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Mots cles : Syste`me frigorifque ; Dioxyde de carbone ; Mode´lisation ; E´ changer de chaleur ; Regime transitoire. 1. Introduction ... the area of mobile/automotive air-conditioning and refrig- eration [2,3]. ... ambient temperature is near or higher than the critical .... cially the base classes and partial components, is very.
International Journal of Refrigeration 27 (2004) 42–52 www.elsevier.com/locate/ijrefrig

Modelling and transient simulation of CO2-refrigeration systems with Modelica Torge Pfafferott, Gerhard Schmitz* Technical University Hamburg-Harburg (TUHH), Department of Technical Thermodynamics (6-08), Denickestr. 17, D-21073 Hamburg, Germany Received 13 September 2002; received in revised form 12 June 2003; accepted 23 June 2003

Abstract This paper presents the current results of the development of a Modelica library for CO2-refrigeration systems based on the free Modelica library ThermoFluid. The development of the library is carried out in a research project of Airbus Deutschland and the TUHH and is focused on the aim to obtain a library for detailed numerical investigations of refrigeration systems with the rediscovered refrigerant carbon dioxide (CO2). A survey of the concept of an integrated on-board cooling system of airliners, the modelling language ModelicaTM and the CO2-library is given and the modelling of CO2-heat exchangers is described. A comparison with steady state results of heat exchangers shows a fair agreement. The presented transient simulation results are compared with experimental data showing also a fair agreement. # 2003 Elsevier Ltd and IIR. All rights reserved. Keywords: Refrigeration system; Carbon dioxide; Modelling; Heat exchanger; Transient regime

Mode´lisation et simulation du re´gime transitoire des syste`mes frigorifiques fonctionnant au CO2 a` l’aide de Modelica Mots cle´s : Syste`me frigorifque ; Dioxyde de carbone ; Mode´lisation ; E´changer de chaleur ; Regime transitoire

1. Introduction In a research project financed by the German federal government and Airbus Deutschland, Hamburg (Germany) and executed by the Department of Technical Thermodynamics of the Technical University HamburgHarburg (TUHH), Hamburg (Germany) a system simulation of a cooling system is to be realised, using the refrigerant carbon dioxide (CO2). The main objective of the project is a proof of concept of a CO2 based integrated on-

* Corresponding author. Tel.: +49-40-42878-3144; fax: +49-40-42878-2632. E-mail address: [email protected] (G. Schmitz). 0140-7007/$35.00 # 2003 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/S0140-7007(03)00098-7

board cooling system of future airliners. For this purpose, numerical and experimental investigations are in progress. The fact of climate changes due to ozone depletion and global warming has been directed to significant research activities on the field of refrigeration and airconditioning since the 1990s [1]. The objective of the investigations may yield to a long-term solution, which is especially important for aerospace application due to the long life cycle of airliners. Therefore so called natural, resp. alternative refrigerants with no Ozone Depleting Potential (ODP) and no or a very low Global Warming Potential (GWP) are investigated and new technical developments are driven. Carbon dioxide (CO2, R 744) as a natural refrigerant was rediscovered and has recently demonstrated a very

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Nomenclature A F:  I KV M N6 U Y V g h f n p x xT p : loss Ws z

area (m2) scaling factor for medium momentum flux (kg m s2) flow coefficient (m3 h1) total mass (kg) numeric factor total internal energy (J) expansion factor volume (m3) gravitational constant (kg m1 s2) specific enthalpy (J kg1) compressor speed (s1) discretisation of flow in simulation model pressure (Pa) differential pressure ratio critical differential pressure ratio pressure loss due to friction (Pa) shaft work (J s1) length of control volume (m)

high potential to substitute currently used refrigerants in the area of mobile/automotive air-conditioning and refrigeration [2,3]. This development is caused by the thermodynamic, transport and environmental properties of CO2. In order to obtain a better understanding of the complex thermodynamic and hydraulic behaviour of CO2-refrigeration processes under the specific boundary conditions of aircrafts the modelling of components of a CO2-system has been realised. For the modelling the object-oriented modelling language ModelicaTM is used [4,5]. The scope of the CO2-library is the modelling of the system behaviour by consideration of the most important physical effects like compressible flow, heat transfer, pressure drop and time delays.

Fig. 1. Schematic diagram of a CO2-refrigeration cycle for an on-board cooling system [7].

: m: Q

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mass flow (kg s1) heat flow (J s1)

Greek letters  angle of flow (deg)  density (kg m3) l volumetric efficiency  isentropic efficiency  difference

Subscripts co compressor dv displaced volume ev expansion valve in inlet is isentropic out outlet 0 initial state

2. CO2-refrigeration system Carbon dioxide was used as a refrigerant until the 1930s, but was then replaced by the synthetical refrigerants (HCFCs) that offered lower absolute pressures, simpler techniques and higher efficiencies in conventional vapour compression cycle. Due to the ODP and the GWP of the synthetical refrigerants, the substitution of these by more environment friendly refrigerants is aspired. Automotive air-conditioning and refrigeration is an active area of recent research. It focused on the development of a transcritical cycle [6]. The temperature and pressure at the critical point of CO2 are 304.13 K and 7.377 MPa. Therefore, the refrigerant cycle has to be operated transcritically when the ambient temperature is near or higher than the critical temperature. In this case the heat rejection takes place at supercritical state. However, in the aerospace application, the system operates in flight in condensation mode but on ground a transcritical process has to be realised. As shown in Fig. 1, the on-board cooling system is designed as a direct expansion cycle. The remote components, expansion valve and evaporator are placed at the cooling points in the cabin. They are supplied by the piping, which connects remote and centralised components. The centralised components consist of compressor, gas cooler, internal heat exchanger, lowpressure receiver and control unit, which are placed outside the cabin. So the heat rejection at the gas cooler is to the ambient (ambient temperatures in flight can be

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243.15 K). The idea of such a concept is to get more flexibility by the design of the cabin layout since only the remote components and the piping are in the cabin.

3. Modelica Modelica is an object-oriented modelling language to model large, complex and heterogeneous physical systems. The language is designed for convenient, component-oriented modelling of physical multi-domain systems. A basic design idea of modelling with Modelica is that it can be utilised in a similar way as an engineer builds a real system: first trying to find standard components like compressor and heat exchanger from manufacturers’ catalogues with appropriate specifications and interfaces. Only if a particular subsystem does not exist, a component model would be newly constructed based on standardised interfaces [8]. The manufacturers’ catalogues are represented as a collection of components to be used together in Modelica by libraries. The models in Modelica are mathematically described by differential, algebraic and discrete equations. This means that no particular variable needs to be solved for manually. A Modelica tool will have enough information to decide that automatically by the causality between components in a complete physical system. Therefore, models in Modelica do not pre-define the computational causality. This leads to better reusability of the developed models because they contain fewer assumption about the context of their use [4]. The causality between components of a system model is determined by special algorithm. In Modelica connectors are used to specify the interaction between components. Therefore, a connector should contain all quantities needed to describe the interaction. The connector variables can be characterised as across and through (resp. flow) variables; the across variables represent the driving force across a component e.g. pressure in a thermohydraulic network, whereas through variables represent the quantities flowing through a component like the flow rate. The through variables sum to zero at a node (resp. connector) and are declared by the prefix flow. So, the application of the sum-to-zero equations of conservation laws results in additional equations determining the overall system equations. They are formulated in all physical domains, e.g. Kirchhoff’s law, Newton’s law. As mentioned above the reuse of models is possible as well as a hierarchical structure of models due to the fact that Modelica is an object-oriented language. The ability of reuse (by inheritance and aggregation), hierarchical decomposition and model exchange enables the handling of complexity in an advantageous way. Furthermore Modelica supports arrays, the handling of time and state events and the use of external C- and FORTRAN-functions.

For the utilisation of the Modelica language, a Modelica translator is needed to transform a Modelica model into a Differential Algebraic Equation (DAE) system. with a fixed causality. Therefore, symbolic transformation algorithms have to be applied to transform the equations into a form which can be integrated with standard methods. These transformation algorithms and solvers are available in two commercial simulation environments, DymolaTM [9] and MathModelicaTM [10]. Both simulation environments include a graphical user interface (GUI) for model editing and browsing, Modelica translator, simulation engine and visualisation of results. We are using Dymola, which provides some more features like a convenient interfaces to Matlab/SIMULINKTM and the ability of hardware-in-the-loop simulation. The development and promotion of Modelica is organised by the non-profit Modelica Association [5].

4. CO2-library The aim of the modelling is to create a library with physical based models of the components above mentioned. Such a library with models of these components and of additional components for testing, like sinks and sources, can be used for investigations of components and complete refrigeration cycles. Furthermore it is of great interest to make dynamic simulation as well as steady state simulation of CO2-systems and single components, especially heat exchangers. The numerical investigation of heat exchanger components is of particular interest to find optimised heat exchangers for limited space. On the other hand, the concept of connectors in Modelica provides the opportunity of using the same heat exchanger models for single component simulation as well as for a complex cycle simulation. There are different backgrounds for modelling and simulation of CO2-refrigeration cycles. The first aim is a better understanding of the complex, coupled thermodynamic, fluid-mechanic and heat transfer effects in a CO2-system on typical aerospace boundary conditions. Furthermore, aspects of the control of the system should be investigated. Finally, the library can be used for simulation and evaluating of different system designs in various applications.

5. ThermoFluid library The CO2-library is based on free Modelica library ThermoFluid [11–13]. The ThermoFluid library, especially the base classes and partial components, is very well suited for modelling of CO2-systems with respect to the implementation of the three balance equations and the method of discretisation. The basic design principles of the library are:

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 models are designed for system level simulation,  one-dimensional one- and two-phase flow is considered,  one unified library for lumped and distributed parameter models,  bi- and unidirectional flows are supported,  conservation laws are implemented separate from the medium models, in order to improve reusability.

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6.1. Heat transfer and pressure loss relations for the whole fluid region These constitutive equations are used for the calculation of heat flux and pressure drop due to friction, which are added to the balance equations of energy and momentum [16–18]. 6.2. Models for the air side of heat exchangers

The use of distributed parameter models suggests the finite volume method as discretisation method. The finite volume method is very common for system modelling and one-dimensional discretisation [14]. By the implementation of the conservation laws of energy, mass and momentum using the finite volume method, the thermodynamic model and the flow model can be separated, since the storage of momentum is calculated in a control volume which usually is staggered by a half grid length versus the grid of the control volume of mass and energy. The thermodynamic model holds the equations for total mass and internal energy for control volume with constant volume:

The balance equation of energy is implemented by the finite volume method [14]; heat transfer correlations for the air side have been implemented [19] as well as medium properties of air using polynomial fitting.

dM : : ¼ min  mout dt

6.4. Compressor ð1Þ

: : dU : : ¼ min  hin  mout  hout þ Q þ Ws dt

ð2Þ

The fluxes on the border of the control volume are calculated by the half grid staggered flow model, which holds either a stationary pressure drop model or the dynamic momentum balance: : : dm : Dz  ¼ Iin  Iout þ ðpin  pout ÞA dt ð3Þ  Dploss A  M  g  sinðÞ: The state variables of {M, U} for the thermodynamic model are numerical not efficient. Therefore, Eqs. (1) and (2) are transformed into a form with {, h} or {, T} as state variables. The constitutive equations needed for the calculation of pressure drop and heat flow in Eqs. (2) and (3) are not implemented in the ThermoFluid library yet. In cooperation with the developers of ThermoFluid we have implemented a high accuracy medium model for CO2 based on an equation of state for the whole fluid region [15].

6. Survey of CO2-library So far, the following models and classes have been implemented:

6.3. Pipes and heat exchangers Based on the medium model, classes of ThermoFluid, the heat transfer and pressure drop correlations and the air side models, pipes and heat exchangers have been modelled. The pipes are modelled as one-dimensional discretised flow paths as well as the air flow.

The model is made for a reciprocating compressor. Therefore, the mass flow is calculated by the general equation (4) of a reciprocating compressor and the enthalpy change is calculated according to the isentropic efficiency by Eq. (5): : mco ¼ f  l  in;co  Vdv ð4Þ Dhco ¼ hout;co  hin;co ¼

hout;co;is  hin;co 

ð5Þ

The efficiencies can be provided by measured characteristic fields of a known component or are set as constant parameters if they are unknown and must be estimated. 6.5. Expansion valve The throttling process is treated as isenthalpic and the pressure drop is calculated according to the flow coefficient of the valve using an algebraic equation [20]: 1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  KV  Y  N6  x  pin;ev  in;ev 3600 pin;ev  pout;ev where is : x ¼ pin;ev x Y¼1 3  F  xT : mev ¼

ð6Þ ð7Þ ð8Þ

Since the flow coefficient KV and the critical differential pressure ratio xT result from specific valve data and construction, the model has to be parameterised with corresponding data.

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6.6. Receiver For modelling the receiver is separated in a separator, a tube for the gaseous outflow, an orifice for the liquid outflow and a junction mixing the two outflows. This modelling approach is similar to [21]. The incoming two phase flow is separated into its liquid and vapour phase. The outlet condition is calculated by the mixing of the two mass flows through the tube and the orifice, which are modelled as flow resistance with specific friction factors. The friction factors can be estimated for steady state; then the vapour fraction at the receiver outlet is the same as the receiver inlet. The receiver is modelled as adiabatic. 6.7. Flow splits and junctions For this models classes of ThermoFluid are used. The pressure drop in the momentum equation uses special correlations for splits and junctions taking the ratio of mass flow into account [22]. The change of mass flow direction is also taken into account in the implementation.

7. Modelling of heat exchangers So far, available heat exchangers for CO2-refrigeration systems are mostly compact prototype components of automotive applications [Fig. 2(a)]. The heat exchangers are built up as follows: the CO2-flow is split into different streams through so called flat-tubes (Multiport-Micro-Tubes or micro-channels) [Fig. 2(b)]. The flat-tubes consist of a number of parallel channels in which the CO2 flows. The refrigerant is splitted and collected at the feeder and manifold of the heat exchanger. Outside the heat exchanger air passes over multilouvered fins enhancing the air side heat transfer area

and heat transfer coefficient [Fig. 2(c)]. In a heat exchanger, different flow paths for the CO2 are possible. Usually gas coolers are constructed as cross-flow heat exchangers and evaporators are built as cross-counterflow heat exchangers. For the modelling of the CO2-flow a homogenous distribution of the flow is supposed. Using this assumption, the flow is modelled with one single pipe. The heat transfer area and the flow cross section are determined by the geometry and the number of all concurrently flowed pipes; whereas the heat transfer coefficient and the pressure loss is calculated with the mass flow rate and the geometry of a single channel. The assumption of homogenous mass flow and temperature distribution is also made for the air side. Therefore, it is possible to model the air flow through one air channel. The wall is modelled as a capacitive, cylindrical wall. For a more detailed explanation of the modelling see [23]. These specific models of CO2-pipe, wall and air have to be connected in the right way to get a reasonable model of a heat exchanger. For the connection, the heat connectors of ThermoFluid can be used; the connecting variables are temperature and heat flux. In Fig. 3 the graphical representation of the heat exchanger model in a Modelica composition diagram is shown. This is the Table 1 Absolute, resp. relative error of measurement Pressure at suction line Pressure at high pressure side CO2 temperature Air temperature evaporator in/out Air temperature gas cooler in Air temperature gas cooler out CO2 mass flow rate Air mass flow rate

50 kPa 100 kPa 0.7 K 1 K 1 K 3 K 0.2% 4%

Fig. 2. Air–CO2 heat exchanger from the automotive application and elemental breakdown into the heat transfer and fluid flow parts for the refrigerant and the air.

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top level of the model consisting of the connected instances of the models for the air side, the wall and the pipe. Furthermore, the interfaces for the CO2 (symbolised by filled and hollow rhombs) can be seen as well as the inports for the air side boundary conditions (symbolised by the triangles). The extensive parametrisation of the heat exchanger is realised with a record, symbolised by the rectangle geoHX. A record forms a container for many parameters.

8. Experimental setup The experiments were carried out at the CO2-experimental system built at the Department of Aircraft Systems Engineering of the TUHH described in detail by Schade [24]. The test rig were built up with prototype components of the automotive application. It has been

realised the flow circuit of a transcritical cycle introduced by Lorentzen and Pettersen [25], which differs in the realisation of three, parallel cooling points as shown in Fig. 1. The main objective of the experimental investigations is control-oriented. Furthermore, steady state and transient data from the test rig should be used for the validation of the simulation models. The gas cooler is a cross-flow heat exchanger with three passes at the refrigerant side. The evaporators are cross-counter flow heat exchanger. They have eight passes in two layers. The internal heat exchanger is built as a counter-flow heat exchanger with coaxial tubes. The used compressor consists of an axial piston unit with variable or fixed displacement. The gas cooler is installed in an open channel whereas the evaporators are built in closed loop air-cycles. The temperature and mass flow rate of the air at the heat exchanger inlet is conditioned by electrical air heaters and fans. The temperature of CO2 at inlet and exit of each component is measured with thermocouples put on the surface. The pressure is also measured at inlet and exit of each component. The CO2 mass flow rates are measured at different points in the system by using Coriolis type meter. Hot-wire anemometer are used for measuring the air mass flow rates through the heat exchangers. The air inlet and exit temperatures are measured by thermocouple grids. The uncertainties for the measurements are listed in Table 1. Especially the uncertainties of the air temperature after the gas cooler is very high due to the inhomogenes distribution of temperature. Due to error propagation the resulting uncertainty of the calculated capacities can be up to 12% for both gas cooler and evaporator.

9. Validation of air-CO2 heat exchanger models

Fig. 3. Modelica composition diagram of a heat exchanger model.

Simulations in a test configuration have been run with the gas cooler model discretised with nCO2 ¼ 9 for the CO2 flow and nair=4 for the air-side flow; the evaporator was discretised with nCO2 ¼ 8 and nair=4. These

Table 2 Comparison of measured data at a gas cooler with simulation results in steady state Boundary conditions from measured data : mCO2 (kg s1)

pCO2 in (MPa)

0.0133 0.0197 0.0129 0.0553 0.0370 0.0497 0.0642 0.0274

11.30 9.80 9.60 8.92 8.80 8.21 8.13 7.02

Measured data

TCO2 in (K)

: mair (kg s1)

Tair,in (K)

TCO2 out (K)

398.1 386.3 395.4 373.7 380.7 364.4 346.0 345.6

0.499 0.551 0.605 0.442 0.596 0.467 0.556 0.467

302.2 312.5 308.8 307.9 312.8 307.9 307.6 297.2

302.9 314.2 309.5 315.1 315.4 311.9 311.6 301.4

Simulation

Tair,out (K)

: QCO2 (kW)

TCO2 out (K)

Tair,out (K)

: QCO2 (kW)

311.3 321.5 315.6 325.1 324.4 321.4 318.4 305.3

3.53 4.01 3.10 7.89 5.31 6.04 5.93 3.36

304.7 315.9 312.0 317.4 316.4 314.0 313.4 301.9

309.0 319.1 313.5 323.0 321.0 319.0 316.6 304.1

3.45 3.71 2.91 6.85 5.03 5.32 5.14 3.31.

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discretisations were chosen for the simulation due to acceptable execution time for a simulation run of a complete refrigeration cycle. The test configuration consists of a source providing pressure and enthalpy at the heat exchanger inlet and a mass flow sink generating a defined mass flow at the outlet. The source and sink are used to set the boundary conditions resulting from measured data at the component. Table 2 shows the measured data at the gas cooler and the simulation results for a set of operating conditions. What can be seen from the comparison is that most of the simulated capacities are in within the error of

12%. The deviation becomes near the critical point higher what can be traced back to the chosen discretisation of the model. A higher discretisation would include the influence of the pseudo-critical point more exact. The discretisation affects also the exit CO2 temperature which the model predicts for supercritical gas cooling within 1.1 and 2.6 K higher than the experimental data and outside the error of 0.7 K. For operating conditions below the critical pressure the model predicts the capacity very well. The influence of discretisation with regard to the consistence with experimental data is shown by Limperich [26].

Table 3 Comparison of measured data at an evaporator with simulation results in steady state Boundary conditions from measured data : mCO2 (kg s1)

pCO2 in (MPa)

0.0394 0.0320 0.0314 0.0172 0.0308 0.0370 0.0129 0.0277

5.01 4.91 4.48 4.05 4.06 3.68 3.46 3.04

Measured data

hCO2 in (kJ kg1)

: mair (kg s1)

Tair,in (K)

310.6 295.3 293.6 304.0 302.2 278.1 222.1 266.1

0.178 0.210 0.214 0.156 0.196 0.217 0.212 0.219

303.2 301.6 297.9 286.5 293.4 291.6 285.2 283.2

Simulation

Tair,out (K)

: Qair (kW)

Tair,out (K)

: Qair (kW)

289.9 289.8 286.1 280.2 281.7 278.7 275.7 272.5

2.38 2.49 2.54 0.99 2.31 2.82 2.03 2.36

290.6 289.6 286.3 280.5 282.2 279.0 275.6 271.7

2.26 2.54 2.50 0.94 2.21 2.75 2.05 2.54

Fig. 4. Modelica object diagram of the simulated CO2-cycle.

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Table 3 compares the results of the evaporator model with experimental data. As Table 3 shows, the model predicts the capacity within 7.4% and the exit air temperature within 0.8 K which is within the uncertainty of measurement. The humidity of the air was not taken into account since the evaporator is integrated in a closed loop air-cycle. Therefore it can assumed that the air is dehumidified after a short time of operation. The refrigerant pressure drop is clearly underestimated by the models since they consider only the pressure drop of the flat tubes and not the main pressure drop of the heat exchanger arising from the refrigerant distributors. The supplement of the models with such pressure drop correlations is possible but this detailing was not implemented with regard to the aim of modelling on system level.

10. Transient simulation of a CO2-system

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compared with data of a start up of the system and following step changes in compressor speed as shown in Fig. 5. The air inlet temperature of the evaporator changed also during the experiment (Fig. 5). The other boundary conditions were constant and are listed together with the initial states in Table 4. All these data were taken from the experiment. In Figs. 6 and 7 the simulated and measured pressure at compressor inlet and exit is plotted versus time. The plotted experimental data are filtered due to the very high measurement noise. What can be seen from the comparison is a fair agreement of the absolute values as well as the time response for the pressure at the compressor inlet. At the compressor exit there is only a partial agreement; especially at the beginning there is a clear deviation in absolute values and time response. The model predicts a pronounced undershoot whereas the experimental data show a smaller undershoot. This behaviour can also be seen in the comparison of the

In the following, results of the transient simulation of the above mentioned CO2-system are presented. The simulated model is shown in the object diagram in Fig. 4. This configuration represents the available CO2-test rig at the basic level with one evaporator. The results are

Fig. 6. Transient run of the pressure at compressor inlet; comparison between simulation and measurement.

Fig. 5. Step changes in compressor speed and run of air inlet temperature at the evaporator in the experiment; set as boundary condition of simulation run.

Table 4 Boundary conditions and initial values of the simulation run corresponding to the experiment Compressor Expansion valve Gas cooler Evaporator System volume Specific refrigerant charge Initial value Initial value receiver

fixed displacement Vdv=33.5 ccm 100% open; Kv=0.0264 m3 h1 : mair ¼ 2100 kg h1 , Tair,in=312 K : mair ¼ 760 kg h1 Vtot=3.62 l 267 kg m3 p0=5.7 MPa, h0=425 kJ kg1 p0=5.7 MPa, h0=295 kJ kg1

Fig. 7. Transient run of the pressure at compressor exit; comparison between simulation and measurement.

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mass flow rate at the expansion valve in Fig. 8. In general, there is a systematic underestimation of the mass flow rate by the model, which is larger then the tolerance of the used mass flow meter. The run of pressures and mass flow rates are coupled in such systems. Therefore deviation of one value influences the other values and vice versa. Reasons for this could be seen in the modelling of the compressor using algebraic equa-

Fig. 8. Transient run of the mass flow rate at the expansion valve; comparison between simulation and measurement.

tions instead of a physical model. This leads to the use of characteristic fields for the efficiencies, which were generated by measurements of steady state. Especially at the start up of the system the used efficiencies in the model are probably different from the real behaviour of the compressor. Furthermore the available values of the flow coefficient of the expansion valve are independent from the inlet state and the pressure difference at the valve. The flow coefficient is only a function of the open ratio. From physical point of view it seems to be obviously that this simplified characteristic does not represent the complete operating range. So, the uncertainty of component-specific parameters like compressor efficiencies and flow coefficient of the valve influences the simulation results. This known influence can be accepted for the level of system simulation and has to be taken into account for the validation of the models. Finally, it is possible to illustrate the steady state of the simulated and measured processes in a p,h-Diagram of CO2 (Fig. 9). The shown processes are representing the states after 520 s. This comparison shows also a fair agreement. The pressures are calculated correctly and also the conditions at the compressor, the gas cooler and the evaporator show a good agreement. The most significant deviation can be seen in the enthalpy change at the internal heat exchanger. The transferred heat flux

Fig. 9. Process in a p,h-Diagram of CO2; comparison between measurement and simulation after 520 s; (1) compressor in; (2) compressor out; (3) gas cooler out; (4) internal heat exchanger out; (5) evaporator in; (6) internal heat exchanger in.

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is underpredicted in the simulation. Therefore, the inlet and outlet states of the evaporator are delayed, but the absolute value of enthalpy change is calculated correctly. The state at the compressor exit differ a bit due to the position of the thermocouple installed after the oil filter. So, the measured temperature is lower than the predicted one.

[7]

[8]

[9]

11. Conclusion [10]

The object-oriented modelling language Modelica is well suited for the physical modelling and transient simulation of CO2-refrigeration cycles. The implemented library provides both base models for modelling of CO2-components and usable models of components for the available test rig. The intention is to create a library for the simulation of single components and complete cycles. Such a library can be used to make fundamental investigations of a CO2-system. Furthermore, it can be used for the optimisation of specific heat exchangers, for the evaluating of an optimal system configuration and for the layout and optimisation of the system control. The presented simulation results for the steady state of two different types of CO2-heat exchangers show a fair correspondence with measured data. The results of the transient simulation show a good agreement in comparison with experimental data. Therefore, future work comprises the use of the library for investigations of aircraft applications. For further investigations of the system control and the exploration of the dominant system dynamics it is possible to use a moving boundary model for evaporators, which is implemented in Modelica and is an extension of ThermoFluid [27]. This model will give the possibility for a reduced-order model for more control-oriented investigations.

[11]

[12]

[13]

[14] [15]

[16] [17]

[18]

[19] [20]

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