An exact integral (field panel) method for the calculation of two-dimensional transonic potential flow around complex configurations

Abstract

SummaryAn exact integral formulation of the two-dimensional full potential equation is presented. The well developed standard surface panel method based on the linear Prandtl-Glauert equation is extended by means of sources in the field surrounding the configuration, allowing the calculation of transonic flows.A major attraction of the Field Panel Method is that solutions can be obtained using standard surface panelling together with a field grid which has no special form. The surface panels are used to satisfy the boundary conditions so that the field grid does not have to be surface-fitted which is a requirement for existing field methods. Further, the grid need only be in a region close to the configuration where nonlinear compressibility effects are non-negligible and need not extend to the far field as generally required. Grid generation is therefore trivial allowing solutions for arbitrary configurations. Convergence, especially for flows with shock waves, is enhanced by use of a modified Approximate Factorisation scheme. Results for single aerofoils are compared with Garabedian-Korn solutions and show good agreement; and to demonstrate the ease of grid generation, results for multicomponent aerofoils are also presented. Finally, an outline is given of how the method can be extended to threedimensions.The work was carried out in conjunction with the Department of Applied Mathematics, University of Leeds together with Procurement Executive, Ministry of Defence.