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Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer
Journal Pre-proofs Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer Jie Pan, Jinghan Wang, Linghong Tang, Junhua Bai, Ran Li, Yinbin Lu, Gang Wu PII: DOI: Reference:
S1359-4311(19)35841-7 https://doi.org/10.1016/j.applthermaleng.2019.114447 ATE 114447
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
21 August 2019 22 September 2019 25 September 2019
Please cite this article as: J. Pan, J. Wang, L. Tang, J. Bai, R. Li, Y. Lu, G. Wu, Numerical investigation on thermalhydraulic performance of a printed circuit LNG vaporizer, Applied Thermal Engineering (2019), doi: https://doi.org/ 10.1016/j.applthermaleng.2019.114447
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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.
© 2019 Published by Elsevier Ltd.
Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer Jie Pana,*, Jinghan Wanga, Linghong Tangb, Junhua Baia, Ran Lia, Yinbin Lu b, Gang Wua a
College of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi Province,
China b
College of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi Province,
China *Corresponding author. Tel.: +86 29 88382932; fax: +86 29 88382932 E-mail address: [email protected]
Abstract As a new type of micro-channel heat exchanger, printed circuit heat exchanger (PCHE) is widely applied to floating storage and regasification unit (FSRU) as LNG vaporizer for high efficiency and compactness. In this paper, a three-dimensional numerical model of counter-flow printed circuit LNG vaporizer is established, applying supercritical LNG and propane as cold source and heat source respectively. The flow and heat transfer characteristics in semicircular channels, and the effects of channel bending angle on them are studied. The results indicate that the channel bending causes the accelerating core of cold and hot fluids close to the inner wall of the corner, thinning or even destructing the boundary layer, which is conducive to convective heat transfer, although causes greater flow resistance. The larger the channel bending angle, the better the heat transfer and the greater the pressure drop. The criterion ]
Nu / Nu / f / f 0
0
is used to evaluate the thermal-hydraulic
performance of the printed circuit LNG vaporizer, and it shows that the channel
bending angle 15° offers the best comprehensive performance. Key words: printed circuit LNG vaporizer; numerical model; supercritical LNG; propane; flow and heat transfer characteristics; comprehensive performance. 1. Introduction As a clean energy source, LNG attracts more and more attention in recent years. It needs to be vaporized and heated to ambient temperature using LNG vaporizers before entering natural gas pipelines. PCHE developed by HEATRIC [1] is a compact heat exchanger with high efficiency. Using photo-chemical etching technique and diffusion bonding method, a PCHE usually has semicircular channels of 0.5-5.0 mm diameter and the durability under high pressure [2]. In terms of great advantages, PCHE is widely used in oil and gas industry, chemical industry, fuel processing, electric power, refrigeration and other fields. As the demand for LNG increases, the demands for LNG transportation, supply facilities and FSRU are increasing. Due to its high safety and reliability, PCHE has been widely used in LNG-FRSU as the key equipment of LNG regasification process [3]. Numerous scholars have conducted various investigations regarding the thermal-hydraulic performance of PCHE. Lai et al. [4] developed a numerical model for refrigerant condensation in zigzag semicircular channels. They obtained the flow patterns of refrigerant R134a in zigzag channel under different operating conditions. Kim et al. [5] numerically studied the thermal-hydraulic characteristics of zigzag channels with semicircle cross-sections using a helium-helium condition and a helium-water condition. Khan et al. [6] performed a three-dimensional numerical
simulation on wavy-channel based PCHE, and studied the flow and heat transfer characteristics of fluids at different channel bending angles and different Reynolds numbers. It is believed that the spatially periodic flow separation or tripping of boundary layer does not allow the flow to be fully-developed, resulting in heat transfer enhancement. Baik et al. [7] numerically investigated the thermal performance of wavy-channeled PCHEs, and the effects of amplitude and period. It was concluded that the wavy-channeled PCHEs have better thermal performance due to the increased area for heat transfer, and the performance enhancement can be predicted by the ration between amplitude and period, which is linear. Kim et al. [8] studied the effects of channel size and channel length on the thermal-hydraulic characteristics of PCHE, and proposed a mathematical expression for predicting the thermal performance of parallel, cross and counter-flow PCHE. Other studies [9-12] numerically investigated PCHEs with airfoil shaped fins. It is considered that streamlined shape of airfoil fins can reduce the pressure drop remarkably at same heat transfer performance, and the optimal configuration of airfoil shaped fins and the effects of various design parameters in PCHEs were investigated. Wu et al. [13] carried out a size-scaling experiment on PCHE using LNG and propane as cold source and heat source respectively. The results show that PCHE has good heat transfer performance and high gasification efficiency, which can meet the requirements of low-temperature and high-pressure conditions in LNG-FSRU. Even though many studies were performed on the thermal-hydraulic characteristics of PCHE, most of them used supercritical carbon dioxide and
supercritical water as working fluids, and there are few studies applying PCHE in LNG regasification process. The thermal-hydraulic performance of printed circuit LNG vaporizer involves micro-channel flow, the variation of thermophysical properties and the condensation of propane, which makes it more complicated. In this paper, a three-dimensional numerical model is constructed on zigzag as compared to straight channeled PCHE, applying supercritical LNG and propane as cold source and heat source respectively. A commercial FLUENT code is used for the numerical solution. In the light of the numerical results, the thermal-hydraulic performance of printed circuit LNG vaporizer and the effects of channel bending angle are studied. 2. Numerical model and solution method 2.1. Description of physical problem A counter-flow printed circuit LNG vaporizer is constructed of several plates that contain semicircular micro-channels, where supercritical LNG and propane flow in opposite directions as cold and hot fluids respectively, as shown in Fig. 1. Due to heat release, the propane in hot channel is cooled by cryogenic LNG, and gradually condenses after reaching the condensation temperature. Meanwhile, cryogenic LNG in cold channel is heated by propane, and the temperature increases continuously. Fig. 1. Schematic diagram of a counter-flow printed circuit LNG vaporizer 2.2. Modeling assumptions In the printed circuit LNG vaporizer, all flow channels have the same geometry and are arranged in parallel. In this study, the calculation takes only one hot channel and one cold channel considering the symmetry. The flow channels are zigzag
semicircular channels with various bending angles of 0° (straight), 15°, 30° and 45° respectively. As Fig. 2 illustrates, the height of each plate is 1.6mm, and the diameter of the hot and cold channels is 1.8mm. The periodic length of flow channels is 26mm and the overall horizontal length of flow channels is 520mm. (a) cross-section of simulation domain (b) geometry dimension of zigzag channel (c) 3D model Fig. 2. Geometric diagram of simulation domain 2.3. Mesh generation In this paper, the structured grid technology is used to generate hexahedron element meshes by ANSYS ICEM software. With the aim to ensure the gradients of thermophysical properties in boundary layer being properly resolved, smaller mesh spacing is adopted in near wall zone. The boundary layer has the initial height of 0.05mm with ratio of 1.2 for 4 layers. The surface meshes in cross-section are shown in Fig. 3. Various grid numbers, including 0.73, 1.43, 2.5, 3.2, 4 million, are applied in the numerical solution to validate the grid independence. When the gird number is greater than 2.5 million, the relative deviations of average outlet temperature and pressure drop are less than 0.5%, indicating that the numerical solutions are mesh-independent, as shown in Fig. 4. Therefore, the grid number of 2.5 million is selected in this paper. Fig. 3. Surface meshes of cross-section Fig. 4. Mesh dependency test
2.4. Numerical method Based on existing investigations, the volume of fluid (VOF) model is used to distinguish the liquid and gas phases, and to track the interface between them. The governing equations based on the volume fraction of the gas and liquid phases in the VOF model are listed as follows: Continuity equation w D v Uv D v UvQ v Sm wt w D l U l D l U lQ l S m wt
(1)
(2)
Dv Dl 1
(3)
Momentum equation
UQQ QQ wt
w UQ Q
T 2 ª º p « P Q Q P Q » U g FV 3 ¬ ¼
(4)
Energy equation w UE ª¬Q U E p º¼ kT Q wt
(5)
The shear stress transport (SST) k-ω model is selected in the present work to capture the structural features of turbulent flow in the channels. The SST k-ω turbulence model combines the merits of k-ε model and k-ω model, and it has stable algorithm and high accuracy near the wall [14]. The equations are written as below: U u j ui
wUui k wxi
§ wu wu 2 · Pt ¨ i j kG ij ¸ ¨ wx wx 3 ¸ i © j ¹
§ wk § P w¨ t P ¨ ¨ wwxx Vk © j© wx j
·· ¸ ¸¸ ¹¹
Gk Yk
(6)
(7)
wU uiZ wxi
§ wZ § P w¨ P t ¨ wx ¨ VZ © j© wx j
·· ¸ ¸¸ ¹¹ GZ YZ DZ
(8)
2.5. Model validation To verify the present model, a numerical simulation of zigzag-channeled PCHE is conducted, and the experimental inlet conditions are used as inlet boundary conditions for numerical solution. The simulation results are compared with the experimental data from Wu et al. [13], and the outlet temperature differences of cold/hot side were evaluated using the following equation: Error (%)
experiment data - numerical data u100 experiment data
(9)
The results show that the relative error of outlet temperature at propane side is 0.6%, and that at LNG side is 2.8%. The numerical results were in a good agreement with the experimental data, which indicates that the numerical model is reliable. 2.6 Simulation conditions The thermophysical properties of LNG and propane, considerably depend on both temperature and pressure, are obtained from NIST-REFPROP software. In this paper, LNG is composed of 90mol% methane, 7mol% ethane and 3mol% propane. The thermophysical properties of LNG at supercritical pressure vary drastically, especially close to the pseudo-critical point, which have significant effects on heat transfer. Fig. 5 shows the thermophysical properties of supercritical LNG versus temperature at the pressure of 7.3 MPa, including dynamic viscosity, density, specific heat and thermal conductivity. Fig. 5. Thermophysical properties of LNG at 7.3MPa
In this paper, the inlet boundary conditions of hot and cold channels are constant mass flow rate and constant temperature. The outlet boundary conditions of hot and cold channels are constant pressure. The boundary conditions of the top and bottom walls, the left and right side walls are set up to periodic condition. The inlet and outlet conditions are shown in Table 1. Table 1 Boundary conditions in CFD approach 3. Numerical results and discussion 3.1. Local flow and heat transfer characteristics Based on the simulation results, the flow and heat transfer characteristics in printed circuit LNG vaporizer with zigzag channels (bending angle θ=15°) are analyzed. The temperature profiles of propane and supercritical LNG are shown in Fig. 6. It can be seen that the propane completely condenses due to heat release, and its temperature decreases from 293.15K to 251.8K. Simultaneously, the supercritical LNG absorbs the heat, and the temperature rises from 128.9K to 273.7K. Fig. 6. Temperature profiles of propane and supercritical LNG in 15° zigzag channels Fig. 7 and Fig. 8 respectively give the temperature and velocity contours of propane and supercritical LNG at different cross-sections. It can be seen that periodic flow and heat transfer occur in both cold and hot channels. Each local low-temperature region of LNG and high-temperature region of propane in temperature contour respectively corresponds well to its accelerating core in velocity contour. Therefore, the temperature distribution is considered to be determined mainly by the velocity distribution. It also shows that the accelerating core of propane and
supercritical LNG all close to the inner wall of the corner. The main reason is that the periodic channel forces the fluid to change its flow direction, resulting in a centrifugal force. The shifting of accelerating core thins or even destructs the boundary layer, which is conducive to convective heat transfer [15]. Thus, local low-temperature region of LNG and high-temperature region of propane show similar trends. (a) temperature contour (b) velocity contour Fig. 7. Temperature and velocity contours of propane at different cross-sections (a) temperature contour (b) velocity contour Fig. 8. Temperature and velocity contours of supercritical LNG at different cross-sections Fig. 9 and Fig. 10 respectively show the secondary flow of propane and supercritical LNG at different cross-sections. Compared with straight channel, the combined effects of the flow acceleration/development and the secondary flow cause a significant difference in vorticity pattern for a zigzag channel [6]. As shown in Fig. 9, at z=494mm, no vortex appears and the streamlines are all to the right, since propane have just passed through the inlet straight section, and continue flowing into the zigzag channel section. This is also the reason why the LNG shown in Fig. 10 has no vortex at z=26 mm, and the streamlines are all to the left. At other cross-sections, the propane vortice distribution is negative in the upper regions, and positive in the lower regions, while the LNG vortice distribution is opposite. The number and
location of vortices of propane and LNG change constantly along the flow direction. The secondary flow generated by flow separation and vortex formation has a great influence on heat transfer enhancement, fluid mixing and displacement of accelerating core. Fig. 9. Secondary flow of propane at different cross-sections Fig. 10. Secondary flow of supercritical LNG at different cross-sections 3.2. Effects of channel bending angle on fluid flow Fig. 11 indicates the streamlines of supercritical LNG in different angled channels (θ=0°, 15°, 30°, 45°). It can be observed that the zigzag channel has a disturbing effect on fluid, and the increase in the bending angle results in a more drastic change in the flow direction. When the bending angle of channel is 30° and 45°, the backflow occurs near the bending parts, and the backflow area generated in 45° zigzag channel is larger, which reduces actual flow area and increases its resistance. Fig. 11. Streamlines of supercritical LNG in different angled channels Fig. 12 shows the Reynolds number of supercritical LNG in different angled channels, it shows a tendency to increase rapidly and then gradually flatten. The main reason is that the dynamic viscosity gradually decreases along the flow direction resulting from the increase in LNG temperature. It can be seen that the larger the channel bending angle, the larger the Reynolds number, indicating that larger channel bending angle causes the flow more intense. Fig. 12. Reynolds number of supercritical LNG along flow direction
3.3. Effects of channel bending angle on thermal performance Fig. 13 shows the bulk temperature profiles of supercritical LNG and propane in printed circuit LNG vaporizer with different angled channels (θ=0°, 15°, 30°, 45°). As Fig. 13 shows, the supercritical LNG temperature continuously increases along the flow direction. Compared with straight channel, the LNG temperature in zigzag channels increases more rapidly, and the larger the bending angle, the higher the temperature increase rate, resulting in a higher outlet temperature. Fig. 14 shows the liquid volume fraction of propane along the flow direction in different angled channels. From Fig. 13 and Fig. 14, it can be seen that in the inlet section, the propane temperature decreases along the flow direction on account of heat absorption. As the channel bending angle increases, the temperature drop rate of propane decreases slightly. This is because in the counter-flow printed circuit LNG vaporizer, the propane in the inlet section exchanges heat with the LNG in the outlet section. The larger the channel bending angle, the higher the outlet temperature of LNG, that is, the smaller the temperature difference between the cold and hot fluids. At this time, the heat transfer is weakened as the bending angle increases, since small temperature difference plays a dominant role in heat transfer. When the condensation point 286.55K is reached, the propane gradually condenses and the temperature remains the same. In the outlet section, the propane temperature decreases once again, and the decline becomes rapid. The larger the channel bending angle, the faster the propane cools, and the lower the outlet temperature. The reason is that, by enhancing heat transfer area geometrically and increasing local flow velocity at channel bending
points, the zigzag channel enhances the heat transfer performance compared with straight channels. Fig. 13. Temperature profiles of propane and supercritical LNG in different angled channels Correspondingly, the liquid volume fraction of propane in channels remains at zero at the beginning until the condensation temperature is reached. Then, the condensation rate of propane first decreases slightly with increasing channel bending angle, and finally increases significantly with increasing channel bending angle. The larger the bending angle, the earlier the liquid volume fraction of propane reaches 1 near the outlet. As shown in Fig. 14, propane in 45° zigzag channel is the first to completely condensate, while the liquid volume fraction of propane in the straight channel does not reach 1 at the outlet. Fig. 14. Liquid volume fraction of propane along the flow direction The overall heat transfer efficiency of a counter-flow printed circuit LNG vaporizer can be expressed as:
K
Tc ,o Tc ,i Th ,i Tc ,i
(10)
Therefore, for a printed circuit LNG vaporizer, the larger the channel bending angle, the higher the overall heat transfer efficiency. In this paper, the vaporizer with 45° zigzag channels has the highest efficiency, which can reach 0.957. Whereas, for the vaporizer with straight channel, the heat transfer efficiency is the lowest, which is 0.85. 3.4. Effects of channel bending angle on pressure drop
Fig. 15 shows the pressure variety of supercritical LNG in different angled channels. On the whole, the pressure loss of supercritical LNG tends to increase with increasing flow distance. The larger the channel bending angle, the greater the pressure drop. This is mainly because that with the increase of the bending angle, the flow separation of boundary layer at the corner become more obvious, which leads to a significant increase in pressure loss. Fig. 15. Pressure of supercritical LNG at different positions 3.4. Comprehensive performance of a printed circuit LNG vaporizer It is concluded that the increase in the channel bending angle is conducive to heat transfer, but it also leads to a greater pressure drop. Therefore, it is unreasonable to evaluate the flow or heat transfer performance unilaterally. The criterion
]
Nu / Nu / f / f 0
0
is used as the evaluation index to reflect the
thermal-hydraulic characteristics of printed circuit LNG vaporizers with different channel bending angles (0°, 15°, 30°, 45°) comprehensively. The relevant parameters are calculated as follows [6,16]: Nu
h
hDe
O qw T T Tw i o 2
(11) (12)
De
4A L
(13)
f
'pDe 2 U u 2l
(14)
]
Nu Nu0 f f0
(15)
Fig. 16 gives the Nusselt number and Fanning friction factor of the cold channel versus channel bending angle. It can be seen that both the Nusselt number and Fanning friction factor increase with the increase of channel bending angle. When the channel bending angle rises from 0° to 15°, the Nusselt number increases obviously, and the Fanning friction factor has a little increase, indicating that the effect of bending angle on heat transfer is dominant. Conversely, its effect on flow resistance is more significant when the channel bending angle is larger than 15°. The main reason is that the drastic change in flow direction leads to excessive flow resistance. The comprehensive performance evaluation results of the printed circuit LNG vaporizers with different angled channels are shown in Table 2. It indicates that the channel bending angle 15° offers the best comprehensive performance. Fig. 16. Nu and f of the cold channel Table 2 Comprehensive performance evaluation results 5. Conclusions In this paper, a three-dimensional numerical model of counter-flow printed circuit LNG vaporizer is established, the thermal-hydraulic performance of hot and cold fluids in channels, and the effects of channel bending angle on it is studied. Based on the numerical results, the following conclusions are derived. (1) Periodic flow and heat transfer occur in both cold and hot channels, and the temperature distribution is considered to be determined mainly by the velocity
distribution. The channel bending causes the accelerating core of cold and hot fluids close to the inner wall of the corner, thinning or even destructing of the boundary layer, which is conducive to convective heat transfer. In addition, the secondary flow generated by flow separation and vortex formation has a great influence on heat transfer enhancement, fluid mixing and displacement of accelerating core. (2) The increase in channel bending angle results in a more intense flow. The larger the bending angle of the channel, the larger the Reynolds number of the supercritical LNG. When the bending angle of the channel is 30° and 45°, the fluid backflow occurs near the corner, which reduces the actual flow area and increases the flow resistance. (3) For both cold and hot fluids, the temperature differences between the inlet and outlet increase with the increase of channel bending angle. The larger the bending angle, the better the heat transfer between cold and hot fluids, and the faster the hot fluid (propane) completely condenses, although accompanying larger pressure drop. Among the printed circuit LNG vaporizers with different angled channels, the vaporizer with 45° channels has the highest overall heat transfer efficiency, which can reach 0.957. (4) The thermal-hydraulic performance of printed circuit LNG vaporizers with various angled channels is evaluated, and the results show that the channel bending angle 15° offers the best comprehensive performance. Acknowledgement This study was supported by the National Natural Science Foundation of China
(Grant No.51774237, 51304160), and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No.15JK1581). Reference [1] S. J. Dewson, C. Grady, HEATRIC workshop at MIT, Cambridge, MA, USA, October 2, 2003. [2] X. Li, R.L. Pierres, S.J. Dewson, Heat exchangers for the next generation of nuclear reactors, International Congress on Advances in Nuclear Power Plants (ICAPP) 2006, Reno, NV, USA, June 4-8, 2006. [3] S. Baek, G. Hwang, J. Kim, S. Jeong, Development of compact heat exchanger for LNG FPSO, 21st International offshore and polar engineering conference (ISOPE 2011 Maui), Maui, Hawaii, USA, June 19-24, 2011. [4] Z.C. Lai, J.R. Li, H.T. Hu, D.W. Zhuang, X.M. Weng, G.L. Ding, Numerical simulation of refrigerant flow condensation characteristics in zigzag channel of printed circuit heat exchanger, Chinese Journal of Refrigeration Technology 36(4) (2016) 29-35 (in Chinese). [5] I.H. Kim, Experimental and numerical investigations of thermal-hydraulic characteristics for the design of a Printed Circuit Heat Exchanger (PCHE) in HTGRs, Ph.D. Dissertation, Korea Advanced Institute of Science and Technology, 2012. [6] H.H. Khan, A.A. M, A. Sharma, A. Srivastava, P. Chaudhuri, Thermal-hydraulic characteristics and performance of 3D wavy channel based printed circuit heat exchanger, Applied Thermal Engineering, 87 (2015) 519-528.
[7] Y.J. Baik, S. Jeon, B. Kim, D. Jeon, C. Byon, Heat transfer performance of wavy-channeled PCHEs and the effects of waviness factors, International Journal of Heat and Mass Transfer, 114 (2017) 809-815. [8] W. Kim, Y.J. Baik, S. Jeon, D. Jeon, C. Byon, A mathmatical correlation for predicting the thermal performance of cross, parallel, and counterflow PCHEs, International Journal of Heat and Mass Transfer, 106 (2016) 1294-1302. [9] D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermal-hydraulic performance of new printed circuit heat exchanger model, Nuclear Engineering and Design, 238 (2008) 3269-3276. [10]S.H. Yoon, J.G. Kwon, T.H. Kim, H.S. Park, M.H. Kim, Analysis on optimal configuration of air-foil shaped printed circuit heat exchanger in supercritical carbon dioxide power cycle, 15th International Heat Transfer Conference (IHTC-15), Kyoto, Japan, August 10-15, 2014. [11]J.G. Kwon, T.H. Kim, H.S. Park, J.E. Cha, M.H. Kim, Optimization of airfoil-type PCHE for the recuperator of small scale brayton cycle by cost-based objective function, Nuclear Engineering and Design 298 (2016) 192-200. [12]T.H. Kim, J.G. Kwon, S.H. Yoon, H.S. Park, M.H. Kim, J.E. Cha, Numerical analysis of air-foil shaped fin performance in printed circuit heat exchanger in a supercritical carbon dioxide power cycle, Nuclear Engineering and Design 288 (2015) 110-118. [13]W.W. Wu, D.B. Wang, L.M. Zhao, Z.Q. Yuan, Experimental investigation of printed circuit heat exchanger as LNG vaporizer, Ocean Engineering Equipment and Technology, 3(1) 2016 20-24 (in Chinese). [14]Z.X. Zhang, Z.N. Dong, Viscous fluid mechanics, Beijing: Tsinghua University Press, 1998.
[15]J.M. Choi, N.K. Anand, Turbulent heat transfer in a serpentine channel with a series of right-angle turns, International Journal of Heat and Mass Transfer, 38(7) (1995) 1225-1236. [16]I.H. Kim, H.C. No, J.I. Lee, B.G. Jeon, Thermal hydraulic performance analysis of the printed circuit heat exchanger using a helium test facility and CFD simulations, Nuclear Engineering and Design, 239(11) (2009) 2399-2408.
Highlights
¾
the secondary flow in cold and hot channels is analyzed.
¾
the effects of channel bending angle on thermal-hydraulic performance are discussed.
¾
periodic flow and heat transfer occur in both cold and hot channels.
¾
zigzag channel can enhance convective heat transfer.
¾
channel bending angle 15° offers the best comprehensive performance.
Nomenclature A
cross-sectional area (m2)
cp
specific heat at constant pressure (kJ·kg-1·K-1)
coeff
configurable mass transfer parameter
De
hydraulic diameter (m)
Fσ
surface tension term
f
Fanning friction factor (–)
g
acceleration of gravity (m·s-2)
h
surface heat transfer coefficient (W·m-2·K-1)
L
circumference (m)
l
length of channel (m)
m
mass flow rate (kg·s-1)
m
mass transfer rate (kg·s-1)
n
phase interface function
Nu
Nusselt number (–)
p
pressure (MPa)
Δp
pressure drop (Pa)
Q
latent heat source term
q
heat flux (W·m-2)
Re
Reynolds number (–)
Sm
quality source term
T
temperature (K)
u
velocity (m·s-1)
Greek symbols α
volume fraction (–)
γ
latent heat (J·kg-1)
ζ
comprehensive evaluation index (–)
η
overall heat transfer efficiency (–)
θ
channel bending angle (°)
β
contact angle (°)
λ
thermal conductivity (W·m-1·K-1)
μ
dynamic viscosity (Pa·s-1)
ρ
density (kg·m-3)
Subscript c
cold fluid
h
hot fluid
i
inlet
l
liquid phase
lv
liquid phase evaporates into gas phase
o
outlet
sat
saturation
v
vapor phase
vl
gas phase condenses into liquid phase
w
inner wall
Table 1 Comparison between simulation results and experimental data Experimental data
Numerical data
Error(%)
Cold channel temperature difference (K)
167.44
159.24
4.8
Hot channel temperature difference (K)
23.39
21.74
7.05
Table 2 Boundary conditions in CFD approach mc (kg/s)
mh (kg/s)
Tci (K)
Thi (K)
pco (MPa)
pho (MPa)
0.0002995
0.00045
128.9
293.15
7.3
0.64
Table 3 Comprehensive performance evaluation results bending angle (θ)
evaluation index (ζ)
15°
1.124293
30°
0.573075
45°
0.295884
Conflict of Interest Statement: We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer”.
S1359-4311(19)35841-7 https://doi.org/10.1016/j.applthermaleng.2019.114447 ATE 114447
To appear in:
Applied Thermal Engineering
Received Date: Revised Date: Accepted Date:
21 August 2019 22 September 2019 25 September 2019
Please cite this article as: J. Pan, J. Wang, L. Tang, J. Bai, R. Li, Y. Lu, G. Wu, Numerical investigation on thermalhydraulic performance of a printed circuit LNG vaporizer, Applied Thermal Engineering (2019), doi: https://doi.org/ 10.1016/j.applthermaleng.2019.114447
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. 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.
© 2019 Published by Elsevier Ltd.
Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer Jie Pana,*, Jinghan Wanga, Linghong Tangb, Junhua Baia, Ran Lia, Yinbin Lu b, Gang Wua a
College of Petroleum Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi Province,
China b
College of Mechanical Engineering, Xi’an Shiyou University, Xi’an 710065, Shaanxi Province,
China *Corresponding author. Tel.: +86 29 88382932; fax: +86 29 88382932 E-mail address: [email protected]
Abstract As a new type of micro-channel heat exchanger, printed circuit heat exchanger (PCHE) is widely applied to floating storage and regasification unit (FSRU) as LNG vaporizer for high efficiency and compactness. In this paper, a three-dimensional numerical model of counter-flow printed circuit LNG vaporizer is established, applying supercritical LNG and propane as cold source and heat source respectively. The flow and heat transfer characteristics in semicircular channels, and the effects of channel bending angle on them are studied. The results indicate that the channel bending causes the accelerating core of cold and hot fluids close to the inner wall of the corner, thinning or even destructing the boundary layer, which is conducive to convective heat transfer, although causes greater flow resistance. The larger the channel bending angle, the better the heat transfer and the greater the pressure drop. The criterion ]
Nu / Nu / f / f 0
0
is used to evaluate the thermal-hydraulic
performance of the printed circuit LNG vaporizer, and it shows that the channel
bending angle 15° offers the best comprehensive performance. Key words: printed circuit LNG vaporizer; numerical model; supercritical LNG; propane; flow and heat transfer characteristics; comprehensive performance. 1. Introduction As a clean energy source, LNG attracts more and more attention in recent years. It needs to be vaporized and heated to ambient temperature using LNG vaporizers before entering natural gas pipelines. PCHE developed by HEATRIC [1] is a compact heat exchanger with high efficiency. Using photo-chemical etching technique and diffusion bonding method, a PCHE usually has semicircular channels of 0.5-5.0 mm diameter and the durability under high pressure [2]. In terms of great advantages, PCHE is widely used in oil and gas industry, chemical industry, fuel processing, electric power, refrigeration and other fields. As the demand for LNG increases, the demands for LNG transportation, supply facilities and FSRU are increasing. Due to its high safety and reliability, PCHE has been widely used in LNG-FRSU as the key equipment of LNG regasification process [3]. Numerous scholars have conducted various investigations regarding the thermal-hydraulic performance of PCHE. Lai et al. [4] developed a numerical model for refrigerant condensation in zigzag semicircular channels. They obtained the flow patterns of refrigerant R134a in zigzag channel under different operating conditions. Kim et al. [5] numerically studied the thermal-hydraulic characteristics of zigzag channels with semicircle cross-sections using a helium-helium condition and a helium-water condition. Khan et al. [6] performed a three-dimensional numerical
simulation on wavy-channel based PCHE, and studied the flow and heat transfer characteristics of fluids at different channel bending angles and different Reynolds numbers. It is believed that the spatially periodic flow separation or tripping of boundary layer does not allow the flow to be fully-developed, resulting in heat transfer enhancement. Baik et al. [7] numerically investigated the thermal performance of wavy-channeled PCHEs, and the effects of amplitude and period. It was concluded that the wavy-channeled PCHEs have better thermal performance due to the increased area for heat transfer, and the performance enhancement can be predicted by the ration between amplitude and period, which is linear. Kim et al. [8] studied the effects of channel size and channel length on the thermal-hydraulic characteristics of PCHE, and proposed a mathematical expression for predicting the thermal performance of parallel, cross and counter-flow PCHE. Other studies [9-12] numerically investigated PCHEs with airfoil shaped fins. It is considered that streamlined shape of airfoil fins can reduce the pressure drop remarkably at same heat transfer performance, and the optimal configuration of airfoil shaped fins and the effects of various design parameters in PCHEs were investigated. Wu et al. [13] carried out a size-scaling experiment on PCHE using LNG and propane as cold source and heat source respectively. The results show that PCHE has good heat transfer performance and high gasification efficiency, which can meet the requirements of low-temperature and high-pressure conditions in LNG-FSRU. Even though many studies were performed on the thermal-hydraulic characteristics of PCHE, most of them used supercritical carbon dioxide and
supercritical water as working fluids, and there are few studies applying PCHE in LNG regasification process. The thermal-hydraulic performance of printed circuit LNG vaporizer involves micro-channel flow, the variation of thermophysical properties and the condensation of propane, which makes it more complicated. In this paper, a three-dimensional numerical model is constructed on zigzag as compared to straight channeled PCHE, applying supercritical LNG and propane as cold source and heat source respectively. A commercial FLUENT code is used for the numerical solution. In the light of the numerical results, the thermal-hydraulic performance of printed circuit LNG vaporizer and the effects of channel bending angle are studied. 2. Numerical model and solution method 2.1. Description of physical problem A counter-flow printed circuit LNG vaporizer is constructed of several plates that contain semicircular micro-channels, where supercritical LNG and propane flow in opposite directions as cold and hot fluids respectively, as shown in Fig. 1. Due to heat release, the propane in hot channel is cooled by cryogenic LNG, and gradually condenses after reaching the condensation temperature. Meanwhile, cryogenic LNG in cold channel is heated by propane, and the temperature increases continuously. Fig. 1. Schematic diagram of a counter-flow printed circuit LNG vaporizer 2.2. Modeling assumptions In the printed circuit LNG vaporizer, all flow channels have the same geometry and are arranged in parallel. In this study, the calculation takes only one hot channel and one cold channel considering the symmetry. The flow channels are zigzag
semicircular channels with various bending angles of 0° (straight), 15°, 30° and 45° respectively. As Fig. 2 illustrates, the height of each plate is 1.6mm, and the diameter of the hot and cold channels is 1.8mm. The periodic length of flow channels is 26mm and the overall horizontal length of flow channels is 520mm. (a) cross-section of simulation domain (b) geometry dimension of zigzag channel (c) 3D model Fig. 2. Geometric diagram of simulation domain 2.3. Mesh generation In this paper, the structured grid technology is used to generate hexahedron element meshes by ANSYS ICEM software. With the aim to ensure the gradients of thermophysical properties in boundary layer being properly resolved, smaller mesh spacing is adopted in near wall zone. The boundary layer has the initial height of 0.05mm with ratio of 1.2 for 4 layers. The surface meshes in cross-section are shown in Fig. 3. Various grid numbers, including 0.73, 1.43, 2.5, 3.2, 4 million, are applied in the numerical solution to validate the grid independence. When the gird number is greater than 2.5 million, the relative deviations of average outlet temperature and pressure drop are less than 0.5%, indicating that the numerical solutions are mesh-independent, as shown in Fig. 4. Therefore, the grid number of 2.5 million is selected in this paper. Fig. 3. Surface meshes of cross-section Fig. 4. Mesh dependency test
2.4. Numerical method Based on existing investigations, the volume of fluid (VOF) model is used to distinguish the liquid and gas phases, and to track the interface between them. The governing equations based on the volume fraction of the gas and liquid phases in the VOF model are listed as follows: Continuity equation w D v Uv D v UvQ v Sm wt w D l U l D l U lQ l S m wt
(1)
(2)
Dv Dl 1
(3)
Momentum equation
UQQ QQ wt
w UQ Q
T 2 ª º p « P Q Q P Q » U g FV 3 ¬ ¼
(4)
Energy equation w UE ª¬Q U E p º¼ kT Q wt
(5)
The shear stress transport (SST) k-ω model is selected in the present work to capture the structural features of turbulent flow in the channels. The SST k-ω turbulence model combines the merits of k-ε model and k-ω model, and it has stable algorithm and high accuracy near the wall [14]. The equations are written as below: U u j ui
wUui k wxi
§ wu wu 2 · Pt ¨ i j kG ij ¸ ¨ wx wx 3 ¸ i © j ¹
§ wk § P w¨ t P ¨ ¨ wwxx Vk © j© wx j
·· ¸ ¸¸ ¹¹
Gk Yk
(6)
(7)
wU uiZ wxi
§ wZ § P w¨ P t ¨ wx ¨ VZ © j© wx j
·· ¸ ¸¸ ¹¹ GZ YZ DZ
(8)
2.5. Model validation To verify the present model, a numerical simulation of zigzag-channeled PCHE is conducted, and the experimental inlet conditions are used as inlet boundary conditions for numerical solution. The simulation results are compared with the experimental data from Wu et al. [13], and the outlet temperature differences of cold/hot side were evaluated using the following equation: Error (%)
experiment data - numerical data u100 experiment data
(9)
The results show that the relative error of outlet temperature at propane side is 0.6%, and that at LNG side is 2.8%. The numerical results were in a good agreement with the experimental data, which indicates that the numerical model is reliable. 2.6 Simulation conditions The thermophysical properties of LNG and propane, considerably depend on both temperature and pressure, are obtained from NIST-REFPROP software. In this paper, LNG is composed of 90mol% methane, 7mol% ethane and 3mol% propane. The thermophysical properties of LNG at supercritical pressure vary drastically, especially close to the pseudo-critical point, which have significant effects on heat transfer. Fig. 5 shows the thermophysical properties of supercritical LNG versus temperature at the pressure of 7.3 MPa, including dynamic viscosity, density, specific heat and thermal conductivity. Fig. 5. Thermophysical properties of LNG at 7.3MPa
In this paper, the inlet boundary conditions of hot and cold channels are constant mass flow rate and constant temperature. The outlet boundary conditions of hot and cold channels are constant pressure. The boundary conditions of the top and bottom walls, the left and right side walls are set up to periodic condition. The inlet and outlet conditions are shown in Table 1. Table 1 Boundary conditions in CFD approach 3. Numerical results and discussion 3.1. Local flow and heat transfer characteristics Based on the simulation results, the flow and heat transfer characteristics in printed circuit LNG vaporizer with zigzag channels (bending angle θ=15°) are analyzed. The temperature profiles of propane and supercritical LNG are shown in Fig. 6. It can be seen that the propane completely condenses due to heat release, and its temperature decreases from 293.15K to 251.8K. Simultaneously, the supercritical LNG absorbs the heat, and the temperature rises from 128.9K to 273.7K. Fig. 6. Temperature profiles of propane and supercritical LNG in 15° zigzag channels Fig. 7 and Fig. 8 respectively give the temperature and velocity contours of propane and supercritical LNG at different cross-sections. It can be seen that periodic flow and heat transfer occur in both cold and hot channels. Each local low-temperature region of LNG and high-temperature region of propane in temperature contour respectively corresponds well to its accelerating core in velocity contour. Therefore, the temperature distribution is considered to be determined mainly by the velocity distribution. It also shows that the accelerating core of propane and
supercritical LNG all close to the inner wall of the corner. The main reason is that the periodic channel forces the fluid to change its flow direction, resulting in a centrifugal force. The shifting of accelerating core thins or even destructs the boundary layer, which is conducive to convective heat transfer [15]. Thus, local low-temperature region of LNG and high-temperature region of propane show similar trends. (a) temperature contour (b) velocity contour Fig. 7. Temperature and velocity contours of propane at different cross-sections (a) temperature contour (b) velocity contour Fig. 8. Temperature and velocity contours of supercritical LNG at different cross-sections Fig. 9 and Fig. 10 respectively show the secondary flow of propane and supercritical LNG at different cross-sections. Compared with straight channel, the combined effects of the flow acceleration/development and the secondary flow cause a significant difference in vorticity pattern for a zigzag channel [6]. As shown in Fig. 9, at z=494mm, no vortex appears and the streamlines are all to the right, since propane have just passed through the inlet straight section, and continue flowing into the zigzag channel section. This is also the reason why the LNG shown in Fig. 10 has no vortex at z=26 mm, and the streamlines are all to the left. At other cross-sections, the propane vortice distribution is negative in the upper regions, and positive in the lower regions, while the LNG vortice distribution is opposite. The number and
location of vortices of propane and LNG change constantly along the flow direction. The secondary flow generated by flow separation and vortex formation has a great influence on heat transfer enhancement, fluid mixing and displacement of accelerating core. Fig. 9. Secondary flow of propane at different cross-sections Fig. 10. Secondary flow of supercritical LNG at different cross-sections 3.2. Effects of channel bending angle on fluid flow Fig. 11 indicates the streamlines of supercritical LNG in different angled channels (θ=0°, 15°, 30°, 45°). It can be observed that the zigzag channel has a disturbing effect on fluid, and the increase in the bending angle results in a more drastic change in the flow direction. When the bending angle of channel is 30° and 45°, the backflow occurs near the bending parts, and the backflow area generated in 45° zigzag channel is larger, which reduces actual flow area and increases its resistance. Fig. 11. Streamlines of supercritical LNG in different angled channels Fig. 12 shows the Reynolds number of supercritical LNG in different angled channels, it shows a tendency to increase rapidly and then gradually flatten. The main reason is that the dynamic viscosity gradually decreases along the flow direction resulting from the increase in LNG temperature. It can be seen that the larger the channel bending angle, the larger the Reynolds number, indicating that larger channel bending angle causes the flow more intense. Fig. 12. Reynolds number of supercritical LNG along flow direction
3.3. Effects of channel bending angle on thermal performance Fig. 13 shows the bulk temperature profiles of supercritical LNG and propane in printed circuit LNG vaporizer with different angled channels (θ=0°, 15°, 30°, 45°). As Fig. 13 shows, the supercritical LNG temperature continuously increases along the flow direction. Compared with straight channel, the LNG temperature in zigzag channels increases more rapidly, and the larger the bending angle, the higher the temperature increase rate, resulting in a higher outlet temperature. Fig. 14 shows the liquid volume fraction of propane along the flow direction in different angled channels. From Fig. 13 and Fig. 14, it can be seen that in the inlet section, the propane temperature decreases along the flow direction on account of heat absorption. As the channel bending angle increases, the temperature drop rate of propane decreases slightly. This is because in the counter-flow printed circuit LNG vaporizer, the propane in the inlet section exchanges heat with the LNG in the outlet section. The larger the channel bending angle, the higher the outlet temperature of LNG, that is, the smaller the temperature difference between the cold and hot fluids. At this time, the heat transfer is weakened as the bending angle increases, since small temperature difference plays a dominant role in heat transfer. When the condensation point 286.55K is reached, the propane gradually condenses and the temperature remains the same. In the outlet section, the propane temperature decreases once again, and the decline becomes rapid. The larger the channel bending angle, the faster the propane cools, and the lower the outlet temperature. The reason is that, by enhancing heat transfer area geometrically and increasing local flow velocity at channel bending
points, the zigzag channel enhances the heat transfer performance compared with straight channels. Fig. 13. Temperature profiles of propane and supercritical LNG in different angled channels Correspondingly, the liquid volume fraction of propane in channels remains at zero at the beginning until the condensation temperature is reached. Then, the condensation rate of propane first decreases slightly with increasing channel bending angle, and finally increases significantly with increasing channel bending angle. The larger the bending angle, the earlier the liquid volume fraction of propane reaches 1 near the outlet. As shown in Fig. 14, propane in 45° zigzag channel is the first to completely condensate, while the liquid volume fraction of propane in the straight channel does not reach 1 at the outlet. Fig. 14. Liquid volume fraction of propane along the flow direction The overall heat transfer efficiency of a counter-flow printed circuit LNG vaporizer can be expressed as:
K
Tc ,o Tc ,i Th ,i Tc ,i
(10)
Therefore, for a printed circuit LNG vaporizer, the larger the channel bending angle, the higher the overall heat transfer efficiency. In this paper, the vaporizer with 45° zigzag channels has the highest efficiency, which can reach 0.957. Whereas, for the vaporizer with straight channel, the heat transfer efficiency is the lowest, which is 0.85. 3.4. Effects of channel bending angle on pressure drop
Fig. 15 shows the pressure variety of supercritical LNG in different angled channels. On the whole, the pressure loss of supercritical LNG tends to increase with increasing flow distance. The larger the channel bending angle, the greater the pressure drop. This is mainly because that with the increase of the bending angle, the flow separation of boundary layer at the corner become more obvious, which leads to a significant increase in pressure loss. Fig. 15. Pressure of supercritical LNG at different positions 3.4. Comprehensive performance of a printed circuit LNG vaporizer It is concluded that the increase in the channel bending angle is conducive to heat transfer, but it also leads to a greater pressure drop. Therefore, it is unreasonable to evaluate the flow or heat transfer performance unilaterally. The criterion
]
Nu / Nu / f / f 0
0
is used as the evaluation index to reflect the
thermal-hydraulic characteristics of printed circuit LNG vaporizers with different channel bending angles (0°, 15°, 30°, 45°) comprehensively. The relevant parameters are calculated as follows [6,16]: Nu
h
hDe
O qw T T Tw i o 2
(11) (12)
De
4A L
(13)
f
'pDe 2 U u 2l
(14)
]
Nu Nu0 f f0
(15)
Fig. 16 gives the Nusselt number and Fanning friction factor of the cold channel versus channel bending angle. It can be seen that both the Nusselt number and Fanning friction factor increase with the increase of channel bending angle. When the channel bending angle rises from 0° to 15°, the Nusselt number increases obviously, and the Fanning friction factor has a little increase, indicating that the effect of bending angle on heat transfer is dominant. Conversely, its effect on flow resistance is more significant when the channel bending angle is larger than 15°. The main reason is that the drastic change in flow direction leads to excessive flow resistance. The comprehensive performance evaluation results of the printed circuit LNG vaporizers with different angled channels are shown in Table 2. It indicates that the channel bending angle 15° offers the best comprehensive performance. Fig. 16. Nu and f of the cold channel Table 2 Comprehensive performance evaluation results 5. Conclusions In this paper, a three-dimensional numerical model of counter-flow printed circuit LNG vaporizer is established, the thermal-hydraulic performance of hot and cold fluids in channels, and the effects of channel bending angle on it is studied. Based on the numerical results, the following conclusions are derived. (1) Periodic flow and heat transfer occur in both cold and hot channels, and the temperature distribution is considered to be determined mainly by the velocity
distribution. The channel bending causes the accelerating core of cold and hot fluids close to the inner wall of the corner, thinning or even destructing of the boundary layer, which is conducive to convective heat transfer. In addition, the secondary flow generated by flow separation and vortex formation has a great influence on heat transfer enhancement, fluid mixing and displacement of accelerating core. (2) The increase in channel bending angle results in a more intense flow. The larger the bending angle of the channel, the larger the Reynolds number of the supercritical LNG. When the bending angle of the channel is 30° and 45°, the fluid backflow occurs near the corner, which reduces the actual flow area and increases the flow resistance. (3) For both cold and hot fluids, the temperature differences between the inlet and outlet increase with the increase of channel bending angle. The larger the bending angle, the better the heat transfer between cold and hot fluids, and the faster the hot fluid (propane) completely condenses, although accompanying larger pressure drop. Among the printed circuit LNG vaporizers with different angled channels, the vaporizer with 45° channels has the highest overall heat transfer efficiency, which can reach 0.957. (4) The thermal-hydraulic performance of printed circuit LNG vaporizers with various angled channels is evaluated, and the results show that the channel bending angle 15° offers the best comprehensive performance. Acknowledgement This study was supported by the National Natural Science Foundation of China
(Grant No.51774237, 51304160), and the Scientific Research Program Funded by Shaanxi Provincial Education Department (Program No.15JK1581). Reference [1] S. J. Dewson, C. Grady, HEATRIC workshop at MIT, Cambridge, MA, USA, October 2, 2003. [2] X. Li, R.L. Pierres, S.J. Dewson, Heat exchangers for the next generation of nuclear reactors, International Congress on Advances in Nuclear Power Plants (ICAPP) 2006, Reno, NV, USA, June 4-8, 2006. [3] S. Baek, G. Hwang, J. Kim, S. Jeong, Development of compact heat exchanger for LNG FPSO, 21st International offshore and polar engineering conference (ISOPE 2011 Maui), Maui, Hawaii, USA, June 19-24, 2011. [4] Z.C. Lai, J.R. Li, H.T. Hu, D.W. Zhuang, X.M. Weng, G.L. Ding, Numerical simulation of refrigerant flow condensation characteristics in zigzag channel of printed circuit heat exchanger, Chinese Journal of Refrigeration Technology 36(4) (2016) 29-35 (in Chinese). [5] I.H. Kim, Experimental and numerical investigations of thermal-hydraulic characteristics for the design of a Printed Circuit Heat Exchanger (PCHE) in HTGRs, Ph.D. Dissertation, Korea Advanced Institute of Science and Technology, 2012. [6] H.H. Khan, A.A. M, A. Sharma, A. Srivastava, P. Chaudhuri, Thermal-hydraulic characteristics and performance of 3D wavy channel based printed circuit heat exchanger, Applied Thermal Engineering, 87 (2015) 519-528.
[7] Y.J. Baik, S. Jeon, B. Kim, D. Jeon, C. Byon, Heat transfer performance of wavy-channeled PCHEs and the effects of waviness factors, International Journal of Heat and Mass Transfer, 114 (2017) 809-815. [8] W. Kim, Y.J. Baik, S. Jeon, D. Jeon, C. Byon, A mathmatical correlation for predicting the thermal performance of cross, parallel, and counterflow PCHEs, International Journal of Heat and Mass Transfer, 106 (2016) 1294-1302. [9] D.E. Kim, M.H. Kim, J.E. Cha, S.O. Kim, Numerical investigation on thermal-hydraulic performance of new printed circuit heat exchanger model, Nuclear Engineering and Design, 238 (2008) 3269-3276. [10]S.H. Yoon, J.G. Kwon, T.H. Kim, H.S. Park, M.H. Kim, Analysis on optimal configuration of air-foil shaped printed circuit heat exchanger in supercritical carbon dioxide power cycle, 15th International Heat Transfer Conference (IHTC-15), Kyoto, Japan, August 10-15, 2014. [11]J.G. Kwon, T.H. Kim, H.S. Park, J.E. Cha, M.H. Kim, Optimization of airfoil-type PCHE for the recuperator of small scale brayton cycle by cost-based objective function, Nuclear Engineering and Design 298 (2016) 192-200. [12]T.H. Kim, J.G. Kwon, S.H. Yoon, H.S. Park, M.H. Kim, J.E. Cha, Numerical analysis of air-foil shaped fin performance in printed circuit heat exchanger in a supercritical carbon dioxide power cycle, Nuclear Engineering and Design 288 (2015) 110-118. [13]W.W. Wu, D.B. Wang, L.M. Zhao, Z.Q. Yuan, Experimental investigation of printed circuit heat exchanger as LNG vaporizer, Ocean Engineering Equipment and Technology, 3(1) 2016 20-24 (in Chinese). [14]Z.X. Zhang, Z.N. Dong, Viscous fluid mechanics, Beijing: Tsinghua University Press, 1998.
[15]J.M. Choi, N.K. Anand, Turbulent heat transfer in a serpentine channel with a series of right-angle turns, International Journal of Heat and Mass Transfer, 38(7) (1995) 1225-1236. [16]I.H. Kim, H.C. No, J.I. Lee, B.G. Jeon, Thermal hydraulic performance analysis of the printed circuit heat exchanger using a helium test facility and CFD simulations, Nuclear Engineering and Design, 239(11) (2009) 2399-2408.
Highlights
¾
the secondary flow in cold and hot channels is analyzed.
¾
the effects of channel bending angle on thermal-hydraulic performance are discussed.
¾
periodic flow and heat transfer occur in both cold and hot channels.
¾
zigzag channel can enhance convective heat transfer.
¾
channel bending angle 15° offers the best comprehensive performance.
Nomenclature A
cross-sectional area (m2)
cp
specific heat at constant pressure (kJ·kg-1·K-1)
coeff
configurable mass transfer parameter
De
hydraulic diameter (m)
Fσ
surface tension term
f
Fanning friction factor (–)
g
acceleration of gravity (m·s-2)
h
surface heat transfer coefficient (W·m-2·K-1)
L
circumference (m)
l
length of channel (m)
m
mass flow rate (kg·s-1)
m
mass transfer rate (kg·s-1)
n
phase interface function
Nu
Nusselt number (–)
p
pressure (MPa)
Δp
pressure drop (Pa)
Q
latent heat source term
q
heat flux (W·m-2)
Re
Reynolds number (–)
Sm
quality source term
T
temperature (K)
u
velocity (m·s-1)
Greek symbols α
volume fraction (–)
γ
latent heat (J·kg-1)
ζ
comprehensive evaluation index (–)
η
overall heat transfer efficiency (–)
θ
channel bending angle (°)
β
contact angle (°)
λ
thermal conductivity (W·m-1·K-1)
μ
dynamic viscosity (Pa·s-1)
ρ
density (kg·m-3)
Subscript c
cold fluid
h
hot fluid
i
inlet
l
liquid phase
lv
liquid phase evaporates into gas phase
o
outlet
sat
saturation
v
vapor phase
vl
gas phase condenses into liquid phase
w
inner wall
Table 1 Comparison between simulation results and experimental data Experimental data
Numerical data
Error(%)
Cold channel temperature difference (K)
167.44
159.24
4.8
Hot channel temperature difference (K)
23.39
21.74
7.05
Table 2 Boundary conditions in CFD approach mc (kg/s)
mh (kg/s)
Tci (K)
Thi (K)
pco (MPa)
pho (MPa)
0.0002995
0.00045
128.9
293.15
7.3
0.64
Table 3 Comprehensive performance evaluation results bending angle (θ)
evaluation index (ζ)
15°
1.124293
30°
0.573075
45°
0.295884
Conflict of Interest Statement: We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled, “Numerical investigation on thermal-hydraulic performance of a printed circuit LNG vaporizer”.