Optimal design of a standing wave thermoacoustic refrigerator using GAMS

This work proposes a multi-objective optimization approach to model and optimize small scale standing wave thermoacoustic refrigerator (TAR). This study aims to optimize the geometric variables namely the stack position, the stack length, the blockage ratio and the plate spacing involved in designing thermoacoustic refrigerators. Unlike most previous studies, these variables are considered interdependent. System parameters and constraints that capture the underlying thermoacoustic dynamics have been used to define the models. The cooling load, the coefficient of performance and the acoustic power loss have been used to measure the performance of the device. The optimization task is formulated as a three-criterion nonlinear programming problem with discontinuous derivatives (DNLP). A practical example considering three different gases is given to illustrate the approach. This approach has been implemented in the software GAMS (General Algebraic modelling System) and Pareto optimal solutions describing the most preferred geometry for maximum performance of the device are computed using the augmented s-constraint method.