M.Sc Thesis | |

M.Sc Student | Felman Daniel |
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Subject | Phase-Exchange Thermoacoustics: A unified derivation and stability analysis |

Department | Department of Applied Mathematics |

Supervisor | ASSOCIATE PROF. Guy Ramon |

Thermoacoustics is a highly promising technology for the upcoming decades. Based on the heat transfer between a temperature gradient stack and an oscillating acoustic wave, it is expected to replace current heat pumps or heat engines, such as air conditioners or solar panels, due to its improved efficiency and durability compared to conventional methods. However, it is yet a young research topic with many improvements and tests to come. One of the most recent improvements is the addition of a reactive component to the inert media as it creates an adsorptive coating layer over the stack pore's walls and forms an additional concentration gradient as a result of its phase-exchange interaction with the active component, encouraging the oscillating amplitudes for a more desirable performance and efficiency.

This thesis develops the mathematical non-dimensional approach established by the physical parameters of the system building it from the conservation of momentum, concentration and energy equations while applying the required boundary conditions to solve for the velocity, concentration and temperature fluctuations, respectively, all in terms of the local pressure. After plugging these results into the continuity equation, it describes the behavior of the pressure along the stack, which is also known as the wave equation. At this point, it is possible to find the acoustic work flux and determine the efficiency of the system based on all the physical parameters involved.

The results evaluation includes the analysis of limiting cases, such as the inviscid limit or the boundary layer approximation, and their theoretical impact on the overall performance; but it mainly focuses on the engine optimization to achieve the minimum required concentration and temperature gradients to trigger self-sustained wave oscillations correspondent to the imposed environment. The derived model enables the particular investigation of any variable or parameter constituent in the system and the impact of its variation on the onset temperature gradient.

A theoretical
thermoacoustic reference setup with a selected set of parameters and variables
serves as a benchmark for this study. It is based on a resonator with a
parallel plates stack placed along its span, which holds two components: air as
the inert one and water vapor as the reactive for phase-exchange interactions
under a saturated environment. The system is subjected to change of certain
variables in order to find their optimal position for a minimum required onset
temperature difference between the stack edges. These variables include: the
starting position of the stack, the Womersley number, average reactive
component's concentration, the speed of phase-exchange interactions at the
boundary and finally Henry's coefficient. For the presented scenario, a
temperature difference of 47 K between the hot and cold sides of the stack was
required for the onset of the unstable oscillations, which induces a
concentration gradient of 7.1 m?^{-1} given the saturated environment.
The present paper is hoped to be a landmark for theoretical and experimental
future investigation on phase-exchange thermoacoustics.