Sensitivity analysis of ultrasonics for measuring helium abundance and ortho-para hydrogen fraction

Helium abundance on Saturn remains a long-standing open question, limiting understanding of theories of planetary formation, and also holds relevance to atmospheric dynamics. Sensitivity analysis of an ultrasonic sensing technique for measuring helium abundance and ortho-para hydrogen ratio in mixtures of helium and hydrogen gas is presented. Ultrasound-based techniques using the speed of sound and absorption spectra of hydrogen–helium gas mixtures are a candidate for measuring helium abundance and hydrogen ortho-para fraction in the atmospheres of the giant planets, particularly Saturn and Uranus. In this work, a Jacobian-based sensitivity analysis of the sensor system was conducted. The speed of sound and absorption of various gas mixtures were obtained utilizing a theoretical model. These model predictions were used to estimate the partial derivatives (sensitivities) of the speed of sound and absorption with respect to the four parameters (temperature, pressure, helium abundance, and ortho-para hydrogen ratio) at 500 kHz and 1 MHz. The achievable speed of sound and absorption resolution were estimated from the repeatability of experimental values. A total of 16 different cases for different temperatures, pressures, and concentrations were investigated. At 500 kHz, the worst case measurement resolution achieved was 0.78% for helium abundance and 4.96% for an ortho-hydrogen fraction. At 1 MHz, these worst case resolutions were improved to 0.48% for helium abundance and 1.28% for an ortho-hydrogen fraction.