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

Abstract

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– f μ model of Park and Sung (Fluid Dyn. Res., 20 (1997) 97) is extended to a nonlinear formulation. The stress–strain relationship is derived from 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 f λ function. Emphasis is placed on the model performance on the truncated strain terms. The model performance is shown to be generally satisfactory.