Unsteady Force Calculations on Circular Cylinders and Elliptical Airfoils with Circulation Control

摘要

A numerical method is developed to study the unsteady circulation control aerodynamics of two-dimensional airfoils. Two cases of unsteadiness in flow are considered. The first case is the unsteadiness arising from an unsteady, periodic freestream and the second is the unsteadiness due to unsteady blowing momentum. A simple solution for the potential flow is obtained using conformal mapping. The changes due to the presence of the separated wake region behind the airfoil is calculated by distributing a set of source panels in the wake region along the surface. The source strengths are determined by using the condition of constant pressure at the control points and that the velocity at the separation points must be zero. The unsteady potential flow is assumed to be a periodic variation of the steady potential flow, in phase with the periodic freestream. The boundary layer flow is calculated by solving the unsteady boundary layer equations using an implicit finite difference method. The flow due to the wall jet is calculated from quasi one-dimensional flow upto the slot on the surface and further downstream the mixing shear layer is computed numerically as part of the boundary layer solution. The finite difference method uses backward differences whenever reverse flow is encountered. The potential flow and the boundary layer and wall jet calculations are combined in an iterative procedure to get a converged solution for the entire flow field. The solution provides the velocity and pressure fields which is used to determined the lift and drag forces under given freestream and jet momentum conditions. The pressure distribution obtained from the potential flow is used to calcualte the lift and pressure drag forces. The wall shear data obtained from the boundary layer flow gives the skin friction drag.Satisfactory correlation of predicted results with experimental data is achieved for steady lift over circular cylinders as well as elliptic airfoils.