Locally analytical prediction of the steady inviscid incompressible flow through an airfoil cascade

Abstract

A mathematical model and locally analytical solution technique are developed to analyze the steady, inviscid, incompressible, flow through a two-dimensional turbomachinery cascade comprised of cambered, thick, airfoils. The cascade is analyzed by considering a single flow channel. The boundary conditions require a zero velocity normal to the airfoil surfaces, the Kutta condition to be satisfied, and the inlet and exit flow from the cascade to be periodic. The flow field velocity potential is separated into circulatory and noncirculatory components, each individually described by a Laplace equation. A body fitted computational grid is utilized which permits grid points to be specified along the entire computational boundary and results in a smoothly spaced, nonoverlapping grid. General analytic solutions to the Laplace equations in the transformed computational plane are determined by separation of variables. Locally analytical solutions are then developed by applying these solutions to individual grid elements, i.e. the integration and separation constants are determined from the boundary conditions in each grid element. The complete flow field solution is then obtained by assembling these locally analytical solutions. The validity of this locally analytical solution and the flow modelling are then demonstrated by correlation predictions with data from various cascade experiments.