A multi-objective optimisation approach for small-scale standing wave thermoacoustic coolers design

Abstract

Thermoacoustic heat engines provide a practical solution to the problem of heat management where heat can be pumped or spot cooling can be induced. This is new among emerging technology with a strong potential towards the development of sustainable and renewable energy systems by utilising solar energy or wasted heat. The most inhibiting characteristic of current thermoacoustic cooling devices is the lack of efficiency. Although simple to fabricate, the designing of thermoacoustic coolers involves significant technical challenges. The stack has been identified as the heart of the device where the heat transfer takes place. Improving its performance will make thermoacoustic technology more attractive. Existing efforts have not taken thermal losses to the surroundings into account in the derivation of the models. Although thermal losses can be neglected for large-scale applications, these losses need to be adequately covered for small-scale applications. This work explores the use of a multi-objective optimisation approach to model and to optimise the performance of a simple thermoacoustic engine. This study aims to optimise its geometrical parameters—namely the stack length, the stack height, the stack position, the number of channels and the plate spacing—involved in designing thermoacoustic engines. System parameters and constraints that capture the underlying thermoacoustic dynamics have been used to define the models. Acoustic work, viscous loss, conductive heat loss, convective heat loss and radiative heat loss have been used to measure the performance of the thermoacoustic engine. The optimisation task is formulated as a five-criterion mixed-integer nonlinear programming problem. Since we optimise multiple objectives simultaneously, each objective component has been given a weighting factor to provide appropriate user-defined emphasis. A practical example is provided to illustrate the approach. We have determined a design statement of a stack describing how the design would change if emphasis is placed on one objective in particular. We also considered optimisation of multiple objective components simultaneously and identified global optimal solutions describing the stack geometry using the augmented ε-constraint method. This approach has been implemented in GAMS (General Algebraic Modelling System). In addition, this work develops a novel mathematical programming model to optimise the performance of a simple thermoacoustic refrigerator. This study aims to optimise its geometrical parameters—namely the stack position, the stack length, the blockage ratio and the plate spacing—involved in designing thermoacoustic refrigerators. 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 optimisation task is formulated as a three-criterion nonlinear programming problem with discontinuous

derivatives (DNLPs). Since we optimise multiple objectives simultaneously, each objective component has been given a weighting factor to provide appropriate user-defined emphasis. A practical example is provided to illustrate the approach. We have determined a design statement of a stack describing how the geometrical parameters described would change if emphasis is placed on one objective in particular. We also considered optimisation of multiple objective components simultaneously and identified global optimal solutions describing the stack geometry using a lexicographic multi-objective optimisation scheme. The unique feature of the present mathematical programming approach is to compute the stack geometrical parameters describing thermoacoustic refrigerators for maximum cooling or maximum coefficient of performance. The present study highlights the importance of thermal losses in the modelling of small-scale thermoacoustic engines using a multi-objective approach. The proposed modelling approach for thermoacoustic engines provides a fast estimate of the geometry and position of the stack for maximum performance of the device. The use of a lexicographic method introduced in this study improves the modelling and the computation of optimal solutions and avoids subjectivity in aggregation of weight to objective functions in the formulation of mathematical models. The unique characteristic of this research is the computing of all efficient non dominated Pareto optimal solutions allowing the decision maker to select the most efficient solution. The present research experimentally examines the influence of the stack geometry and position on the performance of thermoacoustic engines and thermoacoustic refrigerators. Thirty-six different cordierite honeycomb ceramic stacks are studied in this research. The influence of the geometry and the stack position has been investigated. The temperature difference across the stack and radiated sound pressure level at steady state are considered indicators of the performance of the devices. The general trends of the proposed mathematical programming approach results show satisfactory agreement with the experiment. One important aspect revealed by this study is that geometrical parameters are interdependent and can be treated as such when optimising the device to achieve its highest performance. The outcome of this research has direct application in the search for efficient stack configurations of small-scale thermoacoustic devices for electronics cooling.