Ultrasonic measurement and methods for reconstruction of temperature fields for the use in bioreactors

When operating bioreactors, monitoring the process temperature is of great importance. Ultrasonic temperature measurement enables this without the need for sensors inside the bioreactor. The average speed of sound can be determined from the travel time of ultrasonic waves along the path of known length between a transmitter and a receiver positioned in the reactor wall. Due to the temperature dependence of the speed of sound, the average temperature along the path can be calculated from the average speed of sound. If this measurement is carried out for a sufficiently large number of measurement paths in a slice plane of the bioreactor, the temperature field in this plane can be reconstructed. In this article, a measurement setup for measuring temperature distributions is presented. Two different methods are then used to reconstruct temperature fields from the travel times measured with this setup. The first method is the Tikhonov regularization, which is widely used to solve inverse problems. The second method is derived from compressed sensing and can only be used under certain conditions. However, if these conditions are met, this method always provides better results than Tikhonov regularization. In addition to reconstruction results from measured travel times, results from simulated travel times are also presented.