Skip to main content

Advertisement

SpringerLink
Log in

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

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

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of this paper is a presentation of a dynamic phenomena in a real world application that has previously been unpublished.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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kim, M.-H., Pettersen, J., Bullard, C.W.: Fundamental process and system design issues in CO2 vapor compression systems. Prog. Energy Combust. Sci. 30, 119–174 (2004)

    Article  Google Scholar 

  2. Neksa, P.: CO2 heat pump systems. Int. J. Refrig. 25, 421–427 (2002)

    Article  Google Scholar 

  3. Dhar, M., Soedel, W.: Transient analysis of a vapor compression refrigeration system: Part: I and II. In: Int. Inst. Refrig., Paris, France, by Organ and Sci. Comm. of the 15th Int. Congr. of Refrig., Padova, Italy, pp. 1049–1067 (1980)

  4. Yasuda, H., Touber, S., Machielsen, C.H.M.: Simulation model of a vapor compression refrigeration system. ASHRAE Trans. 89(2), 408–425 (1983)

    Google Scholar 

  5. He, X., Liu, S., Asada, H.: Modeling of vapor compression cycles for multivariable feedback control of HVAC systems. ASME J. Dyn. Syst. Meas. Control 119, 183–191 (1997)

    Article  MATH  Google Scholar 

  6. Rasmussen, B., et al.: Control-oriented modeling and analysis of automotive transcritical AC system dynamics. Proc. Am. Control Conf. 4, 3111–3116 (2002)

    Google Scholar 

  7. Svensson, M.C.: Model-based optimizing control of a water-to-water heat pump unit. Mod. Identif. Control 17(4), 279–295 (1996)

    MATH  Google Scholar 

  8. Gordon, B.W., Asada, H.: Modeling, realization, and simulation of thermo-fluid systems using singularly perturbed sliding manifolds. ASME J. Dyn. Syst. Meas. Control 22, 699 (2000)

    Article  Google Scholar 

  9. Grald, E.W., MacArthur, J.W.: A moving-boundary formulation for modeling time-dependent two-phase flows. Int. J. Heat Fluid Flow 13(3), 266–272 (1992)

    Article  Google Scholar 

  10. Robinson, D.M., Groll, E.A.: Theoretical performance comparison of CO2 transcritical cycle technology vs. HCFC-22. HVAC&R Res. 6(4) (2000)

  11. Bauer, O.: Modelling of two-phase flows with modelica. Masters Thesis, Department of Automatic Control, Lund Institute of Technology, ISSN 0280-5316 (1999)

  12. Aldridge, C.J., Fowler, A.C.: Stability and instability in evaporating two-phase flows. Surv. Math. Ind. 6, 75–107 (1996)

    MATH  MathSciNet  Google Scholar 

  13. Broersen, P., van der Jagt, M.: Hunting of evaporators controlled by a thermostatic expansion valve. ASME J. Dyn. Syst. Meas. Control 102 (1980)

  14. Nyers, J., Stoyan, G.: A dynamical model adequate for controlling the evaporator of a heat pump. Int. J. Refrig. 17(2) (1994)

  15. Gruhle, W.D., Isermann, R.: Modeling and control of a refrigerant evaporator. ASME J. Dyn. Syst. Meas. Control 107, 235–239 (1980)

    Article  Google Scholar 

  16. Pettersen, J., Rieberer, R., Munkejord, S.T.: Flow vaporization of CO2 in microchannel tubes. Exp. Therm. Fluid Sci. 28(2–3), 111–121 (2004)

    Article  Google Scholar 

  17. Yun, R., Kim, Y., Kim, M.S.: Convective boiling heat transfer characteristics of CO2 in microchannels. Int. J. Heat Mass Transf. 48, 235–242 (2005)

    Article  Google Scholar 

  18. Hwang, Y.: Comprehensive investigation of carbon dioxide refrigeration cycle. PhD Thesis, University of Maryland (1997)

  19. Thomas, P.: Simulation of Industrial Processes. Butterworth-Heinemann, Oxford (1999)

    Google Scholar 

  20. Rasmussen, B.P., Alleyne, A., Musser, A.: Model-driven system identification of transcritical vapor compression systems. IEEE Trans. Control Syst. Technol. 13(3), 444–451 (2005)

    Article  Google Scholar 

  21. Chen, G., Moiola, J.L., Wang, H.O.: Bifurcation control: theories, methods, and applications. Int. J. Bifurc. Chaos 10(3), 511–548 (2000)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of California, Santa Barbara, USA

    Bryan A. Eisenhower

  2. University of Oklahoma, Norman, USA

    Thordur Runolfsson

Authors
  1. Bryan A. Eisenhower
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Thordur Runolfsson
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bryan A. Eisenhower.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Eisenhower, B.A., Runolfsson, T. System level modeling of a transcritical vapor compression system for bistability analysis. Nonlinear Dyn 55, 13–30 (2009). https://doi.org/10.1007/s11071-008-9341-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-008-9341-7

Keywords

Search

Navigation