A NONLINEAR GEOMETRICAL ACOUSTIC MODEL FOR SONIC BOOM PROPAGATION

摘要

Sonic boom prediction is a typical multi-scale problem, since the pressure signature generated by the shock structure at the length scale of the aircraft, L, in the "near-field", is transmitted through the atmosphere a long distance away, of the order of 100L, to the "far-field". The propagation of the pressure perturbation is the most important aspect of the phenomenon: small amplitude nonlinear effects accumulate over long distances and distort the pressure signature significantly, giving rise to the coalescence of the pressure distribution into shocks and typically resulting in an asymptotic N-wave'. The goal of the present work is not to propose a new comprehensive theory of sonic boom propagation but rather to formulate an analytical model which can predict accurately, under limited conditions, the pressure signature on the ground in the vertical plane below an aircraft (where its sonic boom of maximum intensity lays, due to its minimum distance from the ground) in steady horizontal supersonic flight. To this aim, we propose to combine a revisited formulation of the nonlinear treatment of the pressure wave evolution due to Friedman and coauthors2 with the simplified calculation of its nonlinear distortion due to George and Plotkin', supplemented by the "area rule" for the shock waves formation; straightforward adaptations of the ray-tracing system obtained by Randall5 and ray-tube area calculated by Pierce and Thomas6 are then employed to complete the set of necessary equations, along with the standard atmosphere model. This combined method is simple and, although limited to a constant horizontal aircraft speed and a still atmosphere, allows a very accurate and efficient prediction of the boom propagation starting from a given pressure signature in the near-field.