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International Conference School of

2018 Transfer Analysis of Linear Compressor Based on a Lumped Parameter Model Han Gyeol Ji Graduated School of Smart Interdisciplinary Engineering, Pusan National University, Busan, Korea, [email protected]

G.M. Choi Pusan National University, [email protected]

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Ji, Han Gyeol and Choi, G.M., " Analysis of Linear Compressor Based on a Lumped Parameter Model" (2018). International Compressor Engineering Conference. Paper 2585. https://docs.lib.purdue.edu/icec/2585

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Heat Transfer Analysis of Linear Compressor Based on a Lumped Parameter Model

Han-Gyeol Ji1, Gyung-Min Choi2*

1Graduated School of Smart Interdisciplinary Engineering, Pusan National University, Busan, Korea [email protected]

2Department of Mechanical Engineering, Pusan National University, Busan, Korea [email protected]

* Corresponding Author

ABSTRACT

In this study, Heat transfer and distribution in a linear compressor was analyzed by lumped parameter model. The linear compressor has a more complicated suction structure than the conventional compressor because the acts as a suction muffler. For this reason, superheating in suction is a very important factor in linear compressor design. The control consists of the solid element and the fluid elements divided into simplified elements assumed to have uniform thermodynamic properties. To verify the numerical analysis, an experiment was conducted by using calorimeter at steady state. The results of the numerical analysis show good agreement with the experimental data. Suction refrigerant temperature is influenced by mixing ratio at inlet of a muffler. As the mixing ratio approaches to 1, the suction refrigerant flows indirectly. In case of the mixing ratio is 0, the suction refrigerant temperature is 3.45% higher than the mixing ratio is 1. In addition, insulating gasket which prevent heat transfer from discharge part decrease temperature of suction refrigerant.

1. INTRODUCTION

Refrigerator is made up of compressor, condenser, expansion valve and to produce the cooling capacity. Approximately 80% of the total power is consumed in the compression process (Kim et al., 2011). Therefore, studies on the efficiency improvement of have been actively carried out.

In order to improve the efficiency of the compressor, it is necessary to increase the volume efficiency, which is closely related to the temperature of the suction refrigerant. The heat transfer to the suction refrigerant occurs for various reasons. The density of suction refrigerant is decreased as the temperature of suction refrigerant is increased. In the linear compressor, the inside of the piston serves as a muffler to reduce the flow resistance, and an indirect suction type is used (Sim et al., 2000). Therefore, since the temperature rise of the suction refrigerant in the linear compressor has a complicated mechanism, a method of predicting the heat transfer phenomenon and the temperature distribution in the compressor is required.

In this study, the heat transfer and temperature distribution of a linear compressor are analyzed using lumped parameter model and investigate the cause of temperature increase of the suction refrigerant.

2. HEAT TRANSFER MODEL

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Figure 1: Simplified compressor parts used in the model

The control volume consists of dividing the solid element and the refrigerant passage in the linear compressor. For each control volume the thermodynamic quantities and the temperature are constant throughout each control volume (Ooi, K. T, 2003). The components of compressor were divided with a relatively simpler geometry as shown in Figure 1. In the case of the refrigerant flow path, the flow path from the suction to the discharge process was divided considering mixing and circulation.

Table 1 : Elements number and description

No. Element No. Element No. Element No. Element 1 Suction shell 7 Piston 13 Discharge cover RF5 Gas in port 2 Mid shell 8 Cylinder 14 Discharge RF6 Gas in compression chamber 3 Suction pipe 9 Inner stator RF1 Gas in mixing region RF7 Gas in discharge cover 4 Discharge shell 10 Rotor RF2 Gas in muffler entrance RF8 Gas in discharge pipe 5 Cover rear 11 Motor RF3 Gas in mid of muffler RF9 Gas in discharge shell 6 Muffler 12 Outer stator RF4 Gas in muffler exit RF10 Gas in suction shell

Table 1 presents the list of element number and description and Figure 1 shows a schematic view of simplified compressor parts

2.1 Governing Equations Applying the first law of for i element can be expressed by equation (1).

푛 푛 푑(푚푖푢푖) 푄̇ + ∑ 푚̇ ℎ = 푊̇ + ∑ 푚̇ ℎ + (1) 푖 푗,푖 푗,푖 푖 푗,푘 푗,푘 푑푡 푗=1 푗=1

Since the control volume is assumed to be a uniform temperature, it can be assumed that the of the inlet and outlet are the same for each control volume. Also, since the volume change of each control volume is negligible, Equation (1) can be simplified to equation (2).

̇ 푄푖 = 0 (2)

The total heat transfer rate is the sum of the heat transfer rate to or from other elements and heat generation within i element. Therefore, it can be expressed by equation (3).

푄̇푖 = ∑ 퐻푖,푗(푇푗 − 푇푖) + 푆푖̇ = 0 (1) 푗=1

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Convective heat transfer can be expressed by equation (4) according to Newton's cooling law. Also, the conduction heat transfer is expressed by equation (5) and radiative heat transfer is expressed by equation (6)

퐻푖,푗 = ℎ푖퐴푖,푗 (4) 퐻푖,푗 = 푘푖퐴푖,푗⁄∆푥 (5) 2 2 퐻푖,푗 = 퐴푖,푗휀휎(푇푖 + 푇∞)(푇푖 + 푇∞) (6)

However, since the temperature difference between the elements is relatively small, radiative heat transfer is not considered in this study. Applying the first law of thermodynamics for compression chamber can be expressed by equation (7). And compression work can be expressed by equation (8)

푚̇ 푠푢푐ℎ푠푢푐 + 푊̇푐표푚푝 = 푚̇ 푑푖푠ℎ푑푖푠 + 푄̇푅퐹6→8 + 푄̇푅퐹6→7 (7) 1 푛 푃푑푖푠 푃푠푢푐 푛 (8) 푊푐표푚푝 = ( ) 푃푠푢푐(푉1 − 푉4)(1 − ( ) ) ∙ 퐻푧 푛 − 1 푃푠푢푐 푃푑푖푠

2.2 Convective Heat Transfer Coefficient Since the compression process is similar to a reciprocating compressor, Adair's heat transfer equation is used for the compression process.

푁푢 = 0.053푅푒0.8푃푟0.6 (9)

Convective heat transfer coefficients for the other elements were calculated using the convective heat transfer equation of plate flow, the internal flows and external flows in the tube considering the shape of elements as well as the flow pattern of the refrigerant.

푁푢 = 5 + 0.015푅푒푎푃푟푏 , a=0.88-0.24/(4+Pr), b=0.3333+0.5e0.6Pr ( 10) 5 4/5 0.62푅푒1/2푃푟1/3 푅푒 8 푁푢 = 0.3 + [1 + ( ) ] (11) [1 + (0.4/푃푟)2/3]1/4 282000 푁푢 = 0.037푅푒0.8푃푟1/3 for 푅푒 < 5 × 105 (12)

2.3 Mixing Ratio To reduce noise and vibration in the compressor, refrigerant flows through the indirect suction structure during the compression process. As a result, the suction refrigerant and the refrigerant in the shell are mixed. The mixing ratio(MR) refers to the ratio of the mass flow rate of the suction refrigerant to the refrigerant inside the shell. MR can be expressed by equation (13). The closer the mixing ratio is to zero, the more suction refrigerant flow directly (Park et al., 2017).

푄̇푀푅 = 푀푅 ∙ 푄̇푠ℎ푒푙푙 + (1 − 푀푅) ∙ 푄̇푠푢푐푡푖표푛 (13)

3. RESULTS AND DISCUSSION

3.1 Experimental Validation To verify the model, the temperature measurement in linear compressor with the refrigerant R600a was carried out. The temperature was measured at the outside temperature 25℃ in the steady state. Figure 2 shows the result of comparing the temperature of each part of the linear compressor with the experimental value. Prediction is in reasonably good agreement with the measured results. The maximum discrepancy occurs at number 11 located motor and is about 13%. The discrepancies are caused from geometric simplification and convective heat transfer coefficient.

3.2 Sensitivity Analysis The heat transfer analysis of the compressor for the ambient temperature change was performed. The inlet

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110 Measured 100 Predicted

) 90

 ( 80

70

60

50

40 Normalized temperature Normalized 30

20

1

2

3

4

5

6

7

8

9

10

11

12

13

14

RF1

RF2

RF3

RF4

RF5

RF6

RF7

RF8 RF9 Element no. RF10 Figure 2: Comparison between the measured results and prediction 110 110 100 70 100 90 90 80 60

70 80 C)

 50 60 70

50 60 40 40

Temperature( 50 30

30 temperature(%) Normalized Normalized temperature(%) Normalized 20 40

10 20 30 0 10 20 300 140 2 50 3 60 4 5 0 6 1 2 3 4 5 6 Ambient temperature(C) Air flow rate(CMM) Air flow rate(CMM) Piston(7) Gas in muffler exit(RF4) Piston(7) Discharge shell(4) Gas in Gasmuffler in muffler exit(RF4) entrance(RF2) Discharge shell(4) Gas in muffler entrance(RF2) Gas in discharge pipe(RF8) Gas in mid of muffler(RF3) Gas in discharge pipe(RF8)Suction shell(1) Gas in mid of muffler(RF3) Suction shell(1) Figure 3: Ambient temperature versus compressor Figure 4: Air flow over compressor versus compressor temperature temperature of refrigerant was maintained at 25℃ and the ambient temperature was increased from 10℃ to 50℃. Figure 3 shows the compressor temperatures with the ambient temperature. As expected, the temperature of all the compressor elements increases as the ambient temperature increases. Figure 4 shows the temperature change of the compressor with air flow rate. As the air flow rate increases, the convective heat transfer coefficient increases and the temperature decreases in the all the compressor elements. Since the convective heat transfer coefficient is a nonlinear value for the air flow rate, the temperature also shows the same nonlinear decreasing trend. The temperature of the shell and gas in discharge pipe were the most sensitive to ambient temperature and air flow rate because of the direct heat transfer with the ambient condition.

3.3 Effects of Mixing Ratio In general, as the mixing ratio decreases, the efficiency of the compressor increases because the temperature of the suction refrigerant decreases. However, the lower mixing ratio reduces the cooling effect of compressor components and the heat transfer to the suction refrigerant increases.

Figure 5 shows the temperature of the mixing region(RF1) which decrease as the mixing ratio decreases. However, the temperature of the compressor components increases except for the muffler due to the reduction of the cooling effect. Figure 6 shows the temperature change of the suction refrigerant according to the variation of the mixing ratio. As the mixing ratio increased, the temperature of the piston decreased by up to 3.72%, and the temperature of

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1348, Page 5 the mixing region increased by up to 39.96%. As a result, the temperature of the suction refrigerant is 3.45% higher than when the mixing ratio is 0. This result mean that the suction refrigerant is more affected by the mixing region than heat transfer from piston. Also, these results show the possibility of improving the efficiency of the compressor by changing the mixing ratio according to the suction structure.

110 110 Direct(MR = 0) 100 Indirect(MR = 1) 100

90 %)

( 90 80

70 80

60 70

50 60 40

Piston(7) Normalized temperature Normalized Normalized temperature(%) Normalized 50 30 Gas in port(RF5) Gas in Mixing region(RF1) 20 40

0.0 0.2 0.4 0.6 0.8 1.0

1

2

3

4

5

6

7

8

9

10

11

12

13

14

RF1

RF2

RF3

RF4

RF5

RF6

RF7 RF8 RF9 Mixing ratio(MR) Element no. RF10 Figure 5: Prediction for effect of mixing ratio Figure 6: Effect of the mixing ratio

3.4 Effects of Insulating Gasket The temperature distribution for the material of the components is analyzed. Figure 7 shows the temperature of compressor about effect of conduction heat transfer coefficient in relation to insulating gasket. It is positioned between cylinder and discharge cover to prevent heat transfer from the discharge part to the suction part. the temperature decreases at all parts except gas in discharge pipe, discharge pipe and discharge cover. As expected, the effect of the insulating gasket on the compressor body is much bigger than on the shell. The heat flux in the suction line decreases about 9.7% by the insulating gasket. As a result, the suction refrigerant temperature decreases. The suction refrigerant temperature difference is 3.1℃ and 2.3℃ for measured results and prediction, respectively.

5 1200 12 Measured without gasket Reduction rate of heat flux 4 Predicted with gasket 1000 10

3

800 8

) 2 2

C) 600 6

 (

T 1  400 4

0 Heat flux(W/m Heat

-1 200 2 Reduction rate of heat flux(%) heat of rate Reduction T=Twithout gasket-Twith gasket

-2 0 0

2 3 4 5 6 7 8 9

1 RF2 RF3 RF4 RF5

10 11 12 13 14

RF1 RF2 RF3 RF4 RF5 RF6 RF7 RF8 RF9

RF10 Element no. Element no. Figure 7: Effect of the insulating gasket

4. CONCLUSION

In this study, the temperature distribution of the linear compressor is analyzed through the lumped parameter model. the model is verified by comparing with the experiment. The heat transfer mechanism in linear compressor is analyzed and the following conclusions are obtained.

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• Comparing with measured data of the linear compressor, the maximum discrepancy is 13% • As the mixing ratio decreased, the temperature of the suction refrigerant decreased by 3.45% • The insulating gasket is effective in decreasing the suction refrigerant temperature by preventing the heat transfer from the discharge part.

NOMENCLATURE

푄̇푖 Rate of heat transfer (J/s) 푚̇ 푗,푖 mass flow rate of the refrigerant (kg/s) ℎ푗,푖 enthalpy (J/kg) Ẇ 푖 Rate of work done (J/s) 푆푖̇ Heat generation of element i (J/s) 푇푖 temperature of element i (K) 푇∞ (K) 퐻푖,푗 Thermal conductance (J/s∙K) 2 ℎ푖 Convective heat transfer coefficient (J/s∙m ∙K) 2 퐴푖,푗 Area of heat transfer (m ) 푘 thermal conductivity (J/s∙m∙K) △ 푥 Thickness (m) 휀 emissivity (-) 휎 Stefan-Boltzmann constant (J/s∙m2∙K4) V Volume of cylinder (m3) n polytropic coefficient (-) P (Pa)

Subscript MR Mixing ratio Nu Nusselt number Re Reynolds number Pr Prandtl number

REFERENCES

Kim, J. K., Roh, C. G., Kim, H., & Jeong, J. H. (2011). An experimental and numerical study on an inherent capacity modulated linear compressor for home , Int. J. , 34, 1415-1423. Sim, Y. H., Youn, Y., & Min, M. K. (2000). A Study on Heat Transfer and Performance Analysis of Hermetic Reciprocating Compressors for Refrigerators, International Compressor Engineering Conference. Ooi, K. T. (2003). Heat transfer study of a hermetic refrigeration compressor, Applied thermal engineering, 23, 1931-1945. Oliveira, M. J., Diniz, M. C., & Deschamps, C. J. (2017). Predicting the temperature distribution and suction gas superheating of an oil-free linear compressor. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 23, 47-56. Padhy, S. K., & Dwivedi, S. N. (1994). Heat transfer analysis of a rolling-piston rotary compressor. International journal of refrigeration, 17, 400-410. Park, M., Lee, J., Kim, H., & Ahn, Y. (2017). Experimental and numerical study of heat transfer characteristics using the heat balance in a linear compressor. International Journal of Refrigeration, 74, 550-559. Lawton, B. (1987). Effect of compression and expansion on instantaneous heat transfer in reciprocating internal . Proceedings of the Institution of Mechanical Engineers, Part A: Power and Process Engineering, 201, 175-186. Zhou, R., Guo, B., Chen, X., Tuo, J., Wu, R., Fagotti, F., & Xu, B. (2017). Heat Transfer Simulation for Reciprocating Compressor with Experimental Validation. In IOP Conference Series: Materials Science and Engineering, 232, 012011

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Diniz, M. C., Pereira, E. L., & Deschamps, C. J. (2015). A lumped-parameter thermal model for scroll compressors including the solution for the temperature distribution along the scroll wraps. International Journal of Refrigeration, 53, 184-194. ACKNOWLEDGEMENT

This work was supported by “Human Resources Program in Energy ” of the Korea Institute of Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20164010201000)

24th International Compressor Engineering Conference at Purdue, July 9-12, 2018