Improved Potential Flow Computational Methods with Euler Corrections for Airfoil and Wing/Body Design

摘要

The development of two and three dimensional Euler correction methods based on the Clebsch transformation is described. In these methods, the velocity field is decomposed into irrotational and rotational parts. A multigrid full potential method based on both the finite difference and finite volume formulations is modified to solve for the rotational part. Two approaches are developed to solve for the rotational field. The approximate Euler-Clebsch approach assumes the entropy is convected along mesh lines, while the exact Euler-Clebsch approach solves the convection of entropy numerically along streamlines. The two approaches agree well in the airfoil application. Only the approximate Euler-Clebsch approach is employed in the three dimensional calculations. A study of finite difference and finite volume formulations of the full potential equation is also included. Solutions are presented for various airfoils, wings and an F-14 wing/body and are compared with results of the full potential and the time marching Euler methods.