Stability analysis of refrigeration systems for electronics cooling

In modeling studies of vapor compression cycles, the momentum balance equation is usually ignored in the dynamic heat exchanger models. However, in micro-scale heat exchangers, significant pressure drop has been observed. In this paper, we investigate the effects of the momentum balance through a systematic study of the open loop stability of a heat exchanger. We consider 1D compressible fluid flow in a general circular channel with heat transfer exits. The mass, momentum, and energy conservation equations are all included in the analysis. For the complete cycle, we model the compressor and valve as static elements, since they have much faster dynamics. Based on the finite difference approximation of the dynamic model, we obtained a necessary and sufficient condition for the open loop stability of the vapor compression cycle about a given operating point. A simple simulation example shows that the stabilizing condition agrees with the numerical simulation results. The results of this study form the foundation to investigate the open loop stability and closed loop control design for vapor compression cycles used in electronics cooling systems.