Turbulence Modeling Effects on the Prediction of Equilibrium States of Buoyant Shear Flows
Abstract
The effects of turbulence modeling on the prediction of equilibrium states of turbulent buoyant shear flows were investigated. The velocity field models used include a twoequation closure, a Reynoldsstress closure assuming two different pressurestrain models and three different dissipation rate tensor models. As for the thermal field closure models, two different pressurescrambling models and nine different temperature variance dissipation rate ∊_{τ}) equations were considered. The emphasis of this paper is focused on the effects of the ∊_{τ}equation, of the dissipation rate models, of the pressurestrain models and of the pressurescrambling models on the prediction of the approach to equilibrium turbulence. Equilibrium turbulence is defined by the time rate of change of the scaled Reynolds stress anisotropic tensor and heat flux vector becoming zero. These conditions lead to the equilibrium state parameters, given by ~ {P}/∊, \tilde{P}_{τ}/∊_{τ}, R /line{θ ^{2}/2} ǎrepsilon_{θ }/(k/ǎrepsilon), Sk/∊ and G/∊, becoming constant. Here, ~ {P} and \tilde{P}_{τ} are the production of turbulent kinetic energy k and temperature variance \overline{\theta^2}, respectively, ∊ and ∊_{τ} are their respective dissipation rates, 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 ∊_{τ}equation has a significant effect on the prediction of the approach to equilibrium turbulence. For a particular ∊_{τ}equation, all velocity closure models considered give an equilibrium state if anisotropic dissipation is accounted for in one form or another in the dissipation rate tensor or in the ∊equation. It is further found that the models considered for the pressurestrain tensor and the pressurescrambling vector have little or no effect on the prediction of the approach to equilibrium turbulence.
 Publication:

Theoretical and Computational Fluid Dynamics
 Pub Date:
 2001
 DOI:
 10.1007/s001620100036
 Bibcode:
 2001ThCFD..14..399Z