Purdue UniversityPurdue e-Pubs

International Compressor Engineering Conference School of Mechanical Engineering

2006

Transient Modeling of Flows Through Suction Portand Valve Leaves of Hermetic ReciprocatingCompressorsHusnu KerpicciArcelik A.S.

Emre OguzArcelik A.S.

Follow this and additional works at: http://docs.lib.purdue.edu/icec

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Complete proceedings may be acquired in print and on CD-ROM directly from the Ray W. Herrick Laboratories at https://engineering.purdue.edu/Herrick/Events/orderlit.html

Kerpicci, Husnu and Oguz, Emre, "Transient Modeling of Flows Through Suction Port and Valve Leaves of Hermetic ReciprocatingCompressors" (2006). International Compressor Engineering Conference. Paper 1806.http://docs.lib.purdue.edu/icec/1806

C122, Page 1

TRANSIENT MODELING OF FLOWS THROUGH SUCTION PORT AND

VALVE LEAVES OF HERMETIC RECIPROCATING COMPRESSORS

Husnu KERPICCI1* (Ph.D), Emre OGUZ2

1Arcelik A.S. R&D Center, Fluid Dynamics Group, 34950 Tuzla, Istanbul, Turkey

Phone: +90 216 585 8496 Fax: +90 216 423 3045

E-mail: husnu.kerpicci@arcelik.com

2Arcelik A.S. R&D Center, Thermodynamics Group, 34950 Tuzla, Istanbul, Turkey

Phone: +90 216 585 8446 Fax: +90 216 423 3045

E-mail: emre.oguz@arcelik.com

*Corresponding Author

ABSTRACT The thermodynamic performance of hermetic reciprocating compressors is strongly effected by the design of the suction and discharge port and valve leaves. The experimental indicator or the so called pV diagrams are frequently used to identify the losses caused by the vibration of the valve leaves. In addition to such experimental techniques, extensive research efforts have been spent on the simulation of the thermodynamic cycle of compressors coupled with valve vibrations. However, such simulation models require the so-called flow coefficients both for the ports and the valve leaf openings where these coefficients can be obtained either experimentally or numerically. In this study, the results of the steady state computational fluid dynamics (CFD) analysis conducted for a typical suction port and valve leaf at different lifts and pressure drops are presented. The mass flow rates obtained for different lifts are correlated according to the series orifice model which is widely used in the literature. In the second part of the study, a dynamic pressure difference is applied through the port and the valve leaf and the momentary mass flow rate is calculated via both CFD and the series orifice model employing the flow coefficients derived from the steady state analysis. Both the transient and the cycle integrated characther of the mass flow rates obtained by the two methods are compared to each other and the effects of adapting such a method to the simulation programs are discussed.

1. INTRODUCTION The suction and discharge valves used in hermetic reciprocating compressors are one of the main sources for thermodynamic losses during the operation of the compressors. Although there are experimental techniques such as the indicator or the so called pV diagram to determine the effect of valve vibrations on cylinder pressure, compressor cycle simulation has also been an important tool to investigate the effects of different valve designs. Though the ideal solution of the problem requires a fluid-solid interaction (FSI) solution procedure, simpler methods such as series orifice model for the flow and one degree of freedom modeling of the valve leaf are widely used in the literature because of the computational time and hardware requirements of FSI techniques. Yu et al. (2004) assumed an adiabatic one dimensional flow through the port and the valve leaf and used a single effective flow area coefficient which had been a function of the valve lift. The flow coefficients at different lifts were determined experimentally and incorporated into the compressor simulation program developed by the same authors. Machu et al. (2004) stated that the calculation of transient flow pulsations had been necessary to obtain accurate results from compressor simulation programs and solved the one dimensional, transient, frictionless adiabatic flow equations through the piping system. Coupled with the finite element modeling of the reed valve this approach was stated to give accurate results when the calculated and measured momentary cylinder pressure and valve lift were compared to each other. However, no spesific arguments about the flow thorugh the valve opening

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 2

was cited in this paper. Longo and Caracciolo (2002) applied a transient analytical model for the calculation of mass flows through port and valve leaves where the momentary refrigerant velocity through the valve was correlated to the pressure difference with additional terms to compensate for the inertia effects. However, no spesific arguments about the comparison of steady state and transient models was cited. Courtois et al. (2002) and An et al. (2002) also used steady state formulations for the flow through the valves. Matos et al. (2002) presented a different approach where the pressure distribution and the flow through the valve was simulated based on two dimensional, incompressible, turbulent and isothermal Navier-Stokes equations. Effective viscosity approach was used to model the turbulence effects and the control volume formulation with QUICK interpolation scheme was implemented to obtain the velocity field. However, a simple periodic flow rate condition was assigned to test the validity of the solution for the fluid solid coupling and the real pressure boundary condition was stated to be the next step. Longo and Gasparella (2003), Zhou et al. (2001) and Srinivas and Padmanabhan (2002) also used the effective flow area concept to model the refrigerant flow through the port and valve leaf. Ferreira et al. (1989) simulated the flow through the port and the valve as incompressible, laminar and isothermal and experimentally investigated the pressure distribution on the disk representing the reed valve. Prata et al. (1995) investigated the heat transfer for radial flow through parallel disks with the aid of the naphtaline sublimation technique. Possamai et al. (2001) experimentally investigated the pressure distribution on the disk representing the valve reed for different opening angles and Reynolds numbers. However, most of these studies were conducted at steady state conditions. In the first part of this study, steady state CFD analysis are conducted to determine the flow rate through the port and the valve leaf of a typical hermetic reciprocating compressor at different valve lifts and pressure differences between the suction plenum and the cylinder. The port flow coefficient required for the analytical model was calculated according to the classical discharge coefficient formulations where the orifice coefficient for the valve opening was obtained from the CFD results as a function of the valve lift. In the second part of the study, transient CFD simulations are conducted for specified valve lifts and the temporary mass flow rate calculated by the analytical model was compared to the CFD results. The accuracy of adopting flow coefficients obtained from steady state analysis to a transient calculation is discussed.

2. STEADY STATE ANALYSIS 2.1 CFD Analysis for Flows Through Port and Valve Leaves The geometry of the suction plenum, valve leaf and cylinder assembly considered in this study is given in Figure 1. As it can be seen from the figure, two cross sections are chosen to visualize the pressure distribution and the velocity field. The solid model and the elastic curve of the valve leaf is obtained via FEM analysis and the geometry and the surface mesh were generetad by commercial softwares. TGRID is used to generate volume mesh which is composed of 400,000 cells and Fluent 6.1.22 was used for the CFD analysis. Different valve lifts between 0.5 and 4.5 mm were investigated and pressure differences between 0.1 and 0.4 bar was employed as the boundary condition.

Figure 1. The geometry of the suction plenum, valve leaf and cylinder assembly.

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 3

The velocity field obtained for a pressure difference of 0.2 bar and 1.5 mm valve lift is presented in Figure 2. As it can be seen from the figure, the refrigerant (R600a) tends to flow through the tip opening of the valve and higher velocities occur at the area close to the root. It can also be seen that the flows through the left and right sections of the valve are not balanced due to the geometry of the suction plenum. The mass flow rates for different valve lifts at a pressure difference of 0.4 bar are given in Figure 3 where the actual CFD results are scaled with the nominal mass flow rate of the compressor under investigation at ASHRAE test conditions. It may be interesting to see that the mass flow rates obtained via CFD analysis are as high as 30 times the nominal mass flow rate. However, there are two important factors that should be considered while interpreting these results. First of all, the presented results are for a pressure difference of 0.4 bar which can only occur, if any, at the very first opening of the valve leaf. As it will be seen in the following sections, the time integrated average of the pressure difference during the suction phase is much lower, approximately 0.06 bar. The other factor is that, the nominal rate of mass flow should already be multiplied by a factor of approximately 2.4 to obtain the time integrated average of rate of mass flow during the suction phase since this phase lasts for only 8-9 ms. An interesting feature observed in Figure 3 is the exponential characther of the mass flow rate. When the valve lift is around 0.5 mm, 100 % increase in the lift gives an almost 400 % increase in the flow rate. However, for a lift of 1.5 mm doubling the lift yields an increase of 50% in the mass flow rate. Since this figure shows the combined throttling effects of the port and the valve leaf, it may be argued that the restriction of the port becomes dominant after a certain valve lift and it may not be feasible to have higher lifts anymore.

Figure 2. Velocity contours for ∆p: 0.2 bar, x: 1.5 mm

Valve lift (mm)

0 1 2 3 4 5

Nor

mal

ized

Rat

e of

Mas

s Fl

ow

0

5

10

15

20

25

30

35

Figure 3. Normalized rate of mass flow as a function of valve lift for ∆p: 0.4 bar.

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 4

2.2 Analytical Modeling and Derivation of Flow Coefficients The compressor simulation programs need to calculate the momentary flow through the port and the valve leaf as a function of both the relevant pressure difference and the valve lift. Most of the models available in the literature adapt the so called flow coefficients which are derived either experimentally or numerically. Although there are various approaches to the definiton of flow coefficients, the series orifice model which is given by equation (1) is employed in this study:

( ) p2KAm e

.∆ρ= (1)

The left hand side of this equation represents the momentary rate of mass flow in kg/s through the port and the valve and the (KA)e term represents the combined effective flow area of the port and the valve. The density of the refrigerant at the upstream is represented by ρ where ∆p, the total pressure difference through the port and the valve leaf, is calculated according to the flow direction (i.e. for flows during the suction phase the pressure difference is calculated by subtracting the cylinder pressure from the plenum pressure and vice versa for back flows). The combined effective flow area can be calculated by equation (2):

( ) ( ) ( )2

v2p

2e KA

1KA

1KA

1+= (2)

In this equation Kp and Kv represent the flow coefficients for the port and the valve leaf and Ap and Av are the geometric flow area of the port and the valve opening. It should be noticed that the geometric area of the port is a constant where the geometric flow area of the valve is a function of the valve lift. In addition to this, the flow coefficient for the valve can also be a function of the valve lift and the flow conditions (i.e. Reynolds number). The first step in the derivation of the flow coefficients is the calculation of the orifice coefficient for the port which is based on the emprical discharge coefficient formulations in the literature. Since the mass flow rate, density and the pressure difference are known from the CFD results, the combined effective flow area can be obtained via equation (1). After calculating the port discharge coefficient and the geometric flow area of the valve, equation (2) will yield the desired flow coefficient for the valve as a function of the valve lift. The normalized coefficients for the spesific model under consideration are given in Figure 4, where the actual coefficients are normalized with the maximum value obtained for 1.5 mm valve lift.

Valve lift (mm)

0 1 2 3 4 5

Nor

mal

ized

coe

ffici

ents

for t

he v

alve

0.6

0.7

0.8

0.9

1.0

1.1

Figure 4. Normalized flow coefficients for the valve leaf

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 5

3. TRANSIENT ANALYSIS 3.1 Transient CFD Analysis for Specified Valve Lifts After the steady state analysis, transient CFD analysis at certain valve lifts are also conducted for the geometry under consideration. The suction plenum – cylinder pressure difference as a function of time obtained from experimental studies on a different compressor model is given in Figure 5, where the pressure difference for the suction phase is repeated for several cycles without the compression and discharge phases. The results of the CFD analysis after the cyclic convergence are presented in Figure 6 where the momentary mass flow rates are normalized with the nominal mass flow rate of the compressor. As it can be seen from Figure 6 the mass flow rate follows a similar pattern to the pressure drop variation for both of the valve lifts under consideration. It may be noticed that the time integrated average mass flow rate that would be obtained from this figure would still be higher than the actual mass flow rate of the compressor. The reasons for this situation are as follows: 1) The applied experimental pressure difference belongs to another compressor model with a higher capacity, 2) There is still a factor around 2.5 to account for the suction phase within a cycle and 3) Since the suction phase pressure difference is repeated continuously, the negative influence of the compression and discharge phases on the momentum of the flow is not taken into account (i.e. in the real case the flow should always start from zero at the beginning of the cycle).

Time (sec)

0.00 0.01 0.02 0.03 0.04 0.05

Pres

sure

diff

eren

ce (P

a)

0

5000

10000

15000

20000

25000

Figure 5. Transient pressure difference for suction plenum and cylinder (suction phase repeated)

Time (sec)

0.020 0.022 0.024 0.026 0.028 0.030 0.032

Nor

mal

ized

rate

of m

ass

flow

0

5

10

15

20

25

30Lift: 1.5 mmLift: 3.5 mm

Figure 6. Transient CFD analysis results for two different valve lifts.

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 6

3.2 Transient Calculations via Flow Coefficients The transient mass flow rate that would occur under the pressure drop profile given in Figure 5 is also calculated via the flow coefficients obtained from steady state CFD analysis. As it can be seen from Figure 7, the analytical mass flow rate closely follows the pressure drop profile for a certain valve lift. As a consequence of equation (1), when the valve lift is constant the mass flow rate scales with the square root of the pressure difference. As expected, even very small pressure pulsations such as the one that occurs at around 0.032 sec may establish flow rates. This is of course due to the analytical formulation which does not contain any inertia/momentum terms.

Time (sec)

0.020 0.022 0.024 0.026 0.028 0.030 0.032 0.034

Pres

sure

dro

p

0

5000

10000

15000

20000

25000

Nor

mal

ized

mas

s flo

w ra

te

0

5

10

15

20

25

30Pressure drop Normalized mass flow rate

Figure 7. Analytical mass flow rate and the pressure drop relationship (Lift: 3.5mm)

3.3 Comparison of Results The analytical mass flow rate which is based on flow coefficients derived from steady state CFD analysis is compared to the mass flow rate obtained directly from transient CFD analysis and is presented in Figure 8. As it can be seen from the figure, when compared to the analytical results, the computational mass flow developes slower because of the inertia at the beginning of the cycle. In addition to this, computational results show that higher peaks in the flow rate could be achieved when the momentum of the flow is taken into account. A slight shift in the time domain can also be observed because of these effects. One interesting point to note is the behaviour of the flow under small amplitude oscillations. It can be seen that the small pressure pulsation around 0.021 sec establishes some flow whereas this low amplitude flow oscillation can not be observed in the CFD results. Although the valve lift has been constant during these analysis, it is thought that the comparison of the time integrated average mass flow rates obtain by the two methods would be a good indicator about the transient flow effects and the accuracy of such an analytical method. For a valve lift of 1.5 mm it is found that the analytical method gives 3.1% less mass flow rate than that of the computational result. However, for a valve lift of 3.5 mm the analytical mass flow rate is 7.7% higher than the computational counterpart. If it is assumed that the average valve lift during the suction phase is approximately 2 mm, then it can be concluded that the error associated with such a method would be on the order of ± 5 %. However, these numerical results are closely coupled with the spesific geometry and pressure pulsation profile under consideration. Therefore it may be necessary to examine the spesific situation before implementing such a method to a compressor simulation program.

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 7

Time (sec)

0.020 0.022 0.024 0.026 0.028 0.030 0.032

Nor

mal

ized

mas

s flo

w ra

te

0

5

10

15

20

25

30AnalyticalComputational

Figure 8. Comparison of analytical and computational mass flow rates (Lift: 3.5mm)

4. CONCLUSIONS

In this study, steady state CFD analysis are conducted for a spesific suction plenum-valve leaf-cylinder assembly of a hermetic reciprocating compressor for different valve lifts and pressure drops. The well known flow coefficient and series orifice concepts are applied as the analytical model and the necessary coefficients are derived from the steady state analysis. In the second part of the study a transient pressure drop profile is applied as the boundary condition with specified valve lifts and the mass flow rates calculated via the flow coefficients and the transient CFD analysis are compared to each other. According to the results of this study it may be concluded that: • The suction plenum geometry may have a strong effect on the velocity field through the port and valve leaves

of hermetic reciprocating compressors and therefore detailed simulations or experimental observations are needed to obtain the flow coefficients in a realistic manner.

• The flow coefficients associated with the valve leaves may be a function of the valve lift and pressure drop. In

order to increase the accuracy of cycle simulation programs detailed knowledge on these functions is needed. • When the flow coefficients derived from steady state CFD simulations are used to calculate the transient mass

flow rate for a cycle, the flow would develop quicker; however the peak flow rates tend to be lower because of the inertia/momentum effects. The error associated with the time integrated average mass flow rate calculation is found to be on the order of 5% for the spesific geometry and pressure pulsation profile.

• The mass of the fluid entrained in the port and valve leaf opening can be incorporated as an inertia term to the

classical steady-state flow formulations to enhance the accuracy of such methods.

REFERENCES An, K.H., Lee, J.H., Lee, I.W., Lee, I.S., Park, S.C., 2002, Performance Prediction of Reciprocating Compressor,

16th Int. Compressor Engineering Conference at Purdue, C7-4. Courtois, S., Arnoult, E., Wagstaff, P., Gavric, L., 2002, On Finite Element Modeling of Valve Dynamics: Impacts,

Oil Stiction, Gas Flow…, 16th Int. Compressor Engineering Conference at Purdue, C13-2. Ferreira, R.T.S., Deschapms, C.J., Prata, A.T., 1989, Pressure Distribution Along Valve Reeds of Hermetic

Compressors, Experimental Thermal and Fluid Science, vol: 2, 201-207.

International Compressor Engineering Conference at Purdue, July 17-20, 2006

C122, Page 8

Longo, G.A., Caracciolo, R., 2002, Unsteady State Analysis of Hermetic Reciprocating Compressor: Heat Transfer

Inside the Cylinder and Valve Dynamics, 16th Int. Compressor Engineering Conference at Purdue, C4-4. Longo, G.A., Gasparella, A., 2003, Unsteady State Analysis of the Compression Cycle of a Hermetic Reciprocating

Compressor, Int. Journal of Refrigeration, vol: 26, 681-689. Machu, G., Albrecht, M., Bielmeier, O., Daxner, T., Steinrück, P., 2004, A Universal Simulation Tool for Reed

Valve Dynamics, 17th Int. Compressor Engineering Conference at Purdue, C045. Matos, F.F.S., Prata, A.T., Deschamps, C.J., 2002, Numerical Simulation of the Dynamics of Reed Type Valves,

16th Int. Compressor Engineering Conference at Purdue, C15-2. Possamai, F.C., Ferreira, R.T.S., Prata, A.T., 2001, Pressure Distribution in Laminar Radial Flow Through Inclined

Disks, Int. Journal of Heat and Fluid Flow, vol: 22, 440-449. Prata, A.T., Pilichi, C.D.M., Ferreira, R.T.S., 1995, Local Heat Transfer in Axially Feeding Radial Flow Between

Parallel Disks, Journal of Heat Transfer Transactions of the ASME, vol: 117, 47-53. Srinivas, M.N., Padmanabhan, C., 2002, Computationally Efficient Model for Refrigeration Compressor Gas

Dynamics, Int. Journal of Refrigeration, vol: 25, 1083-1092. Yu, P.Y., Hsiao, T.L., Cheng, Y.C., Chang, Y.C., 2004, Performance Estimation of Hermetic Reciprocating

Compressor with Computer Model, 17th Int. Compressor Engineering Conference at Purdue, C021. Zhou, W., Kim, J., Soedel, W., 2001, New Iterative Scheme in Computer Simulation of Positive Displacement

Compressors Considering the Effect of Gas Pulsations, Journal of Mechanical Design Transactions of the ASME, vol: 123, 282-288.

ACKNOWLEDGEMENT The authors would like to thank to Mr. Semsettin Eksert, director of the R&D Center, Mr. Fatih Ozkadi, manager of the mechanical technologies group at the R&D Center and to Mr. Tekin Tekkalmaz, manager of the product development department at the Eskisehir Compressor Plant for their endless encouragement.

International Compressor Engineering Conference at Purdue, July 17-20, 2006