High-amplitude thermoacoustic flow interacting with solid boundaries

Abstract

Thermoacoustics concerns phenomena in which an interaction of acoustics with thermodynamics takes place. In an acoustic wave the gas parcels always undergo temperature variations, which is a consequence of their compression and expansion. In adiabatic sound waves these temperature variations go unnoticed. However, when a solid is present near the acoustic wave, the wave interacts with the solid and can cause a transfer of heat from one location in the solid to another. This is called the thermoacoustic heat-pumping effect. This effect is the driving mechanism in stack-based coolers and heat pumps. Vice versa, when a sound wave interacts with a solid with a temperature gradient above a certain critical value, the temperature gradient enhances the sound wave. One of the major disadvantages of thermoacoustics is that the power density of acoustic waves is relatively low. One way to increase the power density is to use higher drive ratios. Unfortunately the linear theory of thermoacoustics is only valid at low amplitudes (drive ratios up to 5%). Nonlinear effects that are not taken into account by the linear theory include vortex shedding at the ends of a stack, dissipation at the ends of a stack due to the sudden change in cross section, transition to turbulence in-between plates, and streaming. The objective of this PhD work is to gain a better understanding of different phenomena that are occurring in thermoacoustic devices with an emphasis on nonlinear effects, that occur at high amplitudes. Thermoacoustics is a complicated but also very interesting phenomena, since three fields of research, i.e. acoustics, flow dynamics, and thermodynamics all come together and all of them bring different key quantities, i.e. pressure, velocity, and temperature. To gain a better understanding of different phenomena that are occurring in thermoacoustic devices we have measured, calculated, and studied all three quantities. In order to measure the pressure, three microphones were installed in the resonator on each side of the stack. Following the multi-microphone method, we determined the acoustic-energy flows at both sides of the stack. The found difference between the acoustic-energy flows at both sides of the stack equals the energy absorbed by the stack. We have been able to show that at low amplitudes the absorbed energy is in good agreement with the linear theory of thermoacoustics. Unfortunately at high drive ratios the linear theory underestimates the energy losses in the stack, which is mainly caused by minor losses at the two stack ends. Furthermore, the multi-microphone method is used to determine the transfer matrix of a stack. These transfer-matrix elements are employed to determine the Rott functions as functions of the frequency, which we found to be in good agreement with analytical fits. A flow visualization technique called PIV is used to measure the velocity. By determining the displacement of very small oil droplets (typically 1 µm in diameter) that move along with the gas during a short time interval (typically 1 µs), a velocity vector field is determined. Even using a measurement window as small as 3 mm x 2 mm, a velocity vector field of 100 x 75 vectors can be obtained, during a time interval as small as 0.1 µs. Moreover, the powerful PIV technique is used to study the vortex shedding behind the plates of a parallel-plate stack, the velocity profile in-between two parallel plates, and a time-average velocity, called streaming velocity. The velocity profiles in-between two plates show a change in phase dependency when above a critical Reynolds number, indicating a transition from laminar to turbulent flow. In order to register the stack temperature profile as a function of time, we installed 32 thermometers in a stack plate. Furthermore we made a model of the energy balance of the stack. The calculated temperature profiles as functions of time were found to be in good agreement with the temperature measurements. We have used different measurement techniques, microphones, thermometers, and PIV, to get a more complete view of different thermoacoustic phenomena. We have studied various nonlinear effects: minor losses at the stack ends, streaming, and a transition to turbulence in a parallel-plate stack. Also we have made a complete model of linear thermoacoustics, based on the established linear theory, that can predict the temperature profile in a stack, even dynamically. We have gained more insight in thermoacoustics and nonlinear effects in particular and we hope that other researchers and the industry will benefit from this.