Abstract

Modelling and Numerical Simulation of Superboom Reflection at the Ground

P.L.Rendon Garrido, R.Marchiano, F.Coulouvrat (Laboratoire de Modelisation en Mecanique, Universite Pierre et Marie Curie, CNRS, Paris, France)

e-mail: rendon@lmm.jussieu.fr

Superboom, or sonic boom focusing, occurs during certain manoeuvres (sharp turns, low Mach flight, acceleration) of the aircraft, leading to amplification of ground pressures up to 2 to 5 times the primary boom. In the free-field, sonic boom focusing is modelled by the nonlinear Tricomi equation, which generalises catastrophe theory for fold caustics in the time domain to include nonlinear effects. Nonlinear effects are essential in predicting the amplitude of focused shock waves. This transonic (mixed elliptic & hyperbolic) equation is solved numerically by a new algorithm combining finite differences in the frequency domain to treat diffraction, and a shock fitting algorithm specially designed for handling complex waveforms with multiple shocks. However, to evaluate superboom noisiness, it is important to describe properly ground reflection, including finite ground impedance. Using asymptotic analysis, a new model has been derived. It shows that the incident and the reflected focused wavefields are described by two nonlinear Tricomi equations, coupled to one another by boundary conditions, including finite ground impedance. An estimation of the influence of impedance for different types of outdoor grounds on the amplification of sonic boom will finally be presented [work supported by the European Commission, contract G4RD-CT-2000-00398].

Section : 6