Computational Modeling and Analysis of Multiple Steady States in Vapor Compression Systems

In this paper, we present a well-posed two-point boundary value problem framework for computing, via continuation, the steady states of interconnected vapor compression systems. We illustrate the ease and utility of our approach by employing the path following software AUTO to compute steady solutions of an experimental air-to-water heat pump that uses $CO2$ as a refrigerant. We validate some of the computational solutions against the experimental data and carry out continuation and bifurcation analysis in external parameters of practical interest. The results of these computations show that multiple and qualitatively distinct distributed steady-state solutions can arise for the problem, and that our approach provides for a simpler alternative to the much harder problem of dynamic simulation.