Thermodynamic physical-mathematical models of multi-phase flows of external heat supply networks

The design of 4th generation heat supply systems involves the use of advanced digital technologies, including the analysis and processing of big data to predict the behavior of the heat supply system as a whole. Therefore, the development of digital models is an issue in modern heat supply studies. This study investigates the thermodynamic processes of multiphase flows in external heat supply networks. A description and calculation methodology for constructing thermodynamic physical-mathematical models of multiphase flows in external heat supply networks using the Runge-Kutta/WENO method is provided. It is mathematically possible to express these thermodynamic processes as continuous. These representations can be obtained by averaging the parameters of the phases of the flow. Continuity implies that small changes in the argument lead to small changes in the value of the function. However, from a physical point of view, the flow can be considered heterogeneous, and thus, include interphase interactions which need to be taken into account when formulating the equations.