Purdue University
Purdue e-Pubs
International Compressor Engineering Conference
School of Mechanical Engineering
2018
Heat 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., "Heat Transfer Analysis of Linear Compressor Based on a Lumped Parameter Model" (2018).
International Compressor Engineering Conference. Paper 2585.
1348, Page 1
Heat Transfer Analysis of Linear Compressor Based on a Lumped Parameter Model
Han-Gyeol Ji
1, Gyung-Min Choi
2*
1
Graduated School of Smart Interdisciplinary Engineering, Pusan National University,
Busan, Korea
[email protected]
2
Department of Mechanical Engineering, Pusan National University,
Busan, Korea
[email protected]
* Corresponding Author
ABSTRACT
In this study, Heat transfer and temperature 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 piston acts as a suction muffler. For this reason, Gas superheating in suction refrigerant is a very important factor in linear compressor design. The control volume 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 evaporator 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 compressors 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.
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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 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 thermodynamics for i element can be expressed by equation (1).
𝑄̇𝑖+ ∑ 𝑚̇𝑗,𝑖ℎ𝑗,𝑖 = 𝑊̇𝑖+ ∑ 𝑚̇𝑗,𝑘ℎ𝑗,𝑘+ 𝑑(𝑚𝑖𝑢𝑖) 𝑑𝑡 𝑛 𝑗=1 𝑛 𝑗=1 (1)
Since the control volume is assumed to be a uniform temperature, it can be assumed that the enthalpy 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).
𝑄̇𝑖= 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).
𝑄̇𝑖= ∑ 𝐻𝑖,𝑗(𝑇𝑗− 𝑇𝑖) + 𝑆̇𝑖= 0 𝑛
𝑗=1
(1)
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 pipe 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
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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)
𝐻𝑖,𝑗= ℎ𝑖𝐴𝑖,𝑗 (4)
𝐻𝑖,𝑗= 𝑘𝑖𝐴𝑖,𝑗⁄∆𝑥 (5)
𝐻𝑖,𝑗= 𝐴𝑖,𝑗𝜀𝜎(𝑇𝑖+ 𝑇∞)(𝑇𝑖2+ 𝑇∞2) (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)
𝑚̇𝑠𝑢𝑐ℎ𝑠𝑢𝑐+ 𝑊̇𝑐𝑜𝑚𝑝= 𝑚̇𝑑𝑖𝑠ℎ𝑑𝑖𝑠+ 𝑄̇𝑅𝐹6→8+ 𝑄̇𝑅𝐹6→7 (7) 𝑊𝑐𝑜𝑚𝑝= ( 𝑛 𝑛 − 1) 𝑃𝑠𝑢𝑐(𝑉1− 𝑉4)(1 − 𝑃𝑑𝑖𝑠 𝑃𝑠𝑢𝑐 (𝑃𝑠𝑢𝑐 𝑃𝑑𝑖𝑠 ) 1 𝑛 ) ∙ 𝐻𝑧 (8)
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.
𝑁𝑢 = 0.053𝑅𝑒0.8𝑃𝑟0.6 (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.
𝑁𝑢 = 5 + 0.015𝑅𝑒𝑎𝑃𝑟𝑏 , a=0.88-0.24/(4+Pr), b=0.3333+0.5e0.6Pr (10) 𝑁𝑢 = 0.3 + 0.62𝑅𝑒 1/2𝑃𝑟1/3 [1 + (0.4/𝑃𝑟)2/3]1/4[1 + ( 𝑅𝑒 282000) 5 8 ] 4/5 (11) 𝑁𝑢 = 0.037𝑅𝑒0.8𝑃𝑟1/3 for 𝑅𝑒 < 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).
𝑄̇𝑀𝑅= 𝑀𝑅 ∙ 𝑄̇𝑠ℎ𝑒𝑙𝑙+ (1 − 𝑀𝑅) ∙ 𝑄̇𝑠𝑢𝑐𝑡𝑖𝑜𝑛 (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
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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
Figure 2: Comparison between the measured results and prediction
1 2 3 4 5 6 7 8 9 10 11 12 13 14 RF1 RF2 RF3 RF4 RF5 RF6 RF7 RF8 RF9 RF10 20 30 40 50 60 70 80 90 100 110 Element no. Norm alized te mp er atu re ( ) Measured Predicted
Figure 3: Ambient temperature versus compressor
temperatures 0 1 2 3 4 5 6 20 30 40 50 60 70
Gas in muffler entrance(RF2) Discharge shell(4)
Suction shell(1) Gas in muffler exit(RF4)
Gas in mid of muffler(RF3) Air flow rate(CMM)
Te m pe ratur e( C) Piston(7)
Gas in discharge pipe(RF8)
Figure 4: Air flow over compressor versus
compressor temperature 0 10 20 30 40 50 60 10 20 30 40 50 60 70 80 90 100 110 Norm alized te mp er atu re (%) Ambient temperature(C) 0 1 2 3 4 5 6 30 40 50 60 70 80 90 100 110
Gas in muffler entrance(RF2) Discharge shell(4)
Suction shell(1) Gas in muffler exit(RF4)
Gas in mid of muffler(RF3) Air flow rate(CMM)
N orm al ized t emperat ure( %) Piston(7)
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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.
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.
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.
Figure 5: Prediction for effect of mixing ratio Figure 6: Effect of the mixing ratio
1 2 3 4 5 6 7 8 9 10 11 12 13 14 RF1 RF2 RF3 RF4 RF5 RF6 RF7 RF8 RF9 RF10 20 30 40 50 60 70 80 90 100 110 Element no. Norm alized te mp er atu re (%) Direct(MR = 0) Indirect(MR = 1) 0.0 0.2 0.4 0.6 0.8 1.0 40 50 60 70 80 90 100 110 Norm alized te mp er atu re (%) Mixing ratio(MR) Piston(7) Gas in port(RF5) Gas in Mixing region(RF1)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 RF1 RF2 RF3 RF4 RF5 RF6 RF7 RF8 RF9 RF10 -2 -1 0 1 2 3 4 5
T=Twithout gasket-Twith gasket
Element no. T ( C) Measured Predicted
Figure 7: Effect of the insulating gasket
RF2 RF3 RF4 RF5 0 200 400 600 800 1000 1200 Heat flux( W/m 2 ) without gasket with gasket 0 2 4 6 8 10 12
Reduction rate of heat flux
Element no. Redu ction ra te of he at flux( %)
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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
𝑄̇𝑖 Rate of heat transfer (J/s)
𝑚̇𝑗,𝑖 mass flow rate of the refrigerant (kg/s)
ℎ𝑗,𝑖 enthalpy (J/kg)
Ẇ𝑖 Rate of work done (J/s)
𝑆̇𝑖 Heat generation of element i (J/s)
𝑇𝑖 temperature of element i (K)
𝑇∞ (K)
𝐻𝑖,𝑗 Thermal conductance (J/s∙K)
ℎ𝑖 Convective heat transfer coefficient (J/s∙m2∙K)
𝐴𝑖,𝑗 Area of heat transfer (m2)
𝑘 thermal conductivity (J/s∙m∙K) △ 𝑥 Thickness (m) 𝜀 emissivity (-) 𝜎 Stefan-Boltzmann constant (J/s∙m2∙K4) V Volume of cylinder (m3) n polytropic coefficient (-) P Pressure (Pa) Subscript MR Mixing ratio Nu Nusselt number Re Reynolds number Pr Prandtl number
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ACKNOWLEDGEMENT
This work was supported by “Human Resources Program in Energy Technology” of the Korea Institute of Energy Technology Evaluation and Planning (KETEP), granted financial resource from the Ministry of Trade, Industry & Energy, Republic of Korea. (No. 20164010201000)
