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Numerical analysis of evaporator frosting in automotive air-conditioning system with a variable-displacement compressor
APPLIED ENERGY
Applied Energy 82 (2005) 1–22
www.elsevier.com/locate/apenergy
Numerical analysis of evaporator frosting in automotive air-conditioning system with a variable-displacement compressor Changqing Tian, Xianting Li *, Xinjiang Yang Department of Building Science, School of Architecture, Tsinghua University, Beijing 100084, PR China Received 24 June 2004; revised 2 August 2004; accepted 28 August 2004 Available online 21 December 2004
Abstract A steady-state mathematical model of the automotive air conditioning system with a variable-displacement compressor (VDC) is developed to find out the reasons causing evaporator frosting. To validate the system model, a test system is established and the simulated results are compared with experimental data: the predicted results agree well with the experimental data. After analyzing the influence of different factors with the system model, three reasons causing evaporator frosting have been found and corresponding countermeasures have been proposed: (1) the system performance band caused by the frictional forces among the moving components of the VDC can contribute to evaporator frosting, which may be avoided by decreasing the frictional forces between the moving components while designing, manufacturing and operating the VDC; (2) the mismatch between the parameters of the control valve and the resistance pressure of suction pipe or the condenser size can also contribute to evaporator frosting and the control valve with a proper initial compressive force should be selected for a given suction pipe and condenser; and (3) a higher air temperature at the condenserÕs inlet may cause evaporator frosting one needs to consider the influence of the air temperature at the condenser inlet while designing the new control valve. Ó 2004 Elsevier Ltd. All rights reserved.
*
Corresponding author. Tel.: +86 10 62785860; fax: +86 10 62773461. E-mail address: [email protected] (X. Li).
0306-2619/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2004.08.006
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Keywords: Frosting; Evaporator; Automotive; Air conditioning; Variable displacement compressor; Control valve
Nomenclature A Ao C cps d h i L M Nc n P R Sp T Tsc ms xi a DPs e g
area (m2) exterior surface area of evaporator per metre pipe length (m2/m) constant that expresses initial compressive force of the control valve (N) specific heat of superheated vapor (J/(kg K)) diameter (m) convective coefficient of heat transfer (W/(m2 K)) enthalpy (J/kg) length (m) mass-flow rate (kg/s) compressorÕs rotary-speed (r/min) cylinder number pressure (MPa) radius of ball valve (m) piston-stroke length (mm) temperature (°C) degree of subcooling at the condenser outlet (°C) refrigerant specific volume at suction end (m3/kg) refrigerant quality at the evaporator inlet valve wall-angle or wobble-plate angle (°) pressure loss in suction pipe (kPa) compression ratio efficiency
Subscripts a air c condenser or critical state or compressor or cylinder cd critical state where the piston-stroke length goes down cdm critical state of decrease in piston-stroke length from its maximum value cu critical state where the piston-stroke length goes up d discharge e evaporator or evacuated bellows of control valve i isentropic or inlet or inner 1 liquid m maximum or mean o out or outlet r refrigerant
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s tp v w 0
3
suction or superheated vapor two-phase volumetric or vapor or thermal expansion valve wobble plate case or wall or wet bulb preset or reference
1. Introduction The infinitely-variable displacement wobble-plate compressor (VDC) changes the piston-stroke length (or wobble-plate angle) and the displacement consequently to exactly match the vehicleÕs air-conditioning demand. Compared to the traditional automotive air-conditioning (AAC) system with a fixed-displacement compressor that cycles the compressor off-and-on to adjust the refrigerating capacity, the AAC system with a VDC has advantages, such as smooth continuous compressor operation, more comfortable environment inside the car and improved fuel-economy [1–3]. So more and more AAC systems with VDC have been used. As represented in [1,2], the VDC can maintain the evaporatorÕs surface-temperature just slightly above freezing temperature to prevent evaporator frosting, so there is no frosting prevention device in the AAC system with a VDC. However, the frost forms on the exterior surface of evaporator sometimes when the actual AAC system with a VDC is used. When the frost is formed at the evaporator, there is an additional thermal resistance on the exterior surface of the evaporator finÕs. The flow area between the fins decreases, air flow resistance increases and air-flow rate decreases, which results in the decrease of convective heat-transfer between air and fins. The additional thermal resistance and decreasing convective heat-transfer will reduce the heat-transfer rate of evaporator, which may result in the air flow path completely blocked by the frost layer in certain conditionÕs. So it is necessary to find out the reasons causing the evaporator frosting and to bring forward the methods for frosting prevention. Numerical simulation is an important way to analyze the frost formation and refrigeration system performance because it can simulate a wide range of operating conditions. Some research had been carried out on the simulation of frost formation on simple geometries [4,5] or finned heat-transfer surfaceÕs [6,7], which mainly analyzed the effects of various parameters (including air temperature and relative humidity, air flow rate, surface temperature and structural parameters) on the frost growth and heat transfer. Other research, such as Tantakitti and Howell [8], Yasuda et al. [9] and Ameen [10], focused on the simulation of heat-pump performance under frosting conditions using a lumped-parameter model. There is no published literature analyzing the reasons why the evaporator frosting forms in the AAC system with a VDC. In the present study, a steady-state mathematical model of the AAC system with a VDC is developed and verified by the experimental data, with which the evaporating temperature and evaporatorÕs surface-temperature at different conditions are simulated and the factors causing the evaporator frosting are analyzed.
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2. Mathematical model The AAC system studied here is a well matched actual system, which is composed of a VDC, an evaporator, a condenser and receiver, a thermal expansion-valve and connection pipes. Among the connection pipes, only the suction pipe model is included in the system model since the pressure loss in the suction pipe influences the piston-stroke length control much more than that of other connection pipes. Only the evaporating temperature and evaporator surfaceÕs temperature under no frosting conditions are needed in the mathematical model since the purpose of this paper is not to study the frost growth but to find out the reasons causing the evaporator frosting. HFC-134a (1,1,1,2-tetrafluoroethane) is used in this system. 2.1. Variable-displacement compressor The VDC, with its wobble plate connected to the pistons with the piston rods, consists of a mainshaft-drive lug assembly, a shaft sleeve, a rotating journal and a wobble plate which converts the rotary motion of the rotating journal into linear reciprocation of the pistons. The VDC studied here is a five-cylinder, wobble-plate type, infinitely-variable displacement compressor, with the displacement range from 10 to 156 cc (cubic centimetre per revolution) (Fig. 1). For details of the VDC refer to [1]. The control valve, mounted in the rear head of the compressor, consists of a cone valve and a ball valve (Fig. 2). The preset suction pressure of the control valve, Ps0, is
Fig. 1. Variable-displacement compressor.
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Fig. 2. Control valve.
defined as the suction pressure that decreases till the ball valve is just open and it can be calculated with following expression [11]: 2
P s0 ¼
106 C pP d ðR sin aÞ 0:1Ae 2
Ae pðR sin aÞ
;
ð1Þ
where the constant C expresses initial compressive force of the control valve. It can be seen, from Eq. (1), that Ps0 is linearly proportional to constant C and linear inversely proportional to the discharge pressure (Pd). When the automotive air-conditioning load decreases and the suction pressure (Ps) falls to or becomes less than the preset suction-pressure, the evacuated bellows of the control valve stretches. The spring force of the evacuated bellows, together with other forces acting on the valve rod, makes it move, reduces the opening of the cone valve and increases the opening of the ball valve. The cone valve controls the passage between the wobble-plate case and suction cavity and the ball valve controls the passage between the discharge cavity and wobble-plate case, so the latter pressure rises gradually. When the suction pressure falls to the critical suction-pressure of the piston-stroke length, the force moments acting on the wobble plate are great enough to make the piston-stroke length (or wobble-plate angle) decrease and the displacement falls to match the decrease of the air-conditioning load. In the similar way, the piston-stroke length and displacement will increase when the air-conditioning load rises. The VDC model is composed of the control-valve model, dynamic model of moving components and compression process model. The relationship between the parameters of these three parts in the VDC is presented in Fig. 3. 2.1.1. Control-valve model The steady-state model of the control valve is composed of force balance equations of valve rod and ball valve, mass conversion equation and energy conversion equation of wobble-plate case. With this model, the wobble-plate case pressure,
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Fig. 3. VDC model.
Pw, can be calculated with Pd and Ps. The details of the control-valve model are available in [11]. 2.1.2. Dynamic model of moving components The dynamic model of moving components of VDC, which is used to determine the relationship between the piston-stroke length, Sp (or wobble-plate angle, a) and Pd, Ps, Pw, Nc (compressor rotary speed), is composed of force balance equations of moving components including the piston, piston rod, wobble plate, rotating journal and shaft sleeve [12]. The resultant frictional-force between the moving components when the piston-stroke length decreases is opposite in direction to that when the piston-stroke length increases. The force moment from Ps is identical with the resultant frictional moment when the piston stroke length decreases and in the opposite direction to the resultant frictional moment when the piston-stroke length increases. So the critical suction-pressure of the pistonstroke length decreasing (Ps,cd) is less than the critical suction-pressure of the piston-stroke length increasing (Ps,cu) at the same Sp, Pd and Nc. Sp is kept invariable when Ps,cd 6 Ps 6 Ps,cu and will go down only when Ps < Ps,cd and go up only when Ps > Ps,cu. Ps,cd and Ps,cu can be calculated together with the mathematical model of the control valve [11] and dynamical model of moving components [12]. From the calculation results, Ps,cd and Ps,cu can be fitted into the function of Pd, a and Nc: P s;cd ¼ Ad ða; N c Þ þ ðP d P d0 ÞBd ða; N c Þ;
ð2Þ
P s;cu ¼ Au ða; N c Þ þ ðP d P d0 ÞBu ða; N c Þ:
ð3Þ
In Eqs. (2) and (3), Pd0 is the reference discharge pressure, Ad(a, Nc), Bd(a, Nc), Au(a, Nc) and Bu(a, Nc) are the coefficients which are functions of a and Nc. The application range of Eqs. (2) and (3): Pd = 0.8–1.9 MPa, Nc = 1000–4000 r/min, a = 9.3– 24.4°.
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With the geometrical relationship of VDC moving components, Sp can be calculated from a [13]. So Eqs. (2) and (3) show the relationship of Sp and Pd, Ps, Nc. 2.1.3. Compression process model The compression process model is used to calculate the refrigerant mass flow rate through the compressor, Mr,c, and discharge temperature, Td with Pd, Ps, Nc and Ts (suction temperature). Mr,c and the refrigerant enthalpy at discharge end ði0d Þ can be calculated by following equations: p M r;c ¼ n d 2c S p N c gv =ð60000 vs Þ; 4 i0d ¼ is þ gm
id is ; gi
ð4Þ ð5Þ
where is is the refrigerant enthalpy at suction end and id is the refrigerant enthalpy at discharge end when the compression process is isentropic. The equations of the volumetric efficiency (gv) and isentropic efficiency (gv) at maximum piston stroke length are given in polynomial fitted by our experiment data. gv at maximum piston stroke length is gv ¼ 1:81 0:35e þ 0:026e2 0:00081N c þ 2:51 107 N 2c þ 0:00026eN c 2:07 105 e2 N c 8:68 108 eN 2c þ 7:70 109 e2 N 2c :
ð6Þ
The application range: e = 3.8–6.2, Nc = 900–3000 r/min, suction superheat 15 °C. gi at maximum piston stroke length is gi ¼ 1:17 P s 0:088 P d 6:79 105 N c þ 0:342:
ð7Þ
The application range: Ps = 0.25–0.45 MPa, Pd = 0.9–1.7 MPa, Nc = 900–3000 r/min and suction superheat 15 °C. The relative volumetric-efficiency and relative isentropic-efficiency are used to express the performance at partial piston-stroke length. The relative volumetric-efficiency, gv , is the ratio of gv at partial piston-stroke length and gv at maximum piston stroke-length at the same work condition and compressor rotary-speed. The relative isentropic-efficiency, gi , is the ratio of gi at partial piston stroke length and gi at maximum piston stroke length for the same work condition and compressor rotary-speed. The relative displacement, Sp , is the ratio of actual piston strokelength and maximum piston stroke-length. With the test data, gv and gi can be fitted by following equations: ð8Þ gv ¼ 1:0 þ 0:545 log Sp ; gi ¼ 0:58Sp þ 0:4:
ð9Þ
The application range of Eqs. (8) and (9): Sp ¼ 0:52–1. The steady-state model of a VDC is composed of Eqs. (2)–(9): Ps,cd and Ps,cu can be calculated when Pd, Nc and Sp are known, and Mr,c and discharge state parameters can be determined from given Pd, Ps, Ts and Nc.
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2.2. Evaporator The evaporator is a plate-fin-tube evaporator with four paths and five rows. The evaporator length is 0.262 m, the height is 0.228 m, the thickness is 0.084 m and the exterior surface-area is 5.5 m2. The evaporator model is a lumped model and the evaporator is divided into a two-phase region and a superheated-vapor region. The frost growth model is not included in the evaporator model since only the evaporating temperature and evaporator surface temperature under no frosting conditions are calculated. It is assumed in the model that: The refrigerant flow in pipes can be considered as a one-dimensional flow. The two-phase flow is considered in the equilibrium state; the evaporating temperature and convective coefficient of heat transfer are constant and the pressure loss in the two-phase region is concentrated at its outlet. The kinetic energy and potential energy are neglected in the energy-balance equation of the refrigerant. The axial heat-conduction through the pipe wall is neglected. The refrigerant flows in the four paths are uniform. By the energy-balance equation in the two-phase region, the evaporatorÕs surfacetemperature (i.e. the pipe wall temperature of the evaporator in the two-phase region in this paper), Tew, and length of the two-phase region in one path, Ltp, can be calculated using the following equations: T ew ¼
ho Ao go hi pd i
T eam þ T e
1 þ hho iApdo gi o
;
ð10Þ
and Ltp ¼
M r ð1 xi Þðiv i1 Þ : hi pd i ðT ew T e Þ
ð11Þ
By the energy-balance equation in the superheated-vapor region, the refrigerant temperature at the evaporator outlet, Teo, can be deduced as
T eo
! 1 1 ¼ T eam ðT eam T e Þ exp 1 ðL Ltp Þ : þ ho A1o go M r cps his pd i
ð12Þ
The pressure loss of the refrigerant in the two-phase region is calculated using the equations in [14] and the pressure loss of refrigerant in superheated vapor region is calculated with the equations in [15]. The mean convective coefficient of heat transfer in the two-phase region between the refrigerant and the pipeÕs interior surface is calculated with the equations in [16] and the convective coefficient of heat transfer between the air and evaporator fin is calculated with the equations in [17].
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START
INPUT PARAMETERS: Nc, Sp, Teai, ϕeai, Tcai, Mea, Mca, Tsc0
SET STARTNG VALUES FOR P d, P s , T s
CALL VDC MODEL (TO GET Mr,c ) TO CORRECT ASSUMED Pd
CALL CONDENSER MODEL (TO GET Tsc )
No
TO CORRECT ASSUMED Ts IS ©¦Tsc-Tsc0©¦< ¦Å? Yes CALL SUCTION PIPE MODEL (TO GET ∆ Ps, T'eo)
TO ADJUST EXTERNAL PARAMETER
TO CORRECT ASSUMED Ps
CALL EVAPORATOR MODEL (TO GET Te, Tew, Teo) CALL THERMAL EXPANSION VALVE MODEL (TO GET Mr,v)
IS ©¦Mr,c-Mr,v©¦< ¦Å?
No
Yes No IS ©¦T'eo-Teo©¦< Yes ¦Å? Yes COMPUTE Psc
No
IS ©¦Ps-Psc©¦< ¦Å? Yes RESULT OUTPUT: Ps0, Ps, ∆ Ps, Te, Tew END
Fig. 4. Flow diagram for numerical solution procedure.
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2.3. Other components The condenser is a parallel-flow type condenser. Its length is 0.35 m, height 0.56 m, thickness 0.02 m and its exterior surface area 5.58 m2. The condenser model is a lumped model and the condenser is divided into three regions including superheated vapor, two-phase and subcooled liquid region. The mean convective coefficient of heat transfer in the two-phase region between the refrigerant and the pipe interior surface is calculated using the equations in [18], the convective coefficient of heat transfer between the air and condenser fin is calculated with the equations in [19] and the refrigerant pressure loss in condenser is calculated using the equation in [20]. The thermal expansion valve is a cross and absorptive charge H type expansion valve, whose nominal refrigerating capacity is 7032 W. The opening of the thermal expansion valve is calculated by the force balance equation of the valve rod and the flow area can be deduced. The refrigerant mass-flow rate through the thermal expansion valve (Mr,v) can be calculated when the refrigerant states at the thermal expansion valve inlet and outlet are known. The pressure loss and heat loss for the suction pipe are considered. Forced-convection between the superheated vapor and the interior surface of suction pipe occurs whereas free convection between the air and exterior surface of the suction pipe ensues. The pressure loss of refrigerant in the suction pipe is calculated with the equations in [15]. With the inlet and outlet parameter relationship between every component in the AAC system with a VDC, the steady-state system model is developed to combine the mathematical models of the VDC, evaporator, condenser, thermal expansion valve and suction pipe. 2.4. Solution procedure Fig. 4 shows the flow diagram for a numerical solution procedure of the steadystate mathematical model. Firstly, input the parameters and set the starting values for Pd, Ps and Ts. The set value of the degree of subcooling at the condenser outlet, Tsc0, must be given as an input parameter. Then call the subroutines of the VDC, condenser, suction pipe, evaporator and thermal expansion valve. Finally the simulation of a steady-state point is undertaken to correct the assumed starting value till the calculation results satisfy the required precision. By continuing the solution procedure, a critical state of the pistonÕs stroke-length can be simulated by adjusting the external parameter.
3. Experimental verification of the system model 3.1. Test system The test system, shown in Fig. 5, was built inside two chambers. The VDC, the condenser and receiver were placed in the outdoor chamber, the evaporator and
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Fig. 5. Test system.
the thermal expansion valve in the indoor one. Both chambers were kept at constant temperature and constant humidity needed in the experiment. The whole system consisted of the main experimental body, control system and measurement system. The main body was identical with the AAC system introduced in the mathematical model. The parameters controlled in this test system were the compressorÕs rotary speed, air temperature at the condenser inlet, air flow rate through the condenser, air drybulb temperature and wet-bulb temperature at the evaporator inlet and air flow rate through the evaporator. The compressor was driven by a variable-frequency motor and the compressorÕs rotary speed was changed by adjusting the power frequency. The condenser fan was also driven by a variable frequency motor, so the air flow rate through the condenser could be controlled by adjusting the power frequency of the condenserÕs fan motor. The air-flow rate through the evaporator was controlled by a three-speed fan and the booster fan (also driven by a variable-frequency motor) was adjusted meanwhile to maintain the air pressure at the evaporator outlet at atmospheric pressure in order to attain an actual condition for the evaporator. The air temperature at the condenser inlet, air dry-bulb temperature and wet-bulb temperature at the evaporator inlet were controlled by the two chambers. The parameters measured in this test system included the compressorÕs rotary speed, piston-stroke length, refrigerantÕs mass flow-rate, refrigerant temperatures and pressures at different test points, evaporatorÕs surface-temperature, air dry-bulb and wet-bulb temperatures at the evaporator inlet and at the evaporator outlet (Teai, Teaiw, Teao and Teaow), air temperatures at the condenser inlet and at the condenser outlet (Tcai and Tcao), air-flow rateÕs through the evaporator and through the condenser (Mea and Mca). The compressorÕs rotary speed was measured with an electric eddy current sensor, the pistonÕs stroke-length was measured [13] and the refrigerantÕs mass-flow rate was measured with Coriolis flow-meter. The refrigerant
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temperatures and evaporator surface temperature were measured with copper–constantan thermocouples and the refrigerant pressures were measured with voltageoutput type pressure-sensors. The air dry-bulb and wet-bulb temperatures were measured with platinum-resistance temperature sensors and the air-flow rate was measured with the standard nozzle and differential pressure transducer. These sensors all produced electric voltageÕs or currentÕs, which were sent to a data logger and a computer to record the test data. Table 1 shows the measurement devices and precision used in this test system. 3.2. Comparison between measured and simulated results The critical evaporating temperature and critical evaporator surface-temperature of the pistonÕs stroke-length (Te,cd and Tew,cd), the critical evaporating temperature and critical evaporator surface temperature of the pistonÕs stroke-length (Te,cu and Tew,cu) are used in the following evaporator frosting analysis. The simulated results of Te,cd, Tew,cd, Te,cu and Tew,cu are compared with corresponding experimental data. In the experiment, the compressorÕs rotary speed increased gradually and the pistonÕs stroke-length fell. The measured evaporating temperature and evaporator surface temperature could be considered as Te,cd and Tew,cd, respectively (the saturation temperature of refrigerant at the pressure at the evaporator outlet is the evaporating temperature). Te,cd and Tew,cd could be simulated with the steady-state system model. The comparison between the simulated and measured results for Te,cd and Tew,cd is shown in Fig. 6(a). The deviations between simulated and measured values of Te,cd are less than 0.3 °C and the deviations between simulated and measured values of Tew,cd are less than 0.6 °C. When the compressorÕs rotary speed decreased gradually, the pistonÕs stroke length rises: the measured evaporating temperature and evaporator surface temperature could be considered as Te,cu and Tew,cu, respectively. The comparison between the simulated and measured results of Te,cu and Tew,cu is shown in Fig. 6(b). The deviations between simulated and measured values of Te,cu are less than 0.4 °C and the deviations between simulated and measured values of Tew,cu are less than 0.5 °C. Table 1 Measurement devices and precision Device
Number
Precision
Model
Thermocouple Platinum-resistance sensor Pressure sensor Coriolis flow-meter Electric eddy-current sensor Stroke-measurement device Differential pressure-transducer Data logger
7 6 7 1 1 1 2 1
±0.2 °C <0.1 °C ±0.2% ±1% ±1% <0.01 mm ±0.5%
T type Voltage-output type Mass 2100
1751DR HP 34970A
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Fig. 6. Comparison between simulation results and experimental data. (a) Critical evaporating temperature and critical evaporator surface-temperature of piston stroke-length decreasing. (b) Critical evaporating temperature and critical evaporator surface-temperature of piston stroke-length increasing. (c) Critical compressor rotary-speed, critical evaporating temperature and critical evaporator surfacetemperature of decrease in piston stroke-length from its maximum value.
For a certain air-temperature at the evaporator inlet, there exists a critical compressor rotary-speed when the pistonÕs stroke-length starts to decrease from its maximum value (Nc,cdm). When the corresponding critical evaporating-temperature (Te,cdm) and critical evaporatorÕs surface-temperature (Tew,cdm). Fig. 6(c) shows the comparison between the simulated and measured values of Nc,cdm, Te,cdm and Tew,cdm at different air temperatures at the evaporator inlet. The deviations between the simulated and measured values of Nc,cdm are less than 7%: the deviations between the simulated and measured values of Te,cdm are less than 0.6 °C and the deviations between the simulated and measured values of Tew,cdm are less than 0.75 °C. From the comparisons mentioned above, we can see that the simulated results agree well with experimental data and the systemÕs model can be used to analyze the steady-state performance of the AAC system with a VDC quantitatively.
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4. Analysis of reasons causing evaporator frosting The moisture in wet air will freeze on the evaporatorÕs surface when its surface temperature is below 0 °C the evaporatorÕs surface-temperature is mainly related to the evaporating temperature. The influence of system performance itself, component structural parameters, and external parameters on the evaporating temperature and evaporator surface temperature are simulated and analyzed with the system model to find out the reasons causing the evaporator frosting. 4.1. Influence of performance band With the AAC system model, the steady-state points at the maximum pistonÕs stroke-length can be calculated. Let Psc = Ps,cd in the flow diagram (Fig. 4): adjust the air temperature at the evaporator inlet (Teai) to make Ps = Psc, the critical state of the piston stroke length then decreases. Let Psc = Ps,cu in the flow diagram: adjust Teai to make Ps = Psc, the critical state of the piston stroke length then increases. It can be learnt from the VDC model, due to the frictional forces the moving components of the VDC, Ps,cd < Ps,cu at the same pistonÕs stroke-length, discharge pressure and compressor rotary speed. The variation of Te with Teai is shown in Fig. 7(a). When Teai is high (>24.5 °C), the evaporating temperature and suction pressure are high enough to maintain the VDC running at the maximum pistonÕs stroke-length. When Teai = 24.5 °C, the suction pressure equals the critical suction pressure where the pistonÕs stroke-length starts to decrease from its maximum value (Ps,cdm) and the evaporating temperature is equal to the corresponding critical evaporating temperature (Te,cdm). When T < 24.5 °C, Te,cd and Te,cu at different piston stroke-lengths can be simulated and Te,cu > Te,cd at the same piston stroke-length. The piston strokelength can decrease only when Te < Te,cd, the piston stroke-length can increase only when Te > Te,cu and the piston stroke length will be invariant when Te,cd 6 Te 6 Te,cu. Between Te,cu and Te,cd, one Te Teai curve for a fixed piston stroke-length is equivalent to a performance curve of the AAC system with a fixed displacement compressor and many Te Teai curves for different piston stroke lengths form a band (here we define it as the ‘‘performance band’’). Compared to the one-to-one relationship of Te Teai curve in the AAC system with a fixed displacement compressor, it is multiple-to-one relationship, i.e., there exist many values of Te for just one certain Teai. All steady-state points should fall within the performance band. The evaporator’s surface-temperature (Tew) along with Te, have similar performance bands. Fig. 7(b) indicates that the evaporatorÕs surface-temperatures in part of the Tew Teai performance band are less than zero and so will cause evaporator frosting. The greater the frictional forces among the moving components of the VDC, the broader the Tew Teai performance band and the larger the change range of evaporating temperature and evaporator surface-temperature. The narrower performance band reduces the possibility of evaporator frosting. In order to avoid or reduce the evaporator frosting in the AAC system with a VDC, it is necessary to reduce the frictional forces between the moving components
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Fig. 7. Performance band (compressor rotary speed Nc = 2000 r/min; air temperature at condenser inlet Tcai = 42 °C; air relative humidity at evaporator inlet ueai = 50%; evaporator fan is at high speed). (a) Te Teai. (b) Te Teai and Tew Teai.
while designing and manufacturing the compressor and to assure the lubrication of the compressor to reduce the width of the performance band in the actual operation of AAC system. It can be seen from Fig. 7, when the evaporating temperature or suction pressure is high (then evaporator surface temperature is high enough to ensure that
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no frosting forms), the VDC is at the maximum pistonÕs stroke-length and its behaviour is identical with that of a fixed displacement compressor: the suction pressure changes with the systemÕs external parameters and cannot be controlled by the VDC. Only when the evaporating temperature or suction pressure decreases till the pistonÕs stoke-length varies, then the evaporating temperature can be controlled by VDC to be within the performance band. The influence of the component structural parameters and systemÕs external parameters on the critical state of decrease in the pistonÕs stroke-length from its maximum value is simulated and analyzed. This reveals a transition point from the maximum pistonÕs stroke-length to the critical state of the piston’s stroke-length decreasing and Pe,cdm is the lowest temperature in the performance band. 4.2. Influence of component structural parameters With the AAC system model, let Psc = Ps,cdm in the flow diagram (Fig. 4). Adjust the compressorÕs rotary speed to make Ps = Psc, then the critical state of decrease in the pistonÕs stroke-length can be obtained. For a given VDC (here the constant, C, the initial compressive force of control valve, is 35 N) and evaporator, the suctionÕs pipe-length (the suction pipe is assumed as a straight pipe without local resistance to simplify the analysis and its inner diameter is 16 mm) and condenser size are the main component structural parameters influencing the relationship between the behavior of the control valve and evaporating temperature. 4.2.1. Suction pipe length The variations of the preset suction-pressure (Ps0), refrigerant pressure loss in the suction pipe (DPs), evaporating temperature and evaporatorÕs surface-temperature at the critical state of decrease in pistonÕs stroke-length from its maximum value along with the suction pipe length are shown in Fig. 8(a) (the condenser length, Lc, is kept at 0.56 m). Ps0 and Ps,cdm are almost not influenced by the suction-pipeÕs length. However, DPs falls along with the decrease of suction-pipeÕs length and then Pe,cdm decreases, which will cause Te,cdm and Tew,cdm to decrease. Tew,cdm = 0 °C when the suction pipe length is 4 m and Tew,cdm will be lower than 0 °C and there will be evaporator frosting when the suction pipe length is less than 4 m. The larger the constant C, the greater Ps0 and Ps,cdm at the same discharge pressure. So the larger constant C is suitable for the suction pipe with a smaller resistance pressure to maintain the evaporating temperature higher than 0 °C. 4.2.2. Condenser size Only change the condenser length and keep the other condenser structural parameters invariable, then the relative length of the condenser (Lc/Lc0) is equal to the area ratio of the condenser (Lc0 = 0.56 m). The variations of Ps0, DPs, Te,cdm and Tew,cdm along with the condenser length are shown in Fig. 8(b) (Ls is 4 m). With the decrease of condenser length, the discharge pressure increases, so Ps0 and Ps,cdm become smaller and a higher compressor rotary speed is needed
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17
Fig. 8. Influences of component structure parameters on evaporator frosting: (a) suction-pipe length, (b) condenser size.
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for the critical state of decrease in the piston-stroke-length. The refrigerantÕs mass-flow rate increases then and DPs goes up. But Te,cdm and Pew,cdm go down along with the decrease of condenser length because the decreasing amplitude of Ps,cdm is greater than the increasing amplitude of DPs. When Lc/Lc0 = 1, Tew,cdm = 0 °C; Tew,cdm will be lower than 0 °C and evaporator frosting will form when Lc/Lc0 < 1. Fig. 8(b) indicates that the smaller the condenser size, then the control valve with greater constant C is needed. From the analysis of influence of suction-pipeÕs length and condenser size on the evaporator frosting, it can be found that the value of C should be selected for a given suction pipe or a given condenser when matching the system in order to prevent the evaporator frosting. 4.3. Influence of external parameters For a given control valve (C = 35 N), suction pipe (Ls = 4 m) and condenser (Lc = 0.56 m), the influence of external parameters including the compressorÕs rotary speed, air temperature at the evaporator inlet, air-flow rate through the evaporator and air temperature at the condenser inlet on the critical state of decrease in the pistonÕs stroke-length from its maximum value is studied. With the systemÕs mathematical model, let Psc = Ps,cdm in the flow diagram (Fig. 4). For a given value of one external parameter, there must be a certain value of another external parameter to make Ps = Psc, so the different critical states can be obtained when two external parameters change simultaneously. 4.3.1. Simultaneous change of compressorÕs rotary speed and air temperature at the evaporator inlet The variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary-speed and air temperature at the evaporator inlet are shown in Fig. 9(a). When Teai increases, the compressorÕs rotary speed needed for reaching the critical state of decrease in the pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. Because the air flow rate through the condenser goes up with the increase of the compressorÕs rotaryspeed, the discharge pressure increases just a little and Ps0 and Ps,cdm go down slightly. Meanwhile, DPs rises, which counteracts the decrease of Ps,cdm and maintains Te,cdm and Tew,cdm almost constant. Tew,cdm almost maintains 0 °C in Fig. 9(a), so evaporator frosting will not happen. When the compressorÕs rotary-speed and air temperature at the evaporator inlet increase simultaneously, the increase of discharge pressure is only caused by the rise of the refrigerantÕs flow-rate. Meanwhile, the rise of the refrigerantÕs flow rate causes the increase of the refrigerantÕs pressure-loss in the suction pipe. For the control valve studied here, Ps0 is inversely proportional to the discharge pressure, so the evaporating temperature and evaporatorÕs surface-temperature are almost constant. The control valve provides good control behavior when the
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19
Fig. 9. Influence of external parameters on evaporator frosting. (a) Simultaneous change of compressor rotary speed and air temperature at the evaporator inlet. (b) Simultaneous change of compressor rotary speed and air flow rate through the evaporator. (c) Simultaneous change of compressor rotary speed and air temperature at the condenser inlet.
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compressorÕs rotary-speed and the air temperature at the evaporatorÕs inlet change. 4.3.2. Simultaneous change of compressorÕs rotary-speed and air flow rate through the evaporator Fig. 9(b) shows the variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary speed and air mass flow rate through the evaporator. The air-flow rate through the evaporator Mea = 0.1 kg/s when the evaporator fan is at low speed, Mea = 0.145 kg/s at middle speed and Mea = 0.179 kg/s at high speed. When Mea increases, the compressorÕs rotaryspeed needed for reaching the critical state of decrease in pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. Similar to the simultaneous change of the compressorÕs rotary-speed and air temperature at the evaporatorÕs inlet, the discharge pressure increases a little and Ps0 and Ps,cdm go down slightly. Meanwhile, the increase of refrigerantÕs flowrate causes the rise of DPs, which maintains Te,cdm and Tew,cdm almost constant. Tew,cdm almost maintains 0 °C in Fig. 9(b), so the evaporator frosting will not occur.
4.3.3. Simultaneous change of the compressorÕs rotary-speed and air temperature at the condenser inlet The variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary-speed and air temperature at the condenser inlet are shown in Fig. 9(c). When Tcai increases, the rotary speed needed for reaching the critical state of decrease in the pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. The increase of discharge pressure is caused by the rise of both the refrigerant flow-rate and the air temperature at the condenser inlet: Ps0 and Ps,cdm decrease with a greater amplitude. But the increasing amplitude of DPs is less than the decreasing amplitude of Ps,cdm, so Te,cdm and Tew,cdm decrease along with the increase of Tcai. Tew,cdm < 0 °C when Tcai > 38 °C: evaporator frosting will form. The simulated results indicate that when the compressorÕs rotary-speed, air temperature at the evaporator inlet and air-flow rate through the evaporator change, the control valve can maintain the evaporating temperature and evaporatorÕs surface-temperature at the critical state of decrease in pistonÕs stroke-length from its maximum value almost constant, but the two temperatures change with a greater amplitude when the air temperature at the condenser inlet varies. That is to say, that even the control valve with proper constant C has been selected, the evaporator frosting may happen when the air temperature at the condenser inlet is higher than that of design condition, which is a defect of this type control valve. In order to prevent the evaporator frosting, one needs to consider the influence of the air temperature at the condenser inlet while designing the new controlvalve and to increase the setting value of the air temperature inside the vehicle
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21
if the ambient temperature is high in the actual operation of the AAC system with a VDC.
5. Conclusions A steady-state mathematical model of the AAC system with a VDC has been developed and a test system has been established to validate the system model. It is shown that the simulated results agree well with the experimental data. After analyzing the influence of different kinds of factors, it is found that there are three reasons causing evaporator frosting in the AAC system with a VDC, and corresponding countermeasures have been proposed. The performance band makes the evaporating temperature and evaporatorÕs surface-temperature vary within a certain range, which can contribute to evaporator frosting. The frictional forces between the moving components of the VDC should be reduced while designing, manufacturing and operating the VDC in order to avoid evaporator frosting. The mismatching between constant C (initial compressive force) of the control valve and the resistance pressure in suction pipe or the condenser size can also contribute to evaporator frosting. For the control valve with a given constant C, the smaller the resistance pressure of the suction pipe or condenser size is, the easier evaporator frosting forms. In order to prevent the evaporator frosting, the control valve with a proper constant C should be selected for a given suction pipe and condenser when matching the system. Because the preset suction-pressure of the control valve decreases with the increase of discharge pressure, and the rise of the air temperature at the condenser inlet can cause the discharge pressure to increase but with little influence on the resistance pressure of suction pipe, so evaporator frosting may happen when the air temperature at the condenser inlet is higher than that of the design condition. One needs to consider the influence of the air temperature at the condenser inlet while designing the new control valve.
Acknowledgement The study was supported by Natural Science Foundation of China (Grant No. 50176028).
References [1] Skinner TJ, Swadner RL. V-5 automotive variable-displacement air-conditioning compressor. SAE Congress Paper 850040; 1985. [2] Takai K, Shimizu S, Terauchi K. A 7-cylinder IVD compressor for automotive air-conditioning. SAE Congress Paper 890309; 1989.
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[3] Nadamoto H, Kubota A. Power saving with the use of variable-displacement compressor. SAE Congress Paper 1999-01-0875; 1999. [4] Lee KS, Jhee S, Yang DK. Prediction of the frost formation on a cold flat-surface. Int J Heat Mass Transfer 2003;46:3789–96. [5] Na B, Webb RL. Mass transfer on and within a frost layer. Int J Heat Mass Transfer 2004;47:899–911. [6] Chen H, Thomas L, Besant RW. Modeling frost characteristics on heat-exchanger fins, part I: numerical modeling. ASHRAE Trans 2000;106(2):358–67. [7] Chen H, Thomas L, Besant RW. Fan supplied heat-exchanger fin-performance under frosting conditions. Int J Refrig 2003;26:140–9. [8] Tantakitti C, Howell RH. Air-to-air heat pumps operating under frosting conditions on the outdoor coil. ASHRAE Trans 1986;92(1B):827–42. [9] Yasuda H, Senshu T, Kuroda S, Atsumi A, Oguni K. Heat-pump performance under frosting conditions: part II – simulation of heat-pump cycle characteristics under frosting conditions. ASHRAE Trans 1990;96(1):330–6. [10] Ameen FR. Study of frosting of heat-pump evaporators. ASHRAE Trans 1993;99(1):61–71. [11] Dou CP, Yang XJ, Tian CQ, Li XT. Numerical analysis on the performance of a control valve in variable-displacement wobble-plate compressor. Int J Mech Des [in press]. [12] Tian CQ, Dou CP, Yang XJ, Li XT. A mathematical model of variable-displacement wobble-plate compressor for automotive air conditioning system. Appl Therm Eng 2004;24(17–18):2467–86. [13] Tian CQ, Dou CP, Yang XJ, Li XT. Piston-stroke measurements in variable-displacement compressors. J Tsinghua Univ 2003;43:1412–5. [in Chinese]. [14] de Souza A, Pimenta M. Prediction of pressure drop during horizontal two-phase flow of pure and mixed refrigerants. In: Proceedings of the ASME conference of cavitation and multi-phase flow, USA; 1995. p. 161–71. [15] Churchill S. Friction-factor equation spans all fluid-flow regimes. Chem Eng 1997;84(24):91–2. [16] Shah MM. Chart correlation for saturated-boiling heat-transfer: equations and further study. ASHRAE Trans 1982;88(1):185–96. [17] McQuiston FC. Correlation of heat, mass and momentum transport coefficients for plate-fin-tube heat-transfer surfaces with staggered tubes. ASHRAE Trans 1978;84(1):294–301. [18] Castro F, Tinaut FV, Rahman Ali AA. Automotive evaporator and condenser modeling. SAE Congress Paper 931121; 1993. [19] Jabarda JMS, Mamani WG, Ianella MR. Modeling and experimental evaluation of an automotive air-conditioning system with a variable-capacity compressor. Int J Refrig 2002;25:1157–72. [20] Lee GH, Yoo JY. Performance analysis and simulation of automobile air-conditioning system. Int J Refrig 2000;23:243–54.
Applied Energy 82 (2005) 1–22
www.elsevier.com/locate/apenergy
Numerical analysis of evaporator frosting in automotive air-conditioning system with a variable-displacement compressor Changqing Tian, Xianting Li *, Xinjiang Yang Department of Building Science, School of Architecture, Tsinghua University, Beijing 100084, PR China Received 24 June 2004; revised 2 August 2004; accepted 28 August 2004 Available online 21 December 2004
Abstract A steady-state mathematical model of the automotive air conditioning system with a variable-displacement compressor (VDC) is developed to find out the reasons causing evaporator frosting. To validate the system model, a test system is established and the simulated results are compared with experimental data: the predicted results agree well with the experimental data. After analyzing the influence of different factors with the system model, three reasons causing evaporator frosting have been found and corresponding countermeasures have been proposed: (1) the system performance band caused by the frictional forces among the moving components of the VDC can contribute to evaporator frosting, which may be avoided by decreasing the frictional forces between the moving components while designing, manufacturing and operating the VDC; (2) the mismatch between the parameters of the control valve and the resistance pressure of suction pipe or the condenser size can also contribute to evaporator frosting and the control valve with a proper initial compressive force should be selected for a given suction pipe and condenser; and (3) a higher air temperature at the condenserÕs inlet may cause evaporator frosting one needs to consider the influence of the air temperature at the condenser inlet while designing the new control valve. Ó 2004 Elsevier Ltd. All rights reserved.
*
Corresponding author. Tel.: +86 10 62785860; fax: +86 10 62773461. E-mail address: [email protected] (X. Li).
0306-2619/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.apenergy.2004.08.006
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Keywords: Frosting; Evaporator; Automotive; Air conditioning; Variable displacement compressor; Control valve
Nomenclature A Ao C cps d h i L M Nc n P R Sp T Tsc ms xi a DPs e g
area (m2) exterior surface area of evaporator per metre pipe length (m2/m) constant that expresses initial compressive force of the control valve (N) specific heat of superheated vapor (J/(kg K)) diameter (m) convective coefficient of heat transfer (W/(m2 K)) enthalpy (J/kg) length (m) mass-flow rate (kg/s) compressorÕs rotary-speed (r/min) cylinder number pressure (MPa) radius of ball valve (m) piston-stroke length (mm) temperature (°C) degree of subcooling at the condenser outlet (°C) refrigerant specific volume at suction end (m3/kg) refrigerant quality at the evaporator inlet valve wall-angle or wobble-plate angle (°) pressure loss in suction pipe (kPa) compression ratio efficiency
Subscripts a air c condenser or critical state or compressor or cylinder cd critical state where the piston-stroke length goes down cdm critical state of decrease in piston-stroke length from its maximum value cu critical state where the piston-stroke length goes up d discharge e evaporator or evacuated bellows of control valve i isentropic or inlet or inner 1 liquid m maximum or mean o out or outlet r refrigerant
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s tp v w 0
3
suction or superheated vapor two-phase volumetric or vapor or thermal expansion valve wobble plate case or wall or wet bulb preset or reference
1. Introduction The infinitely-variable displacement wobble-plate compressor (VDC) changes the piston-stroke length (or wobble-plate angle) and the displacement consequently to exactly match the vehicleÕs air-conditioning demand. Compared to the traditional automotive air-conditioning (AAC) system with a fixed-displacement compressor that cycles the compressor off-and-on to adjust the refrigerating capacity, the AAC system with a VDC has advantages, such as smooth continuous compressor operation, more comfortable environment inside the car and improved fuel-economy [1–3]. So more and more AAC systems with VDC have been used. As represented in [1,2], the VDC can maintain the evaporatorÕs surface-temperature just slightly above freezing temperature to prevent evaporator frosting, so there is no frosting prevention device in the AAC system with a VDC. However, the frost forms on the exterior surface of evaporator sometimes when the actual AAC system with a VDC is used. When the frost is formed at the evaporator, there is an additional thermal resistance on the exterior surface of the evaporator finÕs. The flow area between the fins decreases, air flow resistance increases and air-flow rate decreases, which results in the decrease of convective heat-transfer between air and fins. The additional thermal resistance and decreasing convective heat-transfer will reduce the heat-transfer rate of evaporator, which may result in the air flow path completely blocked by the frost layer in certain conditionÕs. So it is necessary to find out the reasons causing the evaporator frosting and to bring forward the methods for frosting prevention. Numerical simulation is an important way to analyze the frost formation and refrigeration system performance because it can simulate a wide range of operating conditions. Some research had been carried out on the simulation of frost formation on simple geometries [4,5] or finned heat-transfer surfaceÕs [6,7], which mainly analyzed the effects of various parameters (including air temperature and relative humidity, air flow rate, surface temperature and structural parameters) on the frost growth and heat transfer. Other research, such as Tantakitti and Howell [8], Yasuda et al. [9] and Ameen [10], focused on the simulation of heat-pump performance under frosting conditions using a lumped-parameter model. There is no published literature analyzing the reasons why the evaporator frosting forms in the AAC system with a VDC. In the present study, a steady-state mathematical model of the AAC system with a VDC is developed and verified by the experimental data, with which the evaporating temperature and evaporatorÕs surface-temperature at different conditions are simulated and the factors causing the evaporator frosting are analyzed.
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2. Mathematical model The AAC system studied here is a well matched actual system, which is composed of a VDC, an evaporator, a condenser and receiver, a thermal expansion-valve and connection pipes. Among the connection pipes, only the suction pipe model is included in the system model since the pressure loss in the suction pipe influences the piston-stroke length control much more than that of other connection pipes. Only the evaporating temperature and evaporator surfaceÕs temperature under no frosting conditions are needed in the mathematical model since the purpose of this paper is not to study the frost growth but to find out the reasons causing the evaporator frosting. HFC-134a (1,1,1,2-tetrafluoroethane) is used in this system. 2.1. Variable-displacement compressor The VDC, with its wobble plate connected to the pistons with the piston rods, consists of a mainshaft-drive lug assembly, a shaft sleeve, a rotating journal and a wobble plate which converts the rotary motion of the rotating journal into linear reciprocation of the pistons. The VDC studied here is a five-cylinder, wobble-plate type, infinitely-variable displacement compressor, with the displacement range from 10 to 156 cc (cubic centimetre per revolution) (Fig. 1). For details of the VDC refer to [1]. The control valve, mounted in the rear head of the compressor, consists of a cone valve and a ball valve (Fig. 2). The preset suction pressure of the control valve, Ps0, is
Fig. 1. Variable-displacement compressor.
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5
Fig. 2. Control valve.
defined as the suction pressure that decreases till the ball valve is just open and it can be calculated with following expression [11]: 2
P s0 ¼
106 C pP d ðR sin aÞ 0:1Ae 2
Ae pðR sin aÞ
;
ð1Þ
where the constant C expresses initial compressive force of the control valve. It can be seen, from Eq. (1), that Ps0 is linearly proportional to constant C and linear inversely proportional to the discharge pressure (Pd). When the automotive air-conditioning load decreases and the suction pressure (Ps) falls to or becomes less than the preset suction-pressure, the evacuated bellows of the control valve stretches. The spring force of the evacuated bellows, together with other forces acting on the valve rod, makes it move, reduces the opening of the cone valve and increases the opening of the ball valve. The cone valve controls the passage between the wobble-plate case and suction cavity and the ball valve controls the passage between the discharge cavity and wobble-plate case, so the latter pressure rises gradually. When the suction pressure falls to the critical suction-pressure of the piston-stroke length, the force moments acting on the wobble plate are great enough to make the piston-stroke length (or wobble-plate angle) decrease and the displacement falls to match the decrease of the air-conditioning load. In the similar way, the piston-stroke length and displacement will increase when the air-conditioning load rises. The VDC model is composed of the control-valve model, dynamic model of moving components and compression process model. The relationship between the parameters of these three parts in the VDC is presented in Fig. 3. 2.1.1. Control-valve model The steady-state model of the control valve is composed of force balance equations of valve rod and ball valve, mass conversion equation and energy conversion equation of wobble-plate case. With this model, the wobble-plate case pressure,
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Fig. 3. VDC model.
Pw, can be calculated with Pd and Ps. The details of the control-valve model are available in [11]. 2.1.2. Dynamic model of moving components The dynamic model of moving components of VDC, which is used to determine the relationship between the piston-stroke length, Sp (or wobble-plate angle, a) and Pd, Ps, Pw, Nc (compressor rotary speed), is composed of force balance equations of moving components including the piston, piston rod, wobble plate, rotating journal and shaft sleeve [12]. The resultant frictional-force between the moving components when the piston-stroke length decreases is opposite in direction to that when the piston-stroke length increases. The force moment from Ps is identical with the resultant frictional moment when the piston stroke length decreases and in the opposite direction to the resultant frictional moment when the piston-stroke length increases. So the critical suction-pressure of the pistonstroke length decreasing (Ps,cd) is less than the critical suction-pressure of the piston-stroke length increasing (Ps,cu) at the same Sp, Pd and Nc. Sp is kept invariable when Ps,cd 6 Ps 6 Ps,cu and will go down only when Ps < Ps,cd and go up only when Ps > Ps,cu. Ps,cd and Ps,cu can be calculated together with the mathematical model of the control valve [11] and dynamical model of moving components [12]. From the calculation results, Ps,cd and Ps,cu can be fitted into the function of Pd, a and Nc: P s;cd ¼ Ad ða; N c Þ þ ðP d P d0 ÞBd ða; N c Þ;
ð2Þ
P s;cu ¼ Au ða; N c Þ þ ðP d P d0 ÞBu ða; N c Þ:
ð3Þ
In Eqs. (2) and (3), Pd0 is the reference discharge pressure, Ad(a, Nc), Bd(a, Nc), Au(a, Nc) and Bu(a, Nc) are the coefficients which are functions of a and Nc. The application range of Eqs. (2) and (3): Pd = 0.8–1.9 MPa, Nc = 1000–4000 r/min, a = 9.3– 24.4°.
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With the geometrical relationship of VDC moving components, Sp can be calculated from a [13]. So Eqs. (2) and (3) show the relationship of Sp and Pd, Ps, Nc. 2.1.3. Compression process model The compression process model is used to calculate the refrigerant mass flow rate through the compressor, Mr,c, and discharge temperature, Td with Pd, Ps, Nc and Ts (suction temperature). Mr,c and the refrigerant enthalpy at discharge end ði0d Þ can be calculated by following equations: p M r;c ¼ n d 2c S p N c gv =ð60000 vs Þ; 4 i0d ¼ is þ gm
id is ; gi
ð4Þ ð5Þ
where is is the refrigerant enthalpy at suction end and id is the refrigerant enthalpy at discharge end when the compression process is isentropic. The equations of the volumetric efficiency (gv) and isentropic efficiency (gv) at maximum piston stroke length are given in polynomial fitted by our experiment data. gv at maximum piston stroke length is gv ¼ 1:81 0:35e þ 0:026e2 0:00081N c þ 2:51 107 N 2c þ 0:00026eN c 2:07 105 e2 N c 8:68 108 eN 2c þ 7:70 109 e2 N 2c :
ð6Þ
The application range: e = 3.8–6.2, Nc = 900–3000 r/min, suction superheat 15 °C. gi at maximum piston stroke length is gi ¼ 1:17 P s 0:088 P d 6:79 105 N c þ 0:342:
ð7Þ
The application range: Ps = 0.25–0.45 MPa, Pd = 0.9–1.7 MPa, Nc = 900–3000 r/min and suction superheat 15 °C. The relative volumetric-efficiency and relative isentropic-efficiency are used to express the performance at partial piston-stroke length. The relative volumetric-efficiency, gv , is the ratio of gv at partial piston-stroke length and gv at maximum piston stroke-length at the same work condition and compressor rotary-speed. The relative isentropic-efficiency, gi , is the ratio of gi at partial piston stroke length and gi at maximum piston stroke length for the same work condition and compressor rotary-speed. The relative displacement, Sp , is the ratio of actual piston strokelength and maximum piston stroke-length. With the test data, gv and gi can be fitted by following equations: ð8Þ gv ¼ 1:0 þ 0:545 log Sp ; gi ¼ 0:58Sp þ 0:4:
ð9Þ
The application range of Eqs. (8) and (9): Sp ¼ 0:52–1. The steady-state model of a VDC is composed of Eqs. (2)–(9): Ps,cd and Ps,cu can be calculated when Pd, Nc and Sp are known, and Mr,c and discharge state parameters can be determined from given Pd, Ps, Ts and Nc.
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2.2. Evaporator The evaporator is a plate-fin-tube evaporator with four paths and five rows. The evaporator length is 0.262 m, the height is 0.228 m, the thickness is 0.084 m and the exterior surface-area is 5.5 m2. The evaporator model is a lumped model and the evaporator is divided into a two-phase region and a superheated-vapor region. The frost growth model is not included in the evaporator model since only the evaporating temperature and evaporator surface temperature under no frosting conditions are calculated. It is assumed in the model that: The refrigerant flow in pipes can be considered as a one-dimensional flow. The two-phase flow is considered in the equilibrium state; the evaporating temperature and convective coefficient of heat transfer are constant and the pressure loss in the two-phase region is concentrated at its outlet. The kinetic energy and potential energy are neglected in the energy-balance equation of the refrigerant. The axial heat-conduction through the pipe wall is neglected. The refrigerant flows in the four paths are uniform. By the energy-balance equation in the two-phase region, the evaporatorÕs surfacetemperature (i.e. the pipe wall temperature of the evaporator in the two-phase region in this paper), Tew, and length of the two-phase region in one path, Ltp, can be calculated using the following equations: T ew ¼
ho Ao go hi pd i
T eam þ T e
1 þ hho iApdo gi o
;
ð10Þ
and Ltp ¼
M r ð1 xi Þðiv i1 Þ : hi pd i ðT ew T e Þ
ð11Þ
By the energy-balance equation in the superheated-vapor region, the refrigerant temperature at the evaporator outlet, Teo, can be deduced as
T eo
! 1 1 ¼ T eam ðT eam T e Þ exp 1 ðL Ltp Þ : þ ho A1o go M r cps his pd i
ð12Þ
The pressure loss of the refrigerant in the two-phase region is calculated using the equations in [14] and the pressure loss of refrigerant in superheated vapor region is calculated with the equations in [15]. The mean convective coefficient of heat transfer in the two-phase region between the refrigerant and the pipeÕs interior surface is calculated with the equations in [16] and the convective coefficient of heat transfer between the air and evaporator fin is calculated with the equations in [17].
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9
START
INPUT PARAMETERS: Nc, Sp, Teai, ϕeai, Tcai, Mea, Mca, Tsc0
SET STARTNG VALUES FOR P d, P s , T s
CALL VDC MODEL (TO GET Mr,c ) TO CORRECT ASSUMED Pd
CALL CONDENSER MODEL (TO GET Tsc )
No
TO CORRECT ASSUMED Ts IS ©¦Tsc-Tsc0©¦< ¦Å? Yes CALL SUCTION PIPE MODEL (TO GET ∆ Ps, T'eo)
TO ADJUST EXTERNAL PARAMETER
TO CORRECT ASSUMED Ps
CALL EVAPORATOR MODEL (TO GET Te, Tew, Teo) CALL THERMAL EXPANSION VALVE MODEL (TO GET Mr,v)
IS ©¦Mr,c-Mr,v©¦< ¦Å?
No
Yes No IS ©¦T'eo-Teo©¦< Yes ¦Å? Yes COMPUTE Psc
No
IS ©¦Ps-Psc©¦< ¦Å? Yes RESULT OUTPUT: Ps0, Ps, ∆ Ps, Te, Tew END
Fig. 4. Flow diagram for numerical solution procedure.
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2.3. Other components The condenser is a parallel-flow type condenser. Its length is 0.35 m, height 0.56 m, thickness 0.02 m and its exterior surface area 5.58 m2. The condenser model is a lumped model and the condenser is divided into three regions including superheated vapor, two-phase and subcooled liquid region. The mean convective coefficient of heat transfer in the two-phase region between the refrigerant and the pipe interior surface is calculated using the equations in [18], the convective coefficient of heat transfer between the air and condenser fin is calculated with the equations in [19] and the refrigerant pressure loss in condenser is calculated using the equation in [20]. The thermal expansion valve is a cross and absorptive charge H type expansion valve, whose nominal refrigerating capacity is 7032 W. The opening of the thermal expansion valve is calculated by the force balance equation of the valve rod and the flow area can be deduced. The refrigerant mass-flow rate through the thermal expansion valve (Mr,v) can be calculated when the refrigerant states at the thermal expansion valve inlet and outlet are known. The pressure loss and heat loss for the suction pipe are considered. Forced-convection between the superheated vapor and the interior surface of suction pipe occurs whereas free convection between the air and exterior surface of the suction pipe ensues. The pressure loss of refrigerant in the suction pipe is calculated with the equations in [15]. With the inlet and outlet parameter relationship between every component in the AAC system with a VDC, the steady-state system model is developed to combine the mathematical models of the VDC, evaporator, condenser, thermal expansion valve and suction pipe. 2.4. Solution procedure Fig. 4 shows the flow diagram for a numerical solution procedure of the steadystate mathematical model. Firstly, input the parameters and set the starting values for Pd, Ps and Ts. The set value of the degree of subcooling at the condenser outlet, Tsc0, must be given as an input parameter. Then call the subroutines of the VDC, condenser, suction pipe, evaporator and thermal expansion valve. Finally the simulation of a steady-state point is undertaken to correct the assumed starting value till the calculation results satisfy the required precision. By continuing the solution procedure, a critical state of the pistonÕs stroke-length can be simulated by adjusting the external parameter.
3. Experimental verification of the system model 3.1. Test system The test system, shown in Fig. 5, was built inside two chambers. The VDC, the condenser and receiver were placed in the outdoor chamber, the evaporator and
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Fig. 5. Test system.
the thermal expansion valve in the indoor one. Both chambers were kept at constant temperature and constant humidity needed in the experiment. The whole system consisted of the main experimental body, control system and measurement system. The main body was identical with the AAC system introduced in the mathematical model. The parameters controlled in this test system were the compressorÕs rotary speed, air temperature at the condenser inlet, air flow rate through the condenser, air drybulb temperature and wet-bulb temperature at the evaporator inlet and air flow rate through the evaporator. The compressor was driven by a variable-frequency motor and the compressorÕs rotary speed was changed by adjusting the power frequency. The condenser fan was also driven by a variable frequency motor, so the air flow rate through the condenser could be controlled by adjusting the power frequency of the condenserÕs fan motor. The air-flow rate through the evaporator was controlled by a three-speed fan and the booster fan (also driven by a variable-frequency motor) was adjusted meanwhile to maintain the air pressure at the evaporator outlet at atmospheric pressure in order to attain an actual condition for the evaporator. The air temperature at the condenser inlet, air dry-bulb temperature and wet-bulb temperature at the evaporator inlet were controlled by the two chambers. The parameters measured in this test system included the compressorÕs rotary speed, piston-stroke length, refrigerantÕs mass flow-rate, refrigerant temperatures and pressures at different test points, evaporatorÕs surface-temperature, air dry-bulb and wet-bulb temperatures at the evaporator inlet and at the evaporator outlet (Teai, Teaiw, Teao and Teaow), air temperatures at the condenser inlet and at the condenser outlet (Tcai and Tcao), air-flow rateÕs through the evaporator and through the condenser (Mea and Mca). The compressorÕs rotary speed was measured with an electric eddy current sensor, the pistonÕs stroke-length was measured [13] and the refrigerantÕs mass-flow rate was measured with Coriolis flow-meter. The refrigerant
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temperatures and evaporator surface temperature were measured with copper–constantan thermocouples and the refrigerant pressures were measured with voltageoutput type pressure-sensors. The air dry-bulb and wet-bulb temperatures were measured with platinum-resistance temperature sensors and the air-flow rate was measured with the standard nozzle and differential pressure transducer. These sensors all produced electric voltageÕs or currentÕs, which were sent to a data logger and a computer to record the test data. Table 1 shows the measurement devices and precision used in this test system. 3.2. Comparison between measured and simulated results The critical evaporating temperature and critical evaporator surface-temperature of the pistonÕs stroke-length (Te,cd and Tew,cd), the critical evaporating temperature and critical evaporator surface temperature of the pistonÕs stroke-length (Te,cu and Tew,cu) are used in the following evaporator frosting analysis. The simulated results of Te,cd, Tew,cd, Te,cu and Tew,cu are compared with corresponding experimental data. In the experiment, the compressorÕs rotary speed increased gradually and the pistonÕs stroke-length fell. The measured evaporating temperature and evaporator surface temperature could be considered as Te,cd and Tew,cd, respectively (the saturation temperature of refrigerant at the pressure at the evaporator outlet is the evaporating temperature). Te,cd and Tew,cd could be simulated with the steady-state system model. The comparison between the simulated and measured results for Te,cd and Tew,cd is shown in Fig. 6(a). The deviations between simulated and measured values of Te,cd are less than 0.3 °C and the deviations between simulated and measured values of Tew,cd are less than 0.6 °C. When the compressorÕs rotary speed decreased gradually, the pistonÕs stroke length rises: the measured evaporating temperature and evaporator surface temperature could be considered as Te,cu and Tew,cu, respectively. The comparison between the simulated and measured results of Te,cu and Tew,cu is shown in Fig. 6(b). The deviations between simulated and measured values of Te,cu are less than 0.4 °C and the deviations between simulated and measured values of Tew,cu are less than 0.5 °C. Table 1 Measurement devices and precision Device
Number
Precision
Model
Thermocouple Platinum-resistance sensor Pressure sensor Coriolis flow-meter Electric eddy-current sensor Stroke-measurement device Differential pressure-transducer Data logger
7 6 7 1 1 1 2 1
±0.2 °C <0.1 °C ±0.2% ±1% ±1% <0.01 mm ±0.5%
T type Voltage-output type Mass 2100
1751DR HP 34970A
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Fig. 6. Comparison between simulation results and experimental data. (a) Critical evaporating temperature and critical evaporator surface-temperature of piston stroke-length decreasing. (b) Critical evaporating temperature and critical evaporator surface-temperature of piston stroke-length increasing. (c) Critical compressor rotary-speed, critical evaporating temperature and critical evaporator surfacetemperature of decrease in piston stroke-length from its maximum value.
For a certain air-temperature at the evaporator inlet, there exists a critical compressor rotary-speed when the pistonÕs stroke-length starts to decrease from its maximum value (Nc,cdm). When the corresponding critical evaporating-temperature (Te,cdm) and critical evaporatorÕs surface-temperature (Tew,cdm). Fig. 6(c) shows the comparison between the simulated and measured values of Nc,cdm, Te,cdm and Tew,cdm at different air temperatures at the evaporator inlet. The deviations between the simulated and measured values of Nc,cdm are less than 7%: the deviations between the simulated and measured values of Te,cdm are less than 0.6 °C and the deviations between the simulated and measured values of Tew,cdm are less than 0.75 °C. From the comparisons mentioned above, we can see that the simulated results agree well with experimental data and the systemÕs model can be used to analyze the steady-state performance of the AAC system with a VDC quantitatively.
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4. Analysis of reasons causing evaporator frosting The moisture in wet air will freeze on the evaporatorÕs surface when its surface temperature is below 0 °C the evaporatorÕs surface-temperature is mainly related to the evaporating temperature. The influence of system performance itself, component structural parameters, and external parameters on the evaporating temperature and evaporator surface temperature are simulated and analyzed with the system model to find out the reasons causing the evaporator frosting. 4.1. Influence of performance band With the AAC system model, the steady-state points at the maximum pistonÕs stroke-length can be calculated. Let Psc = Ps,cd in the flow diagram (Fig. 4): adjust the air temperature at the evaporator inlet (Teai) to make Ps = Psc, the critical state of the piston stroke length then decreases. Let Psc = Ps,cu in the flow diagram: adjust Teai to make Ps = Psc, the critical state of the piston stroke length then increases. It can be learnt from the VDC model, due to the frictional forces the moving components of the VDC, Ps,cd < Ps,cu at the same pistonÕs stroke-length, discharge pressure and compressor rotary speed. The variation of Te with Teai is shown in Fig. 7(a). When Teai is high (>24.5 °C), the evaporating temperature and suction pressure are high enough to maintain the VDC running at the maximum pistonÕs stroke-length. When Teai = 24.5 °C, the suction pressure equals the critical suction pressure where the pistonÕs stroke-length starts to decrease from its maximum value (Ps,cdm) and the evaporating temperature is equal to the corresponding critical evaporating temperature (Te,cdm). When T < 24.5 °C, Te,cd and Te,cu at different piston stroke-lengths can be simulated and Te,cu > Te,cd at the same piston stroke-length. The piston strokelength can decrease only when Te < Te,cd, the piston stroke-length can increase only when Te > Te,cu and the piston stroke length will be invariant when Te,cd 6 Te 6 Te,cu. Between Te,cu and Te,cd, one Te Teai curve for a fixed piston stroke-length is equivalent to a performance curve of the AAC system with a fixed displacement compressor and many Te Teai curves for different piston stroke lengths form a band (here we define it as the ‘‘performance band’’). Compared to the one-to-one relationship of Te Teai curve in the AAC system with a fixed displacement compressor, it is multiple-to-one relationship, i.e., there exist many values of Te for just one certain Teai. All steady-state points should fall within the performance band. The evaporator’s surface-temperature (Tew) along with Te, have similar performance bands. Fig. 7(b) indicates that the evaporatorÕs surface-temperatures in part of the Tew Teai performance band are less than zero and so will cause evaporator frosting. The greater the frictional forces among the moving components of the VDC, the broader the Tew Teai performance band and the larger the change range of evaporating temperature and evaporator surface-temperature. The narrower performance band reduces the possibility of evaporator frosting. In order to avoid or reduce the evaporator frosting in the AAC system with a VDC, it is necessary to reduce the frictional forces between the moving components
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Fig. 7. Performance band (compressor rotary speed Nc = 2000 r/min; air temperature at condenser inlet Tcai = 42 °C; air relative humidity at evaporator inlet ueai = 50%; evaporator fan is at high speed). (a) Te Teai. (b) Te Teai and Tew Teai.
while designing and manufacturing the compressor and to assure the lubrication of the compressor to reduce the width of the performance band in the actual operation of AAC system. It can be seen from Fig. 7, when the evaporating temperature or suction pressure is high (then evaporator surface temperature is high enough to ensure that
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no frosting forms), the VDC is at the maximum pistonÕs stroke-length and its behaviour is identical with that of a fixed displacement compressor: the suction pressure changes with the systemÕs external parameters and cannot be controlled by the VDC. Only when the evaporating temperature or suction pressure decreases till the pistonÕs stoke-length varies, then the evaporating temperature can be controlled by VDC to be within the performance band. The influence of the component structural parameters and systemÕs external parameters on the critical state of decrease in the pistonÕs stroke-length from its maximum value is simulated and analyzed. This reveals a transition point from the maximum pistonÕs stroke-length to the critical state of the piston’s stroke-length decreasing and Pe,cdm is the lowest temperature in the performance band. 4.2. Influence of component structural parameters With the AAC system model, let Psc = Ps,cdm in the flow diagram (Fig. 4). Adjust the compressorÕs rotary speed to make Ps = Psc, then the critical state of decrease in the pistonÕs stroke-length can be obtained. For a given VDC (here the constant, C, the initial compressive force of control valve, is 35 N) and evaporator, the suctionÕs pipe-length (the suction pipe is assumed as a straight pipe without local resistance to simplify the analysis and its inner diameter is 16 mm) and condenser size are the main component structural parameters influencing the relationship between the behavior of the control valve and evaporating temperature. 4.2.1. Suction pipe length The variations of the preset suction-pressure (Ps0), refrigerant pressure loss in the suction pipe (DPs), evaporating temperature and evaporatorÕs surface-temperature at the critical state of decrease in pistonÕs stroke-length from its maximum value along with the suction pipe length are shown in Fig. 8(a) (the condenser length, Lc, is kept at 0.56 m). Ps0 and Ps,cdm are almost not influenced by the suction-pipeÕs length. However, DPs falls along with the decrease of suction-pipeÕs length and then Pe,cdm decreases, which will cause Te,cdm and Tew,cdm to decrease. Tew,cdm = 0 °C when the suction pipe length is 4 m and Tew,cdm will be lower than 0 °C and there will be evaporator frosting when the suction pipe length is less than 4 m. The larger the constant C, the greater Ps0 and Ps,cdm at the same discharge pressure. So the larger constant C is suitable for the suction pipe with a smaller resistance pressure to maintain the evaporating temperature higher than 0 °C. 4.2.2. Condenser size Only change the condenser length and keep the other condenser structural parameters invariable, then the relative length of the condenser (Lc/Lc0) is equal to the area ratio of the condenser (Lc0 = 0.56 m). The variations of Ps0, DPs, Te,cdm and Tew,cdm along with the condenser length are shown in Fig. 8(b) (Ls is 4 m). With the decrease of condenser length, the discharge pressure increases, so Ps0 and Ps,cdm become smaller and a higher compressor rotary speed is needed
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Fig. 8. Influences of component structure parameters on evaporator frosting: (a) suction-pipe length, (b) condenser size.
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for the critical state of decrease in the piston-stroke-length. The refrigerantÕs mass-flow rate increases then and DPs goes up. But Te,cdm and Pew,cdm go down along with the decrease of condenser length because the decreasing amplitude of Ps,cdm is greater than the increasing amplitude of DPs. When Lc/Lc0 = 1, Tew,cdm = 0 °C; Tew,cdm will be lower than 0 °C and evaporator frosting will form when Lc/Lc0 < 1. Fig. 8(b) indicates that the smaller the condenser size, then the control valve with greater constant C is needed. From the analysis of influence of suction-pipeÕs length and condenser size on the evaporator frosting, it can be found that the value of C should be selected for a given suction pipe or a given condenser when matching the system in order to prevent the evaporator frosting. 4.3. Influence of external parameters For a given control valve (C = 35 N), suction pipe (Ls = 4 m) and condenser (Lc = 0.56 m), the influence of external parameters including the compressorÕs rotary speed, air temperature at the evaporator inlet, air-flow rate through the evaporator and air temperature at the condenser inlet on the critical state of decrease in the pistonÕs stroke-length from its maximum value is studied. With the systemÕs mathematical model, let Psc = Ps,cdm in the flow diagram (Fig. 4). For a given value of one external parameter, there must be a certain value of another external parameter to make Ps = Psc, so the different critical states can be obtained when two external parameters change simultaneously. 4.3.1. Simultaneous change of compressorÕs rotary speed and air temperature at the evaporator inlet The variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary-speed and air temperature at the evaporator inlet are shown in Fig. 9(a). When Teai increases, the compressorÕs rotary speed needed for reaching the critical state of decrease in the pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. Because the air flow rate through the condenser goes up with the increase of the compressorÕs rotaryspeed, the discharge pressure increases just a little and Ps0 and Ps,cdm go down slightly. Meanwhile, DPs rises, which counteracts the decrease of Ps,cdm and maintains Te,cdm and Tew,cdm almost constant. Tew,cdm almost maintains 0 °C in Fig. 9(a), so evaporator frosting will not happen. When the compressorÕs rotary-speed and air temperature at the evaporator inlet increase simultaneously, the increase of discharge pressure is only caused by the rise of the refrigerantÕs flow-rate. Meanwhile, the rise of the refrigerantÕs flow rate causes the increase of the refrigerantÕs pressure-loss in the suction pipe. For the control valve studied here, Ps0 is inversely proportional to the discharge pressure, so the evaporating temperature and evaporatorÕs surface-temperature are almost constant. The control valve provides good control behavior when the
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Fig. 9. Influence of external parameters on evaporator frosting. (a) Simultaneous change of compressor rotary speed and air temperature at the evaporator inlet. (b) Simultaneous change of compressor rotary speed and air flow rate through the evaporator. (c) Simultaneous change of compressor rotary speed and air temperature at the condenser inlet.
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compressorÕs rotary-speed and the air temperature at the evaporatorÕs inlet change. 4.3.2. Simultaneous change of compressorÕs rotary-speed and air flow rate through the evaporator Fig. 9(b) shows the variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary speed and air mass flow rate through the evaporator. The air-flow rate through the evaporator Mea = 0.1 kg/s when the evaporator fan is at low speed, Mea = 0.145 kg/s at middle speed and Mea = 0.179 kg/s at high speed. When Mea increases, the compressorÕs rotaryspeed needed for reaching the critical state of decrease in pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. Similar to the simultaneous change of the compressorÕs rotary-speed and air temperature at the evaporatorÕs inlet, the discharge pressure increases a little and Ps0 and Ps,cdm go down slightly. Meanwhile, the increase of refrigerantÕs flowrate causes the rise of DPs, which maintains Te,cdm and Tew,cdm almost constant. Tew,cdm almost maintains 0 °C in Fig. 9(b), so the evaporator frosting will not occur.
4.3.3. Simultaneous change of the compressorÕs rotary-speed and air temperature at the condenser inlet The variations of Ps0, Ps,cdm, DPs, Te,cdm and Tew,cdm with the simultaneous change of the compressorÕs rotary-speed and air temperature at the condenser inlet are shown in Fig. 9(c). When Tcai increases, the rotary speed needed for reaching the critical state of decrease in the pistonÕs stroke-length from its maximum value goes up, which causes the refrigerant flow rate to increase. The increase of discharge pressure is caused by the rise of both the refrigerant flow-rate and the air temperature at the condenser inlet: Ps0 and Ps,cdm decrease with a greater amplitude. But the increasing amplitude of DPs is less than the decreasing amplitude of Ps,cdm, so Te,cdm and Tew,cdm decrease along with the increase of Tcai. Tew,cdm < 0 °C when Tcai > 38 °C: evaporator frosting will form. The simulated results indicate that when the compressorÕs rotary-speed, air temperature at the evaporator inlet and air-flow rate through the evaporator change, the control valve can maintain the evaporating temperature and evaporatorÕs surface-temperature at the critical state of decrease in pistonÕs stroke-length from its maximum value almost constant, but the two temperatures change with a greater amplitude when the air temperature at the condenser inlet varies. That is to say, that even the control valve with proper constant C has been selected, the evaporator frosting may happen when the air temperature at the condenser inlet is higher than that of design condition, which is a defect of this type control valve. In order to prevent the evaporator frosting, one needs to consider the influence of the air temperature at the condenser inlet while designing the new controlvalve and to increase the setting value of the air temperature inside the vehicle
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if the ambient temperature is high in the actual operation of the AAC system with a VDC.
5. Conclusions A steady-state mathematical model of the AAC system with a VDC has been developed and a test system has been established to validate the system model. It is shown that the simulated results agree well with the experimental data. After analyzing the influence of different kinds of factors, it is found that there are three reasons causing evaporator frosting in the AAC system with a VDC, and corresponding countermeasures have been proposed. The performance band makes the evaporating temperature and evaporatorÕs surface-temperature vary within a certain range, which can contribute to evaporator frosting. The frictional forces between the moving components of the VDC should be reduced while designing, manufacturing and operating the VDC in order to avoid evaporator frosting. The mismatching between constant C (initial compressive force) of the control valve and the resistance pressure in suction pipe or the condenser size can also contribute to evaporator frosting. For the control valve with a given constant C, the smaller the resistance pressure of the suction pipe or condenser size is, the easier evaporator frosting forms. In order to prevent the evaporator frosting, the control valve with a proper constant C should be selected for a given suction pipe and condenser when matching the system. Because the preset suction-pressure of the control valve decreases with the increase of discharge pressure, and the rise of the air temperature at the condenser inlet can cause the discharge pressure to increase but with little influence on the resistance pressure of suction pipe, so evaporator frosting may happen when the air temperature at the condenser inlet is higher than that of the design condition. One needs to consider the influence of the air temperature at the condenser inlet while designing the new control valve.
Acknowledgement The study was supported by Natural Science Foundation of China (Grant No. 50176028).
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