Progress on Interacting Boundary-Layer Computations at High Reynolds Number
It is becoming increasingly clear that many viscous-flow problems involving separation can be handled with Prandtl boundary-layer equations which are allowed to interact through the displacement thickness with an outer inviscid flow. We will call this mod
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Progress on Interacting 80undary-Layer Computations at High Reynolds Number 1 R. T. Davis* and M.
J. Werlet
1 Introduction It is becoming increasingly c1ear that many viscous-flow problems involving separation can be handled with Prandtl boundary-Iayer equations which are allowed to interact through the displacement thickness with an outer inviscid flow. We will call this model the interacting-boundary-Iayer (IBL) model. The triple-deck (TD) theory of Stewartson [1.106J, Sychev [2.13J, and Messiter [2.96J, governing the small-separation 2 problem, contains no terms which are not inc1uded in the IBL model, and therefore the model is correct for at least the small-separation problem in a composite sense. In addition, the Sychev [2.13J and Smith [2.18, 2.97J theories ofincompressible massive separation indicate that up to and through separation, the triple-deck theory (and therefore IBL theory) holds if one has properly taken care of the downstream wake in the interaction model. The purpose of this paper is to examine so me of the existing techniques for solving the subsonic laminar and turbulent interacting-boundary-Iayer equations and to propose and demonstrate so me improvements. The first 1 This research was supported (for R.T.D.) by NASA under Consortium Agreement NCA2OR130-901 and ONR under NOOOI4-76-C-0364, and (for M.J.W.) by Naval Air System Command Contract N00019-80-C-0057. * Professor of Aerospace Engineering and Applied Mechanics, University of Cincinnati, Cincinatti, OH 45221. t Manager of Gas Dynamics and Thermophysics, United Technologies Research Center, East Hartford, CT 06108. 2 By small separations we mean those totally contained within the triple-deck structure.
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improvement consists of developing a method for incorporating the influence ofthe upstream and downstream (wake or nonwake) displacement-thickness effect on a strong (nonlinear) inter action region. The other improvements are related to the manner in which the IBL equations are handled in the stronginteraction region. Two methods are examined for coupling the Hilbert integrals (airfoil integrals) to the boundary-Iayer equations. The first is due to Carter [2.98J, and the second is a modification of the method proposed by Veldman [2.2]. In addition, methods for the numerical evaluation of the Hilbert integrals themselves are discussed. Also, an improved method is presented, for the inversion of the coupled set of equations (difference equations for continuity and moment um plus boundary conditions) which result at a given solution station. Finally, a new generalized coordinate system is demonstrated for separated flow calculations where classical surface-oriented coordinates are inappropriate. Several model problems are considered. The first set are laminar flows past a finite flat plate, an infinite flat plate with a depression-induced (CarterWornom trough [2.3J) separatio
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