Computational Fluid Dynamics Analysis of Heat Transfer Enhancement in Flat Plate Solar Air Heaters Using Inclined Wing Vortex Generators

2.1 Physical model

This study presents a numerical investigation of three different configurations of the flat plate: Config. 0: Flat absorber plate (reference case); Config. I: Vortex Generators (VGs) Triangular (wing-type) inclined at 45° on Absorber plate; Config. II: Vortex Generators (VGs) Rectangular (wing-type) inclined at 45° on Absorber plate; All Absorber plates length L = 2.0 m, width w = 1.0 m with h = 20 mm height and b = 30 mm width in each VG in enhanced cases. In both VG configurations, the longitudinal and transverse pitches are the same to allow for a direct performance comparison. The overall geometry of the plate is illustrated in Figure 1, and the geometric parameters are summarized in Table 1. This case smooth plate has the same plate dimensions but vortex elements are not included.

Figure 1. CAD geometry of (a) triangular and (b) rectangular vortex generator configurations

Table 1. Geometric parameters of absorber and vortex generators

2.2 Computational domain and boundary conditions

The size is the rectangular duct, which consist of the inlet section, an absorber section which contains the VGs, and an outlet section where there must be fully developed flow at the exit. Table 2 presents the boundary conditions for the simulations Velocity inlet was applied with velocity values imposed to obtain the Reynolds number. A pressure outlet with zero-gauge pressure was used at the outlet. A uniform incident solar heat flux was imposed at the top surface of the absorber plate, and it was assumed adiabatic and no-slip for the side and bottom walls. The surfaces of vortex generators were treated, also, as no-slip. Air was considered as the working fluid, modeled as an incompressible ideal gas, with its properties being evaluated at the film temperature, for each of the test cases.

Table 2. Boundary conditions and solver setup

2.3 Governing equations

The continuity, momentum and energy equations were solved as steady-state, three-dimensional, incompressible Reynolds-averaged Navier–Stokes (RANS) equations:

Continuity equation:

$\rho(\nabla \vec{V})=0$          (1)

Momentum equation:

$\rho \nabla \vec{V}^2=-\nabla P+\mu \nabla^2 \vec{V}$        (2)

Energy equation:

$\rho C_P(\overrightarrow{\mathrm{~V}} \nabla \mathrm{~T})=K \nabla^2 T$            (3)

where, $V$ is the velocity vector, $\rho$ is the air density, $\vec{V}$ is the velocity vector, $P$ is the pressure, $T$ is the temperature, $C_P$ is the specific heat, and $K$ is the thermal conductivity.

The Reynolds number (Re) employed in defining the flow regime is:

$R e=\frac{\rho u D_{e q}}{\mu}$      (4)

where, $\rho$ represents the fluid density, $D_{e q}$ denotes the hydraulic diameter, $u$ signifies the characteristic velocity, and $\mu$ indicates the dynamic viscosity. The hydraulic diameter is determined by:

$D_{e q}=\frac{4 A}{p_w}$       (5)

where, $A$ is the cross-sectional flow area and $p_w$ is the wetted perimeter.

The RNG k−ε model with improved wall treatment was used for turbulence closure due to its proven capability of predicting separated and recirculating flows associated with VGs. All transport equations were solved with a second-order upwind scheme for accuracy of the solution.

2.4 Mesh generation and grid independence test

The computational meshes consisted of unstructured tetrahedron cells with local refinement around the VGs for capturing the flow separation and vortex structures. All solid surfaces were treated with prism inflation layers specifically so that the prisms could properly resolve the near-wall boundary layer.

An average Nusselt number (Nu) at the absorber plate was used as the grid independence criteria for Config. I as shown in Figure 2. For more than 4 × 10^-6 elements, the changes in Nu were smaller than 0.1%, with further refinement. Thus, a mesh resolution with about 4 million elements was used for all cases (including the smooth plate configuration) to ensure comparability. Figure 3 depicts the final mesh for the triangular VG.

Figure 2. Grid independence test results for Config. I

Figure 6 with respect to smooth duct (Config. 0), triangular configuration of vortex generators (Config. I), and rectangular arrangement vortex generators (Config. II) at airflow velocities of 1.5, 3, and also 4.5 m/s, shows the way the outlet air temperature changes with heat flux. In all cases, the outlet temperature is going up linearly with heat flux, which confirms that there exists a direct relation between the thermal reaction and the last solar input. For the smooth duct at 1.5 m/s, the exit temperature increased from 304.9 K at 200 W/m² to 331.6 K at 1000 W/m², a total increase of 27 K. Config. I and Config. The corresponding outlet temperatures obtained by II were 326 K and 335 K. This indicates that Config. Config set II generated airstream temperatures out of the outlet 3% higher than Config. I at low Reynolds numbers. The maximum outlet temperature for the smooth duct was 322.9 K (at 3 m/s) and 320 ℃ for Config. I and 323 K for Config. II. As residence time decreased with increasing velocity, the differences between configurations attenuated. At the 4.5 m/s, outlet temperatures decreased for all cases, with the smooth duct achieving values as low as 314.1 K, compared to Config. I and Config. II gave nearly identical values (314–315 K). In summary, the outlet temperature for the smooth duct was always the highest, and the vortex-generator configurations yielded the lowest outlet air temperatures; however, the latter was a relatively small difference. Nevertheless, this reduction is compensated with increased convective mixing and superior heat transfer coefficients which is a clear indication of the trade-off between bulk temperature rise and net heat transfer augmentation over wide range.

Figure 6. Variation of outlet air temperature with heat flux for smooth plate (Config. 0), triangular vortex generators (Config. I), and rectangular vortex generators (Config. II) at different airflow velocities

Figure 7 represents the dependence of Nusselt number (Nu) on heat flux for the smooth plate (Config. 0, Config. I and Config. II) and airflow velocities of 1.5, 3, and 4.5 m/s, respectively. Predicted Values of Nu increase with heat flux and with Reynolds number as a result of increasing intensity of heat transfer with convection. Nu values are also still low, 38 < Nu < 76 for the smooth plate, remaining true to a classical smooth-duct behavior. Conversely, thermal performance increases significantly with the introduction of vortex generators. At 1.5 m/s, Config. The maximum increment of Nu is from 48 for the smooth case to nearly 320–330 at high heat flux (a 570% improvement) in II. Similarly, Config. I attain Nu as high as 290, which is a 500% increase over that of the baseline. Config. At Nu boost both these at 4.5 m/s, efficiency (improves over Config. II attains 330 while Config. I reach 320, compared to smooth plate 77. The results indicate that vortex generators induce higher intensity secondary flows, better mixing, and thermal boundary layer disruption that led to significant enhancement of heat transfer. Config. Config. II (triangular vortex generators) is always better than Config. Such that I (rectangular), especially at low velocities where flow mixing is the dominant factor.

Figure 7. Variation of average Nusselt number with heat flux for smooth plate (Config. 0), triangular vortex generators (Config. I), and rectangular vortex generators (Config. II) at different airflow velocities

The enhanced surfaces' relative performance is measured in terms of the normalized Nusselt ratio (Nu/Nu₀) (Figure 8). At all Reynolds numbers and all heat fluxes, Nu/Nu₀ is greater than 4.0, reaffirming strong augmentation. Config. II at 1.5 m/s exhibits the best improvement, where Nu/Nu₀ ≈ 5.0, representing a quintuple augmentation over the smooth plate. Config. I exhibit somewhat lower values (Nu/Nu₀ ≈ 4.1–4.4), yet indicates strong intensification of the heat transfer. For higher velocities (3–4.5 m/s) turbulent mixing dominates forced convection at the smooth plate, and the enhancement thus decreases somewhat (Nu/Nu₀ ≈ 4.3–4.5). Still, both configurations retain a healthy degree of lead with Config. II consistently outperforms Config. I by 6–10%.

Figure 8. Normalized Nusselt number ratio (Nu/Nu₀) as a function of heat flux for triangular (Config. I) and rectangular (Config. II) vortex generator configurations compared to smooth plate baseline

Figure 9 illustrates the variation of the friction factor (f) with increasing heat flux for the three studied configurations at different flow velocities. For the smooth plate (Config. 0), the friction factor remained nearly constant across the range of heat fluxes, stabilizing at approximately f ≈ 0.045. This confirms that in the absence of flow disturbance, pressure drop is mainly governed by velocity rather than heat flux. In contrast, the introduction of vortex generators in Config. I and Config. II led to significant increases in friction factor. At v = 1.5 m/s, Config. II exhibited the highest values, with f reaching 0.42 at 200 W/m², about 9 times higher than the smooth plate baseline. Config. I also showed enhanced friction, with f ≈ 0.38 under the same condition, representing an increase of 8 times compared to Config. 0. At increased flow velocities (v = 3-4.5 m/s), the relative variation slightly decreased owing to the shorter residence time of air and greater inertial forces. At, e.g., v = 4.5 m/s and q = 1000 W/m², Config. II registered f ≈ 0.34, whereas Config. I provided f ≈ 0.29, still 7–8 times higher than the smooth plate. This trend verifies the fact that vortex generators are successful in increasing turbulence significantly, albeit at the expense of a substantially larger pressure drop, especially at lower velocities.

Figure 9. Variation of friction factor (f) with heat flux for different configurations and air velocities

Figure 10 shows the normalized friction factor (f/f₀) so that the penalty imposed by vortex generators can be more clearly seen in comparison with the smooth case. In all cases, f/f₀ remained in the 6–9 range, indicating that losses in pressure with vortex generators were an order of magnitude greater than the losses in the smooth plate. At low velocity (1.5 m/s), Config. II showed the highest penalty, with f/f₀ ≈ 9.0, while Config. I gave f/f₀ ≈ 7.8. The penalty decreased slightly at higher velocities, where Config. II dropped to f/f₀ ≈ 8.1 at 4.5 m/s, and Config. I to f/f₀ ≈ 7.0. This decreases in normalized values at the higher Reynolds numbers indicates that while vortex generators continue to add drag, the penalty becomes less severe with increasing velocity since the inertial effects outweigh the form drags.

Figure 10. Normalized friction factor (f/f₀) comparison of vortex-generator configurations relative to smooth plate at various heat fluxes

The TPF is an important parameter since it encapsulates the twin effects of the augmentation of heat transfer and the penalty of enhanced frictional losses. As can be seen in Figure 11, the enhanced geometries (Config I - triangular wing and Config II - rectangular wing) show substantial gains over the smooth plate baseline (Config 0). Under a 200 W/m² heat flux, Config I resulted in a TPF of 1.7–1.95, whereas Config II resulted in ~.45-1.65. This translates to an increase in performance of almost 20–30% for Config I and 10-15% for Config II over the smooth channel. As the heat flux is increased to 1000 W/m², the TPF values for Config I and Config II increased further, reaching maxima of 2.0 and 1.75, respectively. This suggests that at increased thermal loading, vortex generators become better at sustaining augmentation of heat transfer in spite of the concomitant rise in frictional loss. The air velocity had a contributory effect. At 4.5 m/s, the Config I maintained the maximum TPF, more than 2.0, whereas the Config II stabilized at 1.75. As against, the smooth duct never reached a figure over unity (TPF 1), validating the superior thermo-hydraulic benefit of vortex generator configurations. Overall, the results highlight that incorporating vortex generators, especially triangular designs, can effectively double the thermal-hydraulic efficiency of FPSAHs under turbulent flow conditions.

Figure 11. Variation of Thermal Performance Factor (TPF) with heat flux for different configurations and air velocities

Now to understand why the triangular wings outperform the rectangular wings at that regime we look into the details of the TPF curves at the lower air speed (v = 1.5 m/s, Re ≈ 9.5 × 10³). For these moderate Reynolds numbers, the flow in the main duct is only weakly turbulent, and the recirculation regions created in behind the wings are left relatively coherent. The sharply-shaped peak of the triangular features encourages a quick yet uniform separation resulting in a nicely compact double pair of longitudinal vortex aligned with the bulk flow. Such coherent structures promote wall-normal mixing in the near-wall region while thinning the thermal boundary layer and do not create wake bubbles large enough to significantly increase pressure loss, resulting in a high increase of Nusselt number with respect to the pressure loss. In comparison, the orthogonal wings produce wider separated regions and higher form drag inducing a larger increase in friction factor for a given heat-transfer enhancement. As such, at v = 1.5 m/s the triangular configuration displays the highest TPF values, signifying a more advantageous balance between the heat-transfer augmentation and the pumping-power penalty, while the rectangular configuration becomes competitive predominantly at higher velocities at which inertial effects begin to prevail.

Figure 12 illustrates the parasitic friction design. From a practical design perspective, the higher friction observed in Figures 9–10 indicates that vortex generators require the fan to deliver more power when installed in the duct compared with a smooth duct configuration. The friction factor of the modified ducts is approximately six to nine times greater than that of the smooth duct for the same configurations, hence the pumping power is increased significantly. This penalty is however balanced with an unproportionately large increase in heat transfer, as the Nu increases up to four to five times, and the TPF reaches a value of ∼2.0 for the triangular wings, and ∼1.75 for the rectangular wings. The fan simply consumes more electric energy, in return for a much larger thermal yield on the collector. However, in the case of conventional small and medium flat-plate solar air heaters, the fan power only serves a small portion of the total energy balance while the additional useful heat could be great. Thus, for the range of operation studied in the present work, the implementation of vortex generators — and particularly the triangular-wing design — can be considered an energetically valid and practically sensible choice.