Improvement of the nonlinear eddy diffusivity model for rotational turbulent heat transfer at various rotating axes

This paper presents an improved turbulent heat transfer model for analysis of a turbulent heat transfer in a rotational wall-bounded shear flow. Since a turbulent heat transfer with rotation has often been encountered in physical or engineering problems, a turbulence model should be reconstructed to adequately predict a turbulent heat transfer with rotation. In order to predict turbulent heat transfer with rotation, models of both the velocity and thermal fields are needed. In the velocity field, the modified nonlinear eddy diffusivity for a momentum model (NLEDMM) was proposed to accurately predict rotational wall-bounded turbulent shear flows with arbitrary rotating axes. As for a thermal field, the turbulence model was only improved to predict a heated channel turbulent flow with spanwise rotation. Thus, a turbulence model, which can be applied in heated rotational turbulent shear flows with arbitrary rotating axes, should be modified. In order to improve the turbulent heat transfer model, the adequate data, which are used for evaluation of turbulence model performance are arranged by conducting direct numerical simulations in this study. Since there are few reports on streamwise and wall-normal rotating channel flows with heat transfer, DNSs are carried out under conditions of streamwise and wall-normal rotating axes. In the present study, based on our DNS databases of streamwise and wall-normal rotating channel flows, existing nonlinear two-equation heat-transfer turbulence models were evaluated. Using the results of this evaluation, we then improved the modeled expression of turbulent heat flux for heat transfer in flows with arbitrary rotating axes, i.e. a nonlinear eddy diffusivity for the heat model (NLEDHM) is proposed.