Viscous/inviscid Interacting Shear Flow Theory with Inferences and Their Applications to CFD

Abstract

In the viscous/inviscid interacting shear flow(ISF) theory, interacting shear perturbed flow(ISPF) theory and interacting shear turbulent flow(ISTF) theory suggested by Gao, the ISF consists of viscous shear layer and neighboring outer inviscid flow, which interact each other. The motion laws, definition and governing equations of the above three flows are described in ISF's optimal coordinates, which is a fitted dividing flow surface orthogonal coordinates. The scaling laws of velocity and length of ISF's viscous layer are deduced the scaling laws imply the strength of viscous/inviscid flow interaction. The scaling laws of velocity and length of both ISPF's viscous perturbed layer and ISTF's viscous turbulent layer are also given. The equations governing ISF are the Parabolized Navier-Stokes(PNS) equations, which can be simplified further on the dividing surface. The resultant equations are defined as dividing flows surface criteria, whose two important special cases are wall-surface criteria for viscous and inviscid flows. The ISF's optimal coordinates and length scaling law are used to design the grid. The small scale structures given by the scaling laws can be used to predict local sudden changes of heat flux etc., which are very important for hypersonic flows. The wall-surface criteria are used to validate NS numerical solutions for ISF and flow near walls. The wall-surface criteria method has several advantages over the commonly used grid convergence criteria. The applications of ISF theory indicates its effectiveness and further studies and development are needed.