Lateral cutoff analysis of sonic boom using full-field simulation

Abstract

This paper describes the world's first successful simulation for lateral cutoff phenomena of sonic boom far from the flight path due to variation in atmospheric temperature with altitude. A flow field around an axi-symmetric paraboloid has been analyzed by the full-field simulation method that solves the three-dimensional Euler equations with a gravity term to create a horizontally stratified atmosphere. A solution-adapted structured grid is constructed to align the grid lines with the front and rear shock-wave surfaces in the entire domain, including the near field around a supersonic body and far field reaching the ground beyond lateral cutoff. The flight is assumed to have a speed of Mach 1.2 at an altitude of 10 km, and the computational domain ranges over a distance of 30 km from the axis of symmetry. The computational results show that the evanescent wave in the shadow zone beyond lateral cutoff decays exponentially and changes into a progressive rounding waveform. The characteristics of the waveform transition are in good agreement with those observed in the flight tests. Therefore, the full-field simulation is recognized as a promising approach for investigating sonic boom strength in the full extent of sonic boom noise, including lateral cutoff and evanescent waves. Moreover, the computational results clarify that sonic boom focusing occurs above the ground, except for the vicinity of the ground, and the focusing strength along the lateral cutoff curve detected from the three-dimensional shock-wave surface increases with altitude. The results of ray tracing analysis collaborate the reasonability of the simulation results, and the caustic of downward convex agrees well with the lateral cutoff curve. In the shadow zone, the magnitude of exponential decay increases with altitude, and the lateral distance where the pressure rise decreases rapidly shortens with altitude.