New Frequency Parameter for Unsteady Aerodynamics

Abstract

A new frequency parameter that minimizes the number of points required to represent unsteady aerodynamics has been developed. The parameter expands the low range of the reduced frequencies where the aerodynamics vary rapidly and compresses the moderate to high frequency range into a finite domain. Four examples showing the general applicability of the parameter are presented. I. Background and Basis Aeroelastic analyses require unsteady aerodynamic coefficients at a large number of reduced frequency values (k). For transports the range of reduced frequency that must be accurately defined is from k=O to about k=1.0 (where k = and b is the reference semichord, u is circular frequency and V is freestream velocity). Because the computation of these unsteady coefficients is expensive, many aeroelastic programs rely on precomputed tables which are interpolated to determine the unsteady aerodynamics. An accurate representation of the aerodynamics requires a large number of entries in the table, particularly in the low k area, where the aerodynamics vary most rapidly. The cost of the computation and the need for accuracy, therefore, motivate the search for a parameter that would transform the reduced frequency scale in such a way as to minimize the number of unsteady aerodynamic calculations while retaining the required accuracy. The requirements on such a parameter may be sum