Numerical modeling of a transient state evaporator using object-oriented programming

Abstract

This work presents the dynamic modeling of a refrigeration machine evaporator that uses CO2 (R744) as refrigerant fluid, for the cooling down of a liquid water stream, as required for instance by buildings air handling units. The main goal of such a work is to accurately model the transient evolution of the evaporator outlet superheat, which is one of the main parameters to control, due to its importance in refrigeration systems. A high value of superheat temperature reduces the performance of the system, while a low or null value can generate the suction of liquid which damages the compressor. The theory of moving boundaries [19] with grouped parameters has been used for so. This method allows a precise resolution with a low numerical weight. In this method, the evaporator is divided into only two regions: the two phase region and superheated steam region, in which the energy conservation and mass conservation equations are solved. By using only two control volumes, the number of equations to be solved is smaller, thus reducing the calculation time. The ultimate aim of this work is to serve as a mathematical model usable for the design of efficient refrigeration system controllers, which are one of the most practical ways to improve the performance of these machines. The results of a numerical analysis and of a sensitivity analysis, regarding to the influence of the heat convection coefficient of the two phase region, are also presented. For this sensitivity analysis, the maximum and minimum values available in the literature, see reference [7], have been used. According to this study, the convective coefficient ofCO2 varies from 8000 to 12000 W ·m−2 ·K−1. From this sensitivity analysis, it is observed that, despite the previously mentioned uncertainty about the convective coefficient value, the latter is not influential on the rest of the calculations and on parameters such as internal pressure, length of the two-phase lengths or superheat value. This is due to the fact that the thermal resistance of the liquid hot fluid is much higher than the cold fluid in the phase change region, the global heat transfer coefficient is thus more influenced by the hot fluid thermal resistance. A maximum error of 3 percent is finally estimated in the determination of the transient superheat temperature.