Purdue Uiversity Purdue e-pubs Iteratioal Refrigeratio ad Air Coditioig Coferece School of Mechaical Egieerig 2002 Characterizatio of Refrigeratio System Compressor Performace A. Mackese Uiversity of Wiscosi-Madiso S. A. Klei Uiversity of Wiscosi-Madiso D. T. Reidl Uiversity of Wiscosi-Madiso Follow this ad additioal works at: http://docs.lib.purdue.edu/iracc Mackese, A.; Klei, S. A.; ad Reidl, D. T., "Characterizatio of Refrigeratio System Compressor Performace" (2002). Iteratioal Refrigeratio ad Air Coditioig Coferece. Paper 567. http://docs.lib.purdue.edu/iracc/567 This documet has bee made available through Purdue e-pubs, a service of the Purdue Uiversity Libraries. Please cotact epubs@purdue.edu for additioal iformatio. Complete proceedigs may be acquired i prit ad o CD-ROM directly from the Ray W. Herrick Laboratories at https://egieerig.purdue.edu/ Herrick/Evets/orderlit.html
R9-1 Characterizatio of Refrigeratio System Compressor Performace A. Mackese, Graduate Studet, Solar Eergy Laboratory Uiversity of Wiscosi Madiso *Saford A. Klei, Ph.D., Professor of Mechaical Egieerig Uiversity of Wiscosi, Madiso, WI 53706, USA; Phoe: 608/263-5626; Fax: 608/263-8464 E-Mail: klei@egr.wisc.edu Douglas T Reidl, Ph.D., Associate Professor of Egieerig Professioal Developmet Uiversity of Wiscosi, Madiso, WI 53706, USA; Phoe: 608/262-6381 E-Mail: dreidl@facstaff.wisc.edu *Author for Correspodece ABSTRACT The overall objective of this research is to idetify a physics-based method to characterize compressor performace i refrigeratio systems with limited experimetal data. The focus of this project is o positive displacemet compressors, i.e., reciprocatig, rotary, scroll, ad screw types, cofigured as either semi-hermetic or ope drive. Compressor performace data for these types of compressors with differet sizes were obtaied from various maufacturers. Oe data set cosisted of raw experimetal data, while the others datasets were based o published catalog data. Mass flow estimates are based o the polytropic compressio process with a clearace volume that leads to a volumetric efficiecy expressio. The overall performace of the model was acceptable with maximum average mea weighted errors of 3.7%, 2.3%, ad 0.6% for reciprocatig, scroll, ad screw compressors, respectively. Furthermore, it was foud that the mass flow rate model with parameters estimated usig data for oe refrigerat accurately predicted data for a differet refrigerat. The compressor power requiremet is also based o the polytropic model with the itroductio of a combied efficiecy to accout for frictioal effects, leakage, ad motor performace i hermetic uits. Comparisos of the predicted power requiremets with data showed that the model fell short of predictig compressor power performace withi acceptable accuracy. Average mea weighted errors over a rage of operatig coditios were 8% for the screw, 7.6% for the scroll, 6.4% for the ope-drive reciprocatig, ad 5% for the semi-hermetic reciprocatig compressors. Errors of as much as 40% were observed for some operatig coditios. NOMENCLATURE C: clearace volume fractio P discharge : discharge pressure d, e, f: parameters i Eq (5) P suctio : suctio pressure k: isetropic idex RPM: compressor speed m& : refrigerat mass flow rate v suctio : specific volume at suctio coditios : polytropic coefficiet V: compressor displacemet volume N: umber of data poits w: compressor power per uit mass flow OF: objective fuctio defied i Eq (1) p: parameter defied i Eq (3) P evaporatio : evaporator pressure η combied : efficiecy factor defied i Eq (4) INTRODUCTION Characterizatio of compressor performace is ecessary i order to provide the maufacturer ad the customer with refrigerat mass flow rate ad compressor power requiremets as a fuctio of operatig coditios. ARI Stadard 540 (1999) curretly provides a meas of characterizig the capacity (or refrigerat mass flow rate) ad power for a specific compressor operatig with a specific refrigerat. The ARI stadard is based o a bi-quadratic liear regressio that requires a miimum of 10 calorimeter tests. The primary advatage of the ARI method is that applicatio is relatively simple ad straightforward. There are, however, a umber of sigificat disadvatages with ARI 540. First, coductig calorimeter tests are time-cosumig ad expesive. Secod, the ARI method is completely empirical. As a result, it caot reliably provide estimates of compressor
performace for coditios outside the rage of the test data used i the developmet of the regressio. Fially, separate regressios (ad calorimeter tests) are required for each idividual refrigerat used by the compressor beig tested. The ARI method caot be used for estimatig compressor performace operatig with differet refrigerats. The overall objective of this research was to develop a semi-empirical methodology for characterizig compressor performace that icorporates some of the physical processes occurrig i the compressor, rather tha by relyig o a totally empirical formulatio as is curretly doe with the ARI Stadard 540. Ideally, the resultig methodology will a) reduce the umber of calorimeter tests eeded for characterizig the performace of a compressor operatig with a give refrigerat; b) allow more accurate extrapolatio of compressor performace to coditios beyod the rage for which tests are available; ad 3) leverage the calorimeter tests with oe refrigerat for use to predict compressor performace with a differet refrigerat. COMPRESSOR DATA Compressor performace data for reciprocatig, rotary, scroll, ad screw compressors of differet sizes were collected from maufacturers. Oe data set represets raw experimetal data, while the others datasets are based o published catalog data from various maufacturers. Table 1 list all compressor data sets used i this study. Each data set is assiged with a idetificatio data set umber ad a upper case letter. This data set umber is used to idetify the compressor i the Table 1 also idetifies the compressor maufacturer, the refrigerat type ad the umber of provided data poits. Data Set Compressor Type Maufacturer Refrigerat Number of Data Poits A-1 Semi-Hermetic Reciprocatig Copelad Corp. R134a 96 A-2 Semi-Hermetic Reciprocatig Copelad Corp. R134a 96 A-3 Semi-Hermetic Reciprocatig Copelad Corp. R134a 96 A-4 Semi-Hermetic Reciprocatig Copelad Corp. R134a 96 A-5 Semi-Hermetic Reciprocatig Copelad Corp. R22 56 A-6 Semi-Hermetic Reciprocatig Copelad Corp. R22 64 A-7 Semi-Hermetic Reciprocatig Copelad Corp. R22 64 A-8 Semi-Hermetic Reciprocatig Copelad Corp. R22 64 A-9 Semi-Hermetic Reciprocatig Copelad Corp. R22 64 B-1 Ope-Drive Reciprocatig Vilter R22 134 B-2 Ope-Drive Reciprocatig Vilter R22 134 B-3 Ope-Drive Reciprocatig Vilter R22 134 B-4 Ope-Drive Reciprocatig Vilter R717 78 B-5 Ope-Drive Reciprocatig Vilter R717 78 B-6 Ope-Drive Reciprocatig Vilter R717 78 C-1 Rotary / R22 71 D-1 Scroll / R22 16 D-2 Scroll Copelad Corp. R22 53 D-3 Scroll Copelad Corp. R22 53 D-4 Scroll Copelad Corp. R22 53 D-5 Scroll Copelad Corp. R22 53 E-1 Sigle-Screw Vilter R22 36 E-2 Sigle-Screw Vilter R22 36 E-3 Sigle-Screw Vilter R717 36 E-4 Sigle-Screw Vilter R717 36 Table 1: Summary of Compressor Data Sets used i the study
COMPRESSOR PERFORMANCE MODEL The performace of positive-displacemet compressors have bee well-studied ad may performace models of varyig detail ca be foud i the literature, e.g., Prakash ad Sigh (1974), Röttger ad Kruse (1976), Brok et al. (1980), Sjöholm (1988), Todescat et al. (1992), Cavallii et al. (1996) ad Che et al (1998). However, most of these models require iformatio that is ot readily available ad the detail i the models, although useful for desig, is ot appropriate for the characterizatio that is of iterest i this study. For this reaso, the preset study focused o the simple polytropic model, as described by Kueh et al. (1998) ad recetly used i studies by Haberschill et al. (1994), Popovic ad Shapiro (1995), Browe ad Basal (1998), Jaehig (1999) ad Kim ad Bullard (2001). Our efforts here are aimed at extedig the work of Jaehig (1999) to larger scale reciprocatig compressors, to other compressor techologies (screw, scroll), ad to other compressor cofiguratios (ope-drive). Refrigerat mass flow rate ad compressor power were separately modeled usig a semi-empirical form based o a polytropic model. The empirical parameters i the model were determied usig o-liear regressio with a commercial software applicatio (Klei ad Alvarado, 2001) to miimize the objective fuctio i Eq (1) by alterig the values of the parameters withi specified bouds. Normalizig the error with the average of all measured values, as is doe i Eq (1), esures that all data poits are weighted equally. N X meas X calc i= X 1 mea OF = N where OF objective fuctio N umber of data poits X meas measured mass flow rate or specific power (power per uit mass flow rate) X calc calculated mass flow rate or specific power (power per uit mass flow rate) X average of all measured mass flow rate or specific power (power per uit mass flow rate) data mea 2 (1) Mass Flow Model The mass flow model is based o the cocepts of a polytropic process ad volumetric efficiecy. Volumetric efficiecy is defied as the as the ratio of the volume of suctio gas actually eterig the compressor (at the prevailig suctio ad pressure) to the maximum volume of gas that could be draw ito the cylider (i.e. the compressor displacemet volume). Kueh et al. (1998) show that for a reciprocatig compressor, the refrigerat mass flow rate, m&, ca be expressed as: where C p discharge p suctio V RPM v suctio 1 p discharge V RPM m& = 1+ C C p suctio ν suctio clearace volume ratio discharge pressure suctio pressure polytropic expoet, i.e., the value for for which pv is costat compressor displacemet volume compressor speed specific volume of the refrigerat uder itake coditios (2) The polytropic idex,, should i theory deped o the extet of heat trasfer occurrig durig the compressio process. Limitig values for the polytropic idex are uity for isothermal compressio ad the isetropic idex for adiabatic compressio. Compressors are ofte assumed to operate adiabatically, although heat trasfer ca be particularly sigificat for small compressors ad for larger screw compressors due to oil
coolig. Our study attempted to fid a best value of polytropic idex, both as a costat ad as a fuctio of suctio ad discharge coditios. We foud that the objective fuctio (Eq 1) to be oly slightly affected by varyig the polytropic expoet ad so to simplify the method, is set equal to the isetropic expoet, k, for the respective refrigerat beig used i the compressor. The isetropic expoet was set to a costat value determied at 65 F (18.3 C) ad the evaporator pressure. The pressure of the refrigerat at the compressor suctio is lower tha the evaporatig pressure. This effect is cosidered i the model by itroducig parameter, p, defied i Eq (3). The specific volume, v suctio, is the determied for the specified refrigerat at the compressor suctio temperature ad pressure (p suctio ). suctio evaporatio ( 1 ) p = p p (3) There are two parameters i the mass flow model the clearace volume, C, ad the pressure drop, p. These parameters are selected to miimize the objective fuctio i Eq (1). However, i some cases, the displacemet rate of the compressor, V RPM, was ot kow ad it too had to be estimated from maufacturer s data. I this case, the product (V RPM) was estimated as the ratio the mass flow rate to ilet desity at coditios that provided high volumetric efficiecy, i.e., high refrigerat suctio pressures ad low refrigerat discharge pressures. Although the foudatio of this mass flow model is based o reciprocatig compressors, it was applied to all of the compressors. Screw compressors equipped with variable volume ratio cotrol approximate the behavior of a reciprocatig compressor. Power Model The polytropic model ca be exteded to provide a estimate of the specific compressor power, w, defied as the ratio of the power to mass flow rate, as described i Kueh et al. (1998). We foud it ecessary to modify the polytropic model expressio to iclude a efficiecy factor, η combied so that the specific power is as represeted i Eq (4). ηcombied is called the combied efficiecy sice it represets the combied efficiecy of the electric motor (i hermetic uits) ad iefficiecies i the compressor operatio such as frictio ad leakage. All other parameters i Eq (4) were take as defied i the mass flow aalysis. 1 pdischarge w η combied = psuctio v suctio 1 (4) 1 p suctio By comparig maufacturer s data with w determied from Eq (4), we cocluded that that combied ca ot be cosidered to be a costat. The ivestigatio focused o idetifyig a suitable relatioship to predict the combied efficiecy usig measured variables such as discharge ad/or evaporatig pressure. Jaehig (1999) suggested two differet relatioships for the combied efficiecy that deped oly o the evaporatig pressure. Oe of the early coclusios for this project was that the Jaehig relatioships for the combied efficiecy did ot perform well for larger compressors (icludig both hermetic ad ope-drive cofiguratios). A umber of alterative relatioships were proposed ivolvig both the evaporatig ad discharge pressures. The relatioship show i Eq (5) was foud to perform as well or better tha ay of those ivestigated. η combied = d + e psuctio + f pdischarge (5) where d, e ad f are curve fit parameters fit by regressio to maufacturer s data. RESULTS AND DISCUSSION Figure 1a shows estimated ad reported mass flow rate data for a small semi-hermetic compressor (data set A-1) usig R134a. The average mea weighted error (1.9%) is the objective fuctio, OF, defied i Eq (1). The largest error was 5.8%. Figure 1b shows the results for a large ope-drive reciprocatig compressor (data set B-3) usig R22. The average mea weighted error for this data set is 1.3% ad the largest error is 3.7%. Figures 1c ad d show results for a scroll compressor (data set D-5) ad a screw compressor (data set E-2), respectively. The largest errors i estimated mass flow rate geerally occur at the lowest ad highest codesig temperatures (70 F ad 130 F/140 F) Note that for some data sets, the p parameter determied by the o-liear regressio is η
egative. The oly possible explaatio for a egative value we ca offer is that the parameter, p, is attemptig to compesate for limitatios i the model or errors i the data. Nevertheless, better overall fits were observed if the costrait p > 0 was ot eforced. The overall performace of the mass flow model was acceptable with maximum average mea weighted errors of 3.7%, 2.3%, 0.6%, ad 0.6% for reciprocatig, scroll, rotary, ad screw compressors, respectively. Figure 1: Compariso of mass flow model (lies) ad data (symbols) for data sets A-1, B-3, D-5 ad E-2. A objective of this project was to determie if the performace of a compressor with a specific refrigerat could be accurately estimated usig experimetal data for the same compressor operatig with a differet refrigerat. A prerequisite for testig this possibility is the availability of performace data for a compressor with at least two differet refrigerats. Data were available for three differet ope-drive reciprocatig compressors for both R22 ad R717 (data sets B-1 to B-6). The differet compressors are reciprocatig models of differet sizes with two, six, ad twelve cylider cofiguratios. The results summarized i Table 2 are ecouragig. Although smaller errors were obtaied whe mass flow rate data for the refrigerat of iterest were used, reasoably good accuracy was obtaied usig mass flow rate data for a differet refrigerat.
Data Set Refrigerat Average Mea Weighted Error [%] (best fit to origial data) Average Mea Weighted Error [%] (usig data for other refrigerat) B-1 R22 1.3 3.3 B-2 R22 1.3 3.3 B-3 R22 1.3 3.3 B-4 R717 2.0 3.1 B-5 R717 2.0 3.1 B-6 R717 2.0 3.1 Table 2: Result of estimatig mass flow with compressor data with a differet refrigerat. Figure 2 shows a compariso of the specific power estimates ad maufacturer s data for the same four compressors i Figure 1. Figure 2: Compariso of specific power model (lies) ad data (symbols) for data sets A-1, B-3, D-5 ad E-2.
The specific power model results see i Figure 2 are ot good as evidet by the average mea weighted errors above 5%. Whe all of the compressors i Table 1 are cosidered, the average mea weighted errors were 5% for the semi-hermetic reciprocatig, 6.4% for the ope-drive reciprocatig, 7.6% for the scroll ad 8% for the screw compressors. Errors of as much as 40% were observed for some operatig coditios. The errors are ot radom. The model preseted i Eq (4) seems to be uable to fit the treds observed i the specific power data for some situatios. For example, the model seems to cosistetly uder-predict the specific power at high evaporatig temperatures ad low codesig temperatures. Although may alterative expressios for the combied efficiecy were ivestigated, oe was foud to represet the specific power data i a more satisfactory maer. CONCLUSIONS The polytropic model for compressor performace has bee extesively used i studies of compressor performace. The relatioships used ivestigated i this paper are preseted i the ASHRAE (2000) ad i textbooks, e.g., Kueh et al. (1998). The itet of this ivestigatio was to use established compressor performace theory embodied i the polytropic model alog with empirical determiatio of ukow parameters to establish a method of characterizig compressor performace that: 1. reduces the amout of required compressor test data 2. allows extrapolatio of test data to coditios outside the rage of the tests 3. allows estimates of performace usig differet refrigerats. Ufortuately, the ivestigatio has failed to be successful i achievig all of these goals for a rage of compressio techologies that icluded reciprocatig (ope-drive ad semi-hermetic), screw (ope-drive ad semi-hermetic), ad scroll. Mass flow rate was predicted with reasoable accuracy for most of the compressors ivestigated usig Eqs (2) ad (3) with parameters (V RPM), C ad p determied from maufacturer s data. Eve though this model is strictly applicable to reciprocatig compressors, it was foud to work well for other positive displacemet compressors. I fact, the best agreemet betwee the data ad predictios occurred for the screw compressors. The oe radial compressor ivestigated also showed excellet agreemet. However, much larger differeces betwee predictios ad data were observed whe the polytropic model was used to estimate specific power with Eq (4). A efficiecy factor that depeds o compressor operatig coditios was foud to be a ecessary part of the model. A form for this efficiecy factor was proposed i Eq (5). However, the combiatio of Eqs (4) ad (5) did ot adequately represet the available compressor data over the etire rage of operatio. The model failed most oticeably at low lift coditios resultig from high evaporator ad low codesig temperatures. Attempts to iclude a term for pressure ratio i Eq (5) did ot improve the overall performace. Certaily, better agreemet could be obtaied by addig more parameters to the efficiecy model. However, additioal compressor tests would be eeded to establish estimates for the additioal parameters which dimiishes the advatage of the semi-empirical formulatio provided by the polytropic model over empirical polyomials as used i ARI-540 stadard. ACKNOWLEDGEMENTS The authors wish to thak the compressor maufacturers who provided data to us for this ivestigatio. REFERENCES Air-Coditioig ad Refrigeratio Istitute: Stadard 540, A method for presetatio of compressor performace data, (1991,1999) ASHRAE Hadbook, HVAC Systems ad Equipmet, SI Editio, Chapter 34, (2000) Cavallii, A.; Doretti, L.; Logo, G.A.; Rossetto, L.; Bella, B.; Zaerio, A., Thermal Aalysis of a Hermetic Reciprocatig Compressor, Proceedigs of the 1996 Iteratioal Compressor Coferece, Purdue Uiversity, West Lafayette, Idiaa, pp. 535-540, (1996) Brok, S. W.; Touber, S.; Va Der Meer, J. S., Modelig of Cylider Heat Trasfer Large Effort, Little Effect?, Proceedigs of the 1980 Iteratioal Compressor Coferece, Purdue Uiversity, West Lafayette, Idiaa, pp. 43-50, 1980.
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