Weakly nonlinear gas oscillations in air-filled tubes; Solutions and experiments

The results of a theoretical and experimental investigation into the nonlin ear, planar propagation of an acoustic signal in a cylindrical air-filled t ube is presented. Assuming weakly nonlinear propagation and the distance of propagation smaller than the shock formation distance, the validity of the generalised Burgers' equation is analysed. The theoretical study is based on a dimensional analysis of the conservation equations followed by a calcu lation using asymptotic expansions. The deduced generalised Burgers' equati ons are solved whatever the boundary conditions are, with a numerical-finit e-difference method and using a harmonic balance method. Two cases are inve stigated experimentally: the purely progressive case, and the standing wave with an unknown termination. The results are compared successfully with th eoretical predictions on the three first harmonics of a periodic signal in a high degree of accuracy, when the effects of the thermoviscous dissipatio n and of the non-linear propagation have the same order of magnitude.