Edge Behavior of the k-ε Model in Boundary Layers: Analysis and Improvement

Abstract

We examine the outer-edge behavior in a turbulent boundary layer (TBL) predicted by the [Formula: see text] model with reference to a mathematical analysis of Cazalbou–Spalart–Bradshaw (CSB) (Physics of Fluids, Vol. 6, No. 5, 1994, pp. 1797–1804). Particular attention is given to one-dimensional analyses at the edge of the turbulent region. An inverted parabola analysis demonstrates that the correct edge behaviors of [Formula: see text], [Formula: see text] and [Formula: see text] are reproduced for both high- and [Formula: see text] models. For a ramp analysis following CSB (involving the velocity field), a set of diffusion coefficients for [Formula: see text] [Formula: see text] that violates the CSB constraint, however, yields an unrealistic velocity profile at the interface between the turbulent and nonturbulent regions due to the excessively small turbulent diffusion. We therefore propose improved diffusion coefficients by considering both the CSB constraint and requirements in wall turbulence, and calculate a range of two-dimensional aeronautical flows with [Formula: see text] to clarify if the one-dimensional analyses support the predictions in realistic flows, fully coupled with the velocity field. Indeed, the corrected diffusion coefficients provide reasonable predictions for both the channel and TBL but also TBLs involving turbulent separation when [Formula: see text] becomes large. Over an airfoil, the correction improves the prediction for [Formula: see text] by a few counts.