A New Composite Wall Function for Adverse Pressure Gradient Flows

Abstract

This paper presents a composite wall function, which can be used for a wide range of the adverse pressure gradient (APG) and is derived from the composite wall-law provided in this study. The composite wall-law combines the characteristics of the log-law and the half-power law under the APG, and it degrades to the log-law under the zero pressure gradient (ZPG). A function relationship between the parameters in the composite wall-law and the dimensionless pressure gradient parameter $\mathcal{p}^+$ is provided based on a series of DNS data for the APG. Finally, a generalized wall function incorporating both the viscous sublayer and the buffer layer is presented. The new wall function can accurately predict the mean velocity of both equilibrium and nonequilibrium flows under the APG. The new composite wall function is validated using three test cases: NACA0012, 2D channel with a bump, and turbulent separation bubble. The results demonstrate the accuracy of the new composite wall function under the APG flows.