Flow characteristics of hydrogen gas through a critical nozzle

Critical nozzles are widely used in the flow measurement and can be used for mass flow-rate measurement of hydrogen gas. The effect of real gas state equation on discharge coefficient of hydrogen gas flow through a critical nozzle was investigated. The real gas critical flow factor was introduced which considers the effect of the real gas on discharge coefficient. An analytic solution of real gas critical flow factor of hydrogen gas calculated from the modern equations of state based on Helmholtz energy, over a wider range of temperature 150-600 K and pressure up to 100 MPa was presented. An accurate empirical equation for real gas critical flow factor was determined by the nonlinear regression analysis. The equation was in good agreement with the high-pressure hydrogen gas experimental data by Morioka and CFD solutions by Nagao and Kim. Using this equation, the discharge coefficient can be directly and accurately calculated. It indicates that the discharge coefficient of hydrogen gas should be comprehensively taken into consideration with stagnation temperature, stagnation pressure and nozzle throat diameter. A lot of detailed results about the effect of real gas state equation were obtained.