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

2330 Phys. Fluids, Vol. 15, No. 8, August 2003 Sheikhi et al.FIG. 4. Color Temporal evolution of the scalar with superimposed vorticity iso-lines top and the vorticity bottom fields for VSFDF with E /2 andN E 40 at several times.order moments without any statistical variability. Also, all ofthese moments show very little dependence on the values of E and N E consistent with previous FDF simulations. 7,9,16 Inthe presentation below we only focus on second-order moments.Specifically, the scalar-velocity correlations areshown since all other second-order SGS moments behavesimilarly.Figures 5 and 6 show the statistical variability of theresults for simulations with N E 40. It is observed that thesemoments exhibit spreads with variances decreasing as thesize of the ensemble domain is reduced. Figures 7–10 showthe sensitivity to N E and E . All these results clearly displayconvergence suggested by Eq. 30. As the ensemble domainsize decreases, the VSFDF results converge to those of LES–FD. Ideally, the LES–FD results should become independentof the MC results, as the latter become more reliable, i.e.,when (N E →, E →0). It is observed that best match isachieved with E /2 and N E 40. This conclusion is consistentwith previous assessment studies on the scalar FDF, 7,9and the velocity FDF. 16 All the subsequent simulations areconducted with E /2 and N E 40.D. Comparative assessments of the VSFDFThe objective of this section is to analyze some of thecharacteristics of the VSFDF via comparative assessmentsagainst DNS data. In addition, comparisons are also madewith LES via the ‘‘conventional’’ Smagorinsky 18,51 model:Downloaded 22 Sep 2004 to 140.121.120.39. Redistribution subject to AIP license or copyright, see http://pof.aip.org/pof/copyright.jsp