Full-Field Simulation for Sonic Boom Cutoff Phenomena

Abstract

This study describes an application of full-field, direct simulation in the entire domain involving the near-field around an aircraft, the far-field toward the ground, and the caustic region as an approach to investigate sonic boom cutoff phenomena. A flow field around an axi-symmetric paraboloid has been analyzed by solving three-dimensional (3D) Euler equations with a gravity term for considering atmospheric stratification with altitude. A solution-adapted grid is constructed to align the grid lines with front and rear shock-wave surfaces. The flight is assumed to have a speed of Mach 1.1 at an altitude of 10 km. This study presents the world's first successful numerical simulation for a 3D structure of cutoff phenomena. The results show that the incoming wave generated from the paraboloid is divided into an outgoing wave in the upward direction and an evanescent wave in the downward direction at the cutoff altitude by the diffraction effect. In the cutoff region, the sonic boom reaches the peak intensity by focusing the rays. The evanescent wave under the cutoff region is reduced rapidly. Moreover, the shape of the cutoff surface is obtained for sonic and lateral cutoffs.

Numerical analysis of linear wave propagation in the atmosphere with temperature gradient for Mach cutoff reproduction

“…Figure 10 shows the enlarged sound pressure distributions in the vicinity of the caustic at t = 352.63 s. In the figure, (a) shows the result calculated by the CE-FDTD method, and (b) shows the result by the CFD based on the two-dimensional Euler equation. 9) The color map for the CE-FDTD result is changed so as to have the same color tone with the CFD result, and the CFD result is reversed horizontally. In the results of the CE-FDTD method, striped patterns are generated behind the sound wave and the outline is blurred.…”

“…In this paper, the two-dimensional numerical approach to linear sound wave propagation in the atmosphere with temperature gradient is presented for Mach cutoff reproduction and evanescent wave prediction. In the numerical analysis of sonic boom propagation, the computational fluid dynamics (CFD) 9) or the nonlinear Tricomi method 10,11) have been applied. In these methods, however, it is difficult to implement velocity disturbance because the full-field analysis is required.…”

Propagation of classical and low booms through kinematic turbulence with uncertain parameters

“…Nevertheless, it remains a one way approximation. Finally, high fidelity models, directly solving the Euler equations (Sabatini and Bailly, 2015), have been applied to 3D boom simulations from the aircraft down to the ground (Yamashita and Suzuki, 2015). However, their high computational cost makes it difficult to perform a high number of runs, and thus to achieve the statistical approach required for propagation in a turbulent medium.…”

Numerical Simulation of Blast Wave Due to Meteorite Explosion in Stratified Atmosphere

“…6,15) However, it has been difficult to consider a realistic stratified atmosphere in a simulation for the following reason: The change in atmospheric pressure with altitude is assumed to be a discontinuity in the Riemann solver, which is often used for compressible CFD analysis, and the hydrostatic balance between gas pressure and gravitational force cannot be strictly maintained. 16) For this reason, simplified atmospheric models such as uniform atmospheres and isothermal atmospheres 6) have been used for direct simulation, although the difference in blast wave propagation between the real atmospheres and the simplified atmospheres has not yet been investigated. Thus, a simulation method considering real atmosphere is required to accurately evaluate the strength of the blast wave, and atmospheric effects should be investigated in detail.…”