Modeling of Energy Characteristics of Parabolic Concentrators Based on Monte Carlo Ray Tracing Method

Computer modeling results of energy characteristics in the heat receiver system of the solar plant with a parabolic concentrator are presented. The created numerical algorithm based on the mathematical model for the parabolic concentrator which is developed using the photometric approach. The mathematical model contains special Heaviside type functions that indicate the probability of the beam reflected from the concentrator entering the beam of beams directed at the heat sink, as well as the probability of these beams falling into the inlet of the strip heat sink. The concentrator orientation relative to the Sun, concentrator location relative to the heat receiver, the concentrator surface reflectance, and the concentrator surface errors are taken into account in the developed mathematical model. The angular errors take into account using the normal distribution and Rayleigh distribution. The numerical algorithm is created based on the developed probabilistic mathematical model. This model is realized by the Monte Carlo ray tracing method. The main stages of computer code creation of generation of a random point at the concentrator surface, calculation of the defining vectors and directions, and modeling of normal random values are presented. The numerical analysis at the chosen concentrator geometry and at the constant direct normal irradiance was carried out based on the created in-house software. Obtained distributions for the heat flux density at the concentrator focal surface allow us to evaluate the value of a heat receiver’s optimal hole radius. It is a necessary condition for further optimization of the entire solar energy conversion system. The polynomial-trigonometric approximation function for calculation of the concentrative heat flux were presented. Comparison of the heat flux density values at normal distribution of angular errors and Rayleigh distribution was conducted. Impact of the concentrator surface reflectivity on energy parameters inside the heat receiver was determined.

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