Calculation of compressible indicial response

The present paper addresses thr problem of extracting indicial response fun ctions from solutions of the Navier-Stokes equations. Two approaches are co nsidered. In the first, the indicial response is computed directly by modifying the l ocal grid velocity to reflect the step change in plunge velocity. The compu ted data are then fitted using an assumed form for the response function an d numerical optimisation techniques. In the second (indirect) approach, the general form of the lift transfer op erator is determined analytically from the functional form of the assumed r esponse. Using the lift transfer operator explicit solutions of the in-phas e and quadrature components of the normal force time history can be obtaine d. The unknown coefficients in the response function are then extracted fro m computed data for harmonic motion by fitting the time history using the e xplicit solution. Computed response functions are presented for a range of Mach numbers and a re compared with analytical results and indicial models currently used with in the rotorcraft community. For the cases considered there is no significa nt difference between the response functions determined using the direct or indirect approach. Comparison of the computed results with existing models suggests that generalisation of the response to step changes in incidence using a two-pole approximation of the circulatory response together with th e Prandtl-Glauert factor is not possible. However, comparison with higher o rder semi-empirical models is much improved, providing some justification f or the use of such models. In addition to these observations, the extracted response functions suggest improvements to piston theory to account for th ickness effects. The proposed modification of piston theory is based upon p roperties of the static pressure distribution and so can be used in conjunc tion with both CFD and experimental data.