Analytic equations for the Wilson point in high-pressure steam flow through a nozzle

An analytical method for the position and flow properties of Wilson point in high-pressure steam flow through a nozzle was presented. The thermodynamic properties of real gas and essential empirical equations at high-pressure for both superheated and supercooled steam were used to solve the position of Wilson point. Firstly, the analytic equation for the isentropic flow of real gas before Wilson point was built and a two dimensional bisection method was utilized for solving this nonlinear equation. And then, combining Rayleigh flow relationships, the position and properties of Wilson point can be efficiently solved by only giving the values of the nozzle geometry, inlet stagnation pressure and temperature. The algebraic solutions are well in agreement with high-pressure experimental data by Bakhtar. The relative deviations between calculation results and experimental data for three type nozzles are 0.09-0.56%, 0.09-0.57%, and 0.56-1.20% respectively. At last, a serial of isobaric and isothermal lines for the position of Wilson point were obtained to illustrate the power of this method. This analytic method contributes to the further research of theory, simulation and experiment at high-pressure steam flow.