Acceleration waves in condensing gases

Abstract

The flow of a condensing gas is treated as a two-phase-flow, in which the size of the condensate-droplets may vary due to transfer of mass, momentum, and heat; the formation of new droplets is disregarded. An ordinary differential equation for the temporal variation of the amplitude of a one-dimensional acceleration wave is deduced, which holds along the path of the wave. Especially, if the wave propagates into a mixture at rest with spatial variation of the volume fraction of the droplets, the variation of the amplitude is given by the sum of three terms, one of which is quadratic in the amplitude and the others are linear. The quadratic term is solely determined by nonlinear effects in the pure gas and leads to a growth. The first linear term is given by the dissipative effect of the velocity relaxation; this term is the same as for the flow of a mixture of a gas and small solid particles. The second linear term is determined by the combined dissipative effects of the temperature relaxation and the mass transfer; both linear terms lead to a decay. Further, conditions are discussed, on which shock waves are formed.