Analytical calculation and evolutionary regression method for isentropic exponent of hydrogen gas at the throat of critical nozzle

Abstract

As one of the most promising renewable energy resources, the hydrogen has been used in the fields such as aerospace, industry, and fuel cells. Critical nozzles are widely used for mass flow-rate measurement of high hydrogen gas, since the flow measurement process is not affected by its downstream flow disturbance. The flow rule of real hydrogen gas through a critical nozzle is complicated and the thermophysical property of hydrogen at the nozzle throat is vital to the accurate measurement of hydrogen flow. In this paper, based on explicit Helmholtz energy and entropy-enthalpy equations, the basic flow parameter and isentropic volume change exponent are analytically calculated. In addition, an accurate explicit equation is determined by the nonlinear regression analysis where the ways of selection, exchange and mutation derived from evolutionary algorithm are introduced to search for optimal population individual. The regression standard deviation is 0.0089%, mean residual deviation is 0.0285%, and maximum residual deviation is 0.1781%. The result shows that it not only can rapidly find the optimal solution which has the lowest number of equation items and the great overfitting suppression capability, but also has a high computation accuracy. This algorithm can also be applied to modeling flow characteristic parameters for every other flow device.