On condensation-induced waves

Abstract

Complex wave patterns caused by unsteady heat release due to cloud formation in confined compressible flows are discussed. Two detailed numerical studies of condensation-induced waves are carried out. First, the response of a flow of nitrogen in a slender Laval nozzle to a sudden addition of water vapour at the nozzle entrance is considered. Condensation occurs just downstream of the nozzle throat, which initially leads to upstream- and downstream-moving shocks and an expansion fan downstream of the condensation front. Then, the flow becomes oscillatory and the expansion fan disappears, while upstream and much weaker downstream shocks are repeatedly generated. For a lower initial humidity, only a downstream starting shock is formed and a steady flow is established. Second, homogeneous condensation in an unsteady expansion fan in humid nitrogen is considered. In the initial phase, two condensation-induced shocks are found, moving upstream and downstream. The upstream-moving shock changes the shape of the expansion fan and has a strong influence on the condensation process itself. It is even quenching the nucleation process locally, which leads to a renewed condensation process more downstream. This process is repeated with asymptotically decreasing strength. The repeated interaction of the condensation-induced shocks with the main expansion wave leads to a distortion of the expansion wave towards its shape that can be expected on the basis of phase equilibrium, i.e. a self-similar wave structure consisting of dry part, a plateau of constant state and a wet part. The strengths of the condensation-induced waves, as well for the Laval nozzle flow as for the expansion fan, appear to be in qualitative agreement with the results from the analytical Rayleigh–Bartlmä model.