Dynamic 3D volume element model of a parabolic trough solar collector for simulation and optimization

This paper presents a dynamic three-dimensional volume element model of a parabolic trough solar collector coupled to an existing semi-finite optical model for simulation and optimization. The spatial domain in the volume element model is discretized with lumped control volumes (i.e., volume elements) in cylindrical coordinates according to the predefined collector geometry. The spatial dependency of the model is therefore taken into account without the need to solve partial differential equations. The proposed model combines the laws of thermodynamics and heat transfer as well as empirical correlations to simplify the modeling and expedite the computations, and the resulting system of ordinary differential equations is integrated in time for temperature. The model was validated with the experimental data provided in the literature, and was employed to evaluate the sensitivity of the collector performance described by the first and second law efficiencies to receiver length, annulus gap spacing, concentration ratio, incidence angle, inlet fluid temperature and flow rate. This work also examined the effects of inlet fluid temperature and temperature differential on dynamic collector performance in the transient case study. Results showed that the first law efficiency was most sensitive to the inlet fluid temperature with the maximum variation of 30%, whereas the incidence angle and concentration ratio affected the second law efficiency the most with the maximum variations of 375% and 300%, respectively. The remaining parameters featured trivial effects in all cases. In the transient analysis, higher temperature differential and lower inlet fluid temperature yielded higher total heat gain while the total exergy gain was insensitive to both parameters. The first law efficiency should therefore be of greater importance than the second law efficiency in the control of dynamic collector performance based on these two parameters.