Turbulence Modeling of Channel Flow and Heat Transfer: A Comparison with DNS Data

In the present study, seven turbulence models based on Reynolds Averaged Navier-Stokes (RANS) equations have been used to justify their accuracy and suitability by comparing with direct numerical simulation (DNS) data of turbulent channel flow and heat transfer. The appropriate model is selected to reveal different flow and thermal statistics for various conditions. The flow inside the channel is assumed to be fully developed turbulent Poiseuille flow and uniform heat flux is applied at the top and the bottom walls of the channel. Finite element method is used to solve the governing equations in two-dimensional forms. Numerical simulation is carried out for different frictional Reynolds numbers (Reτ = 180, 395, 640 and 1020) and Prandtl numbers (Pr = 0.71, 5 and 10). Different turbulent statistics such as mean streamwise velocity, mean temperature and streamwise turbulent heat flux are calculated and compared with those of DNS data. Initially, it is found that, low Reynolds number k-ɛ model agrees quite well with DNS data for mean velocity profile during the convergence study. Further comparison of other turbulent statistics computed by this model with DNS data reveals that both first and second order statistics of thermal field converge quite well within certain tolerance.