A dynamical model adequate for controlling the evaporator of a heat pump J6zsef Nyers Technical College, Subotica, Serbia Gisbert Stoyan ELTE University, Budapest, Hungary Received 16 August 1992; revised 15 December 1992 We present a dynamical model for the dry evaporator of a heat pump which is suitable for control purposes. We take into account the expansion valve, the compressor and the condenser to model the evaporator and its surroundings. Our model is of the distributed parameter type and consists of partial differential and algebraic equations. For the solution of discretized equations, Newton iteration with a block-Gauss solution of the linearized systems is applied. Numerical results are presented in graphical form and correspond to simulations of almost all control possibilities. (Keywords:evaporator;, heat pump;expansionvalve;compressor;, condenser; control;modelling; simulation) Mod61e dynamique pour r6guler l'6vaporateur d'une pompe 5. chaleur Les auteurs prdsentent un module dynamique de l'~vaporateur sec d'une pompe ~ chaleur que l'on pourra utiliser pour la r~gulation. Ils ont tenu compte du ddtendeur, du compresseur et du condenseur clans la mod~lisation de l~vaporateur et de son environnement. Ce module est rdalis~ par distribution de paramdtres et se compose d'~quations alg~briques et diff~rentielles partielles. Pour la rdsolution des dquations, on applique I'iteration de Newton avec une r~solution de Gauss des syst~mes lin~aris~s. On pr~sente les r~sultats num~riques sous forme graphique; ils correspondent aux simulations de presque toutes les possibilit~s de r~gulation. (Mots cl6s: 6vaporateur; pompe ~ chaleur; d6tendeur; compresseur; condenseur; contr61e; r6gulation; mod61isation; simulation) Several investigations have been performed recently on the mathematical modelling of the transient behaviour of heat pumps. An important part of these models is the evaporator, which at the beginning has been described by lumped parameter models; however, with the spread of personal computers, distributed parameter models came into use too. Models of this type usually fall into two classes: either the evaporating refrigerant is considered to be a homogeneous mixture of gas and liquid, or these two phases are considered separately. Of course, both approaches represent approximations of the physical sit- uation and both consist of a series of simplifying assump- tions. The non-homogeneous approximation has been used in references 1-5. Essentially, a constant evapo- ration temperature (pressure) has been assumed. This leads to a considerable simplification of the evaporator model and facilitates the numerical solution as well. If one is interested in the energy and mass balance only, then the assumption of a constant evaporator tem- perature gives rise to small errors. However, for control purposes that assumption is already not acceptable. For instance, it is well known that control of the mass flow rate of the refrigerant at the inlet of the evaporator depends on the degree of superheating of the vapour. The latter is the difference between the temperature of the gas streaming out of the evaporator and the tempera- ture of the last evaporated drop of liquid. Taking this and further problems of the control type into account, a model for the mathematical description of transient processes in evaporators has been deve- loped6,7. In these papers, the refrigerant is considered as a homogeneous medium; attention has also been paid to the fact that the temperature of evaporation changes according to the pressure drop. It is important that the appropriate heat transfer coefficients are taken into the mathematical models; less important is a high accuracy of computation of the velocities (which could be reached, e.g. by assuming annular flow and calculating the differ- ent velocities of the fluid core and the gas kernell). Under these presumptions a model of the physical situation in the evaporator has been obtained which is adequate for computer simulation of control actions on the heat pump. In the present paper, which is based on former work and on a great number of numerical experiments per- formed since then, we give a detailed description of our model and of the essential steps of our numerical approach. This description constitutes a refinement of our previous mathematical and numerical model both with respect to the equations used in the different parts of the heat pump and with respect to the details of discreti- zation of the equations and of their numerical solution. Statement of the control problem We consider an evaporator consisting of a bundle of parallel pipes in which the refrigerant is flowing. The pipe 0140-7007/94/020101-08 © 1994Butterworth-Heinemann Ltd and IIR Rev. Int. Froid 1 994 Volume 17 Num6ro 2 101