Direct Numerical Simulation of a Turbulent Channel Flow with a Spanwise Temperature Gradient : Examination on the Turbulence Statistics

Abstract

Direct numerical simulation was performed for a turbulent channel flow where the time mean temperature has a spanwise gradient. As the first step of succesive investigations, turbulence statistics related to the spanwise heat transfer were examined. A computational code based on the finite difference scheme was developed for this purpose. The calculated statistics on the flow field were found to be in good agreement with the result of the existing direct numerical simulation by Kasagi et al. (1992). The eddy diffusivity ratio, ε_nz/ε_m and the Reynolds normal stress ratio, (ω²)^^^-/(υ²)^^^- show rapid increase toward the wall, as pointed out by Maekawa et al. (1991). However, the rapidincrease region of the ε_nz/ε_m was nearer to the wall than the Maekwa's result and found to roughly agree with that of the (ω²)^^^-/(υ²)^^^-. This result implies that, in the near-wall region, the spanwise turbulent heat flux per its production rate shows rough agreement with the wall-normal turbulent heat flux per its production rate. In addition, two point correlation coefficient, Q_wθ also agrees with Q_vθ in the range of y⁺<75. In these points, the heat transfer in the present case has some analogy with that in the heated-wall case. Moreover, the budget of the spanwise turbulent heat flux was examined. It was found that the budget shows near local equilibrium except for the near-wall region.