A unified approach to an augmented Burgers equation for the propagation of sonic booms

Abstract

Nonlinear propagation through a relaxing atmosphere of pressure disturbances extracted from a computational fluid dynamics (CFD) solution of the flow around a supersonic aircraft is simulated using an augmented Burgers equation. The effects of nonlinearity, geometrical spreading, atmospheric inhomogeneity, thermoviscous attenuation, and molecular vibration relaxation are taken into account. The augmented Burgers equation used for sonic boom propagation calculations is often solved by the operator splitting method, but numerical difficulties arise with this approach when dissipation is not effective. By re-examining the solution algorithms for the augmented Burgers equation, a stable method for handling the relaxation effect has been developed. This approach can handle the Burgers equation in a unified manner without operator splitting and, therefore, the resulting scheme is twice as fast as the original one. The approach is validated by comparing it with an analytical solution and a detailed CFD of dispersed plane wave propagation. In addition, a rise time prediction of low-boom supersonic aircraft is demonstrated.

JAXA's S4 Supersonic Low-Boom Airliner – A Collaborative Study on Aircraft Design, Sonic Boom Simulation, and Market Prospects

“…In order to estimate sonic boom loudness on the ground, the near-field pressure signature calculated with the hybrid CFD analysis is modified by the multi-pole analysis (MPnoise [5]) with 20 poles. And it is propagated with the atmospheric propagation code (Xnoise [6,7]) to obtain the ground signatures including a ground reflection factor of 1.9. The sampling rate is 48 kHz.…”

Computational Modeling of Meteor-Generated Ground Pressure Signatures

“…The evolution of the waveform as it descends to the ground is modeled through use of the augmented Burgers' equation. [42][43][44][45] In dimensionless form, the equation is given by…”

Characterization of absorption and non-linear effects in infrasound propagation using an augmented Burgers’ equation

“…The viscous term is computed with a standard second-order centred scheme. Vibrational relaxation effects are calculated using the technique recently proposed by Yamamoto et al (2015). The relaxation term (12) is rewritten in the form (Pierce 1985)…”

“…Similar approaches for long-range infrasound propagation can be found in Gainville et al (2006Gainville et al ( , 2010 and Lonzaga et al (2015). Sonic boom propagation has also been extensively studied using non-linear ray theory (Rogers & Gardner 1980;Cleveland 1995;Rallabhandi 2011;Yamamoto et al 2015).…”

“…Acoustic shocks are handled using a shock-capturing procedure based on low-order filtering (Bogey et al 2009), with a new specific shock detector (Sabatini et al 2016). Vi- brational relaxation is finally taken into account using the analytical technique recently proposed by Yamamoto et al (2015).…”