Efficient time-domain modelling suitable for optimising thermoacoustic devices

Doctoral thesis, 2010

Thermoacoustic heat pumps use acoustic work to transfer heat from cold to hot temperatures. Such devices benefit from being environmentally friendly, robust and simple. However, in practice these devices have too low efficiency and power compared to their conventional counterparts. Attempts to increase the performance have been focused on optimising the different parts separately. More recently, adaptive solutions have been investigated, but there is a need for numerical models and tools for such studies. The primary aims of this thesis have been: (1) to create computationally efficient models and tools for studying thermoacoustic devices in the time domain; and (2) to apply the models to demonstrate a procedure for optimising thermoacoustic devices by controlling a secondary driver. The time-domain approach was chosen to allow for high flexibility in the selection of control laws and in the simulations of optimisation procedures. In order to carry out the optimisation procedures in reasonable times, computational efficiency is essential. The computational cost was reduced by combining two methods: a finite-difference model, including thermal effects, for the small geometries in the stack, and the quicker equivalent source method (ESM), assuming adiabatic plane waves, for the duct parts outside the stack. The control of the secondary driver, included in the ESM formulation, enables adaptation of the acoustic field. One specific case, changing the length of the resonator together with the driving frequency, was carried out through a parameter study and by using a tuning algorithm. The time-domain models were validated with the established linear theory with very good agreement. Moreover, by combining two methods the computational cost was substantially reduced in comparison to using the finite-difference model alone, which allowed parameter studies and adaptive improvements in reasonable times. The presented model can be used as a valuable tool to develop a strategy for an experimental optimisation of thermoacoustic devices by means of an active controlled secondary driver.