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Modeling and performance analyses of evaporators in frozen food supermarket display cabinets at low temperatures H M Getu P K Bansal Department of Mechanical Engineering The University of Auckland Private Bag 92019 Auckland New Zealand Received 7 July 2006 received in revised form 25 January 2007 accepted 9 February 2007 Available online 23 February 2007 Abstract This paper presents modeling and experimental analyses of evaporators in in situ frozen food display cabinets at low tem peratures in the supermarket industry Extensive experiments were conducted to measure store and display cabinet relative hu midities and temperatures and pressures temperatures and mass fl ow rates of the refrigerant The mathematical model adopts variousempirical correlations of heattransfer coeffi cients and frostproperties inafi n tube heat exchangerinorder toinvestigate the infl uence ofindoor conditions on the performance of the display cabinets The model is validated with the experimental data of in situ cabinets The model would be a good guide tool to the design engineers to evaluate the performance of supermarket display cabinet heat exchangers under various store conditions 2007 Elsevier Ltd and IIR All rights reserved Keywords Frozenproduct Displaycabinet Evaporator Modelling Simulation Flow Refrigerant Temperature Relativehumidity Pressure Frost Mode lisation et analyse de la performance des e vaporateurs utilise s dans les meubles de vente de supermarche employe s pour les surgele s Mots cle s Produit congele Meuble de vente E vaporateur Mode lisation Simulation De bit Frigorige ne Tempe rature Humidite relative Pression Givrage 1 Introduction Supermarket refrigeration systems mainly refrigerated display cases consume roughly 20 of the total energy use of the store Getu 1 The fi eld defrosting anti sweat resistance heaters display cabinet lights and fans energy consumption contributes to an additional 14 The energy consumption due to the air conditioning system of the building is as much as 17 of the entire energy use of the supermarket The rest of the supermarket energy use which is around 49 attributes to water heating and lighting sys tems of the establishment Supermarkets often use multi compressor systems racks which are situated in remote machine rooms The compressors operate in parallel at the same saturated suction temperature and are piped with Corresponding author Tel 64 9 373 7599x88176 fax 64 9 373 7479 E mail address p bansal auckland ac nz P K Bansal 0140 7007 35 00 2007 Elsevier Ltd and IIR All rights reserved doi 10 1016 j ijrefrig 2007 02 003 International Journal of Refrigeration 30 2007 1227e1243 Nomenclature Af fi n surface area m2 Areg tubebare tube surface area of superheated two phase region m2 Areg iinternal tube surface area of superheated two phase region m2 Areg ooverall surface area of superheated two phase region m2 Aspair side total surface area in superheated region m2 Atpair side total surface area in two phase region m2 Atotalair side total surface area m2 Cratio of minimum to maximum capacity rate of heat exchanging fl uids Cacapacity rate of air WK 1 Cmaxmaximum heat capacity rate WK 1 Cminminimum heat capacity rate WK 1 Crcapacity rate of refrigerant WK 1 Cp specifi c heat at constant pressure kJkg 1K 1 Ddiameter m DHfrosted hydraulic diameter m ffriction factor dimensionless ff friction factor due to fi ns ftfriction factor due to tubes FoDHFourier number based on frosted surface GFFglass door frozen food G mass fl ux kg s 1m 2 henthalpy Jkg 1 heat transfer coeffi cient Wm 2K 1 hc fi n tube contact conductance Wm 2K 1 hf aair side fouling conductance Wm 2K 1 hf refrefrigerant side fouling conductance Wm 2K 1 hsgsublimation latent heat J kg 1 I0 modifi ed zero order Bessel function of the fi rst kind K0 modifi ed zero order Bessel function of the second kind I1 modifi ed fi rst order Bessel function of the fi rst kind K1 modifi ed fi rst order Bessel function of the second kind jcolburn factor kconductivity Wm 1K 1 Llength m LD frost length in the direction of air fl ow m Lregtube length in superheated two phase region m LewisLewis number mmass kg constant m mass fl ow rate kg s 1 mfstfrost mass accumulation kg m 2 Nttotal number of tubes NTUnumber of transfer units dimensionless NuNusselt number dimensionless Ppressure Pa PrDPrandtl number based on tube inside diameter PrDHPrandtl number based on frosted surface Qrate of heat transfer W rf fi n tip radius m rotube outer radius m ReReynolds number dimensionless ReDReynolds number based on tube inside diameter ReDHReynolds number based on frosted surface RHrelative humidity SF fi n spacing fi n m 1 SLlongitudinal tube spacing m STtransverse tube spacing m ttime s thickness m Ttemperature C Tithe temperature difference between triple point and coil surface K TFFthrough frozen food U overall heat transfer coeffi cient W m 2k 1 xquality dimensionless Greek letters Dchange 3heat exchanger effectiveness 4 effi ciency uhumidity ratio kg moisture kg dry air uNfree air stream humidity ratio kg kg rdensity kgm 3 2constant dimensionless mviscosity kg s 1m 1 Subscripts aair aveaverage ainair inlet aoutair outlet casedisplay cabinet Dtube diameter eevaporator einevaporator inlet eoutevaporator outlet exvinexpansion valve inlet f liquid refrigerant fi n fstfrost iinner iceice ininlet latlatent 1228H M Getu P K Bansal International Journal of Refrigeration 30 2007 1227e1243 common suction and discharge refrigeration manifolds Heat is rejected through multi fan condensers which are commonly located on the roof of the supermarket building The liquid refrigerant from the condenser is distributed through a liquid receiver and a distribution pipe network to theevaporatorsofthedisplaycabinets Medium temperature cabinets 10 C are usually served by separate refrigera tion systems from the low temperature cabinets 40 C Direct Multiplex refrigeration system is the most commonly employed confi guration in supermarkets for providing re frigeration to display cabinets however it requires large amount of refrigerant charge Whenever a refrigerated display case is operating in a store supermarket environment there is an exchange of heat and moisture with the store environment Open type display cases are seriously affected by the amount of mois ture in the supermarket whereas the susceptibility of glass door display cases to moisture is highly dependent on the frequency of usage i e high usage of glass door display cases can result in substantial amount of moisture transfer to the evaporators The moisture is accumulated on evapora tor surfaces in the form of frost based on the surface temper ature Relative humidity inside the store is the main contributor of frost growth on evaporators of display cabi nets Though it is regulated by an air conditioning system it incurs additional operating cost Faramarzi et al 2 inves tigated the performance of a medium temperature open type fi ve deck dairy deli fi xture by retrofi tting with glass doors This decreased the latent and sensible load of the case by 90 and 59 respectively ASHRAE s research project RP 622 by Al Mutawa et al 3e7 used a special test appa ratus to determine the actual defrosting load associated with frosted industrial freezer coils Tassou and Datta 8 carried out fi eld and environmental chamber based tests to demon strate the effect of ambient relative humidity and store tem perature on the evaporator coils of medium temperature cabinets There are also few studies on the performance of heat exchangers under frosted condition Kondepudi et al 9 reported the effects of different fi n confi gurations namely fl at fi n wavy fi n and louver fi n on the performance of fi nned tube heat exchangers They concluded that for the same frontal area and fi n and tube spacing the louvered fi n type had the greatest frost accumulation followed by the wavy and fl at fi n types Similarly Yan et al 10 compared the performance of fi nned tube heat exchangers with three different fi n types fl at plate fi ns one sided louver fi ns and redirection louver fi ns under frosted conditions They found that the amount of frost formation is largest for the heat exchanger with redirection louver fi ns as compared to the heat exchangers with other types of fi ns under the same operating conditions Althoughthereareseveralstudiesconductedonfrostingof heat exchangers most results relate to only the evaluation of the performanceofspecifi clab scaleormedium temperature heat exchangers Therefore extreme care must be enforced before applying the results of these studies to actual low temperature heat exchangers operating under a commercial environment Besides a proper evaporator model normally requires an intelligent application of heat transfer coeffi cients For instance the overall heat transfer resistance of an evaporator can vary up to 20 for changes in refrigerant side heat transfer coeffi cients Admiral and Bullard 11 Consequently several researchers have used different techniques to develop evaporator models Seker et al 12 developed a transient semi empirical model which is specifi c to domestic refrigerators mounted with slit evaporators based on a generic method by which the heat exchangerwas modeled as a single lumped element In their model Karata s correlation 13 was applied to cal culate air side heat transfer coeffi cient the refrigerant side heattransfercoeffi cientwascalculatedfromPierre scorrela tion 14 and Sander s correlation 15 was used to calculate frost conductivity Even though O Neal s 16 method was employedtocomputetheamountofwatervaporcontributing to the increase of frost density no information was provided as to how the frost density was calculated as a function of time Noritwasspecifi edhowthefrostgrowthwassimulated separately in superheated and two phase regions Besides their model was not verifi ed against supermarket display cabinet evaporators having different geometries Chandrasekharan et al 17e19 developed quasi steady state model s for medium temperature display cabinet evaporators by using a technique of handling direct expan sionevaporators on arow to rowfrost distribution basis and handling more than one modulewith different tube pitch and fi n parameters Granryd s 20 and Gnielinski s 21 and Wattelet et al 22 correlations were used for air and refrigerant side heat transfer coeffi cients respectively Empirical correlations of frost density were adopted from Hayashi 23e24 and frost thermal conductivity was taken from Yonko and Sepsy 25 However their model lacked the means to accurately determine the area fraction of super heated and two phase regions in the evaporators Their model was also validated against only medium temperature cabinets but not on low temperature display cabinet evaporators mesmeasured minminimum ooverall outer outoutlet rrefrigerant spsuperheated storstore tptwo phase tottotal wtube wall 1229H M Getu P K Bansal International Journal of Refrigeration 30 2007 1227e1243 Ge and Tassou 26 utilized a lumped element technique where the evaporator was divided into superheated and two phase regions The calculation for heat transfer coeffi cients forsingle phasefl owintubeswasbasedonDittuseBoelter s correlation from Incropera and DeWitt 27 For condensa tion and evaporation of refrigerants in tubes appropriate correlations were obtained from Travis et al 28 and Chaddock and Noerager 29 respectively McQuiston s 30e31 correlations were used for the air side heat transfer coeffi cients A semi empirical correlation reported by Oskarsson et al 32e33 and Krakow et al 34 was utilized for computing frost density and conductivity McDowell et al 35 employed a standard heat ex changer modeling technique to compute the overall heat transfer coeffi cient The refrigerant side heat transfer coeffi cients in their model however were computed for only single phase fl ow inside tubes based on Hausen correlations obtained from Chapman 36 Because the evaporator pipes were assumed to have no fi ns their model used the Churchill and Bernstein correlations Chapman 36 to calculate the air side heat transfer coeffi cient However no information was available in their model regarding frosting phenomenon on the evaporators Numerical modelingof secondary loop refrigeration sys tem was presented by Horton 37 in order to evaluate the feasibility of the system for supermarket applications Their display cabinet evaporators for the secondary loop system were modeled using a fi nite element technique i e each tube within the evaporator was divided into small elements which was analyzed separately The single phase and two phase refrigerant heat transfer coeffi cients were calculated using correlations from Chen 38 The air side heat transfer coeffi cients were calculated using correlations provided from Kim et al 39 However frosting on the display cabinet evaporators was neglected The application of existing correlations for heat transfer coeffi cients needs a thorough understanding of specifi c heat exchanger confi gurations Besides the proper identifi cation of the superheated and the two phase regions is of vital importance for the application of the right correlations for frost and heat transfer coeffi cients In general the literature survey showed that some of the researchers focused on developing models of display cabinets evaporators under dry wet conditions Others developed heat exchanger models for medium temperature applications Therefore there is a need for the development of numerical models to evaluate the performance of heat exchangers of supermarket display cabinets in general and heat exchangers of frozen food cabinets in particular under frosted conditions The analysis of such a model should be based on an accurate area fraction superheated two phase regions of dry expan sion evaporators It is with this motivation that this study has been carried out where the experimental and modeling tech niques for evaporators of frozen food display cabinets are presented in order to investigate the infl uence of indoor conditionsontheirperformanceinthesupermarket environment The present model applies a technique similar to Ge and Tassou 26 However the heat transfer coeffi cient for the two phase refrigerant was adopted from Ohadi et al 40 whereas the air side heat transfer coeffi cient was based on correlations from Kim et al 39 The frost properties were calculated using empirical correlations proposed by Mao et al 41 2 System description The schematic of a low temperature direct expansion re frigerationsystemunderconsiderationisshowninFig 1 The glass door frozen food GFF display cabinets are con structed from insulated walls which consist of inner and outer steel skin plates and a polyurethane foam insulation Thetotallengthofthesedisplaycabinetsis28 33 m Thecon struction materials of the through frozen food TFF display cabinetsarethesameastheGFFbutithassmallertotallength of14 34 m Thedimensionsandschematicoftheevaporators of GFF and TFF cabinets are given in Table 1 and Fig 2 respectively The evaporators of the display cabinets consist of thermostatic expansion valves type DANFOSS TUA TUAE and evaporator pressure regulating valves type DANFOSSPM Thefunctionoftheevaporatorpressurereg ulating valves EPRVs is to keep the evaporating tempera tures of the respective display cabinet at the required level The pressure and temperature at the suction manifold of the compressors are also determined by these valves The size of the expansion valves serving the GFF and TFF display cabinets is considered to be exactly the same Therefore the amount of the mass fl ow rate measured at the common pipe connecting the two display cabinets is equally divided between the two cabinets for the sake of simplicity The rack system consists of one Copeland D6DT 300X and two Copeland D4D 220X semi hermetic reciprocating compressors with six and four cylinders respectively The air cooled condenser whose geometrical parameters are included in Table 1 is made up of copper tubes and fi ns The liquid sub cooler plate heat exchanger which is connected to the outlet pipe of the condenser helps to lower the temperature of the sub cooled refrigerant from 25 C to around to 5 C This takes place through the exchange of heat between the superheated refrigerant of medium temperature and the sub cooled refrigerant of the low temperature refrigeration systems 3 Data collection Measurements were taken from an in situ supermarket charged with R404A refrigerant in Auckland for display cases multiple parallel compressors rack and condenser during December 2004 The measurement points see Fig 1 included 1 suction temperature and pressure 2 discharge temperature 3 condenser inlet temperature and pressure 4 condenser outlet temperature 5 sub cooler inlet temperature 6 sub cooler outlet temperature 1230H M Getu P K Bansal International Journal of Refrigeration 30 2007 1227e1243 pressure and mass fl ow rate 7 mass fl ow rate of refrigerant entering frozen food display cabinets 8 mass fl ow rate of refrigerant entering freezer rooms and 9 mass fl ow rate of refrigerant entering fi sh meat display cabinets A CR23X Micrologger was used for recording tempera ture and relative humidity data from the supermarket over 15 days period at an interval of 16 s A PT878 Portable Ultra sonic Liquid Flow meter was employed to record mass fl ow rate of the refrigerant R404A from meat fi sh frozen food freezer rooms and the common liquid pipelines of the low temperature refrigeration system For pipes with diameter 150 mm the accuracy is typically 2 with cali bration The fl ow meter was calibrated in the laboratory be fore being used on the plant The measurement accuracy 2e5 was confi rmed by comparing the mass fl ow rate of the refrigerant calculated from the measured electric power consumption of the rack considering compressor effi ciencies and enthalpy changes with that of the measured mass fl ow rate from the fl ow meter K type thermocouples whi