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International Engineering Conference School of

1994 Investigation of Discharge Flow Pulsation in Scroll Crompressors T. Itoh Mitsubishi Heavy Industries Ltd.

M. Fujitani Mitsubishi Heavy Industries Ltd.

K. Takeda Mitsubishi Heavy Industries Ltd.

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Itoh, T.; Fujitani, M.; and Takeda, K., "Investigation of Discharge Flow Pulsation in Scroll Crompressors" (1994). International Compressor Engineering Conference. Paper 1056. https://docs.lib.purdue.edu/icec/1056

This document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact [email protected] for additional 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 INVESTIGATION OF DISCHARGE FLOW PULSATION IN SCROLL

TAKAHIDE ITOH * MAKOTO FUJITANI* KIMIHARU TAKEDA**

* Nagoya Research & Development Center MITSUBISHI HEAVY INDUSTRIES, Ltd. Nagoya japan ** Air-Conditioning & Machinery Works MITSUBISHI HEAVY INDUSTRIES, Ltd. Aichi japan

ABSTRACT This paper presents the theoretical and experimental study on the discharge pressure, including high frequency pressure pulsations. FLIC method, which is one of the numerical fluid analysis methods, was applied to evaluation of the scroll discharge pressure. Each of finite element cells changed the mesh shape and the area size as moving the orbiting scroll. The analyzed discharge pressure including the high frequency pressure pulsation was compared with measurement results. The amplitude and the frequency of pressure pulsations had good agreement with experimental results. Finally the pressure wave-guide was developed for reducing the pressure pulsation. Then the reduction effect of the pressure wave-guide was confirmed analytically and experimentally.

INTRODUCTION Noise reduction is one of the most important problems for scroll compressors. A scroll compressor has the finite volume ratio which is determined by scroll involute dimensions.(such as base a circle radius, a orbiting circle radius and turns of scroll ,etc.) When a pressure ratio of discharge pressure to suction pressure is higher than the designed pressure ratio which is given by the volume ratio and the specific. heat ratio of a gas, we call this condition the high pressure ratio condition. In this case, the counter flow from the discharge port to the outer fluid pockets of the scroll occurs at the moment of three fluid pockets joint together. The pressure pulsation is caused by this counter flow. We made it clear that there is the interrelation between the noise and the pressure pulsation and developed the pressure pulsation reduction mechanism. The following items were conducted. ( 1)Analysis of the pressure pulsation in the discharge port and the outer compression fluid pockets by computational (CFD). (2)Experimental investigation of the pressure pulsation in the discharge region. (3)Development of the pressure pulsation reduction device. ( 4) Measurement of the pulsation level in the actual compressor with the reduction devise.

COMPUTATIONAL FLUID DYNAMICS STUDY Method of analysis Computational fluid dynamics(CFD) study was conducted using the FLIC method (fluid­ in-cell method). The FLIC method is one of the CFD code of finite volume method(FVM). It is suitable to analyze compressible non-viscous fluid including shock wave. In this study, The one-dimensional analysis is applied to the pulsation of the discharge port and the outer compression fluid pockets. The refrigerant gas is treated as a ideal gas and the effects of the oil in scroll fluid pockets were not taken into consideration.

683 The fundamental equations of FLIC method in the vector Eulerian equation are given as follows. aF aFu _ f ilt + (!X - (1) iJP iJPu fl= 0 f2 =- - f3 = -- i)X iJX p: density, u:velocity, E:energy, P:pressure, t:time, x:position of x-axis. Fig.1 shows cells in the fluid pocket. Eq( 1) is integrated in cell i.

xi+ 1/2 xi+l/2 aF aFu } _ (2) {iJt + iJX dx- ffdx I Xi-}/2 Xj-J/2

In the first step, the transport term which is the second term of left side in eq(2) is neglected, and eq(2) is approximated in discrete system which is shown in Fig.l. The intermediate value F is given in eq(3).

n .M { xi+ 1 /2 } (3) F. = F - b.X f f dx I Xj-l/2

The upper suffix n is the value in timet. The intermediate value F means the change of the conservation values (such as mass, momentum and energy) in Lagrangian coordinate. In the second step, the intermediate value F is transformed by the transport term for fitting Eulerian coordinate. The boundary velocity between cell i and cell i + 1 is given in eq( 4). Ui + Ui+l (4) ui+l/2 = 2 If the velocity is larger than zero, the intermediate value F flows out from cell i to cell i + 1. The other case, the intermediate value F flows in from cell i + 1 to cell i . The boundary velocity between cell i and cell i- 1 is given in eq( 5). Ui + Ui-1 (5) ui-1/2 = 2 If the velocity is larger than zero, the intermediate value F flows in from cell i -1 to cell i . The other case, the intermediate value F flows out from cell i to cell i -1. At the time t+ M the conservation value is given in eq(6).

I\1+1 ~if-:~ { [Fi+102 + Fi (1-02) ]ui+112-[Fi-101 + Fi (1-01) ]ui-1/2}

1--- 1--- ui-1 /2;e:O ui+112<0 (6) 61 62 = 0--- 0--- ui-112<0 ui+ 1/22:0

684 The upper suffiX n+l is equal to the timet+ M. The compression process is regard as the volume change of each cell. When the 1 volume changes from vn to vn+ after the time I! t , Pressure P and temperature T in fluid pockets are given in eq(7).

yn }K n }K-1 p~+l = ~ _i_ -f.I+l = T.I ~ (7) 1 1 { v~+l 1 1 { v~+l 1 1

K: specific heat ratio The time step is limited by the time in which pressure wave passes through the minimum cell.

Model Fig.2 shows the analysis model for the discharge port and the outer compression fluid pockets in the scroll compressor. Total number of the cell is 53 in this model. Each cell was assumed that it was a straight tube with a same section area. The total length of cells is given the acoustic resonance length of the fluid pocket instead of the real length of scroll. The orifice theory was applied to the thin area between the discharge port and the outer compression fluid pockets. The thin area of the scroll mesh and the opening area of discharge port are calculated by numerical data of the scroll center shape. The boundary condition (such as the velocity, the pressure and the temperature) is determined by method of characteristic curves. The motion of the discharge lead valve is treated as the cantilever. The motion equation of the distributed mass is transformed to the motion equation of the concentrated load by Rayleigh approximation. The motion equation is solved in the method of Runge­ Kana-Gill and results of the motion are applied to the fluid analysis as the discharge coefficient.

PRESSURE MEASUREMENT OF SCROLL COMPRESSOR The pressure in scroll fluid pockets was measured by 7 pressure transducers which were located along by the fixed scroll. Pressure diagrams were drawn combining outputs of pres~ure transducers. The test compressor was a hermetic type compressor for the packaging air­ conditioning having 167 ml displacement. Outputs of 7 pressure transducers were transformed into digital signals by AID converter at a time. The sampling time of AID converter was 20~s. The performance of compressor was measured in the calorimeter.

RESULTS OF ANALYSIS AND MEASUREMENT Fig.3 shows the result of the simulation in the over compression condition (Hp=l.47 MPa, Lp=0.64 MPa), and Fig.4 shows the result of the measurement in same condition. Simulated figures of the over compression power loss were equal to the experiment within the range of 3%. Fig.S and Fig.6 show results of the simulation and measurement in the high pressure condition (Hp=2.35 MPa, Lp=0.39 MPa). The analyzed frequency of the pressure pulsation agreed with the measurement result. From this result, It was confirmed that the hypothesize that the total length of cells was given in the acoustic resonance length was appropriate.

685 Concerning the peak to peak value of the pressure pulsation, the calculated value was 0.2 MPa and the measurement value was 0.28 MPa. The calculated amplitude of pulsation had a tendency to underestimate comparing with results of measurement. However it was confirmed that the error between the simulation and the measurement is within 3 dB in the high pressure condition. The pressure pulsation is amplified in the end of the compression fluid pocket. However this effect is not considered in this modeL It is the reason why the error occurred

NOISE REDUCTION DEVICES The cause of the pressure pulsation in compression fluid pockets is explained with the transient response of the pressure shock wave. The pressure fluctuation is excited in response to the impulsive shock wave which is occurred in the pressure difference between the discharge port and the outer compression fluid pockets. For reducing the pressure pulsation, it is important to prevent the impulsive pressure shock wave from transmitting to the outer compression fluid pockets. In the compressor without the discharge valve, the pressure fluctuation in the outer fluid pockets shows the step response. In this case, the discharge pressure pulsation is reduced, however the performance of the compressor deteriorated in the high pressure ratio condition. From these facts, the pressure balance mechanism through thin gaps of two scroll raps was developed. By this mechanism, the pressure difference between the discharge port and the outer compression fluid pockets was reduced before the joint of two pockets through the discharge port. That mechanism is called the pressure wave-guide. Fig. 7 shows the scheme of the pressure wave-guide. The height of the pressure wave­ guide is 10 mm. Fig.S shows the effect of the pressure wave-guide by the experiment and Fig.9 shows the effect by the simulation in the high pressure ratio condition (Hp=2.35 MPa, Lp=0.39 MPa). In Fig.9 the pressure pulsation is 0.10 MPa. Comparing with Fig.4 the pressure pulsation is reduced about 9 dB. The pressure pulsation in the simulation is reduced about 8 dB similar to the result of the measurement. From these results, it is recognized that the pressure wave-guide has a good effect to reduce the pressure pulsation in the discharge fluid pocket and the effect of the pressure wave-guide can be estimated by the simulation. Fig.lO shows the noise reduction effect of the pressure wave-guide. There is a obvious difference between the noise of the test compressor with the pressure wave-guide and the noise of a current compressor. Fig.ll shows simulation results of the effect changing the, height of the pressure wave-guide when the pressure ratio is 5. The characteristic of the pressure wave-guide effect is a monotone non-decreasing function within the limits of the analysis. However it is considered that the pressure pulsation increases on the contrary in case that the surplus area of the pressure wave-guide is given. The large area of the pressure wave-guide is easy to transmit the impulse pressure shock wave. In addition to the problem mentioned above, the pressure wave­ guide deteriorates the efficacy of compressor in proportion to the area. It is important to find out the best area of the pressure wave-guide making a compromise with the performance and the noise reduction.

CONCLUSION In this study, we get the conclusions as follows. ( 1 )The simulation for analyzing the pressure in the compression fluid pocket including the high frequency pulsation was developed. It is possible to analyze the pressure pulsation in the compression fluid pockets in an error of less than 3 dB. (2)The pressure wave-guide was developed to reduce the pressure pulsation.

686 ( 3 )It is confirmed that the pressure pulsation was reduced about 9 dB in the actual compressor with the pressure wave-guide. , ( 4 )The estimation of the reduction ratio by the simulation had a good agreement with the experiment.

REFERENCE ( 1 )Kato, Adachi, "A Numerical Analysis of Scavenging Efficiency in a Two-Stroke-Cycle Internal Combustion Engine." JSME, Vol. 53, No. 485, Jun. 1987. (Z)Hirano, et al.,. "Development of High Efficiency Scroll Compressors for Heat Air Conditioners." Mitsubishi Heavy Industries, Ltd., Tech. Rev. Vol. 26, No.3, Oct. 1989. (3)Richard ]. R, Timothy C. W, "Scroll Compressor Flow Modeling: Experimental and Computational Investigation." 1990 Int. Comp. Eng. Conf. at Purdue, 1990.

Discharge Pipe(Cells) Cell i-1 Cell i Cell i+l -·---·----·- .----....J...J'----,::>----0 i scha rge Chamber (Volume) 0 iscahrge Valve Boundary Boundary i-1/2 i+l/2

Fig.l Discrete System for FVM

3. 0 ,...._ 2.5 n:! Fig.2 Analysis Model ! 2.0 I~ :~ ), )_ ~ ~ 1.5 ~ / / i?l / ~ 1.0 ' v

Cl.. o. 5 o. 0 360 270 180 90 D -90 -180 -270 -360 Rotating Angle( • ) Fig.3 Pressure Diagram(Simulation) 0.5

0. 0 ..____._ _ _,__-l_ _,___L-...__,__ _,___J 3. 0 360 270 180 90 0 -90 -180 -270 -360 ,...._ 2. 5 "'\ ~ r"\ ~ Rotating.Angle( • ) ~ 2.0 J J Fig.4 Pressure Diagram(Measurement) Q) 3 1.5 ! f VI VI ~ 1.0 / / Cl.. o. 5 ------o. 0 360 270 lBO 90 0 -90 -180 -270 -360 Rotating Angle( • ) Fig.5 Analysis of Pulsation

687 3.0 ,...... , z. 5 ro .._.,51.: 2. 0

(lJ .... 1.5 ::l (I) (I) ..r::. 1.0 -Cl ~ 0> c.. ::.:: 0.5 0.0 ....0 ..,u Pressure 360 270 180 90 0 -90 -180 -270 -360 Wave-guide Rotating Angle( o ) Fig.7 Scheme of Pressure Wave-Guide Fig.6 Measurement of Pulsation

3.0 3.0 -.... r -.... r ..--.. 2. 5 ";;! 2. 5 ro !!!; .._., 2.0 j I .._.,~ 2. 0 (lJ !'/ ~ 1.5 ~ \.5 11 ::l (I) (I) (I) ~ \.0 / / ....Q) 1.0 c... ~ p... 0.5 0.5

0 ~.___._ _ _.__~..___1._....1....-~J.._-----l. _ __.l 0.0 -- o. 360 270 180 90 0 -90 -180 -270 -'360 360 270 180 90 0 -90 -180 -270 -'360 o ) Rotating Angle( o ) Rotating Angle( Fig.8 Pressure Diagram with Wave-Guide Fig.9 Pressure Diagram with Wave-Guide (Measurement) (Simulation)

.f!· e 100 'J' ~ 15 :::j. 0 c w 0 3 > 10 :1 Q) t "' __. :1 95 al "tJ a; &! 5 ?? ~ CD it 0 n.. ~"' 0 2 3 4 5 6 7 0.1 0.2 0.3 Pressure Ratio (Height of Wave - guide) / (Scroll Height) Fig.lO Noise Reduction Effect Fig.ll Noise Reduction Effect (Pressure Ratio Change) (Wave-Guide Height Change)

688