Using Large Eddy Simulation for Reciprocating Compressor

ABSTRACT

This paper considers the application of large-eddy simulation (LES) to predict the performance of hermetic reciprocating compressor utilized in refrigeration. In such devices the pressure difference between the suction/discharge chamber and the cylinder, established by the piston motion, is responsible for the valve opening. Once the valves are open, the flow dictates the pressure distribution on the valve reed surface and, consequently, the resultant force that will govern the valve dynamics and its displacement from the seat. The methodology developed herein applies LES, combined with the Smagorinsky sub-grid model, to account for the compressible turbulent flow through the discharge valve. A one-degree of freedom model is adopted for the valve dynamics, and a finite volume methodology to solve the flow field throughout the discharge valve. For the remainder of the compression cycle, an integral formulation is employed, with effective flow and force areas being used to evaluate the dynamics and mass flow rate for the suction valve. Numerical results demonstrate that the methodology is capable of predicting important flow features in the discharge process, at a reasonable computational cost.

Keywords: Automatic valves, reed valves, reciprocating compressor simulation


--------------------------------------------------------------------------------

Introduction

The role of the compressor in a refrigeration system is to establish the pressure difference between the condensing and evaporating lines and also to supply the required mass flow rate of refrigerant. Compressors can be divided into two groups: roto-dynamic (centrifugal, axial, radial, etc) and positive displacement (reciprocating, rotary, scroll, screw, etc). A roto-dynamic machine subjects a steadily flow of gas to forces that result in a continuous rise in pressure. Positive displacement compressors take in an amount of gas and trap it inside a volume that is diminished by deformation. In this process, the pressure rises and when it reaches a certain value the gas is pushed out against the pressure in the discharge chamber. Hence, in a positive displacement compressor the flow is not steady, occurring rather in pulses.

Figure 1 presents a schematic view of a reciprocating compressor and the indicator diagram for a typical cycle. When the piston moves downwards, it reaches a position where low pressure vapor is drawn in through the suction valve, which is opened automatically by the pressure difference between the cylinder and the suction chamber. The vapor keeps flowing in during the suction stroke as the piston moves towards the bottom dead center (BDC), filling the cylinder volume with vapor at suction pressure, ps. The suction process is represented by curve A-C in the indicator diagram of Fig. 1b. After reaching the BDC, the piston starts to move in the opposite direction, the suction valve is closed, the vapor is trapped, and its pressure rises as the cylinder volume decreases. Eventually, the pressure reaches the pressure in the discharge chamber, pd, and the discharge valve is forced to open. After the opening of the discharge valve, the piston keeps moving towards the top dead center (TDC), represented by point A. It should be noted that suction and discharge processes do not take place at constant pressure. This phenomenon is associated with the dynamics of the valves and the restriction imposed by the valve passage areas. This appears on the indicator diagram, with compression continuing after pressure pd is reached and the same happening for the expansion stroke after pressure ps.





At point A there remains an amount of refrigerant in the cylinder at discharge pressure, since a gap between the piston and cylinder head is necessary to accommodate the valves and also to allow for manufacturing tolerances. The volume resulting from such a clearance may account for up to 5 % of the total cylinder volume. Therefore, as the piston moves downwards, the refrigerant in the clearance is re-expanded and its pressure decreases, as represented by process AB. When the piston reaches point B, the cylinder pressure is lower than the suction chamber pressure, ps, causing the suction valve to open and the gas to flow into the cylinder up to approximately point C. Hence, instead of taking in a volume of vapor equal to the volume (VC-VA), a smaller volume (VC-VB) is drawn from the suction chamber, reducing the compressor volumetric efficiency. Other aspects also affect the compressor efficiency, such as heat transfer between the refrigerant and the cylinder wall, throttling in valve ports, gas leakage through the clearance between the piston and the bore, backflow in the valves, etc.

Most domestic refrigeration systems adopt hermetic reciprocating compressors, due to a number of features: small volume, low levels of noise and energy consumption, absence of leakage, among others. In hermetic models, motor and compressor are directly coupled on the same shaft and the assembly is installed inside a welded steel shell. An important disadvantage of hermetic compressors is that it is not possible to service them without cutting the shell. Therefore, the compressor must be manufactured in such a way that it can last the life of the system.

Reed valves are essential parts in hermetic compressors. These valves are called automatic because they open and close depending on the pressure difference between the cylinder and the suction/discharge chamber, established by the piston motion. Once the valves are open, the pressure flow field is responsible for the resultant force acting on the reed. In designing the valve system for reciprocating compressors four main features related to the valve performance are sought: fast response, high mass flow rate, low pressure drop when opened, and good backflow blockage when closed. For this reason, and in order to obtain an optimum valve system, it is crucial to recognize and predict the phenomena associated with the flow through the valve as well as to its dynamics.

Despite their geometric simplicity, automatic valves possess a complex mathematical description, usually requiring some simplifying hypotheses. For this reason, several studies available in the literature related to automatic valves either model the valve dynamics in detail but pay little attention to the description of the flow field (Khalifa and Liu, 1998), or focus on the fluid mechanics without considering the coupling between valve motion and pressure distribution on the reed (Deschamps et al., 1996). Trella and Soedel (1974) developed a methodology to analyze the non-linear behavior of discharge valve systems, considering a transient compressible flow. The valve dynamics was coupled to the flow field, which was solved from integral conservation laws written for a number of control volumes for the flow through the valve. The study demonstrated the importance of solving the valve dynamics coupled with the flow field of the valve. More recently, Lopes and Prata (1997) developed a numerical methodology to explore the interaction between valve dynamics and fluid flow. By prescribing a periodic velocity profile at the entrance of the valve orifice, and solving the continuity and momentum equations via the finite volume technique, the flow field was obtained. From the pressure on the reed the resultant force was determined and a one-dimensional dynamic model was employed to solve the reed acceleration, velocity and displacement. Later, Matos et al. (2002) extended the model of Lopes and Prata (1997) so as to take into account the turbulent regime that prevail in valves.

In the context of compressor simulation, a number of important studies can be cited. Soedel (1972) presents a model to thermodynamically evaluate the performance of compressors under cyclical conditions, using integral relations for conservation of mass and energy, and a dynamic model for valves. MacLaren et al. (1975) adopted conservation equations in differential form and solved the unsteady one-dimensional compressible fluid flow through suction and discharge systems with the method of characteristics. Pérez-Segarra et al. (1994) proposed a numerical procedure, based on the finite volume method, to simulate the transient compressible one-dimensional flow in the compressor. The most elaborate model put forward so far is that of Matos et al. (2002), where a two-dimensional model was used to simulate the complete compression cycle, including the turbulent flow through the discharge valve. Turbulence contribution to the flow transport was accounted for with the RNG k-e model. The methodology was found to return a precise description of physical mechanisms that influence the compressor efficiency, such as heat transfer at the cylinder wall and transient effects on the valve dynamics. Despite such promising predictions, Matos et al. (2002) pointed out that computational processing time was excessive for compressor design purposes.

The main objective of this work is to offer an alternative to the compressor simulation methodology of Matos et al. (2002), with the same level of accuracy but with a much lower computational cost.



Mathematical Model

The necessary reduction in the computational cost is sought here through two approaches. Firstly, the simulation methodology combines differential and integral formulations for the governing equations. Differential equations are solved to capture flow details during the opening of the discharge valve, which are crucial to correctly predict its dynamics. The flow through the suction valve could be solved in the same way but, following Matos et al. (2002), this treatment was applied to the discharge valve only, at this stage. Therefore, for the remainder of the compressor cycle, including the opening of the suction valve, an integral formulation is used. The other strategy is to replace the RNG k-e turbulence model adopted in Matos et al. (2002) with large-eddy simulation (LES). The number of differential equations in LES is smaller and, given that flow in compressors is naturally transient, this may be effective in reducing the computational effort. More details on both formulations are given next.

Integral Formulation

The integral formulation adopted to simulate the compressor is a simplified version of the code proposed by Ussyk (1984). The code accounts for piston displacement as a function of crankshaft angle, the thermodynamic process inside the cylinder, mass flow rate through the valves, valve dynamics, gas pulsation inside the mufflers and refrigerant thermodynamic properties. Several parameters are calculated during the compressor cycle, such as instantaneous pressure throughout the compressor, mass flow rate, valve dynamics, energy and mass losses, refrigerating capacity, etc.

The transient equations associated with the compressor simulation code are solved via a fourth order Runge-Kutta method. Thermodynamic properties can be evaluated using the perfect gas hypothesis or through a program link to the REFPROP database (Gallanger et al., 1993).

Valve displacement is modeled by a single degree of freedom mass-spring model, in which the natural frequency and damping coefficient have to be specified for the valves. Valve stiction can be obtained from the analytical model proposed by Khalifa and Liu (1998).

The resultant force acting on the reed and the mass flow rate through the valve are obtained with reference to effective force area Aef and effective flow area Aee, respectively. From the pressure difference across the valve, Dpv, Aef is determined from Aef = F/Dpv. The effective force area can be understood as a parameter related to how efficiently the pressure difference Dpv opens the valve. On the other hand, for the same pressure drop, Aee expresses the ratio between the actual mass flow rate through the valve and that given by an isentropic flow condition.

If specified, gas pulsation in mufflers can be modeled following a methodology developed by Deschamps et al. (2002). The thermodynamic process for the gas inside the cylinder can be evaluated either through a polytropic model or by the first law of thermodynamics. More details on the compressor simulation program can be obtained in Fagotti et al. (1994).

Differential Formulation

For the Reynolds averaged flow equations (RANS), the value of a computed variable represents an ensemble average over many engine cycles at a specified spatial location. In general, two-equation closures, such as the k-e model, have been used to model turbulent transport. The shortcomings of RANS models have been widely documented and a discussion of issues related to reciprocating engines is given in El Tahry and Haworth (1992).

Another approach to accounting for turbulent transport is large-eddy simulation (LES). In LES the governing equations are spatially filtered rather than ensemble averaged. Explicit account is taken of flow structures larger than the filter width, which is in the order of the mesh spacing, while the influence of unresolved scales is modeled using a sub-grid scale (SGS) model. Since statistics of small-scale turbulence are expected to be more universal than those of the large scales turbulence, LES offers the promise of wider generality and reduced modeling uncertainty.

LES is particularly appealing for application to reciprocating engines, given its inherent transient operation, despite its rather undeveloped condition for modeling complex engineering flows, as in the case of reciprocating engines, where moving piston and valves are present. In contrast, in RANS turbulence models the formulation and calibration have traditionally been carried out for statistically stationary flows with simple geometric configurations and, therefore, it is uncertain whether such closures will hold for complex three-dimensional transient flows that characterize reciprocating engines. In addition to this, the grid refinement commonly used for RANS simulations in IC engines is comparable to that required in LES for resolving a significant range of flow structure scales. Given the difficulties associated with RANS models, LES might actually be simpler, less computational expensive and more accurate.

LES is composed of four steps: i) a filtering operation that expresses a generic property F(x, t) as the sum of a filtered, or resolved, component, f(x, t), and a residual, or sub-grid scale (SGS), component, f'(x, t), where x and t are the space and time coordinates; ii) the application of a filtering process over the appropriate transport equations, resulting a residual stress tensor for the momentum equation and residual fluxes for scalar transport equations; iii) closure by modeling the residual stress tensor and residual fluxes; iv) the closed filtered equations for f(x, t) are numerically solved for large scale motions.

The contribution of unresolved (sub-grid scale) motions to the resolved scales can be estimated with the concept of an eddy viscosity, µt, similarly to that used for the Reynolds stress tensor in standard RANS turbulence models. One such a model was proposed by Smagorinsky (1963) and expresses the eddy viscosity as:



where Sij is the rate of strain tensor and is a filter width, usually taken as proportional to the local grid spacing, D. According to Deardoff (1970), for non-uniform grids can be evaluated as the geometric average of the grid spacing, ie = (DxDyDz)1/3.

The coefficient Cs is referred to as the Smagorinsky constant and was estimated by Lilly (1967) as being equal to 0.18 for homogeneous and isotropic turbulence. Calibration with respect to benchmark turbulent flows has led modelers to adopt different values for Cs. For homogeneous isotropic decaying turbulence, a value of Cs = 0.17 is found to be in good agreement with the experimental data, whereas for planar channel flow, a value of Cs = 0.1 yields the best agreement. Here Cs is assumed to be 0.17.

An important hypothesis in this study is that density fluctuations are negligible when compared to velocity fluctuations. According to Morkovin (1961), this assumption can be justified for non-reacting subsonic flow condition, which is verified in the present situation. Hence, the density variation effect on the flow is accounted for through its spatial and temporal variations.

LES certainly implies a transient three-dimensional simulation. Despite some works in the literature dealing with two-dimensional LES (Iliescu et al., 2003), it should be said this is not really a rigorous approach. However, at this stage of the research it was decided to adopt an axis-symmetric flow condition for additional savings in the computational processing time. To some extent, one could regard such a modeling like an algebraic eddy-viscosity model.

The positioning of the valve in the cylinder head is an important aspect of the compressor design. Although the axis-symmetric geometry for the discharge valve may seem quite idealized, it is a layout found in refrigeration compressors.

By writing residual stresses through the concept of eddy viscosity, the conservation equations for mass, momentum and energy can be written as follows:

a) Mass conservation



b) Momentum conservation in the axial (x) direction



c) Momentum conservation in the radial (r) direction



where µeff is the effective viscosity, comprised by the molecular viscosity, µ, and the eddy viscosity, µt, ie µeff = µ + µt.

d) Energy conservation



where k is the fluid thermal conductivity and Prt is the turbulent Prandtl number, considered here to be 0.9.

For simplicity, the perfect gas hypothesis was adopted in the state equation required to complete the equation system.

Valve Dynamics

Reeds are usually made of stainless steel and their dynamics can be expressed in a simplified way, using a one degree of freedom model as follows:



where F0 is a pre-load force acting on the reed and F is the force resulting from the pressure distribution on the reed surface. The valve stiffness and damping coefficients, K and C, respectively, as well as the valve mass, m, are determined experimentally. As illustrated in Fig. 2, in this study the reed is considered to be parallel to the valve seat.




In order to solve Eq. (6) for the valve lift d1, a fourth order Runge-Kutta methodology was adopted. The force F is evaluated from the pressure field created by the flow through the valve:



It should be mentioned that for the discharge valve, the valve lift was limited to 0.9 mm and a booster was set to act when the valve displacement was 0.3 mm. Since the flow through the suction valve is not solved, the force F on the suction reed has to be obtained via the effective force area, Aef.



Numerical Methodology

Moving Coordinate System

A key issue in solving the governing equations is the methodology chosen to handle the physical domain that expands and contracts, since both the piston and the valves are in motion. Here, following the practice adopted and fully described in Matos et al. (1999), a moving coordinate system was employed. The main feature of this coordinate system is that it transforms the physical domain shown in Fig. 2 into a computational domain that remains unchanged regardless any surface motion.

Solution Procedure

A finite volume methodology was employed to integrate the partial differential equations governing the flow, with a fully implicit approximation for transient terms. Staggered control volumes were adopted for velocity components. Interpolation of unknown quantities at the control volume faces was obtained using the QUICK interpolation scheme (Hayase et al., 1992). A segregate approach was employed to solve the equations and the coupling between pressure and velocity was handled through the SIMPLEC algorithm.

The system of algebraic equations that result from the integration of the governing differential equations over each control volume are solved using the Tridiagonal Matrix Algorithm (TDMA).

The solution domain was discretized with a computational grid with 110x90 (x, r) volumes, as illustrated in Fig. 2. Grid refinement was specifically adopted in regions where high gradients are expected to occur in the flow field. Of great help was some evidence of the discretization needed for the flow analysis in the discharge valve as made available by Salinas-Casanova et al. (1999). For instance, Fig. 3 shows a typical result emerging from the assessment of truncation error in the numerical results for pressure distribution on the reed surface, considering a fixed reed lift, s/d = 0.05, and a Reynolds number, Re = 25,000, based on the valve orifice diameter d. The results yielded by three grid levels (70x80, 140x160 and 280x320, axial x radial) show that the less refined grid returns a small truncation error and, therefore, a similar grid was adopted for the compressor simulation. Further details on this issue and on the computational domain dimensions can be found in Matos (2002).




The iterative procedure evaluates flow properties for each time step until convergence is reached, which is ascertained by examining whether the compressor operation conditions are cyclically repeated. A time step corresponding to 10-2 rad was employed for the integral approach, whereas a time step of 10-3 rad was needed for the differential formulation to guarantee the numerical convergence. Further refinement in the time step did not produce any modification in the numerical solution. However, it should be mentioned that a smaller time step, 10-4 rad, was required when the discharge valve was open due to steep flow transients. By using such time steps, 4 cycles were required to establish a periodic condition, taking approximately 39 hours on a computer with a single Pentium IV 2 GHz processor.

The differential equation for the valve dynamics, Eq. (6), was solved by considering the force F to be constant during each time step. As already indicated, in the case of the discharge valve F is obtained from the pressure distribution caused by the flow on the reed surface. However, for the suction valve F must be calculated from effective force area data.

The coupling between integral and differential formulations needs to be addressed. The compressor simulation starts at the bottom dead center (BDC) with the integral formulation, as represented in the illustrative diagram shown in Fig. 4. The cylinder pressure is the parameter chosen as the reference for change from one formulation to the other. In this way, during the compression stroke the integral formulation is changed to the differential formulation when the pressure reaches a value set at 12 bar. At this point, values for pressure, p, temperature, T, and density, r, are directly transferred and used as initial fields for the differential formulation. Other quantities given are the instantaneous piston position and cylinder volume V, both related to the crankshaft angle wt [rad], where w = 2pf and f = 60 Hz. No information is available for the velocity field and its initial value is set to zero. For the eddy viscosity, µt, an estimate is obtained from the numerical solution given in Matos (2002). After the gas is pushed out from the cylinder, the discharge valve is closed and the compressor is under the expansion stroke. The procedure is changed back to the integral formulation when the pressure reaches 8.5 bar. Besides allowing the solution of the flow through the discharge valve, the choice of this crankshaft angle range (12 to 8.5 bar) for the differential formulation has also some advantages. Firstly, at 12 bar the piston is very near the top dead center and the in-cylinder flow field is almost zero due the proximity between the piston and the cylinder head, which may be as close as 30 µm. This is an adequate position to change from the integral to the differential formulation. On the other hand, at 8.5 bar, the in-cylinder flow induced by the discharge valve opening is sufficiently damped so that mean values necessary to the integral formulation are not far from the flow field condition.




Since flow quantities are available for each control volume of the domain, an average value is required for pressure, temperature and density.



Boundary Conditions

At the solid walls all velocity components were taken to be zero, except at the surfaces of the reed and piston where u represents their corresponding velocity values; i.e. and , respectively. At the valve axis (r = 0) the axis-symmetry conditions were imposed as v = ¶u/¶r = 0. At the valve outlet, a boundary condition for pressure, equal to 14.8 bar, was prescribed. To obtain the axial velocity from the specified pressure value, a control volume half that of the control volumes adjacent to the boundary was used to integrate the axial momentum equation. By doing so, the velocity could be expressed in terms of the pressure gradient and the neighboring velocity components. More details on this technique can be obtained from Versteeg and Malalasekera (1995). Because the axial velocity obtained from this equation satisfied the momentum conservation but not the mass conservation, such an estimate had to be corrected via the SIMPLEC algorithm, in the same way as in the solution domain. For the velocity component parallel to the outlet boundary, the prescribed condition was ¶v/¶x=0.

Concerning boundary conditions for the energy equation, a value of 90 ºC was prescribed for the wall temperature. For the discharge, a local parabolic flow condition was used when the gas is leaving the domain. If the flow is entering the domain, the temperature at the boundary is considered to be that in the discharge chamber.


Results

The results given next were prepared for four crankshaft positions during the opening of the discharge valve: wt = 2.67 (a); 2.80 (b); 2.99 (c) and 3.13 (d) rad. Such positions are identified in Fig. 5, which shows the results for pressure at the cylinder wall and valve displacement, according to the crankshaft angle. The precise location of the pressure monitoring at the cylinder wall is indicated in Fig. 6a. Each point can be associated with the following events during the compressor stroke: (a) discharge valve is opening and the cylinder pressure is near its highest value; (b) discharge valve is still opening and the pressure has dropped; (c) valve is closing and the pressure has increased; (d) valve is returning to the valve seat and pressure is decreasing.





The pressure increase to a level above that of the discharge chamber is linked to distinct aspects: i) stiction force between reed and valve seat caused by a film of oil; ii) valve inertia; iii) increase in stiffness and natural frequency due to the presence of a booster; iv) flow restriction through the valve. The first two effects are present when the valve is closed.

By examining Fig. 5, it is possible to identify the opening of the valve when the cylinder pressure reached 15 bar. After the valve is opened, the pressure keeps rising up to point (a) due to the flow restriction brought about by a small valve lift.

The discharge valve keeps opening and, when the lift is great enough, the cylinder pressure starts to drop down to point (b). From this crankshaft position the pressure is seen to increase again, reaching a new local maximum condition, point (c). This occurs for two reasons: i) an increase in the viscous friction of the flow, due to the small clearance between the piston and the cylinder head; ii) closing motion of the valve, restricting the flow passage area. The viscous friction effect in the flow along the cylinder clearance can be observed from the results for the isobars, shown in Fig. 6. As can be seen in Fig. 6c, there is a pressure drop of approximately 1 bar between the cylinder wall and the valve orifice. The same level of pressure drop is not observed for points (a) and (b).

For the compressor model here considered, the top dead center (TDC) is reached at a crankshaft angle of 3.10 rad. Since point (d) represents an angle of 3.13 rad, here the piston has already started the expansion stroke, resulting in an abrupt pressure drop in the cylinder that acts to close the discharge valve.

Results for dimensionless streamlines in Fig. 7 show the presence of recirculating regions on the valve seat and inside the valve orifice, during the discharge. This phenomenon has an adverse effect on the valve efficiency since it restricts the flow passage, thus bringing about a further increase in the cylinder pressure. When the valve is almost fully open, the discharge jet at the valve outlet induces a recirculating flow region against the vertical wall present in the right side of the solution domain.




The pressure distribution on the valve surface is a key factor in the valve design since it dictates the resultant force responsible for the reed motion. The presence of a recirculating region on the valve seat may return low pressure levels on the reed surface. This may prevent the perfect valve operating conditions since it reduces the force acting on the reed surface. In view of this, the correct prediction of eventual recirculating regions is a key aspect in the compressor simulation.

The ratio between the diameters of the reed and valve orifices is approximately 1.5 for the compressor being simulated. The diffuser region, situated between the reed and the valve seat, does not have sufficient length to allow either a complete flow development or pressure recovery.

As the valve lift is increased, and the flow inertia becomes stronger, the separation region is increased and the recirculating zone moves into the valve outlet. In such situations, the pressure at the valve outlet may even not reach the discharge pressure condition, giving rise to flow entrainment, as shown in Fig. 7b.

Figure 8 shows the results for vector velocities in zoomed regions of the flow, all of them identified in Fig. 7. Naturally, many of the flow features examined through results for the streamlines can also be observed from these results, such as the flow entrainment in Fig 8a. On the other hand, Fig. 8b shows that the recirculating flow region on the valve seat virtually vanishes at wt = 2.99 rad, point (c), although the valve lift is approximately the same of that at wt = 2.67 rad. There are two reasons for this difference. Firstly, the pressure drop through the valve has significantly decreased when the compressor reaches wt = 2.67 rad. This reduces the mass flow rate through the valve and, as consequence, the same happens with the inertia effects that act on the flow separation. The other aspect, which is less obvious, is that the reed closing motion induces a pressure field that inhibits any flow separation.




An important aspect captured by the simulation, and difficult to detect from streamlines, is the backflow seen between the reed and the seat during the reed closing motion, as can be seen in Fig. 8c for the crankshaft angle wt = 3.13 rad. This is a very undesirable feature related to the valve dynamics that reduces the volumetric efficiency of the compressor. Therefore, in the design of an efficient valve system the dynamics must be tuned so as to minimize this aspect.

At wt = 3.13 rad the piston has already passed through TDC and the in-cylinder flow is seen to occur from the valve orifice to the cylinder wall, owing to the downward piston motion (Fig. 8d).

The pressure field represented in Fig 6d is in line with the valve backflow and also with the flow in the cylinder clearance. Although the pressure difference between the valve outlet and the valve orifice is not very significant, since the backflow rate is not high, the pressure gradient along the cylinder head clearly indicates the flow induced by the piston motion.

Figure 9 shows results for the ratio between effective viscosity, µeff = µt + µ, and molecular viscosity, µ, at two crankshaft positions, wt = 2.80 and 2.99 rad, during the compressor discharge process. The eddy viscosity levels predicted by the Smagorinsky model, Eq. (1), are directly related to the rate of strain Sij. Accordingly, high levels of µeff/µ occur at wt = 2.80, due to the flow strain in the valve orifice and in the cylinder head. As the piston approaches the top dead center, the velocity magnitude in the gap between the piston and the cylinder head decreases and, as a consequence, the same occurs with the levels of µeff/µ there. This can be observed by comparing results of µeff/µ for wt = 2.80 and 2.99 rad.




Conclusions

A methodology has been proposed to simulate reciprocating compressors, with particular attention given to the discharge valve dynamics. In order to reduce the computational time, the solution procedure combines integral and differential formulations. The compressible turbulent flow through the discharge valve was predicted via large-eddy simulation (LES), with the Smagorinsky model for the sub-grid scale motions. Results were seen to capture several important phenomena that occur in the discharge process, such as pressure over shooting in the cylinder and backflow through the discharge valve. Nevertheless, the methodology still requires to be fully validated, with reference to experimental data, before a more conclusive analysis can be provided. In addition to that, future developments will be concentrated on extending the simulation to a three-dimensional geometry and implementing alternative sub-grid scale models.

Auto Air Conditioning Compressor Runs Entire System

When considering how air is cooled in your home or in your car, the auto air conditioning compressor works exactly the same as the one in your house or office. Its job is to move hot air and humidity from an evaporator inside your vehicle to a condenser outside the vehicle by compressing gas inside the system. Without a properly functioning auto air conditioning compressor the cooling effects of the system is nullified.
Since the 1940’s people have been able to ride in comfort the same as they have had the comfort of air conditioning in their homes and in extremely hot and humid climates have been able to enjoy the effects of air conditioning seamlessly, except for short walks between their home and car, and from their car to work. However, if something goes wrong with the auto air conditioning compressor the transit will be much warmer.
The auto air conditioning compressor is essentially a pump with an intake side and a discharge side. On the intake side, refrigerant is pulled from the output of the evaporator coils located inside the vehicle. Inside the auto air conditioning compressor the gas is compressed and sent to the condenser on the outside of the vehicle, along with the heat and humidity drawn from the vehicle.
Newer Requirements Help Protect Environment
In the early days of air conditioning, the gases used in the system were considered dangerous and some, like propane had explosive potential. A gas referred to as R-12, known by its trade name of Freon, has been determined to cause damage to the Earth’s ozone atmosphere. As a result, technicians have to be certified to work with it, or even buy it and in all cases when an air conditioning system is opened the gas must be captured through specialized equipment.
Whenever work is done on an auto air conditioning compressor it must be done by a certified technician and in cases where the compressor must be replaced, a newer upgraded model may be required. A newer gas R-134a is being required in all vehicles after 2010, and if the vehicle is going to have its system filled with the new gas it will also have to be retrofitted with a new auto air conditioning compressor that can produce the higher pressure needed for this gas.
Since the technician has to pay more for the expensive equipment and the gas repair costs are going to be higher as well. Car owners will need to make the decision about paying the cost to replace their auto air conditioning compressor, driving in the heat or perhaps replacing the vehicle.
Roland Parris Jefferson III is an online researcher based out of Los Angeles, California. For free tips, tricks and expert advice on air conditioning, please visit our Auto Air Conditioning Compressor Resource.
Article Source: http://EzineArticles.com/?expert=Roland_Jefferson

Assembly of counter-balance weight of hermetic reciprocating compressor for refrigeration

The assembling process can be divided into two main stages: In the first stage, the sub-assembly of the balancing weight. This involves joining the Crank Weight to the Crank Weight Base by resistance welding. The next stage is to assemble the counter-balance weight to the crankshaft eccentric. The details of the two assembly stages are as follows:

Stage One: Sub-Assembly Process
During the sub-assembly process, the required Crank Weight is welded onto the Crank Weight Base using a resistance-welding machine. Basically, it consists of a jig, a clamp, and two electrodes. Some safety features have also been built into the machine to ensure the safety of the operator.

During operation, the operator will place the required Crank Weight Base onto the jig with the dimples facing upward. The Crank Weight Base will be resting on top of the lower electrode. The correct Crank weight is then placed on top of the Crank Weight Base. By pressing the two “Start” buttons with both hands, the clamp will push the Crank Weight and Crank Weight Base against the jig to align the two parts together. This is followed by the upper electrode moving down to press on the two parts. At this point, high current of about 13kA will flow through the two electrodes, causing the contacts between the Crank Weight and the Crank Weight Base to melt and fuse together. The upper electrode will then retract back, followed by the clamp, and the counter-balance weight is then removed from the jig. The part is now ready for assembly onto the crankshaft.

The sub-assembly process is normally carried out in stand-alone stations to provide the parts required for the main assembly line.

Stage Two: Main Assembly Process
In the main assembly process, the counter-balance weight is assembled onto the crankshaft eccentric by shrink fitting. The equipment used for the shrink fitting process consists of a heater coil, a jig and a timer.

During operation, the operator will place the counter-balance weight onto the jig, which is just above the heater coil. By pressing the “Start’ button, the current will flow through the coil, causing the temperature to rise quickly. This will in turn heat up the counter-balance weight, causing it to expand. After about 3 seconds, the siren will be activated, and the current to the heater coil will be cut off. The operator will then transfer the heated counter-balance weight onto the crankshaft in the main assembly line using a plier and to align the notched portion of the counter-balance weight to the marking on the crankshaft. A punch will then be activated to press on the counter-balance weight against the crankshaft. This will provide good sitting of the balancing weight onto the crankshaft and at the same time helps to cool the counter-balance weight faster by heat transfer.

Processing of counter-balance weight of hermetic reciprocating compressor

Stamping Process
The stamping layout of a counter-balance weight base is divided into eight stations and the operations performed in each station are indicated as hatch area. The detail of each operation is discussed as follows:

a) Station 1: Piercing & Notching
In this station, two pilot holes are pierced to provide accurate positioning of the stock for the subsequent operations. Notching is also performed to make marking on the counter-balance weight base, which will be used for positioning during assembly onto the crankshaft.

b) Station 2: Piercing
The hole for assembly onto the crankshaft is pierced in this station. Stringent but achievable roundness specification has been added to this hole to ensure firm grip with the crankshaft after assembly.

c) Station 3: Piercing
The cavities of the counter-balance weight base are pierced in this station. These cavities are required to control the center-of-gravity position of the part thus providing the necessary balancing force required.

d) Station 4: Chamfering
The hole for assembly onto the crankshaft is chamfered on the reverse side of the stock in this station to facilitate easy insertion during assembly.

e) Station 5: Piercing
The cavity for controlling the heat transfer rate during the assembly process of the counter-balance weight base is pierced in this station.

f) Station 6: Piercing
In this station, the front and the back profile of the design are pierced.

g) Station 7: Nipple
The dimples on the counter-balance weight base are made in this operation to facilitate resistance welding to be carried out later.

h) Profiling & Parting-off
This is the last station of the progressive die, which performs both the profiling and parting off operations. During profiling operation, the top and bottom portion of the stock strip is cut off, revealing almost the complete shape of the counter-balance weight base. At this stage, the part remains attached to the scrap skeleton until the parting-off operation where it is cut off to produce the complete work piece.

Cleaning Process
After the stamping process, the parts are covered with oil, dirt and other contaminants. To remove all these unwanted substances, they will need to undergo a cleaning process. This section is intended to describe the cleaning process of not only the counter-balance weight, but also for all other compressor parts at the end of the fabrication process.

Equipment Used
(a) Aqueous Ultrasonic machine
(b) Baskets to contain parts to be cleaned

Parameters
Cleaning Agent : Petroleum Solvents [3]
Temperature : Room Temperature
Spraying Pressure : 0.2 ~ 0.25 MPa
Cleaning Time : 1.5 ~ 3 minutes
(Actual cleaning time may be adjusted depending on the parts cleaned.)

Procedures
(a) The parts to be cleaned are placed inside the baskets.
(b) The baskets are then placed on the conveyor system that will travel through the Power Washer machine, which includes soaking, rinsing and drying stations.
(c) After going through the ultrasonic machine, the parts are cleaned and ready for compressor assembly.

Process Control
In order to ensure proper cleaning of the parts, the following process control must be adhered:
(a) The direction of spray nozzle must be adjusted to obtain best cleaning effectiveness.
(b) Parts to be cleaned must be placed such that they can be sprayed directly onto the metal surface.
(c) Set up a magnet near the filter of a cleaning bath and spray clean petroleum solvents to the parts at all times.
(d) Care must be taken to clean parts with “Hard to reach area” such as grooves or holes,
(e) After cleaning, the petroleum solvents must be changed if oil films or dirt are remained on the cleaned parts.

Different types of counter-balance weight for hermetic reciprocating compressor

In order to have a better understanding on the design of counter-balance weight, extensive time has been spent on the study of some existing designs commonly used in the industry.

Caulking-Type Balancing Weight
This design is currently used in a series of compressors, and because of its easy availability, it is used as one of the base designs to compare with the new balancing weight. In this design, Caulking Pins are used to fasten the Crank Weight onto the Crank Weight Base. The required number of Crank Weights can be varied to suit the different inertial loads exerted with different model of compressors. Thus for this design, it has the advantage of using the same Crank Weight Base and Crank Weight for different models of compressors. However, this design requires 2 die sets for the production of the parts; one for the Crank Weight Base and the other for the Crank Weight. The design may also involve many parts, especially in the case of volumetric displacement 9.1cm3 and 10.0cm3, which is undesirable for assembly process.

Folding-Type Balancing Weight
In this design, the part is being pressed out and then bent along the fold line. Caulking is then performed to force material into the small hole to hold the folded portion in place. This design reduces the total number of parts required by eliminating the need for caulking pins as required in the caulking-type counter-balance weight. However, this design is found to be patented [1] in the Europe and North America market, and thus cannot be used for the design in this project. This design is currently used in Japan domestic market only.

Welding-Type Balancing Weight
The last type of counter-balance weight observed is the welding-type balancing weight. This design is used in one of the competitor’s compressors. The design is quite similar to the caulking type balancing weight except that the crank weights are spot-welded to the crank weight base instead of caulking. This can help to reduce the number of parts required by eliminating the need for the caulking pins. However, the application of this design is unknown.

The assembly method of the respective types of Counter-Balance Weight to the crankshaft is to be noted. For the caulking- and folding-type balancing weight, they are attached onto the eccentric portion of the crankshaft by interference force fitting, whereas fasteners, such as screws and dowel pins, are used for the welding-type balancing weight. The former will cause formation of slivers during interference force fitting, which is undesirable for quality issue and it also requires higher machining precision, and thus increases the manufacturing cost. The latter will incur additional cost on the fasteners. These existing methods of coupling counter-balance weight to the crankshaft are not cost effective enough, and the formation of the slivers has to be eliminated. Therefore, an alternative way of coupling the balancing weight to the crankshaft has to be explored.

Introduction to Hermetic Reciprocating compressor

Hermetic-Reciprocating compressors typically consist of a crankshaft having an eccentric portion coupled to a compression mechanism, which is driven when the crankshaft rotates. The compression mechanism comprises a piston sliding in a cylinder; the piston operatively coupled to the eccentric portion of the rotating crankshaft by means of a connecting rod, whereby the orbiting motion of the eccentric about the axis of rotation of the crankshaft imparts reciprocating motion to the piston. Due to the dynamic imbalance of the operating compression mechanism, counter-balance weights are often attached to the crankshaft, in some cases directly attached to the eccentric of the crankshaft, to offset the inertial loads generated by the moving members of the compression mechanism and by the eccentric itself.

As the name implies, the function of a counter-balance weight is to serve as the balancing force to offset the inertial load generated in a system. In the case of hermetic reciprocating compressor, the need for an optimum counter-balance weight is of utmost important as it will affect the vibration and noise performance of the compressor. However, with the increasing stiff competition from other compressors’ manufacturers, cost has also become an essential factor in determining the success of the product. Therefore, a new series of welded counter-balance weights have been designed and developed with the intention to minimize compressors’ noise and vibration level at minimal cost.