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Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux
Accepted Manuscript Research Paper Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux Li Ling, Quan Zhang, Yuebin Yu, Yaning Wu, Shuguang Liao, Zhengyong Sha PII: DOI: Reference:
S1359-4311(16)33871-6 http://dx.doi.org/10.1016/j.applthermaleng.2017.03.049 ATE 10053
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
3 December 2016 27 January 2017 10 March 2017
Please cite this article as: L. Ling, Q. Zhang, Y. Yu, Y. Wu, S. Liao, Z. Sha, Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.03.049
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Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux Li Linga,b, Quan Zhanga,*, Yuebin Yub,*, Yaning Wua, Shuguang Liaoc, Zhengyong Shad a
College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, China
b
Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USA c
Changsha Maxxom High-tech Co. Ltd., Changsha, Hunan, 410015, China
d
Xiangjiang Technology Co. Ltd, Yangzhong, Jiangsu, 21200, China
Abstract A micro channel separate heat pipe (MCSHP) has many great features for cooling applications. The design and control of an MCSHP generally employs a numerical simulation. However, the majority of available simulation models were developed for conventional channels where the hydraulic diameter is greater than 3 mm; as well, they generally have high heat flux and high mass flux. With an MCSHP, the channel size, heat flux and mass flow flux are much smaller, which might change the thermodynamics and simulation accuracy of the cycle, especially the two-phase flow section in the evaporator and the condenser. In this study, a distributed-parameter model with a combination of εNTU method and Nusselt laminar liquid film condensation theory was developed for the scenario. Six correlations were tested in the model under different filling ratio conditions. The results show that the model with the Gungor and Winterton correlation provides the best agreement, with an average relative error of about 5%. By using the selected model, the thermal performance of MCSHP under different refrigerant filling ratios, air flow rates and height differences were analyzed and findings were presented. Keywords: micro channel separate heat pipe, numerical, thermal characteristics, two-phase correlation
*
Corresponding authors. E-mail address: [email protected] (Q. Zhang),[email protected](Y. Yu).
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NOMENCLATURE List of abbreviations MCSHP
Micro channel separate heat pipe system
RTPF
Round Tubes and Plate Fins
SHP
separate heat pipe system
TSs
telecommunication stations
List of symbols Ao
total air side surface area,m2
Aw
refrigerant side surface area,m2
cp
specific heat J∙kg-1∙K-1
C1-C3
equation coefficients
d
hydraulic diameter, m
g
gravitational acceleration,m∙s-2
H
Enthalpy, J∙kg-1
ha
heat transfer coefficient of air side , W∙m-2∙K-1
hfg
latent heat of vaporization, J∙kg-1
hr
heat transfer coefficient of refrigerant side , W∙m-2∙K-1
kw
thermal conductivity,W∙m-1∙K-1
m
mass flow rate,kg∙s-1
M
refrigerant charge, kg
NTU
number of heat transfer unit
P
Pressure, Pa
ΔP
pressure drop, Pa
Q
cooling capacity, W
T
temperature, K
u
velocity, m∙s-1
x
axial coordinate
y
radial coordinate
Δz
height difference, m
List of greeks ε
thermal effectiveness
τ
shear stress,N∙m-2
δ
liquid film thickness, m
δw
thickness of wall, m
σ
average relative errors,% 2
μ
dynamic viscosity, Pa∙s
ƞo
surface effectiveness
ρ
density, kg∙m-3
λ
thermal conductivity, W∙m-1∙K-1
List of subscripts a
air side
c
condenser section
e
evaporator section
fr
friction
g
gravity or vapor ascending tube
i
inlet
i,j
calculate unit
l
liquid or condensate descending tube
min
minimum
r
refrigerant side
s
saturation
v
vapor
w
wall
3
1. Introduction A separate heat pipe (SHP) is a device that utilizes the great phase change heat of refrigerant and the temperature difference between sources for cooling. Internally, it circulates the refrigerant by using gravity without mechanical movers and controls, which makes the device relatively simple and energy conservative. With the separated evaporator and condenser, an SHP can transfer heat through a relatively long distance. Compared to a direct medium replacement based cooling, such as natural ventilation, an SHP can better serve indoor air cleanliness by not letting the outdoor air in. This is especially important in telecommunication stations (TSs) where a clean indoor environment is desired for reliable operation of electronic devices[1]. Therefore, SHPs have a promising potential application for TS cooling due to their features, including their simplicity, flexibility, high heat transfer efficiency [2-4].
A number of experimental investigations on the thermal-hydraulic mechanism and improvement of the SHP design and operation have been reported in recent years. For example, to obtain the optimal refrigerant filling ratio, Tong et al. [5] study on the flow region of the SHP with parallel copper tube heat exchangers under different filling ratios experimetally. Ling et al. [4] experimentally investigated the thermal performance of a micro channel separate heat pipe (MCSHP) respect to different filling ratios using R22, and identified the optimal value. Khodabandeh [6] experimentally studied the effects of heat flux (which ranges from 28.3 to 311.5
kW m2 ), system pressures, mass flow rate, vapor fraction, diameter of the evaporator channel and the height difference between evaporator and condenser section on the heat transfer properties of a thermosyphon loop (a device similar to an SHP). Factors like different air velocity and temperature differences between indoor air and outdoor air (10 °C -20 °C) were also 4
experimentally studied by Zhang et al. [7] on the cooling capacity and energy efficiency ratio in thermosyphon mode.
The thermal performance of an SHP can be affected simultaneously by many factors, including geometrical parameters, height difference, refrigerant filling ratio, temperature difference, air flow rate, etc. These factors make a comprehensive experimental investigation difficult. Therefore, it is critical to have a model that can be effective and convenient for simulating the thermal performance of an SHP. In order to explore the thermal characteristics of an SHP with a 7.8 mm diameter copper tube heat exchanger, McDonald et al. [8-10] did an experiment and simulation to explore the effects of refrigerant charge, angles of inclination of evaporator and condenser, temperature difference, and evaporator and condenser tube length and channel diameter. Dube et al. [11] experimentally and theoretically analyzed the non-condensable gases on thermal performance of the loop thermosyphon under various temperature differences 2
(142.8°C -191.2°C). Rao et al. [12] presented the effects of heat flux (40-400 kW m ) on the refrigerant mass flow rate through using a one-dimensional steady state model. Liu et al. [13] developed a one-dimensional steady state model to calculate the upper and lower boundaries of the filling ratio of an SHP with a rectangular heat exchanger (Dh = 21.8 mm) to predict the optimal refrigerant charge for an SHP. The effects of the geometrical parameters of the evaporator, vapor 2
temperature, and heating power (0-0.83 kW m ) on the refrigerant filling boundaries were also presented. Zhang et al. [14] analyzed the effects of temperature difference (4 °C -36 °C) and refrigerant charge on an SHP with a Round Tubes and Plate Fins (RTPF) heat exchanger (Dh = 8.84 mm) through a numerical model. To investigate geometric parameters and temperature
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difference effects on the thermal characteristics of the thermosyphon mode, Zhang et al. [15] built a model using empirical equations for the thermosyphon loop with a micro channel heat exchanger evaporator (Dh = 1.5 mm) and a three-fluid heat exchanger condenser (Dh = 6 mm) to calculate the cooling capacity and circulation flow rate.
From the literature, it can be seen that existing numerical models were proposed and utilized mainly for a heat pipe cycle with a regular channel (Dh > 3 mm), heat flux and flow flux. This is different from an SHP with a micro channel heat exchanger for low heat flux or low temperature difference and low mass flux [16]. In an evaporator section, the heat transfer regimes include bubbly flow, slug flow, annular flow and mist flow, which makes theoretical modeling of the evaporator section very difficult. Empirical correlations play an important role in this regard, which can directly influence the accuracy of overall simulation results. Currently, there exist a lot of correlations for predicting the two-phase boiling flow heat transfer coefficient. These correlations could be classified into two types:
1) conventional channel two-phase heat transfer coefficient, including the enhanced model [17], the superposition model[18-20], and the power-type asymptotic model. There exists a difference in whether the effect of convective and nucleate boiling is taken into account;
2) small or micro channel two-phase heat transfer coefficient [21-25]. There are many different two-phase heat transfer correlations for predicting thermal performance of small or micro channels. Their main difference is the consideration of impact factors, such as heat flux, mass flux, vapor quality, etc., and whether nucleate boiling or convective boiling is dominant or not.
As shown in Table.1, most two-phase correlations were proposed for high heat flux or mass 6
flux scenarios. It remains vague which correlation among them might present a better a micro channel condition with low refrigerant mass flux (3-32 kg m2 s 1 ) and low heat flux (0-0.25
kW m2 ). Table.1
This paper seeks to solve and fill in these gaps outlined above and find the more suitable correlations for predicting the MCSHP heat transfer performance under low heat flux and low mass flux. Firstly, a distributed-parameter model for an MCSHP under low heat flux and low mass flux was developed, using the ε-NTU method and Nusselt laminar liquid film condensation theory. Six different two-phase heat transfer correlations were adopted for the evaporator section modeling. The simulation results were validated using previous experimental results. Then, the precision of models with different correlations was compared. With the most suitable two-phase correlation, this study further investigated the effects of refrigerant filling ratio, air flow rate and height difference on thermal characteristics of the MCSHP.
2. Modeling The simulation model is built for the MCSHP proposed by the authors in [4], as shown in Fig.1. The system comprises a closed circuit, containing an evaporator section, a condenser section, vapor ascending tube and condensate descending tube. Detailed geometrical parameters of the MCSHP can be found in the paper by Ling et al. [4]. Table.2 summarizes the working conditions used for the simulation.
The numerical model of an MCSHP includes mainly three modules: the evaporator section, connection tubes, and condenser section. The refrigerant state, along with the system cycle, as
7
shown in Fig.1, is provided below:
(1) Evaporator section:
i) Region A: single phase liquid flow region (in saturated or subcooling state);
ii) Region B: two-phase flow region;
iii) Region C: single phase vapor flow region (in saturated or superheating);
(2) Vapor ascending tube: adiabatic, two-phase or vapor region;
(3) Condenser section:
i) Region D: two-phase or vapor (in saturated or superheating) region;
ii) Region E: two-phase region;
iii) Region F: single phase liquid flow region (in saturated or subcooling state);
(4) Condensate descending tube: adiabatic, two-phase or liquid region.
The refrigerant flow along the system cycle abides by momentum (pressure), energy (enthalpy) and mass conservation, as follows:
dP 0
(1)
dH 0
(2)
dM M
(3)
i
Fig. 2 illustrates the flow chart of the numerical model of the MCSHP. In the figure, variables in blue are the input parameters, including geometrical parameters and environmental parameters; variables in red are the parameters as in Eqs. (1) - (3), which are solved by iteration of pressure, enthalpy and mass balance in the loop. The allowable convergence errors for pressure, enthalpy 8
and mass were 0.1kPa, 0.1kJ∙kg-1, and 0.01kg, respectively.
Fig.1
Table.2
Fig.2
2.1 Evaporator section model The micro channel evaporator section was modeled using a finite element approach.The main assumptions and calculated steps in this model can be found in the paper by Ling et al. [1]. The cooling capacity of each segment was calculated by the ε-NTU method, and the cooling capacity of every segment can be calculated as follows:
Qi Cmin Tai ,e Tri
Where Cmin min ma c p ,a , mr c p ,r
(4)
The effectiveness of heat exchanger ε [26] in single phase condition is:
1 NTU 0.22 exp(Cr ·NTU 0.78 ) 1 Cr
=1 exp
Where Cr
min ma c p ,a , mr c p ,r
max ma c p ,a , mr c p ,r
(5)
.
The effectiveness of heat exchanger ε [26] in two-phase condition is:
=1 e NTU NTU =
(6)
UAo Cmin
(7)
The overall thermal resistance consists of the refrigerant-side heat convection thermal resistance, the wall heat conduction thermal resistance and the air-side heat convection thermal 9
resistance. Therefore, the overall heat transfer coefficient in terms of air-side heat transfer area is given as follows:
U
1
1 Ao w Ao 1 hr Aw kw Aw o ha
(8)
The correlations used for the heat transfer and pressure drop calculation are summarized in Table.3. Among these, the refrigerant side two-phase heat transfer coefficient inside the tube, especially in MCSHP under low heat flux or low mass flux, is one of the most important issues. Most two-phase heat transfer correlations are not based on experimental results using R22 in an MCSHP under low heat flux or low mass flux. Thus, the suitability of existing correlations in an evaporator section of the MCSHP is unclear. In this paper, six different correlations for predicting the two-phase heat transfer coefficient were adpoted during the development of the evaporator section model.
Table.3
2.2 Connection tube model The vapor ascending tube and condensate descending tube were used to connect the evaporator section and condenser section. Both of two are considered adiabatic process. The pressure drop can be calculated by Eq. (5).
P Pfr Pg
(9)
The friction pressure drop was calculated using the Gnielinski correlation [27] and the Friedel correlation [31] according to the refrigerant is in single phase condition or two-phase condition, respectively.
2.3 Condenser section model 10
For the condenser section of a heat pipe, the heat transfer regime is annular flow [32], thus the Nusselt laminar liquid film condensation theory can be used to predict the two-phase condensing heat transfer process. However, there exists an interfacial shear that could reduce the thickness of liquid film and promote heat transfer [13]. While the heat transfer mechanism of condenser section in an MCSHP is similar to a Nusselt laminar liquid film condensation, the impact due to the interfacial shear should be considered since it can influence the velocity distribution of the liquid film when the diameter is small.
In this study, the heat transfer coefficient and pressure drop of the vapor region or subcooling liquid region is calculated using the Gnielinski correlation [27]. Because the hydraulic diameter of the channels is very small, the interfacial shear has great influence on the liquid film velocity lateral distribution. A significant deviation was found between the calculated and actual values when the interfacial shear stress was neglected [13]. In this study, the heat transfer model of the two-phase region was built with the effect of interfacial shear considered. According to the laws of conservation of momentum and energy in the liquid film, the following governing equations were obtained:
l
2u1 l g 4 i / dv v g 0 y 2
(10)
2Tl 0 y 2
(11)
Subject to the boundary conditions, we have:
y 0:
ul 0, T Tw
(12)
y :
u l l i , T Ts y
(13)
11
From Eqs. (10)–(13) and the law of thermal equilibrium, the correlations of the velocity distribution ul, the mass flow rate per unit width of liquid film qm, the relationship between liquid film thickness δ, shear stress τi, and position along the axial coordinate x, can be expressed as follows:
2 g 2 i i g 2 ul i y 2 y y l l dv 2l 2 l l d v qm
l g 4 i 3 l i 2 3 l l dv 2l
(14)
(15)
3 C C 3C1 C2 C3 4 i C1 C2 4 i 1 2 3 x l dv 8 l 9 3 32 4
(16)
The coefficients C1 to C3 in Eq. (16) were defined as:
C1
l c p l h fg ρg , C 2 , C3 l l Ts Tw μl
The interfacial shear stress τi, composed of the shear stress due to mass transfer τm, and the shear stress due to friction force τf [32]. Therefore, the two-phase region heat transfer coefficient in condenser section can be calculated as:
h j l / j
(17)
For the condenser section, the cooling capacity is calculated by the ε-NTU method. For a given segment j, the cooling capacity can be calculated as:
Q j Cmin Tri Tai ,c
(18)
3. Results and discussion 3.1 Model verification The model was established in Matlab R2016b, and the refrigerant thermodynamic properties was acquired from the NIST Refrigerant Database REFPROP [33]. 12
In order to verify the accuracy of the developed model, the calculated cooling capacity under different refrigerant filling ratios with different correlations were compared to our experimental results of the MCSHP, as shown in Fig.3- Fig.8. The average relative error σ between the simulated and measured results are based on the following euqation:
Calculated value Measured value 100% Measured value
(19)
Fig.3- Fig.8 shows the comparison of the cooling capacity between experimental results and predictions under different refrigerant filling ratios by using different correlations. The agreement between experimental results and calculations by the Gungor and Winterton correlation (Fig.3) is very good except at the refrigerant filling ratio of 44%. The overall average relative error is 4.9%. The Kandlikar and Steinke correlation and the Khodabandeh correlation in Fig.4- Fig.5 underpredicted the experimental results in the refrigerant filling ratio range of 32%-57%, and their average ralative errors are up to 21 and 22%, respectively. When the refrigerant filling ratio ranges from 70%-120%, the simulation results from all three correlations obtain very high precision. Kim and Mudawar, Bertsch, and Li and Wu correlations (Fig.6-8) are widely applied in predicting twophase heat transfer characteristics of microchannels. However, these correlations overpredicted the measured results in the refrigerant filling ratio range of 32%-57%. When the refrigerant filling ratio is between 70% and 120%, the average relative errors became lower than 5%.
Among these figures, Fig.3, Fig.6, Fig.7 and Fig.8 exist a break point (point 1) in the low refrigerant filling ratio range. This is because the change of the overall heat transfer coefficient was dominated by the change of the refrigerant side heat transfer coefficient when the two-phase heat transfer area in the evaporator section increased largely with the increasing refrigerant filling 13
ratio; consequently, the calculated two-phase heat transfer coefficient is larger than the actual value, which leads to the increase on the calculated cooling capacity. However, the magnitude of the deviation is not big. Overall, the cooling capacity calculated by the Gungor and Winterton correlation provides the best agreement with the experimental results, with an average relative error of about 5%. The Gungor and Winterton correlation will be used in the model to further analyze the thermal performance of the MCSHP.
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
3.2 Analysis and discussion 3.2.1 Effects of refrigerant filling ratio Fig.9 and Fig.10 show the refrigerant side heat transfer coefficient distribution along the evaporator section and the condenser section corresponding to four different refrigerant filling ratios. The refrigerant filling ratios directly influence the refrigerant side heat transfer coefficient of evaporator section and condenser section. At a low refrigerant filling ratio (FR≤ 38%), the heat transfer coefficient of the evaporator section (hr,e) is very small at the outlet of the evaporator section because of a superheated phenomenon occurring near the outlet of the evaporator section. When the superheating refrigerant flows into the condenser section, the refrigerant remains as dry 14
vapor but from a superheating state to saturation state. Consequently, the refrigerant heat transfer coefficient is small at the condenser section inlet. Then, the refrigerant condenses quickly to form a liquid film, thereby the heat transfer coefficient at the refrigerant side of the condenser section (hr,c) increased sharply. The heat transfer coefficient at refrigerant side (hr,c) gradually decreases with the increasing of the thickness of liquid film (as shown in Fig.11).
At the optimal refrigerant filling ratio (FR= 82%), the heat transfer coefficient at refrigerant side of the evaporator section and condenser section grows along with the path, which means the MCSHPs were in optimal operating condition. Fig.10-11 also shows that there does not exist superheated phenomenon or liquid flooding at the condenser section. In other words, the refrigerant is in two-phase, thereby the refrigerant side heat transfer coefficients have high values. With the refrigerant filling ratio increased (FR= 126% or 170%), the liquid refrigerant floods at the bottom of the condenser section, which causes the refrigerant side heat transfer coefficient to decrease to low values. Fig.12 illustrates the change of the refrigerant in the 100 segments of the condensing section. When the filling ratio increases to 170%, about 78 segments out of 100 is filled with liquid refrigerant.
Fig.9
Fig.10
Fig.11
Fig.12
3.2.2 Effects of air flow rate Modulating the air flow rate through the evaporator section can impact the cooling capacity. 15
At the same time, it will also influence the air side pressure drop, power and pressure of the fan. In this investigation, the refrigerant filling ratio is kept the same because the optimal refrigerant filling ratio was the same under different air flow rate [4]. The environmental conditions, as in Table.2, were used and the air flow rate ranged from 1500 m3/h to 6000 m3/h. Fig.13 shows the cooling capacity and air side pressure drop with different air flow rates. The cooling capacity increased with the increase of the air flow rate, ranging from 2492 W to 5973 W. However, the increasing rate decreased. This is because the increasing rate of the overall heat transfer coefficient decreased (as shown in Fig.14). With the increasing air flow rate, the air side pressure drop increased, which caused the fan energy consumption to increase. According to the Fan Law [34], the power consumption and pressure of the fan decreased with the third power of the air flow rate ratio and square of the air flow rate ratio, respectively.
Fig.13
Fig.14
3.2.3 Effects of height difference between evaporator section and condenser section The height difference between evaporator section and condenser section is another important factor that could affect the thermal performance of an MCSHP. On the one hand, the driven force of the MCSHP mainly relies on the product of height difference and density difference between the vapor ascending tube and the condensate descending tube – that is (ρl-ρv)˖H. Hence, the driven force increases with increasing height difference, thereby, the mass flow rate and the cooling capacity increase. On the other hand, the length of the vapor ascending tube and the condensate descending tube increased with increasing height difference, which cause flow resistance to increase. Fig.15 shows the cooling capacity and the refrigeration mass flow rate under different 16
height differences between the evaporator section and the condenser section. The refrigerant filling ratio and environmental conditions remain unchanged as before. The geometry of the system is also the same, except the height difference changed from 0 to 2.4 m. With the increase of the height difference between the evaporator and condenser sections, the refrigerant mass flow rate increased rapidly at first and then increased slightly. The cooling capacity had the same trend as the refrigerant mass flow rate. However, the cooling capacity was less sensitive to the change of height difference in the range from 0.4 m to 2.4 m. The cooling capacity remained relatively constant once the height difference was greater than 0.4 m. The reason is with a lesser height difference, both temperature difference and height difference can generate a positive effect on the circulation of the refrigerant. Gradually, the height difference dominates, which causes the rapid increase up to the 0.4 m height difference. When the height difference further increases, the driving force is still much greater than the circulation resistance. However, the cooling capacity starts to be restricted by the overall capacity of the evaporator and condenser. Consequently, the enthalpy difference of the refrigerant across the evaporator starts to drop which can lead to a decrease in the quality of the refrigerant at the outlet. Eventually, the driving force provided by the height difference is consumed by the joint effect from the device capacity limitation and refrigerant side pressure drop.
Fig.15
4. Conclusions In this study, we evaluated six two-phase heat transfer correlations to determine the most suitable one for a micro channel separate heat pipe, where the heat flux and mass flux are small. Modified Nusselt laminar liquid condensation model, considering the effect of interfacial shear, 17
was developed for the condenser. Numerical finite control volume models for the evaporator, the connection tubes, and the condenser were established and integrated to simulate the system of an MCSHP. The momentum, energy and mass conservation in the loop were selected as the convergence criteria.
The simulation results were compared to the experimental data collected under various filling ratio conditions. It was found that under low filling ratio conditions, there all exhibited a certain level of discrepancy. In a transitional region, when the filling ration is about 45%, the error could get up to 25% since the two-phase heat transfer area in the evaporator section increased largely with the increasing refrigerant filling ratio in the model. Overall, the Gungor and Winterton correlation provides the lowest error under all filling ratios; the average relative error is about 5%. Based on the results, the Gungor and Winterton is considered more suitable for predicting the thermal performance of an MCSHP under different refrigerant ratios and operation conditions.
Additionally, the effects of refrigerant filling ratio, air flow rate and height difference on an MCSHP were analyzed by using the developed model. The refrigerant side heat transfer coefficient along the evaporator section and condenser section had the maximum value when the system filling ratio was 82%. Increasing the air flow rate increases the overall cooling capacity, but the impact gradually fades and the fan energy consumption increases. As a design parameter, the height difference has a great impact on the refrigerant mass flow rate and cooling capacity. However, the impact is limited by the evaporator and condenser capacity when it reaches a certain value. All three factors should be considered in the design and operation to achieve an optimal overall energy efficiency.
18
Acknowledgements The present study was supported by secience and inovation for graduate students,Hunan (CX2016B110), University of Nebraska-Lincoln Faculty Start-up Fund, and International Science and TechnologyCooperation Program of China (2015DFA61170 and S2016G2422).
We thank Mrs. Kelly Johnson of the University of Nebraska-Lincoln for her great help on editing this paper.
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[15] H. Zhang, S. Shao, H. Xu, H. Zou, M. Tang, C. Tian, Simulation on the performance and free cooling potential of the thermosyphon mode in an integrated system of mechanical refrigeration and thermosyphon, Appl.Energy 185 (2017) 1604–1612. [16] S.G. Kandlikar, W.J. Grande, Evolution of Microchannel Flow Passages--Thermohydraulic Performance and Fabrication Technology, Heat Transfer Eng. 24 (2003) 3-17. [17] M.M. Shah, A new correlation for heat transfer during boiling flow through pipes, ASHRAE Transactions, 82 (1976) 66-86. [18] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Industrial & engineering chemistry process design and development, 5 (1966) 322-329. [19] K.E. Gungor, R.H.S. Winterton, Simplified general correlation for saturated flow boiling and comparisons with data, Chemical Engineering Research & Design, 65 (1987) 148-156. [20] Z. Liu, R. Winterton, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, Int. J. Heat Mass Transf. 34 (1991) 27592766. [21] S.S. Bertsch, E.A. Groll, S.V. Garimella, A composite heat transfer correlation for saturated flow boiling in small channels, Int. J. Heat Mass Transf. 52 (2009) 2110-2118. [22] S.G. Kandlikar, M.E. Steinke, Predicting heat transfer during flow boiling in minichannels and microchannels, ASHRAE Transactions, 109 (2003) 667-676. [23] S.-M. Kim, I. Mudawar, Universal approach to predicting saturated flow boiling heat transfer in mini/micro-channels – Part II. Two-phase heat transfer coefficient, Int. J. Heat Mass Transf. 64 (2013) 1239-1256. [24] W. Li, Z. Wu, A general correlation for evaporative heat transfer in micro/mini-channels, Int. J. Heat Mass Transf. 53 (2010) 1778-1787. [25] T. Tran, M.-C. Chyu, M. Wambsganss, D. France, Two-phase pressure drop of refrigerants during flow boiling in small channels: an experimental investigation and correlation development, Int. J. Multiphas. Flow. 26 (2000) 1739-1754. [26] S. Yang, W. Tao, Heat Transfer (Fourth edition), in, Beijing:Heiger Education Press, 2006. [27] V. Gnielinski, New equations for heat and mass-transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359-368. [28] L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow, in: European two-phase flow group meeting, Paper E, Vol. 2, 1979, pp. 1979. [29] Y.-J. Chang, C.-C. Wang, A generalized heat transfer correlation for Iouver fin geometry, Int. J. Heat Mass Transf. 40 (1997) 533-544. [30] M.-H. Kim, C.W. Bullard, Air-side thermal hydraulic performance of multi-louvered fin aluminum heat exchangers, Int.J.Refrig. 25 (2002) 390-400. [31] Z. Lu, Two phase flow and boiling heat transfer, Tsinghua University Publishing House, 2002. [32] B. Jiao, L.M. Qiu, X.B. Zhang, Y. Zhang, Investigation on the effect of filling ratio on the steady-state heat transfer performance of a vertical two-phase closed thermosyphon, Appl. Therm. Eng. 28 (2008) 1417-1426. [33] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST reference fluid thermodynamic and transport properties–REFPROP, in, Version, 2002. [34] F.P. Bleier, Fan Handbook: selection, application, and design, McGraw-Hill New York, 1998. 20
Fig.1 Schematic diagram of the MCSHP and the physical model of evaporator section and condenser section Fig.2 Flow chart of the numerical model for MCSHP Fig.3 Comparison of the cooling capacity between calculated and experimental results by using Gungor and Winterton correlations Fig.4 Comparison of the cooling capacity between calculated and experimental results by using Kandlikar and Steinke correlations Fig.5 Comparison of the cooling capacity between calculated and experimental results by using Khodabandeh correlations Fig.6 Comparison of the cooling capacity between calculated and experimental results by using Kim and Mudawar correlations Fig.7 Comparison of the cooling capacity between calculated and experimental results by using Bertsch et al. correlations Fig.8 Comparison of the cooling capacity between calculated and experimental results by using Li and Wu correlations Fig.9 The refrigerant side heat transfer coefficient distribution in the evaporator section under four refrigerant filling ratios Fig.10 The refrigerant side heat transfer coefficient distribution in the condenser section under four refrigerant filling ratios Fig.11 The thickness of liquid film distribution in the condenser section under four refrigerant filling ratios Fig.12 The schematic diagram of liquid film and liquid pool distribution in the condenser section under four refrigerant filling ratios Fig.13 The cooling capacity and air side pressure drop under different air flow rates Fig.14 The overall heat transfer coefficient distribution in the evaporator section under four different air flow rates 21
Fig.15The cooling capacity and refrigerant mass flow rate under different height difference.
x Region C
7
Region B
5 2
4 Region A 1 7 3
y Region D
8
6
Region E
Region F x 1. Evaporator section
2. Condenser section
3. Micro channel heat exchanger
4. Fan
5. Vapor ascending tube
6. Condensate descending tube
7. Vapor
8. Liquid film
Fig.1 Schematic diagram of the MCSHP and the physical model of evaporator section and condenser section
22
Outputs
air-side outputs
Inputs
Qc
Tac,o
Geometrical parameters
Pc,o Hc,o Pl,i
Hl,i
Tl,i
mr
Tc,o Mc
Condenser section Tac,i
Pc,i
Hc,i
Tc,i
mr
Vac
Pg,o
Hg,o
Tg,o
Mg
Outputs Air-side outputs
Pl,o
Hl,o
Tl,o
Ml
Tae,o
Pe,i mr
He,i
Evaporator section
Tae,i
Vae
Air-side inputs
Qe Pe,o He,o Te,o
Pg,i
Hg,i
Tg,i
mr
Me
Geometrical parameters Inputs
Fig.2 Flow chart of the mathematical model for MCSHP
23
Geometrical parameters Inputs
M
Vapor ascending tube
Condensate descending tube
Inputs Geometrical parameters
air-side inputs
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results Simulation Results Relative errors
2000
1000
0 30
15 10
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.3 Comparison of the cooling capacity between calculated and experimental results by using Gungor and Winterton correlations
24
5000
30
Cooling capacity (W)
20 3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.4 Comparison of the cooling capacity between calculated and experimental results by using Kandlikar and Steinke correlations
25
5000
30
Cooling capacity (W)
20 3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.5 Comparison of the cooling capacity between calculated and experimental results by using Khodabandeh correlations
26
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.6 Comparison of the cooling capacity between calculated and experimental results by using Kim and Mudawar correlations
27
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.7 Comparison of the cooling capacity between calculated and experimental results by using Bertsch et al. correlations
28
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.8 Comparison of the cooling capacity between calculated and experimental results by using Li and Wu correlations
29
2
Heat transfer coefficient h r,e(W/(m ·K))
1000 FR=38% FR=126%
FR=82% FR=170%
800
600
400
200
0
0
10
20
30 40 50 60 70 Calculated segment i
80
90
100
Fig.9 The refrigerant side heat transfer coefficient distribution in the evaporator section under four refrigerant filling ratios
30
FR=38% FR=126%
FR=82% FR=170%
2
Heat transfer coefficient h r,c(W/(m ·K))
4000
3000
2000
1000
0
0
10
20
30
40 50 60 70 Calculated segment j
80
90
100
Fig.10 The refrigerant side heat transfer coefficient distribution in the condenser section under four refrigerant filling ratios
31
-5
Thickness of liquid film (mx10 )
10
FR=38% FR=126%
FR=82% FR=170%
8
6
4
2
0
0
10
20
30 40 50 60 70 Calculated segement i
80
90
100
Fig.11 The thickness of liquid film distribution in the condenser section under four refrigerant filling ratios
32
j=1 j=8
j=1
j=1
j=1 j=32
Liquid film Liquid pool
j=100 FR=38%
j=100
FR=82%
j=89 j=100
FR=126%
j=100
FR=170%
Fig.12 The schematic diagram of liquid film and liquid pool distribution in the condenser section under four refrigerant filling ratios
33
7000
50
6000
40
5000
30
4000
20
3000
10
2000 1500
2250
3000
3750
4500
5250
Air side pressure drop (Pa)
Cooling capacity (W)
Cooling capacity Air sider pressure drop
0 6000
3
Air flow rate (m /h)
Fig.13 The cooling capacity and air side pressure drop under different air flow rates
34
2
Overall heat transfer coefficient (W/(m K))
100
1500 4500
3000 6000
90 80 70 60 50 40
0
20
40
60
80
100
Calculated segement i
Fig.14 The overall heat transfer coefficient distribution in the evaporator section under four different air flow rates
35
Q
160
Gr
140
Cooling capacity (W)
3750
120 100
3000 80 60
2250
40 1500 0.0
0.4
0.8
1.2
1.6
2.0
2.4
Refrigerant mass flow rate (kg/h)
4500
20 2.8
Height difference (m)
Fig.15 The cooling capacity and refrigerant mass flow rate under different height difference.
36
Highlights Simulation model for MCSHP under low heat flux and low mass flux is developed. Six different two-phase heat transfer correlations in the literature are compared. Model with Gungor and Winterton correlation provides the best precision for MCSHP. Effects of filling ratio, air flow rate and height difference on performance are investigated.
37
Table.1 Summary of typical two-phase heat transfer correlations Table.2 Geometrical parameters and working conditions Table.3 Heat transfer and pressure drop correlations for simulation
38
Table.1 Summary of typical two-phase heat transfer correlations Hydraulic diameter
Mass flux
Heat flux
Dh (mm)
G ( kg m2 s 1 )
q ( kW m2 )
Shah [17]
6-25
10-1384
1.26-788.7
Chen[18]
--
--
63-2397
Gungor and Winterton[19]
2.95-32
12.4-8179.3
0. 35-2620
Liu and Winterton[20]
2.95-32
12.4-8179.3
0. 35-2620
Bertsch [21]
0.16-2.92
20-3000
4-1150
Kandlikar and Steinke[22]
0.4-2.97
50-1600
5-600
Kim and Mudawar[23]
0.19-6.5
19-1608
--
Li and Wu [24]
0.16-3.1
20.3-3500
0-1150
Tran et al. [25]
2.4-2.92
33-832
2.2-129
Khodabandeh [6]
1.1-3.5
207-1052
28.3-311.5
Author(s)
39
Table.2 Geometrical parameters and working conditions Parameter
value
Vapor ascending tube length/diameter (m)
3.66/0.019
Condensate descending tube length/diameter (m)
4.37/0.016
Height difference(m)
2.0
Indoor space temperature (dry/wet bulb) (ºC)
28/19.5
Exterior space temperature (dry/wet bulb) (ºC)
18/11.4
Air flow rate (m3/h)
2980
Refrigerant filling ratio (%)
32%~120%
Working fluid
R22
40
Table.3 Heat transfer and pressure drop correlations for simulation Item
Correlation Heat transfer coefficient
Gnielinski [27]
Pressure drop
Gnielinski [27]
Single phase condition
(1) Gungor and Winterton[19] (2)Kandlikar and Steinke[22]; Heat transfer coefficient Two phase condition
(3)Kim and Mudawar[23]; (4)Bertsch et al.[21]; (5)Li and Wu[24]; (6)Khodabandeh[6].
Pressure drop Heat transfer coefficient
Friedel [28] Chang and Wang [29]
Air side Pressure drop
41
Kim and Bullard[30]
S1359-4311(16)33871-6 http://dx.doi.org/10.1016/j.applthermaleng.2017.03.049 ATE 10053
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
3 December 2016 27 January 2017 10 March 2017
Please cite this article as: L. Ling, Q. Zhang, Y. Yu, Y. Wu, S. Liao, Z. Sha, Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.03.049
This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
Simulation of a micro channel separate heat pipe (MCSHP) under low heat flux and low mass flux Li Linga,b, Quan Zhanga,*, Yuebin Yub,*, Yaning Wua, Shuguang Liaoc, Zhengyong Shad a
College of Civil Engineering, Hunan University, Changsha, Hunan, 410082, China
b
Durham School of Architectural Engineering and Construction College of Engineering, University of Nebraska-Lincoln, Omaha, NE, USA c
Changsha Maxxom High-tech Co. Ltd., Changsha, Hunan, 410015, China
d
Xiangjiang Technology Co. Ltd, Yangzhong, Jiangsu, 21200, China
Abstract A micro channel separate heat pipe (MCSHP) has many great features for cooling applications. The design and control of an MCSHP generally employs a numerical simulation. However, the majority of available simulation models were developed for conventional channels where the hydraulic diameter is greater than 3 mm; as well, they generally have high heat flux and high mass flux. With an MCSHP, the channel size, heat flux and mass flow flux are much smaller, which might change the thermodynamics and simulation accuracy of the cycle, especially the two-phase flow section in the evaporator and the condenser. In this study, a distributed-parameter model with a combination of εNTU method and Nusselt laminar liquid film condensation theory was developed for the scenario. Six correlations were tested in the model under different filling ratio conditions. The results show that the model with the Gungor and Winterton correlation provides the best agreement, with an average relative error of about 5%. By using the selected model, the thermal performance of MCSHP under different refrigerant filling ratios, air flow rates and height differences were analyzed and findings were presented. Keywords: micro channel separate heat pipe, numerical, thermal characteristics, two-phase correlation
*
Corresponding authors. E-mail address: [email protected] (Q. Zhang),[email protected](Y. Yu).
1
NOMENCLATURE List of abbreviations MCSHP
Micro channel separate heat pipe system
RTPF
Round Tubes and Plate Fins
SHP
separate heat pipe system
TSs
telecommunication stations
List of symbols Ao
total air side surface area,m2
Aw
refrigerant side surface area,m2
cp
specific heat J∙kg-1∙K-1
C1-C3
equation coefficients
d
hydraulic diameter, m
g
gravitational acceleration,m∙s-2
H
Enthalpy, J∙kg-1
ha
heat transfer coefficient of air side , W∙m-2∙K-1
hfg
latent heat of vaporization, J∙kg-1
hr
heat transfer coefficient of refrigerant side , W∙m-2∙K-1
kw
thermal conductivity,W∙m-1∙K-1
m
mass flow rate,kg∙s-1
M
refrigerant charge, kg
NTU
number of heat transfer unit
P
Pressure, Pa
ΔP
pressure drop, Pa
Q
cooling capacity, W
T
temperature, K
u
velocity, m∙s-1
x
axial coordinate
y
radial coordinate
Δz
height difference, m
List of greeks ε
thermal effectiveness
τ
shear stress,N∙m-2
δ
liquid film thickness, m
δw
thickness of wall, m
σ
average relative errors,% 2
μ
dynamic viscosity, Pa∙s
ƞo
surface effectiveness
ρ
density, kg∙m-3
λ
thermal conductivity, W∙m-1∙K-1
List of subscripts a
air side
c
condenser section
e
evaporator section
fr
friction
g
gravity or vapor ascending tube
i
inlet
i,j
calculate unit
l
liquid or condensate descending tube
min
minimum
r
refrigerant side
s
saturation
v
vapor
w
wall
3
1. Introduction A separate heat pipe (SHP) is a device that utilizes the great phase change heat of refrigerant and the temperature difference between sources for cooling. Internally, it circulates the refrigerant by using gravity without mechanical movers and controls, which makes the device relatively simple and energy conservative. With the separated evaporator and condenser, an SHP can transfer heat through a relatively long distance. Compared to a direct medium replacement based cooling, such as natural ventilation, an SHP can better serve indoor air cleanliness by not letting the outdoor air in. This is especially important in telecommunication stations (TSs) where a clean indoor environment is desired for reliable operation of electronic devices[1]. Therefore, SHPs have a promising potential application for TS cooling due to their features, including their simplicity, flexibility, high heat transfer efficiency [2-4].
A number of experimental investigations on the thermal-hydraulic mechanism and improvement of the SHP design and operation have been reported in recent years. For example, to obtain the optimal refrigerant filling ratio, Tong et al. [5] study on the flow region of the SHP with parallel copper tube heat exchangers under different filling ratios experimetally. Ling et al. [4] experimentally investigated the thermal performance of a micro channel separate heat pipe (MCSHP) respect to different filling ratios using R22, and identified the optimal value. Khodabandeh [6] experimentally studied the effects of heat flux (which ranges from 28.3 to 311.5
kW m2 ), system pressures, mass flow rate, vapor fraction, diameter of the evaporator channel and the height difference between evaporator and condenser section on the heat transfer properties of a thermosyphon loop (a device similar to an SHP). Factors like different air velocity and temperature differences between indoor air and outdoor air (10 °C -20 °C) were also 4
experimentally studied by Zhang et al. [7] on the cooling capacity and energy efficiency ratio in thermosyphon mode.
The thermal performance of an SHP can be affected simultaneously by many factors, including geometrical parameters, height difference, refrigerant filling ratio, temperature difference, air flow rate, etc. These factors make a comprehensive experimental investigation difficult. Therefore, it is critical to have a model that can be effective and convenient for simulating the thermal performance of an SHP. In order to explore the thermal characteristics of an SHP with a 7.8 mm diameter copper tube heat exchanger, McDonald et al. [8-10] did an experiment and simulation to explore the effects of refrigerant charge, angles of inclination of evaporator and condenser, temperature difference, and evaporator and condenser tube length and channel diameter. Dube et al. [11] experimentally and theoretically analyzed the non-condensable gases on thermal performance of the loop thermosyphon under various temperature differences 2
(142.8°C -191.2°C). Rao et al. [12] presented the effects of heat flux (40-400 kW m ) on the refrigerant mass flow rate through using a one-dimensional steady state model. Liu et al. [13] developed a one-dimensional steady state model to calculate the upper and lower boundaries of the filling ratio of an SHP with a rectangular heat exchanger (Dh = 21.8 mm) to predict the optimal refrigerant charge for an SHP. The effects of the geometrical parameters of the evaporator, vapor 2
temperature, and heating power (0-0.83 kW m ) on the refrigerant filling boundaries were also presented. Zhang et al. [14] analyzed the effects of temperature difference (4 °C -36 °C) and refrigerant charge on an SHP with a Round Tubes and Plate Fins (RTPF) heat exchanger (Dh = 8.84 mm) through a numerical model. To investigate geometric parameters and temperature
5
difference effects on the thermal characteristics of the thermosyphon mode, Zhang et al. [15] built a model using empirical equations for the thermosyphon loop with a micro channel heat exchanger evaporator (Dh = 1.5 mm) and a three-fluid heat exchanger condenser (Dh = 6 mm) to calculate the cooling capacity and circulation flow rate.
From the literature, it can be seen that existing numerical models were proposed and utilized mainly for a heat pipe cycle with a regular channel (Dh > 3 mm), heat flux and flow flux. This is different from an SHP with a micro channel heat exchanger for low heat flux or low temperature difference and low mass flux [16]. In an evaporator section, the heat transfer regimes include bubbly flow, slug flow, annular flow and mist flow, which makes theoretical modeling of the evaporator section very difficult. Empirical correlations play an important role in this regard, which can directly influence the accuracy of overall simulation results. Currently, there exist a lot of correlations for predicting the two-phase boiling flow heat transfer coefficient. These correlations could be classified into two types:
1) conventional channel two-phase heat transfer coefficient, including the enhanced model [17], the superposition model[18-20], and the power-type asymptotic model. There exists a difference in whether the effect of convective and nucleate boiling is taken into account;
2) small or micro channel two-phase heat transfer coefficient [21-25]. There are many different two-phase heat transfer correlations for predicting thermal performance of small or micro channels. Their main difference is the consideration of impact factors, such as heat flux, mass flux, vapor quality, etc., and whether nucleate boiling or convective boiling is dominant or not.
As shown in Table.1, most two-phase correlations were proposed for high heat flux or mass 6
flux scenarios. It remains vague which correlation among them might present a better a micro channel condition with low refrigerant mass flux (3-32 kg m2 s 1 ) and low heat flux (0-0.25
kW m2 ). Table.1
This paper seeks to solve and fill in these gaps outlined above and find the more suitable correlations for predicting the MCSHP heat transfer performance under low heat flux and low mass flux. Firstly, a distributed-parameter model for an MCSHP under low heat flux and low mass flux was developed, using the ε-NTU method and Nusselt laminar liquid film condensation theory. Six different two-phase heat transfer correlations were adopted for the evaporator section modeling. The simulation results were validated using previous experimental results. Then, the precision of models with different correlations was compared. With the most suitable two-phase correlation, this study further investigated the effects of refrigerant filling ratio, air flow rate and height difference on thermal characteristics of the MCSHP.
2. Modeling The simulation model is built for the MCSHP proposed by the authors in [4], as shown in Fig.1. The system comprises a closed circuit, containing an evaporator section, a condenser section, vapor ascending tube and condensate descending tube. Detailed geometrical parameters of the MCSHP can be found in the paper by Ling et al. [4]. Table.2 summarizes the working conditions used for the simulation.
The numerical model of an MCSHP includes mainly three modules: the evaporator section, connection tubes, and condenser section. The refrigerant state, along with the system cycle, as
7
shown in Fig.1, is provided below:
(1) Evaporator section:
i) Region A: single phase liquid flow region (in saturated or subcooling state);
ii) Region B: two-phase flow region;
iii) Region C: single phase vapor flow region (in saturated or superheating);
(2) Vapor ascending tube: adiabatic, two-phase or vapor region;
(3) Condenser section:
i) Region D: two-phase or vapor (in saturated or superheating) region;
ii) Region E: two-phase region;
iii) Region F: single phase liquid flow region (in saturated or subcooling state);
(4) Condensate descending tube: adiabatic, two-phase or liquid region.
The refrigerant flow along the system cycle abides by momentum (pressure), energy (enthalpy) and mass conservation, as follows:
dP 0
(1)
dH 0
(2)
dM M
(3)
i
Fig. 2 illustrates the flow chart of the numerical model of the MCSHP. In the figure, variables in blue are the input parameters, including geometrical parameters and environmental parameters; variables in red are the parameters as in Eqs. (1) - (3), which are solved by iteration of pressure, enthalpy and mass balance in the loop. The allowable convergence errors for pressure, enthalpy 8
and mass were 0.1kPa, 0.1kJ∙kg-1, and 0.01kg, respectively.
Fig.1
Table.2
Fig.2
2.1 Evaporator section model The micro channel evaporator section was modeled using a finite element approach.The main assumptions and calculated steps in this model can be found in the paper by Ling et al. [1]. The cooling capacity of each segment was calculated by the ε-NTU method, and the cooling capacity of every segment can be calculated as follows:
Qi Cmin Tai ,e Tri
Where Cmin min ma c p ,a , mr c p ,r
(4)
The effectiveness of heat exchanger ε [26] in single phase condition is:
1 NTU 0.22 exp(Cr ·NTU 0.78 ) 1 Cr
=1 exp
Where Cr
min ma c p ,a , mr c p ,r
max ma c p ,a , mr c p ,r
(5)
.
The effectiveness of heat exchanger ε [26] in two-phase condition is:
=1 e NTU NTU =
(6)
UAo Cmin
(7)
The overall thermal resistance consists of the refrigerant-side heat convection thermal resistance, the wall heat conduction thermal resistance and the air-side heat convection thermal 9
resistance. Therefore, the overall heat transfer coefficient in terms of air-side heat transfer area is given as follows:
U
1
1 Ao w Ao 1 hr Aw kw Aw o ha
(8)
The correlations used for the heat transfer and pressure drop calculation are summarized in Table.3. Among these, the refrigerant side two-phase heat transfer coefficient inside the tube, especially in MCSHP under low heat flux or low mass flux, is one of the most important issues. Most two-phase heat transfer correlations are not based on experimental results using R22 in an MCSHP under low heat flux or low mass flux. Thus, the suitability of existing correlations in an evaporator section of the MCSHP is unclear. In this paper, six different correlations for predicting the two-phase heat transfer coefficient were adpoted during the development of the evaporator section model.
Table.3
2.2 Connection tube model The vapor ascending tube and condensate descending tube were used to connect the evaporator section and condenser section. Both of two are considered adiabatic process. The pressure drop can be calculated by Eq. (5).
P Pfr Pg
(9)
The friction pressure drop was calculated using the Gnielinski correlation [27] and the Friedel correlation [31] according to the refrigerant is in single phase condition or two-phase condition, respectively.
2.3 Condenser section model 10
For the condenser section of a heat pipe, the heat transfer regime is annular flow [32], thus the Nusselt laminar liquid film condensation theory can be used to predict the two-phase condensing heat transfer process. However, there exists an interfacial shear that could reduce the thickness of liquid film and promote heat transfer [13]. While the heat transfer mechanism of condenser section in an MCSHP is similar to a Nusselt laminar liquid film condensation, the impact due to the interfacial shear should be considered since it can influence the velocity distribution of the liquid film when the diameter is small.
In this study, the heat transfer coefficient and pressure drop of the vapor region or subcooling liquid region is calculated using the Gnielinski correlation [27]. Because the hydraulic diameter of the channels is very small, the interfacial shear has great influence on the liquid film velocity lateral distribution. A significant deviation was found between the calculated and actual values when the interfacial shear stress was neglected [13]. In this study, the heat transfer model of the two-phase region was built with the effect of interfacial shear considered. According to the laws of conservation of momentum and energy in the liquid film, the following governing equations were obtained:
l
2u1 l g 4 i / dv v g 0 y 2
(10)
2Tl 0 y 2
(11)
Subject to the boundary conditions, we have:
y 0:
ul 0, T Tw
(12)
y :
u l l i , T Ts y
(13)
11
From Eqs. (10)–(13) and the law of thermal equilibrium, the correlations of the velocity distribution ul, the mass flow rate per unit width of liquid film qm, the relationship between liquid film thickness δ, shear stress τi, and position along the axial coordinate x, can be expressed as follows:
2 g 2 i i g 2 ul i y 2 y y l l dv 2l 2 l l d v qm
l g 4 i 3 l i 2 3 l l dv 2l
(14)
(15)
3 C C 3C1 C2 C3 4 i C1 C2 4 i 1 2 3 x l dv 8 l 9 3 32 4
(16)
The coefficients C1 to C3 in Eq. (16) were defined as:
C1
l c p l h fg ρg , C 2 , C3 l l Ts Tw μl
The interfacial shear stress τi, composed of the shear stress due to mass transfer τm, and the shear stress due to friction force τf [32]. Therefore, the two-phase region heat transfer coefficient in condenser section can be calculated as:
h j l / j
(17)
For the condenser section, the cooling capacity is calculated by the ε-NTU method. For a given segment j, the cooling capacity can be calculated as:
Q j Cmin Tri Tai ,c
(18)
3. Results and discussion 3.1 Model verification The model was established in Matlab R2016b, and the refrigerant thermodynamic properties was acquired from the NIST Refrigerant Database REFPROP [33]. 12
In order to verify the accuracy of the developed model, the calculated cooling capacity under different refrigerant filling ratios with different correlations were compared to our experimental results of the MCSHP, as shown in Fig.3- Fig.8. The average relative error σ between the simulated and measured results are based on the following euqation:
Calculated value Measured value 100% Measured value
(19)
Fig.3- Fig.8 shows the comparison of the cooling capacity between experimental results and predictions under different refrigerant filling ratios by using different correlations. The agreement between experimental results and calculations by the Gungor and Winterton correlation (Fig.3) is very good except at the refrigerant filling ratio of 44%. The overall average relative error is 4.9%. The Kandlikar and Steinke correlation and the Khodabandeh correlation in Fig.4- Fig.5 underpredicted the experimental results in the refrigerant filling ratio range of 32%-57%, and their average ralative errors are up to 21 and 22%, respectively. When the refrigerant filling ratio ranges from 70%-120%, the simulation results from all three correlations obtain very high precision. Kim and Mudawar, Bertsch, and Li and Wu correlations (Fig.6-8) are widely applied in predicting twophase heat transfer characteristics of microchannels. However, these correlations overpredicted the measured results in the refrigerant filling ratio range of 32%-57%. When the refrigerant filling ratio is between 70% and 120%, the average relative errors became lower than 5%.
Among these figures, Fig.3, Fig.6, Fig.7 and Fig.8 exist a break point (point 1) in the low refrigerant filling ratio range. This is because the change of the overall heat transfer coefficient was dominated by the change of the refrigerant side heat transfer coefficient when the two-phase heat transfer area in the evaporator section increased largely with the increasing refrigerant filling 13
ratio; consequently, the calculated two-phase heat transfer coefficient is larger than the actual value, which leads to the increase on the calculated cooling capacity. However, the magnitude of the deviation is not big. Overall, the cooling capacity calculated by the Gungor and Winterton correlation provides the best agreement with the experimental results, with an average relative error of about 5%. The Gungor and Winterton correlation will be used in the model to further analyze the thermal performance of the MCSHP.
Fig.3
Fig.4
Fig.5
Fig.6
Fig.7
Fig.8
3.2 Analysis and discussion 3.2.1 Effects of refrigerant filling ratio Fig.9 and Fig.10 show the refrigerant side heat transfer coefficient distribution along the evaporator section and the condenser section corresponding to four different refrigerant filling ratios. The refrigerant filling ratios directly influence the refrigerant side heat transfer coefficient of evaporator section and condenser section. At a low refrigerant filling ratio (FR≤ 38%), the heat transfer coefficient of the evaporator section (hr,e) is very small at the outlet of the evaporator section because of a superheated phenomenon occurring near the outlet of the evaporator section. When the superheating refrigerant flows into the condenser section, the refrigerant remains as dry 14
vapor but from a superheating state to saturation state. Consequently, the refrigerant heat transfer coefficient is small at the condenser section inlet. Then, the refrigerant condenses quickly to form a liquid film, thereby the heat transfer coefficient at the refrigerant side of the condenser section (hr,c) increased sharply. The heat transfer coefficient at refrigerant side (hr,c) gradually decreases with the increasing of the thickness of liquid film (as shown in Fig.11).
At the optimal refrigerant filling ratio (FR= 82%), the heat transfer coefficient at refrigerant side of the evaporator section and condenser section grows along with the path, which means the MCSHPs were in optimal operating condition. Fig.10-11 also shows that there does not exist superheated phenomenon or liquid flooding at the condenser section. In other words, the refrigerant is in two-phase, thereby the refrigerant side heat transfer coefficients have high values. With the refrigerant filling ratio increased (FR= 126% or 170%), the liquid refrigerant floods at the bottom of the condenser section, which causes the refrigerant side heat transfer coefficient to decrease to low values. Fig.12 illustrates the change of the refrigerant in the 100 segments of the condensing section. When the filling ratio increases to 170%, about 78 segments out of 100 is filled with liquid refrigerant.
Fig.9
Fig.10
Fig.11
Fig.12
3.2.2 Effects of air flow rate Modulating the air flow rate through the evaporator section can impact the cooling capacity. 15
At the same time, it will also influence the air side pressure drop, power and pressure of the fan. In this investigation, the refrigerant filling ratio is kept the same because the optimal refrigerant filling ratio was the same under different air flow rate [4]. The environmental conditions, as in Table.2, were used and the air flow rate ranged from 1500 m3/h to 6000 m3/h. Fig.13 shows the cooling capacity and air side pressure drop with different air flow rates. The cooling capacity increased with the increase of the air flow rate, ranging from 2492 W to 5973 W. However, the increasing rate decreased. This is because the increasing rate of the overall heat transfer coefficient decreased (as shown in Fig.14). With the increasing air flow rate, the air side pressure drop increased, which caused the fan energy consumption to increase. According to the Fan Law [34], the power consumption and pressure of the fan decreased with the third power of the air flow rate ratio and square of the air flow rate ratio, respectively.
Fig.13
Fig.14
3.2.3 Effects of height difference between evaporator section and condenser section The height difference between evaporator section and condenser section is another important factor that could affect the thermal performance of an MCSHP. On the one hand, the driven force of the MCSHP mainly relies on the product of height difference and density difference between the vapor ascending tube and the condensate descending tube – that is (ρl-ρv)˖H. Hence, the driven force increases with increasing height difference, thereby, the mass flow rate and the cooling capacity increase. On the other hand, the length of the vapor ascending tube and the condensate descending tube increased with increasing height difference, which cause flow resistance to increase. Fig.15 shows the cooling capacity and the refrigeration mass flow rate under different 16
height differences between the evaporator section and the condenser section. The refrigerant filling ratio and environmental conditions remain unchanged as before. The geometry of the system is also the same, except the height difference changed from 0 to 2.4 m. With the increase of the height difference between the evaporator and condenser sections, the refrigerant mass flow rate increased rapidly at first and then increased slightly. The cooling capacity had the same trend as the refrigerant mass flow rate. However, the cooling capacity was less sensitive to the change of height difference in the range from 0.4 m to 2.4 m. The cooling capacity remained relatively constant once the height difference was greater than 0.4 m. The reason is with a lesser height difference, both temperature difference and height difference can generate a positive effect on the circulation of the refrigerant. Gradually, the height difference dominates, which causes the rapid increase up to the 0.4 m height difference. When the height difference further increases, the driving force is still much greater than the circulation resistance. However, the cooling capacity starts to be restricted by the overall capacity of the evaporator and condenser. Consequently, the enthalpy difference of the refrigerant across the evaporator starts to drop which can lead to a decrease in the quality of the refrigerant at the outlet. Eventually, the driving force provided by the height difference is consumed by the joint effect from the device capacity limitation and refrigerant side pressure drop.
Fig.15
4. Conclusions In this study, we evaluated six two-phase heat transfer correlations to determine the most suitable one for a micro channel separate heat pipe, where the heat flux and mass flux are small. Modified Nusselt laminar liquid condensation model, considering the effect of interfacial shear, 17
was developed for the condenser. Numerical finite control volume models for the evaporator, the connection tubes, and the condenser were established and integrated to simulate the system of an MCSHP. The momentum, energy and mass conservation in the loop were selected as the convergence criteria.
The simulation results were compared to the experimental data collected under various filling ratio conditions. It was found that under low filling ratio conditions, there all exhibited a certain level of discrepancy. In a transitional region, when the filling ration is about 45%, the error could get up to 25% since the two-phase heat transfer area in the evaporator section increased largely with the increasing refrigerant filling ratio in the model. Overall, the Gungor and Winterton correlation provides the lowest error under all filling ratios; the average relative error is about 5%. Based on the results, the Gungor and Winterton is considered more suitable for predicting the thermal performance of an MCSHP under different refrigerant ratios and operation conditions.
Additionally, the effects of refrigerant filling ratio, air flow rate and height difference on an MCSHP were analyzed by using the developed model. The refrigerant side heat transfer coefficient along the evaporator section and condenser section had the maximum value when the system filling ratio was 82%. Increasing the air flow rate increases the overall cooling capacity, but the impact gradually fades and the fan energy consumption increases. As a design parameter, the height difference has a great impact on the refrigerant mass flow rate and cooling capacity. However, the impact is limited by the evaporator and condenser capacity when it reaches a certain value. All three factors should be considered in the design and operation to achieve an optimal overall energy efficiency.
18
Acknowledgements The present study was supported by secience and inovation for graduate students,Hunan (CX2016B110), University of Nebraska-Lincoln Faculty Start-up Fund, and International Science and TechnologyCooperation Program of China (2015DFA61170 and S2016G2422).
We thank Mrs. Kelly Johnson of the University of Nebraska-Lincoln for her great help on editing this paper.
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[15] H. Zhang, S. Shao, H. Xu, H. Zou, M. Tang, C. Tian, Simulation on the performance and free cooling potential of the thermosyphon mode in an integrated system of mechanical refrigeration and thermosyphon, Appl.Energy 185 (2017) 1604–1612. [16] S.G. Kandlikar, W.J. Grande, Evolution of Microchannel Flow Passages--Thermohydraulic Performance and Fabrication Technology, Heat Transfer Eng. 24 (2003) 3-17. [17] M.M. Shah, A new correlation for heat transfer during boiling flow through pipes, ASHRAE Transactions, 82 (1976) 66-86. [18] J.C. Chen, Correlation for boiling heat transfer to saturated fluids in convective flow, Industrial & engineering chemistry process design and development, 5 (1966) 322-329. [19] K.E. Gungor, R.H.S. Winterton, Simplified general correlation for saturated flow boiling and comparisons with data, Chemical Engineering Research & Design, 65 (1987) 148-156. [20] Z. Liu, R. Winterton, A general correlation for saturated and subcooled flow boiling in tubes and annuli, based on a nucleate pool boiling equation, Int. J. Heat Mass Transf. 34 (1991) 27592766. [21] S.S. Bertsch, E.A. Groll, S.V. Garimella, A composite heat transfer correlation for saturated flow boiling in small channels, Int. J. Heat Mass Transf. 52 (2009) 2110-2118. [22] S.G. Kandlikar, M.E. Steinke, Predicting heat transfer during flow boiling in minichannels and microchannels, ASHRAE Transactions, 109 (2003) 667-676. [23] S.-M. Kim, I. Mudawar, Universal approach to predicting saturated flow boiling heat transfer in mini/micro-channels – Part II. Two-phase heat transfer coefficient, Int. J. Heat Mass Transf. 64 (2013) 1239-1256. [24] W. Li, Z. Wu, A general correlation for evaporative heat transfer in micro/mini-channels, Int. J. Heat Mass Transf. 53 (2010) 1778-1787. [25] T. Tran, M.-C. Chyu, M. Wambsganss, D. France, Two-phase pressure drop of refrigerants during flow boiling in small channels: an experimental investigation and correlation development, Int. J. Multiphas. Flow. 26 (2000) 1739-1754. [26] S. Yang, W. Tao, Heat Transfer (Fourth edition), in, Beijing:Heiger Education Press, 2006. [27] V. Gnielinski, New equations for heat and mass-transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359-368. [28] L. Friedel, Improved friction pressure drop correlations for horizontal and vertical two-phase pipe flow, in: European two-phase flow group meeting, Paper E, Vol. 2, 1979, pp. 1979. [29] Y.-J. Chang, C.-C. Wang, A generalized heat transfer correlation for Iouver fin geometry, Int. J. Heat Mass Transf. 40 (1997) 533-544. [30] M.-H. Kim, C.W. Bullard, Air-side thermal hydraulic performance of multi-louvered fin aluminum heat exchangers, Int.J.Refrig. 25 (2002) 390-400. [31] Z. Lu, Two phase flow and boiling heat transfer, Tsinghua University Publishing House, 2002. [32] B. Jiao, L.M. Qiu, X.B. Zhang, Y. Zhang, Investigation on the effect of filling ratio on the steady-state heat transfer performance of a vertical two-phase closed thermosyphon, Appl. Therm. Eng. 28 (2008) 1417-1426. [33] E.W. Lemmon, M.L. Huber, M.O. McLinden, NIST reference fluid thermodynamic and transport properties–REFPROP, in, Version, 2002. [34] F.P. Bleier, Fan Handbook: selection, application, and design, McGraw-Hill New York, 1998. 20
Fig.1 Schematic diagram of the MCSHP and the physical model of evaporator section and condenser section Fig.2 Flow chart of the numerical model for MCSHP Fig.3 Comparison of the cooling capacity between calculated and experimental results by using Gungor and Winterton correlations Fig.4 Comparison of the cooling capacity between calculated and experimental results by using Kandlikar and Steinke correlations Fig.5 Comparison of the cooling capacity between calculated and experimental results by using Khodabandeh correlations Fig.6 Comparison of the cooling capacity between calculated and experimental results by using Kim and Mudawar correlations Fig.7 Comparison of the cooling capacity between calculated and experimental results by using Bertsch et al. correlations Fig.8 Comparison of the cooling capacity between calculated and experimental results by using Li and Wu correlations Fig.9 The refrigerant side heat transfer coefficient distribution in the evaporator section under four refrigerant filling ratios Fig.10 The refrigerant side heat transfer coefficient distribution in the condenser section under four refrigerant filling ratios Fig.11 The thickness of liquid film distribution in the condenser section under four refrigerant filling ratios Fig.12 The schematic diagram of liquid film and liquid pool distribution in the condenser section under four refrigerant filling ratios Fig.13 The cooling capacity and air side pressure drop under different air flow rates Fig.14 The overall heat transfer coefficient distribution in the evaporator section under four different air flow rates 21
Fig.15The cooling capacity and refrigerant mass flow rate under different height difference.
x Region C
7
Region B
5 2
4 Region A 1 7 3
y Region D
8
6
Region E
Region F x 1. Evaporator section
2. Condenser section
3. Micro channel heat exchanger
4. Fan
5. Vapor ascending tube
6. Condensate descending tube
7. Vapor
8. Liquid film
Fig.1 Schematic diagram of the MCSHP and the physical model of evaporator section and condenser section
22
Outputs
air-side outputs
Inputs
Qc
Tac,o
Geometrical parameters
Pc,o Hc,o Pl,i
Hl,i
Tl,i
mr
Tc,o Mc
Condenser section Tac,i
Pc,i
Hc,i
Tc,i
mr
Vac
Pg,o
Hg,o
Tg,o
Mg
Outputs Air-side outputs
Pl,o
Hl,o
Tl,o
Ml
Tae,o
Pe,i mr
He,i
Evaporator section
Tae,i
Vae
Air-side inputs
Qe Pe,o He,o Te,o
Pg,i
Hg,i
Tg,i
mr
Me
Geometrical parameters Inputs
Fig.2 Flow chart of the mathematical model for MCSHP
23
Geometrical parameters Inputs
M
Vapor ascending tube
Condensate descending tube
Inputs Geometrical parameters
air-side inputs
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results Simulation Results Relative errors
2000
1000
0 30
15 10
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.3 Comparison of the cooling capacity between calculated and experimental results by using Gungor and Winterton correlations
24
5000
30
Cooling capacity (W)
20 3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.4 Comparison of the cooling capacity between calculated and experimental results by using Kandlikar and Steinke correlations
25
5000
30
Cooling capacity (W)
20 3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.5 Comparison of the cooling capacity between calculated and experimental results by using Khodabandeh correlations
26
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.6 Comparison of the cooling capacity between calculated and experimental results by using Kim and Mudawar correlations
27
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.7 Comparison of the cooling capacity between calculated and experimental results by using Bertsch et al. correlations
28
5000
30
Cooling capacity (W)
Point 1
20
3000
Experimental results 15 Simulation Results Relative errors 10
2000
1000
0 30
Relative errors (%)
25
4000
5
45
60
75
90
105
0 120
Refrigerant filling ratio (%)
Fig.8 Comparison of the cooling capacity between calculated and experimental results by using Li and Wu correlations
29
2
Heat transfer coefficient h r,e(W/(m ·K))
1000 FR=38% FR=126%
FR=82% FR=170%
800
600
400
200
0
0
10
20
30 40 50 60 70 Calculated segment i
80
90
100
Fig.9 The refrigerant side heat transfer coefficient distribution in the evaporator section under four refrigerant filling ratios
30
FR=38% FR=126%
FR=82% FR=170%
2
Heat transfer coefficient h r,c(W/(m ·K))
4000
3000
2000
1000
0
0
10
20
30
40 50 60 70 Calculated segment j
80
90
100
Fig.10 The refrigerant side heat transfer coefficient distribution in the condenser section under four refrigerant filling ratios
31
-5
Thickness of liquid film (mx10 )
10
FR=38% FR=126%
FR=82% FR=170%
8
6
4
2
0
0
10
20
30 40 50 60 70 Calculated segement i
80
90
100
Fig.11 The thickness of liquid film distribution in the condenser section under four refrigerant filling ratios
32
j=1 j=8
j=1
j=1
j=1 j=32
Liquid film Liquid pool
j=100 FR=38%
j=100
FR=82%
j=89 j=100
FR=126%
j=100
FR=170%
Fig.12 The schematic diagram of liquid film and liquid pool distribution in the condenser section under four refrigerant filling ratios
33
7000
50
6000
40
5000
30
4000
20
3000
10
2000 1500
2250
3000
3750
4500
5250
Air side pressure drop (Pa)
Cooling capacity (W)
Cooling capacity Air sider pressure drop
0 6000
3
Air flow rate (m /h)
Fig.13 The cooling capacity and air side pressure drop under different air flow rates
34
2
Overall heat transfer coefficient (W/(m K))
100
1500 4500
3000 6000
90 80 70 60 50 40
0
20
40
60
80
100
Calculated segement i
Fig.14 The overall heat transfer coefficient distribution in the evaporator section under four different air flow rates
35
Q
160
Gr
140
Cooling capacity (W)
3750
120 100
3000 80 60
2250
40 1500 0.0
0.4
0.8
1.2
1.6
2.0
2.4
Refrigerant mass flow rate (kg/h)
4500
20 2.8
Height difference (m)
Fig.15 The cooling capacity and refrigerant mass flow rate under different height difference.
36
Highlights Simulation model for MCSHP under low heat flux and low mass flux is developed. Six different two-phase heat transfer correlations in the literature are compared. Model with Gungor and Winterton correlation provides the best precision for MCSHP. Effects of filling ratio, air flow rate and height difference on performance are investigated.
37
Table.1 Summary of typical two-phase heat transfer correlations Table.2 Geometrical parameters and working conditions Table.3 Heat transfer and pressure drop correlations for simulation
38
Table.1 Summary of typical two-phase heat transfer correlations Hydraulic diameter
Mass flux
Heat flux
Dh (mm)
G ( kg m2 s 1 )
q ( kW m2 )
Shah [17]
6-25
10-1384
1.26-788.7
Chen[18]
--
--
63-2397
Gungor and Winterton[19]
2.95-32
12.4-8179.3
0. 35-2620
Liu and Winterton[20]
2.95-32
12.4-8179.3
0. 35-2620
Bertsch [21]
0.16-2.92
20-3000
4-1150
Kandlikar and Steinke[22]
0.4-2.97
50-1600
5-600
Kim and Mudawar[23]
0.19-6.5
19-1608
--
Li and Wu [24]
0.16-3.1
20.3-3500
0-1150
Tran et al. [25]
2.4-2.92
33-832
2.2-129
Khodabandeh [6]
1.1-3.5
207-1052
28.3-311.5
Author(s)
39
Table.2 Geometrical parameters and working conditions Parameter
value
Vapor ascending tube length/diameter (m)
3.66/0.019
Condensate descending tube length/diameter (m)
4.37/0.016
Height difference(m)
2.0
Indoor space temperature (dry/wet bulb) (ºC)
28/19.5
Exterior space temperature (dry/wet bulb) (ºC)
18/11.4
Air flow rate (m3/h)
2980
Refrigerant filling ratio (%)
32%~120%
Working fluid
R22
40
Table.3 Heat transfer and pressure drop correlations for simulation Item
Correlation Heat transfer coefficient
Gnielinski [27]
Pressure drop
Gnielinski [27]
Single phase condition
(1) Gungor and Winterton[19] (2)Kandlikar and Steinke[22]; Heat transfer coefficient Two phase condition
(3)Kim and Mudawar[23]; (4)Bertsch et al.[21]; (5)Li and Wu[24]; (6)Khodabandeh[6].
Pressure drop Heat transfer coefficient
Friedel [28] Chang and Wang [29]
Air side Pressure drop
41
Kim and Bullard[30]