Characterization of a scroll compressor under extended operating conditions

Applied Thermal Engineering 30 (2010) 605–615

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Applied Thermal Engineering

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Characterization of a scroll compressor under extended operating conditions

Cristian Cuevas a,*, Jean Lebrun b,1, Vincent Lemort b,2, Eric Winandy b

a Departamento de Ingeniería Mecánica, Facultad de Ingeniería, Universidad de Concepción, Casilla 160-C, Concepción, Chileb Thermodynamics Laboratory, University of Liège, Campus du Sart Tilman – Bâtiment B49, Parking P33, B-4000 Liège, Belgium

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 November 2008Accepted 9 November 2009Available online 13 November 2009

Keywords:Scroll compressorTestingModellingHigh pressure

1359-4311/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.applthermaleng.2009.11.005

* Corresponding author. Tel.: +56 41 2203550; fax:E-mail addresses: [email protected] (C. Cuevas), j.

[email protected] (V. Lemort).1 Tel.: +32 4 3664801; fax: +32 4 3664812.2 Tel.: +32 4 3664824; fax: +32 4 3664812.

Refrigeration and air-conditioning compressors are designed to work under well-defined conditions. Insome applications it is interesting to observe their performances beyond these conditions, for examplein the case of a high temperature two-stage heat pump or of a cooling system working at high temper-ature.

In this study a compressor is characterized experimentally with refrigerant R134a and through 118tests at condensing pressures varying from 8.6 up to 40.4 bar (tsat = 33.9 �C to tsat = 100.8 �C) and evapo-rating pressures varying from 1.6 up to 17.8 bar (tsat = �15.6 �C to tsat = 62.4 �C). Under these conditionsthe compressor motor was pushed at its maximal current in several tests.

This compressor’s performance is mainly characterized by its isentropic and volumetric efficiencies. Itpresents a maximal isentropic efficiency of 72%, corresponding to a pressure ratio of around 2.5–2.6. Thevolumetric efficiency decreases linearly from almost 1.0 (for a pressure ratio of 1.3) to 0.83 (for a pressureratio of 9.7). A slight degradation of the isentropic and volumetric efficiencies is observed when the com-pressor supply and exhaust pressures are increased for a given pressure ratio; this could be due to aninternal leakage.

The compressor tests are used to identify the six parameters of a semi-empirical simulation model.After parameter identification, experimental and simulated results are in very good agreement, exceptfor some points at high compressor power where the compressor is pushed at its maximal current.

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1. Introduction the machine. Morishita et al. [10] seem to be the first authors to

Characterization of thermal machines is not only restricted tothe experimental analysis, modelling is also very important tostudy the behaviour of overall systems during the design or thesimulation step. Both experimental and modelling aspects areapplied here for a refrigeration scroll compressor.

With respect to the compressor modelling, the distinction canbe made between empirical, semi-empirical and deterministic sim-ulation models.

Empirical models are based on polynomial regressions and arecommonly used by manufacturers to present the performance ofthe compressor.

Deterministic models rely on a comprehensive description ofthe compressor based on control volumes analysis (involving heatand mass transfers). Generally, these models associate a geometri-cal description of the machine and a thermodynamic description ofthe compression process and require the exact characteristics of

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+56 41 [email protected] (J. Lebrun),

give an analytical expression for the volume of the suction, com-pression and discharge chambers. Caillat et al. [2] developed oneof the first global simulation models of the scroll compressor in or-der to analyze geometric, dynamic, thermodynamic and heattransfer characteristics under different conditions. Two years later,Yanagisawa et al. [19] developed another simulation model forcharacterizing more in details the influence of flow resistance,leakage and rotational speed on the compressor’s performance. Ni-eter [11] and Nieter and Gagne [12] used a deterministic model toinvestigate the suction and the discharge processes in a scroll com-pressor. Halm [6] summarized most of the previous works andestablished a very detailed model of the scroll compressor. Later,Wang et al. [15] generalized all the proposed analytical descrip-tions of the scroll geometry. Similar models, also based on controlvolumes analysis, have been developed by Chen [3], Schein andRadermacher [14], Lee [9] for an air-conditioning hermetic com-pressor, Huff and Radermacher [8] for CO2 application, and Wanget al. [16] for investigating refrigerant injection.

Semi-empirical models, such as the one introduced in this pa-per, are described by physically meaningful equations and requirea limited number of parameters that can be identified on the basisof measurements. Semi-empirical models are less time-consumingand more numerically robust than deterministic models. Hence,

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Nomenclature

AU heat transfer coefficient (W K�1)C coefficient (–)_H enthalpy flow (W)h enthalpy (J kg�1)_M mass flow rate (kg s�1)

N rotational speed (s�1)n number of tests (–)P pressure (bar) or (Pa)_Q heat flow (W)Rp pressure ratio (–)rv,in built-in volume ratio (–)T temperature (K)t temperature (�C)V volume (m3) or variablev specific volume (m3 kg�1)w specific work (J kg�1)W compression work (J)_W power (W)

Z coefficient (–)

Subscriptsamb ambientcal calorimetercor Corioliscp compressorel electricaleV evaporatorex exhaust

f finali initialin internalloss lossm motormeas measuredmix mixturenom nominaloh overheatingr refrigerantref references isentropic or sweptsat saturationsd slipsim simulatedsu supplyv volumetric or isovolumetricw water

Greek symbolsD differentiala power loss coefficiente efficiency�e errorc isentropic coefficienth error functionr standard deviation

606 C. Cuevas et al. / Applied Thermal Engineering 30 (2010) 605–615

they are easier to integrate into the modelling of the whole refrig-eration system. Moreover, unlike empirical models, semi-empiricalmodels allow the extrapolation of the component’s performancebeyond the range of data used to identify their parameters.

Hiller and Glicksman [7] seem to be the first ones to propose asemi-empirical model of a compressor, in the special case of areciprocating machine. Sauls [13] proposed a simple descriptionof the under-and over-compression processes characteristics ofscroll machines. Haberschill et al. [5] developed a model of a her-metic scroll compressor that accounts for the under- and over-compression processes, the internal leakage and the heat transferto the ambient. This model was improved by Winandy et al. [18],who introduced the description of the suction and exhaust heattransfers and of the electro-mechanical losses.

In this study, the semi-empirical model proposed by Winandyet al. [18] is considered to characterize the scroll compressor ascontinuation of the validation and as verification of the hypothesisof this model under extended conditions.

Regarding the experimental analysis of thermal machines, it iscurrently restricted to one nominal point or two to three dimen-sional testing conditions. The system or its components are rarelyrun at the limits of their operating range. Performance of the sys-tem or component under such extreme conditions can be esti-mated by means of simulation, but without any certainty thatthe system would work reliably. This is the reason why, when atest bench has been set up, it is convenient to exploit it at mostto address these questions at least once. For example, very widetesting conditions, corresponding to different applications, couldbe defined for one component.

It is especially the case with the results presented in this study,where a very large experimental program was carried out on afixed speed hermetic scroll compressor. For instance, severe oper-ating conditions, in terms of pressure and pressure ratio, weredefined.

It is well-known that scroll compressors differ from each other bytheir built-in volume ratio. The selected value depends on the appli-cation. For example in air-conditioning applications a moderatedbuilt-in volume ratio is used; on the other hand, in refrigerationapplications a more important built-in volume ratio is preferred.Moreover, in some compressors that must to work at high pressureratios, manufactures install, at the compressor exhaust, a reed valveto reduce compressor loss related to the non-adaptation of the inter-nal pressure ratio to the external one (Winandy et al. [18]).

In the actual application considered (which is not described indepth here) the system must be able to work at high pressures andat lower pressure ratios, thus compressors with a low built-in vol-ume ratio are more appropriate for this application. The compressorswept volume is selected according to the maximal cooling powerdemand. In the nominal conditions, this maximal cooling power de-mand is of the order of 76 kW for a water–glycol flow rate of 5000 l/hentering at 80 �C at the evaporator which is then rejected to an air-cooled condenser supplied by ambient air at a maximal temperatureof 45 �C and an air flow rate of the order of 2 kg/s.

Again for the special application considered, the refrigerant sys-tem has to be tested under conditions very different from classicalones: condensing pressures varying from 8.6 up to 40.4 bar(tsat = 33.9 �C to tsat = 100.8 �C) and evaporating pressures varyingfrom 1.6 up to 17.8 bar (tsat = �15.6 �C to tsat = 62.4 �C). RefrigerantR134a has been selected for this particular application.

The results presented here could be used, for example, as a basisfor a high temperature two-stage heat pump, or for a high temper-ature cooling system.

2. Test bench description

Some information given in EN 13771-1 Standard [4] areused to determine the refrigerant capacity, the power ab-sorbed, the refrigerant flow rate, the isentropic efficiency and

Fig. 1. Test bench.

Fig. 2. Compressor calorimeter.

C. Cuevas et al. / Applied Thermal Engineering 30 (2010) 605–615 607

the coefficient of performance. In particular, the methods A(secondary fluid calorimeter on the suction side) and E (refrigerantflow meter in the liquid line) of this Standard, as well as an energybalance on the compressor are used in this experimental study.

The test bench is a classical refrigeration loop with: glycol–water heated evaporator, air-cooled and water-cooled condensers,and an electronic expansion valve.

Pressures, temperatures, electrical powers and flow rates aremeasured at main locations of the test rig, in order to check thethermal balances across each component and across the overallsystem, as shown in Fig. 1.

2.1. Compressor description

The tested compressor is a hermetic scroll (see Fig. 2) with thefollowing characteristics:

Theoretical swept volume at 50 Hz 28:8 m3 h�1

Nominal speed 3000 rpmMaximum operating current 19:2 A

Table 1Measurements ranges and uncertainties.

Variable Measurement range Uncertainty

PressuresPr,su,cp 1.55–17.78 bar Between ±0.03 and ±0.04 barPr,ex,cp 8.60–40.44 bar Between ±0.20 and ±0.21 bar

Flows_Mmix;cor 58.2–398.7 g s�1 Between ±0.2 and ±1.3 g s�1

Electrical power_Wcp 4122–16,808 W Between ±46 and ±189 W

Table 2Test conditions.

Supply pressure 1.6–17.8 barExhaust pressure 8.6–40.4 barSupply temperature �10.5 to 70.6 �CExhaust temperature 53.5–136 �CRefrigerant mass flow rate 0.055–0.637 kg s�1

Compressor electric power 4.12–16.81 kW


Usual operating range:

supply temperature : 18—25 �Cexhaust temperature : 70—120 �Csupply pressure : 3—7 barexhaust pressure : 12—25 barrefrigerant mass flow rate : 0:1—0:25 kg s�1

electrical power : 6—11 kW

These values are extracted from a previous characterization of thiscompressor with refrigerant R22 by Winandy et al. [18].

In this kind of compressor, the refrigerant circulates through theelectrical motor, in order to cool it, before entering the suctionchambers delimited by the two scrolls.

In the present study, the following unusual experimental condi-tions are achieved:

– Pressure: the compressor works at higher pressures because ofthe higher evaporating and condensing pressures used here.However, this compressor has been tested in the factory at upto 100 bar, a pressure to which the crankcase must resist. Onthe other hand, the pressure ratio is low; therefore, the wideningof the pressure range should not cause any mechanical problem.

– Motor cooling: at normal operating conditions, the motor is rel-atively well cooled by the suction gas entering the compressorat temperatures of about 20 �C. In the present case, the refriger-ant evaporates at temperatures of up to 67 �C, which can inducecertain problems. But, at these high temperatures, the refriger-ant mass flow rate is also higher, what tends to balance effectsof high temperatures. Indeed, it is demonstrated that there areno problems until 65 �C.

2.2. Measuring system

The compressor calorimeter, shown in Fig. 2, is used to determi-nate the compressor ambient heat loss. In the present case, the cal-orimeter temperature is kept constant by manually tuning thewater flow rate supplying the fan coil.

The total conductance of the calorimeter is estimated, by cali-bration, to 5.26 W K�1. Fig. 3 shows the results of the calorimetercalibration. The intersect of 12.3 W has to be considered as anuncertainty on the calorimeter heat balance.

Table 1 gives the uncertainties associated with pressures, refrig-erant flow rate and compressor electric power measurements. Theuncertainty on the calorimeter water flow rate is estimated to ±2%of the measured value.

Fig. 3. Global conductance of the calorimeter.

3. Experimental results and analysis

The compressor tests were divided in two phases: (a) variationof the pressure ratio at constant supply overheating and (b) varia-tion of the overheating at constant pressure ratio.

The compressor is characterized with 118 tests (the testingrange is given in Table 2) at a constant supply frequency and bytaking a 30-min steady-state period for the experimental analysis,for an acquisition frequency of 1 acquisition every 5 s.

3.1. Compressor ambient loss

The calorimeter thermal balance is based on the control volumeshown in Fig. 4.

The steady-state thermal balance is given by the followingequation:

_Wlamps þ _Wfan � _Hw;cal � _Q cal;amb þ _Q cp;amb ¼ 0 ð1Þ

The compressor ambient loss is correlated with the temperaturedifference between the compressor wall and the calorimeter inter-nal ambient. The wall temperature is measured at four differentlocations. Fig. 5 shows the compressor heat loss versus four tem-peratures differences, where twall,cp,1 is the wall temperature mea-sured on the top of the compressor and twall,cp,2, twall,cp,3, twall,cp,4 arethe temperatures measured on the sides of the compressor at dif-ferent heights.

Fig. 6 shows the same result but using two average compressorwall temperatures: triangles are used for an arithmetic averagewall temperature and circles for a weighted average temperature.When using an arithmetic average temperature, the relationshipobtained between the heat losses and the differential temperaturedoes not cut the y-axis at zero and presents an intercept of �53 W.To eliminate this intercept, a wall temperature has to be defined inthe weighted average, according to the following equation:

twall;cp ¼ m � ðtwall;cp;1Þ þ ð1�mÞ � ðtwall;cp;2 þ twall;cp;3 þ twall;cp;4Þ=3

ð2Þ

The intercept is eliminated with m = 0.163 and the compressorheat transfer coefficient is then evaluated to 18 W K�1. By consid-ering a compressor heat transfer area of around 0.5 m2, a heattransfer coefficient of 36 W m�2 K�1 is obtained. The latter seemsrealistic with regard to the air movement inside the calorimeter.

Calorimeter

Load cell

Reservoir

Heating lamps

Coo

ling

coil

Com

pres

sor

Fan

cal,wH

amb,calQ.

.

.

.

.

lampsW

fanW

amb,cpQ

Fig. 4. Compressor calorimeter thermal balance.

Fig. 5. Compressor ambient loss.

Fig. 6. Compressor ambient loss.

Fig. 7. Comparison of the two methods.


3.2. Refrigerant mass flow rate

Usually, the refrigerant flow rate is measured with a Coriolismass flow meter. Unfortunately, its measuring range is limited to0.35 kg s�1. For higher mass flow rates, it involves pressure lossesup to 3.0 bars, which is unacceptable.

Another possibility is to determine the refrigerant flow rate byexpressing the heat balance across the evaporator (as proposedin the EN 13771-1 Standard [4]), which can be verified at low massflow rate with the Coriolis measurement, as shown in Fig. 7. It isobserved that for flows higher than 0.15 kg s�1, both methods arewithin ±5%. At lower mass flow rates, this difference increases upto ±10%.

In analysis hereunder, the refrigerant mass flow rate obtainedfrom the evaporator thermal balance is used as the reference.

3.3. Compressor power

A first and surprising result is presented in Fig. 8, where thecompressor electric power is plotted against the exhaust pressure.Here a linear dependency is observed. It was already addressed in aprevious study (Winandy [17]) who, by considering the fluid as aperfect gas, obtained the following equation to determine the com-pression work:

W ¼ Pr;su � Vs

c� 1� rc�1

v ;in � c� �

þ Pr;ex � Vs

rv ;inð3Þ

rv,in is the built-in volume ratio, the ratio between the suction anddischarge volume, which is a geometrical characteristic of thecompressor.

Fig. 8. Compressor electric power against exhaust pressure.Fig. 10. Isentropic and volumetric efficiencies for pressure ratios between 2.0 and3.0.


According to this result, the supply pressure effect can be can-celled for a compressor volume ratio given by:

rv;in ¼ c1

c�1 ð4Þ

In that case the compression power depends linearly on the ex-haust pressure.

According to test conditions carried out in this study, c forR134a varies between 0.86 and 1.06 (according to Eq. (4)). By con-sidering an isentropic compression and the R134a as an ideal gas,the corresponding internal pressure ratio is of the order of 2.5 –3.5. As the maximum of the isentropic efficiency is reached whenthe internal pressure ratio is equal to the external one, these re-sults can be compared with the results presented in Fig. 9, wherethe maximal isentropic efficiency is reached for an external pres-sure ratio of the order of 2.5, which explains the surprising resultmentioned previously and shown in Fig. 8.

Fig. 11. Isentropic and volumetric efficiencies for pressure ratios between 2.0 and3.0.

3.4. Compressor isentropic and volumetric efficiency

Fig. 9 shows some orders of magnitude of the compressor’sisentropic and volumetric efficiency.

The isentropic efficiency reaches a maximum value of around72% corresponding to a pressure ratio comprised between 2.5and 2.6. At lower pressure ratios, it decreases strongly due to theun-adapted built-in volume ratio losses. At higher pressure ratios,

Fig. 9. Compressor isentropic and volumetric efficiencies.

isentropic efficiency decreases also, but the effect of the un-adapted built-in volume ratio losses is lower.

The volumetric efficiency decreases linearly when the pressureratio increases. At low pressure ratios, it approaches unity. In fact,the volumetric efficiency is calculated here by using the manufac-turer’s swept volume. Perhaps it is slightly underestimated, whichcan explain the values higher than unity. This could be also ex-plained by the passive supercharging effect described by Nieter[11].

In Fig. 9, a large scattering in the compressor efficiency is ob-served for compressor ratios between 2.0 and 3.0. To explain thisscattering, Figs. 10 and 11 are added. They show the compressorefficiencies against the compressor exhaust pressure and compres-sor power respectively, for pressure ratios between 2.0 and 3.0.

According to Fig. 10, both isentropic and volumetric efficienciesdecrease when the compressor exhaust pressure (or supply pres-sure) increases. This could be attributed to the compressor’s inter-nal leakages, which increase when the compressor works at highpressures. In Fig. 11, an important degradation on the isentropicefficiency is observed. This can be attributed to some additionalelectro-mechanical losses that could appear at this high powerand pressures: it may be due to a lack of lubrication or to somedeformations of the scroll than can increase frictions.

Fig. 12. Schematic diagram of the compressor modelling.


4. Compressor modelling

4.1. Compressor model

The compressor modelling is carried out as proposed by Winan-dy et al. [18], who decomposed the evolution of the refrigerant in-side the compressor in several steps, as shown in Fig. 12: supplyheating-up, isentropic compression, adiabatic compression at con-stant volume and exhaust cooling-down. This model is able to pre-dict the compressor exhaust temperature, the refrigerant flow rate,the ambient loss and the compressor electrical power, by using thecondensing and evaporating pressures, supply temperature, sur-rounding temperature and compressor speed as inputs. It uses fourpredefined parameters and six identified.

The scroll compressor is characterized by a fixed built-in vol-ume ratio rv,in imposed by its geometry. For a given refrigerantand operating conditions, there is an internal pressure ratio corre-sponding to this volume ratio. If the external pressure ratio is dif-ferent to the internal pressure ratio, the compressor is not adapted

(a)

P

V Vi Vf

Psu,1

Pex,1 = Pin

1

2in

P

Psu,1

Pin

Pex,1

Fig. 13. (a) Adapted Pex = Pin, (b) over-compression

and power losses are generated regarded to the adapted process.Three situations can occur: either the internal volume ratio is equalto the external pressure ratio (adapted), or it is higher (over-com-pression) or it is lower (under-compression). These three situationsare illustrated in Fig. 13a, b and c respectively.

The total internal work associated to the compression is:

win ¼ win;s þwin;v ¼ ðhr;in � hr;su1Þ þ v r;in � ðPr;ex1 � Pr;inÞ ð5Þ

The compressor electrical (or shaft) power can be split into twoterms: the internal compression power _Win and the compressorelectromechanical losses _Wcp;loss, which in turn can be split intoother two terms: constant electro-mechanical losses term _Wloss;0

and mechanical losses proportional to the internal compressionpower: a � _Win.

_Wcp ¼ _Win þ _Wcp;loss ¼ _Win þ _Wloss;0 þ a � _Win ð6Þ_Wloss;0 and a are parameters of the model. In this modelling the

compressor electromechanical losses are supposed to be transferreddirectly to the fictitious isothermal wall, as shown in Fig. 12. In

(b)

(c)

P

V Vi Vf

Psu,1

Pin

Pex,1

1

2 2’

2in

V Vi Vf

1

2 2’

2in

Pex < Pin and (c) under-compression Pex > Pin.


addition, this wall transfers heat with the refrigerant and the com-pressor surrounding.

The adapted conditions (called here ‘‘in”) is determined by theisentropic process from su1 to in and by considering the followingconstraint:

rv;in ¼v r;su1

v r;inð7Þ

where rv,in is the built-in volume ratio, a parameter of the model.The refrigerant flow rate id predicted by the following equation:

_Mr;cp ¼Ncp � Vs

v r;su1ð8Þ

where Vs is the compressor swept volume, which is a parameter ofthe model. For electrical motor driven compressors, the actual com-pressor speed is determined as follows:

Ncp ¼ Nnom;cp � ð1� Csd;m � _WcpÞ ð9Þ

The supply and exhaust heat transfer exchange are computedwith the e-NTU method, where the global heat transfer coefficientsare determined as:

AUsu;cp ¼ AUsu;cp;nom �_Mr;cp

_Mref

!0:8

AUex;cp ¼ AUex;cp;nom �_Mr;cp

_Mref

!0:8

ð10Þ

where AUsu,cp,nom and AUex,cp,nom are parameters of the model.

Fig. 14. Simulated against measured compressor electric power.

Fig. 15. Simulated against measured compressor refrigerant mass flow rate.

4.2. Model validation

Table 2 gives an idea of the extreme values for the 118 tests car-ried out to identify the compressor parameters. It can be observedthat the compressor was tested on a wide range of power, pres-sures and temperatures. Undoubtedly, the compressor supply tem-perature and the electrical power are the most constrainingvariables; because both are limited to ensure a safe operation ofthe compressor electric motor. Here, these two variables werepushed to their limits.

In the experimental analysis it was mentioned that some scat-tering in the compressor efficiency could be explained by a com-pressor internal leakage. This effect was analyzed in themodelling and no-remarkable influence was obtained. In fact,internal leakage modelling is complex because the equivalent leak-age area is influenced by the oil circulation, thermal dilatation,internal pressures, compliance on the orbiting scroll. . . and hereit is considered as a constant equivalent area. Moreover, the actualmodel without internal leakage gives reasonable agreement withthe experimental measurement. Thus, it will not be consideredfor this compressor.

To identify the compressor parameters, a function h is defined.It depends on the relative errors of the following variables: com-pressor electric power, refrigerant mass flow rate, compressor walland exhaust temperatures. This function is defined as follows:

h ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1n

Xm

j¼1

Xn

i¼1

Vj;i;sim � Vj;i;meas

Vj;i;meas

� �2vuut ð11Þ

where Vj is the variable ‘‘j”, m is the number of variables consideredfor the minimization and n is the number of tests. The parametersare identified by minimization of the function h.

Prior to the minimization of the function h, by default, the fol-lowing parameters are defined:

Nominal compressor speed : Nnom ¼ 50 HzReference mass flow rate : _Mref ¼ 0:25 kg s�1

Slip coefficient : Csd;m ¼ 0:004

Ambient heat transfer coefficient : AUcp;amb ¼ 18 W K�1

For the slip coefficient Csd,m, the value recommended by Winan-dy [17]. The ambient heat transfer coefficient corresponds to thevalue identified in the experimental analysis with the compressorcalorimeter.

By minimization of the function h, the following parameters areidentified:

Model parameters:

Vs ¼ 173 cm3 rv ;in ¼ 2:609

a ¼ 0:347 _Wloss;0 ¼ 223 W

AUsu;cp ¼ 3000_Mr;cp

_Mref

!0:8

W K�1 AUex;cp ¼ 35_Mr;cp

_Mref

!0:8

W K�1

The identified supply heat transfer coefficient is very high. Infact, according to the modelling results the supply heat exchangerefficiency must reach 1 to satisfy the measured conditions. Thusthe identified supply heat transfer coefficient does not have anyphysical meaning. It shows that the model hypothesis of one ficti-tious isothermal wall is not very appropriate; it could be improvedby using two fictitious isothermal walls.

Fig. 16. Simulated against measured compressor exhaust temperature. Fig. 17. Sensitivity analysis.

Fig. 18. Inputs, outputs and parameters of the compressor model.


Motor slip (Nnom,cp � Ncp) in this modelling varies between 50and 190 rpm for compressor power varying between 4 and 16 kW.

In the case of the swept volume the identified one is 4.5% higherthan that announced by the manufacturer. This could be explainedby the passive supercharging effect described by Nieter [11]. Thesuction gas may start to be compressed before the end of the suc-tion process, because of the decrease of the volume in the suctionpockets near the end of the suction process. In one of the experi-mental studies on a hermetic scroll he carried out, Winandy [17]also identified a swept volume higher (6%) than the one given bythe manufacturer.

Figs. 14–16 show the comparison between simulated and themeasured compressor electric powers, mass flow rates and exhausttemperatures, respectively.

After parameter identification, the model seems to be veryaccurate in the entire tested range, except for some tests at highcompressor power, where the compressor motor works outsideits maximal operating current. These tests were also included inthe parameter identification process, but their influence is mini-mal: they are seven over a total of 118 tests.

The model error is defined using a method similar to the meth-od recommended by the ASHRAE Guideline 2-2005 [1] for theexperimental data analysis. By analogy, the average error and thestandard deviation are defined according to the followingrelationships:

�e ¼ 1n

Xn

i¼1

ðVi;mes � Vi;simÞ ¼1n

Xn

i¼1

ðeiÞ r ¼ 1n

Xn

i¼1

ðei � �eiÞ2" #0:5

ð12Þ

where Vi,mes is the measured variable and Vi,sim is the simulated one.When the sample (or test number) is higher than 20, the confidencelimits are defined by the following equation:

�e� Z � rffiffiffinp ð13Þ

with Z = 1.96 for a probability of 95%.

Table 3Error analysis.

Variable Average error Standard deviation Minim

tr,ex,cp 0.0 K 1.4 K �4.0

Mr,cp 0.001 kg s�1 0.008 kg s�1 �0.00

Wcp �0.129 kW 0.517 kW �2.45

Table 3 presents the average errors, the standard deviations, theminimum and maximum deviation and the confidence limits forthe different outputs of the simulation model.

A sensitivity analysis is also made, by varying the identifiedparameters between ±5%. The response of the model is evaluatedthrough the ratio h/hmin versus the ratio between the actual param-eter and the identified one in Fig. 17. hmin represents the minimumvalue reached by the function h, which is obtained when this isevaluated with the identified parameters. It can be observed thatthe model is highly sensitive to the swept volume parameter (Vs)and, in a lesser way, to the built-in volume ratio parameter (rv,in)and to the power losses coefficient (a). The other parametersslightly disturb the response of the model against this variation.

4.3. Model simulation

In order to understand and to verify the reliability of the simu-lation model, a parametric study is carried out by varying the main

al deviation Maximal deviation Confidence limits

K +6.1 K �0.3 K+0.2 K

8 kg s�1 (�7.2%) 0.030 kg s�1 (+4.8%) �0.001 kg s�1

+0.002 kg s�1

9 kW (�4.6%) +0.375 kW (+15.3%) �0.224 kW�0.034 kW

Fig. 19. Effect of the compressor overheating on the isentropic and volumetricefficiencies.

Fig. 20. Effect of the compressor supply pressure on the isentropic and volumetricefficiencies.

Fig. 21. Effect of the compressor exhaust pressure on the isentropic and volumetricefficiencies.


inputs of the model: supply overheating, supply and exhaust pres-sure and pressure ratio. This simulation is carried out by consider-ing the model flow diagram given in Fig. 18, where are indicatedthe inputs and outputs of the model.

Fig. 19 shows the variation of the isentropic and volumetric effi-ciencies against the compressor pressure ratio at two differentrefrigerant overheating points. Only a slight degradation on theseefficiencies is observed when the overheating decreases.

On the other hand, supply pressure seems to have a very strongeffect on the compressor efficiencies, as shown in Fig. 20. This ef-fect is stronger at low supply pressures (lower than 5 bar), wherethe optimal external pressure ratio increases from around 2.0 to3.0. In this zone, the isentropic efficiency can vary between 10%and 15% and volumetric efficiency around 5%.

A last simulation is carried out to determine the effect of the ex-haust pressure on the efficiencies in Fig. 21. Here the model repro-duces the same trend observed in the experimental results, but it isnot so pronounced at high compressor exhaust pressures. It con-firms the hypothesis of the internal leakage, which is not consid-ered here in the modelling, but which appears in theexperimental results and increases the electro-mechanical losses.

5. Conclusions

A detailed testing methodology is presented to characterizerefrigerant compressors with a very particular example. This meth-odology is able to give the compressor ambient losses, compressorconsumption, compressor refrigerant flow rate and supply and ex-haust pressure and temperature.

The idea of this testing campaign is to take maximum advan-tage of the testing installation by characterizing the compressorin a very wide range of testing conditions, in particular in termsof condensing and evaporation pressures. Compressor perfor-mance is slightly perturbed by testing conditions. A little degrada-tion on the compressor isentropic and volumetric efficiencies wasobserved at high pressures, which is here attributed to an internalleakage. It was observed that this compressor is well adapted tolow pressure ratios, with a maximal isentropic efficiency of 72%for a pressure ratio of the order of 2.5–2.6.

A semi-empirical model is used to simulate the performance ofthis compressor. Here, the parameters of this model are given andcan be used by other authors to simulate its performances individ-ually or in an entire refrigeration system. In spite of the internalleakage identified in the experimental analysis, a compressor mod-el without leakage is sufficient to predict the compressor perfor-mance with an acceptable accuracy, except for some tests at highcompressor power where the compressor motor is pushed at itsmaximal current.

References

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Documents

Characterization of a scroll compressor under extended operating conditions