General method for determining the boundary layer thickness in nonequilibrium flows

Abstract

While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general non-equilibrium flows. In this work, a method is developed based on a local reconstruction of the "inviscid" velocity profile $U_I[y]$ resulting from the application of the Bernoulli equation in the wall-normal direction. The boundary-layer thickness $δ_{99}$ is then defined as the location where $U/U_I = 0.99$, which is consistent with its classical definition for the zero-pressure-gradient boundary layers (ZPGBLs). The proposed local-reconstruction method is parameter free and can be deployed for both internal and external flows without resorting to an iterative procedure, numerical integration, or numerical differentiation. The superior performance of the local-reconstruction method over various existing methods is demonstrated by applying the methods to laminar and turbulent boundary layers and two flows over airfoils. Numerical experiments reveal that the local-reconstruction method is more accurate and more robust than existing methods, and it is applicable for flows over a wide range of Reynolds numbers.