On Travelling Waves in Two-Phase Systems

Abstract

The propagation of travelling velocity waves in multiphase or disperse media results in concentration fluctuations and/or density variations. Peaks may occur connected with the generation of catastrophic events like collision shocks. Without any special interaction (forces) between the droplets or particles of the medium also steep wave fronts may develop. The exact solution of a one dimensional nonlinear equation of motion for such an interaction free multiphase medium explains many observations concerning concentration waves in two phase flow. Contrary to the exponential growth of instability waves in linearized flow the amplitudes of these concentration waves grow in such a manner that at a finite propagation distance infinite amplitudes occur for an initially weak sinusoidal disurbance. Influence of gravity or other volume forces can also be included in the equations and in the exact solution. This influence results in wave length variations during the propagation. As the described phenomena may occur in most two phase flows more or less pronounced these basic considerations are of some principal importance. Related experiments have been performed with a velocity modulated two phase spray of water droplets in air. The corresponding system was also treated theoretically. The exact solution of the one dimensional set of nonlinear equations of motion provides an insight into the kinematics of the travelling concentration waves. To illustrate the wave propagation for certain initial conditions Fig. 1 provides a visualisation of a computational simulation.