Speed of Sound Measurements in Helium at Pressures from 15 to 100 MPa and Temperatures from 273 to 373 K

Abstract

The speed of sound in helium was measured along five isotherms in a temperature range from 273 to 373 K at pressures from 15 to 100 MPa with a relative expanded uncertainty (k = 2) from 0.02 to 0.04%. A dual-path pulse-echo system was utilized to conduct these measurements. The data were compared with the reference equation of state developed by Ortiz Vega et al. At pressures up to 50 MPa, relative deviations were within the uncertainty of our measurements, while, at higher pressures, increasing negative deviations were observed up to -0.26%. We also compared the results with predictions based on the virial equation of state correct to the seventh virial coefficient, using the ab initio virial coefficients reported recently by Gokul et al., finding agreement to within the experimental uncertainty at all investigated states.

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

“…The expanded uncertainty was calculated considering a coverage factor of k = 2. The dual-path pulse-echo technique is very well established for measurements of the speed of sound in the liquid phase [19][20][21] but can also be used for measurements in the gas phase if the acoustic impedance of the gas is high enough [22][23][24]. The measurement setup used in this work was already applied for measurements in liquid n-pentane [25] and recently in gaseous helium [24].…”

“…The dual-path pulse-echo technique is very well established for measurements of the speed of sound in the liquid phase [19][20][21] but can also be used for measurements in the gas phase if the acoustic impedance of the gas is high enough [22][23][24]. The measurement setup used in this work was already applied for measurements in liquid n-pentane [25] and recently in gaseous helium [24]. Wedler and Trusler [24] have shown that the system is capable of measuring the speed of sound in helium, a gas with a high speed of sound and a low acoustic impedance, with an expanded relative uncertainty from 0.03 % to 0.04 %.…”

“…The measurement setup used in this work was already applied for measurements in liquid n-pentane [25] and recently in gaseous helium [24]. Wedler and Trusler [24] have shown that the system is capable of measuring the speed of sound in helium, a gas with a high speed of sound and a low acoustic impedance, with an expanded relative uncertainty from 0.03 % to 0.04 %. As they described the setup in detail, the system and the measurement procedure are only briefly outlined here.…”

“…The transducer was located off-center in axial direction to ensure different distances from the transducer to both ends of the cylindrical cell. Wedler and Trusler [24]. The speed of sound in nitrogen was calculated from the EOS of Span et al [26].…”

“…The influence of temperature and pressure differences between the calibration measurements and the measurement in n-hydrogen on ΔL was accounted for by considering the mean thermal expansion α and the compressibility β of the Invar alloy. Details on this can be found in Wedler and Trusler [24]. The resonator was designed in a way that the same pressure vessel as used for the pulse-echo system could be used, including measurement and control of pressure and temperature.…”