Applied Thermal Engineering

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1 Applied Thermal Engineering 61 (2013) 770e783 Contents lists available at SciVerse ScienceDirect Applied Thermal Engineering journal homepage: Analysis of heat transfer and pressure drop for fin-and-tube heat exchangers with rectangular winglet-type vortex generators Ya-Ling He a, *, Pan Chu a, Wen-Quan Tao a, Yu-Wen Zhang a,b, Tao Xie a a Key Laboratory of Thermo-Fluid Science & Engineering of MOE, Xi an Jiaotong University, Xi an, Shaanxi , PR China b Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA article info abstract Article history: ceived 21 February 2011 Accepted 18 February 2012 Available online 3 March 2012 Keywords: ctangular winglet pairs Fin-and-tube heat exchangers Heat transfer enhancement In present work, heat transfer enhancement and pressure loss penalty for fin-and-tube heat exchangers with rectangular winglet pairs (RWPs) were numerically investigated in a relatively low ynolds number flow. The purpose of this study was to explore the fundamental mechanism between the local flow structure and the heat transfer augmentation. The RWPs were placed with a special orientation for the purpose of enhancement of heat transfer. The numerical study involved three-dimensional flow and conjugate heat transfer in the computational domain, which was set up to model the entire flow channel in the air flow direction. The effects of attack angle of RWPs, row-number of RWPs and placement of RWPs on the heat transfer characteristics and flow structure were examined in detail. It was observed that the longitudinal vortices caused by RWPs and the impingement of RWPs-directed flow on the downstream tube were important reasons of heat transfer enhancement for fin-and-tube heat exchangers with RWPs. It was interesting to find that the pressure loss penalty of the fin-and-tube heat exchangers with RWPs can be reduced by altering the placement of the same number of RWPs from inline array to staggered array without reducing the heat transfer enhancement. The results showed that the rectangular winglet pairs (RWPs) can significantly improve the heat transfer performance of the finand-tube heat exchangers with a moderate pressure loss penalty. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Fin-and-tube heat exchangers are widely used in various industry fields such as chemical process, HVACR (heating, ventilating, air-conditioning and refrigeration) systems, petrochemical industry, and electronics cooling. Improving the heat exchanger performance is very important in meeting efficiency standards and environmental impact. A high-efficiency compact heat exchanger is effective to achieve such goals as improving energy efficiency and reduction of CO 2 emission. The total thermal resistance for such kind of heat exchangers is comprised of three parts: the air-side convective thermal resistance, the wall conductive thermal resistance and the liquid-side (often two-phase heat transfer) convective thermal resistance. The heat transfer coefficient on the air-side is typically low due to the thermo-physical properties of air. Thus the air-side thermal resistance is the dominant part of the overall heat transfer process and efforts to improve the performance of these heat exchangers should focus on the air-side surfaces. * Corresponding author. Tel.: þ ; fax: þ address: yalinghe@mail.xjtu.edu.cn (Y.-L. He). Vortex generation is a new and innovative strategy of enhancing air-side heat transfer. Vortex generators such as wings and winglets can introduce vortices into the flow field causing heat transfer enhancement. Vortex can be divided into two categories based on the axes of these vortices: transverse vortices and longitudinal vortices. Longitudinal vortices have their axes parallel to the main flow direction and transverse vortices have their axes perpendicular to the main flow direction. Vortex generators can be punched, mounted or embossed on a heat transfer surface. When fluid flows through vortex generators, vortices are generated due to the friction and separation on the edge of the vortex generator. Longitudinal vortex generators generate higher heat transfer enhancement for the same pressure penalty than transverse vortex generators. In traditional point of view, there are three mechanisms for passive heat transfer enhancement, (1) developing boundary layers; (2) swirl; and (3) flow destabilization. Longitudinal vortex generators can generate all the three mechanisms for heat transfer enhancement [1]. Extensive studies have been done on heat transfer characteristics and flow structure for heat exchangers with longitudinal vortex generators. In recent years, the implementation of vortex generators in fin-and-tube heat exchangers has received more and more /$ e see front matter Ó 2012 Elsevier Ltd. All rights reserved. doi: /j.applthermaleng

2 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e attention. Fiebig [1] numerically and experimentally investigated embedded vortices in internal flow. He showed that longitudinal vortices gave better heat transfer enhancement than transverse vortices for the same pressure loss penalty and noted that winglets produced the same heat transfer enhancement for less pressure loss as compared to wings. Zhu et al. [2] numerically explored the three-dimensional turbulent flows and heat transfer in a rectangular channel with longitudinal vortex generators on one wall and rib-roughness elements on the other wall. They pointed out that the combined effect of vortex generators and rib-roughness increased the average Nusselt number by nearly 450%. Deb and Biswas [3] numerically analyzed heat transfer characteristics and flow structure in laminar and turbulent flows through a rectangular channel containing built-in vortex generators by means of solutions of the full NaviereStokes and energy equations. Jacobi and Shah [4] gave an excellent review on heat transfer surface enhancement through the use of longitudinal vortices. Biswas et al. [5] experimentally and numerically examined the flow structure and heat transfer effects of longitudinal vortices in a channel flow. They observed that the flow structure was complex and consisted of a main vortex, a corner vortex and induced vortex. The combined effect of these vortices distorted the temperature field in the channel and augmented heat transfer between the fluid and its neighboring surfaces. Lee et al. [6] numerically studied the heat transfer characteristics and turbulent structure in a threedimensional turbulent boundary layer with longitudinal vortices. They indicated that the disturbance of the boundary layer caused the best heat transfer enhancement in the region where the flows are directed toward the wall but the vortex core is the region of relatively lower mixing. Lau et al. [7] experimentally studied the momentum and heat transport in the turbulent channel flow with embedded longitudinal vortices. Liou et al. [8] experimentally investigated heat transfer and fluid flow in a square duct with 12 different shaped vortex generators. They found that the direction and strength of the secondary flow with respect to the heat transfer wall were the most important fluid dynamic factors affecting the heat transfer augmentation through the channel wall. An experimental study was conducted by Torii et al. [9] to obtain heat transfer and pressure loss in a fin-and-tube heat exchanger with inline or staggered tube banks with delta-winglet vortex generators of various configurations. The winglets were placed in a special orientation to augment heat transfer and reduce form drag. They showed that for the ynolds number ranging from 350 to 2100, the enhanced configuration (in case of staggered tube banks) increased the heat transfer coefficient by 30e10% over the baseline case, and the corresponding pressure loss was reduced by 55e34%. Gentry and Jacobi [10] experimentally explored the heat transfer enhancement by delta-wing-generated vortices in flat-plate and developing channel flows. They reported that for the complete channel surface the largest spatially averaged heat transfer enhancement was 55% accompanied by a 100% increase in the pressure drop relative to the same channel flow with no delta-wing vortex generator. Leu et al. [11] numerically and experimentally studied the heat transfer and flow in the plate-fin-and-tube heat exchangers with inclined block shape vortex generators mounted behind the tubes. They pointed out that the proposed heat transfer enhancement technique is able to generate longitudinal vortices and to improve the heat transfer performance in the wake regions. More recently, Joardar and Jacobi [12] experimentally evaluated the potential of winglet-type vortex generator arrays for air-side heat transfer enhancement of a compact plain-fin-and-tube heat exchanger by full-scale wind-tunnel testing. They found that the air-side heat transfer coefficient increased from 16.5% to 44% for the single-row winglet arrangement with an increase in pressure drop of less than 12% and for the three-row vortex generator array the Fig. 1. Schematic diagram of core region of a fin-and-tube heat exchanger with RWPs. heat transfer coefficient increases from 29.9% to 68.8% with a pressure drop penalty from 26% to 87.5%. Pesteei et al. [13] experimentally studied the effect of winglet location on heat transfer enhancement and pressure drop in fin-tube heat exchangers. They found that the winglet pairs were most effective to enhance the heat transfer coefficients when these were placed in the downstream side. Hiravennavar et al. [14] numerically studied the flow structure and heat transfer enhancement by a winglet pair of non-zero thickness. They observed that in comparison with a channel without winglets, the heat transfer was enhanced by 33% when single winglet is used and by 67% when a winglet pair was employed. Joardar and Jacobi [15] numerically investigated the flow and heat transfer enhancement using an array of delta-winglet vortex generators in a fin-and-tube heat exchanger. They adopted common-flow-up arrangement for vortex generators in three different configurations. The 3VG-inline-array configuration (refers to Fig. 4) achieves enhancements up to 32% in total heat flux and 74% in j-factor over the baseline case, with an associated pressure drop increase of about 41%. Wu and Tao indicated that the basic mechanism of heat transfer enhancement by the vortex generators is the improvement in the synergy between velocity and fluid temperature gradient [16]. They also made a parametric study on the effects of the geometric parameters of LVG [17]. He et al. [18] numerically studied the vortex generator in the form of rectangular winglet pairs and explained the results from the viewpoint of filed synergy principle. He et al. [19,20] also explored the air-side performance of wavy fin-and-tube heat exchangers with punched delta-winglet-type vortex generators. There are a few reports of implementation of longitudinal vortex generators on fin-and-oval-tube heat exchangers in open literature. Fig. 2. Four basic vortex generator forms.

3 772 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e Fins Fig. 3. Winglet-type vortex generator dimensions and the placement with respect to the tube (all dimensions are in mm). Chen et al. [21] numerically explored the conjugate heat transfer of a finned-oval tube with a punched longitudinal vortex generator in form of a delta-winglet. They further investigated the heat transfer enhancement of finned-oval tube with inline longitudinal vortex generators [22] as well as with staggered longitudinal vortex generators [23]. Tiwari et al. [24] numerically studied the laminar flow and heat transfer in a channel with built-in oval tube and delta-winglet vortex generators. They revealed that combinations of oval tube and the winglet pairs improved the heat transfer significantly. O Brien et al. [25] experimentally investigated the forced convection heat transfer in a narrow rectangular duct fitted with an elliptical tube and one or two delta-winglet pairs. They found that the addition of the single winglet pair to the oval-tube geometry yielded significant heat transfer enhancement, averaging 38% higher than the oval tube, no-winglet case. The corresponding increase in friction factor associated with the addition of the single winglet pair to the oval-tube geometry was moderate, less than 10% at Dh ¼ 500. He et al. [26] numerically investigated the effects of geometric parameters of LVG on the fin-and-oval-tube heat exchangers and analyzed the mechanism between the heat transfer enhancement and the flow structure. Aris et al. [27] experimentally and numerically studied the thermal-hydraulic R a Top view of the computational domain b Side view of the computational domain Fig. 4. Coordinate system and computational domain (all dimensions are in mm).

4 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e performance of a heat pipe fin stack with shape memory alloy vortex generators in forced air convection. They achieved a heat transfer enhancement of 37% and a reduction in fan operating cost. The foregoing literature review shows that few reports of fullscale implementation of longitudinal vortex generators in finand-tube heat exchangers have been published. The previous investigations were mainly focused on parametric study, and heat transfer enhancement was often explored from the traditional point of view. Moreover, most of the previous studies of fin-and-tube heat exchangers with vortex generators were focused on single heat transfer element (only one tube involved). In addition, the fin efficiency and the influence of thickness of vortex generator were often not taken into account. All these motivate the present study. 2. Model descriptions 2.1. Physical model In this study, a fin-and-tube heat exchanger with longitudinal vortex generators used in air-conditioning system is investigated. The schematic diagram of the heat exchanger is shown in Fig. 1. There are four basic vortex generatorsddelta wing, rectangular wing, delta-winglet pair and rectangular winglet pair (see Fig. 2). In the present study, we adopt the rectangular winglet pair as the vortex generator based the results of previous study in the literature. A pair of rectangular winglets is symmetrically mounted on the fin surface, adjacent to heat transfer tube. The height of the winglets is equal to 60% of the channel height (H). Fig. 3 shows the dimensions of rectangular winglets and their placement with respect to the tube. The rectangular winglet pairs (RWPs) are placed in common-flow-up orientation. In Fig. 4 the computational domain and the coordinate system are presented, where X is the streamwise direction, Y is the spanwise direction and Z stands for the fin pitch direction. Fig. 4(a) gives a top view of the computational domain for a fin-and-tube heat exchanger with RWPs and Fig. 4(b) presents a side view of the computational domain. Two neighboring fins form a channel of height H ¼ 3.63 mm, width B ¼ 12.7 mm, and length L ¼ mm. The first tube of diameter D ¼ mm, is located at X ¼ 12.7 mm from the inlet of the flow channel. Both the longitudinal tube pitch P l and the transverse tube pitch P s are 25.4 mm. The tube rows are arranged in inline. The fin material is aluminum and fin thickness F t ¼ 0.18 mm. Because of the geometry character of symmetry of the fin-and-tube heat exchanger, the region (in XeY plane) outlined by the dashed lines in Fig. 4(a) is selected as the computational domain. Due to the high heat transfer coefficient inside the tube and the high thermal conductivity of the tube wall, the tube temperature is set as constant. However, the temperature distribution on the fin surface is unknown and will be determined during the computational iteration process. In order to solve this conjugated problem, the computational domain should contain the whole fin surface during the numerical simulation. Therefore, the region (in XeZ plane) outlined by the dashed lines in Fig. 4(b) is taken as the computational domain due to the geometry character of periodicity. The actual computation domain is extended by 5H at the inlet to maintain the inlet velocity uniformity and the domain is extended by 30H at the exit to ensure a recirculation-free flow there. The tubes and fins are not included in the upstream and downstream extended domains and for saving space, the extended domain is not pictured in Fig Governing equations and boundary conditions vortices is a quasi-steady phenomenon. Consequently, due to the low inlet velocity and the small fin pitch, the flow in the channel of the compact heat exchanger is assumed to be laminar and steady. Fin thickness and heat conduction in the fins and vortex generators are taken into account. The temperature distribution for the fins can be determined by solving the conjugate heat transfer problem in the computational domain. The governing equations in Cartesian coordinates can be expressed as follows: Continuity equation : Momentum equation : Energy equation : Where v vx i ðru i Þ¼0 (1) v ðru vx i u k Þ ¼ v m vu k i vx i vx i v vx i ðru i TÞ¼ v vx i G vt vx i vp vx k (2) (3) G ¼ l c p (4) The boundary conditions for all surfaces are described as follows: (1) In the upstream extended region At the inlet boundary u ¼ u in ¼ const; v ¼ w ¼ 0; T ¼ T in ¼ const (5a) At the top and bottom boundaries Velocity condition : periodic conditions Temperature condition : periodic conditions At the side boundaries vu vy ¼ vw vy ¼ 0; v ¼ 0; vt vy ¼ 0 (2) In the downstream extended region At the top and bottom boundaries Velocity condition : periodic conditions Temperature condition : periodic conditions At the side boundaries u up ¼ u down u up ¼ u down T up ¼ T down (5b) (5c) T up ¼ T down (6a) The fluid is considered incompressible with constant properties. According to Ferrouillat et al. [28], the generation of longitudinal vu vy ¼ vw vy ¼ 0; v ¼ 0; vt vy ¼ 0 (6b)

5 774 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e783 At the outlet boundary vu vx ¼ vv vx ¼ vw vx ¼ vt vx ¼ 0 (3) In the fin coil region At the top and bottom boundaries Velocity condition : periodic conditions Temperature condition : periodic conditions At the side boundaries u up ¼ u down Fluid region : vu vy ¼ vw vy ¼ 0; v ¼ 0; vt vy ¼ 0 Fin surface region : u ¼ v ¼ w ¼ 0; vt vy ¼ 0 (6c) T up ¼ T down (7a) (7b) (7c) Tube region : u ¼ v ¼ w ¼ 0; T ¼ T w ¼ const (7d) 2.3. Numerical methods The geometry for the three-dimensional vortex-enhanced multi-row fin-and-tube heat exchanger is complex and it can be expected that the velocity and temperature fields are complicated in the computational domain. In order to capture important scales and resolve the near-wall gradients appropriately, the grid must be generated with great care and effort. The computational meshes were generated by using Gambit. Because of the complexity of the computational domain, it is difficult to use a single structured quadrilateral mesh in the whole flow passage. In order to improve the quality of the grid system, a multi-block hybrid method is adopted to generate the mesh. First, the whole computational domain is divided into several subdomains. Then different strategies are employed for each subdomain to generate the mesh. For the blank zone, a structured hexahedral mesh is employed because of its simplicity. So does it for the tube zone. The RWPs zone is complex and an unstructured hexahedral mesh is employed. Generally, the meshes are generated much finer in the regions adjacent to tubes and winglets and much coarser in the extended regions. The grid system generated by the multi-block hybrid method is illustrated in Fig. 5. The NaviereStokes and energy equations (1)e(3) with the boundary condition equations (5)e(7) are solved by using a computational fluid dynamics code (Fluent). The convective terms in governing equations for momentum and energy are discretized with the second-order upwind scheme. The coupling between velocity and pressure is performed with SIMPLE algorithm. The convergence criterion for the velocities is that the maximum mass residual of the cells divided by the maximum residual of the first 5 iterations is less than , and the convergence criterion for the energy is that the maximum temperature residual of the cells divided by the maximum residual of the first 5 iterations is less than Fig. 5. Grid system generated by the multi-block hybrid method.

6 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e Parameter definitions The definitions of number, average Nu number, friction factor f and Colburn j are as follows: ¼ rv m D h =m; Nu ¼ hd h =l (8) f ¼ rv 2 m 2 DP A T A min ; j ¼ St$Pr 2=3 ; St ¼ h rv m c p (9) where V m, m, l are the mean velocity in the minimum flow crosssection of the flow channel, fluid dynamic viscosity and thermal conductivity respectively. D h is the hydraulic diameter, DP is the pressure drop across the fin-core in the computational domain, A T is the total heat transfer surface area, A min is the minimum flow cross-section area, and h is the height of the flow channel. The mean temperature and pressure of a cross-section are defined as: RR RR utda pda A T ¼ RR uda ; p ¼ A RR (10) da A A The total heat transfer, pressure loss and log-mean temperature difference are defined as: Q ¼ _mc p ðt out T in Þ ; DP ¼ p in p out ; DT ¼ ðt w T in Þ ðt w T out Þ ln½ðt w T in Þ=ðT w T out ÞŠ The heat transfer coefficient is defined as : h ¼ Q A T DT 3. Validation of numerical results ð11þ (12) In order to validate the independency of solution on the grid, three different grid systems are investigated, which include about 800,000, 1,260,000, and 1,500,000 cells respectively for the finand-tube heat exchanger with one RWPs.The predicted averaged Nu numbers for the three grid systems are shown in Fig. 6. From the figure we can see that the change of the averaged Nu number is less than 3% among the three different grid systems. For the present study, the final grid number is selected as about 1,260,000. Similar validations are also conducted for other cases. Apart from the investigations on the grid independency, the characteristics of flow and heat transfer are compared with the available experimental results. In order to validate the reliability of the numerical method being used, the numerical simulation is conducted for a fin-and-tube heat exchanger with the same geometrical configurations as presented in Joardar and Jacobi [12]. The inlet air velocity ranges from 1.06 m/s to 1.87 m/s and the corresponding number ranges from 500 to 880. The predicted results are compared with the experimental results from f. [12]. The air-side heat transfer coefficient h air and the overall pressure loss penalty DP are shown in Fig. 7(a) and (b), respectively. As we can see from the figures, the discrepancy between the predicted air-side heat transfer coefficient and the experimental values is 10.02% (at ¼ 525) to 10.08% (at ¼ 880). The discrepancy between the predicted pressure loss and the experimental values is 3.05% (at ¼ 500) to 15.13% (at ¼ 880). In Fig. 7(a), the change rate for experimental results and numerical results is a little different. This is mainly caused by the difference between experimental process and the numerical process. The contact resistance Nu h air / Wm -2 K -1 ΔP/Pa Grid number about Grid number about Grid number about Fig. 6. Variation of the predicted Nusselt number with different grid number Experimental Numerical a Effect of on h air Experimental Numerical b Effect of on ΔP Fig. 7. Experimental-numerical comparison of h air and DP for model validation.

7 776 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e783 and the leakage of the test specimen are inevitable in the experiment. However, the numerical simulation is close to ideal condition. The good agreement between the predicted and experimental results indicates that the present numerical model is reliable to predict heat transfer characteristics and flow structure in compact heat exchangers. 4. sults and discussion The simulation parameters are summarized as follows: Inlet temperature: K. ynolds number: ranges from 550 to 880. Tube wall temperature: K Influence of the angle of attack In order to study the influence of angle of attack of RWPs on the heat transfer characteristics and the flow structure for fin-and-tube heat exchangers, a comparative investigation for fin-and-tube heat exchangers with RWPs of different attack angle is performed. The RWPs are symmetrically mounted adjacent to the tubes. The angle of attack a is set as 0 (baseline case), 10,20,30. The ynolds number based on the hydraulic diameter ranges from 575 to 880. Fig. 8 shows the configurations for fin-and-tube heat exchangers with RWPs of different attack angle. As the incoming flow approaches the RWPs in the flow passage, the longitudinal vortices are generated due to the pressure difference between the upstream side and the downstream side of the RWPs. The strong swirling flow around the axis parallel to the main flow direction can disrupt the growth of boundary layer on the fin surface, drag fluid from the wake region of tube to the mainstream, and enhance the mixing of fluid from the periphery and the core region of the flow. All these effects of the strong swirling flow ultimately bring about enhancement of heat transfer in the flow passage. Moreover, the particular placement and orientation of the RWPs can yield additional enhancement. In our present study, the RWPs are arranged in common-flow-up orientation. With this common-flow-up orientation, a constricted passage between the RWPs and the aft of the tube is formed. In this nozzle-like passage, the fluid is accelerated. As a consequence, the boundary layer separation is suppressed and the tube wake region is narrowed. Furthermore, the fluid accelerated in the constricted nozzle-like passage will impinge directly on the downstream tube resulting in a local heat transfer enhancement. The combination effect of separation delay, narrowing of tube wake and impingement can significantly augment the heat transfer in the flow channel. The velocity distributions in three yez cross-sections for Deg-20 case at ¼ 850 are presented in Fig. 9. We can see from the figure that there are three kinds of longitudinal vortices in the channel, main vortex, corner vortex and induced vortex. The main vortex is formed due to the flow separation and friction on the leading edge of RWPs. However, the corner vortex is formed by the deformation of the near-wall streamlines. The induced vortex which is formed by the interaction between the main vortex and the fin surface rotates opposite to the main vortices. The combined effect of these vortices distorts the temperature field in the channel and serves ultimately to bring about a significant augmentation of heat transfer between the fluid and its neighboring surfaces [5]. The temperature distributions in three yez cross-sections for Deg-20 case at ¼ 850 are presented in Fig. 10. From the figure we can see that the temperature profiles are distorted by the longitudinal vortices. The thermal boundary layer is disrupted by the swirling flow. In the down-wash region the thermal boundary is thinned but in the up-wash region the thermal boundary is thickened. Fig. 11 illustrates the local velocity distributions on the middle cross-section (parallel to the yez plane) at ¼ 850. For the sake of clarity, results are provided only for the first two tube rows in the flow channel (the others are similar to the first two tube rows due to the periodical arrangement of RWPs). As we can see from Fig. 11(a), the plots of velocity of magnitude show that the flow velocity is very low in the rear of the tubes. The streamlines imply that vortices are formed behind the tubes. This kind of vortices is generated due to the flow separation on the tubes and is called as transverse vortices. The transverse vortices recirculate the fluid in the rear of the tube and the fluid in this region is almost isolated from the main flow. For Fig. 11(b)e(d), we can clearly see that the streamlines are stretched and bended toward the wake region behind the first tube. The converged streamlines are generated due to the formation of longitudinal vortices behind the RWPs. The longitudinal vortices bring high-momentum fluid into the wake region. Then the wake region is compressed and the size of this Fig. 8. The configurations for fin-and-tube heat exchangers with RWPs of different attack angle. Fig. 9. Vector-plots and streamlines generated by RWPs in three yez cross-sections for inline-3-rwp case at ¼ 850.

8 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e Fig. 10. Temperature distributions in three yez cross-sections for inline-3-rwp case at ¼ 850 (unit: K). region is reduced. It is interesting to note that with the increase of the angle of attack, the streamlines are bended progressively closer to the center of wake region in the rear of the first tube and the size of the wake region reduces with the increasing attack angle. This phenomenon can be explained by the vortex strength of the longitudinal vortices. With the increase of the angle of attack, the vortex strength is becoming larger. The larger vortex strength will bring higher-momentum fluid into wake region. Then the accelerated flows compress the fluid in the wake region and delay the flow separation on the tube and result in a reduced wake size. It can be seen clearly in Fig. 11(b)e(d) that the size of wake region decreases with the increasing attack angle. We also find that the RWPs have slight effect on the wake region in the rear of the second tube without RWPs. The temperature distributions on the middle cross-section (parallel to the yez plane) at ¼ 850 are presented in Fig. 12. For the baseline configuration (without RWPs), the temperature gradient is very small in the rear of the first and second tubes due to the tube wake. For the enhanced configuration with angle of attack varied from 10 to 30, the temperature gradient increases with the increasing attack angle. The improved temperature gradient is mainly resulted from the enhanced mixing between tube wake and main flow by the swirling longitudinal vortices. Generally, the tube wake region is corresponding to the low heat flux. The augmented temperature gradient in the rear of the first tube will bring a higher heat flux and enhance the heat transfer in the flow channel. As the fluid flows through the region between the RWPs and tubes, the flow is accelerated by the converging geometry. The accelerated flow will impinge on the adjacent downstream tube and result in a high temperature gradient and a local heat transfer enhancement. A larger angle of attack will result in a more converged nozzle-like geometry and finally will result in an intenser flow impingement. From Fig. 12(b)e(d), we can see that the temperature gradient on the front of the second tube is increasing with the increasing angle of attack. We also find that the RWPs almost have not influenced the temperature distribution in the rear of the second tube. Fig. 13(a) presents the variation of the air-side heat transfer coefficient h air versus the ynolds number. It can be seen from Fig. 13(a) that the heat transfer coefficient h air for both baseline case Fig. 11. Local velocity distributions on the middle cross-section for baseline case and enhanced cases at ¼ 850: (a) Baseline case, (b) Deg-10 case, (c) Deg-20 case, (d) Deg-30 case; (unit: m/s). Fig. 12. Local temperature distributions on the middle cross-section for baseline case and enhanced cases at ¼ 850: (a) Baseline case, (b) Deg-10 case, (c) Deg-20 case, (d) Deg-30 case (unit: K).

9 778 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e783 and enhanced cases increases with the increasing ynolds number. With higher value of ynolds number, the thermal boundary layer thickness decreases and the degree of fluid mixing increases. Consequently, a global augmentation in heat transfer is observed with the increase of ynolds number. Compared with the baseline case, the heat transfer coefficient for the Deg-10 case is improved by 28.8e34.5% over the range of the ynolds number considered. The heat transfer coefficient for the Deg-20 case is increased from 54.6% to 61.5% compared to the baseline case. The Deg-30 case improves the heat transfer coefficient h air from 83.3% to 89.7% over the baseline case. These numerical results demonstrate that the winglet vortex generators can significantly improve the heat transfer performance of the fin-and-tube heat exchangers. Fig. 13(b) shows the relation of the pressure drop DP and the number. The heat transfer augmentation is usually accompanied by an additional pressure drop penalty. Compared with the baseline case, the Deg-10 case increase the DP by 21.9e26.9% over the range of the ynolds number considered, the Deg-20 case increase the DP by 58.1e61.9% and from 119.2% to 125.3% for the Deg-30 case. The incremental pressure drop is mainly due to the additionally formed drag induced by the winglet vortex generators. The overall performance of the fin-and-tube heat exchangers with RWPs of different attack angle is evaluated using the criterion of London goodness factor, j/f. The performance of the baseline case a h air / Wm -2 K -1 b ΔP/Pa Baseline Deg-10 Deg-20 Deg Baseline Deg-10 Deg-20 Deg Fig. 13. Variation of the air-side heat transfer coefficient h air and the pressure drop DP versus the number. is compared to the enhanced cases in Fig. 14. The change trend of j/f for baseline case is different from the change trend in Fig. 9(a) of f. [12]. This is mainly caused by the different vortex generator. In our research, rectangular winglet pairs are adopted. In f. [12], triangular winglet pairs are adopted. Different vortex generators result in a different change trend of j and f. For the ynolds number ranges from 575 to 880, the Deg-10 case increases the j/f ratio from 1.4% to 10.3% compared to the baseline case. It implies that the Deg-10 case is superior to the baseline case for heat transfer under the ynolds number considered. It is interesting to note that the ratio for Deg-20 case is smaller than that for the baseline case when the < 800 and larger than that when the > 800. With the increasing ynolds number, the fluid between the RWPs and the tube is accelerated and the wake region size is reduced. This reduction of wake region decreases the form drag of tubes. As the ynolds number increases, the form drag reduction caused by RWPs becomes dominant and the j/f ratio for the Deg-20 case become larger than that for the baseline case. However, the j/f ratio for the Deg-30 case is always smaller than that for the baseline case under the ynolds number range. The j/f ratio of Deg-30 case decreases from 15.5% to 17.0% compared with the baseline case. As the angle of attack increases from 10 to 30, the additional form drag production caused by the RWPs is dominant over the form drag reduction of tubes caused by RWPs. So the Deg-30 case is inferior to the baseline case for the heat transfer enhancement. The overall performances for Deg-10 case and Deg-20 case are better than that for the baseline case, which indicates that the heat transfer enhancement induced by RWPs outweighs the pressure drop penalty introduced by the RWPs. In terms of area goodness, the larger value of j/f means the smaller frontal area for the heat exchanger. Therefore, the Deg-10 case causes a smaller requirement of free flow area than the other cases. However, comparing the h air in Fig. 13, we can find that although the Deg-10 case holds the best overall heat transfer performance, the heat transfer enhancement for Deg-10 case is only about 30% for the ynolds number considered. It doesn t get a lot of advantages compared to the conventional heat transfer techniques like slit or louver fins. For the Deg-20 case, the h air was increased about 60% under the same ynolds number range. Compared with the baseline case, the heat transfer augmentation is considerable and the overall heat transfer performance is better for the Deg-20 case, so we choose the Deg-20 case as the basis for our further research. j/f Baseline Deg-10 Deg-20 Deg Fig. 14. Variation of the overall performance j/f versus the number.

10 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e a Single-RWPs case b 3-RWPs case c 7-RWPs case Fig. 15. The different configurations for fin-and-tube heat exchangers with RWPs Influence of the number of RWPs In order to study the influence of the number of RWPs on the heat transfer characteristics and the flow structure for fin-and-tube heat exchangers with RWPs, a comparative investigation for finand-tube heat exchangers with different RWPs number is performed. The angle of attack a is set as 20. The based on the hydraulic diameter ranges from 575 to 880. Fig. 15 shows different configurations for fin-and-tube heat exchangers with RWPs. The thermal-hydraulic performances of the heat exchangers with different RWPs number are investigated in Figs. 16 and 17. Fig. 16 depicts the velocity distributions on the middle crosssection (parallel to the yez plane) at ¼ 850. Fig. 16 clearly shows the high-velocity region in the downstream of RWPs for all the three enhanced cases. As discussed above, the longitudinal vortices are generated behind the RWPs due to the pressure difference and the friction. The induced spanwise velocity of longitudinal vortices is almost 3 times as much as that of the frontal velocity. This strong swirling flow will transport the fluid in the tube wake region to the main flow regions and vice versa. The improved bulk fluid mixing between the tube wake and main flow by the longitudinal vortices is one of the important heat transfer mechanisms. The high-momentum fluid caused by RWPs will compress the tube wake and reduce the size of it. For the single- RWPs case in Fig. 16(a), the flow is only accelerated behind the first RWPs. However, for the inline-3-rwps case, the flow will be accelerated after each RWPs and Fig. 16(b) indicates that the velocity magnitude downstream of each RWPs becomes progressively larger with the flow direction. The same trend is also Fig. 17. Local temperature distributions on the middle cross-section for heat exchanger with different number of RWPs at ¼ 850 (unit: K). observed in the inline-7-rwps case. In addition to the longitudinal vortices caused by the RWPs, the impingement is another important heat transfer enhancement mechanism. The space between the RWPs and the aft of tube outer surface forms a constricted passage. The nozzle-like passage will accelerate the fluid through it and the accelerated flow will impinge upon the adjacent tube. The high-momentum fluid will compress the wake region behind the tube and cause an adverse pressure gradient upstream of the stagnation point on the tube. As we can see from Fig. 16, comparing the single-rwps case and the 3-RWPs case, the tube wake size about the same behind the first tube. However, the tube wake size for the 3-RWPs case is smaller than that for the single-rwps case behind the third tube and the fifth tube. The reduced tube wake size is attributed to the combined effect of swirling fluid and the impinging fluid caused by the RWPs. Comparing the 3-RWPs case and the 7-RWPs case, we can find that the tube wake size for the 7- RWPs case is smaller than that for the 3-RWPs case behind each tube. The phenomenon is mainly due to the combined effect of the upstream RWPs and the adjacent downstream adjacent RWPs in the 7-RWPs configuration. For the 3-RWPs case, the tube wake region is only modified by its upstream RWPs. However, for the 7- RWPs case, the tube wake region is modified by its upstream and downstream RWPs at the same time. Fig. 17 presents the temperature distributions on the middle cross-section (parallel to the yez plane) at ¼ 850. It can be seen from the figure that the temperature distribution is almost the same for all the three cases before the fluid encounters the second tube. For the single-rwps case, compared with the tube without RWPs, the temperature gradient is larger in the rear of the tube with RWPs. Compared the 3-RWPs case and the single-rwps case, Fig. 16. Local velocity distributions on the middle cross-section for heat exchanger with different number of RWPs at ¼ 850 (unit: m/s).

11 780 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e783 the temperature gradient is larger in the rear of the third and fifth tubes. Compared the 7-RWPs case and the 3-RWPs case, the temperature gradient is larger in the rear of all the seven tubes. The difference of the temperature gradient results from the formation of the longitudinal vortices and the accelerated flow caused by the RWPs as discussed earlier. The temperature of the fluid in the tube wake region is closer to the tube temperature than that in the main flow, and these areas represent regions of low heat transfer coefficient. The presence of RWPs could enhance the mixing from fluid in the tube wake region to the main flow regions and vice versa. Another important enhancement mechanism is the impingement between the RWPs and the tubes. The impingement modifies the near-tube temperature gradients due to the high-momentum flow. The longitudinal vortices make the whole temperature field more even and cause a better thermal mixing and boundary layer modification, which results in an improved heat transfer performance. Fig. 18(a) shows the variation of the air-side heat transfer coefficient h air versus ynolds number. We can see from Fig. 18(a) that the heat transfer coefficient h air for both baseline case and the three enhanced cases increases with the increasing ynolds number. The single-rwps case increases the heat transfer coefficient by 22.7e25.5% compared with the baseline case. The 3-RWPs case augments the heat transfer coefficient from 54.6% to 61.5% a Baseline Single-RWPs 3-RWPs 7-RWPs compared with the baseline case. The 7-RWPs case causes an increase of 87.5e105.1% in the heat transfer coefficient compared with the baseline case. More vortex generators cause more longitudinal vortices and lead to more heat transfer augmentation. However, the heat transfer enhancement is accompanied by the additional pressure losses. The results presented in Fig. 18(b) indicate the pressure loss associated with heat exchangers with different RWPs numbers at different ynolds numbers. In comparison with the baseline case, the single-rwps case increases the pressure loss by 22e24.5%. The 3-RWPs case increases the pressure drop from 58.1% to 62% and the pressure loss of 7-RWPs case is increased by 123e127.6%. The additional pressure loss is mainly due to the form drag of the vortex generators. The overall performance of the fin-and-tube heat exchangers with different RWPs numbers is evaluated using the criterion of the London goodness factor j/f. The heat exchangers with different RWPs numbers are compared with the baseline case in Fig. 19. For the ynolds number ranging from 575 to 880, the overall performance of the 7-RWPs case is inferior to the other cases. The overall performance of the single-rwps case and the 3-RWPs case is larger than that for the baseline case at > 815. The results indicate that the heat transfer enhancement caused by RWPs outweighs the form drag introduced by the RWPs themselves at a relatively high ynolds number. For > 815, the single-rwps case increases the j/f ratio by 1.7e2.7% and the 3-RWPs case improves the j/f ratio by 0.7e2.0%. From the viewpoint of area goodness, the single-rwps case and 3-RWPs case will require smaller frontal areas than the other cases. In fact, the difference of j/f is so small for different cases, it only presents the changing trend of different configurations Influence of the arrangement of RWPs h air / Wm -2 K -1 b ΔP/Pa Baseline Single-RWPs 3-RWPs 7-RWPs Joardar and Jacobi [15] find that the vortex generators can significantly improve the heat transfer performance at a modest pressure loss penalty. However, we also find an interesting result in the study of Joardar and Jacobi [15]. By changing the arrangement of vortex generators array from inline array to staggered array, the performance of heat transfer almost remains in the same level but the pressure loss penalty is reduced by 8%. It implies that the optimization of vortex generators arrangement can result in a better pressure distribution and a reduced pressure loss penalty without reducing the heat transfer enhancement. However, the authors did not explain why this happens. j/f Baseline single-rwps 3-RWPs 7-RWPs Fig. 18. Variation of the air-side heat transfer coefficient h air and the pressure drop DP versus the number Fig. 19. Variation of the overall performance j/f versus the number.

12 Y.-L. He et al. / Applied Thermal Engineering 61 (2013) 770e In order to investigate the influence of different arrangement of rectangular winglets on the thermal-hydraulic performance of finand-tube heat exchangers, a comparative investigation for fin-andtube heat exchanger with inline-rwps array and staggered-rwps array was performed. The angle of attack is set as 15. The ynolds number ranges from 575 to 880. The number of RWPs is 3. Due to the asymmetry of staggered-rwps array, its grid system is also asymmetric. The thermal-hydraulic performance of heat exchanger with staggered-rwps array is compared with the heat exchanger with inline-rwps array in Figs. 20 and 21. Fig. 20 presents the local velocity distributions on the middle cross-section (parallel to the yez plane) at ¼ 850. For the inline-rwps array, the velocity distribution is symmetrical due to the symmetry of the flow passage. The vortex generators pairs are placed in the first, third and fifth tubes. Thus, the tube wake in the rear of the first, third and fifth tube is narrowed due to the longitudinal vortices and the impingement of high-momentum fluid. Each vortex generator pair can create two constricted passages in the aft region of a tube, which will result in two impingements on the adjacent tube downstream. The velocity components of the two impingements are contrary in the transverse direction. Thus, the two impingements will weaken each other in the transverse direction and may bring down their impacts on the tube wake region. For the staggered-rwps array, the placement of vortex generators is asymmetric. Three pairs of vortex generators are placed in the neighbor of the first, second, third, fourth, fifth and sixth tubes. Every vortex generator will independently modify the tube wake region. The vortex generators in the staggered-rwps array can modify six tube wake regions. However, only three tube wake regions are highly influenced by the RWPs in the inline-rwps array. Fig. 21 shows the local temperature distributions on the middle cross-section (parallel to the yez plane) at ¼ 850. For the inline- RWPs array, the local temperature distribution is symmetrical. As discussed above, the temperature of the fluid in the rear of the tube is close to the temperature of the tube due to the recirculating flow. The presence of the RWPs can generate strong swirling flow and impingement which will suppress the recirculation in the rear of the tube and augment the heat transfer in the tube wake region. The low-temperature-gradient areas in the rear of the first, third and fifth tubes are reduced due to the vortex generators. However, the tube wake regions for the tubes without the RWPs extend far downstream, even to the next row of the tube bank, which will jeopardize the heat transfer. For the staggered-rwps array, the temperature distribution is asymmetric due to the staggered arrangement of vortex generators. The low-temperature-gradient regions in the rear of the first, second, third, fourth and fifth tubes are modified, which eventually augment the heat transfer in the tube wake regions. Fig. 20. The local velocity distributions on the middle cross-section for different arrangement of RWPs array at ¼ 850; (unit: m/s). Fig. 21. The local temperature distributions on the middle cross-section for different arrangement of RWPs array at ¼ 850; (unit: K). Fig. 22(a) depicts the variation of the air-side heat transfer coefficient h air versus the ynolds number for the heat exchangers with different arrangement of RWPs. It can be seen from Fig. 22(a) that the heat transfer coefficient for the staggered-rwps array is slightly higher than that for the inline-rwps array. For the ynolds number varying from 575 to 880, the heat transfer coefficient for the staggered-rwps array is increased by 0.5e2.5% in comparison with that of the inline-rwps array. In fact, the difference of heat transfer coefficient is very small for the two cases and it only presents the changing trend of different configurations. a h air / Wm -2 K -1 b ΔP/ Pa Inline-RWPs array Staggered-RWPs array Inline-RWPs array Staggered-RWPs array Fig. 22. Variation of the air-side heat transfer coefficient h air and the pressure drop DP versus the number.