Construction of a mathematical model and approximate analytical solution to the problem of energy exchange in the «sun ‒ paraboloid concentrator ‒ heat receiver» system - Masalykin, Stanislav; Knysh, Lydmila (Eastern-European Journal of Enterprise Technologies, 2023)
The object of research is the processes of radiation transfer in the «Sun – paraboloid concentrator – heat receiver» system. There are many factors that affect the value of the density of the concentrated heat flux that reaches the surface of the heat sink. The study of the influence of these factors on the overall energy indicators of the system is an important scientific problem that was solved in this work. To solve this problem, a generalized mathematical model of the radiation transfer process in the «Sun – concentrator – heat receiver» system was built, which was adapted for a paraboloid concentrator. The constructed mathematical model was solved by an approximate analytical method, which took into account the integral and discrete parameters of the system, as well as the probability distribution of aberrations of the concentrator surface, its defocusing, and other random influences. The dimensionless density of the heat flux on the surface of the heat sink for a mathematically ideal and real paraboloid concentrator of a fixed geometry was determined. Using the found analytical solution, the results obtained on the basis of the Monte Carlo method were verified. Analytical and numerical results for a mathematically ideal and a real concentrator with minor aberrations and a clear orientation to the Sun agree within the permissible error. For a real concentrator with defocusing, a deviation of numerical data from analytical data was observed. The presence of deviations is associated with a simplification in the interpretation of the analytical probability distribution, in which it is impossible to take into account each influence separately. The obtained analytical results will be useful in the development of real power plants and can be used practically at the stage of checking the adequacy of the system model