Design Optimization of a Solar Dish Collector for Its Application With Stirling Engines

Solar concentric dish collectors and Stirling engines with cavity receivers are commonly considered for this purpose due to the high efficiency for converting solar radiation into mechanical energy. The study and design of a solar collector of this type, and of its cavity receiver, require solving a mathematical model that take into account the geometric, optical and thermal behavior of all components. With an adequate sizing, not only the useful energy produced on the solar device will meet the energy required for the process, but also the absorber temperature will be the needed for the operation of the Stirling engine. This paper focuses on the construction of a mathematical model that represents the operational performance of a concentric solar dish with cavity receiver for its applications in Stirling engines. The purpose is to develop a designing tool for optimization and for quantifying the effect of changing the values of design parameters over any specific output behavior or the overall performance of the system. The parameters in the optimization include: geometrical variables, i.e., the solar dish diameter, the receiver aperture diameter or the focal length; and optical variables, i.e., rim and incident angles, and irradiation interception factor. The objective is to minimize the solar dish collector cost and calculate the heat available to the Stirling engine, contained in the receiver cavity, to be converted in to mechanical energy. The numerical model was coded in the MatLab® programming language. The results of the simulation disclosed a model able to predict, adequately, the optical and thermal behavior of the described system, so that the model can be used to study the operation and also to design parameters. The optimal results disclosed the configuration of a solar collector dish with a rim angle of about 41° and for a dish diameter of 6.58 m and an aperture receiver of 0.12 m for a minimum cost of 4717 €. It was also concluded that the maximum temperature reached in the absorber of a receiver cavity, is limited mainly by the geometric relationships between the dish diameter, receiver aperture diameter and the aperture ratio, and it is possible to obtain an ideal thermal efficiency of 64%.