Analytical, simulation, and experimental verification of ultrasonic thermometry technique

Abstract

When an ultrasonic wave travels through a material, such as a rod, the propagation and reflection characteristics are a function of the medium properties. When a material is heated, its mechanical properties, density, and volume change with respect to the medium, and so does the speed of sound. By using ultrasonic waves, the difference in speed can be used to estimate the temperature of a solid material. This technique is known as ultrasonic thermometry. The central hypothesis is that the wave travels slower as the temperature increases. To explain the underlying scientific principles of the technique, we developed analytical methods for estimating the time delays associated with varying temperatures. Time delay curves were developed by repeating the procedure at various temperature values using the corresponding mechanical and thermal properties at those values. That is, young’s modulus, Poisson’s ratio, and the thermal expansion coefficient were considered based on the temperature values. Additionally, this study outlines a numerical study on the temperature dependence of ultrasonic waves propagating through a 304L stainless steel rod using COMSOL software. Numerical results concur with analytically derived estimations, showing a decrease in the wave propagation speed and the wave amplitude as the temperature changes between 20 °C, 100 °C, 300 °C, and 500 °C. The simulated time delays agree well with the analytical calculations, and the displacement–time curve shift occurs due to the mechanical properties and thermal expansion effect. To confirm the accuracy of the technique, additional experiments were conducted on physical samples of 304L stainless steel. However, the frequency was modified to 2.25 MHz to increase spectral resolution given the limited temperature range possible of 25 °C–130 °C. We conclude by indicating that, due to the high accuracy of the analytically derived equations, the equations and technique developed has the potential to be utilized for time delay curves of other metals, in addition to 304L stainless steel.