- Email: [email protected]

Dynamic simulation and analysis of a water chiller refrigeration system Zhao Lei a, M. Zaheeruddin

b,*

a

b

College of Power and Energy, Xi’an Jiao Tong University, Xi’an 710049, PR China Building Civil & Environmental Engineering, Concordia University, Montreal, Canada H3G 1M8 Received 12 November 2003; accepted 7 January 2005 Available online 12 February 2005

Abstract In this paper, a lumped-parameter dynamic model of a water chiller refrigeration system based on mass and energy balance principles is developed. First the component models for an evaporator, compressor, condenser and a thermostatic expansion valve (TEV) were derived. These models were integrated to develop an overall model of a water chiller system. A control-oriented approach to model development was taken and the eﬀect of control inputs such as compressor operational frequency and TEV opening fraction on the output performance of the system was investigated. The transient response characteristics show that the thermal system responses are much slower than pressure and mass ﬂow rate responses revealing a two time-scale property of the system. Steady state performance of the system is also analyzed and graphical relationships between refrigerant mass ﬂow rate, suction vapor superheat temperature, operation frequency and thermostatic expansion valve opening fraction are presented. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Water chiller; Thermal expansion valve; Variable frequency; Dynamic simulation; Steady state analysis

*

Corresponding author. Tel.: +1 514 848 3194; fax: +1 514 848 7965. E-mail address: [email protected] (M. Zaheeruddin).

1359-4311/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2005.01.002

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Nomenclature A cross-sectional area of refrigerant inside or outside of tubes in the ﬂow direction CTV characteristic constant of the TEV valve speciﬁc heat cp Din, Dout inside or outside diameter of tubes G mass ﬂux hin, hout inlet and outlet enthalpy of evaporation or condensation section latent heat of vaporization at evaporation or condensation pressure hlv k ratio of speciﬁc heats k conductivity liquid refrigerant conductivity at condensation and evaporation pressure kl L total length l evaporation or condensation section tube length Mc total mass heat capacity refrigerant mass ﬂow rate at the evaporation and condensation section inlets m_ in m_ r;com refrigerant mass ﬂow rate n number of tubes in evaporator or condenser N compressor motor speed condenser pressure Pc discharge pressure Pd suction pressure Ps S percent slip T temperature discharge temperature Tdis suction temperature Tsuc DTSS static superheat of thermostatic valve DTopr, DTrt actual operating superheat and the rated operating superheat temperature evaporation or condensation temperature Tr tube wall temperature of evaporation and condensation section Tt clearance volume Vc theoretical displacement of compressor VD Wcom compressor work indicated compressor work Wi Greek symbols c average void fraction a condensation or evaporation heat transfer coeﬃcient of refrigerant inside or outside tubes dynamic viscosity of liquid refrigerant under condensation or evaporation pressure ll saturated liquid density of refrigerant at condensation or evaporation pressure ql suction vapor density qsuc

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s gcom gv

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time compressor eﬃciency volumetric eﬃciency of the compressor

Subscripts r refrigerant wa water t tube c condensation e evaporation sh superheat section TEV thermostatic expansion valve com compressor

1. Introduction Building cooling load varies with occupancy and climate changes so that HVAC systems experience unsteady time varying disturbances from time to time and operate under part load conditions most of the time. Thus refrigeration system should regulate its capacity to match the building loads. A refrigeration system can regulate its capacity by modulating compressor speed step by step or continuously with input frequency control. Furthermore, the thermostatic expansion valve can also be adjusted to regulate the cooling capacity. Therefore, it is important to clearly identify and evaluate the dynamic performance of refrigeration systems subject to these changes so that better control strategies can be designed and system operation could be optimized. In recent years, some researches have studied dynamic modeling of refrigeration systems. He et al. [1] developed an 11th order lumped-parameter dynamic model for vapor compression airconditioner and simpliﬁed the model to design a MIMO feedback controller. Wang [2] developed a simulation program for a building central chilling system employing empirical equations to model heat exchangers of the chiller and studied on-line control strategies. It is a suitable tool for evaluating the control performance of large central chilling systems. Deng [3] presented a dynamic model for a direct expansion (DX) water-cooled air-conditioning system. The model was used to study the inﬂuence of refrigerant mass ﬂow rate, evaporation pressure as well as air side state on system performance. Browne [4] presented a dynamic model for vapor compression liquid chillers using regression model for compressor and empirical model for evaporator. Two chillers, one with continuous capacity modulation and the other with a series of capacity steps, were simulated to predict the start-up process. Ding [5] et al. presented a dynamic model of air-to-water dual-mode heat pump screw compressor having four-step capacities. The dynamic responses of adding additional compressor capacity in step-wise manner were studied. Choi and Kim [6] experimentally studied an inverter-driven multi-air conditioner with electronic expansion valves. They proposed an optimal set point for suction vapor superheat temperature. Matsuoka and Nagatmo [7] studied step response transient characteristics as a function of compressor frequency, indoor fan speed, and EEV opening. Koury et al. [8] proposed a model for a refrigeration system with

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distributed parameter model for heat exchangers. Numerical simulations were carried out to verify the possibility of controlling the refrigeration system and the superheating of the refrigerant in the evaporator outlet by varying the compressor speed and the throttling valve position. It is well known that the operation of the expansion device plays a crucial role in refrigeration system performance. This process has to be accurately modeled. Inaccurate superheat temperature prediction will make the TEV give poor regulation. This is especially signiﬁcant in variable frequency refrigeration systems. However, all the studies mentioned above modeled the superheat section of evaporator by neglecting the thermal capacity, or by using either empirical method or a distributed parameter approach. The distributed parameter methods are diﬃcult and timeconsuming to accurately predict the suction vapor superheat. In this paper, refrigerant thermal capacity in the superheated section was taken into consideration using a much simpler lumpedparameter approach. Therefore, a major objective of this study is to develop a relatively accurate and computationally eﬃcient dynamic model of a water chiller useful for control analysis and design.

2. Refrigeration system modeling 2.1. Description of physical system In this paper, a 10.5 kW water chiller was modeled. It has a variable frequency compressor, a condenser, an evaporator and a thermostatic expansion valve (TEV). Refrigerant R22 is used in the system as a working ﬂuid. Both condenser (refrigerant on the shell-side) and evaporator (refrigerant on the tube-side) are counter-cross ﬂow shell-and-tube type with one single shell pass and one tube pass. Tubes are made of copper and have a staggered layout. The design conditions used were 7 °C for outlet chilled water temperature and 30 °C for inlet cooling water temperature to the condenser. 2.2. Mathematical model of chiller 2.2.1. Compressor model Neglecting the eﬀect of the compressor shell on system performance and assuming that compressor reaches operating speed instantaneously, a steady-state model is adopted for the isentropic compression process. Refrigerant mass ﬂow rate through the compressor is a function of compression ratio, refrigerant density and compressor speed, that is, pc V D N gv ; qsuc ; N ¼ ð1Þ m_ r;com ¼ f pe vsuc where, VD is the theoretical displacement volume of compressor; gv is the volumetric eﬃciency of the compressor, and is given by " # 1=k V cl pd 1 ð2Þ gv ¼ 1 VD ps

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where N the compressor speed is a function of frequency N ¼ 120f ð1 sÞ=p The relationship between compressor exit and inlet temperatures is given by k1 p k T dis ¼ T suc c pe

ð3Þ

ð4Þ

The work input to the compressor is given by W com ¼

m_ r;com W i gcom

Neglecting the thermal inertia eﬀects, the indicated work is given by " k1 # k pd k Wi ¼ 1 p vs k1 s ps

ð5Þ

ð6Þ

where gcom is the total eﬃciency of the compressor. 2.2.2. Heat exchanger model By assuming that the pressure drop in the heat exchangers is negligible, lumped-parameter models were set up for both the condenser and the evaporator. In modeling the condenser, only condensation section is considered since the dynamic characteristics of the condenser is mainly dominated by the condensation region. On the other hand, the evaporator was described by a two-phase section and a superheated vapor section because the change of suction vapor superheat temperature greatly inﬂuences the system dynamic characteristics. Each section is divided into three control volumes: refrigerant inside/outside of tubes, the tube walls, and chilled/cooling water outside/inside of tubes. Dynamic model equations were developed by applying the mass and energy balance for each control volume. In the model, the shell surface was considered to be well insulated and longitudinal heat transfer was neglected. 2.2.2.1. Two-phase section model. Both the condensation and evaporation section models will be described together for they have many common characteristics. The moving boundary condition between the two-phases was predicted by computing the rate of change of two-phase section tube length as a function of time, such as dl ð7Þ ¼ m_ in ðhin hout Þ þ ar npDlðT t T r Þ ds where l stands for the evaporation or condensation section tube length; A is the cross-sectional area of refrigerant inside or outside of tubes in the ﬂow direction; Tr represents evaporation or condensation temperature; Tt is the tube wall temperature in evaporation and condensation sections. All other symbols are deﬁned in the nomenclature. The variation of evaporation and condensation pressure with time is due to the change of vapor mass in the evaporator and condenser. This was described by the following equation ql hlv Að1 cÞ

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Al

dqv dP hin hout ar npDlðT t T r Þ ¼ m_ in m_ out þ hlv dP ds hlv

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ð8Þ

where m_ out represents the vapor refrigerant mass ﬂow rate at the outlet of the condensation and evaporation sections. qv is the saturated vapor density of refrigerant at condensation or evaporation pressure. For the tube walls in two-phase region, an energy balance equation yields ðqcp Þt At

dT t ¼ ar npDðT r T t Þ awa npDðT t T wa Þ ds

ð9Þ

where subscript ÔtÕ represents the tube walls; At is the cross-sectional area of tube walls; T wa is the water temperature outside or inside the tubes; awa is the convective heat transfer coeﬃcient of water outside or inside tubes. The energy balance equation for water in the inside or outside of the tubes is dT wa ð10Þ ¼ m_ wa cwa ðT wa;in T wa;out Þ awa pDðT wa T t Þ ds where subscript ÔwaÕ refers to water; Twa,in, Twa,out are inlet and outlet water temperatures in the evaporation and condensation sections. ðqcP Þwa Awa

2.2.2.2. Superheat model of evaporator. By neglecting the refrigerant mass accumulation in the superheat section, we have described the variation in vapor superheat temperature due to changes in evaporation pressure and heat transfer in superheat section using the following energy balance equation AðLe le Þqr;sh

dhr;sh dT r;sh ¼ m_ r;out ðhv;eva hr;sh Þ þ ar;sh npDðLe le ÞðT t;sh T r;sh Þ dT r;sh ds AðLe le Þqr;sh

dðhr;sh Þ dP e dP e ds

ð11Þ

where Le is the total evaporator tube length; le is the tube length of evaporation section. Energy balance for tube wall in superheat section can be written as dT t;sh ¼ ar;sh npDin ðT r;sh T t;sh Þ awa npDout ðT t;sh T wa;sh Þ ð12Þ ds where subscript ÔshÕ represents superheat section, ar,sh is the convective heat transfer coeﬃcient of superheat refrigerant vapor. Similarly an energy balance on water in superheat section yields: ðqcp Þt At

dT wa;sh ¼ m_ wa cwa ðT wa;in;sh T wa;out;sh Þ awa pDout ðT wa;sh T t;sh Þ ds where Twa,in,sh, Twa,out,sh are inlet and outlet water temperatures of the superheat section. ðqcP Þwa Awa

ð13Þ

2.2.2.3. Refrigerant properties. In the model, water and tube properties are deemed as constant, refrigerant thermodynamic properties are functions of state and were computed using CSD

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(Carnanhan–Starling–DeSantis) equation [9]. A computer program was developed to compute various properties of R22. The predicted properties were compared with the values given in ASHRAE Handbook [10]. The error was found to be within 1% for parameters such as density, enthalpy and to be within 10% for the transport properties. 2.2.2.4. Heat transfer coeﬃcient and void fraction. In this model, refrigerant vapor condenses on outside of staggered horizontal smooth tube bundles in shell-and-tube type condenser. Average condensation coeﬃcient was calculated by the following correlation [11] 2 1=4 gql hlv k 3l ð14Þ ac ¼ 0:725 ll DtNDout The average evaporation heat transfer coeﬃcient inside smooth copper tubes in shell-and-tube evaporator was calculated by using the correlation [10] " 2 # n kl Gre Din J Dxhlv ð15Þ ae ¼ C 1 Din ll L where C1 = 0.0225 and n = 0.375. G is the mass ﬂux of refrigerant. Heat transfer coeﬃcient of single-phase refrigerant vapor and water inside tube were calculated by the Dittus–Boelter correlation [10] 0:8 a Din G Din l cp 0:33 ð16Þ ¼ 0:023 k l k Water-side heat transfer coeﬃcient for staggered horizontal tubes is given by [10] 0:6 a Dout Dout Gmax Pr0:33 ¼C k l

ð17Þ

where C = 0.33 for staggered tubes, and reduced factor of 0.95 is considered for tubes with less than 10 rows. The void fraction model recommended in the ASHRAE handbook [10] was used. 2.2.3. Thermostatic expansion valve modeling Thermostatic expansion valve is the valve that controls the refrigerant mass ﬂow rate by sensing the degree of suction vapor superheat temperature. The process is deemed as isenthalpic and the refrigerant mass ﬂow for the fully open TEV is calculated by the following equation pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ð18Þ m_ r;TEV ¼ C TEV ðDT Ope DT SS Þ ql DpTEV where CTEV is the characteristic constant of the valve; Dp is the inlet and outlet pressure diﬀerence of the valve, that is, condensation and evaporation pressure diﬀerence; ql is the refrigerant density at its inlet; DTSS is the static superheat of the valve; DTOpe is the operating superheat temperature. CTEV was approximately calculated according to the nominal conditions of TEV qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ m_ r;rt C TEV ¼ ð19Þ ql;rt Dprt ðDT rt DT ss Þ where the subscript ÔrtÕ represents the nominal work conditions.

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3. Simulation results and analysis 3.1. Transient responses 3.1.1. Transient responses to changes in operational frequency Dynamic responses of the refrigeration system to step changes in compressor speed were simulated. Before introducing a step change in the compressor speed, the refrigeration system was allowed to reach a steady condition at an operational frequency of 70 Hz, and thermostatic valve 85% open. Under these conditions, a step change in frequency was applied. The dynamic responses of the system with respect to the changes in operational frequency are illustrated in Figs. 1–3. From Fig. 1, we can observe that compressor discharge rate increases almost instantaneously as the operational frequency and hence the compressor speed is increased. Under these conditions,

Refrigerant Mass Flowrate (kg/s)

0.12 0.1

20 Hz, discharge rate 20 Hz, valve rate

0.08

80 Hz, discharge rate 80Hz, valve rate

0.06 0.04

120Hz, discharge rate 120Hz, valve rate

0.02 0

0

20

40

60

80

100

time (s)

Fig. 1. Transient response of refrigerant discharge rates from the compressor and expansion valve.

Condensation Pressure (kPa)

2500 2300

20 Hz 80 Hz 120 Hz

2100 1900 1700 1500 1300

0

20

40

60

80

100

time (s)

Fig. 2. Transient response of condensation pressure.

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Evaporation Pressure (kPa)

620 20 Hz 80 Hz 120 Hz

600 580

560

540 520

500

0

200

400

600

800

1000

time (s)

Fig. 3. Transient response of evaporation pressure.

more refrigerant is delivered from the evaporator to the condenser, which causes condensation pressure to increase rapidly while the evaporation pressure drops as illustrated in Figs. 2 and 3 respectively. However, since the thermostatic expansion valve can not follow the change immediately, suction vapor superheat temperature drops because more refrigerant ﬂows out of the evaporator. This causes a decrease in mass ﬂow rate of refrigerant through the valve initially, as shown in Fig. 1. As the time progresses, an increase in pressure diﬀerence causes an increase in the refrigerant mass ﬂow rate through thermostatic expansion valve till it becomes equal to the discharge ﬂow rate of the compressor as the system reaches steady state (Fig. 1). Likewise, responses to reduced operation frequency show opposite trends in compressor and TEV discharge rate to those discussed above. Fig. 4 shows the time wise evolution of chilled water temperature leaving the evaporator. It can be seen that the response time varies with the size of the stimulus. The larger the step change, the longer it takes for the output to reach stable ﬁnal value. And it was also found that at 20 Hz frequency the chilled water temperature rises since the cooling capacity is too low for the load acting on the chiller. From the above results it is noted that the responses of condenser pressure (Fig. 2), refrigerant mass ﬂow rate (Fig. 1) were ﬁve to ten times faster than those of the chilled water temperature (Fig. 4). It was found that the evaporator side responses are slower compared to the condenser side responses. This time scale property of the model can be taken as a basis to further reduce the order of the model for use in control analysis and design. This is presently under investigation. 3.1.2. Transient responses to step variation in valve opening fraction The dynamic responses of the system to step variation in valve opening were studied. The stimulus of enlarging valve opening by 20% was exerted on the system 100s after a step increase in operational frequency. Figs. 5 and 6 show that the condensation and evaporation pressures increase and thus the pressure diﬀerence increases slightly with valve opening. This it is likely to cause a slight increase in

Z. Lei, M. Zaheeruddin / Applied Thermal Engineering 25 (2005) 2258–2271 12 20 Hz 80 Hz 120 Hz

water temperature (°C)

11 10 9 8 7 6 5 0

300

600

900

1200

1500

time (s)

Fig. 4. Transient response of chilled water temperature at the exit of evaporator.

Condensation Pressure (kPa)

1900 1800 1700 1600 1500 1400 1300

0

50

100

150

200

250

300

time (s)

Evaporation Pressure (kPa)

Fig. 5. Transient response of condensation pressure.

620 610 600 590 580 570 560

0

100

200

time (s)

Fig. 6. Transient response of evaporation pressure.

300

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mass ﬂow rate of refrigerant through the valve. It may lead to an increase in cooling capacity and some improvement in compressor total eﬃciency due to a drop in suction vapor superheat temperature. We have analyzed these eﬀects and quantiﬁed the steady state impact of increasing valve opening on system performance. The results are illustrated in the following section. 3.2. Discussion on steady state performance From transient simulation results we note that the refrigerant mass ﬂow rate increases with operational frequency and valve opening. The steady state performance results depicted in Fig. 7 show that the suction vapor superheat temperature increases with operational frequency at a certain valve opening. Likewise, it also tends to decrease with valve opening under certain operation frequency. In other words, the refrigerant mass ﬂow rate and superheat performance maybe the same under diﬀerent combinations of the valve opening and operation frequency. To describe the dependency, a graphical relationship between refrigerant mass ﬂow rate, suction vapor superheat temperature, operation frequency and valve opening under steady state conditions is plotted in Fig. 7. These curves show the balance points among the four variables and are useful in designing good operating strategies in addition to their use in achieving stable capacity regulation. From Fig. 7, it can be seen that the larger the valve opening, the narrower the throttling range of the valve. Refrigerant mass ﬂow rate increases most rapidly with operation frequency when the valve is fully open. When valve opening is gradually closed, refrigerant mass ﬂow rate drops and consequently suction vapor superheat temperature increases. Further analysis of the results show that the smaller the valve opening, the slower the refrigerant mass ﬂow rate increase with operation frequency. At higher operational frequencies, as the valve opening is gradually narrowed, the mass ﬂow rate of refrigerant undergoes a large change in its magnitude and the degree of superheat increases by a large amount compared to the case when the operational frequencies is lower and the valve opening is narrowed by the same amount. This may be the main reason why cooling capacity modularity is strongly inﬂuenced by higher frequencies (Fig. 8). On the other hand, COP drop is not as signiﬁcant at lower frequencies as the valve opening is narrowed, as shown in Fig. 9.

Refrigerant Mass flow rate (kg/s)

0.1

valve 85% open valve 100% open valve 60% open valve 40% open valve 20% open f=20 Hz f=30Hz f=40Hz f=50Hz f=60Hz f=70Hz f=80Hz f=90Hz f=100Hz f=110Hz f=120Hz

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0

2

4

6

8

10

12

14

16

Suction vapor superheat (C)

Fig. 7. Relation between refrigerant mass ﬂow rate, and suction vapor superheat temperature under various operation frequency and valve opening.

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14 valve 20% open valve 40% open valve 60% open valve 85% open valve 100% open

Cooling Capacity (kW)

12 10 8 6 4 2 0

0

20

40

60

80

100

120

140

Frequency (Hz)

Fig. 8. Relation between cooling capacity and operation frequency under diﬀerent valve open positions.

7 valve 20% open valve 40% open valve 60% open valve 85% open valve 100% open

6

COP

5 4 3 2 1 0

0

20

40

60

80

100

120

140

Frequency (Hz)

Fig. 9. Relation between COP and operation frequency under diﬀerent valve open positions.

Refrigerant Mass flow rate (kg/s)

0.1

valve 85% open valve 100% open valve 60% open valve 40% open valve 20% open f=20 Hz f=30Hz f=40Hz f=50Hz f=60Hz f=70Hz f=80Hz f=90Hz f=100Hz f=110Hz f=120Hz minimal valve opening

0.09 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0

0

2

4

6

8

10

12

Suction vapor superheat (C)

Fig. 10. Relationship between refrigerant mass ﬂow rate, suction vapor superheat temperature, various operation frequency and feasible valve operation position.

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In other words, the cooling capacity increases as the valve opening and operation frequency increase. On the other hand, COP drops as the valve opening narrows and frequency increases. It should be noted that a higher frequency with a narrow valve opening may create a condition in which the evaporation temperature will be very low so that the tube temperature may drop below zero. Such operating conditions have to be prevented in water chiller systems. Therefore, the thermostatic valve must have a minimum opening when the compressor is operated at higher frequencies so that water chiller can work safely. The safe region of chiller operation is shown in Fig. 10. Thus, cooling capacity will not be as low as those indicated in Fig. 8 and COP will not be as high as those indicated in Fig. 9 due to the above stated safe operation limits.

4. Conclusion In the refrigeration system model presented in this study, we have shown a simple method of modeling the superheat section in the evaporator. The developed dynamic model was used to study the transient response of the system subject to changes in valve position and operation frequency. The transient response results show that the changes in water temperature take much longer to reach steady state compared to refrigerant mass ﬂow rate and pressure in the system. This reveals that the overall system is a two time-scale dynamic system. The steady state performance under diﬀerent operation frequencies and valve positions was analyzed. It was found that there exists a minimal feasible valve position at a given operation frequency for water chiller to work within a safe operation mode to avoid water freeze up in the secondary system.

References [1] X.D. He et al., Multivariable control of vapor compression systems, Int. J. HVAC Res. 4 (3) (1998) 205–230. [2] S. Wang, Dynamic simulation of a building central chilling system and evaluation of EMCS on-line control strategies, Build. Environ. 33 (1) (1998) 1–20. [3] S. Deng, A dynamic mathematical model of a direct expansion (DX) water-cooled air-conditioning plant, Build. Environ. 35 (7) (2000) 603–613. [4] M.W. Browne, P.K. Bansal, Transient simulation of vapor-compression packaged liquid chillers, Int. J. Refrig. 25 (5) (2002) 597–610. [5] L. Fu, G. Ding, C. Zhang, Dynamic simulation of air-to-water dual-mode heat pump with screw compressor, Appl. Therm. Engng. 23 (13) (2003) 1629–1645. [6] J.M. Choi, Y.C. Kim, Capacity modulation of an inverter-driven multi-air conditioner using electronic expansion valves, Energy 28 (2) (2003) 141–155. [7] F. Matsuoka, H. Nagatmo, Dynamic response and electrical control for the air conditioner, JAR Trans. 5 (1) (1988) 43–50. [8] R.N.N. Koury, L. Machado, K.A.R. Ismail, Numerical simulation of a variable speed refrigeration system, Int. J. Refrig. 24 (2) (2001) 192–200. [9] J. Gallagher, M. Huber, G. Morrison, M. Mclinden, NIST Thermodynamic properties of refrigerants and refrigerant mixtures database, REFPROP standard reference data program, National Institute of Standards and technology, Gaithersburg, MD, 1993.

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[10] Fundamentals: 2001 ASHRAE Handbook, American Society of Heating, Refrigerating and Air-conditioning Engineers, Atlanta, GA. [11] W.M. Rohsenow, H.Y. Choi, Heat, Mass, and Momentum Transfer, Prebtice-Hall International Inc., United Kingdom, 1965.