Effects of circumsolar radiation on the optimal performance of a Stirling heat engine coupled with a parabolic dish solar collector

This paper investigates the effects of circumsolar radiation on the optimal performance of a coupled parabolic dish and a Stirling heat engine, referred to as the Dish/Stirling system. The presence of circumsolar radiation results in the widening of the solar cone in which the solar beam (direct) radiation is received by the parabolic dish. This beam radiation cone enlargement effectively degrades the collector performance, especially for the very high concentration ratio collectors such as the parabolic dish. The enlarged solar beam radiation cone angular width results in enhanced solar radiation flux spillage at the receiver due to the inability of the parabolic dish reflector surface to focus a significant fraction of incoming beam radiation. This reduces both the energy input as well as the maximum temperature of the Stirling heat engine cycle and causes a reduction in the overall thermal efficiency of the Dish/Stirling system. The present study analyzes this effect by considering various levels of circumsolar radiation, characterized by a parameter known as the circumsolar ratio. The data for the intercept factor of the parabolic dish collector is based on the circumsolar radiation measurements obtained by researchers at the Lawrence Berkeley Laboratory, and the results of analysis reported by researchers at the Solar Energy Research Institute (currently the National Renewable Energy Laboratory). For the present analysis, this intercept factor data is curve-fitted for different circumsolar ratio, mirror optical errors and the concentration ratio using a MATLAB (R) program. The overall thermal efficiency of the Dish/Stirling system is maximized with respect to the concentration ratio of the parabolic dish and the maximum temperature ratio of the Stirling heat engine using the first law of thermodynamics. This optimization process is performed using a MATLAB (R) program. Optimal values of concentration ratio for the parabolic dish collector, and the maximum temperature ratio of the Stirling cycle are obtained corresponding to the maximum overall thermal efficiency of the Dish/Stirling system. The study shows that, for a parabolic collector with low mirror optical error and rim angle of 60 degrees, an increase in circumsolar ratio from 0.02 to 0.2 reduces the maximum overall thermal efficiency, optimal concentration ratio and optimal temperature ratio by about 13%, 18% and 7% respectively. In the rase of parabolic collectors with high mirror optical error and rim angle of 60 degrees, an increase in circumsolar ratio from 0.02 to 0.2 reduces the maximum overall thermal efficiency, optimal concentration ratio and optimal temperature ratio by about 10%, 11% and 5% respectively. Similar trends are observed for parabolic dish collectors with rim angle of 40 degrees. Results from this study are presented in the form of performance charts that show the effects of varying circumsolar ratios, mirror optical errors, rim angles, non-dimensional radiation flux and non-dimensional convection loss parameters on the maximum overall thermal efficiency of the Dish/Stirling system.