results obtained on different grids forfraction fluctuations (B).

in comparison to codes using compressibleformulations.

The inflow conditions and the grid-resolutionwere found to be crucial in determining the flowcharacteristics. A significant sensitivity was ob-served with respect to numerical diffusion andthe inflow conditions. Numerical diffusion of themixture fraction leads to artificial mixing of fueland oxidizer, and hence increases the rate of reac-tion, which, in turn, leads to artificial expansionwhich may trigger the shedding of new vortices.The problem was solved by refining the grid. Theapplied inflow-conditions (Dirichlet for velocityand Neumann for pressure) constitute a secondsource of flow instabilities. The problem can besolved by optimized inflow-conditions wherebywe adapted the approach developed by Kleinet al. [51] or by shifting the inflow-plane upstream.The latter requires complex grids or immersedboundary conditions. Klein�s method features ran-dom inflow-velocities that satisfy the prescribedmean velocities, the Reynolds stress-tensor, andthe length-scale. The turbulent structures enteringthe flowfield, as a result of the current transient tur-bulent inflow-conditions, were effective in breakingdown coherent structures, and the results shownappear consistent with the experimental data.

To judge the quality of the LES, two tentativemethods have been used. The first method is to esti-mate the amount of the resolved turbulent kineticenergy according to the so-called index of qualityfor LES [8,11]. This assumes that a Smagorinsky-based LES should resolve approximately 80% ofthe turbulent kinetic energy. Figure 2A shows thecontribution of the resolved part of the total kineticenergy, and values are P84% in the non-reactingcase (panel A) , where the Lilly estimates for thesgs-turbulent kinetic energy were used [8].

The second method performed consists in vary-ing the grid-resolution. For flameHM1e, three sim-ulations were performed using a coarse grid, a

flame HM1e. Mixture-fraction mean (A) and mixture-


normal grid, and a fine grid (see Table 1). The mix-ture fraction fields obtained are compared in Fig. 3.Themeanmixture fraction ismarginally affected bythe grid-resolution, whilst the computed rms fluctu-ations show that the finest gridmust be applied. Forthe flame HM1e, the fine grid resolves more than75% (Fig. 2B). The results shown below have beenobtained with the fine grid.

Based on good results for the mean velocity andvelocity fluctuations (not shown), predictions ofmass fractions of H2O and CO are depicted in Figs.4 and 5. They show good agreement with experi-mental data. This implies that LES provides goodestimates for both the mixture fraction PDF andthe scalar rate of dissipation (not shown) in the cur-rent flame. The computed results illustrate thecapability of LES to deliver accurate predictionsfor non-premixed combustion. More details canbe found in [26].

3.2. Large eddy simulation of premixed flames

To demonstrate the performance of LES forpremixed combustion, a turbulent premixed pro-pane-air-flame experimentally investigated in [54]is simulated. This flame is situated in the corrugatedflamelet regime.Within this regime, the generalizedregime diagram as shown in Fig. 6 supports the useof a thin flamefront compared to the filterwidth.Since Schumann-filtering is used, this correspondsto a thin flamefront compared to the grid-spacing.Because the basic assumption of theG-equation ap-proach is well satisfied, the filtered G-equation [55]is therefore applied. The chemical state on theburned side of the flamefront was estimatedthrough an equilibrium chemistry assumption.

Fig. 4. Mean mass-fract

Fig. 5. Mean mass-f

The thickness of the flame (lf) and the Gibson-length (lG) were estimated with lf � 0.5 mm andlG � 3.2 mm, respectively. The numerical domainwas discretized with an equidistant Cartesian gridof size (L · B · 2 H = 220 mm · 20 mm · 50 mm)with n1 · n2 · n3 = 192 · 16 · 40 grid cells yieldingD > lf and l > lG > D > g in accordance with thegeneralized regime diagram. Since we resolve theGibson-length, the filtered turbulent flame speedequals the laminar flame speed. Thus, a simpleformulation based on the curvature of the filteredflamefront jf was used (st ¼ s0l ð1� L�jf Þ). There-by, L* represents two different Markstein-lengthsL (case 1: L* = L, case 2: L* = 0.1L with L = 2.4mm). For the given configuration, s0l equals0.12 m/s. Figure 7A shows a sketch of the setupand of one realization of the flamefront.

Apart from the flamefront, we apply a signed-distance function and use a newly developed reini-tialization scheme based on the formulations ofRusso and Smereka [56]. To maintain the signeddistance function apart from the flamefront, ageneralization to 3D of the extension velocitymethod developed by Adalsteinsson and Sethian[57] has been applied. Using this method, artificialdiffusion with the G-equation could be avoided.

Since we did not simulate the complete channelin the spanwise direction, we used periodic bound-ary conditions in the x2-direction. At the wallsand the inflow, we considered no-slip conditionsand measured velocity profiles U = 13.3 m/s,while for the pressure Neumann conditions wereused. At the outflow, Neumann conditions wereapplied for the velocity and Dirichlet for the pres-sure. The flamefront was anchored close to theedge of the step.

ion of water–H2O.

raction of CO.

Fig. 8. Comparison of the mean velocity in the x1-direction h~u1i.

Fig. 6. Cut through the generalized regime diagram (ðl=lf ÞRe1=2t ¼ 25, d = 0.1) from [49]. Thick lines depend on thevalue of ðl=lf ÞRe1=2t . Thin lines are independent of ðl=lf ÞRe1=2t .

Fig. 7. (A) Experimental setup and snapshot of the filtered G-field. The bold line shows the flame-front. (B) The meanprogress variable Æcæ (case: 1).


In Fig. 7A, the lines give iso-surfaces of filteredG. The bold line corresponds to the filtered flame-surface. Irregularities of the filtered G-field aredue to the three-dimensional behavior of theflamefront including topology changes. Thisbehavior is recovered in the velocity field. Notethat no irregularities are induced due to the cross-ing of the flamefront and the outflow plane. Fig-ure 7B gives the calculated mean progressvariable Æcæ. Unfortunately, no experimental dataare available for a quantitative comparison.

Figures 8 and 9 show the mean and rms veloc-ity profiles of ~u1 at different x1-positions. Theexperimental data by Pitz and Daily [54] are com-pared to LES-results obtained for both Mark-stein-lengths. In the simulations, the influence ofthe Markstein-length was found to be quite small.For the mean velocities at x1/H = 1.0 and 2.0,simulation and experiment agree well. Furtherdownstream, the velocity is overestimated in thelower part of the channel. This portends to anunderprediction of the flame length.

For x1/H = 1.0, the rms values of the flow areunderestimated. Further downstream, values of

the simulations and the experiments grow simulta-neously. At x1/H = 4.0, the agreement betweensimulations and experiments is solely qualitative.As in Fig. 8 only a weak dependency on L* is ob-

Fig. 9. Comparison of the rms velocity values in the x1-direction ~u1 rms.


served in Fig. 9. The underprediction of the flamelength may be explained by the sensitive interac-tion between velocity fluctuations and wrinklingof the flamefront. An overprediction of the fluctu-ations leads to an overprediction of the flamewrinkling, and thus to an increase in flame sur-face. This amplifies velocity fluctuations further.Moreover, the neglected influence of gravity andthe limited accuracy of the Smagorinsky-modelmay contribute to this phenomenon. For more de-tails, the reader may refer to [39].

4. Conclusions and perspectives

This topical review focussed on numericalmodels for the LES of turbulent reacting flows.We have restricted ourself to single-phase flowsin combustion systems, and presented some phys-ico-chemical and numerical issues related to aclassical, combustion-LES. Reviewing the litera-ture, we identified advances that are needed tosupport future LES-model development. Thesecan be summarized as follows:

• Many LES results have been reported for non-premixed combustion mostly conducted to testthe feasibility of LES. Thereby, LES providesgood estimates for both the flow and mixturefields, as well as for stable components, whereflame characteristics are determined by the flowfield.

• The steady flamelet model in LES allowsimproved predictions of non-premixed com-bustion due to a better capture of the mixturefraction PDF and the scalar rate of dissipationin comparison with RANS-based calculations.

• Finite chemistry effects relied on a preciseknowledge of the chemistry are still challeng-ing. Pollutant emissions and ignition or extinc-tion conditions are some examples.

• Apart from very few studies, premixed com-bustion simulation is far from the expectation.Two main concepts based on the scalar pro-gress variable c- and on the G-equationapproach appear to be well accepted.

• While quality assessment of RANS simulationresults is well established, this is still requiredof LES, and in particular of combustion-LES.To make the best use of modelling capabilities,one must be able to estimate the effect of thenumerical errors and modelling uncertaintiesin providing a true LES solution.

To illustrate these aspects, two applicationshave been presented. In the first case, a conserva-tive formulation for the conserved scalar ap-proach was applied on the basis of a steadyflamelet model to investigate a diffusion flame,the so-called Sydney bluff-body flame. The LESresults agree very well with experimental data,while emphasizing the sensitivity to boundaryconditions. Two tentative methods to evaluatethe reliability of LES results have been presented.They underlined the need for resolution.

Based on a generalized regime diagram, whichincludes numerical requirements, a filtered G-equation approach has been chosen for the simu-lation of a premixed flame (stabilized behind arearward-facing step). The numerical procedurewas based on the level-set method adapted forLES, and the accuracy of the results obtainedwas discussed in comparison with experimentaldata. Good agreement was achieved. With regardto pollutant predictions, an accurate descriptionof the post-flame region needs to be faced in thenear future.

• Although partially premixed combustionoccurs in many technical combustion configu-rations, its numerical prediction using LES isat the beginning and suffers from the lack ofcomprehensive validation data and well-adapted numerical algorithms.

• The extension of the eddy viscosity concept(valid for momentum) to scalar fields by usingan eddy diffusivity model needs to be revisitedaccording to a physically consistent scalar fluxmodelling. Within the PDF-context, the mix-ing modelling is still a downside.

Although a rapid development of computersand application-oriented numerical methods isnotable, DNS cannot and will not be able to meetthe urgent need for reliable predictive methodsto aid combustion safety studies and the designof practical high Reynolds number combustionsystems in the near future. To face the pressingeconomy and reduced pollutant emission require-ments, combustion LES will be most useful. As isgenerally recognized, the possibilities of LES arestrongly related to the magnitude of the subgrid-


terms, the role of discretization errors, and thequality and dynamic consistency of the modelling.To meet the future demands, some perspectivescan be outlined:

• Advanced models are required for an accurateprediction of finite chemistry effects. This con-cerns both non-premixed and premixed com-bustion, while significant efforts in predictingpartially premixed flames are needed. It waspointed out that the most important drawbackof LES is the near wall modelling. New con-cepts in developing wall-adapted SGS-modelsare welcome.

• The application of LES to combustion systemsrequires accurate and robust numerical algo-rithms, in particular for complex geometries.To take the most advantage of LES, an appro-priate balance between computational costsand potential benefit including the accuracyof the numerical method, the accuracy of theinflow and boundary conditions, and the sub-models chosen is necessary. From a predictivepoint of view, a numerical analysis, whichcan serve as guideline in estimating numericalerrors and modelling uncertainties for combus-tion LES, is needed.

• The precision of the LES results is often evalu-ated by a comparison with experimental data.For validation of the subgrid submodels,suitable experiments should provide at leastmeasurement data of subgrid velocities andscalar fluctuations, length- and timescales aswell as conditional measurements. For a prioristudies, combustion LES will still continue tobe supported by comparison with combustionDNS, while the gap between DNS for lowReynolds number and experiments for higherReynolds numbers needs to be filled to providecomprehensive and consistent validationdatabases.

• New key challenges arise from additional phe-nomena in some combustion systems. Subgridscale models for chemical reaction need to beextended to encompass several other importantphenomena, such as enthalpy variation effects,radiative heat loss including radiation fromsoot [58], interaction of flames with walls[59], flame instabilities [18], and acoustics, etc.

• The consideration of multiphase processes, likeliquid spray break-up and vaporization in two-phase flows, droplet combustion, brings addi-tional complexities that must be included insubgrid models [60].

• Unfortunately, even the best current LES mod-elling techniques do not provide fully reliableand accurate predictions in complicated flowsituations. But models for these and manyother flow situations can be developed by for-mally minimizing the mean square error inthe evolution of the resolved field, which may

result in an accurate LES formulation [11].Such techniques can be used to optimize andevaluate any of the various styles of LES.Efforts directed to include these aspects in

advanced combustion modelling, to evaluate thereliability of LES results, and to improve theLES-predictability using accurate inflow andboundary conditions must be pursued. Endeavorsto extend the applicability of accurate LES tocomplex configurations of technical importancemust be encouraged.

Acknowledgments

The first author is grateful to P. Lindstedt forthe honor of being invited to prepare this talk.The authors acknowledge the financial supportof the DFG through the SFB568, Flow and Com-bustion in Future Gasturbine Combustors. Wethank P. Lindstedt and our collaborators (A.Kempf and M. Dusing) for participating in thepreparation of this talk.

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Comment

Bertrand Naud, Zaragoza, Spain. Can you directlyapply RANS models in the context of LES? For in-stance, in FDF approaches don�t you rather model con-ditional statistics?

Reply. Most of the combustion models applied in theRANS context based on physical assumptions (e.g., thin

flame fronts) and a turbulent modelling procedure (scal-ing laws, assumptions regarding PDFs or correlations).The first aspect can without any doubts be used in aLES description; the second requires a more detailedconsideration. In the case of FDF the basic conceptcan be taken from classical RANS-PDF description,modelling of, e.g., the mixing term requires more care.

http://www.ca.sandia.gov/tnf

large eddy simulation of turbulent combustion systems

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