# Modelling of reciprocating and scroll compressors of reciprocating and scroll compressors Marie-Eve

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International Journal of Refrigeration 30 (2007) 873e886www.elsevier.com/locate/ijrefrig

Modelling of reciprocating and scroll compressors

Marie-Eve Duprez1, Eric Dumont1, Marc Frere*

Thermodynamics Department, Faculte Polytechnique de Mons, 31 bd Dolez, 7000 Mons, Belgium

Received 6 June 2006; received in revised form 14 November 2006; accepted 18 November 2006

Available online 22 December 2006

Abstract

This paper presents simple and thermodynamically realistic models of two types of compressors widely used in domesticheat pumps (reciprocating and scroll compressors). These models calculate the mass flow rate of refrigerant and the powerconsumption from the knowledge of operating conditions and parameters. Some of these parameters may be found in the tech-nical datasheets of compressors whereas others are determined in such a way that the calculated mass flow rate and electricalpower match those given in these datasheets.

The two models have been tested on five reciprocating compressors and five scroll compressors. This study has been limitedto compressors with a maximum electrical power of 10 kWand for the following operating conditions: evaporating temperaturesranging from 20 to 15 C and condensing temperatures ranging from 15 to 60 C.

The average discrepancies on mass flow rate and power for reciprocating compressors are 1.10 and 1.69% (for differentrefrigerants: R134a, R404A, R22, R12 and R407C). For scroll compressors, the average discrepancies on mass flow rate andpower are 2.42 and 1.04% (for different refrigerants: R134a, R404A, R407C and R22). 2006 Elsevier Ltd and IIR. All rights reserved.

Keywords: Refrigeration; Air conditioning; Modelling; Performance; Reciprocating piston; Scroll compressor; R134a; R404A; R22; R407C

Modelisation des compresseurs a piston et a spirale

Mots cles : Refrigeration ; Conditionnement dair ; Modelisation ; Performance ; Compresseur a piston ; Compresseur a spirale ; R134a ;R404A ; R22 ; R407C

* Corresponding author. Tel.: 32 65 37 42 06; fax: 32 65 3742 09.

E-mail addresses: marie-eve.duprez@fpms.ac.be (M.-E.Duprez), eric.dumont@fpms.ac.be (E. Dumont), marc.frere@

fpms.ac.be (M. Frere).1 Tel.: 32 65 37 42 08; fax: 32 65 37 42 09.

0140-7007/$35.00 2006 Elsevier Ltd and IIR. All rights reserved.doi:10.1016/j.ijrefrig.2006.11.014

1. Introduction

Since the beginning of the 1990s, under the pressure ofdifferent laws concerning the limitation of CO2 emissions,the heat pumps market has known a new expansion in thedomestic sector.

In the year 2000, there were 5750 heat pumps soldin Germany for house heating, 2750 in Finland, 3000 inNorway (for both water and space heating), 23,000 inSweden, 7200 in Switzerland and 7500 in France [1]. The

mailto:marie-eve.duprez@fpms.ac.behttp://www.elsevier.com/locate/ijrefrigmailto:eric.dumont@fpms.ac.bemailto:marc.frere@fpms.ac.bemailto:marc.frere@fpms.ac.be

874 M.-E. Duprez et al. / International Journal of Refrigeration 30 (2007) 873e886

Nomenclature

d diameter (m)h specific enthalpy (J kg1)HP high pressure (Pa)IP intermediate pressure (Pa)LP low pressure (Pa)m mass (kg)N compressor rotation speed (t min1)p pressure (Pa)P power (W)pvsat saturated vapour pressure (Pa)qm mass flow rate (kg s

1)qv volume flow rate (m

3 s1)s specific entropy (J kg1 K1)T temperature (K)u specific internal energy (J kg1)UA global heat transfer coefficient (W K1)v specific volume (m3 kg1)V volume (m3)W work (J)Dpsuc pressure drop in the suction valve (Pa)DTlog log-mean difference temperature (K)DTsup superheating (K)

3 ratio between the dead space and the sweptvolume (e)

h efficiencyr density (kg m3)

Subscriptsc circulatedcalc calculatedcond condensationconstr constructor datad dead spaceel electricalevap evaporationex exhausti inlet of the compressoriso-s isentropicpseudo-iso-s

pseudo-isentropicmecha mechanicals sweptsuc suctionw fictitious wall

average growth in terms of the number of installed heatpumps between 1997 and 2000 is about 15% a year.

It is important to generalize the use of domestic heatpumps in order to decrease the primary energy consump-tion in the dwelling sector. For each heat pump project,the type of heat pump must be correctly chosen; the de-sign and installation steps must be carried out carefully.For optimization purpose, it would be interesting to dis-pose a calculation tool able to simulate the behaviour ofthe heat pump integrated to the residence so that theenergy consumption could be predicted and the designof the heat pump (and/or of the house) could be adaptedin such a way that the environmental impact is minimized.This simulation tool should remain as simple as possibleso that its use could be widespread.

In this aim of modelling such a complete system, it is im-portant to have the simplest and the most accurate models ofits components. The compressor is one of the main part ofa heat pump as it sets its mass flow rate which governs theheat flows. It is thus the first component of the heat pumpto be modelled.

The types of compressors used in domestic heat pumpsare usually the reciprocating and scroll ones. Reciprocatingcompressors are mainly used as far as low thermal power isconcerned (heating water) whereas scroll compressors arewidespread for space heating.

Many different models of those two types of compressorswith different degrees of complexity are found in theliterature.

On the one hand, there are models of reciprocating com-pressors in which the compressor is divided in several vol-umes (elements such as compression chamber, valves.).Those models require input data very difficult to obtain orknown only by the constructor and non-available in the data-sheets. The volumes of the different elements and the effec-tive area of valves are also required. The transient fluidconservation equations (continuity, momentum and energy)are integrated in the whole compressor domain and the en-ergy balance for the refrigerant inside the cylinder is com-puted for each time step during the operating cycle [2e7].

On the other hand, models in which thermodynamic as-sumptions are made are also found. In those models, dataare not very difficult to obtain: e.g. refrigerant inlet state,outlet refrigerant pressure, clearance volume, motor speed.In Ref. [8] eight input data are sufficient to determinemass flow rate and required compressor power. In Refs.[9e11] (model derived from Ref. [8]) the refrigerant massflow rate is affected by the clearance volume re-expansion,by a pressure drop in the suction valve and by a heat transferfrom a fictitious isothermal wall. The friction power loss iscomposed of a constant contribution and another one propor-tional to the isentropic power. Ref. [12] presents a simplethermodynamic model for reciprocating compressors usedin domestic appliances. It required the knowledge of five pa-rameters easy to determine. The main difference betweenthis model and the one presented in Ref. [9] is the fact thatthe heat transfer phenomena in the compressor are not con-sidered in Ref. [12].

875M.-E. Duprez et al. / International Journal of Refrigeration 30 (2007) 873e886

The same two categories may be defined for scrollcompressors.

Models [13e16] require the knowledge of pocket vol-umes and perimeters for every six degrees of rotation, theheight, thickness and pitch of the scrolls that are quitedifficult to obtain. In those models, the whole compressoris divided in several chambers and the compressionprocess is simulated for every gas pockets. It requiresthe evaluation of areas, volumes, pressures, temperaturesand specific volumes for every crank angle. Mass andenergy conservation equations were developed for eachchamber.

Model [17] is exclusively thermodynamic and has thesame philosophy as [9e11] used for reciprocating compres-sors. The refrigerant mass flow rate is affected by a suctiontemperature increase and the compression process is consid-ered isentropic to the adapted pressure and isochoric untilthe discharge pressure.

The ARI Standard 540 [18] for positive displacementcompressors recommends the use of third-degree-equationsof 10 coefficients for the calculation of power input, massflow rate of refrigerant, current or compressor efficiency.Those coefficients have no physical meaning so that theextrapolation of the performances outside the operatingrange used for the fitting leads to unrealistic performancesvalues.

The purpose of this study is not the development ofa complex model that can relate the performances of thecompressor to its detailed geometry and that could be usedfor technological developments. A simple and thermo-dynamically realistic model is needed. It should be accu-rate enough to give mass flow rates and power valuesthat can be used in a global model of a heat pump.Parameters appearing in such a model should be foundin the technical datasheets of the compressors or shouldbe determined in such a way that the calculated massflow rate and electrical power match those given in thesedatasheets.

2. Reciprocating compressors

2.1. Modelling of reciprocating compressors

The model developed by Lebrun and coworkers [9e11]has been adapted given the particular requirements men-tioned above.

The evolution of the thermodynamic state of the refriger-ant through the compressor is presented in Fig. 1.

The compression process is divided in three steps.

Isenthalpic pressure drop in the suction valve (ie1). Isobaric heating up in the suction pipe due to a heat

transfer with a fictitious wall at temperature Tw(1e2).

Isentropic compression (2e3).

2.1.1. Prediction of the refrigerant mass flow rateThe data are:

Evapora

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