Nonlinear Dynamics

, Volume 55, Issue 1–2, pp 13–30 | Cite as

System level modeling of a transcritical vapor compression system for bistability analysis

  • Bryan A. Eisenhower
  • Thordur Runolfsson
Original Paper


This study seeks to understand the multiplicity of stable solutions in a transcritical hot water heat pump as it has been observed in prototype units that two steady states exist (very efficient and inefficient). Reduced order dynamic modeling highlights the state-dependent heat transfer coefficient in the evaporator dynamics as a contributing cause to this bistable phenomena. Specifically, the bilinear nature of the controlled gas cooler and its coupling to the dynamic nonlinearity in the evaporator induces a system-wide bifurcation in the equilibrium conditions with regard to system efficiency. Model results are presented to illustrate this, along with steady-state and dynamic data to confirm the accuracy of the model. Finally, the bifurcation behavior is presented which is comparable to the behavior found in the experiment. The contribution of this paper is a presentation of a dynamic phenomena in a real world application that has previously been unpublished. In addition to this, this paper motivates a reason for this phenomena from first principles. This is a preliminary step to gaining control over unwanted dynamics in this application by either nonlinear control or component redesign.


CO2 refrigerant Heat pump efficiency Multiple equilibria Heat-exchanger modeling Dynamical analysis 


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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaSanta BarbaraUSA
  2. 2.University of OklahomaNormanUSA

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