On Developments of k-τ and k-ω Models for Near-Wall Turbulence of Engineering Duct Flows

The performance of a modified k-tau model is assessed in predicting the turbulent flow and forced convective heat transfer in ducts with arbitrary cross-sections, under fully developed conditions. The presented model is based on more physical grounds using bounded time-scale, local turbulent Reynolds number, a dynamic C-mu (accounts for variation of C-mu) and dynamic coefficients for the Reynolds stress tensor representations, instead of constant values in common modeling procedures. Because all the key coefficients have dynamic behavior and vary due to local turbulence character, the model is found to be stable and superior to the traditional k-epsilon model. In addition, due to dynamic coefficients and bounded time-scale, the model can be used for a large number of Reynolds numbers, both high and low Reynolds numbers. The presented k-tau model alleviates the major problem of the k-epsilon model namely, the lack of natural boundary conditions. Based on idea of Kolmogorov time-scale a boundary condition at the wall is also proposed. A bounded k-omega model for near wall turbulence is also presented and comparison with other well established two-equation models (k-epsilon model and Wilcox k-omega model) are also made to validate the performance of the presented model in duct flows.