Yurkov R. Modeling of energy flows in thermal energy storage systems with “solid - liquid” phase transition

The purpose of the study is development and generalization of methods of mathematical and computer modeling for heat and mass transfer processes in latent heat thermal energy storage systems with phase change “solid – liquid”; search of methods for increase of thermal efficiency of latent heat thermal energy storage modules; proof of prospects using of latent heat thermal energy storage models as part of solar thermodynamic plants; determination of most energy efficient geometric, thermophysical and hydrodynamic parameters of the latent heat thermal energy modules double-tube design. The 3D mathematical model for coupled Stefan problem, the correspondent numerical algorithm and the customer software for determination of heat transfer features in latent heat thermal energy storage module “solid - liquid” of double-tube design were developed in the first time. Method of taking into account of free convection in the melt of phase change material of the latent heat thermal energy storage module of double-tube was developed in the first time. The impact of the heat transfer fluid flow regime on the free convection intensity in the melt was found. The methods of equalizing temperature distribution in the phase change material, which based on heat transfer fluid velocity variation in space and in time were presented in the first time. The optimal Reynolds numbers, which ensures maximum thermal efficiency of latent heat thermal energy storage module at minimal hydraulic losses of the heat transfer fluid were determined. These numbers were found in the first time based on the principles of non-equilibrium thermodynamics and the carried out entropy analysis. The customer Python software was created using the developed numerical algorithm, which based on the finite volume method. The software is generalized and can use in case of minor correction for analysis of parameters of latent heat thermal energy storage system of double-tube design, which operate in the different temperature regime. Moreover, the created software has flexible structure that allows without significant changes to transform its in depend on chosen phase change materials and heat transfer fluids and the system functioning conditions. The results of presented study can be used during design and operation of modern solar energy plants of different temperature level and purpose in which use the latent heat thermal energy storage systems “solid - liquid”. 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.