Development of a nonlinear near-wall turbulence model for turbulent flow and heat transfer

A new nonlinear near-wall turbulence model is developed on the basis of realizability constraints to predict turbulent flow and heat transfer in strongly nonequilibrium flows. The linear k-ε-fμ model of Park and Sung (Fluid Dyn. Res., 20 (1997) 97) is extended to a nonlinear formulation. The stress-strain relationship is derived f om the Cayley-Hamilton theorem in a homogeneous flow. The ratio of production to dissipation (P_k/ε) is employed to solve an algebraic equation of the strain dependent coefficients. A near-wall treatment is dealt with by reproducing the model coefficients from a modified strain variable. An improved explicit heat flux model is proposed with the aid of Cayley-Hamilton theorem, which includes the quadratic effects of flow deformations. The near-wall asymptotic behavior is incorporated by modifying the λ function. Emphasis is placed on the model performance on the truncated strain terms. The model performance is shown to be generally satisfactory.