Experimental speed-of-sound data and a fundamental equation of state for normal hydrogen optimized for flow measurements

Abstract

Speed-of-sound measurements for normal hydrogen (n-hydrogen) in a temperature range between 273 K and 323 K were carried out using a cylindrical resonator at pressures from 1 MPa to 10 MPa and a dual-path pulse-echo system at pressures from 20 MPa to 100 MPa. The relative expanded uncertainties (k = 2) of the measurements range from 0.04 % to 0.08 %. Based on these measurements and data from the literature, a fundamental equation of state (EOS) was developed for the calculation of thermodynamic properties of n-hydrogen. It is expressed in terms of the Helmholtz energy with the independent variables temperature and density. Due to the fundamental nature of the Helmholtz energy, the equation can be used to calculate all thermodynamic properties from one mathematical expression. In contrast to typical EOS of this kind, the boundary conditions are somewhat more restricted. The relevant temperature and pressure ranges are limited to typical pipeline and storage conditions of gaseous hydrogen, including temperatures relevant for measurements with critical nozzles (140 K to 370 K with pressures up to 100 MPa). The computational speed for the implementation of the correlation in measurement sensors plays a superior role. Therefore, the equation is kept as short as possible, and exponents are of integer-kind. Most of the experimental data are still reproduced within their measurement uncertainties.