A New Approach in Cascade Flow Analysis Using the Finite Element Method

Abstract

A new approach in analyzing the potential flow past cascades and single airfoils using the finite-element method is developed. In this analysis, the circulation around the airfoil is not externally imposed but is directly computed in the numerical solution. Different finite-element discretization patterns, orders of piecewise approximation, and grid sizes are used in the solution. The results obtained are compared with existing experimental measurements and exact solutions in cascades and single airfoils. Nomenclature A = area of a finite element ( = contour length of a finite element n = normal unit vector N = shape functions defined over a finite element p = number of nodes associated with a finite element 5 = total number of finite elements having one or more nodes on one branch of the splitting boundary V = velocity vector Vn = velocity component normal to the exit station x,y = spatial coordinates T = circulation around a lifting body p = flow density = velocity potential