Development of a mathematical model for propagation of ultrasonic waves in thick-walled cylinders in the presence of a thermal gradient - Case of axial scanning.

Investigation of variations in ultrasonic wave velocity and travel path in the presence of thermal gradient is essential for accurate ultrasonic testing of engineering components which are subjected to high temperatures. In this paper, a mathematical model is developed for calculation of the wave velocity and travel path in thick-walled hollow cylinders that are subjected to thermal gradients during axial scanning. The cylinder is assumed to be homogeneous, isotropic, and made from Structural steel. The independent variables are incidence angle, cylinder outer radius, and temperature of the cylinder's inner surface. The results obtained from the theoretical model indicate that the wave velocity and travel path are highly sensitive to inner-surface temperature of the cylinder. Moreover, at incidence angles much lower than critical angles (especially at low temperatures), the wave velocity is almost independent of the incidence angle and the travel path is very close to a straight line. However, as the incidence angle approaches one of the critical angles, the wave travel path considerably deviates from a straight line. An experimental setup was designed and built in-house for measuring the longitudinal wave velocity in a steel hollow cylinder in the presence of a thermal gradient. The preliminary experimental results were found to be in good agreement with theoretical results.