Nonlinear eddy diffusivity models reflecting buoyancy effect for wall-shear flows and heat transfer

Abstract

The main objective of this study is to construct new nonlinear eddy diffusivity models reflecting buoyant effects in wall-bounded turbulent shear flows and heat transfer. It is now well known that the turbulent heat-fluxes, which are the key quantities for the prediction of turbulent flows with buoyancy, are not modeled accurately by employing the conventional turbulence models using eddy diffusivities. In order to appropriately predict wall-bounded turbulent flows with buoyancy, an innovative turbulence heat-transfer model with eddy diffusivities which are composed of the k– ε two-equation model for velocity field and the k θ – ε θ two-equation model for thermal field, must be constructed. Consequently, we should improve the modeled expressions for Reynolds stresses and turbulent heat-fluxes reflecting the buoyant effect in wall-bounded turbulent shear flows. The existing two-equation turbulence models were evaluated on the basis of the DNS data of channel flows with buoyancy. Using the results of evaluation, we constructed new modeled expressions for Reynolds stresses and turbulent heat-fluxes in explicit algebraic models, and reconstructed the nonlinear two-equation turbulence models for the buoyancy-affected wall-shear flows and heat transfer, including the newly proposed nonlinear eddy diffusivity for a momentum model (NLEDM) and the nonlinear eddy diffusivity for heat model (NLEDHM). The proposed nonlinear two-equation turbulence models reflecting buoyancy effect appropriately predict wall-bounded turbulent shear flows with buoyancy given by DNS.