- Email: [email protected]
Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers
Accepted Manuscript Numerical study of the air inlet angle influence on the air–side performance of platefin heat exchangers Zhiying Liu, Hui Li, Lin Shi, Yangjun Zhang PII:
S1359-4311(15)00586-4
DOI:
10.1016/j.applthermaleng.2015.06.032
Reference:
ATE 6720
To appear in:
Applied Thermal Engineering
Received Date: 11 March 2015 Accepted Date: 13 June 2015
Please cite this article as: Z. Liu, H. Li, L. Shi, Y. Zhang, Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers, Applied Thermal Engineering (2015), doi: 10.1016/j.applthermaleng.2015.06.032. 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.
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Graphical Abstract
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Three-dimensional simulations are performed to investigate the effect of air inlet angle on heat transfer coefficient and pressure drop. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are studied first. When the air inlet angle is in the horizontal plane, the air inlet angle effect is mainly in the entrance region and strongly related with the flow flied. When the air inlet angle is in the longitudinal plane, the air inlet angle effect is related with the whole fin channel flow field because the vortex length is much larger. The heat transfer coefficient increases with the air inlet angle increasing, while the total pressure drop increase is much larger than heat transfer. The increase ratios are defined to describe the effect of air inlet angle on heat transfer and pressure drop. The variation laws are obtained from the simulation data of different fin parameters. The flow fields on the cross sections (Fig. 1) show that it is applicable to assume that the effect of the air inlet angle (both and are nonzero) can be regarded as a combination of the effects in the two special cases ( ≠ 0, = 0, and = 0, ≠ 0). Thus prediction model is established to predict the heat transfer coefficient and pressure drop when both the horizontal angle and the longitudinal angle are nonzero. The comparison of prediction results and simulation results for 7 pairs of and shows good agreement. The maximum error is less than 10%.
Fig. 1
Flow fields on the cross sections in the fin channel ( = 2.5 mm, = 9.5 mm, = 8/).
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Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers Zhiying Liu1, Hui Li1*, Lin Shi1, Yangjun Zhang2 (1. Key Laboratory for Thermal Sciences and Power Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China China) *Author for correspondence
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2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084,
Key Laboratory for Thermal Sciences and Power Engineering of the Ministry of Education, Tsinghua University,
Beijing, 100084,China
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E-mail: [email protected]
Abstract
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Numerical work is performed to study the effect of air inlet angle on heat transfer coefficient and pressure drop of the plate-fin heat exchangers. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are simulated on 7 fin channel meshes with different fin parameters. The numerical results show that the different flow fields of the two special air inlet angles cause different effects on heat transfer coefficient and pressure drop. When the air inlet angle is in the horizontal plane, the air inlet angle effect is strongly related with the entrance region flow flied. When the air inlet angle is in the longitudinal plane, the air inlet angle effect is related with the whole fin channel flow field because the vortex size is much larger and comparable to the fin length. The effects of the two angles have different variation laws, which are greatly influenced by fin parameters. Finally, a prediction model is established to calculate the heat transfer coefficient and pressure drop of an arbitrary inlet angle. The comparison of prediction results and simulation results for 7 air inlet angles shows good agreement. The maximum prediction error is within 10%. Keywords: plate-fin heat exchanger; air inlet angle; numerical; prediction model
1. Introduction
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There is a widespread application that the entrance air flow direction is non-orthogonal to the heat exchanger surface. In automotive radiators, the air inlet direction is very complex due to the fan rotation and the geometric restrictions [1]. The air-conditioning evaporators and condensers are usually closed to the fan so that the air flow direction is also non-orthogonal. Furthermore, an air-cooled condenser described by Kroger [2] is arranged obliquely to save land area. X.P.DU et al. [3] have studied the cross-flow finned oval-tube heat exchangers and shown that the entrance air flow direction has an important effect on the heat transfer and pressure drop characteristics. Previous work was made to experimentally study the effect of air flow direction on straight and off-set strip fins. However, the pressure drop measurement may be disturbed by the flow deflector which is used to control the entrance air flow direction and the flow distribution in the fin channel is hard to measure in the experiment. The CFD has been used for various types of studies on heat exchangers [4][5]. Beale and Steven [6] simulated the laminar flow and the heat transfer in an offset-fin heat exchanger surface assuming the fully developed flow and the constant wall temperature. The numerical friction 1
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coefficients agreed well with the experimental data. Muzychka [8] analyzed the flow friction and heat transfer in low Reynolds number flow heat exchangers for three typical configurations. The predictions for the offset strip fin agreed well with experimental data within ±20%. Guo et al. [7] studied the influence of geometrical factors on thermal-hydraulic characteristics for high-pressure-direction type steel offset strip fins using the CFD and Taguchi method. Furthermore, many researches has shown that the three-dimensional simulation had good agreement with the experimental results [11]-[17]. The good agreement proves that CFD is an effective tool for studying the flow and heat transfer of heat exchangers. In the current work, the heat transfer and pressure drop characteristics and flow distribution inside the fin channel of different air inlet direction are studied with CFD. Based on the numerical results, a correction model is established to consider the effect of the air inlet angle for existing correlations [9].
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2. Simulation details 2.1 Parameter definition
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Usually the air entrance flow is orthogonal to the heat exchanger surface when investigating the heat transfer and pressure drop characteristics for the plate fin heat exchangers [10]. Supposing the air frontal velocity is , the Reynolds number is defined as, = / = /
= /
(1) (2) (3)
where is the ratio of the core minimum free-flow area to the frontal area ,
as follows,
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is the maximum average velocity in the core, is the hydraulic diameter. However, the flow and heat transfer may greatly change when the air flow is non-orthogonal to the heat exchanger surface. Fig. 1 shows a general situation of the entrance air flow direction non-orthogonal to the heat exchanger surface. The x axis represents the fin length direction, the y axis represents the fin spacing direction, and the z axis represents the fin height direction. The air flow velocity can be expressed by three perpendicular velocity components , , and "
# = $%& ' $%& (
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(4)
= $%& ' &)* (
(5)
" = sin '
(6)
where ( is the angle between # and the projection of in xy plane, ' is the angle between and its projection in xy plane. Since the characteristic velocity is defined by air flow rate and the minimum free flow area as mentioned previously, the is used as the air frontal velocity instead of to retain consistency. The characteristic velocity is calculated as, (7) = /
#
Before studying a general case, two special cases are discussed as follows, (1) The air inlet angle is in the horizontal plane, " = 0, namely ' equals to zero. The air inlet angle ( is named the horizontal angle. As Fig. 2(a) shown, the air flow direction is changed by the plain fin which causing a 2
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(8)
tan ( = -. /-
(9)
28,3 =
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The increase ratios of the heat transfer coefficient and the static pressure drop are calculated to study the influence of the horizontal angle as follows, 4ℎ63 − 4ℎ6 (10) 2 ,3 = 4ℎ6 4∆:; 63 − 4∆:; 6 4∆:; 6
(11)
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where 4ℎ6 is the air-side heat transfer coefficient at air inlet angle of 0°, and 4∆:; 6 is the static pressure drop at air inlet angle of 0° (2) The air inlet angle is in the longitudinal plane, = 0, namely ( equals to zero. As Fig.
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2(a) shown, the air inlet angle < is named the longitudinal angle. Like case (1), the air inlet angle < is defined as, tan < = -" /- (12) The heat transfer coefficient and the static pressure drop increase ratios are calculated as follows, 4ℎ6= − 4ℎ6 (13) 2 ,= = 4ℎ6 4∆:; 6= − 4∆:; 6 (14) 28,= = 4∆:; 6
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2.2 Governing equations
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Several approximations are made in the numerical simulations as follows, (1) Flow is assumed to be incompressible and steady. (2) Air property is constant and the tube inner wall temperature is fixed. (3) Thermal radiation, nature convection, and gravity force are neglected. The governing equations in the fluid domain are expressed as follows, Continuity equation ∂ ∂@ ∂B + + =0 ∂? ∂A ∂C Momentum equations ∂ ∂ ∂ ∂G HI## HI # HI"# D E +@ +B F=− + + + ∂? ∂A ∂C ∂? H? HA HC D E D E
∂@ ∂@ ∂@ ∂G HI# HI HI" +@ +B F=− + + + ∂? ∂A ∂C ∂A H? HA HC
∂B ∂B ∂B ∂G HI#" HI " HI"" +@ +B F=− + + + ∂? ∂A ∂C ∂C H? HA HC
Energy equation ∂J ∂J ∂J K H/J H/J H/J +@ +B = L + + M ∂? ∂A ∂C D$8 H? / HA / HC /
Heat conduction equation in the solid domain 3
(15)
(16) (17) (18)
(19)
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(20)
2.3 Mesh and boundary conditions
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Three-dimensional numerical work is performed for 7 meshes with different fin parameters to study the air inlet angle effect. The detailed information of the cases is listed in Table 1. The air frontal velocity is 8 - 16 m/s and the air inlet angle is 0° - 80°. As the flow is periodic in the fin height and fin spacing directions, a 2×2 fin channel is used as the calculation domain. Hexahedral mesh is used to ensure the simulation accuracy. Xie et al. [17] compared five turbulence models with experimental data. These models are the RNG O − P model, the standard O − P model, the Reynolds Stress model, the SST O − Q model, and the @ / R model. The results show that all the turbulence models provide similar results except for the SST O − Q model. The two O − P turbulence models are in approximate agreement with the experimental data. Thus the standard O − P turbulence model is used for the simulations. The model constants are set to the default values of FLUENT software package. Fig. 3 shows the hexahedral mesh used for the simulation, the fin channel part is between the inlet section and exit section. The boundary layer mesh is refined to decrease the near-wall temperature gradients. The number of grids is two million to four million depending on the channel size, the mesh quality is over 0.8. Mesh independence was studied on the fin channel 2# with a coarse mesh with one million grids, a normal mesh with two million grids, and a fine mesh with four million grids. The difference between the normal mesh and the fine mesh is within 3% while the difference between the coarse mesh and the fine mesh is more than 10%. Velocity inlet, pressure outlet, and two pairs of periodic boundaries are used in the simulations. The air inlet temperature is 25℃. The tube inner wall temperature is fixed at 80℃. The inlet settings can be classified into five groups as shown in Table 2 for different purposes. The first four groups are used to study the influence of fin parameters, air frontal velocity, and air inlet angle on 2 and 28 . The last group is for model verification.
3. Results and discussion
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The results of case 1# and 3# show that the flow fields of different air frontal velocities are broadly similar. The increase ratios are used to discuss the variation of heat transfer coefficient and pressure drop when air inlet angle is nonzero. Fig. 4 shows that the heat transfer and pressure drop increase ratios have a little difference at different air velocities. Thus the flow field, heat transfer, and pressure drop of different air inlet angles and fin parameters are discussed when air frontal velocity is fixed at 8 m/s. 3.1 Flow field
Fig. 5 shows the flow fields of the middle horizontal plane at ( of 0°, 40°, 60°, and 70° while the air frontal velocity is 8 m/s and < is fixed at 0°. When ( is nonzero, the air flow is askew to the plain fin with a vortex near the leeward side. As the flow is choked by the vortex, the windward-side air velocity is larger than the average velocity at the entrance. After flowing through the vortex, the windward side air velocity is still larger than the leeward side. The air velocity finally becomes uniform under the influence of the fin walls after flowing for some distance. As the horizontal angle ( increases, the vortex size and its influence region become much larger. However, when ( further increases, the flow becomes uniform faster because the vortex heavily blocks the air flow. 4
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the air frontal velocity is 8 m/s and ( is fixed at 0°. When the longitudinal angle < is nonzero, the air flow is askew to the tube with a vortex near the leeward side. As the fin and tube height are much larger than the fin spacing and fin thickness, the vortex length is comparable to the fin length. Thus the flow may be always non-uniform. The trailing vortex size also increases under the influence of the non-uniform flow. When < is more than 70°, the flow becomes unstable and the trailing vortex starts shedding.
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3.2 Heat transfer
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The fin local heat transfer coefficient is compared at different air inlet angles as the fin area is the main contribution to the heat transfer. Fig. 7 shows the local heat transfer coefficient of the fin windward and leeward sides at ( of 0° to 70° while the air frontal velocity is 8 m/s and < is fixed at 0°. The air inlet angle effect on heat transfer is mainly in the entrance region. In the windward side, the near-wall air velocity increases with air inlet angle increasing, thus the local heat transfer coefficient increases in the entrance region. In the leeward side, though the near wall air velocity is much small due to the vortex, the local heat transfer coefficient is also larger than fully developed region because of the vortex. However, the near-wall temperature difference is very small, thus the heat transfer rate of the fin leeward side is not enhanced in the vortex region. Fig. 8 shows the local heat transfer coefficient of the fin at < of 0° to 70° while the air frontal velocity is 8 m/s and ( is fixed at 0°. As the windward and leeward sides are in the tube, the vortex is parallel to the fin. The local heat transfer coefficient decreases in the vortex region and increases above the vortex because the near-wall air velocity is very small in the vortex region and much larger above the vortex. Fig. 9 compares the increase ratio of average heat transfer coefficient at different air frontal velocities and fin parameters. The increase ratio 2T,3 is larger than 2T,= due to the different local heat transfer distribution of fin and tube walls. When ( is variable and < is fixed, the increase ratio 23 increases with fin spacing increasing. The fin height has little effect on 23 . When < is variable and ( is fixed, the increase ratio 2= increases with fin spacing increasing
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and fin height decreasing. 3.3 Pressure drop
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Fig. 10 shows the pressure drop components in one flow passage of a plate-fin heat exchanger [10]. Here the subscripts 1, 2, 3, and 4 represent locations far upstream, passage entrance, passage exit, and far downstream, respectively. As the air flow enters the passage, it contracts due to the free-flow area decrease. ∆P-V/ is the pressure drop at the core entrance due to flow separation and the sudden contraction. ∆P/VW is the pressure drop in the core . ∆PWVX is the pressure rise at the core exit due to the free-flow area increase. 4∆PY 6 = ∆P-V/ + ∆P/VW − ∆PWVX
(21)
Usually, the core frictional pressure drop ∆P/VW is a dominating term, the total core pressure drop can be approximated as,
/ 4\ D] (22) 2 where R is the friction factor, \ is the flow length, is the hydraulic diameter, D is the air density, ] is the velocity calculated by the minimum flow area in the core. When air flow direction is non-orthogonal, total pressure drop increases because the vortex
4∆PY 6 ≈ R
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-
-
-
/ 4:X63 = 4:;X 63 + DX/ = 4:;X 63 + D4X# + 06 / /
(23)
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/ / 4:-63 = 4:;- 63 + D-/ = 4:;- 63 + D^-# + - _ / /
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chokes the air flow in the entrance region and change the velocity distribution in the fin channel. Fig. 11 shows the static and total pressure components along the flow length in the middle horizontal plane when air inlet angle is in the horizontal plane. As the fin spacing is very small, the vortex size is much smaller than the fin length, the influence of air inlet angle can be divided into three regions. In the vortex region, pressure decreases rapidly and then increases gradually. In a partial region after the vortex, the total pressure near the windward side is larger than leeward side due to the air velocity non-uniformity. As the air flow becomes uniform, the total pressure near the leeward and windward sides is almost the same. For the special case (1), the total pressure at the far upstream and downstream can be expressed as,
(24)
is zero. The total pressure drop is,
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where the subscripts t, s, and ( represent total pressure, static pressure, and air inlet angle. When flowing through the fin channel, X# equals to -# because of mass continuity, while X
1 / 1 (25) 4∆: 63 = 4:X 63 − 4:- 63 = 4:;- 63 − 4:;X 63 + D- = 4∆:; 63 + D4-# tan (6/ 2 2 Since the maximum velocity ] is usually used as the characteristic velocity in the heat exchanger design, the total pressure drop can be expressed by a function of ] as,
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1 / 4∆: 63 = 4∆:; 63 + D / ] tan/ ( 2 Likewise, for the special case (2), the total pressure drop can be expressed as, / 4∆: 6= = 4∆:; 6= + D / ] tan/ < /
(26)
(27)
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Thus the total pressure drop is larger than the static pressure drop when air direction is non-orthogonal to the heat exchanger surface. Fig. 12 compares the total and static pressure drop increase ratio varying with ( and < at different fin parameters. When ( is variable from 0° to 80° and < is fixed, the 2ab,3 increases first and then decreases, and the change is within 20%. The 2ab,3 increases with fin spacing increasing. When < is variable from 0° to 70° and ( is fixed, the 2ab,= significantly increase with < and fin height increasing. However, the fin spacing has little influence on 2ab,= . The total pressure drop increase ratio is much larger because of the dynamic pressure loss when air flow direction is non-orthogonal. The 2cb,3 increases with fin spacing increasing while fin height has little influence on 2cb,3 . The 2cb,= increases with fin height increasing and decreases with fin spacing increasing. 3.4 Prediction model for general situations For a general situation, both ( and < are nonzero, the non-orthogonal air velocity can be decomposed into three perpendicular velocity components , . , and d in a
three-dimensional Cartesian coordinate system. The influence of air inlet angle on heat transfer is related to the near-wall air velocity of the fin and tube wall. As show in Fig. 13 (a) and (b), the inlet angle ( mainly causes velocity non-uniformity along the y direction in the entrance region, while inlet angle < mainly causes velocity non-uniformity along the x direction in the whole fin channel. The flow field in Fig. 13(c) can be regarded as a duplicate effect of the flow fields in Fig. 6
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velocity components . and d . Thus it is applicable to assume that the effect of the air inlet
angle (both ( and < are nonzero) can be regarded as a combination of the effects in the two special cases (( ≠ 0, < = 0, and ( = 0, < ≠ 0). Thus the heat transfer coefficient and pressure drop can be calculated as follows,
4ℎ63= = ^1 + 2 ,3 + 2 ,= _ ∙ 4ℎ6
(28)
4∆:; 63= = ^1 + 2ab,3 + 2ab,= _ ∙ 4∆:; 6
(29)
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1 / 4tan/ (30) 4∆: 63= = 4∆:; 63= + D / ] ( + tan/ <6 2 where the subscripts ( and < represent the horizontal angle and the longitudinal angle in the special cases. The 5th simulation group is used to verify the prediction model. Table 3 compares the simulation results and prediction results. Both the heat transfer coefficient and pressure drop are in good agreement. The maximum error is less than 10% when ( and < are less than 70°. It means that when the air frontal velocity is in the range of 6 m/s to 16m/s and air inlet angles ( and < are less than 70°, the assumption is practicable and the prediction error is acceptable in the engineering application.
4. Conclusion
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Three-dimensional simulations are performed to investigate the effect of air inlet angle on heat transfer coefficient and pressure drop. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are studied first. When air frontal velocity is 6-16 m/s, the velocity has a little influence on the heat transfer and pressure increase ratios. Thus the influence of air inlet angle and fin parameters is investigated at a fixed air frontal velocity. The heat transfer coefficient and pressure drop increase with air inlet angle increasing, while the pressure drop increase is much larger. When the air inlet angle is in the horizontal plane, the air inlet angle effect is mainly in the entrance region and strongly related with the flow flied. The heat transfer coefficient increases with the air inlet angle increasing, while the static pressure drop increases first and then decreases. The increase ratios 2 ,3 and 2cb,3 increase with fin spacing increasing and are little affected by
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fin height. However, the total pressure drop increase is much larger than heat transfer. The static pressure drop increase ratios 2ab,3 is very small and can be neglected compared with the total pressure drop. When the air inlet angle is in the longitudinal plane, the vortex length is much larger because the fin height is much larger than fin spacing. The heat transfer coefficient increase ratio 2 ,=
increases with fin spacing increasing and fin height decreasing. The static pressure drop increase ratio 28,= increases with fin height increasing and is little affected by fin spacing.
A prediction model is established to predict the heat transfer coefficient and pressure drop when both the horizontal angle ( and the longitudinal angle < are nonzero. The comparison of prediction results and simulation results for 7 pairs of ( and < shows good agreement. The maximum error is less than 10%.
Acknowledgements This work was supported by the State Key Program of the National Natural Science Foundation of 7
ACCEPTED MANUSCRIPT China (Grant No. 51236004) and Science Fund for Creative Research Groups (No.51321002).
Reference
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[1] Khaled M, Mangi F, Hage H E, et al. Fan air flow analysis and heat transfer enhancement of vehicle underhood cooling system–Towards a new control approach for fuel consumption reduction[J]. Applied Energy, 2012, 91(1): 439-450. [2] D.G. Kröger, Air-cooled heat exchangers and cooling towers, vol. I, PennWell Corporation, Tulsa, Oklahoma, 2004. [3] Du X P, Zeng M, Dong Z Y, et al. Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers[J]. Experimental Thermal and Fluid Science, 2014, 52: 146-155. [4] Sheik Ismail L, Velraj R, Ranganayakulu C. Studies on pumping power in terms of pressure drop and heat transfer characteristics of compact plate-fin heat exchangers—A review[J]. Renewable and Sustainable Energy Reviews, 2010, 14(1): 478-485. [5] Aslam Bhutta M M, Hayat N, Bashir M H, et al. CFD applications in various heat exchangers design: A review[J]. Applied Thermal Engineering, 2012, 32: 1-12. [6] Beale S. Laminar fully developed flow and heat transfer in an offset rectangular plate-fin surface[J]. PHOENICS Journal of Computational Fluid Dynamics, 1990, 3(1), 1-19. [7] Guo L, Qin F, Chen J, et al. Influence of geometrical factors and pressing mould wear on thermal-hydraulic characteristics for steel offset strip fins at low Reynolds number[J]. International Journal of Thermal Sciences, 2007, 46(12): 1285-1296. [8] Muzychka Y S. Analytical and experimental study of fluid friction and heat transfer in low Reynolds number flow heat exchangers[D]. 1999. [9] Corberán J M, Cuadros E, González K. Pressure drop characterisation of compact heat exchanger channels[C].5th European Thermal-Sciences Conference, The Netherlands. 2008. [10] Shah R K, Sekulic D P. Fundamentals of heat exchanger design[M]. John Wiley & Sons, 2003. [11] Peng H, Ling X. Numerical modeling and experimental verification of flow and heat transfer over serrated fins at low Reynolds number[J]. Experimental Thermal and Fluid Science, 2008, 32(5): 1039-1048. [12] Zhu Y, Li Y. Three-dimensional numerical simulation on the laminar flow and heat transfer in four basic fins of plate-fin heat exchangers[J]. Journal of Heat Transfer, 2008, 130(11): 111801. [13] Bhowmik H, Lee K S. Analysis of heat transfer and pressure drop characteristics in an offset strip fin heat exchanger[J]. International Communications in Heat and Mass Transfer, 2009, 36(3): 259-263. [14] Peng H, Ling X, Li J. Numerical simulation and experimental verification on thermal performance of a novel fin-plate thermosyphon[J]. Applied Thermal Engineering, 2012, 40: 181-188. [15] Ben Saad S, Clément P, Fourmigué J F, et al. Single phase pressure drop and two-phase distribution in an offset strip fin compact heat exchanger[J]. Applied Thermal Engineering, 2012, 49: 99-105. [16] He Y L, Tao W Q, Song F Q, et al. Three-dimensional numerical study of heat transfer 8
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characteristics of plain plate fin-and-tube heat exchangers from view point of field synergy principle[J]. International Journal of Heat and Fluid Flow, 2005, 26(3): 459-473. [17] Xie G, Liu J, Ligrani P M, et al. Numerical analysis of flow structure and heat transfer characteristics in square channels with different internal-protruded dimple geometrics[J]. International Journal of Heat and Mass Transfer, 2013, 67: 81-97.
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A diagram of the entrance air flow non-orthogonal to the heat exchanger surface.
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Fig. 1
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Figures:
Schematic diagrams of the special air inlet angles.
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Fig. 2
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Mesh and boundary conditions.
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Fig. 3
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Fig. 4
The increase ratios of heat transfer coefficient and pressure drop at different air velocities (R8 = 2.5 mm, R = 9.5 mm, ( = 0~80°, < = 0~70°). 11
Flow field of the middle horizontal plane at the air frontal velocity of 8 m/s, ( of 0°, 40°, 60°, 70°, and < fixed at 0°.
Flow field of the middle longitudinal plane at the air frontal velocity of 8 m/s, < of 0°, 40°,
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Fig. 6
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Fig. 5
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60°, 70°, and ( fixed at 0°.
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Local heat transfer coefficient in the fin windward and leeward sides at the air frontal velocity of 8 m/s, ( of 0° to 70°, and < fixed at 0°.
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Fig. 7
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Fig. 8
Local heat transfer coefficient in the fin surface at the air frontal velocity of 8 m/s, < of 0° to 70°, and ( fixed at 0°.
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Air-side heat transfer coefficient vs. air inlet angle of different fin parameters ( = 8 m/s).
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Fig. 9
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Pressure drop components in the passages of a plate-fin heat exchanger.
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Fig. 10
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Fig. 11
Pressure components of three lines in the middle horizontal plane of the fin channel when air flow is non-orthogonal.
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The pressure drop increase ratios vs. air inlet angle of different fin parameters. ( = 8 m/s).
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Fig. 12
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Flow fields on the cross sections in the fin channel (R8 = 2.5 mm, RT = 9.5 mm, = 8o/&).
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Fig. 13
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Table 1
Geometry parameters of the fin channels.
fin spacing [mm]
fin thickness [mm]
1# 2# 3# 4# 5# 6# 7#
2.0 2.5 3.0 3.5 2.5 2.5 2.5
0.2 0.2 0.2 0.2 0.2 0.2 0.2
9.5 9.5 9.5 9.5 8.0 12 15
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1# 2# 3# 4# 5#
2# 1# - 4#, 6# 2# 2#, 4# - 7# 2#
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Mesh No.
Table 3
[m/s]
6,8,12,16 8 6,8,12,16 8 8
fin length [mm]
4.0 4.0 4.0 4.0 4.0 4.0 4.0
60 60 60 60 60 60 60
( [°]
0,20,40,50,60,70,75,80 0,20,40,50,60,70,75,80 0 0 0,40,60,70
< [°]
0 0 0,20,40,50,60,70 0,20,40,50,60,70 0,40,50,60,70
Comparison of prediction and simulation results.
Simulation results h
tube height [mm]
Detailed information of each simulation case group.
Group No.
4(, <6
fin height [mm]
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Mesh No.
Table 2
Temperature (K) Air inflow velocity (m/s) Air frontal velocity (m/s) Maximum average velocity (m/s) Velocity components (m/s) Horizontal angle (°) Longitudinal angle (°) Thermal conductivity (W/mK) Kinematic viscosity (m2/s) Air density (kg/m3)
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T
u,v,w ( < K D
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Nomenclature $b Thermal capacity (J/kgK) T Hydraulic diameter (m) f Fanning friction factor (-) h heat transfer coefficient (W/m2K) j Colburn j-factor (-) L Flow length (m) p Pressure (Pa) ∆:a Static pressure drop (Pa) ∆: Total pressure drop (Pa) Re Reynolds number
Prediction results
[W/m K]
P
TP
[Pa]
[Pa]
(0,0)
79.80
87.91
87.90
(40,40)
91.11
(40,60)
h
Error
[W/m K]
P
TP
[Pa]
[Pa]
-
-
104.40 157.80
92.03
98.10
130.60 271.10
(60,40)
101.03
(70,50) (70,70)
h
P
TP
-
-
-
-
105.85
159.02
1.01%
1.39%
0.77%
96.93
136.75
276.62
-1.29%
5.89%
3.50%
113.20 253.60
104.87
111.23
251.10
4.22%
-1.88%
-1.58%
113.56
129.90 470.00
120.78
121.68
460.35
7.92%
-7.87%
-6.12%
129.71
170.00 742.50
128.55
175.38
745.45
-1.27%
5.15%
1.87%
/
/
18
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Highlight Heat transfer coefficient and pressure drop increase as inlet angle increasing.
The pressure drop increase is much larger than heat transfer coefficient.
The effects of inlet angles in horizontal and longitudinal plane are different.
Increase ratios are defined to compare the effects of different fin parameters.
The prediction model agrees well with the simulation results.
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1
S1359-4311(15)00586-4
DOI:
10.1016/j.applthermaleng.2015.06.032
Reference:
ATE 6720
To appear in:
Applied Thermal Engineering
Received Date: 11 March 2015 Accepted Date: 13 June 2015
Please cite this article as: Z. Liu, H. Li, L. Shi, Y. Zhang, Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers, Applied Thermal Engineering (2015), doi: 10.1016/j.applthermaleng.2015.06.032. 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.
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Graphical Abstract
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Three-dimensional simulations are performed to investigate the effect of air inlet angle on heat transfer coefficient and pressure drop. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are studied first. When the air inlet angle is in the horizontal plane, the air inlet angle effect is mainly in the entrance region and strongly related with the flow flied. When the air inlet angle is in the longitudinal plane, the air inlet angle effect is related with the whole fin channel flow field because the vortex length is much larger. The heat transfer coefficient increases with the air inlet angle increasing, while the total pressure drop increase is much larger than heat transfer. The increase ratios are defined to describe the effect of air inlet angle on heat transfer and pressure drop. The variation laws are obtained from the simulation data of different fin parameters. The flow fields on the cross sections (Fig. 1) show that it is applicable to assume that the effect of the air inlet angle (both and are nonzero) can be regarded as a combination of the effects in the two special cases ( ≠ 0, = 0, and = 0, ≠ 0). Thus prediction model is established to predict the heat transfer coefficient and pressure drop when both the horizontal angle and the longitudinal angle are nonzero. The comparison of prediction results and simulation results for 7 pairs of and shows good agreement. The maximum error is less than 10%.
Fig. 1
Flow fields on the cross sections in the fin channel ( = 2.5 mm, = 9.5 mm, = 8/).
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Numerical study of the air inlet angle influence on the air–side performance of plate-fin heat exchangers Zhiying Liu1, Hui Li1*, Lin Shi1, Yangjun Zhang2 (1. Key Laboratory for Thermal Sciences and Power Engineering of the Ministry of Education, Tsinghua University, Beijing 100084, China China) *Author for correspondence
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2. State Key Laboratory of Automotive Safety and Energy, Tsinghua University, Beijing 100084,
Key Laboratory for Thermal Sciences and Power Engineering of the Ministry of Education, Tsinghua University,
Beijing, 100084,China
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E-mail: [email protected]
Abstract
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Numerical work is performed to study the effect of air inlet angle on heat transfer coefficient and pressure drop of the plate-fin heat exchangers. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are simulated on 7 fin channel meshes with different fin parameters. The numerical results show that the different flow fields of the two special air inlet angles cause different effects on heat transfer coefficient and pressure drop. When the air inlet angle is in the horizontal plane, the air inlet angle effect is strongly related with the entrance region flow flied. When the air inlet angle is in the longitudinal plane, the air inlet angle effect is related with the whole fin channel flow field because the vortex size is much larger and comparable to the fin length. The effects of the two angles have different variation laws, which are greatly influenced by fin parameters. Finally, a prediction model is established to calculate the heat transfer coefficient and pressure drop of an arbitrary inlet angle. The comparison of prediction results and simulation results for 7 air inlet angles shows good agreement. The maximum prediction error is within 10%. Keywords: plate-fin heat exchanger; air inlet angle; numerical; prediction model
1. Introduction
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There is a widespread application that the entrance air flow direction is non-orthogonal to the heat exchanger surface. In automotive radiators, the air inlet direction is very complex due to the fan rotation and the geometric restrictions [1]. The air-conditioning evaporators and condensers are usually closed to the fan so that the air flow direction is also non-orthogonal. Furthermore, an air-cooled condenser described by Kroger [2] is arranged obliquely to save land area. X.P.DU et al. [3] have studied the cross-flow finned oval-tube heat exchangers and shown that the entrance air flow direction has an important effect on the heat transfer and pressure drop characteristics. Previous work was made to experimentally study the effect of air flow direction on straight and off-set strip fins. However, the pressure drop measurement may be disturbed by the flow deflector which is used to control the entrance air flow direction and the flow distribution in the fin channel is hard to measure in the experiment. The CFD has been used for various types of studies on heat exchangers [4][5]. Beale and Steven [6] simulated the laminar flow and the heat transfer in an offset-fin heat exchanger surface assuming the fully developed flow and the constant wall temperature. The numerical friction 1
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coefficients agreed well with the experimental data. Muzychka [8] analyzed the flow friction and heat transfer in low Reynolds number flow heat exchangers for three typical configurations. The predictions for the offset strip fin agreed well with experimental data within ±20%. Guo et al. [7] studied the influence of geometrical factors on thermal-hydraulic characteristics for high-pressure-direction type steel offset strip fins using the CFD and Taguchi method. Furthermore, many researches has shown that the three-dimensional simulation had good agreement with the experimental results [11]-[17]. The good agreement proves that CFD is an effective tool for studying the flow and heat transfer of heat exchangers. In the current work, the heat transfer and pressure drop characteristics and flow distribution inside the fin channel of different air inlet direction are studied with CFD. Based on the numerical results, a correction model is established to consider the effect of the air inlet angle for existing correlations [9].
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2. Simulation details 2.1 Parameter definition
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Usually the air entrance flow is orthogonal to the heat exchanger surface when investigating the heat transfer and pressure drop characteristics for the plate fin heat exchangers [10]. Supposing the air frontal velocity is , the Reynolds number is defined as, = / = /
= /
(1) (2) (3)
where is the ratio of the core minimum free-flow area to the frontal area ,
as follows,
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is the maximum average velocity in the core, is the hydraulic diameter. However, the flow and heat transfer may greatly change when the air flow is non-orthogonal to the heat exchanger surface. Fig. 1 shows a general situation of the entrance air flow direction non-orthogonal to the heat exchanger surface. The x axis represents the fin length direction, the y axis represents the fin spacing direction, and the z axis represents the fin height direction. The air flow velocity can be expressed by three perpendicular velocity components , , and "
# = $%& ' $%& (
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(4)
= $%& ' &)* (
(5)
" = sin '
(6)
where ( is the angle between # and the projection of in xy plane, ' is the angle between and its projection in xy plane. Since the characteristic velocity is defined by air flow rate and the minimum free flow area as mentioned previously, the is used as the air frontal velocity instead of to retain consistency. The characteristic velocity is calculated as, (7) = /
#
Before studying a general case, two special cases are discussed as follows, (1) The air inlet angle is in the horizontal plane, " = 0, namely ' equals to zero. The air inlet angle ( is named the horizontal angle. As Fig. 2(a) shown, the air flow direction is changed by the plain fin which causing a 2
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(8)
tan ( = -. /-
(9)
28,3 =
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The increase ratios of the heat transfer coefficient and the static pressure drop are calculated to study the influence of the horizontal angle as follows, 4ℎ63 − 4ℎ6 (10) 2 ,3 = 4ℎ6 4∆:; 63 − 4∆:; 6 4∆:; 6
(11)
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where 4ℎ6 is the air-side heat transfer coefficient at air inlet angle of 0°, and 4∆:; 6 is the static pressure drop at air inlet angle of 0° (2) The air inlet angle is in the longitudinal plane, = 0, namely ( equals to zero. As Fig.
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2(a) shown, the air inlet angle < is named the longitudinal angle. Like case (1), the air inlet angle < is defined as, tan < = -" /- (12) The heat transfer coefficient and the static pressure drop increase ratios are calculated as follows, 4ℎ6= − 4ℎ6 (13) 2 ,= = 4ℎ6 4∆:; 6= − 4∆:; 6 (14) 28,= = 4∆:; 6
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2.2 Governing equations
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Several approximations are made in the numerical simulations as follows, (1) Flow is assumed to be incompressible and steady. (2) Air property is constant and the tube inner wall temperature is fixed. (3) Thermal radiation, nature convection, and gravity force are neglected. The governing equations in the fluid domain are expressed as follows, Continuity equation ∂ ∂@ ∂B + + =0 ∂? ∂A ∂C Momentum equations ∂ ∂ ∂ ∂G HI## HI # HI"# D E +@ +B F=− + + + ∂? ∂A ∂C ∂? H? HA HC D E D E
∂@ ∂@ ∂@ ∂G HI# HI HI" +@ +B F=− + + + ∂? ∂A ∂C ∂A H? HA HC
∂B ∂B ∂B ∂G HI#" HI " HI"" +@ +B F=− + + + ∂? ∂A ∂C ∂C H? HA HC
Energy equation ∂J ∂J ∂J K H/J H/J H/J +@ +B = L + + M ∂? ∂A ∂C D$8 H? / HA / HC /
Heat conduction equation in the solid domain 3
(15)
(16) (17) (18)
(19)
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(20)
2.3 Mesh and boundary conditions
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Three-dimensional numerical work is performed for 7 meshes with different fin parameters to study the air inlet angle effect. The detailed information of the cases is listed in Table 1. The air frontal velocity is 8 - 16 m/s and the air inlet angle is 0° - 80°. As the flow is periodic in the fin height and fin spacing directions, a 2×2 fin channel is used as the calculation domain. Hexahedral mesh is used to ensure the simulation accuracy. Xie et al. [17] compared five turbulence models with experimental data. These models are the RNG O − P model, the standard O − P model, the Reynolds Stress model, the SST O − Q model, and the @ / R model. The results show that all the turbulence models provide similar results except for the SST O − Q model. The two O − P turbulence models are in approximate agreement with the experimental data. Thus the standard O − P turbulence model is used for the simulations. The model constants are set to the default values of FLUENT software package. Fig. 3 shows the hexahedral mesh used for the simulation, the fin channel part is between the inlet section and exit section. The boundary layer mesh is refined to decrease the near-wall temperature gradients. The number of grids is two million to four million depending on the channel size, the mesh quality is over 0.8. Mesh independence was studied on the fin channel 2# with a coarse mesh with one million grids, a normal mesh with two million grids, and a fine mesh with four million grids. The difference between the normal mesh and the fine mesh is within 3% while the difference between the coarse mesh and the fine mesh is more than 10%. Velocity inlet, pressure outlet, and two pairs of periodic boundaries are used in the simulations. The air inlet temperature is 25℃. The tube inner wall temperature is fixed at 80℃. The inlet settings can be classified into five groups as shown in Table 2 for different purposes. The first four groups are used to study the influence of fin parameters, air frontal velocity, and air inlet angle on 2 and 28 . The last group is for model verification.
3. Results and discussion
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The results of case 1# and 3# show that the flow fields of different air frontal velocities are broadly similar. The increase ratios are used to discuss the variation of heat transfer coefficient and pressure drop when air inlet angle is nonzero. Fig. 4 shows that the heat transfer and pressure drop increase ratios have a little difference at different air velocities. Thus the flow field, heat transfer, and pressure drop of different air inlet angles and fin parameters are discussed when air frontal velocity is fixed at 8 m/s. 3.1 Flow field
Fig. 5 shows the flow fields of the middle horizontal plane at ( of 0°, 40°, 60°, and 70° while the air frontal velocity is 8 m/s and < is fixed at 0°. When ( is nonzero, the air flow is askew to the plain fin with a vortex near the leeward side. As the flow is choked by the vortex, the windward-side air velocity is larger than the average velocity at the entrance. After flowing through the vortex, the windward side air velocity is still larger than the leeward side. The air velocity finally becomes uniform under the influence of the fin walls after flowing for some distance. As the horizontal angle ( increases, the vortex size and its influence region become much larger. However, when ( further increases, the flow becomes uniform faster because the vortex heavily blocks the air flow. 4
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the air frontal velocity is 8 m/s and ( is fixed at 0°. When the longitudinal angle < is nonzero, the air flow is askew to the tube with a vortex near the leeward side. As the fin and tube height are much larger than the fin spacing and fin thickness, the vortex length is comparable to the fin length. Thus the flow may be always non-uniform. The trailing vortex size also increases under the influence of the non-uniform flow. When < is more than 70°, the flow becomes unstable and the trailing vortex starts shedding.
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3.2 Heat transfer
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The fin local heat transfer coefficient is compared at different air inlet angles as the fin area is the main contribution to the heat transfer. Fig. 7 shows the local heat transfer coefficient of the fin windward and leeward sides at ( of 0° to 70° while the air frontal velocity is 8 m/s and < is fixed at 0°. The air inlet angle effect on heat transfer is mainly in the entrance region. In the windward side, the near-wall air velocity increases with air inlet angle increasing, thus the local heat transfer coefficient increases in the entrance region. In the leeward side, though the near wall air velocity is much small due to the vortex, the local heat transfer coefficient is also larger than fully developed region because of the vortex. However, the near-wall temperature difference is very small, thus the heat transfer rate of the fin leeward side is not enhanced in the vortex region. Fig. 8 shows the local heat transfer coefficient of the fin at < of 0° to 70° while the air frontal velocity is 8 m/s and ( is fixed at 0°. As the windward and leeward sides are in the tube, the vortex is parallel to the fin. The local heat transfer coefficient decreases in the vortex region and increases above the vortex because the near-wall air velocity is very small in the vortex region and much larger above the vortex. Fig. 9 compares the increase ratio of average heat transfer coefficient at different air frontal velocities and fin parameters. The increase ratio 2T,3 is larger than 2T,= due to the different local heat transfer distribution of fin and tube walls. When ( is variable and < is fixed, the increase ratio 23 increases with fin spacing increasing. The fin height has little effect on 23 . When < is variable and ( is fixed, the increase ratio 2= increases with fin spacing increasing
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and fin height decreasing. 3.3 Pressure drop
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Fig. 10 shows the pressure drop components in one flow passage of a plate-fin heat exchanger [10]. Here the subscripts 1, 2, 3, and 4 represent locations far upstream, passage entrance, passage exit, and far downstream, respectively. As the air flow enters the passage, it contracts due to the free-flow area decrease. ∆P-V/ is the pressure drop at the core entrance due to flow separation and the sudden contraction. ∆P/VW is the pressure drop in the core . ∆PWVX is the pressure rise at the core exit due to the free-flow area increase. 4∆PY 6 = ∆P-V/ + ∆P/VW − ∆PWVX
(21)
Usually, the core frictional pressure drop ∆P/VW is a dominating term, the total core pressure drop can be approximated as,
/ 4\ D] (22) 2 where R is the friction factor, \ is the flow length, is the hydraulic diameter, D is the air density, ] is the velocity calculated by the minimum flow area in the core. When air flow direction is non-orthogonal, total pressure drop increases because the vortex
4∆PY 6 ≈ R
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-
-
-
/ 4:X63 = 4:;X 63 + DX/ = 4:;X 63 + D4X# + 06 / /
(23)
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/ / 4:-63 = 4:;- 63 + D-/ = 4:;- 63 + D^-# + - _ / /
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chokes the air flow in the entrance region and change the velocity distribution in the fin channel. Fig. 11 shows the static and total pressure components along the flow length in the middle horizontal plane when air inlet angle is in the horizontal plane. As the fin spacing is very small, the vortex size is much smaller than the fin length, the influence of air inlet angle can be divided into three regions. In the vortex region, pressure decreases rapidly and then increases gradually. In a partial region after the vortex, the total pressure near the windward side is larger than leeward side due to the air velocity non-uniformity. As the air flow becomes uniform, the total pressure near the leeward and windward sides is almost the same. For the special case (1), the total pressure at the far upstream and downstream can be expressed as,
(24)
is zero. The total pressure drop is,
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where the subscripts t, s, and ( represent total pressure, static pressure, and air inlet angle. When flowing through the fin channel, X# equals to -# because of mass continuity, while X
1 / 1 (25) 4∆: 63 = 4:X 63 − 4:- 63 = 4:;- 63 − 4:;X 63 + D- = 4∆:; 63 + D4-# tan (6/ 2 2 Since the maximum velocity ] is usually used as the characteristic velocity in the heat exchanger design, the total pressure drop can be expressed by a function of ] as,
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1 / 4∆: 63 = 4∆:; 63 + D / ] tan/ ( 2 Likewise, for the special case (2), the total pressure drop can be expressed as, / 4∆: 6= = 4∆:; 6= + D / ] tan/ < /
(26)
(27)
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Thus the total pressure drop is larger than the static pressure drop when air direction is non-orthogonal to the heat exchanger surface. Fig. 12 compares the total and static pressure drop increase ratio varying with ( and < at different fin parameters. When ( is variable from 0° to 80° and < is fixed, the 2ab,3 increases first and then decreases, and the change is within 20%. The 2ab,3 increases with fin spacing increasing. When < is variable from 0° to 70° and ( is fixed, the 2ab,= significantly increase with < and fin height increasing. However, the fin spacing has little influence on 2ab,= . The total pressure drop increase ratio is much larger because of the dynamic pressure loss when air flow direction is non-orthogonal. The 2cb,3 increases with fin spacing increasing while fin height has little influence on 2cb,3 . The 2cb,= increases with fin height increasing and decreases with fin spacing increasing. 3.4 Prediction model for general situations For a general situation, both ( and < are nonzero, the non-orthogonal air velocity can be decomposed into three perpendicular velocity components , . , and d in a
three-dimensional Cartesian coordinate system. The influence of air inlet angle on heat transfer is related to the near-wall air velocity of the fin and tube wall. As show in Fig. 13 (a) and (b), the inlet angle ( mainly causes velocity non-uniformity along the y direction in the entrance region, while inlet angle < mainly causes velocity non-uniformity along the x direction in the whole fin channel. The flow field in Fig. 13(c) can be regarded as a duplicate effect of the flow fields in Fig. 6
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velocity components . and d . Thus it is applicable to assume that the effect of the air inlet
angle (both ( and < are nonzero) can be regarded as a combination of the effects in the two special cases (( ≠ 0, < = 0, and ( = 0, < ≠ 0). Thus the heat transfer coefficient and pressure drop can be calculated as follows,
4ℎ63= = ^1 + 2 ,3 + 2 ,= _ ∙ 4ℎ6
(28)
4∆:; 63= = ^1 + 2ab,3 + 2ab,= _ ∙ 4∆:; 6
(29)
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1 / 4tan/ (30) 4∆: 63= = 4∆:; 63= + D / ] ( + tan/ <6 2 where the subscripts ( and < represent the horizontal angle and the longitudinal angle in the special cases. The 5th simulation group is used to verify the prediction model. Table 3 compares the simulation results and prediction results. Both the heat transfer coefficient and pressure drop are in good agreement. The maximum error is less than 10% when ( and < are less than 70°. It means that when the air frontal velocity is in the range of 6 m/s to 16m/s and air inlet angles ( and < are less than 70°, the assumption is practicable and the prediction error is acceptable in the engineering application.
4. Conclusion
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Three-dimensional simulations are performed to investigate the effect of air inlet angle on heat transfer coefficient and pressure drop. Two special air inlet angles which are in the horizontal plane and in the longitudinal plane are studied first. When air frontal velocity is 6-16 m/s, the velocity has a little influence on the heat transfer and pressure increase ratios. Thus the influence of air inlet angle and fin parameters is investigated at a fixed air frontal velocity. The heat transfer coefficient and pressure drop increase with air inlet angle increasing, while the pressure drop increase is much larger. When the air inlet angle is in the horizontal plane, the air inlet angle effect is mainly in the entrance region and strongly related with the flow flied. The heat transfer coefficient increases with the air inlet angle increasing, while the static pressure drop increases first and then decreases. The increase ratios 2 ,3 and 2cb,3 increase with fin spacing increasing and are little affected by
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fin height. However, the total pressure drop increase is much larger than heat transfer. The static pressure drop increase ratios 2ab,3 is very small and can be neglected compared with the total pressure drop. When the air inlet angle is in the longitudinal plane, the vortex length is much larger because the fin height is much larger than fin spacing. The heat transfer coefficient increase ratio 2 ,=
increases with fin spacing increasing and fin height decreasing. The static pressure drop increase ratio 28,= increases with fin height increasing and is little affected by fin spacing.
A prediction model is established to predict the heat transfer coefficient and pressure drop when both the horizontal angle ( and the longitudinal angle < are nonzero. The comparison of prediction results and simulation results for 7 pairs of ( and < shows good agreement. The maximum error is less than 10%.
Acknowledgements This work was supported by the State Key Program of the National Natural Science Foundation of 7
ACCEPTED MANUSCRIPT China (Grant No. 51236004) and Science Fund for Creative Research Groups (No.51321002).
Reference
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[1] Khaled M, Mangi F, Hage H E, et al. Fan air flow analysis and heat transfer enhancement of vehicle underhood cooling system–Towards a new control approach for fuel consumption reduction[J]. Applied Energy, 2012, 91(1): 439-450. [2] D.G. Kröger, Air-cooled heat exchangers and cooling towers, vol. I, PennWell Corporation, Tulsa, Oklahoma, 2004. [3] Du X P, Zeng M, Dong Z Y, et al. Experimental study of the effect of air inlet angle on the air-side performance for cross-flow finned oval-tube heat exchangers[J]. Experimental Thermal and Fluid Science, 2014, 52: 146-155. [4] Sheik Ismail L, Velraj R, Ranganayakulu C. Studies on pumping power in terms of pressure drop and heat transfer characteristics of compact plate-fin heat exchangers—A review[J]. Renewable and Sustainable Energy Reviews, 2010, 14(1): 478-485. [5] Aslam Bhutta M M, Hayat N, Bashir M H, et al. CFD applications in various heat exchangers design: A review[J]. Applied Thermal Engineering, 2012, 32: 1-12. [6] Beale S. Laminar fully developed flow and heat transfer in an offset rectangular plate-fin surface[J]. PHOENICS Journal of Computational Fluid Dynamics, 1990, 3(1), 1-19. [7] Guo L, Qin F, Chen J, et al. Influence of geometrical factors and pressing mould wear on thermal-hydraulic characteristics for steel offset strip fins at low Reynolds number[J]. International Journal of Thermal Sciences, 2007, 46(12): 1285-1296. [8] Muzychka Y S. Analytical and experimental study of fluid friction and heat transfer in low Reynolds number flow heat exchangers[D]. 1999. [9] Corberán J M, Cuadros E, González K. Pressure drop characterisation of compact heat exchanger channels[C].5th European Thermal-Sciences Conference, The Netherlands. 2008. [10] Shah R K, Sekulic D P. Fundamentals of heat exchanger design[M]. John Wiley & Sons, 2003. [11] Peng H, Ling X. Numerical modeling and experimental verification of flow and heat transfer over serrated fins at low Reynolds number[J]. Experimental Thermal and Fluid Science, 2008, 32(5): 1039-1048. [12] Zhu Y, Li Y. Three-dimensional numerical simulation on the laminar flow and heat transfer in four basic fins of plate-fin heat exchangers[J]. Journal of Heat Transfer, 2008, 130(11): 111801. [13] Bhowmik H, Lee K S. Analysis of heat transfer and pressure drop characteristics in an offset strip fin heat exchanger[J]. International Communications in Heat and Mass Transfer, 2009, 36(3): 259-263. [14] Peng H, Ling X, Li J. Numerical simulation and experimental verification on thermal performance of a novel fin-plate thermosyphon[J]. Applied Thermal Engineering, 2012, 40: 181-188. [15] Ben Saad S, Clément P, Fourmigué J F, et al. Single phase pressure drop and two-phase distribution in an offset strip fin compact heat exchanger[J]. Applied Thermal Engineering, 2012, 49: 99-105. [16] He Y L, Tao W Q, Song F Q, et al. Three-dimensional numerical study of heat transfer 8
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characteristics of plain plate fin-and-tube heat exchangers from view point of field synergy principle[J]. International Journal of Heat and Fluid Flow, 2005, 26(3): 459-473. [17] Xie G, Liu J, Ligrani P M, et al. Numerical analysis of flow structure and heat transfer characteristics in square channels with different internal-protruded dimple geometrics[J]. International Journal of Heat and Mass Transfer, 2013, 67: 81-97.
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A diagram of the entrance air flow non-orthogonal to the heat exchanger surface.
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Fig. 1
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Figures:
Schematic diagrams of the special air inlet angles.
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Fig. 2
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Mesh and boundary conditions.
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Fig. 3
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Fig. 4
The increase ratios of heat transfer coefficient and pressure drop at different air velocities (R8 = 2.5 mm, R = 9.5 mm, ( = 0~80°, < = 0~70°). 11
Flow field of the middle horizontal plane at the air frontal velocity of 8 m/s, ( of 0°, 40°, 60°, 70°, and < fixed at 0°.
Flow field of the middle longitudinal plane at the air frontal velocity of 8 m/s, < of 0°, 40°,
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Fig. 6
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Fig. 5
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60°, 70°, and ( fixed at 0°.
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Local heat transfer coefficient in the fin windward and leeward sides at the air frontal velocity of 8 m/s, ( of 0° to 70°, and < fixed at 0°.
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Fig. 7
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Fig. 8
Local heat transfer coefficient in the fin surface at the air frontal velocity of 8 m/s, < of 0° to 70°, and ( fixed at 0°.
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Air-side heat transfer coefficient vs. air inlet angle of different fin parameters ( = 8 m/s).
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Fig. 9
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Pressure drop components in the passages of a plate-fin heat exchanger.
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Fig. 10
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Fig. 11
Pressure components of three lines in the middle horizontal plane of the fin channel when air flow is non-orthogonal.
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The pressure drop increase ratios vs. air inlet angle of different fin parameters. ( = 8 m/s).
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Fig. 12
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16
Flow fields on the cross sections in the fin channel (R8 = 2.5 mm, RT = 9.5 mm, = 8o/&).
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Fig. 13
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Table 1
Geometry parameters of the fin channels.
fin spacing [mm]
fin thickness [mm]
1# 2# 3# 4# 5# 6# 7#
2.0 2.5 3.0 3.5 2.5 2.5 2.5
0.2 0.2 0.2 0.2 0.2 0.2 0.2
9.5 9.5 9.5 9.5 8.0 12 15
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1# 2# 3# 4# 5#
2# 1# - 4#, 6# 2# 2#, 4# - 7# 2#
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Mesh No.
Table 3
[m/s]
6,8,12,16 8 6,8,12,16 8 8
fin length [mm]
4.0 4.0 4.0 4.0 4.0 4.0 4.0
60 60 60 60 60 60 60
( [°]
0,20,40,50,60,70,75,80 0,20,40,50,60,70,75,80 0 0 0,40,60,70
< [°]
0 0 0,20,40,50,60,70 0,20,40,50,60,70 0,40,50,60,70
Comparison of prediction and simulation results.
Simulation results h
tube height [mm]
Detailed information of each simulation case group.
Group No.
4(, <6
fin height [mm]
M AN U
Mesh No.
Table 2
Temperature (K) Air inflow velocity (m/s) Air frontal velocity (m/s) Maximum average velocity (m/s) Velocity components (m/s) Horizontal angle (°) Longitudinal angle (°) Thermal conductivity (W/mK) Kinematic viscosity (m2/s) Air density (kg/m3)
RI PT
T
u,v,w ( < K D
SC
Nomenclature $b Thermal capacity (J/kgK) T Hydraulic diameter (m) f Fanning friction factor (-) h heat transfer coefficient (W/m2K) j Colburn j-factor (-) L Flow length (m) p Pressure (Pa) ∆:a Static pressure drop (Pa) ∆: Total pressure drop (Pa) Re Reynolds number
Prediction results
[W/m K]
P
TP
[Pa]
[Pa]
(0,0)
79.80
87.91
87.90
(40,40)
91.11
(40,60)
h
Error
[W/m K]
P
TP
[Pa]
[Pa]
-
-
104.40 157.80
92.03
98.10
130.60 271.10
(60,40)
101.03
(70,50) (70,70)
h
P
TP
-
-
-
-
105.85
159.02
1.01%
1.39%
0.77%
96.93
136.75
276.62
-1.29%
5.89%
3.50%
113.20 253.60
104.87
111.23
251.10
4.22%
-1.88%
-1.58%
113.56
129.90 470.00
120.78
121.68
460.35
7.92%
-7.87%
-6.12%
129.71
170.00 742.50
128.55
175.38
745.45
-1.27%
5.15%
1.87%
/
/
18
ACCEPTED MANUSCRIPT
Highlight Heat transfer coefficient and pressure drop increase as inlet angle increasing.
The pressure drop increase is much larger than heat transfer coefficient.
The effects of inlet angles in horizontal and longitudinal plane are different.
Increase ratios are defined to compare the effects of different fin parameters.
The prediction model agrees well with the simulation results.
AC C
EP
TE D
M AN U
SC
RI PT
1