An Air Cooled Tube-Fin Evaporator Model For An Expansion Valve Control Law

For control purposes, a mathematical model of a tube-fin evaporator of a vapour compression plant running with R22 is analyzed. The refrigerant behavior in an evaporating region is described by a homogeneous model. The balance equations, together with the constitutive equations, determine a differential system which makes explicit the mechanism of dynamic behavior. At first, the numerical solution of the steady state is obtained, both in evaporating and superheated regions. Moreover, the numerical analysis allows us to evaluate the transition phase and to locate the interface. Subsequently, various analytical aspects are discussed. For the nonlinear two-phase flow, the dependence of the solution on the boundary data is estimated by means of a qualitative analysis. Then, a linearized model for the single-phase flow is deduced and solved explicitly. The analytical solution is compared with the numerical results and the degree of superheating is estimated in terms of the model parameters.