Masalykin S. Statistical modeling of energy flows in the systems of solar energy concentration

The purpose of the study is development and generalization of models of mathematics and computer modeling of radiative transfer in solar energy systems with concentrators, determination of correlations between geometric and energy parameters of such systems in order to ensuring of maximum efficiency for corresponded conversion cycle, influence on these correlations of errors of concentrator surface and defocusing effect. The Monte Carlo numerical algorithm was developed and the customer software was created for determination of general energy parameters in system of concentration of solar radiation taking into account errors of surface of concentrator and defocusing effect. The numerical algorithm and software are based on generalized mathematical model of process of concentration. The impact of the total errors of surface of real concentrator on heat flux density in its focal area was determined for the first time. Heat flux density values from real concentrator with uniform and normal distribution law of surface errors were compared. The fact of mutual compensation of errors of concentrator surface and defocusing effect was established for the first time. It is founded that real concentrators with insignificant errors and defocusing can be the most energy efficient than mathematical ideal concentrators. The verification of the Monte Carlo numerical data for heat flux density is conducted for the first time using the found analytical solution. The errors of surface are taking into account in analytical solution based on integral probability value. The customer C++ software was created based on developed numerical algorithm. The software is generalized and can use in case of minor correction for analysis of concentrators of any geometry. Moreover, the created software has flexible structure that allows without significant changes to transform its in depend on chosen assumptions and methods of taking into account of errors. The results of presented study can be used during design and operation of modern solar energy plants of different temperature level and purpose with solar concentrators of appropriate geometry. The theoretical and practical provisions have become an integral part of educational subjects “Models and methods of applied mathematics”, “Methods of identification of parameters of mathematical models”, which are taught to students of higher education at the PhD level, specialty 113 Applied Mathematics in Oles Honchar Dnipro National University. Conducted researches and their results make up the corresponding section of initial scientific work “Determinate and stochastic algorithms for computer modeling of objects and processes of different nature” (2022 – 2024, research supervisor Prof. Knysh L.I.) (state registration number: 0122U001467), which is carried out on Department of Computer Technologies, Faculty of Applied Mathematics, DNU.