Viscous-Inviscid Interaction with Higher-Order Viscous-Flow Equations

The partially-parabolic, or parabolised, Navier-Stokes equations for laminar flow, and the corresponding Reynolds equations for turbulent flow, are coupled with an inviscid-flow solution procedure to develop a viscous-inviscid interaction method which can be used three-dimensional flows which cannot be treated by means of the classical boundary-layer equations. Potential applications of such a higher-order matching procedure include thick layers wakes, wall jets, solid-solid and solid-fluid corners. This report provides a detailed overview of the approach for general 3-D flows and presents the results of applications to some simple test cases. The Reynolds equations are derived in nonorthogonal curvilinear coordinates, with velocity components along the coordinate directions, using vector techniques. This approach differs from the commonly-used tensor method but serves to establish a connection with the more familiar boundary layer methods. The k-epsilon model is used for turbulent flows. The partially-parabolic viscous-flow equations are solved using an implicit finite-difference scheme and the SIMPLER algorithm for pressure- velocity coupling. The inviscid-flow solutions are obtained with a conforming panel, source-panel method. Interaction between the viscous and inviscid regions is accounted for using the displacement-body concept.