1、4689 Thermodynamic Modeling and Experimental Validation of Screw Liquid Chillers Tzong-Shing Lee, Ph.D., P.E. Member ASHRAE ABSTRACT This study presents an empirically based model, involving the first and second laws of thermodynamics and the NTU-E method of heat exchanger, to predict the coeficient
2、 ofperfor- mance (COP) of screw liquid chillers under various operating conditions, especially for capacity control by return chilled water sensing. A series of experiments wereperformed to verifi this model. The input operating parameters of the model are readily measured data from the water side o
3、f liquid chillers; they include the chilled water inlet temperature, the cooling water inlet temperature, and the cooling capacity. By incor- porating the experimental data and the theoreticalpredictions, an empirical correlation form can be obtained to predict the performance of a screw liquid chil
4、ler: The result indicates that comparison between the predicted value and the measured data yields an R2 (explained fraction of variance) of around 98.87%, an RMSE (absolute root-mean-square error) of about O. 0524, and an R-RMSE (relative root-mean-square-error) of about 1.43%. The results of this
5、workshould be appliedfor the purposes ofperformance prediction, evaluation of energy-efi- ciency improvements, fault detection, and other diagnoses of screw liquid chillers. INTRODUCTION Vapor-compression liquid chillers have been extensively used as cooling equipment to cool water, brine, or other
6、secondary coolant for air conditioning or refrigeration in the field of commerce and industry. The main components of a vapor-compression liquid chiller unit include a compressor and its driver, a condenser, a throttling device, a liquid cooler (evaporator), accessories, and a control system. The mo
7、st often used types of compressors are reciprocating, screw, and centrifugal. Liquid chillers with screw compressors are often applicable at a cooling capacity of 90 kW (25.6 tons) to about 3,500 kW (995.2 tons) (ASHRAE 2002). Although screw chillers are made up to 3,500 kW (995.2 tons) in capacity,
8、 they are most cost-effective up to 1,000 kW (284.3 tons). Above that size, they are not cost competitive with centrifugal chill- ers. Screw chillers provide continuous capacity modulation from 100% capacity down to 10% or less. For continuous capacity modulation, the leaving chilled liquid temperat
9、ure is sensed for capacity control, while for the step capacity modu- lation, return chilled liquid temperature sensing is normally used by units to help provide good temperature control. The performance of chillers, specified by cooling capac- ity, compressor power consumption, and COP, is commonly
10、 given by the refrigerant-side data, such as condensing temper- ature, evaporating temperature, degrees of superheating, and degrees of subcooling. Practically, especially for the purposes of performance prediction, evaluation of energy-efficiency improvements, fault detection, and other diagnosis o
11、f screw liquid chillers, expressing chiller performance in terms of readily measured water-side data rather than the refrigerant- side data is more convenient. These measurable water-side data include cooling water inlet temperature, chilled water inlet or outlet temperature, and cooling capacity. A
12、ccordingly, the modeling of liquid chillers for these purposes has been the subject of many studies over the last decade. Gorden et al. (1995) successfully developed an empiri- cally based thermodynamic model of centrifugal chillers and validated it experimentally using cooling plant data. As well a
13、s predicting the chiller performance over a broad range of oper- ating conditions, this model can be used as a diagnostic tool to analyze the fouling effect of heat exchangers on chiller perfor- Tzong-Shing Lee is an associate professor in the Department of Air-conditioning and Refrigerating Enginee
14、ring, National Taipei University of Technology, Taiwan. 206 02004 ASHRAE. mance. Ng et al. (1 997) developed a simple thermodynamic analytic method for diagnosing reciprocating chillers. The use of this model to establish optimal operating conditions and evaluate potential improvements to reciprocat
15、ing chillers was demonstrated. After reviewing more than 60 research papers on both steady-state and transient models, Browne and Bansal(l998a) described the philosophy and challenges of developing simu- lation models of vapor-compression refrigeration chillers. Only steady-state simulations were fo
16、und, which, in itself, indicates the need for transient models. Additionally, the surveyed literature exhibited a distinct lack of simulation models associated particularly with vapor-compression liquid chillers. Brown and Bansal (1 998b) presented a steady-state model of vapor-compression-type cent
17、rifugal liquid. They validated the model using experimental data on the perfor- mance under part to full loading of three different chillers, and the agreement was found to be within *lo%. Brown and Bansal (2001) utilized NTU-E methods to develop a steady- state model for predicting the performance
18、of vapor-compres- sion liquid chillers over a wide range of operating conditions. This model extends their previously developed model (Brown and Bansal 1998b). In addition to the readily measured data, the extended model also requires data concerning the heat exchanger, including the geometrical par
19、ameters of the tube bundle and the knowledge of the heat transfer coefficient on both the water and the refrigerant sides. The model was vali- dated with data from two liquid chillers, and the agreement was within %lo%. Swider et al. (2001) and Bechtler et al. (2001) proposed approaches to predict t
20、he performance of a chiller without using any physical or thermodynamic model. Swider et al. (2001) used a generalized radial basis function (GRBF) neural network to predict the chiller performance in the steady state. The input parameters were the chilled water outlet tempera- ture from the evapora
21、tor, the cooling water inlet temperature to the condenser, and the evaporator capacity. Applied to two different chillers, this model predicted the compressor work input and the COP to within *5%. Bechtler et al. (2001) presented a dynamic neural network model of the dynamic processes in vapor-compr
22、ession liquid refrigeration systems. This model was validated by application to two chiller units in different transient operating regimes; the results imply that the trends in any given data set were satisfactorily predicted. Recently, Swider (2003) presented a comparison of empiri- cally based mod
23、els for steady-state modeling of vapor- compression liquid chillers. The models he considered in his work included regression and thermodynamic models, a radial basis function neural network model, and a multilayer percep- tron neural network model. The results showed that the radial basis function
24、neural network model is preferred for predict- ing a chillers performance. The models developed in the literature mentioned above are used for the case of capacity control by the leaving chilled liquid temperature. Models and simulations of the perfor- mance of screw chillers using an empirically ba
25、sed steady- state model, especially one that addresses the capacity control by return chilled liquid temperature sensing, are lacking. This work proposes a thermodynamic model, modified from Gordon and Ng (2000), to predict the performance of vapor- compression screw liquid chillers under various op
26、erating and adjustable parameters. The operating parameters, easily measured from the water-side onsite, are the inlet temperature of the chilled water, the inlet temperature of the cooling water, and the cooling capacity. Thirty-six sets of experiments were performed to verify this model. The input
27、 parameters of the experiments are the inlet temperature of the cooling water, the inlet temperature of the chilled water, and the degrees of super- heating. The degree of superheating set in the experiment was at 0C (OF), 5C (9“F), 10C (18“F), and 15C (27F). The inlet water temperature of the cooli
28、ng water was set to 28OC (82.4“F), 30C (86F) and 32C (89.6“F), while the inlet water temperature of the chilled water was set to 10C (50“F), 12C (53.6“F), and 14C (57.2“F). This model should be used as a convenient tool for the purposes of evaluating energy-efficiency improvements, performance predi
29、ction, fault detection, and other diagnoses of screw liquid chillers. THERMODYNAMIC MODEL In this study, a model modified from that proposed by Gordon and Ng (2000), who developed models used for Centrifugal and reciprocating chillers, is developed to predict the performance of screw liquid chillers
30、. Consider the refrigerant-side of a water-cooled screw liquid chiller (schematic depicted in Figure 1) as a control volume. Assume that this vapor-compression liquid chiller operates in the steady state. The balances of energy and II Condenser I li i 8 Expansion I device n I. Compressor w I I Twi I
31、 Two Evaporator Figure 1 Schematic of a vapor-compression liquid chiller ASH RAE Transactions: Research 207 entropy of this control volume can be expressed as follows (Bejan 1998): -Qc+Qe+ Wc = 0, (1) Qe Qc Te Tc +gen = O where Qe and Q, are the heat transfer rate of the evaporator and the condenser
32、, respectively. W, is the work input to the compressor. and T, are the evaporating and condensing temperatures, respectively. Sgen represents the entropy gener- ation of this cycle. The coefficient of performance (COP) of the chiller is defined as Q COP = 2 WC (3) since the entropy generation of the
33、 refrigeration cycle is due to the internal dissipation and the heat leaks. Therefore, gen = Asleak 9 (4) where ASnt and ASleak are the entropy generation due to inter- nal dissipation and the heat leaks, respectively. The former term can be assumed to be a constant, and the latter term can be expre
34、ssed as a function of the heat losses at the condenser side, the condensing temperature, the heat losses at the evap- orator side, and the evaporating temperature (Gordon et al. 1995) as qe qc Te Tc Asleak = - (5) Combining Equations 1 to 3 and Equation 5 yields Most of the operational conditions of
35、 screw chillers are expressed in terms of the cooling water inlet temperature (Tc) and the chilled water inlet temperature (Twi). Therefore, according to the NTU-E method applied to the heat exchanger, the condensing temperature (T,) and the evaporating temper- ature (TJ can be expressed by the foll
36、owing equations. (7) where Cmin represents the minimum heat capacity, E is the effectiveness, M (= they include the chilled Cooling Water Inlet Conditions Evaporator Superheating Inlet Temperature Flow Rate Degrees Tci FC SH “C (“F) LPM (GPM) “C (“F) 28 (82.4) 800*5 0 (0) 5 (9) 10 (18) 30 (86.0) (21
37、 1.3*1.3) 32 (89.6) O COMPRESSOR i WWER MEIER T: Tempemure Sensa P: Pressure Transduser Flow Meter I cm Figure 2 Details of the conjiguration of the tested screw liquid chillel: water inlet temperature to the evaporator and the cooling water inlet temperature to the condenser. The effects of the deg
38、ree of superheating on the performance of the chiller is also experi- mentally determined. Table 2 lists the experimental conditions used. Thirty-six sets of experiments were performed to cover all combinations of testing conditions. As presented in Table 2, all experiments are performed at the same
39、 chilled water and cooling water flow rates. The flow rates of chilled water and cooling water are first determined experimentally under standard testing conditions at a chilled water inlet temperature of 12C (53.6“F) and an outlet temper- ature of 7C (44.6“F), a cooling water inlet temperature of 3
40、0C (86F) and an outlet temperature of 35C (95“F), and evaporator outlet superheating of 5C (9F). The experimental procedure under each test condition is as follows: 1. The inlet temperatures and the flow rates-both the chilled water and the cooling water-are set on one of the testing conditions show
41、n in Table 2. After a steady state is achieved, we turn on the chiller and run at full loading. The degree of evaporator superheating is adjusted as a desired value via the manually adjustable needle valve. After a steady state is maintained for at least one hour, all of the data are measured and re
42、corded at intervals of one minute. Twenty sets of data under each test condition are recorded, and the average values are used to validate the model. The aforementioned procedures are repeated under the test conditions in Table 2 until all tests are completed. 2. 3. Table 1. The Instruments and Accu
43、racy for Measurement Physical Parameter Instrument Accuracy Temperature Platinum resistance *O.O3“C thermometer (*0.054“F) Pressure Pressure transducer *O. 15% Flow rate Electromagnetic *0.5% flow meter Power Watt meter *OS% consumation Table 2. The Experimental Conditions for the Screw Chiller Unit
44、s Constructed in this Study 15 (27) ASH RAE Transactions: Research 209 Analysis of Experimental Data evaluated by The cooling capacity under each test condition can be Qe = PweCp(wi- wo) 9 (14) where pw is the density of water, Fe is the flow rate of chilled water, and cp is the specific heat of wat
45、er. Equation 3 gives the coefficient of performance (COP) of the chiller under various test conditions. The uncertainty of COP, following the uncertainty analysis proposed by ASHRAE (1996), is about *1 .O%. The statistical performance indicators, used to express the difference between the measured C
46、OP and the predicted COP, are the explained fraction of the variance (R2), the absolute root-mean-square error (RMSE), and the relative root-mean- square-error (R-RMSE). These values are defined as x 100 (15) i N 2 c, = ,(COP -COP,) N 2 z;= ,(COP,-(L,= ,COP,)/N) 2 L, = ,(COP, - COP,) 1“ N RMSE = whe
47、re subscripts p and m for COP denote the predicted and measured values, respectively. Table 3. Experimental Results for Screw Liquid Chiller Tci = 28OC (82.4OF) EXPERIMENTAL RESULTS In this study, a series of experimental measurements are made to quantify the effect of chilled water inlet temperatur
48、e, cooling water inlet temperature, and the set value of evapora- tor superheating on the performance of the chiller. Table 3 presents each measurement and analytical results. The heat balance of all measurements is within *5%. The effects of superheating temperature at the evaporator outlet on chil
49、ler performance, including cooling capacity, power consumed by the compressor, and COP, are shown in Figure 3. As shown in Figure 3, the cooling capacity declines slightly as the superheating increases from 0C to 5C (0F to 9F) but decreases sharply as the superheating increases from 5C to 15C (9F to 27F). The degree of superheating is observed to weakly affect only the power consumed by the compressor. The COP of the chiller decreases as the super- heating temperature increases, like the behavior of cooling capacity. The cooling capacity and COP are
