1、282 2008 ASHRAE ABSTRACT This paper describes how the performance of chillers canbe predicted by the Simple Thermodynamic Model (Gordon-Ng Universal Chiller Model) at steady state conditions thatspan across assorted coolant temperatures. It focuses on diag-nostic capabilities of the simple thermodyn
2、amic approachusing the published data from a 90-ton centrifugal chiller. Fivedifferent types of degrading chiller faults (reduced condenserwater flow, condenser fouling, refrigerant overcharge, non-condensable in refrigerant and excessive oil in compressor)were succinctly detected by the model based
3、 on physicallymeaningful parameters of chillers.INTRODUCTIONThe application of fault detection and diagnosis (FDD)system in chillers plays a pivotal role in minimizing energyconsumption of buildings. In a survey conducted on 105 officebuildings in Singapore (equivalent to 5.8 x 106m2or 62.43 x106ft2
4、of office space) indicates that a total of US $175million, about US$30/m2(US $2.79/ft2), were spent in a yearfor air conditioning, lights, computers, lift and other gadgets.The survey revealed that the most efficient building spent onlyUS$13/ m2 (US $1.21/ft2) in a year for electricity as comparedwi
5、th the least efficient building that spent more than 5 folds forthe same area. As almost half of the electricity consumption ofbuildings in Singapore were utilized for air conditioning andrefrigeration, a reliable FDD tool is essential for maintainingthe chillers at optimum conditions. SIMPLE THERMO
6、DYNAMIC MODEL (GORDON AND NG UNIVERSAL CHILLER MODEL)Coefficient of performance (COP) and cooling capacityare important parameters in determining performance of chill-ers. In this paper, Simple Thermodynamic Model, STM(Gordon and Ng 2000) have been studied with respect to COPprediction. STM is a sim
7、ple analytical model that is derivedfrom the First and Second Laws of Thermodynamics. Themodel is expressed as following:(1)The values of internal entropy generation (ST), heat leak(Qleak,eqv), and thermal resistance (R) could be regressed usingjudiciously selected steady state data. For regression
8、analysis,Equation 1is rephrased as following:(2)(3)(4)TevapinTcondin- 11COP-+1TevapinQevap-STQleak eqv,+=TcondinTevapin()TcondinQevap-RQevapTcondin- 11COP-+Left Term: Y=TevapinTcondin- 11COP-+1Right Term: X1TevapinQevap- X2,TcondinTevapin()TcondinQevap-,=X3QevapTcondin- 11COP-+=Y ST()X1Qleak eqv,()X
9、2R()X3+=Predictive and Diagnostic Methods for Centrifugal ChillersJayaprakash Saththasivam Kim Choon Ng, PhD, PEStudent Member ASHRAEJayaprakash Saththasivam is a postgraduate student and Dr. Kim Choon Ng is a professor in the Department of Mechanical Engineeringat the National University of Singapo
10、re, Singapore.NY-08-0342008, American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc. (www.ashrae.org). Published in ASHRAE Transactions, Volume 114, Part 1. For personal use only. Additional reproduction, distribution, or transmission in either print or digital form is not pe
11、rmitted without ASHRAEs prior written permission.ASHRAE Transactions 283Multiple linear regressions are performed on the data setsby imposing constraints that yield positive values for both Rand STparameters. These constraints (R 0 and ST 0) arenecessary in order to retain the physical characteristi
12、cs of themodel. As for heat leak, it can be either a positive or negativevalue and is less significant compared to the former twoparameters. However, the inclusion of this term will lead to anaccurate COP modeling. COP PREDICTIONBy rearranging Equation 1, the COP can be predictedusing the regressed
13、values of R, ST and (5)Data sets used in this study are based on the publisheddata(Comstock and Braun 1999) gathered from a 90-ton labo-ratory centrifugal chiller. Each data set is comprised of 27steady state points that cover the similar operating regions.Three control variables were utilizedto for
14、m a 3x3x3 matrix for each data set, where the variableswere varied at different ranges to obtain the 27 steady points.was varied from 277.59K (40F) to 283.15K (50F),was varied from 289.82K (62F) to 302.59.6K (85F)while was varied between 25% to 100%. All the datasets have been filtered so that the s
15、ystem energy balance doesnot vary more than 5%. For COP prediction, two fault-free data sets (Data set Aand B) are used. Data set A is utilized to obtain the R, andQleak,eqvthrough regression method. The regressed coeffi-cients are shown in Table 1. COP for data set B is thenpredicted using Equation
16、 5 based on the regressed parametersobtained from data set A. From Figure 1, it can be seen that STM is capable ofpredicting COP with a satisfactory rms error of less than 5%using known inputs like , ,Pin, and Qevap. Owingto the physical significance of STM model, the regressedparameters ( and R) ar
17、e capable to be utilized as a FDDtool for chillers.CAPABILITY OF STM AS A FAULT DETECTION AND DIAGNOSTIC TOOL As mentioned earlier, the regressed parameters in STMcan play a major role in chiller fault detection and diagnostics.Thermal Resistance, R is a parameter associated with the heattransfer re
18、sistance of condenser and evaporator. Internalentropy generation, STis related to expansion valve andcompressor. It is dominated by frictional losses in compres-sors and other dissipative losses (pressure drops, throttling andde-superheating). These two parameters govern all the fourmajor components
19、 of a chiller during its steady state opera-tion, irrespective of new or degraded states of machines.Degrading faults developed in any of this major componentcould be detected by studying these parameters. On the otherhand, Qleak,eqv, is less dominant in chiller FDD if comparedwith the former two pa
20、rameters as there are few problemsrelated to insulation. In this study, we have made some minor modification tothe initial STM model in order to enhance its capabilities as afault detection tool. Qleak,eqv, which is a fictitious heat leakterm, is held constant throughout the analysis as it is unlike
21、lyto exhibit a significant deviation (except due to poor insula-tion). The constant value is obtained by averaging the valuesof Qleak,eqv regressed from 12 fault-free data sets using Equa-tion 4. The average of the regressed values is 120 kW.Due tothe constant value of Qleak,eqv, Equations 2 to 4 ca
22、n be writtenas following:(6)(7)The whole Equation 1 can be rephrased as following:(8)Based on Equation 8, the regression process is againperformed on all the 12 fault-free data sets to obtain the aver-age coefficients of R and . The average values for bothcoefficients, as indicated in Table 2, are u
23、sed as the nominalvalues for fault detection.Five different types of degrading faults have beenanalyzed in this paper. The faults are (i) reduced condenserwater flow, (ii) condenser fouling (iii) refrigerant overcharge(iv) non-condensable in refrigerant and (v) excessive oil incompressor. All the fa
24、ults were artificially induced to the labo-ratory chiller at different levels of severity to study the chillercharacteristics and responses. For a particular type of fault, multiple linear regressionsare performed using Equation 8 at each severity level. Then,the regressed values are compared with t
25、he nominal values.The larger the deviations from the nominal value, the moresevere are the faults. In order to avoid false detection, thethreshold for the nominal values can be regulated using meanstandard errors. If 1-mean standard error is used to determinethe thresholds, then faults are likely to
26、 occur at approximately68% confidence level if the regressed values exceed the upperthreshold of the nominal values. On the other hand, the1COP-predicted=1TevapinQevap-STQleak eqv,TcondinTevapin()TcondinQevap-+TevapinTcondin-RQevapTcondin- 1Tevap outTcondinand Qevap,()Tevap outTcondinQevapSTTevap in
27、TcondinSTLeft Term: Y=TevapinTcondin- 11COP-+1Qleak eqv,TcondinTevapin()TcondinQevap-Right Term: X1TevapinQevap- X2,QevapTcondin- 11COP-+=Y ST()X1R()X2+=ST284 ASHRAE Transactionschances of the faults to occur are at approximately 95% confi-dence level if 2-mean standard error is used as threshold li
28、mit-ers. Table 3 and 4 present the regressed coefficients of STand R for fault-free and faulty runs with the reduction in thecondenser flow rate, ranging from 10% to 40%.From Figure 2 and Table 4, it can be seen that there is aclear deviation in thermal resistance with respect to the reduc-tion in c
29、ondenser flow. This deviation is due to the inefficientheat rejection at condenser. As for ST, the deviation is lesssignificant and still within the upper limit of the nominalvalue. This finding indicates that restriction in condenserwater flow will be greatly reflected in thermal resistance, Rwhile
30、 no significant change can be observed in the internaldissipation, ST. Figure 3 and 4 show the deviations in R and STfor all thefive faults analyzed in this study, where 1-mean standard errorand 2-mean standard error are used as threshold limits respec-tively. Depending on the size of mean standard
31、error as thresh-old for nominal values, the faults can only be detected atdifferent severity level. For instance, reduction in condenserwater flow is detected at severity level of 20% in Figure 3while the similar fault can only be detected at severity level of40% in Figure 4. Thus, the selection of
32、the suitable mean stan-dard error seems to be critical in detecting degrading faultsusing STM. For fault detection using STM model, faults can be cate-gorized into three main divisions, namely (i) Coolant circuitfaults (ii) Refrigerant circuit faults and (iii) Compressor faults.Faults in coolant cir
33、cuits (heat exchanger fouling and reduc-tion in coolant flow rate) will be more related to finite heattransfer between refrigerant and coolant and could be easilydetected by monitoring R. No significant change is anticipatedin STas faults revolving around this category have lessimpact on entropy gen
34、eration. This claim is further justified byFigure 3 and 4. As for faults in refrigeration circuit, incrementis noticeable in both parameters as these faults penalize heattransfer in the heat exchangers and increase entropy genera-tion. Presences of non-condensable in refrigerant and refrig-erant ove
35、rcharge constitute this category. The increment inboth parameters for this fault category can be observed inFigure 3 and 4. On the other hand, faults in compressor suchas excessive oil will be mainly reflected in the increment ofSTdue to higher entropy generationand is unlikely to affectthe thermal
36、resistance in heat exchangers. Excessive oil willaugment the viscous effect in the compressor and contributesto mechanical losses in the compressor. This trend is alsoexhibited in Figure 3 and 4.Based on the findings, a simple diagnostic chart isproposed. If increment is observed in R while ST remai
37、nswithin the threshold then from Figure 5, we can deduce that thefaults are likely to be caused by evaporator or condenser watercircuits. Based on this pattern, we can manually inspect all thepossible faults as suggested in the chart. By experience, it canbe said that condenser is most likely to enc
38、ounter coolantcircuit faults due to its water quality. Evaporator flow reduc-tion can be easily detected by flow meter, which is a requiredmeasurement for STM model. On the other hand, evaporatorfouling is less likely to occur if compared to condenser foul-ing.CONCLUSIONSimple Thermodynamic Model co
39、ntains physically-meaningful parameters which can be used to detect and diag-nose degrading faults. Faults occurring in a chiller could bedetected using the regressed values of thermal resistance andinternal entropy generation. By regressing these two parame-ters on a periodic basis, any noticeable
40、deviation from nominalthresholds can be interpreted using the proposed diagnosticchart. Based on the possible faults suggested in the chart,manual inspection can be performed to diagnose the occurringfaults. As STM model requires merely 4 inputs ( , ,Pin, and Qevap), only partial diagnosis is possib
41、le at themoment. Future work and study will be focusing in enhancingSTM capabilities to perform full diagnostic on chillers.ACKNOWLEDGEMENTThe authors would like to express their deepest gratitudeto Prof James Braun of Purdue University for his kindness inproviding the chiller data, which was used t
42、hroughout thisstudy.Table 1. Standard Mean Error for Coefficients Obtained From Data Set A Coefficients Value Standard Error, kW/K 0.073 0.006R, K/kW 0.075 0.003Qleak,eqv,kW 121.2 26.1STFigure 1 COP for data set B is predicted using the regressedcoefficients obtained from data set A.TevapinTcondinAS
43、HRAE Transactions 285NOMENCLATURE= Condenser Inlet Water Temperature (K)= Condenser Outlet Water Temperature (K)Tcond= Condenser Refrigerant Process Average Temperature (K)= Evaporator Inlet Water Temperature (K)= Evaporator Outlet Water Temperature (K)Tevap= Evaporator Refrigerant Process Average T
44、emperature (K)Qcond = Condenser Heat Transfer (kW)= Condenser Heat Leak (kW)Qevap= Cooling load (kW)= Evaporator Heat Leak (kW)Pin= Compressor Power (kW)= Compressor Heat Leak (kW)COP =Qevap/ Pin= Coolant mass flow rate (kg/s)cpw= Coolant specific heat (kJ/(kg.K) E = Heat exchanger effectiveness= In
45、ternal entropy generation (kW/K)R = Thermal resistance (K/kW) = Qleak,eqv=REFERENCESBraun, J.E. 2003. Automated fault detection and diagnosticsfor vapor compression cooling equipment. Transactionof ASME 125:266-274 Browne, M.W., and Bansal, P.K. 1998. Steady state model ofcentrifugal liquid chillers
46、. Int. J.Refrig.21(5): 343-358.Browne, M.W., and Bansal, P.K. 2001. Different modelingstrategies for in-situ liquid chillers. Proc Inst MechEngrs 215 (Part A):357-374Table 2. Average Coefficients Obtained from 12 Faults Free Data SetsCoefficients Average Value 1 Mean Standard Error, kW/K 0.073 0.001
47、R, K/kW 0.077 0.002Table 3. Regressed Parameters for Each Severity Level for Reduction in Condenser Flow Rate (1-Mean Standard Error)Analysis (Reduction in Condenser Flow) ST, kW/K R, K/kWNormal Condition 0.073 0.001 0.077 0.00210% Flow Reduction 0.073 0.002 0.081 0.00220% Flow Reduction 0.073 0.001 0.084 0.00230% Flow Reduction 0.073 0.002 0.088 0.00340% Flow Reduction 0.072 0.002 0.098 0.003Table 4. Deviations of the Regressed Parameters from Nominal ValuesDue to Reduction in Condenser Flow RateFault (Reduction in Condenser Flow) 10% 20% 30% 40%deviation (%) 0.02 0.19 0.46 -1.26R devia
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