Size effects of vane-type rectangular vortex generators installed on high-lift swept-back wing flap on lift force and flow fields

Abstract

Vane-type vortex generators (VGs) are often installed on the flaps of high-lift systems of aircraft as retrofit devices for increasing the lift by suppressing flow separation. To reduce the number of VGs, increasing their heights is a viable solution for generating strong vortices. However, the maximum size of the VGs cannot be determined based on the available literature. We investigated the effect of size of a vane-type rectangular VG on the lift force of a half-span high-lift swept-back wing model. The experiments were performed in a low-speed wind tunnel at Reynolds number 1.86 × 10⁶. In this study, three different heights (H_v) of the VGs with co-rotating vortex configurations were tested, all of which were larger than the boundary layer thickness δ at the VG’s installation position of the flap. We observed that moderately sized VGs (H_v/δ = 4.8) maximized the increase in the lift coefficient, while excessively large VGs (H_v/δ = 9.6) reduced this increase. To examine this further, we measured the flow fields over the flap for VGs with both H_v/δ = 4.8 and 9.6 via stereoscopic particle image velocimetry. Results showed that VGs with H_v/δ = 9.6 generated a larger flow separation area as compared to that with H_v/δ = 4.8. For H_v/δ = 9.6, almost half of the vortex core interacted with the main wing wake; this implies that vortices generated by VGs with H_v/δ = 9.6 produce low-momentum fluid entrainment in the wake toward the boundary layer on the flap, thus diminishing the effect of the VGs.

Graphic abstract

Appendix: Quantitative evaluation of momentum transfer

To evaluate the flow-field condition downstream of VGs quantitatively, we calculated MT, the dimensionless momentum flux near the flap surface, using the following equation:

$${\text{MT}} = \frac{1}{{\rho U_{\infty } }}\frac{1}{{D_{{{\text{gap}}}} W_{{{\text{surface}}}} }}\iint {\rho \overline{u} {\kern 1pt} dYdZ},$$

(4)

where $\overline{u}$ is the average of the streamwise velocity components, u (obtained from Type-B measurements), and ρ is the density of the free stream, which is assumed to be constant. The calculation MT could indicate and evaluate the efficiency of the VGs depending on their height H_v.

The calculation domain for Eq. (4) was set on a measurement plane as shown in Fig. 16a.

Fig. 16

Calculation domain for solving Eq. (4): a cross-sectional view of calculation domain, and b locations of measurement cross sections along X direction

The height of the domain, D_gap (= 8.9 mm), is calculated as the gap between the main wing’s trailing edge and the flap surface in the Z direction, averaged along the width of the domain. The width of the domain was set to −0.5 ≤ Y/W ≤ 0.5, where W_surface = 80 mm, at X = −90, -80, and −70 mm. For X = −60 mm and −45 mm, both flap-wall and non-flap-wall regions exist within the −0.5 ≤ Y/W ≤ 0.5 range, as shown in Fig. 16b. Therefore, the calculation domain along the Y direction was set to -0.21 ≤ Y/W ≤ 1 (W_surface = 68.3 mm) at X = -60 mm, and 0.11 ≤ Y/W ≤ 0.5 (W_surface = 31.7 mm) at X = −45 mm.

The variation of MT along the X direction is plotted in Fig. 17a

Fig. 17

Variation of momentum transport (MT) at near-flap surface along X direction. a Value of MT calculated by Eq. (4). b Distribution of difference between MT in the baseline configuration and configurations with VGs (ΔMT) (α = 10°, U_∞ = 53 m/s, and Re = 1.86 × 10⁶)

17a. This figure quantitatively indicates that the flow condition was improved by the VGs in the downstream region; in this region, MT was higher for configurations with VGs than it was for the baseline configuration. In contrast to our expectations, with the excessively large VGs (H_v/δ = 9.6), MT was lower in the midstream region than it was with the baseline configuration. Figure 11c shows that the starting point of the wedge-shaped low-speed area could be observed in the cross section at X = −90 mm. The existence of the leading edge in this cross section decreased the value of MT in the midstream region with the excessively large VGs.

For a comparison of the VG configurations, ΔMT was calculated as follows:

$$\Delta {\text{MT}} = \left( {{\text{MT}}} \right)_{{{\text{VGs}}}} - \left( {{\text{MT}}} \right)_{{{\text{baseline}}}},$$

(5)

where (MT)_VGs corresponds to the value of MT for a configuration with VGs, and (MT)_baseline corresponds to the value for the baseline configuration.

The relationship of ΔMT to the X location is plotted in Fig. 17b. This figure indicates that the flow condition was better with the moderately-sized VGs (H_v/δ = 4.8) than it was with the excessively large VGs, as with the former, ΔMT was higher in the whole measurement region.

From these results, the amount of the momentum transfer and its changes for streamwise direction were confirmed. Additionally, we could also confirm that using moderately-sized VGs (H_v/δ = 4.8) is more efficient in terms of the momentum transfer than using excessively large VGs (H_v/δ = 9.6), quantitatively.