Development of a Steady Potential Solver for Use with Linearized Unsteady Aerodynamic Analyses
The need for accurate and numerically efficient response predictions for vibrating turbomachinery blading has resulted in the development of linearized unsteady aerodynamic analyses for cascade flows. One such model is the linearized inviscid flow (LINFLO) analysis developed by Verdon and Caspar, (1982,1984). This model assumes that the unsteady flow can be represented as a perturbation of the underlying nonuniform mean flow. Thus, in order to predict the unsteady aerodynamic response of a cascade using this technique, the steady flow field must first be calculated. A full potential solver developed explicitly for use with the LINFLO analysis is described herein. The solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least-squares, finite-difference approximation to solve for the steady flow field. The difference equations are developed on a composite mesh which consists of a C-grid embedded in a rectilinear (H-grid) cascade mesh. The composite mesh is capable of resolving blade-to-blade and farfield phenomena on the H-grid, while accurately resolving local phenomena on the C-grid. The resulting system of algebraic equations are arranged in matrix form using a sparse matrix package and solved by Newton’s method.
Steady and unsteady results are presented for two cascade configurations, a high speed compressor, and a turbine with high exit Mach number. The compressor configuration is composed of airfoils having a NACA 6% thickness distribution superimposed on a circular arc camber line. The turbine cascade is the fourth standard configuration reported on by Bölcs and Fransson (1986).
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