Characterization of the Flow and Surface Temperature Around Multiple Vortex Generators

Characterization of the flow induced by vortex generators (VGs) has been a matter of intense research in a host of applications ranging from aerodynamic efficiency to turbulence mixing for mass and heat transfer applications. VGs that generate strong longitudinal vortices may enhance turbulence mixing and heat transfer [1–3]. The streamwise-oriented vortices improve the convective process by entraining the high-momentum fluid in the outer flow toward the wall and ejecting the low-momentum counterpart to the outer region [1–5]. Multiple studies have noted that the flow is accelerated in the streamwise direction in the downward flow region, resulting in enhanced thermal transport [1–4]. In addition, VGs also lead to increased local turbulence intensity, which contributes to heat and mass transfer in the downwind region [6,7].

Many VG geometries have been proposed and examined to understand flow structures and their effects on heat transfer. Fiebig et al. [5] and Tiggelbeck et al. [8] conducted experiments using delta (triangular) and rectangular wing VGs as well as delta winglet and rectangular winglet VG pairs. Fiebig et al. [5] found that the wing-type VGs produce more stable longitudinal vortices than the winglet-type VGs. They also noted that a delta wing VG may be more effective on heat transfer enhancement under a laminar regime. However, Tiggelbeck et al. [8] found that a delta winglet VG pair is more effective in terms of heat transfer under turbulent flow conditions. Liou et al. [9] studied the effects of various VG geometries on the local Nusselt number (Nu) in a square channel. They included ribs, V-shaped ribs, delta wing VGs, and delta winglet VGs. They found that a 45 deg V-shaped rib led to maximum heat transfer with an average enhancement of 270%, but this also resulted in a significant pressure drop penalty as high as 280%. A delta wing VG produced the second-highest heat transfer enhancement (170%) with a minor pressure drop penalty of 30%. They also observed that the vertical velocity distributions were consistent with the local Nusselt number ratio (Nu/Nu₀), showing the highest and the lowest Nu/Nu₀ in the downward and upward flow regions, respectively.

Vortex generators in compact channels or heat exchanger pipes may induce vortical mixing structures that can enhance heat transfer in a host of applications. Depending on the spacing, height, and rotational direction of the longitudinal vortices, each vortex pair could display a unique path along the downstream direction [10]. In counter-rotating vortex structures with common down-flow, a vortex pair moves apart along the downwind direction and may affect the boundary layer [10–12]. As VG spanwise spacing increases, the thickness of the boundary layer between the vortices may increase [12]. Counter-rotating vortices tend to move closer in the common up-flow region and lift away from the surface as they develop along the downwind direction [10,11,13–15]. However, as the vortex pair rises from the surface, its ability to influence the boundary layer diminishes considerably [10].

For greater turbulent mixing and heat transfer enhancement, VGs should accelerate locally the flow within the boundary layer and keep the vortices adjacent to the surface [10,16]. Torii et al. [16] combined the common up-flow vortex system with round tubes by using winglet VGs located symmetrically behind the tubes. The configuration of VGs and tubes were designed to accelerate the flow by constricting the passage between the tube and VGs (i.e., the venturi effect). The accelerated flow experienced a delay in separation from the tube, which minimized zones of poor heat transfer [4,10,16]. Specifically, for the in-line tube arrangement, the heat transfer increased by 20%, but with a pressure decrease of 15%. In the case of staggered tube arrangement, heat transfer increased by 30% but pressure decreased by 55%. Fiebig et al. [4] used the common down-flow vortex system with round tubes and observed a heat transfer increase of 65% with a friction factor increase of 45% for the in-line tube arrangement. The staggered tube arrangement led to a heat transfer increase of 9% and a friction factor increase of 33%.

Unlike conventional geometries, trapezoidal VGs facing downwind generate a counter-rotating vortex pair (CVP) with a common upward flow region located between the two vortices. Various studies [14,15,17–22] have noted that the mean shear flow present at the trailing edge of the trapezoidal VGs leads to the formation of periodic hairpin vortex structures in the intermediate wake region. However, near the wake, the CVP appears to be dominant (x/h < 1.5–2, where h is the VG height) [14,15,17–19]. In the far wake region, the CVP breaks down and the flow is dominated by hairpin-like vortices (2 < x/h < 10) [17–19].

Habchi et al. [21] related vorticity flux with Nusselt number for the case of single trapezoidal VGs. Using Reynolds-averaged Navier–Stokes equations, they postulated a correlation between the cross-area averaged vorticity flux (Ω) and spanwise-averaged Nu. However, they pointed out that the Nu correlation may not be a single function of vorticity and must consider other topological characteristics of the vortical structure. Kaci et al. [23] performed numerical simulations using Reynolds-averaged Navier–Stokes to investigate the effects of multiple trapezoidal VGs on heat transfer in a circular pipe. They found that heat transfer increased mainly by the presence of CVPs. The study also claimed that the vortices increased heat transfer and were responsible for the uniform temperature distribution within the flow. Habchi et al. [24] also numerically studied the heat transfer effects of multiple trapezoidal VGs in a circular pipe. They simulated seven successive rows of trapezoidal VGs with various configurations under turbulent conditions at Reynolds number (Re) values between 7500 and 15,000, with Re based on a hydraulic diameter. They found that the hemispherical protrusions placed between the trapezoidal VG rows greatly enhanced heat transfer with only a small pressure decrease. Among all the cases from the study, inverted trapezoidal VGs with protrusions showed the highest Nusselt number values.

Conventional VGs that induce longitudinal vortices have been used in many thermal management systems. However, comparatively few studies have investigated heat transfer phenomena caused by trapezoidal VGs. Specifically, most of the work on single trapezoidal VGs has explored the induced flow dynamics and the effects of VG parameters on heat transfer in a system of multiple trapezoidal VGs are not well understood. Furthermore, CVPs are efficient for heat transfer enhancement; here, we explored geometric parameters necessary to induce strong structures near the wall. To achieve the goal, we investigated the effects of taper and inclination angles of single trapezoidal VGs, spanwise spacing in a single row of VGs, and streamwise spacing for multiple rows of VGs on heat transfer using an experimental approach appropriate for thermal management systems and applicable in heat exchangers. The experimental results reveal that a specific configuration of multiple VGs may achieve optimal heat transfer enhancement.

An experimental apparatus was especially designed for characterizing the flow and heat transfer of CVPs induced by trapezoidal VGs. The setup consisted of a 3.6 m long duct of acrylic glass with a 0.1 m × 0.1 m square cross section. The inlet has a round entrance followed by honeycomb structures to minimize mean flow inhomogeneity. Figure 1 illustrates a basic schematic. A 12 V DC power supply controlled a 12 V DC brushless fan used to blow air through the duct at room temperature, and a thermo-anemometer was used to measure airflow with an accuracy of ±3%. The VGs were placed in the test section at 2.75 m downwind of the outlet of the air settling chamber containing the honeycomb structures or about 2.4 m from the flat rough turbulator section to ensure developed turbulent flow. Three-dimensional printed VGs were used for the particle image velocimetry (PIV) and heat transfer experiments. The VGs were made of polycarbonate so that they resist temperatures up to 90 °C by the heater used in the heat transfer experiments. When testing multiple rows of VGs, the center VGs were fabricated using germanium (Ge), which is translucent in the infrared (IR) wavelength range of 8 μm–12 μm. The germanium VGs were placed in the middle of multiple rows to measure the surface temperature below and at the bottom corner of the VGs.

We explored single arrays of VGs. Inspection of single VGs considered VGs with taper angles (β) of 0 deg and 7.6 deg, i.e., rectangular and trapezoidal shapes. Both were tested at inclination angles (α) of 45 deg and 60 deg. The taper angles of the VGs were adapted from Habchi et al. [21]. The length (l) and the base width (w) were 41 mm and 28.7 mm, as shown in Fig. 2. Assessment of multiple VGs considered different horizontal arrangements, the VG length (l) and the base width (w) were 18.5 mm and 13 mm; it allowed three VGs side-by-side inside the duct without producing significant edge effects. Also, the inclination (α) and taper angles (β) were set at 45 deg and 7.6 deg, respectively, to investigate the effects of spanwise and streamwise spacings on heat transfer. Specifically, the spanwise spacing-to-width ratio (STW) was varied from 1 to 2.5 and the streamwise spacing (S) was varied from 2 h to 3 h.

Particle image velocimetry experiments were conducted using air seeded with smoke particles from a water-based glycol solution, with an associated Stokes number less than 10⁻³ for an air flow velocity of 0.75 m/s. A 5 W diode-pumped solid-state laser (continuous, 532 nm wavelength) and a high-speed camera (Photron SA3, San Diego, CA) with a Micro-NIKKOR 105 mm f/2.8 lens captured the illuminated seeding particles. Cross-correlation analyses of the PIV images were performed using pivlab software [25], which has been widely used [26–29]. IR thermography was used to measure surface temperature near the VGs using an IR camera (FLIR A325). As shown in Fig. 3, a 12.7 mm (0.5 in) a thick piece of acrylic glass was used as a thermal insulator on the walls of the test section to minimize heat loss. Moreover, rigid foam insulation was used to minimize heat losses. A customized heater, 0.6 m in length, provided uniform, constant heat flux. A smooth, 0.5 mm thick stainless-steel sheet [30–32] coated with black paint (emissivity, ε = 0.92) was attached to the heated surface to ensure uniform heat flux from the heater. An infrared window made of zinc selenide allowed optical access to the heat transfer surface and its transmissivity was 98% in the IR wavelength range of 8 μm–12 μm. Aluminum foil (emissivity, ε = 0.09) covered the walls of the experimental system to minimize radiative heat losses. Considering the radiation view factors from the heated bottom surface to the side and top surfaces [32–34], the radiation losses between the bottom surface and the side and top surfaces of the baseline case (no VGs) were less than 5% of the total heat flux. Sample IR images for the baseline case and the single trapezoidal VG case (θ = 60 deg, top view) are shown in Fig. 4. The color scale indicates the temperature on the heat transfer surface in degrees Celsius (°C). Additional details of the experimental setup, including experimental validation, can be found in Park [35].

Particle image velocimetry experiments were conducted using a plain duct at Reynolds number of 4800 based on the hydraulic diameter. Figure 5(a) shows the time-averaged streamwise velocity (U) distribution along the center plane, normalized using the center velocity (U₀) in the plain duct. The velocity measurements by Gavrilakis [36] and Niederschulte [37] in the fully developed regime in square ducts at Reynolds numbers (Re) of 4410 and 4915 are included for comparison. The agreement between the measurements and both Refs. [36] and [37] falls within the margin of error, which implies that developed turbulent conditions were achieved at the measurement location using the system developed for this study. The logarithmic region followed the u⁺ = 3.2 ln(y⁺) + 3.9 relationship over the range 30 < y⁺ < 100 as shown in Fig. 5(b), which is in agreement with Gavrilakis [36] for turbulent flows in a straight square duct at Re of 4400. The second-order flow statistics of the flow in the plain duct are shown in Fig. 6, which are also compared with those obtained by Gavrilakis [36] and Niederschulte [37].

Figure 7(a) illustrates spanwise-averaged surface temperatures without VGs. It also includes the flow bulk temperatures estimated by linear interpolation based on the temperature measurements before and after the heat transfer test section using T-type thermocouples. For the constant heat flux boundary condition, the surface temperature first increased sharply and followed a gradual linear increase. The results imply that the flow in the heating section was thermally developing for 0 < x/D_h < 2 and developed beyond this location. Figure 7(b) shows spanwise-averaged Nusselt number (Nu) values without VGs, which includes results from the Gnielinski correlation for a Reynolds number of 4800 [38,39]. Nusselt number was calculated based on the hydraulic diameter of the duct $(Nu = hDhk)$⁠. In general, the Gnielinski correlation is used for constant uniform heat flux when heat flux is applied symmetrically. The difference between the experimental results and the Gnielinski correlation was less than 7%. Previous studies have indicated Nu values for the asymmetrical heating cases varying ±20% for turbulent flows; therefore, a 7% difference between the asymmetric and symmetric cases is considered reasonable [40–44].

First, we explore the flow induced by the trapezoidal and rectangular VGs at inclination angles (α) of 45 deg and 60 deg. Streamlines induced those structures on the spanwise-vertical plane (y-z) in the near wake of the VGs at x/h = 0.5 are shown in Fig. 8, where x is the streamwise direction, h is the VG height, and x/h = 0 is at the trailing edge of the VG. The structures induced a CVP with the relatively strong vertical or common up flow in between the two vortices at around z/w = 0. The results also reveal that the cores of the vortices were located closer to the wall for the VGs with a higher inclination angles (α). These streamlines also illustrate the mechanism of the CVP inducing near-wall and outer flow exchange, which promotes a stronger convection process.

Time-averaged vertical profiles of the streamwise velocity (U) component in the common up-flow region along the central plain (z/w = 0) are shown in Fig. 9, where x/h = 0 denotes the trailing edge of the VG. The relatively strong negative flow in the vicinity of VGs, particularly at higher inclination angle (α), implies greater recirculation flow near the bottom corner [21]. A relatively high inclination angle (α) affects the formation of the CVP resulting in lower vertical velocity and circulation [20]. Figure 10 shows the mean vertical velocity (V) profiles in the common up-flow region along the central plane of the VGs. The vertical velocity decreased as the inclination angle increased. As stated by other studies that higher vertical velocity increases circulation strength in the vortices [7,45,46], Fig. 10 indirectly suggests that the VGs at lower inclination angle produced CVPs with stronger circulation. The VG taper angle (β) had minor effects on the velocity distribution at the central plane at a Reynolds number of 4800.

Turbulence intensities of the streamwise (I_u = u_rms/U₀) and vertical (I_v = v_rms/U₀) directions, along the central plane are, shown in Figs. 11 and 12. They reveal increased levels of turbulence at y/h ≈ 1 modulated by the mean shear (∂U/∂y). Likewise, lower magnitudes of I_u and I_v occurred in the region below the tip of the VGs, where ∂U/∂y was relatively lower.

where T_w (x,z) is the local surface temperature with $Tw0$ representing the baseline (no VG) case. Three and six thermocouples (T-type) were installed before and after the heat transfer section to measure bulk air temperature. The local bulk temperature, T_b (x), was obtained by linear interpolation between the inlet and outlet bulk temperatures. Constant and uniform heat flux, q″, was applied such that the fluid bulk experienced a temperature difference of at least 2 °C between the inlet and outlet of the test section. During the experiments, the maximum surface temperature was 80 °C at the end of the heat transfer section with a heat flux of 510 W/m². In this study, the local θ^* was used to describe the effects of CVP on local heat transfer characteristics in the wake region (x/h < 1.5) [17–21].

Figure 13 shows the effects of CVPs on the local θ^* using a color scheme reproduced based on IR-based surface temperatures and local bulk temperatures. In general, greater heat transfer was found in the downward region. The CVP had a direct effect on convective heat transfer to x/h ≈ 1.5. The maximum θ^* did not significantly change with taper angle (β), but it increased with higher inclination angles (α). Furthermore, the local θ^* was lower along the central axis (z/w = 0) near the VG where the local streamwise velocity was low due to recirculation. Also, a greater heat transfer or higher θ^* was observed at the edge of the CVP (z/w ≈±0.7) due to the accelerated flow near the wall [4,10,16]. However, as the CVP developed along the downstream direction, its effect on convective heat transfer decreased for x/h > 1.5.

where the Nusselt number is based on hydraulic diameter of the duct, $Tw0(x)$ is the spanwise-averaged local surface temperature for the baseline (no VG) case, $Tw(x)$ is the spanwise-averaged local surface temperature for the corresponding VG case. $Nu$/Nu₀ was calculated using experimental data within the spanwise range (z/w) between −0.7 and 0.7, in which the peak values of θ^* occurred in the downward region, z/w ≈±0.7. The ratio Nu/Nu₀ reached the highest value in the wake region for all the VG cases and gradually decreased until x/h ≈ 1.5; then it increased between x/h of 1.5 and 3.0 as shown in Fig. 14. In the near wake of the VGs, the Nusselt number for the rectangular and trapezoidal VGs increased by 14% and 13%, respectively. Since Nu/Nu₀ takes into account both the upward and downward flow regions, it is not straightforward to relate flow statistics shown in Figs. 9–12 to the trends observed in Fig. 14. However, the PIV measurements imply that enhanced local heat transfer between 1.5 < x/h < 3 may be modulated by turbulent mixing associated with hairpin-like vortices and secondary eddies. Furthermore, this result is supported by Hamed et al. [22], who found a generation of hairpin structures at x/h ≈ 2–3 for rectangular and trapezoidal VGs using 3D PIV.

Studies have shown that better convective heat transfer occurs in the common down-flow regions of the counter-rotating vortex pairs [3,6,7,46,47]. In such cases, the common down-flows are generated in between VGs, when more than two trapezoidal VGs are used. Here, we put three VGs in a row, as shown in Fig. 15(a). The STW = s/w was varied from 1.0 to 2.5 while taper angle (β) and inclination angle (α) were set at 7.6 deg and 45 deg, respectively, to quantify the effects of spanwise spacing on heat transfer. In the case of STW of 1.0, the three VGs were aligned without any spacing between them. Figure 15(b) shows velocity contours in the spanwise-vertical plane (y-z) plane indicating the common up-flow (z/w = 0, center plane) and common down-flow (a plane in between the VGs) from the PIV.

Figures 16 and 17 show the streamwise and vertical velocity profiles in the common up-flow region (z/w = 0, center plane) for different STWs. The trailing edge of VG was located at x/h = 0. They indicate that as the CVPs developed downstream, the streamwise velocity increased but the vertical component decreased. This suggests that CVP circulation weakened downwind of the VGs [7,45,46]. Furthermore, the locations of the peak velocity shown in Figs. 16 and 17 indicate that the CVPs stayed closer to the bottom wall along the channel when STW was set to 1.5.

Figure 18 shows the streamwise velocity profiles measured in the common down-flow region, at a plane in between the VGs, when three VGs were placed in a single row with different STWs. The flow in the common down-flow region accelerated and led to greater streamwise velocity downwind, except in the STW = 1. Here, the VGs had no spanwise spacing and the V-shaped space between the VGs restricted the flow path. As a result, the CVP structures could not completely form in the wake of VGs, and the flow did not accelerate much in between the VGs. Also, the flow accelerated in the streamwise direction significantly for STW = 1.5. Previous studies have found that accelerated flows near the surface increase thermal energy transport in the streamwise direction [6,16]. Therefore, it is expected that VGs with STW = 1.5 should provide better heat transfer performance, which is further discussed in Sec. 3.3.2. Figure 19 shows the vertical velocity profiles measured in the common down-flow region when the three VGs were placed in a row at different STWs. The vertical velocity reached a maximum for STW = 1.5 due to the CVP interactions, but the vertical velocity decreased rapidly downstream for x/h >1.5.

The VGs configuration in a single row was identical to those in the PIV experiments, as described above. Surface temperatures were measured using an IR camera under the steady-state condition at Reynolds number 4800. The local temperature ratio, θ^* in Eq. (1) was obtained based on the IR and thermocouple measurements.

Figure 20 shows the effects of the CVPs on the local θ^* for a single row of VGs with different STW. A lower θ^* or lower heat transfer occurred for STW = 1.0, especially in a region of −1 < z/w < 1. This is due to lower streamwise and vertical velocities in the common up-flow and down-flow regions, as shown in Figs. 16(a), 17(a), 18(a), and 19(a). Also, higher θ^* occurred for STW = 1.5, especially in the common down-flow region (z = s/2), as shown in Fig. 20(b). As the PIV shown in Figs. 18(b) and 19(b) indicate VGs with an STW = 1.5 induced CVPs with strong common down-flow and the flow acceleration in the streamwise direction, resulting in significantly enhanced heat transfer in this region as shown in Fig. 20(b). While the effects induced by CVPs on heat transfer diminished with increasing STW, the results indicate that the CVP flow mechanism enhanced the convective heat transfer up to approximately x/h = 1.5 for STW = 1.5. This is also consistent with the velocity data from Figs. 18(b) and 19(b), where acceleration and vertical velocity decreased significantly at x/h >1.5.

Understanding the effects of multiple rows of VGs on the flow is important in many applications including mixing chambers and heat exchangers. Here, we explored the effects of multiple rows of trapezoidal VGs on the vortical flow structures. Three VGs were used in each row with a spacing-to-width ratio (STW) of 1.5 due to the comparatively high heat transfer performance on a single row, as shown in Fig. 20(b). Taper angle (β) and inclination angle (α) were set at 7.6 deg and 45 deg (Fig. 21). The arrangement of the multiple rows of VGs is shown in Fig. 21. Initially, each row of VGs was separated by a streamwise spacing S/h = 2 because the effect of the vortical flow on heat transfer decreased significantly for x/h > 1.5, as noted in Fig. 20(b).

For characterization of the flow in the wake region of multiple rows of VGs, PIV analysis was conducted to obtain velocity data in the wake of the first, second, and third rows of VGs. The mean velocities, turbulence intensities, and Reynolds stress were obtained in the common up- and common down-flow regions in the wake of each row. Figure 22 shows the mean streamwise and vertical velocities in the common up-flow region (z/w = 0, center plane) in the wake of the first, second, and third row of VGs, at an axial distance of x/h = 1 from the trailing edge of VGs. In the wake of the first row, the mean streamwise velocity of the flow decreased while the mean vertical velocity increased due to the presence of strong CVPs. However, the mean vertical velocity of the CVPs decreased while the streamwise velocity increased in the wake of the second and third rows of VGs. This indicates that the CVPs became weaker in the wake of the second and third rows.

Figure 23 shows the mean streamwise and vertical velocities in the common down-flow region (z/s = 1/2, a half-way plane in between of VGs) in the wake of the first, second, and third row of VGs, measured at x/h = 1. The interaction of the center CVP with the neighboring CVPs in the wake of the first row induced strong common down-flow with significant acceleration along the streamwise direction. However, the strengths of the CVPs decreased significantly in the wake of the second and third rows. In summary, the mean velocity data measured in the common up-flow and common down-flow regions suggest that the CVPs were strong in the wake of the first row of VGs but became weaker after the second and third rows.

Turbulence intensities of the streamwise and vertical components in the common up-flow region (z/w = 0, center plane) in the wake of the first, second, and third rows of VGs were measured at the local x/h = 1 from the trailing edge of the VGs (see Fig. 24). In general, I_u increased significantly for y/h > 1 due to the relatively strong shear flow (∂U/∂y) induced by the trailing edge of VGs. In addition, I_v increased throughout 0 < y/h < 2 for all cases. Especially, I_v increased significantly and reached a maximum in the wake of the second row of VGs.

Figure 25 shows the streamwise and vertical turbulence intensity in the common down-flow region (z/s = 1/2 or half-way plane in between of VGs). These quantities increased significantly and reached a maximum within the second and third rows of VGs and decreased in the wake of the third row of VGs. Figure 26 shows the Reynolds stress $−u′v′¯$ in the common up-flow (z/w = 0, center plane) and common down-flow region (z/s = 1/2, or half-way plane in between of VGs) in the wake of the first, second and third rows of VGs, measured at x/h = 1 from the trailing edge of VGs. It was comparatively low in the wake of the first row. However, it increased significantly and reached a maximum value in the wake of the second row of VGs, specifically in the common down-flow regions. It is worth noting that the strength of the CVPs and their corresponding mean streamwise and vertical velocities were greater in the wake of the first row and decreased significantly in the wake of the second and third rows, as seen in Figs. 22(b) and 23. Therefore, the mean velocities (U and V) and turbulence statistics (I_u, I_v, and $−u′v′¯$⁠) suggest that the mean motion of the CVPs should be the dominant mechanism inducing greater convection in the wake of the first row, specifically in the common down-flow regions by inducing strong vertical down-flow and significant streamwise acceleration in the near-wall region. However, convective momentum increased in the wake of the second row since the turbulence intensity and Reynolds shear stress increased significantly, as shown in Figs. 24–26, specifically in the common down-flow regions. As the turbulent intensities and Reynold stress decreased in the wake of the third row, the convective momentum was expected to be lower compared than in the wake of the second row, specifically in the common down-flow regions.

Figure 27 shows the local temperature ratio (θ^*) for multiple rows of VGs. It significantly increased in the common down-flow regions in the wake of the first row. The PIV showed that U and V increased significantly in the common down-flow region in the wake of the first row, specifically in the near-wall region as shown in Fig. 23, while I_u, I_v, and $−u′v′¯$ were lower, as shown in Figs. 24–26. This suggests that the increase of θ^* in the common down-flow regions in the wake of the first row was mainly driven by the mean motion of CVPs.

It is important to note in Fig. 27 that θ^* increased significantly in the wake of the second row. As discussed above, the PIV results show that the strength of the CVPs decreased significantly while turbulence intensities and Reynolds shear stress increased significantly in the wake of the second row, specifically in the common down-flow regions. This clearly indicates that the level of turbulent mixing after the second row of VGs is greater given the higher values of these second-order statistics in the common down-flow regions, where higher θ^* values occurred. In summary, the PIV and IR results show that the increase in heat transfer was driven by the mean motion of CVPs when the turbulence intensity was comparatively weak in the wake of the first row. However, turbulence became the dominant local mechanism that led to an increase in heat transfer specifically after the second row of VGs.

To further understand the effects of VGs on heat transfer, the spanwise range-averaged Nusselt number ratio (Nu/Nu₀) was obtained in the common up- and down-flow regions. Nu/Nu₀ was calculated within the spanwise range (z/w) between −0.15 and 0.15 for the common up-flow and 0.55 and 0.85 for the common down-flow regions along the streamwise direction. Figure 27(b) shows data points that could be measured and calculated directly while avoiding the segments associated with the VGs in the common up-flow region, as seen in Fig. 27(a). Nu/Nu₀ values shown in Fig. 27(b) in the common up-flow region in the wake of the first row were lower due to the decrease of the mean streamwise velocity. The acceleration in the streamwise direction and the strong down-flow in the common down-flow regions led to higher Nu/Nu₀ in the common down-flow region in the wake of the first row. Nu/Nu₀ reached the highest value in the wake region of the second row for both the common up- and down-flow regions due to greater turbulence intensities and Reynolds stresses. As the turbulence intensities and Reynolds stress decreased in the wake of the third row, Nu/Nu₀ also decreased. In the wake of the first, second, and third rows, Nusselt numbers increased by 16%, 21%, and 16% in the common-up flow regions, respectively; and 18%, 22%, 17% in the common-down flow regions, respectively.

Park et al. [35] and other studies [13,48] have found that recirculation occurs at the bottom corners of trapezoidal VGs, which possibly result in poor heat transfer and create high temperature regions. Therefore, it was necessary to measure the surface temperature distributions at the bottom corner of the VGs to determine the local heat transfer enhancement, if any, when using multiple rows of VGs. To measure the surface temperature at the bottom corner of the VGs using an IR camera, three trapezoidal VGs were fabricated using germanium (Ge), which is transparent in the IR wavelength range of 8 μm to 12 μm. Germanium VGs had the same shape that was used for the PIV and other heat transfer experiments. Three germanium VGs were attached using small plastic support structures in the middle of each row. Germanium VGs were placed in the middle of each row to take advantage of flow structure symmetry along the spanwise direction. Local θ^* using the germanium VGs revealed no hot-spots or high-temperature regions underneath or at the bottom corners of VGs (see Fig. 28). Therefore, a 45 deg trapezoidal VG had no negative effect on heat transfer.

The strength of the CVPs depends on the configuration and arrangement of VGs [10], and we considered four arrangements to identify optimized heat transfer performance. Specifically, rows of VGs were either aligned and staggered with respect to the preceding rows of VGs at two streamwise spacings S/h = 2 and 3, as shown in Fig. 29. In each row, three VGs were used with a STW of 1.5 and taper angle (β) and inclination angle (α) were set at 7.6 deg and 45 deg, respectively.

Figure 30 shows the local temperature ratio (θ^*) for VGs in the aligned and staggered arrangements with S/h = 2 and 3. By comparing the aligned and staggered arrangements at the same streamwise spacing S/h = 2, as shown in Figs. 30(a) and 30(b), higher θ^* was obtained with the aligned arrangements. Furthermore, θ^* was greater with the aligned arrangement at S/h = 2 compared to S/h = 3, indicating the better arrangement when compared to the other cases. In summary, Table 1 shows an optimal configuration for multiple rows of VGs based on experimental heat transfer results.

Particle image velocimetry and heat transfer experiments were performed to understand the effects of configurations of trapezoidal VGs on the mean velocity, turbulence levels, and surface temperature distributions in a square channel. The results show that counter-rotating vortex pairs induced by trapezoidal VGs enhanced local heat transfer within a streamwise range of x/h < 1.5. A higher inclination angle (α) led to higher local convective heat transfer, but the taper angle (β) had minor effects on temperature and velocity distributions at a Reynolds number of 4800.

A STW of 1.5 for a single row of VGs induced CVPs with the strong downward flow. As a result, CVPs moved close to the surface, where the flow experienced streamwise acceleration. The resulting vortical structures led to enhanced heat transfer in the wake regions of VGs up to x/h = 1.5.

In the cases with multiple rows of VGs, the increase in heat transfer was driven by the mean motion of CVPs when the level of turbulence was comparatively weak, especially in the wake of the first row of VGs. However, turbulence became the dominant local mechanism that led to an increase in heat transfer specifically after the second row of VGs. Furthermore, it was found that an aligned arrangement with streamwise spacing S/h = 2 led to optimized heat transfer performance. In summary, PIV and heat transfer results clearly indicate that configuration parameters such as inclination angle, spacing-to-width ratio, streamwise spacing, and arrangement of multiple VGs can lead to advantageous heat transfer performance in heat transfer systems with vortex generators.

The authors are grateful for the support provided by the U.S. Army Corps of Engineers, Engineer Research and Development Center, under U.S. Army Research, Development, Test, and Evaluation Program Element T23, Basic Research/Military Construction, cooperative agreement No. W9132T-14-2-0022, Experimental Characterization of Multiscale Vortical Flow Structures.

• Engineer Research and Development Center (W9132T-14-2-0022; Funder ID: 10.13039/100006505).

CVP =

counter-rotating vortex pair

D_h =

hydraulic diameter, mm

h =

height of vortex generator, mm

k =

thermal conductivity, W/m·K

l =

length of vortex generator, mm

Nu =

Nusselt number based on hydraulic diameter

q′′ =

heat flux, W/m²

Re =

Reynolds number based on the hydraulic diameter

s =

spanwise spacing between vortex generators

S =

streamwise spacing between rows of vortex generators

T_b =

bulk flow temperature, °C

T_w =

surface temperature, °C

w =

base width of vortex generator, mm

α =

inclination angle of vortex generator, deg

β =

taper angle of vortex generator, deg