SCAMP: Application of Nonlinear Progressive-wave Equation to Sonic Boom Transition Focus

Abstract

The Nonlinear Progressive-wave Equation (NPE) is one of three numerical models of focused sonic boom prediction being validated as part of the Superboom Caustic Analysis and Measurement Project (SCAMP). Formulated in the time domain, the NPE begins with a far-field acoustic signature and propagates it into the region with caustics, accounting for nonlinear steepening, refraction, dissipative processes, and narrow-angle diffraction. Proper initialization of the NPE requires scaling the sonic boom signature to a rippled wavefront that will generate the desired caustic curvature as it propagates. Details of the scaling and its limitations are described. Numerical results corresponding to SCAMP flight conditions are compared with measurements and results for low-boom conditions are presented. Nomenclature = acoustic pressure = ambient density ! = ambient sound speed eff = effective dissipation coefficient for weak shocks in air = propagation direction of computational domain = transverse spatial coordinate of computational domain = parameter of acoustic nonlinearity wf , wf = parameters describing ripple shape of initial sonic boom wavefront sh = peak amplitude of sonic boom signature ! = length of sonic boom "N" wave ! = radius of curvature of focusing caustic = nonlinear parameter in Tricomi scaling = diffraction layer thickness in Tricomi scaling = ratio of specific heats

SCAMP: Application of PCBoom to Measured Sonic Boom Focus Analysis

“…Those irregularities were at a scale inconsistent with the smooth gradient requirements of ray tracing. Smoothed modeling of atmosphere and flight data eliminated the artifacts, and provided a reliable interface to the lossy nonlinear Tricomi equation (LNTE) 12 and Nonlinear Progressive wave Equation (NPE) 13 methods. The success of those methods, using the PCBoom inputs presented in this paper, are presented in References 12 and 13.…”