A methodology termed the “filtered density function” (FDF) is developed and implemented for large eddy simulation (LES) of chemically reacting turbulent flows. In this methodology, the effects of the unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities. A transport equation is derived for the FDF in which the effect of chemical reactions appears in a closed form. The influences of scalar mixing and convection within the subgrid are modeled. The FDF transport equation is solved numerically via a Lagrangian Monte Carlo scheme in which the solutions of the equivalent stochastic differential equations (SDEs) are obtained. These solutions preserve the Itô-Gikhman nature of the SDEs. The consistency of the FDF approach, the convergence of its Monte Carlo solution and the performance of the closures employed in the FDF transport equation are assessed by comparisons with results obtained by direct numerical simulation (DNS) and by conventional LES procedures in which the first two SGS scalar moments are obtained by a finite difference method (LES-FD). These comparative assessments are conducted by implementations of all three schemes (FDF, DNS and LES-FD) in a temporally developing mixing layer and a spatially developing planar jet under both non-reacting and reacting conditions. In non-reacting flows, the Monte Carlo solution of the FDF yields results similar to those via LES-FD. The advantage of the FDF is demonstrated by its use in reacting flows. In the absence of a closure for the SGS scalar fluctuations, the LES-FD results are significantly different from those based on DNS. The FDF results show a much closer agreement with filtered DNS results.
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February 1998
Research Article|
February 01 1998
Filtered density function for large eddy simulation of turbulent reacting flows
P. J. Colucci;
P. J. Colucci
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4400
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F. A. Jaberi;
F. A. Jaberi
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4400
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P. Givi;
P. Givi
Department of Mechanical and Aerospace Engineering, State University of New York at Buffalo, Buffalo, New York 14260-4400
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S. B. Pope
S. B. Pope
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York 14853-1301
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Physics of Fluids 10, 499–515 (1998)
Article history
Received:
December 16 1996
Accepted:
September 29 1997
Citation
P. J. Colucci, F. A. Jaberi, P. Givi, S. B. Pope; Filtered density function for large eddy simulation of turbulent reacting flows. Physics of Fluids 1 February 1998; 10 (2): 499–515. https://doi.org/10.1063/1.869537
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