General method for determining the boundary layer thickness in nonequilibrium flows

While the computation of the boundary-layer thickness is straightforward for canonical equilibrium flows, there are no established definitions for general nonequilibrium flows. In this paper, 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 delta(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. 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.