Abstract
This thesis addresses the mathematical aspects of thermoacoustics, a subfield within
physical acoustics that comprises all effects in which heat conduction and entropy variations
of the gaseous medium play a role. We focus specifically on the theoretical basis
of two kinds of devices: the thermoacoustic prime mover, that uses heat to produce
sound, and the thermoacoustic heat pump or refrigerator, that use sound to produce
heating or cooling.
Two kinds of geometry are considered. The first one is the so-called standing-wave
geometry that consists of a closed straight tube (the resonator) with a porous medium
(the stack) placed inside. The second one is the so-called traveling-wave geometry that
consists of a resonator attached to a looped tube with a porous medium (regenerator)
placed inside. The stack and the regenerator differ in the sense that the regenerator uses
thinner pores to ensure perfect thermal contact. The stack or regenerator can in principle
have any arbitrary shape, but are modeled as a collecting of long narrow arbitrarily
shaped pores. If the purpose of the device is to generate cooling or heating, then usually
a speaker is attached to the regenerator to generate the necessary sound.
By means of a systematic approach based on small-parameter asymptotics and dimensional
analysis, we have derived a general theory for the thermal and acoustic behavior
in a pore. First a linear theory is derived, predicting the thermoacoustic behavior
between two closely placed parallel plates. Then the theory is extended by considering
arbitrarily shaped pores with the only restriction that the pore cross-sections vary
slowly in longitudinal direction. Finally, the theory is completed by the inclusion of
nonlinear second-order effects such as streaming, higher harmonics, and shock-waves.
It is shown how the presence of any of these nonlinear phenomena (negatively) affects
the performance of the device.
The final step in the analysis is the linking of the sound field in the stack or regenerator
to that of the main tube. For the standing-wave device this is rather straightforward,
but for the traveling-wave device all sorts of complications arise due to the complicated
geometry. A numerical optimization routine has been developed that chooses the right
geometry to ensure that all variables match continuously across every interface and the
right flow behavior is attained at the position of the regenerator. Doing so, we can predict
the flow behavior throughout the device and validate it against experimental data.
The numerical routine can be a valuable aid in the design of traveling-wave devices;
by variation of the relevant problem parameters one can look for the optimal travelingwave
geometry in terms of power output or efficiency.
Original language | English |
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Qualification | Doctor of Philosophy |
Awarding Institution |
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Supervisors/Advisors |
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Award date | 25 Jun 2009 |
Place of Publication | Eindhoven |
Publisher | |
Print ISBNs | 978-90-386-1862-3 |
DOIs | |
Publication status | Published - 2009 |