Numerical investigations on fluid flow and heat transfer characteristics of different locations of winglets mounted in fin-tube heat exchangers

Journal Pre-proofs Numerical investigations on fluid flow and heat transfer characteristics of dif‐ ferent locations of winglets mounted in fin-tube heat exchangers Hemant Naik, Shaligram Tiwari PII: DOI: Reference:

S2451-9049(20)30315-2 https://doi.org/10.1016/j.tsep.2020.100795 TSEP 100795

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Thermal Science and Engineering Progress

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30 August 2020 22 November 2020 23 November 2020

Please cite this article as: H. Naik, S. Tiwari, Numerical investigations on fluid flow and heat transfer characteristics of different locations of winglets mounted in fin-tube heat exchangers, Thermal Science and Engineering Progress (2020), doi: https://doi.org/10.1016/j.tsep.2020.100795

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Numerical investigations on fluid flow and heat transfer characteristics of different locations of winglets mounted in fin-tube heat exchangers Hemant Naik*, Shaligram Tiwari Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, 600036, India Email*: [email protected]

Abstract A three-dimensional numerical investigation of airflow through heated fin-tube heat exchangers with winglet type vortex generators is performed for both inline and staggered arrangements of circular tubes. Heat transfer augmentation of such heat exchangers strongly depends on the mounting locations of the winglet pair corresponding to tubes. The present numerical study shows the effect of location of rectangular winglet pairs (RWPs) on thermal performance for both the arrangements. Among numerous considered RWP locations, all promising locations of RWPs are identified which give higher heat transfer enhancement with less flow loss. The effects of RWP locations on flow features and heat transfer are demonstrated by streamlines and Nusselt number contours respectively. Estimation of enhancement in heat transfer is achieved by Colburn’s factor and flow loss is quantified from the measured pressure drop. The thermohydraulic effect is analyzed by using the thermal performance factor. Locations of RWPs, which are capable of producing higher thermal performance, have been optimized and found that upstream RWP location, i.e. X = 2.0, Y =  1.25 delivers higher heat transfer enhancement with maximum thermal performance factor value for both arrangements. Evaluation of secondary flow induced by RWPs is achieved by secondary flow intensity and is correlated with heat transfer.

Keywords: Heat transfer enhancement, fin-tube heat exchangers, rectangular winglet pair, promising location, secondary flow intensity, thermal performance factor

1

1. Introduction Fin-tube heat exchangers are frequently employed in several engineering grounds such as refrigeration and air conditioning, power plants, automotive and chemical industries. Such heat exchangers consist of tube bundles positioned normal to parallel fins. In general, gas flows in between fins and liquid flows through the tubes. Extended surfaces of fins and outer surfaces of tubes augment heat transfer by reducing the thermal resistance of the gas side. Flow structure consists of horseshoe vortices in upstream near the fin-tube junction and recirculation region in the wake of tubes that determine heat transfer and flow losses [1]. Horseshoe vortices augment the heat transfer while the recirculation region causes lower heat transfer [2]. Different geometrical parameters such as tube shapes (circular, flat, oval etc.) [3-4], fin shape (flat, wavy etc.) [5-7], tube arrangements (inline and staggered) [8-10] and spacing between tubes and fins [11-12] have a strong influence on flow structure. For example, in the case of inline arrangement, the generation of horseshoe vortices does not take place in front of tubes other than the first tube from the inlet while these appear in front of each tube for staggered case. Hence, flow structure influenced by horseshoe vortices is more for the arrangement of staggered tubes [13]. Heat transmission can be enhanced by reducing the thermal resistance of gas and it can be made possible by increasing the heat transfer surface area. Normally, due to size constraints, the increasing area may not be a preferred approach. Hence, another approach for the reduction of gas side thermal resistance is to enhance the gas side heat transfer coefficient, which can be accomplished by producing secondary flow [14]. Generation of secondary flow can be achieved by mounting vortex generators (VGs) on fin surfaces. It has been confirmed by Biswas et al. [15] that VGs mounted on fin surfaces are advantageous for heat transfer enhancement. Longitudinal vortices produced by VGs augment heat transfer by improving fluid mixing in both regions i.e., near and away from the fin surfaces [16]. Systematic numerical and experimental studies on the effect of four commonly known VGs, i.e., delta wing, rectangular wing, delta winglet pair (DWP) and rectangular winglet pair (RWP), on flow and heat transfer characteristics are performed by Biswas et al. [15], Tiggelbeck et al. [17] and Fiebig et al. [18]. Their observations reveal that winglet type VGs execute improved thermal performance than wing type VGs. Tian et al. [19] reported by their heat transfer investigations that RWP performs better than DWP. They also reported that in channels mounted with RWP, common flow down (CFD) configuration demonstrates superior overall performance than common flow up 2

(CFU) configuration. For CFD configured surface mounted RWPs, numerical investigations of Naik and Tiwari [20] reveal that heat transfer enhancement depends upon various geometrical parameters of RWP. They reported that heat transfer enhances with increment in length of RWP, angle of attack (  ) and Reynolds number (Re). Arrangement of tubes and mounting configurations of winglet pair plays a significant role in the improvement of heat transfer in fin-tube heat exchangers. Numerous studies based on tube arrangements and VG configurations are performed by researchers. Effect of downstream located winglet pairs for both the arrangements has been experimentally investigated by Fiebig et al. [21]. They reported that in the presence of VGs, both reductions in pressure loss and enhancement in heat transfer are higher for inline arrangement than staggered arrangement. Experimental investigations of CFU and CFD configured VGs on thermal performance by Wu et al. [22] report that for CFU and CFD configurations augmentation in heat transfer is around 16.5% and 28.2% respectively while the reduction in pressure loss is about 10% for CFU and it remains almost unchanged for CFD configuration. Experimental investigations for inline and staggered arrangements with winglets placed adjacent to tubes by Torii et al. [23] report that heat transfer gets augmented by 10-21% with 8-15% pressure loss for inline tube bundles while for staggered tube bundles heat transfer increases by 10-30% with 34-55% reduction in pressure loss. Experimental investigations of Kwak et al. [24] for both the arrangements in the presence of winglet pairs report that enhancement in heat transfer is higher for inline tube arrangement than staggered tube arrangement. Numerical comparison of the influence of  and Re on heat transfer is carried out by Sinha et al. [25] for the adjacent location of RWP in both the arrangements. For inline arrangement, they found that heat transfer enhances with increasing  at all Re, whereas the value of  corresponding to maximum augmentation in heat transfer is different with change in Re for staggered arrangement. Thermal performance of a VG mounted heat exchanger majorly relies on numerous geometric parameters of VGs such as  , length, height and mounting location corresponding to the center of tube. Qian et al. [26] investigated for different  , length and height of rectangular winglets for staggered tube arrangement and observed higher thermal performance for higher length and lower height combination of VG with  = 45o. Numerical investigations for three different locations of 3

VG (such as VG before the tube, beside the tube and behind the tube) with three different angles of attack in staggered tube arrangement have been performed by Wang et al. [27]. By heat transfer and flow resistance consideration they suggested that the VGs located before and behind the tubes are better for heat exchanger design. Zeeshan et al. [28-29] reported that for RWPs located behind the inline tubes having a lower span angle is better for both heat transfer enhancement and pressure loss penalty. Experimental and numerical investigations of Leu et al. [30] for an effective  in case of CFD configured RWPs mounted downstream of inline tubes reveal that augmentation in heat transfer is maximum for  = 45o. Naik and Tiwari [31-32] examined the effect of different mounting locations such as upstream, adjacent and downstream located CFD configured RWPs for single tube [31] and three inline tubes [32]. Their numerical investigations for different RWP locations corresponding to tube center report that RWPs located in upstream and away from the tube has higher thermal performance than other locations. Experimental investigations by Pesteei et al. [33] for five different winglet locations having CFD configuration report that downstream located winglets with  = 45o show better thermal performance than other locations. Jang et al. [34] numerically investigated the influence of  and transverse locations of CFD configured winglet pairs mounted downstream of tubes for both arrangements on thermal performance. As the location of winglets moved away from tubes and  increases, they observed increment in heat transfer and pressure loss. They also reported that in the presence of winglet pairs, inline arrangement performs better than staggered arrangement. Sarangi and Mishra [35] numerically investigated the influence of number of RWPs in inline arrangement and observed that increase in number of RWPs gives an increment in both heat transfer and pressure loss. Effects of  and height of winglets located behind the staggered tubes are investigated by Hu et al. [36]. They reported that heat transfer enhances with an increase in  and height of winglets. Arora et al. [37] investigated the influence of locations of CFU configured DWPs behind the inline tubes on thermal performance. They evaluated Colburn’s factor for each location of winglet pairs and reported various promising and counter-productive locations. Available studies in the literature suggest that there is much scope exists in fin-tube heat exchangers to find the most promising position of VGs for improvement in heat transfer. Present study focuses on the influence of different possible RWP locations concerning to center of each 4

tube of the fin-tube heat exchanger on flow and heat transfer characteristics. Identification of the best promising location has been carried out for both inline and staggered tube arrangements by considering several performance parameters, such as Colburn’s factor, friction factor and thermal performance factor. The relationship between heat transfer and secondary flow is also reported. 2. Problem Formulation 2.1. Computational domain and problem statement The detailed dimensions of the computational domain of inline and staggered arrangement of the fin-tube heat exchanger are depicted in Fig. 1(a). For the considered computational domain having three inline and staggered arranged circular tubes with the diameter (D) as characteristic length scale, the length, width and height of channel formed by fins is taken as L = 24D, W = 4D and H = 0.6D respectively. Figure 1(b) depicts the positional views of CFD configured rectangular winglet pairs (RWPs) concerning to center of each tube. The selected dimensions of RWPs such as length, height and thickness are 1.0D, 0.3D and 0.02D respectively. The positions of RWPs concerning to each tube center are measured with the help of numerous streamwise ( X ) and spanwise ( Y ) winglet locations. For each tube, the location of X has been varied from -2.0 to 2.0 with step size equal to 0.5 whereas Y is varied from  0.5 to  1.5 with step size equal to 0.25. Three different terminologies as illustrated in Fig. 1(b) are made to distinguish the locations of RWPs, which depend on the value of X . If the value of X is negative, the location of RWPs relative to the tube center is said to be upstream located RWPs, for positive values of X , it refers to downstream located RWPs and for X = 0, it refers to RWPs located adjacent to the tube. Accordingly, positive and negative values of Y depict that the location of each winglet from the pair is located on either side of the tube. Figure 1(c) shows the array of physically possible and impossible RWP locations concerning to each tube for both arrangements having a fixed angle of attack (  ) equal to 45o. The flow Reynolds number (Re) is varied from 2000 to 4000.

5

(a)

(b)

(c) Fig. 1 (a) Schematic of top and side view of the computational domain for inline and staggered tube arrangement in presence of RWPs; (b) Positional view of RWP; (c) Physically possible and impossible winglet locations concerning to center of each tube in both arrangements 6

2.2. Governing equations and boundary conditions 2.2.1. Governing equations The assumptions made for airflow are incompressible, steady, turbulent and three-dimensional with constant physical properties. The fundamental governing equations used in present computations are mass, momentum and energy conservation equations and non-dimensional form of these are illustrated in Eqs. (1) to (3) respectively in the Cartesian coordinate system.

U j X j

0

(1)

Uj

 U U j U i  ( P  2k 3) 1     (1  t )  i   X j X i X j X i Re X j   

Uj

 1      (1   t )  X j Re Pr X j  X j 

   

(2)

(3)

The space coordinates are non-dimensionalized by tube diameter (D) as a characteristic length scale. Velocity terms are non-dimensionalized by free stream velocity ( U  ) as the characteristic velocity. Temperature and pressure terms are non-dimensionalized by   (T  T ) ( Tw  T ) and P  p ( U 2 ) respectively are used, where Tw denotes the constant surface temperature, while T

is free stream temperature of fluid. For the simulations of airflow in the present computational domain, the physical properties of air such as density (  ), specific heat capacity (cp), thermal conductivity (  ), dynamic viscosity (  ) and Prandtl number (Pr) are calculated at the free stream temperature of fluid i.e., T = 300 K and the values are shown in Table 1. Table 1 Properties of air used for simulations Thermal conductivity W/m-K

Dynamic viscosity kg/m-s

Prandtl number

kg/m3

Specific heat capacity J/kg-K

1.1765

1006.3

0.0261

1.8538  105

0.7143

Property

Density

Unit Air

Since the flow in the present study is turbulent, the governing equations mentioned above are supplemented by using a turbulence closure model for the calculation of turbulent flows. Previous studies on the comparison of different turbulence closure models for heat exchanger type problems 7

by Naik and Tiwari. [32, 38-39], Qian et al. [26], Wang et al. [27] and Jain et al. [40] show that the realizable k   model gives better performance than others. The governing equations for the realizable k   model are expressed in the form of conservation equations for turbulent kinetic energy (k) and its dissipation rate (  ). Uj

k 1   X j Re X j

  t    k

 k    Gk     X  j 

(4)

  t    2 (5)    C S C   1  2 k       X j  Information associated with the details of definitions and values of coefficients and constants Uj

 1   X j Re X j

presented in Eqs. (4) and (5) are discussed in Shih et al. [41]. 2.2.2 Boundary conditions Boundary conditions are prescribed on different surfaces of the domain. Uniform velocity and temperature (U = 0, V = 0, W = 0,  = 0) boundary conditions are set at the channel inlet. The inlet boundary conditions prescribed for k and  are k 

k3 2 3 2 I and   C3 4 respectively, where 0.07D 2

the turbulent intensity (I) at the inlet of the computational domain is defined with the help of correlation I  0.16 Re 1 8 . On the other hand, pressure outlet (P = 0) boundary condition is employed at channel outlet with zero gradient condition of temperature. In addition, k and  are prescribed as boundary conditions for the channel outlet. No-slip, impermeable and isothermal boundary conditions (U = 0, V = 0, W = 0,   1 , k = 0,  = 0) are considered at surfaces of fins, tubes and RWPs. Periodic boundary conditions are prescribed at the side surfaces of the computational domain in accordance with Patankar et al. [42]. The side surfaces have been chosen as periodic structures having a constant translation width of W. The periodic boundary conditions at the side surfaces can be expressed as  (X, Y, Z)   (X, Y+W, Z) =  (X, Y+2W, Z) = .... , where,  is a scalar transport function representing U, V, W,  , k or  . 2.3. Parameter definitions Heat transfer and flow features of present study are understood by following relevant parameters Reynolds number (Re) is estimated as 8

Re  U  D 

(6)

Friction factor (f) in the channel is evaluated as f 

D p  2 1 2 U  L

(7)

Colburn’s factor (j) is considered to describe the thermal behavior and determined as

j

Nu Re Pr1 3

(8)

where, overall Nusselt number (Nu) is calculated as Nu 

hD

(9)



Thermal performance factor (JF) is used for the evaluation of thermohydraulic performance and expressed as [43]

JF 

SCF SFF1 3

(10)

Here SCF is scaled Colburn’s factor and SFF is scaled friction factor. The influence of employing RWPs on heat transfer performance is characterized by SCF which is the ratio of Colburn’s factor of the system in the presence and absence of RWPs. Similarly, SFF is the ratio of friction factor in the presence and absence of RWPs. Secondary flow intensity (Se) based on absolute vorticity flux is calculated to estimate the heat transfer enhancement and the relation for volume-averaged Se is denoted as [44, 45]

  n d  D   Se     d   2

    

(11)

The effect of employing RWP on secondary flow generation in fin-tube heat exchanger is characterized by scaled secondary flow intensity (SSFI) and is estimated as the ratio of Se in the presence and absence of RWPs. 3. Numerical Methodology 3.1. Grid mesh and grid sensitivity test 3.1.1. Grid mesh 9

Grid mesh for the present computational domain is created by ANSYS ICEM-CFD 17.2. Figures 2(a) and (b) depict the schematic representation of grid mesh near tubes and RWPs for inline and staggered arrangements respectively. Before starting the computations for different geometries, it is important to have strategies for making good quality mesh that should be independent of grid sensitivity. Grid mesh strategy around tubes and winglets for three RWP locations such as upstream, adjacent and downstream of tubes as illustrated in Figs. 2(c), (d) and (e) respectively require more attention. A structured hexahedral grid with non-uniform distribution is created for the whole domain. To resolve the problem of large gradients near tubes and RWPs, very refine Otype grids with non-uniform distribution are created.

(a)

(c)

(f)

(b)

(d)

(e)

(g) 10

Fig. 2 Grid mesh for (a) inline (b) staggered arrangement; grid mesh strategy near tubes and winglets for (c) upstream (d) adjacent (e) downstream located RWPs; grid sensitivity test for (f) inline (g) staggered arrangement 3.1.2. Grid sensitivity test A meticulous grid sensitivity test is performed by considering a systematic grid refinement method to obtain a satisfactory solution with better accurateness of the computation. This method is applied in the present study for both the arrangements by considering three RWP locations i.e., X = -1.0, 0.0 and 1.0 with Y =  1.0 and five different grid sizes. Figures 2(f) and (g) illustrate the grid sensitivity for both inline and staggered arrangements respectively in terms of Nu and f variation with grid nodes. Ranges of grid numbers considered for different RWP locations in inline as well as staggered arrangement lie between 1 million to 7.5 million. The values of considered parameters do not vary appreciably beyond the grid numbers approximately equal to 5.69 and 5.71 million respectively for inline and staggered cases. Change in computed values of considered parameters for the grid size higher than the mentioned values are reported in Table 2 for both the arrangements and all three RWP locations. Accordingly, all computations are executed for grid sizes approximately equivalent to 5.69 and 5.71 million respectively for inline and staggered cases. Table 2 Change in the value of Nu and f with grid nodes RWP location

Inline Change in grid

Staggered

%age difference

Change in grid

%age difference

nodes (million)

Nu

f

nodes (million)

Nu

f

X = -1.0

5.691 to 7.453

0.15%

0.32%

5.705 to 7.468

0.17%

0.38%

X = 0.0

5.671 to 7.443

0.17%

0.41%

5.681 to 7.460

0.24%

0.42%

X = 1.0

5.692 to 7.456

0.15%

0.26%

5.710 to 7.465

0.12%

0.26%

3.2. Numerical technique and validation of computation 3.2.1. Numerical technique For the high complexity of the flow in the present complex domain, three-dimensional computations are performed in ANSYS Fluent 17.2. The turbulence closure model used for present computations is a realizable k   two-equation eddy-viscosity turbulence closure model with 11

enhanced wall treatment. Wall y-plus approximately equal to 1 has been considered to capture the wall effect. A robust algorithm known as the SIMPLE algorithm is considered to resolve pressurevelocity coupling. Second-order upwind discretization technique is employed for convective terms whereas for diffusive terms, second-order central difference discretization technique is used. The computational convergence is ensured by setting absolute convergence criteria as 10-6 for all residuals of governing equations. 3.2.2. Validation of computation For confirmation of the suitability of the numerical scheme, computations have been performed to obtain similar experimental results as described in Fiebig et al. [21]. Computations are executed for similar geometrical configurations and operating situations as illustrated in Fiebig et al. [21], which correspond to three inline and staggered circular tubes built-in a rectangular channel. For validation of present inline and staggered tube arrangement cases, parameters such as Nu, f and Re are calculated based on channel height. Variations of overall Nu and f with increment in Re are compared with Fiebig et al. [21] and are depicted in Figs. 3(a) and (b) respectively. There is close agreement between present computed and reported experimental [21] results with a maximum deviation of 3.19% and 5.46% for Nu and f respectively in case of inline tube arrangements. On the other hand, the maximum percentage differences of Nu and f are 4.01% and 4.86% respectively for staggered tube arrangement.

(a)

(b) 12

Fig. 3 Comparing variation of (a) Nu (b) f from present computations against experimental results [21] with change in Re 4. Results and Discussion Research on vortex generators mounting on fin surfaces shows that VGs have the capacity to intensify the heat transfer rate. The location of VGs on the fin-tube heat exchanger plays a significant role in heat transfer augmentation. The task for the present work is to identify the promising locations of CFD configured RWPs in both inline and staggered arrangements which gives higher thermal performance, by analyzing the effect of RWP locations on flow and heat transfer characteristics. For  = 45o, as illustrated in Fig. 1(c), a total of forty-one RWP locations concerning to center of each tube in the present domain is physically possible for both the arrangements of tubes. Initially, the influence of angle of attack for adjacent located RWPs ( X = 0.0, Y =  1.0) on the thermal performance of fin-tube heat exchangers has been carried out for both inline and staggered fin-tube heat exchangers by varying  from 15o to 60o and Re from 2000 to 4000. It has been observed from Figs. 4 (a) and (b) that the heat transfer enhancement is maximum at  = 45o for both inline and staggered arrangements of tubes. Moreover, it has been found from the literature [26, 30, 33] that an angle of attack equal to 45o in fin-tube heat exchangers delivers maximum heat transfer enhancement. Consequently, all the further study of identifying most effective location of RWPs has been carried out for a fixed value of  = 45o.

(a)

(b) 13

Fig. 4 Variation of Nu with change in  and Re for adjacent RWP locations in (a) inline [32] (b) staggered tube arrangements 4.1. Flow structure and heat transfer analysis Computations have been carried out to analyze the flow field obtained from different RWP locations corresponding to the tube center in inline and staggered arrangement. When the flow approaches the RWPs and tubes, the generation of different types of vortices is observed. In the upstream and near the junction of fin-tubes and fin-RWPs, the formation of horseshoe vortex takes place. Apart from horseshoe vortex, longitudinal and transverse vortices are generated from different edges of RWPs. All vortices can be differentiable by their axis of rotation and region of generation [16, 20]. Horseshoe vortices roll up around the base of tubes and RWPs and move away from the wake of tube and RWPs in downstream. Longitudinal vortices rotate about an axis parallel to flow direction, while the rotation axis is perpendicular to flow direction for transverse vortices. Horseshoe and longitudinal vortices are found to improve the mixing of fluids by swirling the primary flow in downstream direction [32, 45]. However, transverse vortices show poor transport of fluid, thereby fluid mixing decreases. Another region which shows poor fluid transport, commonly known as the recirculation region and is observed in the wake of tubes. The velocity of fluid is found to be very small in the recirculation region. To achieve higher heat transfer enhancement from heated surfaces of fins, tubes and RWPs, the region of better fluid mixing should be bigger in size and the recirculation region which shows poor transport of fluid should be smaller in size. Location of RWPs plays a vital role in the improvement of fluid mixing and reduction in the recirculation region. Flow patterns for different RWP locations are analyzed with the help of three-dimensional streamlines. Figures 5 and 6 collectively represent the threedimensional streamlines colored with velocity magnitude for different locations of RWPs in inline and staggered tube arrangements respectively. It has been observed from Figs. 5 and 6 that the region behind the tubes and RWPs such that the wake region has lower velocity magnitude due to the presence of recirculation regions and transverse vortices. The recirculation region and transverse vortices show lower velocity because in this region fluids get trapped and the same fluids rotate in that reason for a long duration. Hence, transport of fluids becomes very poor in this region, by which mixing of fluids gets affected and enhancement in heat transfer decreases. The recirculation region and transverse vortices present in the wake region of the tubes and RWPs get 14

influenced by the location of winglets and the arrangement of tubes. The longitudinal and horseshoe vortices generated from the first tube-RWP combination reduce the influences of the recirculation region and transverse vortices generated from the upcoming tube-RWP combinations. As a result, enhancement in heat transfer is more in these regions. Figures 5(a), (b) and (c) respectively illustrate flow behavior of RWPs in inline arrangement located at upstream ( X = -1.0), adjacent ( X = 0.0) and downstream ( X = 1.0) of each tube at Y =  1.0.

Observations on the three-dimensional streamlines colored with velocity magnitude illustrate the effect of all kinds of vortices on flow behavior from the considered RWP locations. The influences of longitudinal and horseshoe vortices generated due to the first tube-RWP combination on the recirculation region and transverse vortices generated due to the upcoming tube-RWP combination can be seen for all the considered cases of inline tube arrangement. The size of the recirculation region i.e., region of low-velocity magnitude is found to be bigger for adjacent RWP locations, while it is smaller for the downstream RWP locations. The regions of high-velocity magnitude i.e., the regions influenced by the horseshoe and longitudinal vortices are larger in the case of adjacent located RWPs followed by upstream and downstream located RWPs. Overall, it has been observed that the horseshoe and longitudinal vortices cover a bigger area for upstream located RWPs followed by adjacent and downstream located RWPs. Hence it can be said that upstream RWP locations produce better mixing and transportation of fluids. Similarly, for staggered tube arrangement, Figs. 6(a), (b) and (c) respectively demonstrate the flow behavior of different RWP locations as considered for inline arrangement. Observations of streamlines colored with velocity magnitude reveal that the size of low as well as high-velocity region is larger for adjacent located RWPs, while it is smaller for downstream located RWPs. In the case of staggered tube arrangement, the influences of longitudinal and horseshoe vortices generated due to the first tubeRWP combination on the recirculation region and transverse vortices generated due to the upcoming tube-RWP combination are found to be less as compared to the case of inline tube arrangement. The downstream located RWPs deliver higher influence of longitudinal and horseshoe vortices generated from the first tube-RWP combination on the recirculation region generated due to the upcoming tube as compared to other RWP locations. Furthermore, horseshoe and longitudinal vortices cover bigger area for upstream located RWPs i.e., the overall velocity magnitude is higher for that location. In comparison of inline and staggered tube arrangements, 15

larger region of low-velocity magnitude is observed for staggered tube arrangement, whereas size of high-velocity magnitude region is larger for inline arrangement.

(a)

(b)

(c) Fig. 5 Three-dimensional streamlines colored with velocity magnitude for inline tube arrangement at (a) upstream (b) adjacent (c) downstream RWP location

16

(a)

(b)

(c) Fig. 6 Three-dimensional streamlines colored with velocity magnitude for staggered tube arrangement at (a) upstream (b) adjacent (c) downstream RWP location Influence of RWP locations on heat transfer behavior is demonstrated by comparing Nusselt number contours at different fin surfaces of considered cases. Figures 7(a), (b), (c) and (d) respectively present contours of Nu at bottom (upper) and top (lower) fin surfaces of inline tube arrangement for cases such as without RWPs, upstream located RWPs at X = -1.0, Y =  1.0, adjacent located RWPs at X = 0.0, Y =  1.0 and downstream located RWPs at X = 1.0, Y =  1.0. Zones having high Nu in the contours depict the increment in heat transfer, while low Nu zones describe the reduction in heat transfer. Convective heat transfer enhances when the flow gets 17

destabilized i.e., the development of both thermal and hydrodynamic boundary layers get disturbed, by which improvement in mixing and transportation of fluids occurs. As discussed earlier that transport and mixing of fluids are better for horseshoe and longitudinal vortices, while these are poor in case of recirculation region and transverse vortices. Hence, it can be said that the observed high Nu zones near tubes and RWPs in Nu contours are because of horseshoe and longitudinal vortices, whereas low Nu zones give the impression of transverse vortices and recirculation region. For tubes without RWPs, an increment in heat transfer i.e., the zone of high Nu value is observed in front of the first tube for both the fin surfaces. The wake regions corresponding to all tubes which are associated with recirculation regions show a zone of low Nu value for both the fin surfaces, thereby less convective heat transfer is produced in these regions. Presence of RWPs provides intensification in the size of high Nu zone and decrement in the size of low Nu zone, as compared to their absence. In all cases, the size of low Nu zones is found to grow for both the fin surfaces, as travels from the first tube towards the next ones. Presence of RWPs delivers decrement in size of high Nu zone concerning to a tube and RWP for bottom fin surface, however, for top fin surface, high Nu zone is found to be larger corresponding to the second tube than others, due to influence of longitudinal vortices generated from first RWP. For adjacent RWP locations, sizes of both high and low Nu zones concerning to first tube and RWP combination at bottom fin surfaces are found to be larger than those for other cases. For top fin surfaces, high and low Nu zones are larger in the case of adjacent located RWPs and corresponding to the second tube. In the case of bottom fin surface, as travels from the first tube towards the next, the size of high Nu zone reduces drastically for adjacent and downstream located RWPs. However, for upstream RWP locations, gradual decrement in the size of high Nu zone is observed. Overall augmentation in heat transfer from fin surfaces can be estimated by calculation surface averaged Nu. The surface-averaged Nu of both bottom and top fin surfaces has been calculated for all the cases (upstream, adjacent and downstream located RWPs) and variation of Nu with Re is depicted in Fig. 7(e). With an increase in Re, the increasing trend of Nu has been observed for all the fin surfaces. In the comparison of bottom and top fins, bottom fin surfaces always show the higher notch in terms of heat transfer. Overall for all value of Re, bottom and top fin surfaces of upstream located RWPs respectively provide the higher and lower Nu value. Further, the heat transfer behavior has been examined from the different tube surfaces. Figure 8 shows the comparison of 18

Nu contours at tube surfaces of inline arrangement for cases such as without RWPs, upstream, adjacent and downstream located RWPs. The value of surface averaged Nu for each tube is also shown in Fig. 8. For all the tubes, front and side surfaces which come in contact with horseshoe and longitudinal vortices, are found to have high Nu zone as compared to rear surfaces. For all the considered cases, front and side surfaces of the first tubes show high Nu zones. Same is true for the second and third tubes of upstream and downstream located RWPs. In case of without RWPs and adjacent located RWPs, only side surfaces of second and third tubes show high Nu zones. As moves from the first tube towards the next ones, the size of high Nu zone reduces and this can be confirmed from the value of surface averaged Nu. For all cases, the value of surface averaged Nu decreases from first tubes to second followed by the third tube. From the value of surface averaged Nu of considered cases, downstream located RWPs are found to have higher overall heat transfer from tube surfaces.

(a)

(b)

(c)

(d)

19

(e) Fig. 7 Contours of Nu at bottom (upper) and top (lower) fin surfaces of inline tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs; (e) comparison of surface-averaged Nu variation of top and bottom fin surfaces of inline tube arrangement with Re for different RWP locations

(a)

(b)

(c)

(d)

Fig. 8 Contours of Nu at tube surfaces of inline tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs

20

Heat transfer characteristics on fin surfaces i.e. bottom (upper) and top (lower) fin surfaces of staggered tube arrangement are demonstrated in Fig. 9. Figures 9(a), (b), (c) and (d) depict contours of Nu at fin surfaces for cases such as without RWPs, upstream located RWPs at X = -1.0, Y =  1.0, adjacent located RWPs at X = 0.0, Y =  1.0 and downstream located RWPs at X = 1.0, Y =  1.0 respectively. For the case of without RWPs, the size of both high and low Nu zones concerning to first and second tubes is almost same for both the fin surfaces. The size of high Nu zone corresponding to the third tube is smaller, whereas the size of low Nu zone is larger as compared to other tubes. In presence of RWPs, the size of high Nu zones are larger for bottom fin surfaces as compared to top fin surfaces. As moves from upstream tubes towards downstream one, the size of high Nu zone corresponding to tube reduces for all fin surfaces, except for top fin surfaces of adjacent and downstream located RWPs. Larger size of high Nu zone corresponding to second tube is observed for top fin surfaces of adjacent and downstream located RWPs as compared to other tubes. In the comparison of bottom fin surfaces, adjacent located RWPs show larger size of high Nu zone followed by upstream and then downstream located RWPs. Figure 9(e) presents the variation of surface-averaged Nu of both bottom and top fin surfaces with the change in Re for upstream, adjacent and downstream RWP locations. For all considered cases, increment in the value of surface-averaged Nu is found with increasing Re. Similar to the inline tube arrangement case, bottom fin surfaces always show the higher surface averaged Nu than top fin surfaces for all Re. Overall, for all Re, bottom fin surfaces of upstream located RWPs and lower for top fin surfaces of downstream located RWPs display higher Nu. Contours of Nu at different tube surfaces of staggered arrangement are depicted in Figs. 10(a), (b), (c) and (d) respectively for the cases of without RWPs, upstream located RWPs at X = -1.0, Y =  1.0, adjacent located RWPs at X = 0.0, Y =  1.0 and downstream located RWPs at X = 1.0, Y =  1.0. For all the tubes, front and side surfaces are found to have high Nu zone as compared to rear surfaces. The size of high Nu zones can be estimated by the value of surface averaged Nu given for each tube. For all the considered cases, the value of surface averaged Nu is higher for the second tube followed by first and then third, except the case of upstream located RWPs. First tube gives the higher value of surface averaged Nu for upstream located RWPs. In the comparison of inline and staggered tube arrangement, surface averaged Nu is maximum for the first tube of adjacent located RWPs in inline case. Similar to inline arrangement, the overall heat transfer from tube surfaces is 21

also higher for downstream located RWPs as compared to other considered cases in staggered arrangement.

(a)

(b)

(c)

(d)

(e) Fig. 9 Contours of Nu at bottom (upper) and top (lower) fin surfaces of staggered tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs; (e) comparison of surface-averaged Nu variation of top and bottom fin surfaces of staggered tube arrangement with Re for different RWP locations 22

(a)

(b)

(c)

(d)

Fig. 10 Contours of Nu at tube surfaces of staggered tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs 4.2 Secondary flow analysis Secondary flows generated by RWPs and tubes play a vital role in heat transfer augmentation. Quantification of the intensity of secondary flow is done with the use of a non-dimensional parameter acknowledged as secondary flow intensity (Se). The ability of generating secondary flow from different locations of RWPs has been investigated by the contours of Se. Figures 11(a), (b) and (c) present the comparison of Se contours on various cross-stream locations in inline arrangement for upstream ( X = -1.0), adjacent ( X = 0.0) and downstream ( X = 1.0) located RWPs respectively at Y =  1.0. Observations of the flow structures from different Se contours on various cross-stream locations illustrate the existence of different kinds of vortex structures as reported by Biswas et al. [15]. By considering vorticity contours in a cross-stream plane located behind the winglet, they examined flow structures of air stream over the winglet and observed that three types of vortex structures are formed due to the winglet i.e. main vortex (longitudinal vortex), corner vortex (horseshoe vortex) and induced vortex. Similar flow structures from RWPs have 23

also been observed in the present study which can be clearly seen in the magnified view of a crossstream plane as depicted in Fig. 11(a). For all considered cases, the generation of main vortices begins from the edges of the RWPs, while the generation of corner vortices starts in front of RWPs as well as tubes. An induced vortex generates as a result of the influence of rotation of main and corner vortices which appears in between them. In a cross-stream plane, for the case of the left winglet of an RWP, it has been observed that the main and corner vortices rotate in a clockwise direction and the direction of rotation for induced vortices is in the anti-clockwise direction. The presence of induced vortices does not augment the heat transfer from heated surfaces of the fintube heat exchanger. These are found to have weak strength than the main vortices. Hence, in downstream with the flow direction, these weaker induced vortices merge with the stronger main vortices [32]. The strength of secondary flows is measured with the help of Se values observed in the Se contours at different cross-stream locations i.e., the zone of high Se value represents the higher strength of secondary flows. Variations in the strength of Se are studied in various crossstream located planes and are compared for different considered cases. As moves from one crossstream location to another in downstream, the strength of Se generated from the winglets is found to increase up to a certain location and then decrease in the strength of Se begins. In the comparison of upstream, adjacent and downstream located RWPs, the upstream located RWPs are found to have a longer range of high Se in the domain. Similar to the inline arrangement, Figs. 12(a), (b) and (c) collectively present the comparison of Se contours on various cross-stream planes in staggered arrangement for different locations of RWPs i.e., upstream ( X = -1.0), adjacent ( X = 0.0) and downstream ( X = 1.0) located RWPs at Y =  1.0 respectively. Investigations on the main, corner and induced vortices for all considered cases of staggered tube arrangement have been carried. It has been observed that the main vortices cover a larger area in the domain as compared to others. In the flow direction, the weaker induced and corner vortices are found to merge with the strong main vortices. Overall upstream located RWPs show larger region of higher Se followed by downstream and then adjacent located RWPs.

24

(a)

(b)

(c)

Fig. 11 Contours of Se at different cross-stream locations for inline arrangement (a) upstream (b) adjacent (c) downstream located RWPs

25

(a)

(b)

(c)

Fig. 12 Contours of Se at different cross-stream locations for staggered arrangement (a) upstream (b) adjacent (c) downstream located RWPs Figures 13(a) and (b) show the variations of SSFI for different RWP locations in inline and staggered tube arrangements respectively. In case of inline tube arrangement, the spanwise shift of RWPs in the direction such that away from tubes delivers rise in SSFI for all X and reaches 26

its maxima at Y =  1.25, further shift shows decrement in SSFI. For a streamwise shift of RWPs in the direction such that away from tubes in the upstream and downstream region, the value of SSFI is found to increase at fixed Y =  0.5,  0.75 and  1.0, while at fixed Y =  1.25 and  1.5, gradual decrement of SSFI is observed with shifting of RWPs from X = 0.0 to -1.0 and from X = 0.0 to 1.0. Again shifting of RWPs from X = -1.0 to -2.0 and from X = 1.0 to 2.0 delivers

small growth of SSFI. In the case of staggered tube arrangement, the variation of SSFI with spanwise RWP shift are not similar for every fixed X locations. The value of SSFI is maximum at Y =  1.5 for the locations of RWPs nearer to the tube i.e., X = -0.5, 0.0, 0.5 and 1.0, whereas it is maximum for Y =  1.25 for RWPs located far away from tubes in both upstream and downstream. The streamwise shift of RWPs in the direction such that away from tubes shows an increment in SSFI for Y =  1.0 and  1.25. For Y =  1.5 and  0.75, streamwise and away RWP shift delivers decrement in SSFI. In case of Y =  0.5, increment in SSFI is found for streamwise and away shift of upstream located RWPs. On the other hand, the trend of SSFI is opposite for streamwise and away shift of downstream located RWPs.

(a) (b) Fig. 13 Variation of SSFI with RWP locations for (a) inline (b) staggered tubes arrangement 4.3 Thermal performance analysis Influence of different mounting RWP locations on thermal performance has been evaluated by considering scaled Colburn’s factor (SCF), scaled friction factor (SFF) and thermal performance factor (JF). The values of SCF, SFF and JF represent physical characteristics of heat transfer, flow 27

field and thermohydraulic features respectively. Flow field is majorly affected by the change in the location of RWPs, by which temperature distribution from surfaces of fins, tubes and RWPs to fluid is affected, hence these mutual influences lead to the variation of thermohydraulic performances with change in RWP locations. Figures 14(a), (b) and (c) respectively show the variations of SCF, SFF and JF for different RWP locations at Re = 3000 in inline tube arrangement. For fixed spanwise locations ( Y ) of RWPs, interesting effects of considered parameters have been observed with variation in streamwise RWP locations ( X ). In upstream as well as in downstream region of each tube, for streamwise shift of RWPs in the direction such that away from the tube at fixed Y =  0.5,  0.75 and  1.0, an increment in SCF is observed. On the other hand, for fixed Y =  1.25 and  1.5, value of SCF decreases with shifting of RWPs from X = 0.0 to -1.0 and from X = 0.0 to 1.0. Further, streamwise shift of RWPs away from tubes in both upstream and downstream regions shows gradual increase in the value of SCF. Nature of variation of SFF is found to be similar for fixed values of Y =  1.0,  1.25 and  1.5. The value of SFF decreases for streamwise shift from X = 0.5 to -1.0 and further shift in upstream region gives gradual rise in the value of SFF. However, streamwise shift of RWPs away from tubes in downstream region shows decrement in SFF. For fixed Y =  0.5 and  0.75, streamwise shift of RWPs away from tubes delivers increment in the value of SFF in upstream and decrement in downstream region. In case of thermal performance factor, the value of JF is found to increase for all fixed Y locations with streamwise shift of RWPs away from tubes in upstream as well as downstream direction except for upstream located RWPs having fixed value of Y =  0.5 and  0.75. In upstream located RWPs for Y =  0.5 and  0.75, the value of JF increases with streamwise shift of RWPs away from tubes. For spanwise shift of RWPs in the direction such that away from the tube at fixed X , the value of SCF increases and reaches to their maximum value at Y =  1.25, beyond which gradual decrease of SCF is observed. For all fixed X , spanwise shift of RWPs away from tubes contributes in an increment of SFF, except for X = -0.5, 0.0 and 0.5. The nature of variation of SFF for X = -0.5, 0.0 and 0.5 is found to be similar as SCF variation. For all fixed X , spanwise shifts from Y =  0.5 to  1.5 produce a similar variation of JF as SCF variation. The maximum value of SCF is observed for adjacent RWP location i.e., X = 0.0, Y =  1.25, whereas the maximum SFF is found for RWP location X = 0.5, Y = 

1.25. Even though augmentation in heat transfer is supreme for RWP located at the adjacent region 28

of tube, the value of JF is lower here because of much increase in pressure loss. Overall, higher value of JF is observed for upstream RWP locations than others, because upstream RWP locations show higher heat transfer enhancement and lower pressure loss. Similar investigations have been carried out for staggered arrangement of tubes. Figures 14(d), (e) and (f) respectively demonstrate the variations of SCF, SFF and JF for different RWP locations at Re = 3000 in staggered tube arrangement. In case of streamwise shift of RWPs in the direction such that away from tubes, value of SCF increases for fixed values of Y =  1.0 and  1.25, while it decreases for Y =  0.75. Streamwise shift of RWPs away from tubes in downstream region shows decrement in SCF for Y =  1.5. Whereas in upstream region, the value of SCF decreases from X = 0.0 to -1.0 and a

further shift in the location of RWPs in upstream direction gives gradual rise in the value of SCF. In case of Y =  0.5, increment in SCF is found for streamwise shift of RWPs away from tubes in upstream region. On the other hand, for downstream region, the trend is opposite with streamwise shift of RWPs away from tubes. As RWP locations shift towards the tubes in upstream region, an increment in the value of SFF is observed for all fixed Y locations, except for Y =  0.75. The value of SFF decreases gradually for Y =  0.75, when the location of RWPs is shifted from X = -2.0 to -1.0 and it increases with the further shift in the location of RWPs towards the tube. In downstream region of tubes, a streamwise shift of RWPs away from tubes produces decrement in SFF for all fixed Y . Variation in the value of JF with a change in X is found to be opposite to that of SFF variation for all fixed Y . The variations of SCF with the change in Y are not similar for every fixed X location. For RWPs located away from the tubes such that X = -2.0, -1.5, -1.0, 1.0, 1.5 and 2.0, RWPs located at Y =  0.75 shows lower SCF value. However, for X = -0.5, 0.0 and 0.5, value of SCF is lower for RWPs located at Y =  1.0. For Y =  1.5, the value of SCF is higher than others for almost all X locations. For RWPs located far away from tubes in upstream as well as downstream, Y =  1.25 show slightly higher values of SCF than Y =  1.5. For all fixed value of X , pressure loss i.e., the value of SFF is found to be higher for Y =  1.5 except at X = 0.0 and 0.5 where Y =  1.0 shows higher SCF. The value of SCF is lower at Y =  0.5 for all fixed X locations. For fixed values of X , the variation of JF of upstream located RWPs is similar to that of SCF variation from Y =  0.5 to  1.5. Spanwise RWP shift away from tubes delivers increment in JF. For downstream RWP locations, value of JF decreases from Y =  0.5 to  1.0 and then it increases for all fixed location of X , 29

except for X = 2.0. In case of X = 2.0, the value of JF decreases from Y =  0.5 to  0.75 and then it increases. At the adjacent located RWPs, i.e. X = 0.0, the value of SCF is maximum for Y =  1.5, whereas SFF is maximum for RWPs location X = 0.5, Y =  1.0. Similar to inline arrangement, higher JF is observed for upstream RWP locations followed by downstream and adjacent. Maximum JF value is found for upstream RWP location i.e., X = -2.0, Y =  1.25.

(a)

(d)

(b)

(e)

30

(c)

(f)

Fig. 14 Thermohydraulic performance analysis for inline arrangement (a) SCF (b) SFF (c) JF and for staggered arrangement (d) SCF (e) SFF (f) JF with different RWP locations 4.4 Identification of promising locations Figures 15(a) and (b) show the promising and counter-productive locations of rectangular winglets in the computational domain for inline and staggered arrangement respectively at Re equal to 3000. Selection of all promising locations of CFD configured RWPs for both inline as well as staggered arrangement is carried out for forty-one physically possible RWP locations, which helps to identify the optimum location having maximum thermal performance. Since the prior goal of the considered heat exchanger is the improvement in heat transfer compared to the penalty in pressure loss, for thermal performance factor (JF) estimation, the ratio of pressure loss is weighted by 1/3rd power to that of heat transfer ratio [32, 43]. A given location of RWP is declared as a promising location if the value of JF is greater than unity otherwise the location is treated as counterproductive. In Fig. 15(a) and (b), promising locations of RWPs are shown with the help of checkmark symbols (black color) while counter-productive locations of RWPs are shown with the help of hollow circle symbols (red color). Hence, in the case of an inline arrangement, a total of four counter-productive locations of RWPs has been observed while for staggered arrangement, the total number of counter-productive locations of RWPs is ten.

31

(a)

(b)

Fig. 15 Promising and counter-productive locations of rectangular winglets in the computational domain for (a) inline (b) staggered arrangement 4.5 Relationship between heat transfer and flow loss Locations of RWPs, which are capable of producing higher thermal performance, have been optimized by plotting SCF against SFF as shown in Fig. 16. Figures 16(a), (b) and (c) respectively show the variation of SCF with respect to SFF for all possible locations, all promising locations and selected best promising locations of RWPs in inline arrangement at Re equal to 3000. Even though the value of Re is same for all locations, each location of RWPs provides different thermal performance. For maximum cases, it has been found that the location which has higher rise in pressure loss, produces higher augmentation in heat transfer. To understand the thermal performance behavior of locations of RWPs, models have been established by fitting the correlation between SCF and SFF. For all possible locations, it has been observed that there exists a positive correlation between SCF and SFF, but it is weak which can be observed by the small Rsquared values for locations with linear as well as second-order polynomial relation. Correlation is weak, which means data are more scattered in the corresponding plot. If the R-squared value is higher, i.e. R-squared greater than 0.9 then it can be said that variation in SCF with SFF bears a strong correlation. For all promising locations of RWPs, it is noticed that the R-squared values of the correlations have been improved but still, these are small. Further, to get higher R-squared values of said correlations, higher values of JF have been retained and others have been ignored. It is found that the R-squared values of the correlations improve from 0.75 to 0.95 for linear and 0.77 to 0.97 for polynomial relation between SCF and SFF, as depicted in Fig. 16(c). For the case of selected best promising locations of RWPs, the location of RWPs that delivers maximum heat transfer enhancement, i.e. X = 2.0, Y =  1.25 also gives maximum JF value. In the case of 32

staggered arrangement, variation of SCF with SFF for all possible locations, all promising locations and selected best promising locations of RWPs are presented in Fig. 16(d), (e) and (f) respectively. Similar to inline arrangement cases, the R-squared values are smaller for all possible and all promising locations of RWPs. Significant improvement in R-squared values of correlations is observed for selected best promising locations of RWPs. It is found that the R-squared values of the correlations improve from 0.72 to 0.90 for linear and 0.73 to 0.95 for polynomial relation between SCF and SFF. Similar to the inline arrangement, the location of RWPs, i.e. X = 2.0, Y =  1.25 also delivers higher heat transfer enhancement with maximum JF value for the case of selected best promising locations of RWPs.

(a)

(d)

(b)

(e) 33

(c)

(f)

Fig. 16 Variation of SCF Vs SFF for inline arrangement (a) all locations of RWPs (b) all promising locations of RWPs (c) selected best promising locations of RWPs and for staggered arrangement (d) all locations of RWPs (e) all promising locations of RWPs (f) selected best promising locations of RWPs 4.6 Relationship between heat transfer and secondary flow The relationship between SCF and SSFI for different RWP locations in inline and staggered tube arrangements respectively is depicted in Fig. 17(a) and (b) respectively. A positive correlation between SCF and SSFI is observed for all considered cases. The strength of correlations is understood by R-squared values. The R-squared value greater than or equal to 0.9 shows a strong correlation between SCF and SSFI. From Figs. 17(a) and (b), the strong correlation between SCF and SSFI is observed for all locations in both the arrangements. Hence, it can be said that the thermal performance of the present system can also be estimated by investigating the variation of secondary flow intensity.

34

(a)

(b) Fig. 17 Relationship between SCF and SSFI for (a) inline (b) staggered tubes arrangement

5. Conclusion In the present three-dimensional numerical study, rectangular winglet pairs (RWPs) are used to disturb the flow and enhance the heat transfer from heated surfaces of fin-tube heat exchangers. As is known that the locations of RWPs play a major part in improvement in heat transfer. Hence, the influence of forty-one possible locations of the common flow down configured RWP on heat transfer augmentation for both inline and staggered tube arrangements has been performed. It has been observed that the adjacent located RWPs produce a maximum augmentation in heat transfer for both the arrangements. For inline arrangement, in comparison to the absence of RWPs, the presence of RWPs located at X = 0.0, Y =  1.25 provides a maximum 39.6 % heat transfer augmentation with a high rise in a pressure loss of 60.2%. In the case of staggered arrangement, the presence of RWPs located at X = 0.0, Y =  1.5 gives a maximum 29.4% heat transfer augmentation with a pressure loss of 22.1%. The thermohydraulic performance estimated by thermal performance factor (JF) is used for the identification of promising and counter-productive locations of RWPs. A total of thirty-seven and thirty-one promising locations of RWPs have been observed for inline and staggered arrangements respectively. Due to higher heat transfer augmentation with lower flow loss, RWPs located upstream and away from the tubes produce higher JF value and is maximum at X = 2.0, Y =  1.25 for both the arrangements. For inline as well as staggered cases, downstream RWP locations provide higher overall heat transfer from 35

tube surfaces and upstream RWP locations deliver higher overall heat transfer from bottom fin surfaces. Investigations on the trend of secondary flow show that the thermal performance analysis of the present heat exchanger can also be performed by considering secondary flow intensity. Nomenclature cp

specific heat capacity

D

diameter of tube

f

friction factor

H

channel height

J

Colburn’s factor

JF

thermal performance factor

k

turbulent kinetic energy

L

channel length

N

number of cells

Nu

Nusselt number

P

pressure

Pr

Prandtl number

Re

Reynolds number

Se

secondary flow intensity

T

temperature

U

free stream velocity

Uj

Cartesian velocity component (U, V, W) in X j - coordinate direction (X, Y, Z)

W

channel width

Greek symbols

t

turbulent thermal diffusivity



angle of attack

X

streamwise distance between tube and winglet

Y

spanwise distance between tube and winglet



turbulent dissipation rate 36



thermal conductivity



dynamic viscosity



kinematic viscosity of fluid



volume of domain

n

vorticity component normal to a cross-section



density of fluid



scalar transport function



non-dimensionalized temperature

y

wall y-plus

Subscripts 

inlet

w

wall

Abbreviations CFD

common flow down

CFU

common flow up

DWP

delta winglet pair

RWP

rectangular winglet pair

SCF

scaled Colburn’s factor

SFF

scaled friction factor

SSFI

scaled secondary flow intensity

VG

vortex generator

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LIST OF TABLES Table 1

Properties of air used for simulations

Table 2

Change in the value of Nu and f with grid nodes LIST OF FIGURES

Fig. 1

(a) Schematic of top and side view of the computational domain for inline and staggered tube arrangement in presence of RWPs; (b) Positional view of RWP; (c) Physically possible and impossible winglet locations concerning to center of each tube in both arrangements

Fig. 2

Grid mesh for (a) inline (b) staggered arrangement; grid mesh strategy near tubes and winglets for (c) upstream (d) adjacent (e) downstream located RWPs; grid sensitivity test for (f) inline (g) staggered arrangement

Fig. 3

Comparing variation of (a) Nu (b) f from present computations against experimental results [19] with change in Re

Fig. 4

Variation of Nu with the change in  and Re for adjacent RWP locations in (a) inline [32] (b) staggered tube arrangements

Fig. 5

Three-dimensional streamlines colored with velocity magnitude for inline tube arrangement at (a) upstream (b) adjacent (c) downstream RWP location

Fig. 6

Three-dimensional streamlines colored with velocity magnitude for staggered tube arrangement at (d) upstream (e) adjacent (f) downstream RWP location

Fig. 7

Contours of Nu at bottom (upper) and top (lower) fin surfaces of inline tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs; (e) comparison of surface-averaged Nu variation of top and bottom fin surfaces of inline tube arrangement with Re for different RWP locations

Fig. 8

Contours of Nu at tube surfaces of inline tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs

Fig. 9

Contours of Nu at bottom (upper) and top (lower) fin surfaces of staggered tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs; (e) comparison of surface-averaged Nu variation of top and bottom fin surfaces of staggered tube arrangement with Re for different RWP locations 43

Fig. 10

Contours of Nu at tube surfaces of staggered tube arrangement for (a) without RWPs (b) upstream (c) adjacent (d) downstream located RWPs

Fig. 11

Contours of Se at different cross-stream locations for inline arrangement (a) upstream (b) adjacent (c) downstream located RWPs

Fig. 12

Contours of Se at different cross-stream locations for staggered arrangement (d) upstream (e) adjacent (f) downstream located RWPs

Fig. 13

Variation of SSFI with RWP locations for (a) inline (b) staggered tubes arrangement

Fig. 14

Thermohydraulic performance analysis for inline arrangement (a) SCF (b) SFF (c) JF and for staggered arrangement (d) SCF (e) SFF (f) JF with different RWP locations

Fig.15

Promising and counter-productive locations of rectangular winglets in the computational domain for (a) inline (b) staggered arrangement

Fig. 16

Variation of SCF Vs SFF for inline arrangement (a) all locations of RWPs (b) all promising locations of RWPs (c) selected best promising locations of RWPs and for staggered arrangement (d) all locations of RWPs (e) all promising locations of RWPs (f) selected best promising locations of RWPs

Fig. 17

Relationship between SCF and SSFI for (a) inline (b) staggered tubes arrangement

Declaration of interests

☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

44

Hemant Naik

CRediT authorship contribution statement Hemant Naik: Conceptualization, Metodology, Software, Formal analysis, Writing - original draft, Writing - review & editing. Shaligram Tiwari: Conceptualization, Metodology, Formal analysis, Writing - review & editing.

Highlights of present research 

Performance of winglet locations on fin-tube heat exchanger is analysed.



Longitudinal and horseshoe vortices promote heat transfer enhancement.



Upstream located RWPs show higher thermal-hydraulic performance.



Best promising locations for both inline and staggered arrangements are identified.



Relationship between heat transfer and secondary flow is reported.

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