Frequency response of separated flows on a plunging finite wing with spoilers

Abstract

The effectiveness of lift and bending moment reduction on a plunging wing was investigated in an experimental study to understand the effects of unsteady wing motion. The frequency response of the lift/moment reduction was studied for finite-span mini-spoilers placed on a finite wing. Single, multiple, and spanwise periodic mini-spoilers located at various spanwise locations all exhibit a decaying frequency response of the effectiveness of lift/moment reduction with increasing frequency and amplitude of the oscillations. This happens for pre-stall angles of attack as the mini-spoilers induce shear layer separation, roll-up of vorticity, and recirculation regions, generating additional lift. For the post-stall angles of attack, stronger leading-edge vortices are already shed from the clean wing at high frequencies, and the spoilers are not able to influence the development of the vortices, resulting in a decaying frequency response. The cut-off frequency for all spoiler configurations is similar and scales with the reduced frequency at pre-stall angles of attack, whereas the Strouhal number based on the peak-to-peak amplitude of the plunge oscillations becomes the scaling parameter at post-stall angle of attack. The spoilers exhibit similar cut-off frequency to their two-dimensional counterparts. The finite-spoilers delay or displace the shear layer away from the wing surface, similar to the two-dimensional mechanisms.

1 Introduction

Consideration of extreme forces and moments on wings during gusts, turbulence, and maneuvers dictates the structural design of wings. Often the wing structures are made more rigid and heavier because of concerns about the uncontrolled excessive loads, which result in a weight penalty that decreases the fuel efficiency. Therefore, loads alleviation becomes essential. Conventionally, this is achieved by using relatively large mechanical surfaces such as trailing-edge flaps and spoilers, which are heavy and limit the applications to low-frequency unsteady encounters. Fluidic actuators have been proposed to overcome these limitations in various studies as summarized by Li and Qin (2022) in a recent review article. However, fluidic actuation, even when applied near the trailing-edge for “circulation control,” does not necessarily make the lift/moment reduction faster (Al-Battal et al. 2019). This inherent limitation of the unsteady lift response is due to the shedding of vorticity from the wing and the “wake effect” (Wagner 1925). Nonetheless, this issue could be solved by early detection of the gusts using LIDAR technology (Schmitt et al. 2007).

The need for light-weight actuators and more efficient lift/moment reduction methods remains the main objective of designing aerodynamically efficient aircraft. Conventional “circulation control” actuators can produce good lift/moment reduction, but their capability decreases with increasing angle of attack of wing or gust angle, since they are located near the trailing-edge. In contrast, mini-spoilers placed near the leading edge (see Fig. 1a) produce little lift/moment reduction at small angles of attack, but increasing lift/moment reduction with increasing angle of attack or gust angle (see the sketch in Fig. 1b). The magnitude of lift reduction for leading-edge mini-spoilers becomes substantially larger than that of circulation control methods with increasing angle of attack. This is due to the flow separation produced by the “Kirchhoff–Rayleigh flow” (Kirchhoff 1869; Rayleigh 1876) as sketched in Fig. 1b for static airfoils. In this model, the fully separated flow behind a flat-plate is modeled using the free-streamline theory. Flow separation is fixed at the leading edge and the trailing edge. The theory predicts that the lift force coefficient for small angles of attack can be written as C_L = 2 $\pi \alpha$/4, which is the quarter of the lift coefficient predicted by the thin-airfoil theory for attached potential flow. This is in agreement with the wind-tunnel experiments for small angles of attack (Heathcote et al. 2018). This large reduction in the static lift curve is the biggest advantage of lift reduction with flows separated near the leading edge.

Fig. 1

(a) Mini-spoiler attached to the upper surface near leading edge; (b) schematic variation of lift coefficient with effective angle of attack for baseline wing and with spoiler

When there is already flow separation from the leading edge of the airfoil (due to aeroelastic deflections, gusts, turbulence, and maneuvers), there is the possibility of formation of leading-edge vortices (McCroskey 1982). This may increase the unsteady lift force on airfoils. There are additional considerations for finite wings. Even for static wings, flow separation is highly three-dimensional in the post-stall regime (Winkelman and Barlow 1980). For unsteady pitching or plunging wings, leading-edge vortices become highly three-dimensional (Yilmaz and Rockwell 2012; Visbal et al. 2013; Visbal and Garmann 2019; Son et al. 2022) and affect the bending moment about the root (Chiereghin et al. 2020; Son et al. 2023). Bending moment about the root is the most important design parameter for the structural design of wings. Leading-edge vortex formation and its three-dimensionality may affect the effectiveness of any lift/moment reduction methods on finite wings.

For unsteady wing or unsteady freestream, the effectiveness of lift reduction with mini-spoilers depends on the magnitude of the unsteady effects. For a plunging airfoil, if the plunge velocity is not too large and a weak leading-edge vortex develops, the mini-spoiler is highly effective (Bull et al. 2020). This is illustrated in Fig. 1b with the dashed lines as a function of effective angle of attack, which is defined as:

$$\alpha_{{{\text{eff}}}} \left( t \right) = \alpha - {\text{tan}}^{ - 1} \frac{1}{{U_{\infty } }}\frac{{{\text{d}}h}}{{{\text{d}}t}} = \alpha + {\text{tan}}^{ - 1} \frac{{V_{{{\text{pl}}}} }}{{U_{\infty } }}$$

(1)

where α is the mean angle of attack (also called “geometric” angle of attack), h is the displacement of the airfoil, U_∞ is the freestream velocity, and ${V}_{{\text{pl}}}$ is the plunge velocity. The sketch of the lift variation is based on the interpretation of the data in Bull et al. (2020). Large variations of the dynamic lift loops and large phase lags occur for the baseline airfoil (with a rounded leading edge), which are typical of dynamic stall vortices. With the spoiler, the Kirchhoff–Rayleigh flow can prevent or delay the roll-up of the leading-edge vortex at the highest effective angle of attack (Bull et al. 2020).

However, with increasing unsteady effects and shear layer roll-up, leading-edge vortices become stronger. The effectiveness of the leading-edge spoilers ceases (Bull et al. 2020). The conditions for which the effectiveness is lost (frequency and amplitude of the plunging motion) when the leading-edge separation occurs would be valuable for the design of effective loads reduction. This scenario may happen during an encounter with gusts or turbulence, during unsteady maneuvers, and more importantly due to the aeroelastic deflections of wings, resulting in the loss of lift/moment alleviation.

The effectiveness of two-dimensional Kirchhoff–Rayleigh flows for lift/moment alleviation in steady freestream as well as on plunging airfoils has been demonstrated in previous work (Heathcote et al. 2018; Bull et al. 2020). However, realistic applications involve finite-span spoilers on finite-wings with tip vortices, resulting in substantial three-dimensional flows. The location of the part-span spoilers is expected to be close to the wing-tip to maximize the reduction of the root-bending moment acting on the wing. Recent measurements of the unsteady bending moment on plunging finite wings (Chiereghin et al. 2020; Son et al. 2023) revealed that the dynamics of the leading-edge vortices significantly affects the unsteady bending moment. Son et al. (2022) showed that the three-dimensionality of the leading-edge vortices near the wing-tip increases with increasing frequency and amplitude of the wing oscillations. The main objective of the present study is to understand the unsteady aerodynamics of finite-span mini-spoilers placed near the leading edge of a plunging wing. For this purpose, various mini-spoiler configurations were examined experimentally in a water tunnel. Figure 2 shows the placement of single spoilers and multiple spoilers with varying spans on a half-wing model at different spanwise locations.

Fig. 2

Mini-spoiler configurations tested in the water tunnel

2 Experimental methods

The main considerations in selecting the spoiler configurations are as follows. To maximize the bending moment reduction by placing the spoiler near the wing tip, the first two configurations (from left in Fig. 2) have been selected. Finite-span spoilers may or may not be more effective than the two-dimensional counterparts, depending on the flow conditions near both edges of the spoilers. For spoilers away from the wing-tip region, an improvement might occur as the separated regions are expected to be larger due to the decreasing effect of the tip vortices, although the moment arm decreases. Two separate spoilers increase the edge-effect and also the magnitude of total lift/moment reduction. Because of this reasoning the multiple-spoiler configuration (the third from left in Fig. 2) has been selected. The last three configurations (from right in Fig. 2) are targeted to understand whether spanwise instabilities can be introduced to the leading-edge vortices and the lift/moment can be decreased because of the increasing three-dimensionality of the vortex filaments. For both high-aspect-ratio wings and airfoils, spanwise instabilities have been observed on the vortex filaments. The tip vortices, trailing-edge vortices, and secondary vortices were found to trigger the spanwise instabilities on plunging wings and airfoils (Son et al. 2022). The wavelengths of the spanwise instabilities were found to be in the range of λ/c = 0.3 to 1.5 (where c is the chord length of the wing). For all spoiler configurations, the chordwise location of the spoiler from the leading edge is x/c = 0.08 and the spoiler height from the surface of the wing is H/c = 0.04, consistent with the previous study with two-dimensional spoilers on two-dimensional airfoils (Heathcote et al. 2018; Bull et al. 2020).

The experiments were carried out in the free surface closed-loop water tunnel at the University of Bath (see Fig. 3). The water tunnel can achieve speeds of up to 0.5 m/s in the test section of 381 mm wide × 508 mm deep × 1530 mm long. The turbulence intensity was identified to be less than 0.5% using laser Doppler velocimetry (LDV). The Reynolds numbers tested were Re = 10,000 and Re = 20,000. The experiments comprise of a wing plunging in a sinusoidal motion normal to the freestream as shown in Fig. 3. The models used were a rectangular wing with a NACA 0012 profile that served as the baseline case. They had a semi-aspect ratio of sAR = 5 as they represented half-wing models. The same wing with the addition of the mini-spoilers located near the leading edge on the suction surface is tested at the mean angles of attack $\alpha$ = 5°, 7°, 9°, 12° and 15°. For Reynolds number Re = 20,000, the stall angle of attack is approximately α_s ≈ 9° (Chiereghin et al. 2020).

Fig. 3

Schematic of experimental setup in water tunnel

The wing had a chord length of c = 62.7 mm and was manufactured using PA-2200 polyamide using selective laser sintering with a polished smooth surface and painted matt black to reduce reflectivity during flow measurements. To further support the wing structure in the spanwise direction and prevent the wing from bending a 25 x 5 mm T800 CFRP bar was inserted into the wing. The spoiler was made of 3-ply zero-degree layout T800 carbon fiber-reinforced polymer (CFRP) and had a thickness of t = 0.75 mm.

The wing is connected to a manual rotation stage that can set the geometric angle of attack with an accuracy of ± 0.2°. The rotation stage is connected to the moving carriage through the six degree of freedom sensor that gathers the data for the lift force and bending moment. A Zaber LSQ150B-T3 translation stage is providing the plunging motion powered by a X-MCB1 controller. In order to minimize friction, the carriage is moved by four air bearings that absorb bending and torque loads. The system can produce an accuracy of 2% sinusoidal motion that follows the function (see the inset in Fig. 3):

$$h\left( t \right) = a\cos \;(2\pi ft) = \frac{A}{2}\cos \;(2\pi ft)$$

(2)

where a = A/2 and f is the plunging frequency. In this study, the normalized peak-to-peak amplitude was varied in the range from A/c = 0.1 to 2.0. The reduced frequency is defined as k = πfc/U_∞ and is varied up to k = 3 for Re = 10,000 (because the freestream velocity is lower) and up to k = 1.2 for Re = 20,000. Another important parameter is the Strouhal number based on the peak-to-peak plunge amplitude, which is defined as:

$$St_{A} = \frac{fA}{{U_{\infty } }}$$

(3)

2.1 Force and moment measurements

The lift force and the root-bending moment were measured by an ATI Industrial Automation Mini40 six-axis force/torque sensor. The sensor is attached to the wing at quarter-chord axis location. The lift and moment data were acquired with a sampling frequency that is 2000 times the plunging frequency and then were processed to obtain phase-averaged quantities using 50 cycles. The lift and bending moment due to the inertia were then removed by subtracting the product of the moving mass and the instantaneous acceleration. After the inertial forces/moments were subtracted, the signal was filtered using two zero-phase Butterworth third-order band-stop filters from 6 to 10 Hz and from 20 to 60 Hz to remove the unwanted structural frequencies. Subsequently, a zero-phase 200 point moving average filter was applied to reduce random noise. For static cases, the measurements were acquired with a sampling frequency of 1,000 Hz for 40 s. The changes in lift coefficient ($\Delta C_{{L,{\text{max}}}}$) and bending moment coefficient ($\Delta C_{{M{\text{,max}}}}$) about the root are given by the following:

$$\Delta C_{{L,{\text{max}}}} = \max \left( {C_{{L,{\text{spoiler}}}} } \right) - \max \left( {C_{{L,{\text{baseline}}}} } \right) = \frac{{2\Delta L_{{{\text{max}}}} }}{{\rho U_{\infty }^{2} {\text{bc}}}}$$

(4)

$$\Delta C_{{M,{\text{max}}}} = \max \left( { C_{{M,{\text{spoiler}}}} } \right) - \max \left( {C_{{M,{\text{baseline}}}} } \right) = \frac{{2\Delta M_{{{\text{max}}}} }}{{\rho U_{\infty }^{2} b^{2} c}}$$

(5)

where b is the span of the wing. To compare with the two-dimensional spoilers, we also define

$$\Delta c_{{l,{\text{max}}}} = \max \left( {c_{{l,{\text{spoiler}}}} } \right) - \max \left( {c_{{l,{\text{baseline}}}} } \right) = \frac{{2\Delta L_{{{\text{max}}}} }}{{\rho U_{\infty }^{2} {\text{sc}}}}$$

(6)

where s is the span of the spoiler. The experimental uncertainty has been estimated as ± 0.04 for $C_{{L,{\text{max}}}}$ and ± 0.03 for $C_{{M,{\text{max}}}}$ at Re = 20,000, and ± 0.05 for $C_{{L{\text{,max}}}}$ and ± 0.03 for $C_{{M,{\text{max}}}}$ at Re = 10,000.

For validation of the baseline (clean wing), the time-averaged and the maximum lift and moment coefficients are presented in Fig. 4 for reduced frequencies up to k = 3 for α = 15°. The mean data are shown in the left vertical axis, whereas the maximum data, representing the peak values in a plunging period, are shown in the right vertical axis. Note that the scales of the left and right axis are very different. Two plunging amplitudes of A/c = 0.1 and A/c = 0.5 are tested. The present time-averaged lift and moment coefficients for Re = 20,000 are compared with the corresponding data of Chiereghin et al. (2020) for the same Reynolds number and amplitude, and a good agreement is found. The Reynolds number of Re = 10,000 was also tested which enabled us to perform experiments at higher reduced frequencies. The Reynolds number effect seems insignificant in this range. For Re = 10,000, two peaks are observed at around k = 1.3 and k = 2.3 on the mean data for A/c = 0.5 amplitude. Also, there is a local minimum at around k = 1.7, which is due to the interaction of the leading-edge and trailing-edge vortices around this reduced frequency as discussed by Son et al. (2023). For the amplitude of A/c = 0.1, a local peak is observed around k = 1.1. The variation of the lift coefficients and bending moment coefficients is qualitatively similar. Unlike the variation of the time-averaged lift and moment coefficients, the maximum lift and moment coefficients increase monotonically with reduced frequency. As expected, there is virtually no Reynolds number effect in this range.

Fig. 4

Time-averaged and maximum (a) lift and (b) moment coefficients for the clean wing plunging at the mean angle of attack α = 15° and comparison with literature

2.2 Volumetric velocimetry measurements

The three-dimensional velocimetry measurements were performed over the suction surface of the wing. The volumetric three-dimensional velocimetry system (TSI V3V™) was utilized for this purpose. It uses the same techniques developed by Pereira et al. (2000) and Pereira and Gharib (2002) for defocusing digital particle image velocimetry. It is essentially a particle tracking method for which a particle tracking algorithm based on the relaxation method is used (Baek and Lee 1996). This method uses iterations to update the probability of two particles matching between two frames, based on the relative displacements of neighboring particles (Pereira et al. 2006).

In the present experiments, two interrogation volumes were used to capture the vortical structures from the wing-tip to around 20% of the wing-span from the root, with one measurement volume covering approximately 40% of the wing-span. The data for each volume were collected separately because of the need to calibrate for each volume. The processing of the data was also performed separately, interpolating the vectors in each volume. The two volumes were then merged using reference points marked on the wing. The overlap between them is one grid cell which is 4 mm (6% of the chord length), and the merging was performed using linear interpolation.

The water was seeded with 50 μm PSP polyamide seeding particles that were illuminated with an EverGreen2 neodymium-doped yttrium aluminum garnet (Nd:YAG) 200 mJ pulsed laser. The laser beam was converted into a cone before passing through a 45° mirror to project it to the test section. Three 4-megapixel 12-bit CCD cameras with Nikon AF Nikkor 50 mm f/1.8D lenses were used to acquire the images. The calibration was done by focusing the cameras at a calibration plate with regularly spaced grid dots at the center of the test section. Then, the calibration plate was moved through the volume section at 5 mm increments and images were captured at each interval. In the experiments, the images are acquired at instants by 0.125 T (where T is the period) increments in a period for 50 cycles. These images were processed in four steps: particle detection, triplet processing, particle tracking and velocity interpolation to regular grid. This allowed the INSIGHT™ V3V-4G acquisition and data analysis software to obtain three components of the velocity field and then interpolate the vectors using Gaussian weighting. The uncertainty is estimated to be less than 3% of the freestream velocity.

3 Results

3.1 Cut-off frequency

For the static wing with a single spoiler, the changes in the time-averaged (sectional) lift coefficient per span $\Delta c_{{l,{\text{max}}}}$ in Fig. 5a and bending moment coefficient $\Delta C_{{M,{\text{max}}}}$ in Fig. 5b are shown as a function of angle of attack for Re = 20,000. The single outboard and the inboard spoilers are compared to the full-span spoiler on a two-dimensional airfoil (Bull et al. 2020). For angles of attack α ≤ 2° the spoiler acts detrimentally, increasing the lift. This was attributed to the laminar separation bubble at this Reynolds number (Bull et al. 2020) and is not observed at higher Reynolds numbers (Heathcote et al. 2018). Beyond this angle of attack, the lift reduction increases with angle of attack and becomes a maximum around the stall angle. The single inboard spoiler has larger lift reduction than the single outboard spoiler and even the full-span spoiler on the airfoil. This is expected as the finite-span spoiler will generate larger separation regions due to the spoiler-edges. In contrast, the finite-spoiler near the wing-tip does not have the same edge-effect at both ends. The tip vortices induce downwash near the wing-tip region and counteract the effect of the spoiler. As the local sectional lift at the wing-tip will vanish, it is not surprising to see that the total lift reduction is less than that of the inboard spoiler.

Fig. 5

Change of (a) lift and (b) moment coefficients with single spoilers for the stationary wing at Re = 20,000

There is not much advantage of the increased moment arm for the outboard spoiler as the reduction of the bending moment is still less than that of the inboard spoiler. The case of the outboard spoiler is likely to have more nonuniformity of the sectional lift force due to the wing-tip vortex and asymmetric edge effects of the spoiler. This can be seen by comparing the measured bending moment with the prediction using the strip theory. It is assumed in the strip theory that the total lift force is uniformly distributed over the clean wing (which means constant sectional lift per span). For the wing with the spoiler, the same uniform sectional lift per span exists over the wing, except in the part where the spoiler is located. (It is assumed that the effect of the spoiler is limited to the span of the spoiler only.) Hence, the (measured) total lift reduction comes from the spoiler only. In addition, it is assumed that the lift reduction (the difference between the measured lift forces for the clean wing and wing with the spoiler) is uniformly distributed over the spoiler span. Using the measured total lift force reduction and the spanwise location of the mid-span of the spoiler, the strip theory prediction of the bending moment has been calculated and is added to Fig. 5. The discrepancy between the measured bending moment coefficient and the strip theory prediction is larger for the outboard spoiler.

For the inboard spoiler and the baseline wing, Fig. 6 shows an example of the variations of the phase-averaged lift in part (a) and moment coefficients in part (b) as a function of the effective angle of attack (see Eq. (1)) during a plunge oscillation cycle for k = 0.24 and A/c = 0.5 at Re = 20,000. Here, the following angles of attack were selected as α = 5° (pre-stall), 9° (stall), and 15° (post-stall). The effective angle of attack is minimum when the upward plunge velocity is maximum (t/T = 0.75, h = 0), and it becomes maximum when the downward plunge velocity has its maximum magnitude (t/T = 0.25, h = 0) (see Eqs. (1), (2) and the inset in Fig. 3). When the displacement h is maximum or minimum, the effective angle of attack is equal to the mean angle of attack (geometric angle of attack). For this reduced frequency and amplitude, the phase-averaged lift and bending moment become maximum near the maximum effective angle of attack for both wings at all three mean angles of attack.

Fig. 6

(a) Lift and (b) moment coefficients versus effective angle of attack for baseline wing and single inboard mini-spoiler during a plunging cycle for k = 0.24, A/c = 0.5 at Re = 20,000

We considered the effect of added mass on the maximum lift and lift reduction by using the thin airfoil theory for unsteady flows. The theoretical added mass contribution for periodic plunge oscillations was calculated by Karman and Sears (1938). (An alternative approach for the calculation of the added mass contribution is presented by Corkery et al. (2019) using the measured flow field for a flat-plate in transient linear and angular motion.) The theoretical added mass contribution is proportional to the second derivative of plunge displacement (or the first derivative of the plunge velocity). Therefore, the added mass contribution is zero when the plunge velocity is maximum (or when the effective angle of attack is maximum). This means that the added mass effect has zero contribution to the maximum lift force for the case in Fig. 6. In the whole range of plunge amplitude and reduced frequency tested, the peak loads always occur near t/T = 0.25, when the added mass contribution is near zero, as also confirmed by Chiereghin et al. (2019). Therefore, changes to the loads come mostly from the effects of vorticity distribution.

The reduction in the maximum lift and bending moment is observed with the spoiler in all cases, but the maximum reductions are found for the post-stall angle of attack of α = 15°. This is similar to the observations for the two-dimensional spoilers on a nominally two-dimensional airfoil (Bull et al. 2020). In Fig. 6, all cases exhibit some hysteresis which increases with increasing angle of attack. The direction of the lift/moment loops becomes clockwise with increasing angle of attack (and the extent of the separated flows). Only for the pre-stall angle of attack, the direction of the loop is counter-clockwise with small hysteresis, which is known to exist for mildly separated flows.

For the single inboard and the single outboard spoiler, the frequency response of the lift/moment reduction was investigated for α = 5° (pre-stall), 9° (stall), and 15° (post-stall) for A/c = 0.5. The percent change of the lift/moment coefficient reduction normalized by the corresponding maximum lift/moment coefficient of the baseline (clean) wing is shown in Fig. 7 as a function of reduced frequency (see Eqs. (4–6)). These quantities can be considered as the effectiveness of the spoiler in reducing the lift/moment. Generally, the variations of the effectiveness of the lift and moment reduction are similar. For the pre-stall and stall angle of attack, the frequency responses look qualitatively similar. There is maximum effectiveness of the lift/moment reduction at k = 0, followed by a rapid decrease with increasing reduced frequency and remaining small at higher reduced frequencies. The cut-off frequency can be defined as the condition for which the lift/moment reduction crosses zero or remains nearly constant at a much-decreased level for higher frequencies. For the post-stall angle of attack, the local maximum occurs at around k = 0.2, but the decay of the effectiveness with reduced frequency is similar to that at the other angles of attack.

Fig. 7

Lift and moment reduction for plunging wing with single mini-spoilers at Re = 20,000 and A/c = 0.5

There are some similarities of the lift reduction for the finite spoilers and full-span spoilers (Bull et al. (2020). For the two-dimensional full-span case, Bull et al. (2020) showed that lift reduction (or increase) depends on the mean angle of attack, reduced frequency, and amplitude of the plunging motion A/c. It was also suggested that the lift reduction/increase could be correlated with the presence or absence of the roll-up of leading-edge vortices (LEVs). Four types of flow fields are defined based on whether the formation of leading-edge vortex (LEV) is observed for the clean airfoil and with the spoiler. These are Type A (there is no LEV roll-up for the clean airfoil and with the spoiler), Type B (there is LEV roll-up for the clean airfoil, but there is not with the spoiler), Type C (there is not LEV roll-up for the clean airfoil, but there is with the spoiler), and Type D (there is LEV roll-up for both cases). These different types of flow fields determine the regions over which the lift change can be correlated. The loss of effectiveness of the lift reduction at high reduced frequencies on two-dimensional airfoils with full-span spoilers has been discussed by Bull et al. (2020). This is due to the formation of stronger vortices from the clean airfoil at high reduced frequencies and the spoiler losing its effectiveness in the separated flow (corresponding to type D flow in Bull et al. (2020)). The results in Fig. 7 suggest that the same mechanism is in play. The inboard spoiler is more effective than the outboard spoiler at low reduced frequencies.

The reduced frequency of k = 0.24 was selected to examine the flow fields at α = 5°, 9°, and 15° for both single spoilers. These cases are between types A and C (no roll-up of vortex for the clean wing, but borderline case with the spoiler) for α = 5°, and type B (vortex roll-up for the clean wing, but delayed roll-up with the spoiler) for α = 9° and 15° in the 2D classification of Bull et al. (2020). This reduced frequency was chosen for the following reasons. For the pre-stall angle of attack, the lift and moment reductions are considerably decreased for both spoilers at this reduced frequency. For the stall angle of attack, there are still reductions but more for the inboard spoiler, and for the post-stall angle of attack, the lift/moment reductions become maximum. Figures 8, 9 and 10 show the isosurfaces of the Q-criterion (Hunt et al. 1988; Jeong and Hussain 1995), colored by the spanwise vorticity component, to compare the cases of the baseline wing, and with single outboard and inboard spoiler at eight phases in the cycle k = 0.24, A/c = 0.5, Re = 20,000. The positive and negative vortical structures correspond to the vortices shed from the leading-edge and trailing-edge. Here, Q* is defined as Q* = Qc²/U_∞².

Fig. 8

Top views of vortical structures with isosurfaces of Q* = 2 on the baseline case and single spoilers at inboard and outboard locations for the case of α = 5°, k = 0.24, A/c = 0.5, Re = 20,000

Fig. 9

Top views of vortical structures with isosurfaces of Q* = 3 on the baseline case and single spoilers at inboard and outboard locations for the case of α = 9°, k = 0.24, A/c = 0.5, Re = 20,000

Fig. 10

Top views of vortical structures with isosurfaces of Q* = 5 on the baseline case and single spoilers at inboard and outboard locations for the case of α = 15°, k = 0.24, A/c = 0.5, Re = 20,000

For α = 5° in Fig. 8, the baseline case (clean wing) does not exhibit flow separation at the beginning of the cycle (t/T = 0, when the effective angle of attack is equal to the mean angle of attack), while there is mild flow separation at the maximum effective angle of attack (t/T = 0.25). At this instant, the small vortices are visible in the shear layer. In contrast, there is already flow separation over both spoilers at t/T = 0, while smaller separation regions are still visible during the phases the wing moves upwards (t/T = 0.50 to 1.0). The separation region grows in size during the phases of the wing plunging downwards. Inboard of the spoilers, the flows are broadly similar to those of the baseline wing. In Fig. 11, spanwise vorticity contours ($\omega_{z}^{*} = \omega c/U_{\infty }$) in the spanwise plane at the mid-span of the inboard spoiler (z/b = 0.70) are shown at the maximum effective angle of attack (t/T = 0.25) for all three angles of attack. For α = 5°, the clean wing (top row) reveals the weak separation, whereas there is a recirculation region with the inboard spoiler (bottom row). The roll-up of the vorticity is visible at this phase. Although not shown here, in the next phase t/T = 0.375, the center of the recirculation region moves closer to the wing surface and the streamlines appear to reattach near the trailing-edge. It is thought that the formation of the recirculation region and the roll-up vorticity due to the unsteady effects decrease the effectiveness of the lift reduction observed for k = 0. For the static case, it is expected that the spoiler separates the flow, but the shear layer does not roll-up, therefore reducing the loads. This benefit is canceled around the “cut-off frequency,” and the spoiler is not effective for higher reduced frequencies.

Fig. 11

Spanwise vorticity contours and streamlines for the clean wing (top row) and inboard spoiler (bottom row) at t/T = 0.25 for the case of k = 0.24 and A/c = 0.5, Re = 20,000

In contrast, for α = 9° and α = 15°, there is already roll-up of the vortex for the clean wing, which is known to increase the lift. The formation and roll-up of the leading-edge vortex are visible during the downward plunge motion of the cycle. With the spoilers, there is weakening of the formation of the leading-edge vortex. In Fig. 9, for the stall angle of attack of α = 9°, there is no indication of the leading-edge roll-up in the region between the wing-tip and the inboard spoiler during the downward plunge motion. This is thought to reduce the vortex lift (hence the total lift), making the inboard spoiler better than the outboard spoiler (see Fig. 7). The spanwise vorticity contours in Fig. 11 confirm that at the maximum effective angle of attack, the clean wing (top row) reveals the roll-up of the vorticity, whereas the inboard spoiler displaces the roll-up process further away from the wing. For the post-stall angle of attack, these features are more visible (see Fig. 10 for α = 15°). In this case, the stronger leading-edge vortex formation for the clean wing and more significant disruption of the leading-edge vortex due to the inboard spoiler are observed. In Fig. 11, the difference between the strong leading-edge vortex for the clean wing and the displaced vortex roll-up is the most striking between the three angles of attack, resulting in the largest lift/moment reduction at this reduced frequency. These features are very similar to those observed for the full-span spoilers on airfoils (Bull et al. 2020).

3.2 Effect of plunge amplitude

For the inboard spoiler, the lift force and moment measurements were extended to cover A/c = 0.5, 1.0, 1.5, and 2.0. (However, the frequency range is reduced with increasing amplitude due to the limitations of the stepping motor (Turhan et al. 2022).) Figures 12 and 13 show the percent changes in the maximum lift and moment as a function of the reduced frequency (left column) and the Strouhal number based on the peak-to-peak amplitude (right column) for α = 5°, 7°, 9°, 12°, and 15°. The qualitative similarities exist between the lift and moment reductions. For all angles of attack, the “cut-off frequency” beyond which the spoiler is not effective for higher reduced frequencies is observed. We note that, for pre-stall angles of attack and the stall angle of attack, the data for different plunge amplitudes A/c collapse as a function of the reduced frequency. However, for the post-stall angle of attack, we observe the data do not collapse with the plunge amplitude. Conversely, for the pre-stall angles of attack up to the stall angle of attack, the data do not show good collapse with the Strouhal number, and there is much better collapse for the post-stall angle of attack.

Fig. 12

Percent reduction of maximum lift for inboard spoiler for various plunging amplitudes at Re = 20,000

Fig. 13

Percent reduction of maximum bending moment for inboard spoiler for various plunging amplitudes at Re = 20,000

The different scalings in the pre-stall and post-stall regimes with the reduced frequency and the Strouhal number suggest different mechanisms. For pre-stall angles of attack, there is mild separation from the leading-edge or none for the clean wing. Consequently, the Strouhal number (equivalently the Strouhal number and the maximum effective angle of attack) is not the primary parameter. The spoiler induces the forced separation, and the roll-up and the convection of the vortical structures are determined by the reduced frequency. Note that the reduced frequency can be interpreted as a ratio of the advection time of the vortices to travel one chord-length to the plunging period. In contrast, for the post-stall flows, there is already separation from the leading edge of the baseline wing. The strength of the vortices mainly depends on the Strouhal number (equivalently the maximum effective angle of attack). The displacement of the separated shear layer is still enforced by the spoiler; however, the strength of the vortices and its contribution to the vortex lift for the clean wing ultimately determines the lift/moment reduction. This explains why the Strouhal number is the dominant parameter for loads reduction. This will be discussed further together with the data obtained for the multi-spoilers later in the paper.

In the post-stall regime, since the Strouhal number is the dominant factor, the effect of the oscillation amplitude A/c is significant. This is illustrated in Fig. 14 by comparing the A/c = 0.5 and 1.0 cases for k = 0.31 at α = 15° for the inboard spoiler. At this reduced frequency, the case of A/c = 0.5 (type B in the classifications of Bull et al. (2020)) has substantial lift/moment reduction (close to the local maximum), whereas A/c = 1.0 exhibits nearly zero reduction (see Figs. 12 and 13). It is shown in Fig. 14 that, for A/c = 0.5, the spoiler disturbs the formation of the leading-edge vortex over it and effectively breaks into two separate filaments. At early stages, a horse-shoe vortex is shed from the spoiler into the wake. In contrast, for A/c = 1, a stronger leading-edge vortex develops and appears less affected by the spoiler. Following the shedding of the horse-shoe vortex from the spoiler, at the instant of the maximum angle of attack (t/T = 0.25), the shear layer shed from the spoiler helps the formation of a connected leading-edge vortex. These differences in the vortex topology explain why the larger amplitude case is less effective in reducing the lift/moment.

Fig. 14

Top views of vortical structures with isosurfaces of Q* = 5 for A/c = 0.5 and 1.0, single inboard spoiler, α = 15°, k = 0.31, Re = 20,000

3.3 High reduced frequencies

It is clear that at high reduced frequencies, regardless of the mean angle of attack, the spoiler effectiveness becomes small or vanishes. Generally, this is due to the increasing maximum effective angle of attack, which makes the leading-edge vortex development more similar for the clean wing and with the spoiler. This is illustrated for a high reduced frequency (k = 0.94) for the pre-stall angle of attack of α = 5° (between types C and D) in Fig. 15 and for the post-stall angle of attack of α = 15° (type D) in Fig. 16, for A/c = 0.5.

Fig. 15

Top views of vortical structures with isosurfaces of Q* = 3 for baseline wing and with inboard spoiler for α = 5°, k = 0.94, A/c = 0.5, Re = 20,000

Fig. 16

Top views of vortical structures with isosurfaces of Q* = 5 for baseline wing and with inboard spoiler for α = 15°, k = 0.94, A/c = 0.5, Re = 20,000

For the pre-stall angle of attack of α = 5°, the leading-edge vortex roll-up continues during the plunging downwards of the wing. At the lowest displacement (t/T = 0.5), the leading-edge vortex is located at roughly mid-chord of the wing for this high reduced frequency. It reaches the trailing-edge around t/T = 0.75, while the leg of the vortex moves inboard. With the spoiler, the initial flow separation from it during the increase of the effective angle of attack is visible (see t/T = 0.125 and 0.25), but the horse-shoe vortex is shed, leaving the roll-up of the vortex from the wing mostly unaffected. Later at t/T = 0.625 and 0.75, the leading-edge vortices look similar for the clean wing and with the spoiler.

For the post-stall angle of attack of α = 15°, there is slight influence of the spoiler separation on the formation and further evolution of the leading vortex. The shedding of the horse-shoe vortex from the spoiler can be seen best between t/T = 0.25 and 0.5, but at later times the leading-edge vortex shed from the wing reconnects with the horse-shoe vortex. We also note that the leg of the leading-edge vortex remains slightly outboard with the spoiler. Overall, the effect of the spoiler is small at high reduced frequencies regardless of the mean angle of attack. This is due to the increasing strength of the leading-edge vortices from the wing that rapidly rolls-up. Either the leading-edge vortex does not interact with the horse-shoe vortex shed from the spoiler into the wake (for the pre-stall angle of attack) or reconnects with the horse-shoe vortex (for the post-stall angle of attack). In both cases, the leading-edge development seems relatively unaffected by the spoiler.

3.4 Multiple spoilers

As discussed previously, multiple spoilers may increase the effectiveness of the total lift/moment reduction on the wings. It is not only that the total span of the spoilers is increased, but also there is a possibility of increasing the three-dimensionality of the vortex filaments due to the inherent spanwise instabilities. For α = 15°, Fig. 17 compares the effectiveness of one, two, and three spoilers as a function of reduced frequency up to k = 3 at a Reynolds of Re = 10,000. The upper row presents the high amplitude A/c = 0.5 cases in Fig. 17a, and the bottom row presents the low amplitude A/c = 0.1 cases in Fig. 17b.

Fig. 17

Effectiveness of the lift and moment reduction as a function of reduced frequency for one, two, and three spoilers for (a) A/c = 0.5 (top row) and (b) A/c = 0.1 (bottom row), Re = 10,000, α = 15°

The enhanced effectiveness is only limited to the reduced frequencies below the cut-off frequency for both oscillation amplitudes. At higher frequencies, the lift/moment reduction diminishes regardless of the number of spoilers. However, at reduced frequencies below the cut-off frequency, there are cumulative benefits of increasing the number of spoilers. With increasing number of spoilers, maximum lift/moment reduction is possible at optimal reduced frequencies (typical frequency response of spoilers in the post-stall angles of attack as discussed previously). For A/c = 0.5, the highest lift/moment reduction is obtained at k = 0.25 and the reduction increases as the number of spoilers is increased. In Fig. 17, for A/c = 0.5, for reduced frequencies higher than k = 0.5, the spoilers seem not to have a significant impact on maximum force and moment reductions. For A/c = 0.1 (low amplitude cases), the maximum reduction in lift and moment is obtained at k = 0.375. Lift and moment reduction are increased as the number of spoilers is increased, similar to the high amplitude A/c = 0.5 plunging cases. As the cut-off frequency is somewhat larger, there is a wider reduced frequency range of effectiveness of spoilers compared to the A/c = 0.5 cases. The spoilers are contributing to the reduction of lift and bending moment up to k = 1.3.

To illustrate the effects of the oscillation amplitude on the flow fields and to compare the two plunge amplitudes, the case of k = 1 is selected for the three spoilers case. For the amplitude of A/c = 0.1, the change in maximum lift is around 13%, and for the amplitude of A/c = 0.5, the change is around 1.5%. The flow structures represented by the Q-criterion isosurfaces are shown in Figs. 18 and 19 and also compared to the corresponding clean wing cases.

Fig. 18

Effect of three spoilers on the flow structures (Q* = 2) for the case of k = 1, A/c = 0.1, Re = 10,000, α = 15°

Fig. 19

Effect of three spoilers on the flow structures (Q* = 2) for the case of k = 1, A/c = 0.5, Re = 10,000, α = 15°

For the small amplitude A/c = 0.1 in Fig. 18, there is a train of small and weak leading-edge vortices, rather than a single rolled-up vortex for the baseline wing. The coherency of the trains of the weak leading-edge vortices is disrupted by the spoilers. However, the roll-up of the shear layer separated from the spoiler is not strong enough to produce lift-increasing vortices.

For the high amplitude case in Fig. 19, the large leading-edge vortex is stronger for the baseline case compared to the low amplitude plunging case. The spoilers cause the growth of the horse-shoe vortices at t/T = 0.25, which shed as vortex rings at t/T = 0.375. However, soon after this stage, the vortex rings are re-combined with the leading-edge vortex that shed from the leading-region of the wing. The disturbances produced by the spoilers cannot cause significant changes of the leading-edge vortex and resulting forces/moments. On the other hand, the leading-edge vortices are weaker and can be disturbed more easily in the low amplitude case. These results suggest that the effectiveness of spoilers depends on the wing plunge velocity, which we will discuss later in the paper.

Finally, the effectiveness of the lift and moment reduction is presented in Fig. 20 for different spans of the spoilers (0.5c, 1c and 1.5c), corresponding to the different wavelengths of the disturbances generated by the spoilers. The inset of the upper left image shows the spoiler configurations. The ratio of the total spoiler span to wing span is 50% for the smallest spoiler span and 60% for the two other cases. This may have a slight effect on the lift reduction at k = 0, but appears to have very little effect on the shape of the curves and the cut-off frequencies. The largest effect is at k = 0 and very small reduced frequencies. This is because, for these quasi-steady cases, the separated shear layers from the spoiler do not exhibit roll-up of vorticity, reattachment, and recirculation regions over the wing at the post-stall angle of attack of α = 15°. The spoiler span of 1c is the most effective at k = 0. As discussed in the Introduction, the leading-edge vortex filaments exhibit three-dimensional spanwise instabilities with preferred wavelengths. This aspect remains to be investigated further. With increasing reduced frequency, the differences between different spoiler spans decrease before the peak reduction is achieved. With further increases in the reduced frequency, there is virtually no effect of the spoiler wavelength for the large amplitude A/c = 0.5 in Fig. 20a. However, there are minor differences for the small amplitude A/c = 0.1 in Fig. 20b for low reduced frequencies. The shapes of the variation of the effectiveness of the lift/moment reduction are similar for a given oscillation amplitude, and the cut-off frequency is unaffected by the wavelength of the spoilers. The peak effectiveness of lift/moment reductions is obtained at k = 0.25 for A/c = 0.5 and k = 0.375 for A/c = 0.1. Note that these peaks are the same for one, two, and three spoilers (each having 1c span) shown in Fig. 17.

Fig. 20

Effectiveness of the lift and moment reduction for varying spoiler wavelength, for (a) A/c = 0.5 (top row) and (b) A/c = 0.1 (bottom row), Re = 10,000, α = 15°

In Fig. 21, first, we compare the flow fields for these spoiler configurations for the small-amplitude A/c = 0.1 at the peak lift/moment reduction (k = 0.375) at which there are diminishing differences between the spoiler configurations. The vortical structures around the baseline case and the wings with spoilers are presented in Fig. 21. The separated shear layers from the spoilers do not form coherent vortices and cannot increase the lift. For the 1c spoiler span, two arch-type vortices are visible at the instant t/T = 0.250 when the maximum plunging velocity is achieved. We do not observe the arch-type vortical structures for the spoilers of 0.5c span. Nevertheless, these differences do not cause significant changes in the effectiveness of the spoiler configurations examined. For all cases, there is a local maximum of the lift/moment reduction effectiveness.

Fig. 21

Effect of spoiler span on the flow structures (Q* = 2) for the case of k = 0.375, A/c = 0.1 at Re = 10,000, α = 15°

In contrast, in Fig. 22, for k = 1 and A/c = 0.5, the leading-edge vortex is much stronger for the baseline (clean) wing. With different spoilers, the disturbances introduced to the leading-edge vortices are visible during the plunging down but appear to be reconnected to the vortices during the plunging up motion. As the leading-edge vortices are much stronger (due to the larger plunge velocity), the spoilers cannot disrupt the strong leading-edge vortices. Consequently, the maximum lift and moment are not significantly affected.

Fig. 22

Effect of spoiler span on the flow structures (Q* = 2) for the case of k = 1, A/c = 0.5 at Re = 10,000, α = 15°

In Fig. 23, we attempt to summarize the cut-off frequency as a function of mean angle of attack for different oscillation amplitudes. The corresponding cut-off reduced frequency ($k_{{{\text{cut-off}}}}$) in Fig. 23a and cut-off Strouhal number (${\text{St}}_{{{\text{cut-off}}}}$) in Fig. 23b are plotted. Each oscillation amplitude A/c is shown with a different symbol. Multiple spoilers (red), single inboard spoiler (black), and single outboard spoiler (blue) are colored separately. The Reynolds number cases of Re = 10,000 and 20,000 are differentiated by the open and filled symbols. In addition, the full-span spoiler case for the nominally two-dimensional airfoil (Bull et al. 2020) is included for comparison (colored orange and connected with solid lines). There is a good collapse of all data with $k_{{{\text{cut-off}}}}$ at pre-stall angles of attack, but the scatter increases with increasing mean angle of attack. The data collapse is not as good for the cut-off Strouhal number ${\text{St}}_{{{\text{cut-off}}}}$ at small angles of attack, but there is better collapse at the post-stall angles of attack (relative to the pre-stall angles of attack), with the exception of the lowest oscillation amplitude A/c = 0.1. The opposing trends displayed with the reduced frequency and the Strouhal number are somewhat counter-intuitive as the Strouhal number represents the maximum plunge velocity. This is because flow separation and vortex formation are expected to depend on the magnitude of the plunge velocity.

Fig. 23

(a) Cut-off reduced frequency and (b) Strouhal number as a function of mean angle of attack, Re = 10,000 (open symbols), Re = 20,000 (filled symbols), inboard spoiler (black), outboard spoiler (blue), multiple spoilers (red), full-span spoiler on airfoil (orange, Bull et al. 2020)

The differences in the scaling of lift reduction for the 2D and 3D spoiler cases cannot be attributed only to the difference in the geometry as the amplitude A/c range for the 2D and 3D spoilers is different. The only common amplitude between the 2D and 3D spoilers is A/c = 0.5. Between the 2D and 3D spoilers, both of the scaling parameters (k, St) agree very well for A/c = 0.5 at pre-stall angles of attack, but less so at post-stall angles of attack. As the agreement between the 2D and 3D spoilers is reasonable for A/c = 0.5, this figure can also give an indication of the effect of amplitude A/c. It is seen that, for the cut-off reduced frequency shown in Fig. 23a, the effect of the amplitude A/c is relatively small at α = 5°, but becomes substantial with increasing mean angle of attack. In contrast, for the cut-off Strouhal number shown in Fig. 23b, the scatter for varying amplitude A/c is the largest at α = 5° and decreases with increasing mean angle of attack. Figure 23a also suggests that, for A/c > 0.5, the cut-off frequency becomes roughly constant with amplitude and mean angle of attack.

Clearly, both the reduced frequency and the Strouhal number determine the effectiveness of spoilers. Nevertheless, for pre-stall angles of attack, separation from the baseline wing is mild and forced separation from the spoiler appears to depend on the reduced frequency. This implies that the travel time of the vortices from the wing leading edge to the trailing-edge is more important. On the other hand, for the post-stall flows, there is already vortex formation from the plunging baseline wing. The strength of the vortices, dictated by the magnitude of plunge velocity, determines the relative ratio of the amplitude of spoiler-induced disturbances to the vortex strength. This results in a better collapse of the data at post-stall angles of attack. The trends displayed by spoilers, regardless of the number of spoilers, spanwise location, or Reynolds number are similar.

An even more interesting conclusion is that the data for the finite-span spoilers agree well with the data for the two-dimensional case (full-span spoiler on airfoil). This observation suggests that the frequency response of the effectiveness of finite-span spoilers is governed by the mostly two-dimensional mechanisms. The similarities of the results between the 2D and 3D spoilers are found in both the force and flow field measurements: the lift reduction of stationary wings as a function of angle of attack (Fig. 5), the shape of the frequency response curves (Figs. 7, 12, 17, 20), the cut-off frequencies (Fig. 23), and the two-dimensional slices of the flow fields (Fig. 11).

4 Conclusions

This experimental work investigates the effectiveness of lift and bending moment reduction on a plunging wing, which simulates a gust or turbulence encounter, unsteady maneuver, or aeroelastic bending deflections. For nominally two-dimensional airfoils, the effectiveness of forced separation for lift/moment alleviation in steady freestream as well as on plunging airfoils has been known, although the unsteadiness results in limitations at high frequencies and amplitudes of the oscillations. In this study, we examine finite-span mini-spoilers placed near the leading edge on a plunging finite wing in order to understand the effects of three-dimensionality and unsteady wing motion. Single, multiple, and spanwise periodic mini-spoilers located at various spanwise locations were studied in water tunnel experiments.

For single finite-span mini-spoilers, regardless of the mean angle of attack, there is significant decay of the effectiveness of the lift and bending moment reduction. For low reduced frequencies, the inboard spoiler is more effective than the outboard spoiler, similar to the static wing cases (k = 0). Above a cut-off reduced frequency, the effectiveness is lost substantially. For pre-stall mean angles of attack, the decreasing effectiveness is related to the roll-up of the shear layer separated from the spoiler developing into a recirculation region just behind the spoiler. With increasing mean angle of attack, at high reduced frequencies and amplitudes (high Strouhal numbers based on the peak-to-peak amplitude), the leading-edge vortices become stronger for the clean wing. This makes the development of the leading-edge vortices more similar for the clean wing and with the spoiler and makes the spoiler less effective. Below the cut-off frequency, the spoiler may delay or displace the shear layer away from the wing surface, resulting in maximum effectiveness. These features are similar to those over two-dimensional airfoils and full-span spoilers, suggesting that the same mechanisms exist. The data for the effectiveness of the lift/moment reduction for pre-stall angle of attack scale with the reduced frequency, whereas for the post-stall angles of attack the data scale with the Strouhal number because the strength of the vortices for the clean wing depends on this parameter.

At post-stall angles of attack, there are cumulative benefits of increasing the number of spoilers, but only below the cut-off frequency. The qualitative shape of the frequency response of the lift/moment reduction is similar to that of the single spoilers. The cut-off frequency remains the same regardless of the number of spoilers. The unsteady flow fields generated by the multiple spoilers have broad similarities to those of the single spoilers in terms of the effects of frequency and amplitude. Varying the span of each spoiler (and the wavelength) has small impact on the effectiveness. Both the shapes of the frequency response and the cut-off frequency are unaffected. Again, the flow fields reveal that, similar to the case of a single spoiler, the lift/moment reduction effectiveness depends on the Strouhal number at the post-stall angle of attack.

The cut-off frequency exhibits good collapse with $k_{{{\text{cut-off}}}}$ for single and multiple spoilers as well as full-span spoilers, and for varying mean angle of attack and oscillation amplitude at two different Reynolds numbers (except for the lowest amplitude case). The agreement with the full-span spoilers on airfoils suggests that two-dimensional mechanisms are dominant. For pre-stall angles of attack, for which there is mild separation for the clean wing and forced separation from the spoiler, the dominant parameter is the reduced frequency rather than the Strouhal number. The scatter of the $k_{{{\text{cut-off}}}}$ data increases at the post-stall angles of attack for which the Strouhal number becomes a better scaling parameter. Because the strength of the leading-edge vortices from the baseline wing mainly depends on the Strouhal number, whereas the spoiler-induced separation becomes less important.