Turbulence modeling effects on the prediction of equilibrium states of buoyant shear flows

The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field mode ls used include a two-equation closure, a Reynolds-stress closure assuming two different pressure-strain models and three different dissipation rate t ensor models. As for the thermal field closure models, two different pressu re-scrambling models and nine different temperature variance dissipation ra te (epsilon (theta)) equations were considered. The emphasis of this paper is focused on the effects of the epsilon (theta)-equation, of the dissipati on rate models, of the pressure-strain models and of the pressure-scramblin g models on the prediction of the approach to equilibrium turbulence. Equil ibrium turbulence is defined by the time rate of change of the scaled Reyno lds stress anisotropic tensor and heat flux vector becoming zero. These con ditions lead to the equilibrium state parameters, given by (P) over tilde/e psilon, (P) over tilde (theta)/epsilon (theta), R = (<(<theta>(2))over bar> /2 epsilon (theta))/(k/epsilon), Sk/epsilon and G/epsilon, becoming constan t. Here, (P) over tilde and (P) over tilde (theta) are the production of tu rbulent kinetic energy k and temperature variance <(<theta>(2))over bar>, r espectively, epsilon and epsilon (theta) are their respective dissipation r ates, R is the mixed time scale ratio, G is the buoyant production of k and S is the mean shear gradient. Calculations show that the epsilon (theta)-e quation has a significant effect on the prediction of the approach to equil ibrium turbulence. For a particular epsilon (theta)-equation, all velocity closure models considered give an equilibrium state if anisotropic dissipat ion is accounted for in one form or another in the dissipation rate tensor or in the epsilon -equation. It is further found that the models considered for the pressure-strain tensor and the pressure-scrambling vector have lit tle or no effect on the prediction of the approach to equilibrium turbulenc e.