Modern wind turbines are following a trend of increasing rotor diameters . Recently deployed offshore wind turbines have blades of more than 100 m in length, such as the Siemens Gamesa SG 14-222 turbine with a blade length of 108 m and the Vestas V236 turbine with a blade length of 115 m. This trend is driving blade sections being made from thicker airfoils to ensure structural integrity and to balance the aero-structural loads, as seen in the newest reference wind turbines such as the IEA 15 MW and 22 MW turbines . These thicker airfoils are more prone to flow separation, with the consequent loss of lift decreasing the annual energy production and the fatigue lifetime of the blades . The use of vortex generators (VGs) as passive flow control devices has become a common practice in wind turbine design . Vortex generators are also being used to mitigate the effects of leading-edge erosion and are being retrofitted on existing turbines to partly restore original performance .

Unsteady aerodynamics around the blade sections is becoming increasingly important in the design of large wind turbine blades. The occurrence of cyclic variations in the angle of attack on rotor blades leads to the flow detaching and reattaching on the blade sections as the local angle of attack moves above and below the static stall angle. This phenomenon is referred to as dynamic stall. Early investigations such as , , , and studied dynamic stall in the context of helicopter rotor blades. In the context of wind turbines, measurements from the NREL Combined Experiment were one of the first to show the occurrence of rotating wind turbine blades. showed that dynamic stall occurred on operational wind turbine blades upon cyclic variations of the local angle of attack due to yaw misalignment. further investigated the occurrence of dynamic stall on wind turbine blades and pointed to reasons such as yaw misalignment, fluctuating wind speed and direction, and tower shadow for the occurrence of dynamic stall. Dynamic stall on wind turbine blades can lead to cyclic load variations and higher loads on the blade. showed that dynamic stall on wind turbine blades increases the chances of fatigue failure and reduces turbine lifetime. have shown that the coupling of pitch motions with structural vibrations can lead to negative aerodynamic damping in the edgewise direction and positive damping in the flapwise direction. Negative damping imparts energy into the structural vibrations, causing uncontrolled growth of the vibrations and rapid failure.

At the airfoil level, the unsteady flow variations leading to dynamic stall are experienced as time-varying motions such as pitching and plunging, which lead to cycles of flow detachment and reattachment. The works of , , , and detail the various flow phenomena occurring during dynamic stall. For an airfoil undergoing pitch oscillations, list three kinds of stall based on the occurrence and propagation of flow separation during the pitch cycle: leading-edge stall, trailing-edge stall, and mixed stall. Leading-edge stall is said to occur when flow separation first appears near the leading edge and moves towards the trailing edge with increasing angle of attack, while trailing-edge stall is said to occur when the separation front moves from the trailing edge towards the leading edge with increasing angle of attack. Mixed stall usually occurs either when separation fronts originating from both the leading and trailing edge move towards each other and merge somewhere near mid-chord, or when the separation front originates in the middle of the airfoil and moves both in leading-edge and trailing-edge directions. Trailing-edge stall is the most common type of turbulent stall for thick airfoils, typical of inboard and midboard wind turbine blade sections, and is also the type of stall observed on the airfoil section used in this work. When the unsteady angle of attack exceeds the static stall angle, flow reversal starts at the trailing edge and spreads upstream over much of the airfoil chord. At a certain angle of attack, the separated flow reaches a critical point and a strong vortex called the leading-edge vortex (LEV) forms near the leading edge and starts convecting downstream towards the trailing edge. The lift keeps increasing with increasing angle of attack during this process. Dynamic stall is observed when the LEV convects past the trailing edge into the wake.

shows that dynamic stall causes the integrated aerodynamic forces on a rotating wind turbine blade section to deviate significantly from the static characteristics of the airfoil section. show that the local pressure distributions on a wind turbine blade airfoil section differ significantly from the static pressure distributions during dynamic stall. The pressure and flow measurements presented by , , , , and , among many others, on several airfoils undergoing pitch oscillations show that the changed flow characteristics during dynamic stall lead to significant differences in the steady and unsteady pressure distributions, boundary layer characteristics, and flow separation behaviour. Since VGs control flow separation through energizing the boundary layer with streamwise vortices, the difference between steady and unsteady boundary layer characteristics around a pitching airfoil creates the need to investigate the behaviour of VGs in unsteady conditions.

The impact of VGs on the steady aerodynamic performance and flow around wind turbine blade sections has been well studied in detail in the past. We point readers to the works of and for detailed reviews on the use of VGs for steady flow separation control. Vane-type VGs are the most commonly used VG type for flow separation control on wind turbine blades. On wind turbine blades, VGs are designed to delay the stall onset and increase maximum lift of the airfoil section, while minimizing the drag increase caused by the presence of the VGs. The works of , , and , among others, have investigated a wide range of VG configurations varying different geometric parameters such as vane height, spacing, angle, and chordwise location on the airfoil, studying the impact of these parametric variations on the steady performance using the aforementioned lift, drag, and stall metrics. All these studies concluded that the vane height is the most critical geometrical parameter affecting VG performance. Other parameters like vane spacing and vane inclination, have a significantly smaller impact than vane height. This follows from the fact that the strength of the streamwise vortices that energize the boundary layer and delay flow separation under adverse pressure gradients is proportional to the vane height, as shown by and , among others. However, larger vane sizes also increase the drag caused by the VGs due to their increased surface area. Thus, designers seeking to optimize VGs designs make a trade-off between using larger vanes to delay stall to a higher angle of attack, and using smaller vanes to limit the drag increase. As solutions to this trade-off, low-profile VG designs aiming to reduce drag while maintaining the stall delay benefits have also been proposed in the past by works like , .

Besides the vane size, literature is also divided on the best vane shape for vane-type VGs. Most literature compares triangular and rectangular vanes. recommend choosing triangular vanes over rectangular vanes due to their lower drag penalty for the same size. However, show that rectangular vanes produce a higher maximum lift and lower skin friction coefficient than triangular vanes of the same size. The lower skin friction coefficient especially should lead to lower drag and is thus a finding contrary to the work of . also show that rectangular vanes generally produce a higher lift-to-drag ratio, but some configurations may perform poorly due to higher drag. The differences in performance between triangular and rectangular vanes in different studies create an additional variable leading to uncertainty in the optimal VG design.

The impact of VG designs on unsteady airfoil aerodynamics has been primarily studied through numerical simulations using computational fluid dynamics (CFD). Typically for unsteady studies, VGs have been designed based on steady-state performance, with the assumption that the performance in unsteady conditions would be similar. In recent work, studied the effect of single and double-row VGs on the lift drag and moment characteristics of an NREL S809 airfoil undergoing pitch oscillations using URANS simulations. extended the same investigation to combine the effect of leading-edge roughness and VGs using URANS simulations and equivalent sand grain roughness models. Both of these studies based their VG designs on guidelines established through steady investigations from the work of and . Experimental studies focussing on the effect of VGs on unsteady aerodynamic characteristics are challenging to conduct, since they require matching both the high chordwise Reynolds numbers and high degree of unsteadiness at which modern wind turbine blades operate. Representative dynamic stall tests thus require operating at high angles of attack with high wind speeds and high pitching frequencies, which can generate enormous loads, making safe operation of experimental setups a challenge. These experimental studies have also used VGs designed for optimal steady performance due to the limited prior experimental data on unsteady conditions, including VGs. The authors of this paper have also based their VG design used in a previous experimental work on the optimal VG design proposed by the steady investigations of , with the assumption that the steady optimal VG design will hold true for unsteady investigations as well. This previous investigation focussed on the ability of VGs to counteract the performance loss on a pitching airfoil due to leading-edge erosion (simulated via forced transition with a zigzag tape) when the airfoil is passing through various phases of dynamic stall. This paper will instead focus on investigating various VG designs in both steady and unsteady conditions, with the objective of verifying the assumption that steady and unsteady performance of all VG designs will be similar. The test conditions in this paper are also different from in covering a wider range of unsteadiness regimes and to ensure transition to turbulence far upstream of the VGs so that the effects discussed in this work can solely be attributed to VG design variation.

The simulations of on the NREL S809 airfoil with VGs show that VGs bring about a sharp decrease in the phase-averaged lift coefficient when the airfoil starts to pitch down from the maximum angle of attack and also slow down the reattachment process near the minimum angle of attack. Moreover, the phase-averaged Cp distributions indicate the presence of a stall vortex that oscillates near the trailing edge. Similar behaviour is also observed in the phase-averaged pressure distributions from the simulations of on the same airfoil and VG combinations with forced transition added and from the experimental results of on a NACA 0012 airfoil with VGs. These results indicate that the interaction between the stall vortex and the streamwise vortices generated by the VGs may lead to complex unsteady flow separation behaviour that is lost when the results are phase averaged.

In this work, we conduct wind tunnel experiments on a DU-97-W-300 airfoil section equipped with different VG configurations undergoing pitch oscillations. The DU-97-W-300 airfoil has a maximum thickness-to-chord ratio of 30 % and was designed for wind turbine root sections . Several reference wind turbines such as the DTU 10 MW , AVATAR , IEA 15 MW , and IEA 22 MW use an airfoil of 30 % thickness-to-chord ratio for inboard and midboard sections where the positive stall angle of attack and the aerodynamic efficiency (lift-to-drag ratio) are important design criteria. The tested VGs are thus optimally designed for stall delay and lift-to-drag ratio for steady conditions.

First, we focus on varying the vane height of the VGs to study whether vanes smaller than the local boundary layer height generally recommended by literature for steady applications can prevent unsteady flow separation during pitch oscillations. Second, we also compare rectangular and triangular VG vane shapes to investigate which design can better prevent flow separation in unsteady conditions.

The lift and drag characteristics of the airfoil without VGs in free and fixed transition for a Reynolds number of 1 million are shown in Fig. . As mentioned in Sect. , the static stall angle of attack, maximum lift coefficient, and lift-to-drag ratio are typically considered the important aerodynamic performance metrics for airfoils used in inboard and midboard sections of wind turbine blades where VGs are typically placed. In free transition, the airfoil stalls at around a 16° angle of attack with a maximum lift coefficient of about 1.6. The aerodynamic efficiency (lift-to-drag ratio) peaks at around a 14° angle of attack. When transition to turbulence is fixed at 5 % chord, the airfoil stalls earlier around a 9° angle of attack, with the maximum lift coefficient reduced by nearly 40 % to 0.95, displaying a strong sensitivity to leading edge roughness.

In the presence of VGs, the lift polars in Fig. a show VGs delaying stall to a higher angle of attack. As expected from the literature , the larger the vane height, the stronger the vortices and the greater the stall delay and maximum lift. The increasing frontal area of the larger VG vanes brings a higher drag penalty due to larger vanes even when flow is attached over the airfoil, as seen in Fig. b. However, since the drag increases drastically when flow separates, the smaller vanes provide a higher peak lift-to-drag ratio but only over a narrow range of angles of attack, while the larger vanes provide a slightly lower peak lift-to-drag ratio but over a wider range of angles of attack, as seen in Fig. c. Of the three sizes of triangular vanes tested, the 5 mm VGs provide the best compromise between significant stall delay from the no-VG case, a high maximum lift, and a lower added drag.

Rectangular vanes of 10 mm vane height delayed stall further than triangular vanes of the same size. The rectangular vanes were also observed to generate lower drag when flow is attached. This led to rectangular vanes producing a significantly higher lift-to-drag ratio than triangular vanes of the same size, and even matching the peak lift-to-drag ratio from the smallest triangular vanes. To understand this behaviour, the flow separation characteristics over the suction side of the airfoil was compared for the different vane heights and shapes, by examining the flow separation location (determined as described in Appendix ) with increasing angle of attack in Fig. . In the no-VG case, trailing-edge flow separation gradually progresses upstream towards the leading edge with increasing angle of attack. The airfoil stalls when the separation front reaches slightly upstream of 40 % chord. With the addition of VGs, flow separation starts at a higher angle of attack. With the smallest 2.5 mm VGs, the separation front moves upstream at a slower rate than without VGs until the stall angle of attack of 10°, indicating energization of the boundary layer by the streamwise vortices from the VGs. At stall, the separation front moves upstream at a much faster rate, unlike the gradual upstream migration in the no-VG case. Trailing-edge separation appears at a higher angle of attack with VGs of increasing vane height. However, the larger the VG vane, the more abrupt the upstream migration of the trailing-edge separation front, leading to stall. The rectangular VGs both delay the appearance of trailing-edge separation and slow down the upstream migration of the separation front than triangular VGs of the same size. The separation front remains downstream of the VG location (x/c=0.3), up to a higher angle of attack than with the triangular VGs.

The steady measurements indicate that rectangular vanes whose height is larger than the boundary layer height at the VG placement location are the best VGs for delaying both the appearance and the upstream progression of trailing-edge flow separation. As a result, the rectangular vanes provide the largest stall delay, the highest maximum lift, and the highest lift-to-drag ratio before stall among the compared VG configurations. This result is contrary to the conventional recommendation in literature that low-profile VG designs with vane heights smaller than the local boundary layer thickness provide the best compromise between maximizing stall delay and lift-to-drag ratio. The higher lift-to-drag ratio also runs counter to the common practice in wind turbine applications of using triangular rather than rectangular vanes, due to the perceived lower drag penalty of triangular vanes. The slower upstream progression of trailing-edge separation with rectangular vanes indicates that they energize the boundary layer more effectively than triangular vanes. This result calls for future measurements of airfoil boundary layers at high angles of attack in the presence of triangular and rectangular vanes to better understand the differences in streamwise vortices and turbulent boundary layer interactions for each vane shape.

For the dynamic cases, we use the normal force coefficient polar and the spatio-temporal evolution of the suction side (upper surface) flow separation location to investigate the development of the trailing-edge separation front and the unsteady aerodynamic loading on the airfoil.

The existence of different paths in the normal force coefficient polar and the trailing-edge separation front progression for the 5 and 10 mm triangular VGs points to the existence of cycle-to-cycle variations due to insufficient energization of the boundary layer by the VGs. This insufficient energization makes the flow around the airfoil susceptible to separation. Not only does this delay reattachment over the airfoil surface, lowering the aerodynamic performance, but the constant switching between attached and separated states also lowers the fatigue lifetime of the blade section due to the cycle-to-cycle variance. The number of cycles following the late reattachment path for each VG design is presented in Fig. . To quantify the number of late reattachment cycles, we calculate the percentage of cycles where flow over the airfoil is separated at x/c=0.5 at a 10° downstroke angle of attack. As we observed in Sects.  and , it is only in the late reattachment cases that the separation front goes beyond x/c=0.6. A 10° downstroke lies between the reattachment angles of the early and late reattachment paths for all VGs, making it a suitable angle for this comparison. Note that the early and late reattachment paths are only observed for the 5 mm triangular, 10 mm triangular, and 10 mm rectangular VG cases. Thus, the number of separated cycles for these cases represents the cycles where the VGs fail to prevent upstream propagation of the separation front, resulting in the late reattachment path. For the no-VG and 2.5 mm triangular VG cases, the flow separation map and normal force coefficient polar follow only one path, and hence nearly 100 % of the cycles are separated. In Sect.  and , we discuss the implications of the number of cycles with late reattachment for different VG designs for unsteady flow separation and dynamic stall control.

One of the central recommendations of this paper is that VGs selected for unsteady flow control during pitching motions should have a vane height larger than the local boundary layer thickness for as much of the pitching angle of attack range as possible. The reference used for this is the steady no-VG boundary layer thickness at the VG chordwise location calculated using RFOIL. While RFOIL calculations come with their own uncertainties quantified in the literature , using the steady no-VG boundary layer thickness as a reference for preliminary VG vane height selection also comes with limitations. During pitching motions, the flow around the airfoil depends on various factors like the phase of motion (upstroke or downstroke) and the pitching frequency which leads to how the flow responds to the motion. Cycles of flow separation and reattachment due to the pitching motion can cause the instantaneous boundary layer thickness and its unsteady characteristics to deviate from the steady characteristics calculated from RFOIL. This can cause the exact range of angles of attack in the pitching cycle where the vane height is larger than the local boundary layer thickness and can deviate from the range presented in this work. In an attempt to provide practical VG design recommendations while overcoming this limitation, our analysis is statistical in nature. We base our comparisons of VG vane height and shape on their impact on the percentage of separated and attached flow cycles. The greater the range of angles of attack in the pitching cycle where the vane height is larger than the local boundary layer thickness, the greater the likelihood of preventing flow separation during the pitching cycle. Overall, the recommendation of this paper is to use larger rectangular VGs considering the need for unsteady flow separation control, even when smaller triangular VGs may prove sufficient for steady flow control.

Some other uncertainties in the data arise from the measurement setup itself. Particularly for the unsteady results, we base our analysis on quasi-2D chordwise pressure coefficient distributions. The angled placement of the pressure ports (described in Sect. ), which covers the spanwise length of at least one VG pair for every VG design tested, can average over the spanwise periodic flow variations caused by the vortices from the counter-rotating VGs. However, unsteady trailing-edge separation is 3D and the spanwise variation in flow due to separation cannot be covered by the pressure ports. This can lead to some uncertainty in predicting the exact chordwise location of the separation front from the measured pressure data. The relatively low aspect ratio of the wing section means that the boundary layer growing on the top wall of the wind tunnel can also introduce spanwise variation in the flow, affecting the pressure measurements. These sources of uncertainty mean that the conclusions of this work should rather be interpreted in the context of the general trends in the flow separation behaviour and aerodynamic polars in presence of different VG designs.

Past literature and industrial practice on designing vortex generators for wind turbine blades have assumed that the optimal VG designs for steady conditions will also perform optimally in unsteady conditions. This paper presents arguments against that hypothesis by showing that VGs which prevent steady flow separation can still allow unsteady flow separation in a significant portion of the pitching cycles. Variations in the onset and progression of separation lead to significant variations in aerodynamic loads between cycles, which can reduce the fatigue lifetime of the blade section and detrimentally impact the aerodynamic damping on structural vibrations. To demonstrate this, we use wind tunnel measurements in the TU Delft Low Speed Tunnel on a DU-97-W-300 airfoil section, a typical representative in terms of aerodynamic performance of midboard and inboard sections of modern wind turbines, equipped with various VG array designs. The airfoil is subjected to pitching motions that pitch the airfoil above and below the static stall angle of attack in the presence of VGs with various pitching frequencies for 150 pitching cycles. A transition to turbulence is fixed using zigzag tape close to the leading edge to simulate the effect of leading-edge erosion often experienced in wind turbine blades where VGs are used. The forces on the airfoil are calculated using surface pressure measurements (and wake rake measurements for the steady cases). The VGs were fixed at a 30 % chordwise location to simplify the test matrix, also owing to the fact that a 30 % chord has been shown to be the most effective VG location for this airfoil. The results of VG design selection are contextualized with local steady boundary layer development with increasing angle of attack to translate the results to other VG placement locations not covered by this study. Primarily, the VG vane size and vane shape have been varied to investigate their impact on steady and unsteady flow separation control and the onset of static and dynamic stall.

In steady conditions, triangular vane VGs followed the expected trend from the literature, where both the angle of attack of trailing-edge separation onset and the added drag simultaneously increase with vane height, resulting in the selection of an optimal vane height to balance the trade-off between delayed stall and a high lift-to-drag ratio. In this study, the VGs with vane height approximately equal to the local boundary layer thickness at 0° angle of attack (i.e. the 5 mm vanes) provided this optimal balance. However, when considering both vane height and vane shape, rectangular vane VGs whose vane height is larger than the local boundary layer thickness at a 0° angle of attack (i.e. the 10 mm vanes) outperformed all other VG designs by both delaying trailing-edge separation onset (and hence static stall too) and producing a smaller drag penalty than even the smallest triangular VGs tested. This is contrary to recommendations from literature to opt for low-profile triangular VGs, and indicates that rectangular vane VGs overall energize the boundary layer more effectively than triangular vane VGs.

When pitching, only VGs whose vane height exceeds the local boundary layer thickness for a significant portion of the pitching cycle (i.e. the 10 mm vanes in this study) energized the boundary layer enough to significantly delay the onset of trailing-edge flow separation and prevent upstream propagation of the separation front (thus preventing dynamic stall) for more than 90 % of the pitching cycles at all pitching frequencies. The smaller 5 mm vanes, whose boundary layer energization was considered sufficient in steady conditions to optimally balance static stall delay with lift-to-drag ratio, could only prevent flow separation for 75 % of the cycles at the lowest pitching frequency, resulting in two distinct flow separation maps and two distinct paths of early and late reattachment in the normal force coefficient polars. For 25 % of the pitching cycles, flow separated over a significant portion of the airfoil surface to cause a large drop in the normal force coefficient. These large variations between cycles can detrimentally impact the aerodynamic damping on structural vibrations and reduce the fatigue lifetime of the blade section. The overall results show that the greater the chance that the vane height exceeds the local boundary layer thickness during the oscillation cycle, the more effective the boundary layer energization and the more likely that trailing-edge separation and large variations in aerodynamic loads can be prevented. Rectangular vanes proved the best at preventing trailing-edge separation at all pitching frequencies and were the only VG design to prevent flow separation for all pitching cycles, regardless of pitching frequency. This indicates that rectangular vanes overall energize the boundary layer more effectively than triangular vane VGs. Finally, motions of faster pitching frequencies were less sensitive to the choice of VG vane size, since the larger lag between flow and airfoil motion ensured a lower tendency for flow separation and a higher tendency for faster reattachment if flow does separate.

Overall, the conclusions of this paper highlight the importance of designing VGs that keep unsteady flow conditions under consideration. The importance of longer measurement durations spanning numerous pitching cycles to capture the significant variations between cycles is also emphasized. The findings of this paper can serve as a basis for choosing more optimal VG designs to prevent unsteady flow separation for wind turbine blades facing dynamic stall. The presented results also motivate the need for further research of the interaction of streamwise vortices generated by VGs of different geometries with the trailing-edge separation front and the dynamic stall vortex through flow field measurements that can resolve these complex interactions. Finally, the dataset associated with this paper and the larger experiment are also intended to aid with the validation and development of numerical models for airfoils with VGs undergoing dynamic stall. A deeper understanding of the impact of VGs on the unsteady aerodynamic characteristics of wind turbine blade sections and the underlying flow interactions will help to create more accurate numerical models to aid in the optimal design of VGs for modern wind turbines. This will lead to the smarter deployment of these flow control devices for improved performance and lifetime of wind turbine blades.