Numerical Simulation of Diffracted U-Shaped Sonic Boom Waveform

U-shaped sonic booms associated with the dive maneuver of a supersonic vehicle are numerically simulated in this paper. Usual prediction tools for ordinary sonic booms are not suitable for such a waveform because of the breakdown of geometrical acoustics near the caustic. In this paper, nonlinear Tricomi equation approach is used near the caustic to take diffraction into account, whereas augmented Burgers equation analysis is applied away from the caustic where geometrical acoustics is applicable. The U-shaped waveforms predicted by this method are in good agreement with measured data. The effects of atmospheric turbulence are also considered by replacing one-dimensional analysis using augmented Burgers equation with multidimensional wave propagation analysis near the ground surface. Results with the atmospheric turbulence effects show better agreement with measured U-shaped waveform than ones without such effects. It is also found that the amplitude of the tail shock wave, which is much larger than the front shock wave, is more sensitive than the front shock to atmospheric turbulence.