Velocity-scalar filtered density function for large eddy simulation of ...

Phys. Fluids, Vol. 15, No. 8, August 2003Velocity-scalar filtered density function2335FIG. 16. Cross-stream variations of some of the components of R¯ at t60.FIG. 18. Cross-stream variations of r¯ at t60.SDEs. These SDEs are discretized via the Euler–Maruyamma approximation. The consistency of the VSFDFmethod and the convergence of its MC solutions are assessedin LES of a two-dimensional 2D temporally developingmixing layer. This assessment is done by comparing the resultsobtained by the MC procedure with those of the finitedifferencescheme LES–FD for the solution of the transportequations of the first two moments of VSFDF. Byincluding the third moments from the VSFDF into the LES–FD, the consistency and convergence of the MC solution aredemonstrated by good agreements of the first two SGS momentswith those obtained by LES–FD.The VSFDF predictions are compared with LES resultswith the Smagorinsky 18 SGS model. All of these results arealso compared with direct numerical simulation DNS dataof a three-dimensional, temporally developing mixing layer.It is shown that the VSFDF performs well in predicting someof the phenomena pertaining to the SGS transport. Most ofthe overall flow features, including the mean field, the resolvedand total stresses as predicted by VSFDF are in goodagreement with DNS data. However, the model does requirethe input of three empirical constants. Also, the numericalimplementation of VSFDF is more expensive than the traditionalmodels. It may be possible to improve the predictivecapabilities of the VSFDF by two ways: 1 development ofa dynamic procedure to determine the model coefficients,and/or 2 implementation of higher order closures for thegeneralized Langevin model parameter G ij . 50 Future work isrecommended for development and application of the jointfiltered velocity-scalar mass density function VSFMDF toallow for LES of variable density flows with/or without thepresence of chemical reaction.FIG. 17. Cross-stream variations of some of the components of R¯ at t80.FIG. 19. Cross-stream variations of r¯ at t80.Downloaded 22 Sep 2004 to 140.121.120.39. Redistribution subject to AIP license or copyright, see http://pof.aip.org/pof/copyright.jsp