Effects of Vibrational Relaxation on Sonic Boom Waveforms in a Stratified Atmosphere

Abstract

This paper describes the effects of vibrational relaxation on sonic boom waveforms in a stratified atmosphere. Full-field direct simulations with vibrational nonequilibrium are performed over uniform and stratified atmospheres, extending from a supersonic body to the ground level. The governing equations are the three-dimensional Euler equations, combined with the conservation equations for vibrational energies of and . The translational–vibrational energy exchange is evaluated using the Landau–Teller rate model. The full-field simulations reproduce the Drop test for Simplified Evaluation of Non-symmetrically Distributed sonic boom (D-SEND) #1, by the Japan Aerospace Exploration Agency. The computational results show that weak shock waves at a moderate relaxation time are dispersed, and the rise time occurs. A wave structure in one relaxing mode is classified according to the relaxation time. The effects of two relaxing modes are comparable to those obtained from a superposition of each mode. For a stratified atmosphere, the effects of vibrational relaxation at each altitude are similar to those for uniform atmospheres at the same altitudes. However, a wave structure does not monotonically change toward the ground, unlike the case of uniform atmosphere. Such a complex transition mechanism of wave structure in real atmospheric environments is clarified.