An Integral Equation Method for Boundary Interference in a Perforated-Wall Wind Tunnel at Transonic Speeds.

摘要

The wind tunnel boundary interference at transonic speeds on a thin airfoil in a two-dimensional perforated-wall wind tunnel was determined. The interference was found by applying an integral equation method to the nonlinear transonic small disturbance equation including embedded supersonic regions with shock waves. The kernels of the ensuing integral equation were replaced by series approximations, and the integrals were evaluated in closed form. The iterative technique used to calculate the interference from the integral equation method is shown to converge rapidly, and the computing time for the integral equation method is typically an order of magnitude less than present numerical methods. As a special case, the integral equation method for a thin airfoil in free air was also examined. It was found that the introduction of a novel influence function yields, for the first time, a self-contained integral equation for a lifting airfoil. In addition, a systematic study of the classical assumption used to simplify the integral equation shows that the integral method can provide solutions in good agreement with results from the numerical methods.