# NUMERICAL AND ANALYTICAL SOLUTION OF SINGLE-PHASE PROBLEM OF STEFAN DURING SIMULATION OF PROCESS OF STEAM-AIR MIXTURE DRYING IN HEAT PUMP EVAPORATOR-COOLER

A.A. Shevtsov, L.I. Lytkina, T.N. Tertychnay, S.S. Kulikov
Abstract: The task of simulating the process of condensation of moisture from a steam-air mixture on the surface of the evaporator-cooler pipe of a heat pump with the formation of an ice crust, represented by a system of one-dimensional equations of thermal conductivity, is formulated. The numerical and analytical solution of the mathematical model is reduced to the single-phase Stefan problem, according to which the movable interface of the phases «ice crust - steam-air mixture» moves over time, while maintaining similarity, remaining parallel to the cooling surface of the evaporator-cooler pipe. A functional transformation is built based on the replacement of the movable interface with a fixed one. Based on the theory of Stefan's classical problem at the interface, it was assumed that the boiling refrigerant energy released on the cooling surface due to heat transfer to the phase conversion front is compensated by the flow of thermal energy from condensation of moisture from the steam-air mixture. At the first stage, the surface temperature of the evaporator pipe was determined, which, depending on the steady-state value of the boiling temperature of the refrigerant, took a fixed value in the absence of heat flow from the steam-air mixture. The second stage of the solution under the conditions of phase transition was to determine the time of formation of the ice crust. The error of the simulation results was 10... 12 %. The model can be used in the study of the process of condensation of wet air with the formation of an ice crust, in solving direct and inverse problems of mathematical physics and in the problems of optimal control of the process of drying of wet air in installations operating using a heat pump.
Index terms: steam-air mixture, evaporator-cooler, moisture condensation, mathematical model, heat pump, «ice crust».