In this paper we present a dynamic three-dimensional volume element model (VEM) of a parabolic trough solar collector (PTC) comprising an outer glass cover, annular space, absorber tube, and heat transfer fluid. The spatial domain in the VEM is discretized with lumped control volumes (i.e., volume elements) in cylindrical coordinates according to the predefined collector geometry; therefore, the spatial dependency of the model is taken into account without the need to solve partial differential equations. The proposed model combines principles of thermodynamics and heat transfer, along with empirical heat transfer correlations, to simplify the modeling and expedite the computations. The resulting system of ordinary differential equations is integrated in time, yielding temperature fields which can be visualized and assessed with scientific visualization tools. In addition to the mathematical formulation, we present the model validation using the experimental data provided in the literature, and conduct two simple case studies to investigate the collector performance as a function of annulus pressure for different gases as well as its dynamic behavior throughout a sunny day. The proposed model also exhibits computational advantages over conventional PTC models-the model has been written in Fortran with parallel computing capabilities. In summary, we elaborate the unique features of the proposed model coupled with enhanced computational characteristics, and demonstrate its suitability for future simulation and optimization of parabolic trough solar collectors.
Contribution to the Parametric Study of the Performance of A Parabolic Trough Collector
