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RESEARCH PAPERS

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

[+] Author and Article Information
Prashant G. Mehta

Department of Mechanical Science & Engineering, University of Illinois, Urbana Champaign, IL 61801mehtapg@uiuc.eduDepartment of Mechanical Engineering, University of California, Santa Barbara, CA 93106mehtapg@uiuc.edu

Bryan A. Eisenhower

Department of Mechanical Science & Engineering, University of Illinois, Urbana Champaign, IL 61801bryane@engineering.ucsb.eduDepartment of Mechanical Engineering, University of California, Santa Barbara, CA 93106bryane@engineering.ucsb.edu

J. Comput. Nonlinear Dynam 2(2), 132-140 (Nov 28, 2006) (9 pages) doi:10.1115/1.2447237 History: Received May 11, 2006; Revised November 28, 2006

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.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic representation of the experimental CO2 air–water heat pump

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Figure 2

Experimentally observed inefficient and efficient thermodynamic cycles (for similar nominal operating conditions). During the inefficient cycle, there is a lack of the so-called free energy absorbed from the air in evaporating the CO2 in the evaporator.

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Figure 3

Experimentally observed: (a) coefficient of performance (COP); and (b) temperature sensor outputs for the efficient and inefficient cycles during startup (T0 denotes the inlet water temperature and T0nom is it’s nominal value, Tset is the set-point for exit water temperature Th2oout)

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Figure 4

Schematic representation of the two-point boundary value problem

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Figure 5

Constitutive relationship for CO2 showing isotherms and the (approximation of) saturated vapor line

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Figure 6

The numerically obtained thermodynamic cycle and the experimentally obtained efficient cycle (for nominal values of T0=T0nom, TAIR=TAIRnom). The table lists the relative errors expressed as percentage—here (P1,T1) are pressure, temperature sensor readings for CO2 at Station 1 (Stations 1–4 are shown in the figure).

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Figure 7

COP as the solution is continued in the primary continuation parameter: (a) inlet water temperature T0; and (b) air temperature TAIR; the numbers correspond to distinct cycles shown in the Fig. 8

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Figure 8

Cycles as the solution is continued in the primary continuation parameter: (a) inlet water temperature T0; and (b) air temperature TAIR

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Figure 9

Distributed profiles of water temperature Th2o(x) as the solution is continued in the primary continuation parameter: (a) inlet water temperature T0; and (b) air temperature TAIR; “x” denotes the collocation points for discretization along the axial direction

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Figure 10

Water flow rate Fh2o as the solution is continued in the primary continuation parameter: (a) inlet water temperature T0; and (b) air temperature TAIR; the numbers correspond to distinct cycles shown in Fig. 9

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Figure 11

(a) Bifurcation diagram obtained from varying the mass of CO2 in the system together with (b) resulting cycles

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