Performance analysis of reciprocating compressors through computational fluid dynamics

Transcription

1 SPECIAL ISSUE PAPER 183 Performance analysis of reciprocating compressors through computational fluid dynamics ELLPereira 1, C J Deschamps 1 and F A Ribas Jr 2 1 Department of Mechanical Engineering, Federal University of Santa Catarina, Florianopolis, SC, Brazil 2 Embraco, Joinville, SC, Brazil The manuscript was received on 19 December 2007 and was accepted after revision for publication on 21 May DOI: / JPME194 Abstract: An experimentally validated numerical analysis of reciprocating refrigeration compressors is presented. The finite-volume methodology is adopted to solve the flow field and a one-degree-of-freedom model is used to describe the valve dynamics. The variation of the computation domain, associated with the valve and piston displacements, is taken into account and the time-dependent flow field and the valve dynamics are coupled and solved simultaneously. The three-dimensional formulation considered in the analysis allowed the simulation of actual suction and discharge muffler geometries. Numerical results were validated with reference to experimental data for valve displacement and pressure in the suction and compression chambers obtained in a calorimeter facility. A study was carried out to identify the contributions of mufflers and valves to the compressor thermodynamic losses. Keywords: reciprocating compressor, compressor simulation, valve dynamics 1 INTRODUCTION Computational fluid dynamics (CFD) is a methodology that has been developed over many years and reached the maturity required for use as a design tool in many engineering applications. The main aim of CFD is to predict fluid flow and heat transfer involved in a specific design, allowing a detailed analysis of components more cost effectively and more rapidly than with experimental methods. The impressive growth in interest in CFD in recent years is mainly associated with the fact that computers are steadily becoming more powerful and less expensive, making CFD feasible for simulations of much larger problems. However, CFD is still behind experimental analysis as a design tool because several numerical approximations and physical models have to be adopted to solve the governing equations, which may not be adequate in some situations. A good account of CFD applied to positive displacement compressors is presented in reference [1]. Corresponding author: Department of Mechanical Engineering, Federal University of Santa Catarina, Campus Universitario, Florianopolis, SC , Brazil. deschamps@polo.ufsc.br JPME194 IMechE 2008 In the case of reciprocating compressors, most simulation methodologies are still based on integral formulations, usually evaluating the compression process through the use of polytropic exponents or the first law of thermodynamics. In such simplified approaches, the flow through valves is taken into account through the concept of effective flow and force areas. Some studies have employed CFD to design components of reciprocating compressors, such as valves and mufflers, analysing their performance in isolation from the other components [2, 3]. The fluid flow and heat transfer phenomena in a 1.5 ton A/C hermetic compressor were numerically analysed in reference [4] using a commercial CFD code. A steady-state condition was used for the simulation, with the mass flowrate and suction gas temperature being prescribed at the inlet. The entire computational domain was solved for conjugate heat transfer and the numerical results were found to be in good agreement with the experimental data. An approach similar to that in reference [4] has been used to predict the temperature at various locations of a refrigeration compressor operating with R404a [5]. A domain decomposition technique was proposed in reference [6] to reduce the computational processing time. The fluid and the solid domains were Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering

2 184 ELLPereira, C J Deschamps, and F A Ribas Jr solved separately from each other, and their coupling was accomplished through boundary conditions at their interfaces. Suction and discharge mufflers were not included in the simulations and no details were given about the valve dynamics modelling. Recently, a numerical analysis of a double-acting, two-cylinder, air reciprocating compressor was presented [7]. A commercial code was adopted for twoand three-dimensional flow simulations, but the flow and dynamics associated with the valves were evaluated with reference to effective flow and force areas, so as to reduce the computational cost. A two-dimensional differential methodology to simulate the whole operating cycle of a small refrigeration reciprocating compressor has been developed [8], including the compressible turbulent flow inside the cylinder and the time-dependent flow field through the discharge valve. Results for the cylinder pressure field demonstrated a significant restriction for the flow along the cylinder clearance when the piston approaches the top dead centre and the discharge valve is open. A numerical procedure was developed [9] to simulate the strong fluid and structure interaction in a suction valve of a linear compressor, with a good agreement being verified between numerical and experimental results for the compressor cooling capacity. The present paper presents a three-dimensional numerical model for the analysis of small reciprocating compressors employed for household refrigeration purpose, taking into account the flow in the cylinder and through valves, suction, and discharge mufflers. The interaction between valve motion and fluid flow is also included in the model, using a simple one-degree-of-freedom model to solve the valve dynamics. 2 MATHEMATICAL MODEL The compressible turbulent flow that prevailed in the compressor was solved through the concept of Reynolds-averaged quantities, in which the value of a computed variable represents an ensemble average over many engine cycles at a specified spatial location. The turbulence transport contribution was modelled through the RNG k ε model, which has been extensively used and validated for flow through simple geometries of compressor valves [10]. An equation of state for an ideal gas completes the system required to solve the compressible flow. In this study, the reed was considered to be parallel to the valve seat and its dynamics represented by a one-degree-of-freedom model [11] m eq x + c ẋ + k ẍ = F p + F o (1) where m eq, c, and k are the reed equivalent mass, damping coefficient, and stiffness, respectively. On the other hand, F p is the flow induced force on the reed and F o can accommodate any other force, such as reed pre-tension and also stiction that may occur due to the presence of a lubricating oil film between the reed and valve seat. Finally, x, ẋ, and ẍ are the instantaneous reed lift, velocity, and acceleration, respectively. The equivalent mass m eq is determined from data for reed stiffness, k, and natural frequency, f n. In order to solve equation (1) for the valve displacement x, force F p has to be evaluated from the pressure distribution on the reed surface, p, associated with the flow through the valve F p = p da (2) A For the discharge valve, a booster is set to act when the reed valve reaches a specified displacement and the valve lift is limited to a maximum value. 3 NUMERICAL SOLUTION PROCEDURE The computational model was developed with a commercial CFD code [12] based on the finitevolume methodology. The solution domain includes the geometries of the suction and discharge mufflers, the valves, and the compression chamber formed by the cylinder and the piston. However, the compressor shell is not included at this stage. Because of the geometric complexity of the compressor mufflers, the solid model was first generated with CAD software and then imported into a pre-processor to generate the computational grid. For suction and discharge mufflers, the solution domain discretization required the use of tetrahedral grid elements, whereas for the much simpler compression chamber geometry, hexahedral elements could be adopted. Figure 1 shows the compressor geometry and a partial view of a typical computational grid employed in the simulations, which had approximately control volumes. Because of the presence of moving boundaries such as the piston inside the cylinder and suction and discharge valves, a moving grid strategy had to be applied to simulate the compression process. Evaporation and condensation pressures, p e and p c, were imposed as boundary conditions for the suction and discharge mufflers, respectively. At the solid walls, all velocity components are zero, but for the reed and piston surfaces, the velocities were obtained from equation (1) and the crankshaft mechanism, respectively. A turbulence intensity of 3 per cent and turbulence length scale corresponding to the tube hydraulic diameter were adopted as the inlet boundary condition for the turbulent flow in the mufflers. With the exception of the compression chamber wall, all the Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering JPME194 IMechE 2008

3 Performance analysis of reciprocating compressors through CFD 185 Fig. 1 Compressor geometry and computational grid Because of the numerical stability aspects of the solution procedure and also because of constraints associated with the deforming mesh method, two different time steps had to be used according to whether the valves were open or closed. Thus, the time steps were set to values corresponding to 0.5 of crankshaft angle when the valves were closed and 0.1 otherwise. The convergence of the procedure was assessed by examining whether the compressor operation conditions were cyclically repeated. By using the aforementioned time steps, three cycles were required to establish a periodic condition, with a processing time of 20 h per cycle on a computer with a single Pentium IV 3 GHz processor. remaining solid walls were assumed to be adiabatic. This major simplification was needed in this study because no reliable data were available for the heat transfer condition at the external surfaces of mufflers. For this reason, the inlet temperature in the suction muffler was set to the value measured in the suction chamber, so as to have the correct temperature for the gas entering the cylinder. The temperature of 77 C prescribed at the wall of the compression chamber was obtained from a second simulation code [13], which evaluates the temperature in eight control volumes through energy balances and using some of the compressor simulation programme outputs. The control volumes considered in this thermal simulation code are: gas in the suction muffler, compression chamber wall, gas in the discharge muffler, discharge gas, internal environment, compressor shell, electric motor, and bearings. The evaporation pressure and suction temperature were employed as initial estimates for the suction muffler and for the compression chamber, whereas for the discharge muffler, the condensation pressure and discharge line temperature were used instead. The differential equation for the valve dynamics (equation (1)) was solved using an explicit Euler method and by considering the force F p to be constant during each time step. A stiction force, due to the presence of lubricating oil in the valve system, was assumed to act on the reed valves up to a valve lift of 10 μm. The values prescribed were 0.5 and 1.5 N for the suction and discharge valves, respectively. A second-order upwind scheme was adopted to interpolate the flow quantities needed at the control volume faces. The coupling between the pressure and velocity fields was achieved with the PISO scheme, which has been specifically developed for simulation of reciprocating engines. The system of algebraic equations was solved with a segregated implicit algorithm. JPME194 IMechE EXPERIMENTAL SETUP AND PROCEDURE A calorimeter facility was employed to investigate the compressor performance and to supply data required to validate the simulation model. Measurements were obtained for energy consumption, mass flowrate, valve displacement, as well as fluid temperature and pressure in different parts of the compressor. As can be seen in the schematic representation of the calorimeter (Fig. 2(a)), the experimental setup is composed of pipelines, control valves (CV), a mass flow meter (FM), heat exchangers (HX), a thermocouple (TC) and pressure transducers (PT). The calorimeter is designed in a way that refrigerant fluid can flow through the high and low pressure lines in the superheated state, as indicated in the pressure enthalpy diagram of Fig. 2(b). According to this arrangement, refrigerant enters the compressor (C) at point 1 and is compressed to point 2. Then, after being cooled by a heat exchanger (HX1) to point 3, the refrigerant is adiabatically throttled to an intermediate pressure level (point 4), by means of a control valve (CV1), in which its mass flowrate is obtained with a Coriolis flowmeter (FM). The refrigerant is cooled again with a heat exchanger (HX2) to point 5 and then throttled via a control valve (CV2) to the evaporation pressure (point 6). Finally, with the assistance of an electrical heater (EH1) and a thermocouple (TC1), the compressor suction line temperature is adjusted to the required superheated condition (point 1), completing the operating cycle. By adjusting the refrigerant charge in the system and the settings of control valves, heat exchangers and heaters, the thermodynamic conditions at points 1 and 2 can be adjusted to any required test condition. The main advantage of this experimental setup is that the compressor can be analysed without any reference to a specific refrigeration system. The first step in the experimental procedure is to submit the compressor and the pipeline to an adequate vacuum condition, in order to remove air, Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering

4 186 ELLPereira, C J Deschamps, and F A Ribas Jr Fig. 2 Experimental setup: (a) layout schematic and (b) superheated cycle representation humidity, and any other contaminant inside the system. Then, the system receives a charge of refrigerant and the flowmeter reading is set to zero. After the compressor is switched on, a period of 6 h is needed to establish a fully periodic operating condition because of compressor thermal inertia. During this process, the control valves in the high and low pressure lines have to be continuously adjusted to establish the specified suction and discharge pressure conditions and the required mass flowrate. The system is considered to have reached a steady operating condition when, in a period of 45 min, the temperatures in several locations of the compressor vary less than 1 C and the mass flowrate and compressor energy consumption do not change more than 1 per cent. When this condition is satisfied, data for energy consumption and mass flowrate are acquired during a period of 10 min. Finally, data for pressure in the suction and discharge chambers, pressure in the cylinder and displacements of suction and discharge valves are collected for 50 operation cycles of the compressor, allowing the evaluation of an average value for each quantity and, as a consequence, a reduction in the measurement uncertainty. Piezoelectric pressure transducers were selected for the measurements in the suction and discharge chambers and inside the cylinder, due to its high response frequency, small size, and reliability regarding the hostile conditions inside the compressor. It is not possible to flush mount the transducer at the cylinder wall, and therefore, a pressure tap hole was provided in the dead volume region. To correlate the pressure measurement with the crank angle, a sensing winding was assembled to the crankcase to collect the signal emitted by a magnet fixed to the crankshaft. The instantaneous crankshaft position is calculated taking into account the compressor mechanism characteristics. Small sensing windings were also assembled into the valve plate seat to give the valve lift according to the crankshaft position. Measurements for pressure and crank angle position, needed to construct the indicator diagram, are obtained with a sampling rate of 60 khz. Such a high rate of sampling is adopted to satisfy the following requirements: (a) correct characterization of pressure time variation in the compression chamber and in the suction and discharge chambers; (b) accuracy for the piston location along its motion; (c) adequate time resolution to allow the evaluation of power consumption from the indicator diagram. In the present work, measurements were carried out for two 60 Hz compressors operating with R134a and with cooling capacities of 170 and 270W. Both compressors were tested following the ASHRAE LBP rating condition, represented by evaporating and condensing temperatures equal to 23.3 and 54.4 C, respectively. All measurements represent an average of experimental data obtained in five independent tests for each condition analysed. The uncertainty associated with the measurements of compressor energy consumption is estimated to be ±4%. 5 RESULTS Figure 3 shows a comparison between numerical and experimental results for the compressor indicator diagram, corresponding to the suction and discharge processes. It should be mentioned that the numerical result represents a volumetric average of the instantaneous pressure field inside the cylinder. In this figure, the pressure value was normalized by the pressure condition either in the suction line or in the discharge line, depending on the process being examined, and the instantaneous compression chamber volume was normalized by the compressor total volume displacement. The agreement between numerical results and experimental data is very good in the case of the suction process. For the discharge process, the overall prediction consistency is also satisfactory, although Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering JPME194 IMechE 2008

5 Performance analysis of reciprocating compressors through CFD 187 Fig. 3 Indicator diagram: (a) suction process and (b) discharge process Fig. 4 Valve displacement: (a) suction valve and (b) discharge valve some discrepancy is observed for the second pressure peak. The first pressure peak in the discharge process is a consequence of the valve dynamics, since the pressure inside the cylinder keeps rising until the valve lift is enough to allow a large mass flowrate through the discharge valve. The second peak is directly linked to the increase in the flow restriction along the cylinder clearance as the piston approaches the top dead centre. Figure 4 indicates that, despite the use of a simple one-degree-of-freedom model for the valve dynamics, the predictions of displacements for the suction and discharge valves are acceptable when compared with the measurements, even for the more complex dynamics of the suction valve. The short delay observed in the numerical result for the opening of the discharge valve (Fig. 4(b)) can be attributed in part to the great uncertainty associated with estimates for the oil stiction force. JPME194 IMechE 2008 Pressure pulsations in the suction chamber are depicted in Fig. 5 for two system conditions, represented by condensation temperatures T c = 54.4 and 40.5 C, while maintaining the same evaporation temperature (T e = 23.3 C). Here, the numerical results for pressure in the suction chamber also represent a volumetric average. The agreement between numerical and experimental data is again very good, concerning both phase and amplitude. Since the pressure pulsation in the suction chamber directly affects the valve dynamics and the mass flowrate through the valve, its correct prediction is of primary importance for the compressor simulation. A further important part of the validation procedure was to verify the capability of the model to predict variations in the compressor performance due to modifications in its design. Table 1 presents the results for power consumption for the larger capacity compressor (270 W) when the orifice diameter of the Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering

6 188 ELLPereira, C J Deschamps, and F A Ribas Jr Fig. 5 Suction chamber pressure: (a) T c = 54.4 C and (b) T c = 40.5 C Table 1 Effect of discharge orifice diameter on power consumption (W) Experimental data Predictions Indicated Suction Discharge Indicated Suction Discharge Small diameter Large diameter Variation % discharge valve is increased by 30 per cent. Although the observed variations in the indicated power consumption and in the suction process energy loss are within the experimental uncertainty, the measurements clearly demonstrate a substantial decrease in the discharge process energy loss when a larger orifice diameter is adopted in the discharge valve. Although overestimating the overall compressor power consumption, the numerical model is able to predict a power consumption decrease of approximately 30 per cent in the discharge process, in close agreement with the measurements. Table 2 was prepared for the smaller capacity compressor (170 W) and is concerned with the effect of the condensation temperature T c on the power consumption. In this case, the measurements demonstrate a significant power consumption decrease in the compression process when T c decreases from 54.4 to 40.5 C, since the discharge pressure becomes smaller. However, there is an increase in the power consumption on both valves because the mass flowrate is increased as the pressure ratio is decreased. Similarly, as observed in Table 1, here again the simulation model is seen to correctly predict relative variations in the power consumption as indicated by the experimental data. Based on both test situations, and in spite of some discrepancies between numerical and experimental results for pressure inside the cylinder during the discharge process (Fig. 3(b)), there is a clear evidence that the numerical model is capable of predicting variations in the power consumption originated by modifications in the compressor design. Figures 6, 7 and 8 show typical results for the flow field that can be obtained with the present simulation methodology. For instance, vector velocities along the suction chamber, valve passage, and in the cylinder are plotted in Fig. 6 at the cylinder longitudinal midplane. As can be seen, the flow velocity magnitude in the valve passage reaches 40 m/s and, after entering the cylinder, a wall jet flow is created along the Table 2 Effect of condensation temperature on power consumption (W) Experimental data Predictions T c Indicated Suction Discharge Indicated Suction Discharge 54.4 C C Variation % Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering JPME194 IMechE 2008

7 Performance analysis of reciprocating compressors through CFD 189 Fig. 6 Numerical results for velocity vectors in the suction process plate valve. Naturally, this flow feature brings about a favourable condition for heat transfer between the refrigerant and the wall, decreasing the gas density and hence the compressor volumetric efficiency. Another aspect that can also be noticed in Fig. 6 is the presence of two recirculating flow regions inside the cylinder, one below the discharge valve and other underneath the suction valve. Despite the higher density of the gas in the discharge process, Fig. 7 shows that velocity magnitudes are much higher than those in the suction process, reaching values up to 100 m/s. This phenomenon is a consequence of two aspects. First, discharge valve orifices are usually smaller than suction valve orifices, in order to reduce the clearance volume and, as a consequence, increase the volumetric efficiency. For instance, the protuberance identified in the piston surface is aimed at reducing the volume left by the discharge orifice. The second aspect that contributes for such high velocity magnitudes is the time interval associated with the discharge process, which is approximately three times shorter than that of the suction process. Figure 8 depicts contours of differential pressure p(= p p s ) and temperature at the cylinder midplane during the suction process. As can be seen in Fig. 8(a), the downward motion of the piston gives rise to a pressure drop of 4 kpa across the valve, which is responsible for the gas intake. Inside the cylinder, as one expects, the pressure field is nearly uniform. Contours of temperature in Fig. 8(b) are useful to assist Fig. 7 Numerical results for velocity vectors in the discharge process Fig. 8 Flow field predictions: (a) differential pressure (kpa) and (b) temperature ( C) JPME194 IMechE 2008 Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering

8 190 ELLPereira, C J Deschamps, and F A Ribas Jr Fig. 9 Numerical results for pressure: (a) cylinder and suction muffler and (b) cylinder and discharge muffler the understanding of the superheating process in the cylinder and its effect on the volumetric efficiency. In this regard, it is interesting to note a very thin thermal boundary layer next to the compression chamber wall. Mechanical energy losses in the suction and discharge processes are influenced mainly by three parameters: valve orifice, reed valve, and muffler. The results for pressure in the cylinder and in the suction and discharge chambers, shown in Fig. 9, can be used to separate energy losses associated with the valves from those occurring in the mufflers. Accordingly, the area between the curves defined by the pressure in the cylinder and the pressure in the suction chamber gives the energy loss due to the valve restriction. On the other hand, the area delimited by the pressure in the muffler and the pressure in the suction line, indicated by the horizontal line, is a measure of the energy loss in the suction muffler. The same considerations can be applied to analyse the discharge system. Thermodynamically, an ideal muffler should impose no restrictions to the flow and should also prevent any unfavourable pressure pulsation in the suction, or discharge, chamber. In order to separate the energy loss due to the reed valve dynamics from that associated with the valve orifice, simulations were performed considering the presence of ideal valves and without the use of mufflers. For this idealized situation, the reed valve is forced to move out of the way instantaneously when the pressure in the cylinder reaches the pressure in the suction or discharge line, depending on the valve system under analysis. When the piston reaches the top dead centre in the case of the discharge process, or the bottom dead centre for the suction process, the reed valve closes instantaneously. Hence, by eliminating the presence of the reed valve, the only flow restriction that remains is that established by the valve orifice itself, allowing the evaluation of the associated energy loss and its comparison with Table 3 Distribution of energy losses between muffler, valve reed, and valve orifice in the suction and discharge systems Muffler Reed valve Valve orifice Suction system 40% 40% 20% Discharge system 15% 25% 60% that which would result in the presence of the reed valve. Table 3 summarizes the results of an analysis directed to evaluate the contribution of mufflers, valve reeds, and valve orifices on the compressor energy losses and to identify possible alternatives for their optimization. Initially, the numerical simulations showed that 40 per cent of the energy losses in the suction process is due to the muffler. Although not shown here, the adoption of a less restrictive muffler allowed a decrease of 20 per cent in the suction energy loss and a small increase in the compressor capacity. The new muffler affected the valve dynamics also, reducing the energy loss in the valve. This is an example of the strong coupling between the valve dynamics and the flow in the muffler, which responded favourably in the present situation. The energy loss predicted for the discharge muffler was very small, accounting for approximately 15 per cent of the total energy loss in the discharge system. The replacement of the discharge muffler was only effective in the energy loss reduction when the discharge chamber volume was increased three-fold. However, such a reduction did not represent a significant increase in the compressor efficiency. Therefore, an optimization of the discharge system should focus on the valve itself. In the suction process, the valve reed is responsible for approximately 40 per cent of the total energy Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering JPME194 IMechE 2008

9 Performance analysis of reciprocating compressors through CFD 191 loss. Simulations revealed that an increase of 4 per cent in the compressor efficiency can be obtained through an optimization of the reed valve, whereas an increase of just 1 per cent resulted when the area of the suction valve orifice was doubled. This is a clear indication that the suction valve orifice is already large enough. For the discharge valve, the numerical predictions showed an energy loss distribution very different from that in the suction valve. For instance, the discharge valve orifice was responsible for nearly 60 per cent of the total energy loss. For this reason, when the valve orifice area was doubled, the energy loss could be reduced by more than half. However, in contrast to the suction valve, a larger discharge valve orifice leads to an increase in the cylinder dead volume and, as a consequence, a decrease in the compressor capacity. This is the reason for adopting a protuberance on the piston surface, as explained previously. Before concluding, it should be said that the present model has a number of advantages in relation to more traditional simulation approaches, such as the zerodimensional methodology. For instance, heat transfer at the solid walls is directly evaluated from the temperature field, taking into account the flow effects originated in the suction and discharge valves. On the other hand, zero-dimensional methodologies adopt empirical heat flux correlations developed for specific geometries, which are not capable to predict most effects resulting from changes in the compressor design. Another advantage of the present methodology is the fact that no reference to effective flow-and force areas is needed to evaluate the mass flowrate through the valve and the flow-induced force acting on the reed valve. This is particularly important because under strong flow transients such steadystate correlations may be totally inadequate to predict the actual conditions prevailing in the compressor valve [14, 15]. 6 CONCLUSIONS This paper presented a numerical analysis of reciprocating refrigeration compressors, based on a threedimensional CFD model. The solution domain included suction and discharge mufflers, valves, and the compression chamber. The numerical results were validated with reference to experimental data of valve displacement and pressure in the suction and compression chambers. The model was applied to investigate the effect of modifications in the design of suction and discharge systems and in the compressor operation conditions, allowing a detailed analysis of energy losses in mufflers and valves. For the compressors analysed, the predictions were able to identify JPME194 IMechE 2008 a significant increase in the compressor efficiency brought about by modifications in the suction muffler and discharge valve orifice. ACKNOWLEDGEMENTS This study forms part of a joint technical-scientific program of the Federal University of Santa Catarina and EMBRACO. Support from FINEP (Federal Agency of Research and Projects Financing) and CAPES (Coordination for the Improvement of High Level Personnel) is also acknowledged. REFERENCES 1 Shiva Prasad, B. G. CFD for positive displacement compressors. In Proceedings of the International Compressor Engineering Conference at Purdue, 2004, paper C Fagotti, F. and Possamai, F. C. Using computational fluid dynamics as a compressor design tool. In Proceedings of the International Compressor Engineering Conference at Purdue, 2000, pp Ottitsch, F. CFD: a viable engineering tool for compressor valve design or just a toy? In Proceedings of the International Compressor Engineering Conference at Purdue, 2000, pp Chikurde, R. C., Loganathan, E., Dandekar, D. P., and Manivasagam, S. Thermal mapping of hermetically sealed compressors using computational fluid dynamics technique. In Proceedings of the International Compressor Engineering Conference at Purdue, 2002, paper C Birari, Y.V, Gosavi, S. S., and Jorwekar, P. P. Use of CFD in design and development of R404a reciprocating compressor. In Proceedings of the International Compressor Engineering Conference at Purdue, 2006, paper C Abidin, Z., Almbauer, R. A., Burgstaller, A., and Nagy, D. Domain decomposition method for 3-dimensional simulation of the piston cylinder section of a Hermetic reciprocating compressor. In Proceedings of the International Compressor Engineering Conference at Purdue, 2006, paper C Aigner, A., Meyer, G., and Steinrück, H. Valve dynamics and internal waves in a reciprocating compressor. In Proceedings of the 4th Conference of the EFRC European Forum for Reciprocating Compressors, Antwerp, Belgium, Matos, F. F. S., Prata, A. T., and Deschamps, C. J. A two-dimensional simulation model for reciprocating compressors with automatic valves. In Proceedings of the International Compressor Engineering Conference at Purdue, 2006, paper C Suh, K. H., Heo, D.N, and Kim, H. S. CAE/CFD application for linear compressor. In Proceedings of the International Compressor Engineering Conference at Purdue, 2006, paper C Salinas-Casanova, D. A., Deschamps, C. J., and Prata, A. T. Turbulent flow through a valve with inclined reeds. In Proceedings of the International Conference Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering

10 192 ELLPereira, C J Deschamps, and F A Ribas Jr on Compressors and their Systems, London, 1999, pp Matos, F. F. S., Prata, A. T., and Deschamps, C. J. Numerical simulation of the dynamics of reed type valves. In Proceedings of the International Compressor Engineering Conference at Purdue, West Lafayette, USA, 2002, paper C ANSYS, Inc. FLUENT user s guide, v , 2006 (Lebanon/NH, USA). 13 Fagotti, F., Todescat, M. L., Ferreira, R. T. S., and Prata, A. T. Heat transfer modeling in a reciprocating compressor. In Proceedings of the International Compressor Engineering Conference at Purdue, West Lafayette, USA, 1994, pp Ahuja, V., Hosangadi, A., Cavallo, P. A., and Daines, R. Analyses of transient events in complex valve and feed systems. In Proceedings of the 41st AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit, Tucson, USA, 2005, paper AIAA Habing, R. A. and Peters, M. C. A. M. An experimental method for validating compressor valve vibration theory. J. Fluids Struct., 2006, 22(5), APPENDIX Notation c D f n F o F p k m eq p p c p e p s T c T e x ẋ ẍ reed damping coefficient reed diameter reed natural frequency oil stiction force acting on the reed valve flow-induced force on the reed valve reed stiffness reed equivalent mass local pressure condensation pressure evaporation pressure suction line pressure condensation temperature evaporation temperature reed lift reed velocity reed acceleration Proc. IMechE Vol. 222 Part E: J. Process Mechanical Engineering JPME194 IMechE 2008