The existence of back pressure will cause shock wave in the Laval nozzle of the supersonic separator, which will lead to the condensed droplets to evaporate and reduce the separation efficiency of the separator. It is of great significance to determine the shock position and avoid the secondary evaporation of droplets for improving the separation efficiency. In this paper, one-dimensional isentropic flow function method was used to calculate the shock position in nozzle. A mathematical model of methane-water vapor was established. The results show that the pressure energy recovery leads to the shock wave. With the increase of energy recovery efficiency, the position of shock wave moves to the throat, which shortens the droplet growth space and reduces the liquefaction of Laval nozzle. When the pressure energy recovery efficiency is 56.25%, the liquid mass fraction is 1.63% at the outlet. The shock wave position error of theoretical calculation and numerical simulation increases with the enlargement of divergent angle when considering condensation. The average error between numerical simulation and theoretical calculation results was less than 5%, thus the one-dimensional isentropic flow function method can provide a theoretical basis for predicting the shock position.

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