Calculation of Unsteady Transonic Pressure Distributions by the Indicial Method

Abstract

A method for the rapid estimation of complete unsteady transonic pressure distributions is developed. The two key elements of this method are (1) the indicial method and (2) the strained coordinate technique. The indicial method permits the determination of the response of a system to an arbitrary schedule of perturbations once the response of the system to a step change in one of the perturbing variables (the indicial response) is known. The strained coordinate permits the movement of discontinuities in the solution (e.g., shock waves) to occur as the solution develops in time. Together, these two techniques provide detailed information on the time development of pressure distributions over an airfoil that is of use in aeroelastic applications such as control surface flutter and active control design. Examples of both oscillatory and transient perturbations are given, as well an example that demonstrates the potential of this method for aeroelastic tailoring and active control. In all cases, the agreement with more expensive finite-difference calculations is good, and the time savings is about an order of magnitude.