Characterization of Refrigeration System Compressor Performance

The overall objective of this research is to identify a physics-based method to characterize compressor performance in refrigeration systems with limited experimental data. The focus of this project is on positive displacement compressors, i.e., reciprocating, rotary, scroll, and screw types, configured as either semi-hermetic or open drive. Compressor performance data for these types of compressors with different sizes were obtained from various manufacturers. One data set consisted of raw experimental data, while the others datasets were based on published catalog data. Mass flow estimates are based on the polytropic compression process with a clearance volume that leads to a volumetric efficiency expression. The overall performance of the model was acceptable with maximum average mean weighted errors of 3.7%, 2.3%, and 0.6% for reciprocating, scroll, and screw compressors, respectively. Furthermore, it was found that the mass flow rate model with parameters estimated using data for one refrigerant accurately predicted data for a different refrigerant. The compressor power requirement is also based on the polytropic model with the introduction of a combined efficiency to account for frictional effects, leakage, and motor performance in hermetic units. Comparisons of the predicted power requirements with data showed that the model fell short of predicting compressor power performance within acceptable accuracy. Average mean weighted errors over a range of operating conditions were 8% for the screw, 7.6% for the scroll, 6.4% for the open-drive reciprocating, and 5% for the semi-hermetic reciprocating compressors. Errors of as much as 40% were observed for some operating conditions. NOMENCLATURE C: clearance volume fraction Pdischarge: discharge pressure d, e, f: parameters in Eqn (5) Psuction: suction pressure k: isentropic index RPM: compressor speed m& : refrigerant mass flow rate vsuction: specific volume at suction conditions n: polytropic coefficient V: compressor displacement volume N: number of data points w: compressor power per unit mass flow OF: objective function defined in Eqn (1) ∆p: parameter defined in Eqn (3) Pevaporation: evaporator pressure ηcombined: efficiency factor defined in Eqn (4) INTRODUCTION Characterization of compressor performance is necessary in order to provide the manufacturer and the customer with refrigerant mass flow rate and compressor power requirements as a function of operating conditions. ARI Standard 540 (1999) currently provides a means of characterizing the capacity (or refrigerant mass flow rate) and power for a specific compressor operating with a specific refrigerant. The ARI standard is based on a bi-quadratic linear regression that requires a minimum of 10 calorimeter tests. The primary advantage of the ARI method is that application is relatively simple and straightforward. There are, however, a number of significant disadvantages with ARI 540. First, conducting calorimeter tests are time-consuming and expensive. Second, the ARI method is completely empirical. As a result, it cannot reliably provide estimates of compressor performance for conditions outside the range of the test data used in the development of the regression. Finally, separate regressions (and calorimeter tests) are required for each individual refrigerant used by the compressor being tested. The ARI method cannot be used for estimating compressor performance operating with different refrigerants. The overall objective of this research was to develop a semi-empirical methodology for characterizing compressor performance that incorporates some of the physical processes occurring in the compressor, rather than by relying on a totally empirical formulation as is currently done with the ARI Standard 540. Ideally, the resulting methodology will a) reduce the number of calorimeter tests needed for characterizing the performance of a compressor operating with a given refrigerant; b) allow more accurate extrapolation of compressor performance to conditions beyond the range for which tests are available; and 3) leverage the calorimeter tests with one refrigerant for use to predict compressor performance with a different refrigerant. COMPRESSOR DATA Compressor performance data for reciprocating, rotary, scroll, and screw compressors of different sizes were collected from manufacturers. One data set represents raw experimental data, while the others datasets are based on published catalog data from various manufacturers. Table 1 list all compressor data sets used in this study. Each data set is assigned with a identification data set number and an upper case letter. This data set number is used to identify the compressor in the Table 1 also identifies the compressor manufacturer, the refrigerant type and the number of provided data points. Data Set Compressor Type Manufacturer Refrigerant Number of Data Points A-1 Semi-Hermetic Reciprocating Copeland Corp. R134a 96 A-2 Semi-Hermetic Reciprocating Copeland Corp. R134a 96 A-3 Semi-Hermetic Reciprocating Copeland Corp. R134a 96 A-4 Semi-Hermetic Reciprocating Copeland Corp. R134a 96 A-5 Semi-Hermetic Reciprocating Copeland Corp. R22 56 A-6 Semi-Hermetic Reciprocating Copeland Corp. R22 64 A-7 Semi-Hermetic Reciprocating Copeland Corp. R22 64 A-8 Semi-Hermetic Reciprocating Copeland Corp. R22 64 A-9 Semi-Hermetic Reciprocating Copeland Corp. R22 64 B-1 Open-Drive Reciprocating Vilter R22 134 B-2 Open-Drive Reciprocating Vilter R22 134 B-3 Open-Drive Reciprocating Vilter R22 134 B-4 Open-Drive Reciprocating Vilter R717 78 B-5 Open-Drive Reciprocating Vilter R717 78 B-6 Open-Drive Reciprocating Vilter R717 78 C-1 Rotary / R22 71 D-1 Scroll / R22 16 D-2 Scroll Copeland Corp. R22 53 D-3 Scroll Copeland Corp. R22 53 D-4 Scroll Copeland Corp. R22 53 D-5 Scroll Copeland Corp. R22 53 E-1 Single-Screw Vilter R22 36 E-2 Single-Screw Vilter R22 36 E-3 Single-Screw Vilter R717 36 E-4 Single-Screw Vilter R717 36 Table 1: Summary of Compressor Data Sets used in the study COMPRESSOR PERFORMANCE MODEL The performance of positive-displacement compressors have been well-studied and many performance models of varying detail can be found in the literature, e.g., Prakash and Singh (1974), Rottger and Kruse (1976), Brok et al. (1980), Sjoholm (1988), Todescat et al. (1992), Cavallini et al. (1996) and Chen et al (1998). However, most of these models require information that is not readily available and the detail in the models, although useful for design, is not appropriate for the characterization that is of interest in this study. For this reason, the present study focused on the simple polytropic model, as described by Kuehn et al. (1998) and recently used in studies by Haberschill et al. (1994), Popovic and Shapiro (1995), Browne and Bansal (1998), Jaehnig (1999) and Kim and Bullard (2001). Our efforts here are aimed at extending the work of Jaehnig (1999) to larger scale reciprocating compressors, to other compressor technologies (screw, scroll), and to other compressor configurations (open-drive). Refrigerant mass flow rate and compressor power were separately modeled using a semi-empirical form based on a polytropic model. The empirical parameters in the model were determined using non-linear regression with a commercial software application (Klein and Alvarado, 2001) to minimize the objective function in Eqn (1) by altering the values of the parameters within specified bounds. Normalizing the error with the average of all measured values, as is done in Eqn (1), ensures that all data points are weighted equally.