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Conference on Turbulence and Interactions TI2006 May June Porquerolles France

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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France LARGE EDDY SIMULATIONS OF TURBULENT COMBUSTION D. Veynante Laboratoire E.M2.C. CNRS et Ecole Centrale Paris, 92295 Châtenay-Malabry, France Email: ABSTRACT In large eddy simulation (LES), the larger turbulent motions in a flow field are explicitly computed when only the effects of the small ones are modelled. This approach is very well adapted to turbulent reacting flows which are generally dominated by such structures, especially when combustion instabilities occur. The instantaneous location of cold and burnt gases are then identified at the resolved scale level. As they may have very different characteristics in terms of turbulence, pollutant emissions or radiative heat transfers, this identification is expected to allow a better description of the flame / turbulence interactions. Nevertheless, models are still required to describe small scale effects and this approach is computationally expensive. To compare numerical results with experimental data is also a challenge. Despite of these difficulties, very impressive results have already been achieved using LES in complex configurations. INTRODUCTION Large eddy simulation (LES), where the larger turbulent motions in a o w eld are explicitly computed whereas only the effects of the small ones are modelled, has now reach a high level of maturity for non reacting o ws [1–4].

  • dynamic models

  • turbulent structure

  • features - models required - reduced modeling

  • prohibitive numerical

  • premixed ame

  • predict unresolved

  • ame


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Conference on Turbulence and Interactions TI2006, May 29 - June 2, 2006, Porquerolles, France
LARGE EDDY SIMULATIONS OF TURBULENT COMBUSTION
D. Veynante
Laboratoire E.M2.C. CNRS et Ecole Centrale Paris, 92295 Châtenay-Malabry, France Email: denis.veynante@em2c.ecp.fr
ABSTRACT
In large eddy simulation (LES), the larger turbulent motions in a ow eld are explicitly computed when only the effects of the small ones are modelled. This approach is very well adapted to turbulent reacting ows which are generally dominated by such structures, especially when combustion instabilities occur. The instantaneous location of cold and burnt gases are then identied at the resolved scale level. As they may have very different characteristics in terms of turbulence, pollutant emissions or radiative heat transfers, this identication is expected to allow a better description of the ame / turbulence interactions. Nevertheless, models are still required to describe small scale effects and this approach is computationally expensive. To compare numerical results with experimental data is also a challenge. Despite of these difculties, very impressive results have already been achieved using LES in complex congurations.
ITNORUDTCNIObehave differently in terms of turbulence, radia-tive heat transfers or pollutant emissions. Then, a better description of turbulence / combustion Large eddy simulation (LES), where the larger interactions is expected. turbulent motions in a o w eld are explicitly computed whereas only the effects of the small Models are still required to describe small scale ones are modelled, has now reach a high level of effects even if their importance is reduced com-maturity for non reacting o ws [1–4]. This tech- pared to usual ReynoldsAveraged Navier-Stokes nique also appears to be well adapted to reacting (RANS) equation closures. Unfortunately, typi-o ws [5–7] as they generally exhibit large scale cal ame thickness, of the order of tenths of mil-motions [8]. LES gives access to unsteady phe- limetre, are smaller than practical grid meshes nomena that may control the overall system be- (burner sizes go from tens of centimetres for gas haviour: combustion instabilities, generally due turbines or combustion engines up to several me-to a coupling between hydrodynamics, heat re- ters for industrial furnaces). Combustion is then lease rate and acoustics waves [9] may lead to mainly a sub-grid scale phenomenon and adapted the burner destruction; cycle-to-cycle variations approaches have to be developed. Most models in internal combustion engines in uence com- extend the usual concepts devised to describe bustion ef cienc y and pollutant formation. From mean o w elds (mixing approach, ame sur-a modelling point of view, a decisive advantage face quanti cation or probability density func-of LES for combusting o ws lies in the identi - tions) [10] but new approaches take advantage cation, at the resolved scale level, of the instan- of the knowledge of the resolved scales (simi-taneous location of cold and burnt gases which larity models, dynamic formalisms where model
parameters are automatically adjusted during the simulation). LES also require larger computing resources than RANS but has already provide very good results even combined with quite simple models as shown below. Note also that LES experiences dif culty near walls but com-bustion processes generally take place far away from them. Table 1 brie y compares advantages and drawbacks of direct numerical simulation (DNS), large eddy simulation (LES) and RANS. Large eddy simulation is obviously a challenge for modellers and computing science but also for experimentalists: as computations provide re ned o w descriptions, ne experimental data are required for validation (three-dimensional time and spatially resolved velocity, temperature and mass fraction measurements are ideally ex-pected!). A precise comparison between numer-ical results and experimental data also require care. Basic principles of LES are rst brie y recalled. A main part is then devoted to subgrid scale com-bustion modelling. Some numerical aspects and comparison between experimental data and nu-merical results are brie y discussed before dis-playing some recent practical examples.
FILTERING AND BALANCE EQUATIONS
Resolved (i.e. larger scales) and unresolved o w motions are separated by convolution of any lo-cal quantityQsuch as velocity, mass fraction or reaction rate with the LES lterF[1]: Q(x, t) =ZQ(x0, t)F(xx0)dx0(1) V
with ZF(x)dx= 1 V
(2)
whereVis the domain volume. For reacting o ws, the lter operates usually in the physical space and corresponds to a weighted average over a given volume. A mass-weighted ltering is also introduced according to: ρ Qe(x, t) =ρQ=Zρ Q(x0, t)F(xx0)dx0(3) V
whereρdenotes the density. Equations for large eddy simulations are derived by ltering the in-stantaneous balance equations. This operation re-quires the exchange of ltering and derivative op-erators which is possible only under restrictive assumptions, for example when the lter size, generally implicitly linked to the mesh size, is constant. In general, this exchange introduces commutation errors [11,12], usually neglected. Filtered continuity, momentum and mass fraction balance equations read respectively, with usual notations [6]: e ∂ρ+ρui ∂t ∂xi= 0(4) ∂ρe+ρuexiieuj+xi[ρ tuj(uiujuiuej)] = g e ∂P ∂ ∂xjxτiji(5) + e e ρYtk+uρexiiYk+∂xihρuigYkueiYeki= ∂Jik+ ˙ωk(6) ∂xi Unresolved transport terms such asuigujeuieuj g e anduiYkeuiYk w motions lostdue to the o in the ltering operation, ltered viscous (τij) and molecular diffusion (Jik) ux es and ltered chemical reaction rates˙ωkhave to be modelled. Balance equations are formally similar in RANS and LES but their physical meaning is different. In RANS, mean quantities implicitly contain the