An analytical method for Wilson point in nozzle flow with homogeneous nucleating

Abstract

The prediction of properties at the Wilson point is the key to both theoretical and numerical researches of the condensation of pure vapor or moist gas by homogeneous nucleation. An analytical solution for position and flow properties of Wilson point in nozzle flow at low pressure was presented. This method is adopted the classical nucleation rate and the droplet growth rate by Young and based on Lagrangian momentum, energy and Clausius–Clapeyron equations. Compared with the rapid change of the heat release rate, the changes of many properties and parameters are reasonably simplified or ignored. In addition, the expansion rate coefficient obtained by Rayleigh line relationships was considered. The position of Wilson point and the corresponding properties can be efficiently and effectively found by this method, only with the given values of the nozzle geometry, inlet stagnation pressure and temperature. The analytical solution agrees well with the numerical results and the experiment by Wyslouzil. Finally, some important results about the variation tendency of the parameters were obtained to illustrate the power and contribution of the present method, which would be helpful to research in further theory, simulation and practice.