Numerical investigation of homogeneous condensation in Prandtl–Meyer expansion flows

Abstract

The effect of heat addition induced by condensation of water vapor on Prandtl–Meyer flows is investigated numerically. Two configurations are considered to study the formation of the stationary waves and the movement of the oscillatory shocks caused by homogeneous condensation. One is a nozzle-shaped channel bounded by lower and upper walls, and the other is an upper unbounded corner expansion. For the first configuration, cases with a sharp corner and a rounded corner are compared to highlight the influence of the sharp corner, where the cooling rate is very large. The density variation in the zone near the corner is smoothed, and the influence on the flow structure caused by the sharp corner is very limited in the neighborhood of the sharp corner. For a relatively low initial saturation, the structures of the condensation shock in the numerical simulation agree well with the experimental results in the literature. The increase of the initial saturation makes the condensation shock move upstream, and eventually leads to an unsteady shock motion. The tendency is similar to that in the condensation process in nozzles. For the unbounded corner expansion, the wave structure forms a two-dimensional distribution. Multiple shock waves are observed in the numerical schlieren image, which are caused by a sequence of quenching (by the condensation shock) and rebuilding (by the Prandtl–Meyer expansion) of the condensation. This mutual interaction can also be recognized by the wavy shape of the nucleation rate distribution.