An analytical solution for the Wilson point in homogeneously nucleating flows

The calculation of conditions at the Wilson point is the key to both theoretical and numerical studies of the condensation of pure vapours by homogeneous nucleation. Nucleation and droplet growth occur in a very short period of time, during which the changes of many vapour properties due to the normal thermofluid dynamic processes are negligible compared with the change of the heat release rate. This feature is exploited in an analysis leading to all approximate solution for the maximum subcooling and other properties at the Wilson point. The analysis is general but attention is focused on the main application of interest, which is the condensation of steam in high-speed flows by homogeneous nucleation. Crucial approximations are justified over a wide range of steam pressures and the analytical results reveal the dependency of steam properties at the Wilson point on controlling parameters such as the rate of pressure decrease. A direct link is established between the steam properties at the saturation point and those at the Wilson point, which, when used in multidimensional condensation flow calculations, should remove the need for very fine meshes and excessive computing resources which are otherwise required.