Euler code prediction of near-field to midfield sonic boom pressure signatures

A new approach is presented for computing sonic boom pressure signatures in the near field to midfield that utilizes a fully three-dimensional Euler finite-volume code capable of analyzing complex geometries. Both linear and nonlinear sonic boom methodologies exist, but for the most part rely primarily on equivalent area distri- butions for the prediction of far-field pressure signatures. This is due to the absence of a flexible nonlinear methodology that can predict near-field pressure signatures generated by three-dimensional aircraft geometries. It is the intention of the present study to present a nonlinear Euler method that can fill this gap and supply the needed near-field signature data for many of the existing sonic boom codes. UCH of the existing sonic boom prediction and opti- mization methods are based on the modified linear the- ory analysis originated by Whitham1 and extended by Walkden2 for lifting bodies. The linear methods have also been modified to include the effects of a stratified atmosphere.3 Other meth- ods have included a nonlinear Euler analysis using a modified method of characteristics that approximately accounts for three- dimensional effects.4^7 Several experimental studies8 and analytical studies9 have questioned the validity of linear methods in both analysis and design of configurations for low sonic boom as the freestream Mach number approaches 3. In the higher Mach number re- gime, strong shocks are generated which have significant higher order entropy production. These effects are totally neglected by the linear methods. These higher order terms are addressed by the quasiaxisymmetric nonlinear modified method of char- acteristics (MMOC).4"7 The drawback to the MMOC method is that it requires nonlinear near-field initial data to compute the far-field solution. The near-field initial data could be ac- quired by wind-tunnel tests. This is an expensive solution, and it is not clear whether wind-tunnel tests could even supply all of the needed parameters such as pressure, flow angularity, velocities, shock angles, etc., required by the nonlinear code. In the last decade, computational fluid dynamics (CFD) has matured tremendously due to the simultaneous development of fast algorithms to solve nonlinear flow equations and the tremendous advances in computer technology. The high-speed flow about complex three-dimensional geometries represen- tative of realistic aircraft can now be computed in a matter of minutes on present day supercomputers with grids con- taining from 100,000 to 500,000 mesh points. One such method to solve the Euler equations for high-speed flows is docu- mented in Refs. 10 and 11. This method uses a central dif- ference finite volume method in the crossflow planes, and an implicit upwind finite difference technique in the marching