Simultaneous method for calculating interacting boundary layers using a solid body mode

1995 by Paul G. A. Cizmas Published by the American Institute of Aeronautics andAstronautics, Inc. with permission. A viscous-inviscid interacting procedure valid for computing steady and unsteady low Mach number viscous flows is proposed. The viscous region is modeled by Prandtl's boundary layer equations using a differential formulation. The inviscid region is modeled by the full potential equation and discretized using a variational finite element method. The two regions are simultaneously coupled through the requirement that the edge velocities of the two regions be equal. Also, the outer flow computational domain is deformed so that the edge of the inviscid region is displaced from solid walls and wakes a distance equal to the displacement thickness of the boundary layer. For unsteady flows, the unsteady flow is decomposed into a nonlinear mean flow plus a linear harmonically varying unsteady flow. The nonlinear mean flow equations are solved using Newton iteration. The resulting mean flow solution is then used to form the coefficients of the linearized unsteady equations, which are solved using LU decomposition. Results are presented for channel and cascade flows that exhibit strong interaction between the viscous and inviscid regions. In the case of unsteady flows, the method is able to compute the motion of the separation and reattachment points.

Simultaneous method for calculating interacting boundary layers using a solid body mode Conference Paper