THE EFFECTS OF WINGLET VORTEX GENERATOR POSITION IN RECTANGULAR-DUCT-TYPE SOLAR AIR HEATERS

The aim of this work is to numerically investigate the effect of mounting winglet vortex generators on different positions in rectangular-duct-type air heaters. The two investigated positions were the absorber plate and the insulation plate, opposite to the absorber plate. Four shapes of winglet vortex generator, i.e. perforated rectangular winglet vortex generators (P-RWVG), rectangular winglet vortex generators (RWVG), perforated trapezoidal winglet vortex generators (P-TWVG) and trapezoidal winglet vortex generators (TWVG), were used. Results showed that heat-transfer capability would be better if the winglet vortex generators were mounted on the opposite insulation plate in the cases of P-RWVG, RWVG and P-TWVG.


INTRODUCTION
Unlike fossil fuels, renewable energy is unlimited and clean .The sources of renewable energy, namely geothermal, hydro energy, wind power, biomass, and solar energy, have long been a major global issue for decades .Their sustainability and non-toxic emissions are great advantages, making them relatively cost-efficient and environmentally friendly. Governments around the world have consequently promoted the usage of renewable energy sources instead of limited and toxic fossil fuels .Solar energy, which is an energy source of renewable energy, has long been harnessed .Since the sun releases both light and heat, there are many methods to make use of its energy; for example, solar electricity, solar ventilation, solar thermal energy for refrigeration or air conditioning and solar heating .
Heating with solar energy needs solar collectors to absorb solar energy and convert it to heat .Then the heat is used to heat either water or air, which are working fluids. The working fluids are finally utilized for specific objectives .For solar air heating, solar collectors are roughly categorized into two groups, i.e. photovoltaic (PV) and solar air heater (SAH). A typical SAH is principally composed of a heat exchanger, a blower and connecting pipes as shown in Fig. 1(a). The heatexchanging parts of SAHs can be constructed with pipes or tubes (Afshari et al., 2020) but rectangular ducts or channels, as shown in Fig. 1(b), have often been used in solar -energy harvesting systems owing to the larger areas of their solar-energy absorbers Thianpong et al., 2009;Xiao et al., 2020). A conventional rectangular-duct -type heat exchanger generally consists of four walls .One of them is the solar -energy absorber, so -called absorber plate, as illustrated in Fig.1. The absorber plate could be positioned as either the upper or lower wall. For instance, absorber plates were assigned as upper walls in the work of , Leander Antony et al. (2020) and Skullong et al. (2018), but were assigned as lower walls in the work of Abdullah et al. (2020), Alam et al. (2014), Boulemtafes-Boukadoum et al. (2019), Gopi et al. (2021) and Korpale et al. (2020). While the other walls are customarily insulation walls .
Although heat exchange ducts, composed of four smooth-flat plates, have long been developed for several years (Madhwesh et al., 2019), many surface roughness variants have been proposed for mounting on the walls of the heat exchange ducts of high-performance SAHs in order to produce strong longitudinal vortex flows inside the heat exchangers, resulting in faster rates of heat transfer. Grooves and dimples are surface variations which do not intrude the flow fields inside heat exchangers, and have been selected for use in some work (Eiamsa-ard et al., 2008;Liu et al., 2015). Some kinds of surface roughness intrude the flow fields inside the heat exchangers to increase heat transfer rates; for example, ribs, fins and winglets. Ribs have been utilized in many projects (Aharwal et al.,2008;Bansal et al., 2020;Barik et al., 2021;Patel et al., 2020;Komolafe et al., 2019;Kumar and Layek, 2019a;Kumar et al., 2019;Mahanand and Senapati, 2020;Wang et al., 2020). But some researchers have exploited fins (Hassan et al., 2021;Hosseini et al., 2019;Murali et al., 2020;Singh and Negi, 2020), whereas winglets were used in the work of , Kumar and Layek (2020a) and Kumar and Layek (2020b). Although baffles have regularly been employed to control the flow direction in heat exchangers, they can also induce the vortex flows, thereby increasing heat transfer rates in the heat exchangers (Luan and Phu, 2020;Tamna et al., 2014). Additionally, some of these roughness geometries could be combined and applied for better heat transfer rates (Saravanakumar et al . . , 2020). In rectangular-duct-type SAHs, the above-mentioned roughness geometries were usually only mounted on the absorber plate, which is

Frontiers in Heat and Mass Transfer
Available at www.ThermalFluidsCentral.org *Corresponding author Email: Boonchai.L@Chula.ac.th the solar -energy collecting part of the heater (Abdullah et al . . , 2020;Alam et al., 2014;Boulemtafes -Boukadoum et al., 2019;Gopi et al., 2021;Korpale et al., 2020;Leander Antony et al., 2020;Pandey et al., 2016), although some researchers studied the effects of applying roughness geometries on multiple surfaces (Promvonge et al., 2009;Skullong et al., 2015). However, the literature cited above shows that there has not yet been any research into the consequences of repositioning roughness geometries to the insulation wall, opposite to the absorber plate, as illustrated in Fig. 1(b).  The objective of this work is, thus, to numerically investigate the effects of the positions of winglet vortex generators (WVGs) in rectangular-duct-type SAHs on the capacity of heat transfer, as indicated by the Nusselt number.

EXPERIMENTAL SETUP
The solar air heater, proposed in Skullong et al. (2018), was employed for this investigation. There were four types of winglet vortex generators, categorized by the shapes of their winglets as shown with their dimensions in Fig. 2: the perforated rectangular winglet vortex generator (P-RWVG), the rectangular winglet vortex generator (RWVG), the perforated trapezoidal winglet vortex generator (P-TWVG) and the trapezoidal winglet vortex generator (TWVG). All winglet vortex generators had the same height ( e = 12 mm) and the same length of longer base edges ( c = 25 mm). Both the P-TWVG and the TWVG were right trapezoids, whose longer base edges ( c ) were 12 millimeters longer than their shorter base edges ( s c = 13 mm). winglet vortex generators were circular, with five millimeter diameter ( d = 5 mm). The vertical locations of the punched holes were at the middle of the height of both P-RWVG and P-TWVG .The horizontal locations of the punched holes were exactly at the middle of the longer base edges. This means that the punched holes were eccentric to the inclined lateral side in the P-TWVG case. The setup of the heat exchanging part of the SAH is presented in Fig. 1   For each computational domain, the absorber plate was posted with the boundary condition of a no-slip wall, releasing constant heat flux ( q ) of 600 W/m 2 , whereas the opposite plate was a no-slip insulation wall .The left and right boundaries were symmetrical planes . The front and back boundaries were periodical inlets and outlets where constant mass flow rates were maintained in order to achieve six conditions of Reynolds number ( Re = 3000, 5000, 7000, 10000, 15000 in which the area-averaged velocity of the influx air (2) and the hydraulic diameter At the inlet, the temperature of the air ( i T ) was maintained at 300 K.

Fig. 4
The computational domains for flows around perforated trapezoidal vortex generators.
Although most of the winglet vortex generators in the cited literature could conduct heat, the winglet vortex generators in Skullong et al. (2018) were treated as insulation plates because they were mounted on the absorber plates with superglue, which is a heat insulator .In addition to the work of Skullong et al. (2018), there was also some other research, utilizing insulation winglet vortex generators (Tamna et al., 2014;Tanda, G., 2004). Moreover, Luan, and Phu (2020) found that vortex generators only disturbed the air near the absorber plates where they were mounted, but did not conduct heat to air far away from the absorber plates. Hence, all winglet vortex generator surfaces were assumed to be no -slip heat -insulation walls in the present work .This boundary condition neutralized any effects of heat transfer, resulted from the extended surfaces.
The realizable k -epsilon model, supplemented with a wall function, was selected in this work, as it was suggested in the work of Skullong et al. (2018). The assumptions used in the simulations were; (1) thermal radiation was neglected, (2) flows were steady fully developed periodic flows, (3) flows were turbulent and incompressible, (4) body forces were neglected and (5) air was a Newtonian fluid whose properties were density (  ) = 1.177 kg/m 3 , dynamic viscosity (  ) = 1.846  10 -5 kg/m-s, specific heat capacity ( P C ) = 1004.9 j/kg-K and thermal conductivity ( K ) = 0.02624 W/m-K.

Parameters of Interest
The two parameters of interest, i.e. the Nusselt number (Nu) and friction factor ( f ), have often been used to evince the performance of SAHs ( et al., 2002;Singh et al.,2014). Therefore, they were exploited in this work. The Nusselt number is computed from Herein, h stands for the area -averaged convection heat transfer coefficient and is defined as where q is the constant heat flux of 600 W/m 2 from an absorber plate, sur T is the area-averaged temperature of the absorber plate and air T is the mass-average temperature of the air in the domain .The friction factor is computed from where i u is the area-averaged velocity of the influx air andis   P p L  the area-averaged pressure gradient across the length of the periodic boundaries, which is longitudinal pitch spacing ( l P ).

Criteria of Solution Convergence and Grid Independence
Simulation solutions were accepted when the residual values of all governing equations were less than 10 -5 . There were two meshes that were exploited to ensure the independence of the grid resolution for each case of the investigation .Coarser and finer meshes respectively consisted of approximately 16000 and 32000 elements .For all cases, the average differences of Nu and f between the coarser and finer meshes were 2.57% and 5.73%, respectively.

Verification of Simulation Model
The reliability of the simulation model was confirmed by comparing the These empirical correlations were proposed in Skullong et al. (2018). The % errors, indicated in each correlation, were the deviations of the predicted data from the empirical equations and the measured data from their experiment. The Prandtl number ( Pr ) was a constant, equal to 0.7070, and the relevant dimensional parameters are defined as follows: The area of a punched hole on a perforated winglet vortex generator is The area of a winglet vortex generator )one side only( is w A c e   for rectangular winglets or for trapezoidal winglets.
The winglet blockage ratio is The longitudinal pitch length ratio is Comparisons between simulated results and empirical results, calculated using empirical correlations, are depicted in Fig. 5(a) -(d) as functions of the Reynolds number .The abscissas of the simulation results were the six chosen Reynolds numbers ( Re = 3000, 5000, 7000, 10000, 15000 and 20000). The Nusselt numbers, from most of the simulations, were a little less than those of the empirical correlations when the Reynolds number was below 15000, but were a bit greater when the Reynolds number increased beyond this .The exception to this was the case of TWVG because the Nusselt numbers, from the simulations, were almost coincident on the empirical curve .Friction factors, obtained from the simulations, were slightly less than those of the empirical correlations, except the leftmost point in the case of RWVG .These figures show that simulation results were very similar to those of the empirical correlations, and therefore acceptable.

The Effects of Winglet Vortex Generator Position
The percentage of difference between Nusselt numbers, obtained from cases in which the winglet vortex generator is mounted on the absorber plate and in which it is mounted on the opposite insulation plate, was an indicator of the change in heat-transfer capability when the winglet vortex generators were repositioned .The four curves of %diffNu are presented in Fig .6 as functions of Reynolds number .These four curves are categorized by shape of winglet vortex generator .This figure reveals that the positions of the winglet vortex generators significantly affected the capability of heat transfer between absorber plates and airflows in the heat exchange duct .In cases of P-TWVG, P-RWVG and RWVG, %diffNu increased when the Reynolds number rose from 3000 to 10000, after which it tended to level off .This implied that %diffNu did not depend on Reynolds number when Reynolds number was greater than 10000, for these winglet vortex generators .Because maximum magnitudes of %diffNu were much greater than the magnitudes of the % r e rors that were indicated in empirical correlations, i.e. Eq. (7), Eq. (9) and Eq. (11), it could be inferred that the positions of these winglet vortex generators significantly influence heat transfer capacity in SAHs. The curve of TWVG was different from the others since the value of the %diffNu declined from the positive to the negative zone as the Reynolds number increased .The change of the sign ) positive and negative( of the %diffNu values took place within the region of 5000 < Re < 7000 .This meant that mounting winglet vortex generators on the opposite insulation plate gave worse heat transfer capabilities when the Reynolds number was higher .Although the magnitudes of the %diffNu were not much greater than the magnitude of the % error in the empirical correlation, Eq. (13), the curve of %diffNu still decreased as Reynolds number increased .It is, thus, expected that the magnitude of the %diffNu would be more significant if the Reynolds number was higher.
In the same way, the percentage of difference between friction factors, obtained with different positions of winglet vortex generator is defined as Since the simulated airflows were assumed to be incompressible and body forces were neglected, the simulated flow fields were almost independent of winglet vortex generator position for each Reynolds number and winglet vortex generator shape .The only difference between any two simulated flow fields, obtained from the two different positions of winglet vortex generators under the same Reynolds number, was that they were mirror images of each other .
Consequently, %difff in all cases was approximately zero. This means that repositioning the winglet vortex generators only affected the heattransfer capability of SAHs but did not affect friction loss inside the heat exchange duct.

Fig. 6
Percentage differences between Nusselt numbers (from cases in which winglet vortex generators were mounted on absorber plates and in which they were mounted on the opposite insulation plates) for the four different shapes of winglet vortex generator.

Discussion
The distributions shown in Fig. 7 are the relationships between Reynolds number and turbulent kinetic energy ( k ), averaged over all computational domains .It was found that domain-averaged k , in cases that P-RWVG, RWVG and P-TWVG were mounted on absorber plates, was much greater than domain-averaged k of TWVG. Domainaveraged , k in cases of winglet vortex generators mounted on opposite insulation plates, were identical to Fig .7; hence they are not depicted here .For the same Reynolds number, the highest domain-averaged k belonged to RWVG, followed by P-RWVG and R-TWVG, whereas the lowest domain-averaged k belonged to TWVG .This order was the same for %diffNu. However, there is no limiting asymptote for the domain-averaged k curves in Fig. 7, which is different from the %diffNu curves for RWVG, P-RWVG and P-TWVG in Fig. 6. The similarities between domain-averaged k and %diffNu implied that turbulent kinetic energy played an important role in %diffNu.  Fig. 8(a) on a horizontal axis .This is because the winglet vortex generators were repositioned from the upper absorber plate to the lower opposite insulation plate .For the reason that the distributions of area-averaged k in Fig. 8(b) skewed to the upper side where the absorber plate was, the diffusion (due to fluctuation) should be strong on this side .This enhanced heat transfer capability in the region adjacent to the absorber plate .Hence, just a small temperature difference between the absorber plate and the airflow was needed for the fixed q of the absorber plate. And, according to Eq. (4) and Eq. (5), the Nusselt number will be higher if the temperature difference   sur air T T  is smaller, since q , D and K were constants in this work .Conversely, the distributions of area-averaged k in Fig. 8(a), skewing to the lower side, caused lower Nusselt numbers in the cases that winglet vortex generators were mounted on the opposite insulation plate .This was why all %diffNu values were positive and increased alongside Reynolds number in the P-RWVG case .
The distributions of area-averaged k for the RWVG case are displayed in Fig. 9(a) and Fig. 9(b). They were quite similar to those of P-RWVG, except their magnitudes were greater and their skewness was more distorted .Consequently, the %diffNu values of RWVG were greater than those of P-RWVG at the same Reynolds number .
The distributions of area-averaged k for the cases of P-TWVG in Fig. 10(a) and Fig. 10(b) could be used to confirm that the magnitudes of the area-averaged k and the skewness of area-averaged k distributions played an important role in %diffNu. Both figures display both smaller magnitudes of area-averaged k and less distorted skewness of the areaaveraged k distributions, which corresponds to the smaller %diffNu values of P-TWVG (compared to those of P-RWVG and RWVG).        The distributions of area-averaged k for TWVG were different to the previous three cases .However, the influence of area -averaged k could be minimal, as the magnitudes of the area-averaged k were very small in these cases. Heat transfer due to convection, thus, was the only factor, influencing %diffNu.

CONCLUSION
The simulated results of the four winglet vortex generator shapes show that winglet vortex generator position in solar air heaters influence the capability of the heat transfer from the absorber plate to the air, flowing through the heat exchange duct .When winglet vortex generators were mounted on the opposite insulation plate, heat transfer between the absorber plate and airflows in the heat exchange duct was better with winglet vortex generators of P-RWVG, RWVG or P-TWVG design. However, the opposite result was obtained for TWVG as shown in Table 1. This could be explained by considering both the magnitudes of domain-averaged k and the skewness of area -averaged k distribution along the z-axis, i.e .heat transfer is better on the side to which the areaaveraged k distribution skews. Results also show that the higher the domain-averaged k, the greater the %diffNu magnitude.