A Near-Wall Eddy Conductivity Model for Fluids With Different Prandtl Numbers

Abstract

Near-wall turbulence models for the velocity and temperature fields based on the transport equations for the Reynolds stresses, the dissipation rate of turbulent kinetic energy, and the temperature variance and its dissipation rate are formulated for flows with widely different Prandtl numbers. Conventional high-Reynolds-number models are used to close these equations and modifications are proposed to render them asymptotically correct near a wall compared to the behavior of the corresponding exact equations. Thus formulated, two additional constants are introduced into the definition of the eddy conductivity. These constants are found to be parametric in the Prandtl number. The near-wall models are used to calculate flows with different wall thermal boundary conditions covering a wide range of Reynolds numbers and Prandtl numbers. The calculated Nusselt number variations with Prandtl number are in good agreement with established formulae at two different Reynolds numbers. Furthermore, the mean profiles, turbulence statistics, heat flux, temperature variance, and the dissipation rates of turbulent kinetic energy and temperature variance are compared with measurements and direct numerical simulation data. These comparisons show that correct near-wall asymptotic behavior is recovered for the calculated turbulence statistics and the calculations are in good agreement with measurements over the range of Prandtl numbers investigated.