Mathematical models and methods for analyzing flow properties in hydraulic circuits with closed circulation circuits

The article is devoted to the problems of calculating the distribution of flow quality parameters over the elements of the hydraulic system. The main attention is paid to the problem of such a calculation in the presence of closed circulation circuits in the system, when traditional methods and algorithms become ineffective. Mathematical models of the distribution of quality parameters are given, the results of the analysis of their properties in the presence of closed circulation circuits are presented. Against the background of the analysis of the applicability of general mathematical methods for solving the problem, two new methods are proposed based on the special properties of this problem - the “iterative topological” algorithm and the “algebraic-topological” method. Both methods are universal and provide a solution in the presence of closed circulation loops, and in their absence they coincide with the traditional “topological” algorithm