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Modeling of AC&R
Systems
Chi, J., and Didion, D., "A Simulation of the
Transient Performance of a Heat Pump," Int. J. Refrigeration, Vol. 5, No. 3,
pp. 176-184, 1982.
Dhar, M., and Soedel, W., "Transient
Analysis of a Vapor Compression Refrigeration System," Proc. 25th
Int. Cong. of Refrigeration, Venice, Italy, 1979.
Abstract
A mathematical model of the refrigeration system is developed by zoning the overall system
into various control volumes which keep track of vapor and liquid refrigerant regions. The
state of refrigerant in each control volume is established by writing the conservation of
mass, conservation of energy and the state equations which correlate the various
refrigerant properties. The overall mathematical model is formulated by combining the
above basic engineering principles with empirical parameters for system intricacies such
as heat transfer coefficients, oil transportation, rate of release of refrigerant from
oil, etc. This was done to make the system equations more readily solvable while still
retaining the representation of complex phenomena associated with the refrigeration
system.
Grald, E. W., and MacArthur, J. W., "A Moving
Boundary Formulation for Modeling Time-Dependent Two-Phase Flows," Int. J. Heat
and Fluid Flow, Vol. 13, No. 3, pp. 266-272, 1992.
Hemami, T., and Dunn, W., “Development of a Transient System Model of
Mobile Air-Conditioning Systems,” ACRC Technical Report 143, University of Illinois
at Urbana-Champaign, Sep. 1998.
Kapadia, M., and Wolgemuth, C. H., "A Dynamic Model of a Condenser in a Closed Rankine Cycle Power Plant,"
Proc. 1984 American Control Conf., pp. 79-84, 1984.
Abstract
This paper describes a simple model to predict the transient behavior of a condenser when
subjected to changes in inlet enthalpy as well as changes in inlet and exit mass flow
rates. The model predicts the pressure, fluid temperature, wall temperatures, mass in the
condensing region, mass in the subcooled liquid region and the position of the liquid
interface, all as a function of time during a transient. Five ordinary differential
equations along with several algebraic equations are solved numerically to obtain the
behavior during a transient. Sample results are presented for ramp and sinusoidal
variations of inlet and exit mass flow rates.
MacArthur, J. W., " Transient Heat Pump
Behavior: A Theoretical Investigation," Int. J. Refrigeration, Vol. 7, No., pp.
123-132, 1984.
MacArthur, J. W., and Grald, E. W., "Unsteady Compressible
Two-Phase Flow Model for Predicting Cyclic Heat Pump Performance and a Comparison with
Experimental Data," Int. J. Refrigeration, Vol. 12, pp. 29-41, 1989.
Pfafferott, T., and Schmitz, G., “Numeric Simulation of an Integrated
CO2 Cooling System,” Modelica Workshop 2000 Proceeding, pp. 89-92, 2000.
Robinson, D., and Groll, A., “Introducing ACCO2 – A Public
Domain Air-To-Air Simulation Model of the Transcritical Carbon Dioxide Cycle,”
Preliminary Proceedings of the 4th IIR – Gustov Lorentzen Conference on
Natural Working Fluids at Purdue, pp. 33-42, 2000.
Sami, S. M., et al., "Prediction of the
Transient Response of Heat Pumps," ASHRAE Trans., Vol. 93, Part 2, pp.
471-489, 1987.
Abstract
The development of an improved computer program to simulate the dynamic response of heat
pumps is presented. The proposed model is a lumped parameter model. A control volume
formulation is employed for heat pump components. The mathematical formulation of this
model is based on mass, momentum, and energy balances. Several constitutive relationships
are adopted in this model to describe the different phenomena encountered in heat pump
operation. In addition, the proposed model includes the consequent effect of different
refrigerant flow regimes and slip between two phases. Numerical results indicate that the
present model predicts fairly the heat pump response and that is compares well with
experimental data.
Shoureshi, R., and McLaughlin, K., "Modeling and Dynamics of Two-Phase Flow Heat Exchangers Using
Temperature-Entropy Bond Graphs," Proc. 1984 American Control Conf., pp.
93-98, 1984.
Abstract
Two-phase flow heat exchangers have many industrial and residential applications, such as
in nuclear power plants, HVAC systems, steam generators, and heat pumps. Dynamic response
of such heat exchangers are of interest in order to increase reliability and decrease
energy consumption. This paper utilizes true bond graphs, with temperature and rate of
change of entropy as power variables, to model the dynamics of two-phase flow heat
exchangers. A bond graph for variable density flow is derived such that it satisfies mass,
momentum, and energy equations. Due to thermofluid bond graphs requirements, a specific
entropy-specific volume plane is developed and an algorithm to calculate two-phase flow
properties from this plane is discussed. For stability purposes, the resulting nonlinear
system equations are nondimensionalized. Simulation results of the model for a condenser
of a residential air-conditioning unit is compared with experimental data. Comparison
shows good agreement in both magnitude and shape of the response between the bond graph
model and the experiments.
Tummescheit, H., Eborn, J., and Wagner, F. J., “Development of a
Modelica Base Library for Modeling of Thermo-Hydraulic Systems. Modelica Workshop 2000 Proceedings, pp. 41-51,
2000.
Air
Conditioning System Control
Broersen, P., and van der Jagt, M., "Hunting of Evaporators Controlled by a Thermostatic Expansion Valve,"
ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 102, pp. 130-135,
June 1980.
Abstract
Evaporators controlled by a thermostatic expansion valve can exhibit an undesirable
oscillating behavior known as hunting. The equations describing the hunting can be
characterized by an open-loop transfer function, the coefficients of which are the
physical parameters of a refrigeration system. Several known experimental facts are
explained theoretically by means of this transfer function, which also provides a starting
point for finding new methods to improve the behavior. A particular improvement was
verified experimentally.
Gruhle, W.-D., and Isermann, R., "Modeling and Control of a Refrigerant Evaporator," ASME Journal
of Dynamic Systems, Measurement, and Control, Vol. 107, pp. 235-239, June 1980.
Abstract
Based on the balance equations for enthalpy, mass, and momentum a theoretical model of a
refrigerant evaporator has been developed. The distributed parameter process is
approximated by several lumped parameter models. The model is completed by equations for
the expansion valve, the compressor and the superheater. Various effects, e.g., the random
fluctuations of the liquid dry-out-point can be explained by the model. The dynamic
behavior of the evaporator is investigated as a function of the manipulating signal Uev
(position of the expansion valve) and various disturbances (air temperature Ta, condenser
pressure Pc, and compressor rotation speed Nc), considering the superheating temperature
Ts as control variable and the evaporator performance Qe, which has to be optimized. Two
controllers are considered. First, the control behavior with a conventional thermostatic
expansion valve is shown, which often operates unstable. The control performance can be
considerably improved by a controller whose structure and parameters are better adapted to
the evaporation process. For the experiments a process computer is connected on-line to
the process. It will be demonstrated that the performance of the evaporator and therefore
its efficiency can be increased by at least 5 percent.
He, X., Liu, S., and Assada, H., "Modeling of Vapor Compression Cycles for Multivariable Feedback Control of HVAC
Systems," ASME Journal of Dynamic Systems, Measurement, and Control, Vol.
119, pp. 183-191, June 1997.
Abstract
This paper presents a new lumped-parameter model for describing the dynamics of vapor
compression cycles. In particular, the dynamics associated with two heat exchangers, i.e.,
the evaporator and the condenser, are modeled based on a moving interface approach by
which the position of the two-phase/single-phase interface inside the one-dimensional heat
exchanger can be properly predicted. This interface information has never been included in
previous lumped-parameter models developed for control design purpose, although it is
essential in predicting the refrigerant superheat or subcool value. This model relates
critical performance outputs, such as evaporating pressure, condensing pressure, and the
refrigerant superheat, to actuating inputs including compressor speed, fan speed, and
expansion valve opening. The dominating dynamic characteristics of the cycle around an
operating point is studied based on the linearized model. From the resultant transfer
function matrix, an interaction measure based on the Relative Gain Array reveals strong
cross-couplings between various input-output pairs, and therefore indicates the inadequacy
of independent SISO control techniques. In view of regulating multiple performance outputs
in modern heat pumps and air-conditioning systems, this model is highly useful for design
of multivariable feedback control.
Najork, H., "Investigations on the Dynamical
Behavior of Evaporators with Thermostatic Expansion Valve," Proc. 13th
Int. Cong. of Refrigeration, Washington, pp. 759-769, 1973.
Stoecker, W. F., "Stability of an
Evaporator-Expansion Valve Control Loop," ASHRAE Transactions, Vol. 72, No. 2007,
1966.
Wedekind, G. L., "An Experimental
Investigation into the Oscillatory Motion of the Mixture-Vapor Transition Point in
Horizontal Evaporating Flow," ASME J. Heat Transfer, Vol. 93, pp. 47-54,
1971.
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