Computational Modelling of Control of Laminar Separation Bubble over an Airfoil Using an Integrated Tubercle and Vortex Generator

1  Introduction

A wind turbine generally operates at low chord-based Re numbers and different angles of attack. The viscous flow at low Reynolds numbers can cause leading-edge separation or stall over an airfoil [1–4]. Separation and leading-edge stall phenomena can cause undesired effects, resulting in decreased aerodynamic performance at a level that reduces lift coefficients. and increased fatigue loads damaging the structure of the wings [5–9], with higher noise levels disturbing the environment and reduced energy outputs [10,11]. To mitigate these adverse effects, various flow control mechanisms have been investigated numerically with Large Eddy Simulation (LES) and Reynolds Averaged Navier Stokes (RANS) models [6,7]. Besides, other numerical methods, including the ABC algorithm, were also performed to enhance the aerodynamic performance of airfoils [8–11]. Furthermore, different flow control strategies were applied as protrusion shapes and some acoustic techniques [12–14]. Recently, in computational modelling and experimental studies, bio-inspired solutions such as tubercles [15], dimples [9], serrations [16], grooves [17], flexible materials [18], and bionic airfoils [19–21] have been preferred as flow control techniques. Due to experimental challenges, numerous alternative flow control methods have been successfully studied using computational modelling techniques. These numerous numerical studies conducted with Large Eddy Simulation (LES) and Reynolds Averaged Navier Stokes (RANS) models [6,7] and flow control strategies [21–23] have shown that flow improvements can be achieved through the use of biomimetic designs. Compared to other passive flow control techniques, vortex generators are more frequently utilized because of their straightforward design and reduced operation cost [22,23].

Biomimetics is the study of replicating and imitating the characteristics of living organisms to apply them to engineering issues. In terms of numerical and experimental aerodynamic studies, these methods could be investigated for owls [24], the flight of butterflies [20,25,26], seagulls [25], tubercles [26], and humpback whales [27]. Swallowtail butterflies, characterized by their tail-like projections, exhibited increased aerodynamic performance, resulting in enhanced lift and reduced drag forces [20]. Flow can be controlled with leading-edge serrations (bioinspired grooves) by damping the adverse effects on the airfoil/wings [28–31]. Other types of bionic airfoils and tubercle structures were also investigated, and the breaking down of laminar separation bubbles (LSB) was observed [32,33]. Bio-inspired aerodynamic strategies have proven effective in enhancing performance and reducing flow-induced losses. Wang et al. [34] showed that leading-edge serrations and helical blade geometries improve the efficiency of vertical axis wind turbines, while Jaworski and Peake [35] demonstrated the noise-mitigation potential of poroelastic edges. Furthermore, Bechert et al. [36] and Sagong et al. [37] reported substantial skin-friction drag reductions using riblet-based and fish-inspired surface modifications.

The flow control techniques could be categorized into two classes: (i) active [38] and (ii) passive [39] control methods. These days, active control methods have started to lag behind passive ones, as they consume external energy. Moreover, the passive flow controllers are relatively simple in terms of their implementation. Several of those passive ones are referred to as employing riblet [34–37], taking into account dimples [9] and grooves [28–30], considering bio-inspired methods utilizing vortex generators (VGs) [22,23,40–42], performing leading-edge slats [43], using slits [44] and control rods [45].

Among the various passive flow control techniques observed in humpback whales, the bio-inspired leading-edge tubercles are rounded protuberances that have the capacity to enhance their power output compared to traditional straight leading-edge blades. A greater momentum transfer occurs within the boundary layer with the help of these surface shapes compared to their uncontrolled counterparts. Although formations of adverse pressure gradients (APGs) exist, this additional momentum exchange contributes to the flow remaining attached to the airfoil surface. As a passive flow device that enhances lift, tubercles alter the flow field around the airfoil [27,46,47]. The method by which vortex generators operate is to create rotating regions of fluid motion along surfaces in contact with airflow, thereby transferring momentum to the boundary layer. These vortices alter the structure of the thin boundary layer adjacent to the surface, where viscous effects are dominant. Thus, the VG structures intervene in the flow and provide momentum to the boundary layer. In addition, they offer a stronger boundary layer that can better withstand APGs and maintain attachment at higher angles of attack by promoting early transition to turbulence [40–42].

The aerodynamic behavior of the NACA0020 airfoil with and without tubercles was experimentally investigated by Miklosovic et al. at Reynolds numbers of 5.05 × 105 and 5.20 × 105 [27]. The results denoted that the stall angle and the overall maximum lift coefficient increased by 40% and 6%, respectively. Moreover, the drag forces decreased when the airfoil was in the post-stall regime. The uncontrolled case and different models, which had varied amplitude and wavelength, were examined by Johari et al. [46]. They found that airfoils performed differently from the baseline model in terms of stalling, with a postponement in separation when tubercles were applied. Additionally, it was observed that the leading-edge bumps had an adverse effect, decreasing the lift coefficient when the angle of attack was lower than the stall angle of the uncontrolled case. Wei et al. [47] investigated the control of flow on a hydrofoil, taking into account leading-edge serrations at a Reynolds number of 1.4 × 104. Their findings indicated that the counter-rotating vortex pairs advanced on each serration, resulting in decreasing flow separations at angles of attack of 15° and 20°. Watts and Fish [48] attempted a numerical investigation to compare the aerodynamic characteristics of airfoils with and without tubercles. Their results demonstrated that an increment of 17.6% in lift-to-drag ratio was ensured at the airfoil with tubercles in comparison to the uncontrolled airfoil when the angle of attack was α = 10°. The application of tubercles on a delta wing was experimentally investigated by utilizing the stereoscopic particle image velocimetry (SPIV) by Goruney and Rockwell [49]. It was noted that the surface flow topology was influenced when the Reynolds number and angle of attack were 1.5 × 104 and α = 25°, respectively. Hansen et al. [15] tested NACA0021 and NACA65-021 airfoils with tubercles to understand how the tubercles affected different full-span wings. The results showed that applying a tubercle to the NACA65-021 airfoil yielded more benefits than using it on the NACA0021, as the extent of the laminar boundary layer of the NACA65-021 was greater.

During the decades, applications of bio-inspired passive flow control with tubercles have been widely studied in a variety of fields such as the designs of micro air vehicles (MAVs) [50] and unmanned aerial vehicles (UAVs) [51], vertical [52,53] and horizontal [54] wind turbine blades, and fan blades [55]. Moreover, studies focusing on the separation-induced transition were performed in order to understand the mechanism of flow control in deep [56].

From the past to the present, the aerodynamic community has been investigating improved flow control techniques for aerodynamic and hydrodynamic vehicles, aiming to achieve desired outputs such as enhanced maneuverability, lift and thrust augmentation, and drag reduction. Thanks to advancements in technology, computational techniques are successfully employed and enable the accurate characterization of complex flow structures as well as delicate flow phenomena such as the laminar separation bubble (LSB). Rather than bio-inspired techniques, vortex generators were also considered to detect their effects on controlling and damping of LSB by Singh [57], and it is examined whether conventional vortex generators and lower boundary layer vortex generators controlled the LSB. The influence on the flow characteristics of these three-dimensional vortex generators with two distinct heights of 0.33 δ and 0.66 δ was examined. According to simulations, positioning vortex generators with a height of 0.33 δ reduces the LSB’s length by 62%, and adding vortex generators with a height of 0.66 δ eliminates the LSB. As the last study also shows, in the literature, tubercles and other passive flow control methods have been studied considerably, but independently. They were not investigating the computational modelling of the bubble dynamics together. Therefore, the combined effect of utilizing a tubercle and another passive flow controller together on the LSB dynamics was unclear. As a novelty of this study, the flow phenomena, as well as the LSB and vortex formations, were numerically investigated using a transition model on the NACA0015 airfoil with a tubercle and VGs combination at a Reynolds number of 1.25 × 105 and different angles of attack.

Regarding the essential path of this study, a detailed literature review was conducted to identify numerical studies on the formation of LSB and to locate studies related to passive flow control with the tubercle in advance. This was seen in Section 1 of the paper. Section 2 consisted of the basic approaches. A detailed explanation of numerical simulations and a validation study was performed in Section 3. The ensured data from the experiments and numerical simulations were post-processed, evaluated, and then discussed in Section 4. The final remarks and limitations were ensured in the Section 5.

2  Organization of Experimental Approach

To examine the undesired flow phenomena such as boundary layer separation or the formation of LSB on both uncontrolled and controlled airfoils, and to understand how the modified model with both the whale’s tubercle form and the VG array behaves with the flow characteristics, the experimental apparatus is discussed as follows.

2.1 The Airfoil

In this study, a symmetric NACA0015 airfoil was selected as a test specimen. The reason for choosing the symmetric airfoil was to be more suitable and similar to the cross-sectional profile of a whale’s flipper [15]. As seen in Fig. 1, the chord length of the airfoil was 180 mm, while its span was 300 mm. Moreover, the position of VGs was at x/c = 0.25. The optimum location of the VGs was selected based on previous studies [22,23]. In the literature, there are two types of VG configurations: co-rotating and counter-rotating arrays. Rectangular and counter-rotating VG configurations were employed on the surface of the NACA0015 airfoil in this study. The detailed and technical information, including VG dimensions, is demonstrated in Table 1. After designing the modified airfoil, it was manufactured using a 3D printer, a fast prototype method, as shown in Fig. 1b. The dimensions of the airfoil used in the study were determined based on the Re number. Having a smoother surface was more important in terms of maintaining fluid flow over the airfoil’s surface. Hence, all surfaces of the modified airfoil were cleaned and rubbed with sandpaper. Then, rectangular plexiglass and transparent end plates were mounted at each tip of the airfoil to avoid the influence of tip vortices.

Figure 1: The geometry of the modified NACA0015 airfoil, (a) dimensions of VGs, (b) the tubercle structure created along the spanwise.

Related to the tubercle geometry at the leading edge, Eq. (1) has been extensively utilized in the literature [48,58]. The non-uniform tubercle geometry at the leading edge of the airfoil was produced to ensure a more truthful approximation according to the modified equation derived by Seyhan et al. [59].

zLE=(a1cos(2πxλ1))+(a2cos(2πxλ2))(1)

In this equation, λ1 and λ2 represent the wavelengths, and a1 and a2 represent the amplitudes. The tubercle structure generated along the spanwise direction has a function defined by zLE. As shown in Table 2, regarding design parameters, λ1 and λ2 were set to c, 0.5, and 0.125 c, respectively. Meanwhile, a1 and a2 were selected to be 0.025 c and 0.0125 c, respectively.

In this study, three types of airfoils are included: the baseline case, the model with the whale’s tubercle form (Fig. 1b), and the modified model with both the whale’s tubercle form and VG arrays (Fig. 1a). Hereinafter, the baseline case, the model with the whale’s tubercle form, and the modified model with both the whale’s tubercle form and VG arrays were considered.

2.2 The Wind Tunnel

As a test facility, the suction-type and low-speed wind tunnel was used, belonging to the Wind Engineering and Aerodynamic Research Group Laboratory (WEAR) at Erciyes University. The tunnel has a square test section of 0.5 × 0.5 m. It has a nearly 4 m length and a transparent plexiglas coating around it to show the flow phenomenon. The wind tunnel can handle wind up to 45 m/s. It was possible to change the free stream velocity in the tunnel from 3 to 40 m/s. More elaborate information related to the wind tunnel was ensured. For Re = 0.63 × 105 and 1.25 × 105, where the tests are conducted, the velocity of the tunnel corresponds to 12.43 and 24.86 m/s, respectively. A change in velocity causes a change in the inertial force, and consequently, a change in the Reynolds number. This change, in turn, can reduce the adverse effects on flow caused by viscous forces. This change was observed in this study. The test chamber was scanned along the vertical axis using the DANTEC 55P15 probe, and the turbulence intensity was measured to be 0.6%. The blockage ratio in the test section was less than 7%, and the uncertainty of the test systems was less than 3%.

2.3 Oil Flow Visualization

The surface oil flow visualization technique was employed to gain a deeper understanding of the flow events in the boundary layer and to investigate how the modified passive flow controller with whale and VG configurations affected the aerodynamics of the airfoil. The consistency must be appropriate to successfully identify the flow phenomena in the boundary layer using this technique. The inertia forces of the moving oil should also be less than the forces of viscosity and surface tension to prevent altering the conditions at the surface. The most popular pigments were titanium dioxide and fluorescent chrysene, whereas the most widely utilized oils are kerosene, light diesel, and transformer oil [60]. Oleic acid can also be added to the mixture to see the pigment deposit on the oiled surface. The oil mixture contained oleic acid, oil, kerosene, and titanium dioxide. Compared to other components, titanium dioxide was present in significantly less quantity. They were added to a beaker and mixed for five minutes. With the help of a thin brush, the produced oil combination was then applied to the airfoil surface.

2.4 Aerodynamic Force Measurement

Both the mean and time-dependent lift forces (FL) were measured with the aerodynamic force measurement. The experimental setup consists of strain gauges placed on the airfoil, which is fixed in the wind tunnel, and a data converter, as illustrated in Fig. 2. The joint of the strain gauge, airfoil, and force system shaft section is precisely integrated, and the measured strain is integrated with the data acquisition system. The calibration process was carried out to ensure that the measuring devices gave accurate and reliable results by applying known weights. During the experiment, airflow at various velocities was provided in the wind tunnel, and the lift force experienced by the airfoil was measured with the strain data obtained from strain gauges. Signals from the strain gauges were recorded at a sampling frequency of 1 kHz, resulting in a total of 1000 data points, each with a duration of 1 s. This high sampling frequency ensures measurements are more sensitive and accurate, allowing instantaneous changes to be detected. Thus, for the airfoils considered in the wind tunnel, the lift force measured at α = 0°–18° was converted into a lift coefficient using Eq. (2).

CL=2FLρU∞2(2)

Figure 2: An illustration of the aerodynamic force measurement system.

3  Numerical Modelling

In this section, detailed information is provided regarding numerical attempts, including the flow domain, computational grid, boundary conditions, and other relevant details.

3.1 The Flow Domain, Computational Grid, and Boundary Conditions

In this numerical study, information about the numerical model is presented in Fig. 3. Fig. 3a shows the flow field used in the model. The mesh structure created in the flow field is presented in Fig. 3b. The mesh structure designed for the airfoil using WG is given in Fig. 3c. The grid independence study for numerical modelling is shown in Fig. 4. Four different mesh structures were tested for Re = 1.25 × 105 and α = 8°. Based on the results of the mesh independence study, a mesh size of approximately 15 million cells was selected. In this study, the computational grid was meshed in conjunction with a structured tetragonal grid (Fig. 3). The total number of grid nodes for Case-B, Case-W, and Case-WVG was nearly 15 million, as determined by the grid independence study. In relation to the numerical model, the Reynolds-Averaged Navier-Stokes (RANS) equations were employed to analyze the flow in this study. The second-order upwind approach was used to achieve spatial discretization and minimize numerical diffusion, following the selection of the Semi-Implicit Method for Pressure-Linked Equations (SIMPLE) solution methodology. To obtain the aerodynamic characteristics of all cases, the four-equation transition Shear Stress Transport (SST) turbulence model was used. The SST k-ω transport equations and two other transport equations formed the basis of this model [61]. This was derived based on the well-known two-equation k-ω Menter’s SST turbulence model, which models the turbulence kinetic energy (k) and its dissipation rate (ω) [62]. The fluid flow is governed by the incompressible Navier-Stokes equations, representing the conservation of mass and momentum.

Figure 3: Geometrical definition of (a) numerical domain and boundary condition, (b) mesh structure of the model and (c) mesh structure around WG.

Figure 4: The grid independence study for numerical modelling.

Continuity equation:

∇⋅u=0(3)

Nondimensionalized equation of conservation of momentum:

∂u∂t+(u⋅∇)u=−∇p+1Re∇2u(4)

The transport equations for the turbulence kinetic energy (k), specific dissipation rate (ω), intermittency (γ) and transition onset momentum thickness Reynolds number (Re~θt) are defined as follows:

Turbulence kinetic energy (k) equation:

∂(ρk)∂t+∂(ρujk)∂xj=Pk~−Dk~+∂∂xj[(μ+σkμt)∂k∂xj](5)

Specific dissipation rate (ω) equation:

∂(ρω)∂t+∂(ρujω)∂xj=αPkνt−Dω+Cd+∂∂xj[(µ+σωµt)∂ω∂xj](6)

Intermittency (γ) equation:

∂(ργ)∂t+∂(ρujγ)∂xj=Pγ1−Eγ1+Pγ2−Eγ2+∂∂xj[(µ+µtσγ)∂γ∂xj](7)

Transition onset momentum thickness Reynolds number (Re~θt) equation:

∂(ρRe~θt)∂t+∂(ρujRe~θt)∂xj=Pθt+∂∂xj[σθt(µ+µt)∂Re~θt∂xj](8)

This turbulence model was selected because it yielded reasonable results, providing a better explanation of the estimation of LSB, or laminar boundary layer separation, as well as improved accuracy in experiments [38,49,63].

The Transition SST model directly captures the effects of turbulent reattachment and laminar separation by incorporating local flow variables and governing equations for intermittency transport. In-depth examinations of turbulence generation, intermittency distribution, and velocity fields provide insight into the limitations of existing transition models at low Reynolds numbers, while also offering a deeper understanding of LSB dynamics. The equations were solved employing the ANSYS-Fluent 18.2 solver.

Related to the flow domain and mesh generation, as shown in Fig. 3, the mesh distribution and flow domain were ensured to be close to the airfoil’s surfaces. The airfoil’s chord was utilized to determine the domain dimensions. As was implemented in the authors’ previous studies [64–66], the airfoil was positioned 5c from the inlet and 6c from the outlet. It was indicated that the airfoil’s wake zone needed to be longer to allow for the full development of the wake in the downstream region. U∞ = 12.43 and 24.86 m/s was at the inlet, constant pressure was at the outlet, and stationary non-slip conditions were on the airfoil and flow domain walls. The mesh structure’s first layer was 4 × 10−6 m thick, and inflation layers with a 1.2 growth rate were employed. The convergence criterion for the residuals was 1 × 10−5. The dynamic viscosity was taken as μ = 1.789 × 10−5 kg/m s. Detailed information regarding the computational mesh was provided, as shown in Table 3.

3.2 Validation

Fig. 5 displays the results of the aerodynamic lift (CL) and drag (CD) coefficients belonging to the uncontrolled and the controlled (whale-shaped model and the modified model with whale and VGs) cases at Re = 0.63 × 105. Furthermore, the results of the current study are compared with those of Seyhan et al. [59] in terms of accuracy. In the validation case, the results are pretty consistent with one another. Furthermore, although there are slight differences due to experimental conditions and uncertainties, the trends appear consistent. However, depending on the turbulence model used in numerical modelling, there can be some variations in aerodynamic force coefficients. It was noted that, despite experimental differences resulting from the experimental environment and uncertainties, the trends remained consistent. Based on the previous experience of the current authors [65–67], the lack of linearity in the lift coefficient curves indicates the formation of LSB in low Reynolds number flows, and the sudden drop in the lift coefficient curve suggests abrupt stall and leading-edge separation due to a long LSB. Similar flow behaviors were observed in previous studies examining the aerodynamic performance of different airfoils [67–69].

Figure 5: Comparison of aerodynamic force coefficients for (a) uncontrolled baseline case, (b) controlled whale-shaped airfoil at Re = 0.63 × 105.

The graph for the modified model with whale tubercle and VG combinations (a novelty of the current paper) is illustrated in Fig. 6. For the baseline and the whale-shaped controlled case, the lift curves indicated that CL increased up to α = 11° at Re = 0.63 × 105 (Fig. 6a). After α = 11°, the curves showed an abrupt stall. This was caused by the leading-edge separation due to the bubble bursting at low Reynolds number flows. The CL, max of the baseline case was around 0.76, whereas the maximum coefficient of the controlled case, just with the tubercle, was around 0.85. The maximum lift coefficient increased by 12%, while the drag coefficients decreased; however, the stall angle remained unchanged. For the controlled case of the modified model with the W+VGs case, it was observed that CL reached a maximum of 0.87. This indicates that utilizing VGs on the wind turbine blade with a tubercle provides an additional lift coefficient, increasing by 14.5% compared to other cases. The maximum lift coefficient was not just increased, but the stall angle was also postponed from α = 11° to α = 14°, and the drag coefficients decreased significantly. According to numerical modelling results at Re = 0.63 × 105 and α = 14°, the lift coefficients for the baseline, W, and W+VGs were 0.42, 0.78, and 0.87, respectively. Under the same modelling conditions, the drag coefficient was 0.23, 0.22, and 0.13, respectively. The best CL/CD ratio was obtained for the case with W+VGs. Additionally, the stall characteristics changed, transitioning from an abrupt stall to a mild one. This, particularly with the combined use of the whale tubercle and VG configurations, resulted in a change in LSB dynamics due to the small vortices created, resulting in a flow with high momentum. Additionally, although small vortices formed in low-angle-of-attack flows reduce lift formation, these vortices control the flow and LSB by imparting momentum to the flow, particularly at stall and post-stall angles of attack. In real-world applications, this control translates to increased energy output and blade stability. Although there are anticipated challenges in manufacturing these types of blades, since the blades are produced in molds, these designs can be tested with new molds to achieve this increase in energy output, despite the initial costs. Moreover, considering the existence of VG applications in real turbine applications, this suggests that the new concept design presented in this study will not show significant difficulties in its applicability.

Figure 6: Comparison of experimental aerodynamic force coefficients for the uncontrolled and the controlled cases at (a) Re = 0.63 × 105, (b) Re = 1.25 × 105.

When examining all cases at Re = 1.25 × 105 in Fig. 6b, a more linear trend was observed in the lift coefficient curve, with an increase in inertia and a decrease in LSB formation in the uncontrolled case. In the tuberculated controlled airfoil, minor improvements in lift coefficient and mild stall were observed before the stall due to the whale structure. In the W+VG-controlled airfoil, due to the use of VGs in addition to the whale structure, the resulting small vortices provide less improvement to the flow, resulting in an early stall. It was noted that an abrupt stall occurred in the uncontrolled case, whereas this situation was mitigated to a mild stall phenomenon by utilizing a passive flow controller. Additionally, a decrease in drag forces was observed in the controlled cases due to the formation of small vortices.

4  Results and Discussions

4.1 Experimental Results and Validation

The experimental results for both the baseline and controlled NACA0015 airfoils are presented in this section. Force measurements and oil flow visualization were performed to investigate the aerodynamic behavior at various angles of attack. The baseline airfoil serves as a reference, while the controlled airfoil allows evaluation of the effects of modifications on lift, drag, and flow separation. Experimental findings are further compared with numerical results from skin friction coefficient (Cfx) simulations and vorticity analyses to provide a comprehensive understanding of the flow characteristics.

Fig. 7 presents the changes in L/D ratios resulting from increases in lift coefficients and decreases in drag coefficients. An examination of these graphs demonstrated that controlled cases contributed to aerodynamic performance at both Reynolds numbers. When Fig. 7a is examined in detail, it can be seen that for Re = 0.63 × 105, the highest CL/CD ratio is obtained for case W at the pre-stall angles, while after the post-stall angle, it is obtained for the case W+VGs. After a 20-degree angle of attack, the CL/CD ratios become very close to each other. At angles of attack greater than 20 degrees, the CL/CD ratios become very close to each other. According to the numerical modelling results obtained with a Re value of 1.25 × 105 and α = 9°, the CL/CD ratio for the baseline, the W, and the W+VG cases is approximately 7.3, 10.1, and 10.6, respectively. In the post-stall case (α > 16°), W and W+VG give roughly the same values, and these values are greater than the base case. While the aerodynamic performance of the airfoil with a tubercle increased at all angles of attack, the increase was greater after stall for the W+VG airfoil. This means that while the vortices generated by VGs negatively impact LSB dynamics, in higher Reynolds number flows, the higher inertia before the stall results in smaller, higher-frequency vortices. These vortices impart momentum, positively impacting LSB dynamics.

Figure 7: Comparison of L/D ratios of the uncontrolled and the controlled cases at (a) Re = 0.63 × 105, (b) Re = 1.25 × 105.

The time-dependent lift force results, which yield undulated lift curves, may provide more detailed and reasonable information than those obtained at their mean values. Driven by this motivation, apart from the mean CL results, the time-dependent CL histories of the uncontrolled and controlled cases obtained from experiments at Re = 1.25 × 105 were compared with each other, as illustrated in Fig. 8. Each pair of columns represents an angle of attack in the graphs. Additionally, a moving average, calculated as the average of the previous 100 data points, was added to the graphs. This graph shows the lift fluctuations of the airfoil as it is affected by the unsteady changing LSB dynamics and flow conditions. The critical results were evident when Fig. 8 was carefully evaluated. For both graphs, the mean values of CL as lift fluctuations increased when the angle of attack increased gradually. The amplitude of those fluctuations before α = 10° was more pronounced in the curve of the uncontrolled cases. This indicated that the flow could not attach to the surface of the airfoil; instead, LSB formation occurred due to the presence of adverse pressure gradients. After α = 13°, a stall phenomenon occurred. It was also foreseen that the aerodynamic vibration was pronouncedly increased after the stall angle, as the fluid-structure interactions were more pronounced in the boundary layer. Regarding the results of the controlled cases, it was observed that utilizing a combination of tubercle and VGs application on NACA0015 not only increased the lift coefficient but also affected the LSB dynamics and reduced the aerodynamic vibration. Moreover, the spectral analysis results belonging to α = 10° and α = 16° were specifically provided to understand the effect of the passive flow controller on the LSB dynamics in Fig. 9. When looking at the spectral analysis graphs, it was seen that while the baseline case had lower-frequency peaks due to large vortices caused by the LSB and flow separation, the whale-shaped airfoil had shrunk in size due to the tubercle shape, increasing the peak frequency. In the W+VG airfoil case, the number of peak frequencies has risen to two due to the formation of small vortices, due to both the tubercle shape and the VGs.

Figure 8: Time-dependent CL vs. time (s) at Re = 1.25 × 105 for (a) the uncontrolled case, (b) the controlled (W+VGs) case.

Figure 9: The spectral analysis results of time-dependent CL for all cases at Re = 1.25 × 105.

In order to see the effect of whale tubercle airfoil shape and VGs on LSB dynamics in controlled cases in more detail, the flow physics results obtained from computational modelling results were discussed in the rest of the paper. Surface flow visualization and numerical Cfx results for NACA0015 airfoil at Re = 1.25 × 105 were provided to capture the surface flow patterns along the suction surface of the uncontrolled cases, as seen in Fig. 10. Cfx was obtained from the x-wall shear stress in the numerical results. The negative values in the Cfx legend indicate the flow separation. The oil flow visualization results of the current study were investigated by comparing surface flow visualization for NACA634-021 airfoil at Re = 1.8 × 105 in a literature study [67]. Fig. 10 clearly showed that laminar flow formed at the leading-edge part of the uncontrolled airfoils, followed by the formation of LSB at the middle part in both our computational modelling and experimental analysis. After the presence of LSB, a turbulent flow region occurred at the trailing edge. And, the tip vortex effects were seen in all cases. Furthermore, the numerical flow patterns obtained in the current study were in agreement with the results from the literature. Therefore, it was anticipated that the numerical findings of the current research would accurately provide knowledge related to the LSB dynamics and flow patterns formed in the controlled cases.

Figure 10: Comparison of surface flow visualization and numerical skin friction coefficient results.

The impacts of the controlled cases with the tubercle (W) and tubercle/VGs (W+VGs) combination on the flow features were comprehensively investigated through both computational modelling and experimental analysis at α = 8° and Re = 1.25 × 105 as illustrated in Figs. 11 and 12, respectively. In terms of better clarifying the flow features on the controlled case (W), a sketch was joined at the top of the graph in Fig. 11. The results of surface oil flow visualization revealed that there was an oil accumulation in the downstream trough. Those flow patterns exerted by the oil accumulation clearly demonstrated the flow recirculation in this region, resulting in the existence of counter-rotation vortex pairs (CRVPs). Those surface CRVPs were primarily responsible for the spanwise pressure differences, in agreement with the findings of Wei et al. [67,70,71]. As explained, there was less pressure downstream of tubercle troughs compared to tubercle peaks due to the separated flow. This refers to the downstream flow of tubercle peaks, which are moved by pressure gradients into the trough regions, leading to oil accumulation in these regions. Additionally, the less dark region behind the CRVPs showed slight flow separations, which means the surface CRVP. As for the experimental and numerical flow patterns on the suction surface of the controlled case (W+VGs), the combination of tubercle and VGs, with the close-up inspection of VGs, was demonstrated numerically and experimentally in Fig. 12. As usual, oil accumulation and flow separation regions also existed in all cases. However, it was observed that their size was relatively smaller than that of the controlled case (W), as indicated by the numerical turbulence intensity contours in Fig. 13. Additionally, the reattached flow structures with the momentum transfer were visualized behind the VGs (Figs. 12 and 13) through numerical modelling, allowing for more detailed analyses. Focused on close-up inspection, the counter-rotation vortex pairs produced by VGs caused the flow to become reattached with momentum increasing (Fig. 13). It was also revealed that the formation of surface CRVPs had disappeared. This showed that the passive flow control combinations effectively impact the flow patterns compared to the baseline and the controlled case (W), as illustrated in Figs. 11–13. Apart from those findings, it was thought that separation reduction occurred due to the VG combination, which harmonized the spanwise flow disturbances when the modification was utilized. This played a dominant role in the lift curves in Fig. 5. It was noted that using a combination of passive flow control methods enabled higher lift than the controlled and controlled (W) cases.

Figure 11: Surface oil flow visualization for the controlled (W) case, α = 8°, Re = 1.25 × 105.

Figure 12: Surface oil flow visualization and numerical vorticity results for the controlled (W+VGs) case, α = 8°, Re = 1.25 × 105.

Figure 13: Numerical turbulence intensity of the uncontrolled and the controlled cases at (a) α = 8°, (b) α = 12°, and Re = 1.25 × 105.

4.2 Numerical Results

Turbulent kinetic energy distributions, turbulence intensity, and intermittency contours are analyzed to investigate the flow structures around both baseline and controlled NACA 0015 airfoils. Q-Criterion vortex regions are visualized to identify coherent vortex structures, while comparisons of Q-Criterion colored with TKE distributions over the airfoil surface and x-component velocity contours in the wake region provide a detailed understanding of the flow dynamics. These numerical observations are analyzed at the considered angles of attack to highlight the key aerodynamic characteristics of both baseline and controlled airfoils. The results regarding turbulence intensity obtained from numerical modelling are presented in Fig. 13 for three different cases with Re = 1.25 × 105. According to these results, no change in turbulence intensity was observed in any of the planes in the baseline case. In the W case, the turbulence intensity in the region with the short protrusion is higher than in other areas. The same situation applies to W+VGs. To reveal the flow control capability of our new concept (W+VG) configuration in more detail, the numerical study results are depicted in Fig. 14. In these figures, turbulence kinetic energy contours were shown in detail in the controlled cases through the planes at troughs (T) and hills (H). As seen in Fig. 14, the transition to turbulence was accelerated at the troughs due to the flow circulations as mentioned in Fig. 11, and increases were observed in the turbulence kinetic energies after the transition to turbulence. In addition to these increases, the presence of vortex generators at the troughs increased the momentum gain to the flow, further improving the flow and reducing the LSB formations and trailing edge separations. In addition, the flow circulations were less at the hills, and therefore, the flow improvement and the decrease in trailing edge separation in the whale cases were limited. When the VGs coincided with these hills, the flow separations decreased with the momentum gain in the flow. Other parameters considered in evaluating the aerodynamic performance of the flow are turbulence, kinetic energy, and intermittency, as shown in Fig. 15.

Figure 14: Numerical turbulent kinetic energy distributions of the controlled cases of (a) W and (b) W+VG at α = 12° and Re = 1.25 × 105.

Figure 15: Turbulence intensity and intermittency contours at (a) α = 4°, (b) α = 8°, (c) α = 12° and Re = 1.25 × 105.

As the freestream momentum energizes the shear layer at a distance from the boundary layer, it starts to reattach to the surface. At that point, intermittency and TKE are crucial in predicting the onset of transition, as shown in Fig. 15. Intermittency generally represents the time-averaged velocity fluctuations. A transition can usually be considered initiated when this value exceeds 0.5. Because it is used as a transport equation in some Computational Fluid Dynamics (CFD) codes, such as Transition-SST, it plays a critical role in accurately calculating the transition onset. Furthermore, the increase in turbulent kinetic energy along the flow direction, accompanied by intermittency, makes the transition to turbulence easier to observe and interpret. An examination of Fig. 15a reveals higher intermittency and TKE levels at the same x/c points in the W and W+VG profiles compared to the base profile. The same trend is observed, albeit more pronounced with increasing angle of attack, for the α = 8° case in Fig. 15b. In this scenario, TKE and intermittency reach higher intensities upstream than at α = 4°, indicating a shift toward the leading edge. At the α = 12° shown in Fig. 15c, while the W-shaped profile again exhibits an earlier and more stable transition to turbulence than the base profile, it can be argued that the W+VG profile requires improvement with increasing angle, particularly at the VG positions. This is because the transition to turbulence tends to occur earlier in the upstream direction. Additionally, another concept, the Q-criterion, an effective parameter for analyzing three-dimensional flow behavior, which was proposed by Hunt et al. in 1988 [72]. The Q-criterion term expresses the ratio of the vortex structure (rotation rate) to the strain in a flow. This phenomenon was formulated more clearly by Chong et al. as follows [73].

Q=12[(∇⋅u)2−∇u:∇uT]=12[(∇⋅u)2+|Ω|22−|S|22]

Above is the u, S, Ω representing the velocity, strain and vorticity tensors, respectively.

In Fig. 16a, after a baseline leading edge, there are low-density Q structures and minimal, thin traces towards the tip, which can be considered indicators of weak 3-dimensionality and a laminar or semi-laminar boundary layer. Moreover, the sparseness of Q traces and low TKE indicate that LSB tends to be long and thin, limiting the transition to turbulence after the flow reattaches. Besides, considering the discontinuities in Q structures, it can be stated that the transition is delayed and spanwise coherence is high. Next, in Fig. 16a, which shows the whale-structured airfoil, the formation of vortex filaments is observed in the streamwise direction, aligning with the whale wave number along the leading edge. These vortices thickened the laminar boundary layer locally in upper regions from the surface by increasing the momentum transport, and therefore, LSB is divided into multiple short LSBs. An increase in the Q density indicates an early, yet local, transition. In addition to the leading-edge whale structure, vortex generators were integrated in Fig. 16 (W+VG), where the Q-criterion volume is the densest and continuous. This means that the boundary layer becomes fully turbulent earlier, and the LSB is either significantly shortened or entirely suppressed. When these conditions are examined in relation to angle of attack, the highest separation resistance is observed in the whale+vortex generator scenario. The flow most prone to separation occurs in the baseline profile. However, as the angle increases to 8° and 12° in Fig. 16b,c, this difference becomes even larger. When considered in terms of transition location, the transition shifts upstream as the angle increases in the baseline profile. In the whale configuration, the transition appears as local islands within the wave gaps. When the vortex generator is added, a displacement toward the leading edge also occurs as the angle increases. These conditions also affect the LSB dynamics, resulting in a single, long LSB in the baseline profile, a multi-segmented LSB that is shorter than the baseline in the whale profile, and a significantly shorter or even completely suppressed LSB in some areas of the W+VG configuration. This also indicates that the three-dimensionality is enhanced in both the W and W+VG profiles. To gain a detailed understanding, Fig. 17 illustrates the view of Fig. 18, which represents both Q structures and the wake (U-velocity) section from a plane at x/c = 0.23.

Figure 16: Q-Criterion vortex regions over the airfoil’s upper surface at (a) α = 4°, (b) α = 8°, (c) α = 12°, and Re = 1.25 × 105.

Figure 17: Visual explanation of the Q-Criterion and wake region shown in a combined figure.

Figure 18: Comparison of Q-criterion colored with TKE distribution over the surface and x-component velocity contours at wake region at (a) α = 4°, (b) α = 8°, (c) α = 12°, and Re = 1.25 × 105.

In Fig. 18 above, a cross-section of the U-velocity wake region is shown in the background and the Q-criterion iso-surfaces in the front (explained in Fig. 17). At α = 4°, in Fig. 18a, a narrow and spanwise coherent U-deficit band (low velocity region) and sparse Q structures are observed in the baseline profile, indicating a long LSB and a delayed transition. Conversely, in the whale profile, streamwise cores emerging in the troughs modulate the wake region in synchrony with the whale structure at the leading edge, breaking up the LSB and creating local early transition regions. In the W+VG configuration, the early and fully turbulent boundary layer can be explained by the presence of dense hairpin vortices and double-core wakes. At α = 8°, as shown in Fig. 18b, the KH-wavy and continuous shear layer together with the thickening wake showed a tendency towards flow separation. At the same time, in the whale profile, the cores maintained a better level of reattachment with a longer structure. At the α = 12° shown in Fig. 17c, the baseline profile approached stall with a wider shear plate. In the whale profile, there was continuity of flow between the channels, and separation was limited locally. The W+VG profile was again observed as the last to separate. However, it is essential to emphasize that whale profiles without vortex generators do not have the proper capabilities to eradicate the LSB since hairpin vortices are broken into smaller particles or distributed uniformly by VGs, which prevents the LSB from occurring as a single long form.

5  Conclusions

The objective of this study is to investigate the aerodynamic performance and the effect of the new concept passive control mechanism of the controlled NACA0015 airfoil using tubercles and VG on the LSB over the airfoil at different Reynolds numbers and angles of attack. Related to the passive flow control strategy, a new concept employing both tubercles and VGs simultaneously was used near the leading edge of the NACA0015 airfoil. Numerical simulations were conducted for this study to understand the effect of the new concept of passive flow control on the LSB over the airfoil. In this regard, the current study revealed the following conclusions:

–   In the validation study, it was shown that an LSB formed near the leading edge of the uncontrolled airfoils in both numerical and experimental analysis. After the presence of LSB, a turbulent flow region occurred at the rear part. Consequently, the numerical findings of the current study provide valuable insights into the LSB dynamics and flow patterns observed in the controlled cases.

–   At aerodynamic lift coefficient graphs, in the uncontrolled case, CL, max was around 0.76 at α = 11°, while it was approximately 0.85 at α = 11° and 0.87 at α = 14° in the controlled case (W) and case (W+VGs), respectively. Apart from increasing the lift coefficient, the aerodynamic stall was postponed.

–   The stall characteristics changed, transitioning from an abrupt stall to a mild stall. This, particularly with the combined use of the whale tubercle and VG configurations, resulted in a change in LSB dynamics due to the small vortices created, resulting in a flow with high momentum. Additionally, although small vortices formed in low-angle-of-attack flows reduce lift formation, these vortices control the flow and LSB by imparting momentum to the flow, particularly at stall and post-stall angles of attack. Additionally, a decrease in drag forces was observed in the controlled cases due to the formation of small vortices.

–   Time-dependent lift coefficient graphs show the lift fluctuations of the airfoil as it is affected by the unsteady changing LSB dynamics and flow conditions. The results demonstrated that the fluctuations were reduced by utilizing passive control techniques, thereby suppressing the LSB. Additionally, on NACA0015, the application of a combination of tubercle and VGs not only raised the lift coefficient but also reduced aerodynamic vibrations.

–   At lower Reynolds numbers, while aerodynamic performance increased at all angles of attack for the airfoil with a tubercle, the increase was greater after the stall for the W+VGs airfoil. This means that while the vortices generated by VGs negatively impact LSB dynamics. At higher Reynolds number flows, aerodynamic performance increased at all angles of attack; particularly, the increase was most notable at moderate angles of attack (in the pre-stall region).

–   In the numerical study results, turbulence kinetic energy contours in the controlled cases (W and W+VG) through the planes at troughs and hills were discussed. It was shown that the transition to turbulence was accelerated at the troughs due to the flow circulations, and increases in turbulence kinetic energy were observed after the transition to turbulence. In addition to these increases, the presence of VGs at the troughs enhanced the momentum gain to the flow, further improving the flow and reducing trailing-edge separations. The flow circulations were lower at the hills; therefore, the flow improvement and the decrease in trailing edge separation in the whale (W) cases were limited when the vortex generators coincided with these hills. The flow separations decreased with the increase in momentum of the flow. Moreover, although controlled cases showed a better transition characteristic in terms of aerodynamic performance, their positions should be optimized due to the deficiency at higher angles of attack, such as 12°, to dominate LSB formation and enhance the transition to turbulence, as indicated by the Q-Criterion and wake region results.

–   Concerning the findings obtained from oil flow visualization and numerical simulations, the flow behind the VGs was energized with momentum transfer to the LSB region. Those energized flow structures enabled the formation of LSB to disappear at the middle part of the controlled NACA0015 airfoil, resulting in higher lift performance compared to the uncontrolled case.

The use of commercial CFD software has led to 0 s in modelling. In future studies, if open-source code is used to modify the transport equations of the transition model, more realistic empirical expressions derived from experimental results can be used to obtain more accurate results. This would allow for a better understanding of the effects of viscous forces, especially in modelling low-Reynolds-number flows, and enable a more comprehensible observation of LSB dynamics over the airfoil.

Consequently, the improvement in aerodynamic performance resulting from the new concept of passive flow control method leads to an increase in payload capacity for unmanned air vehicles or energy output in turbine blades. One may argue that the novel idea and combination of those passive flow controllers would offer a viable, affordable, and efficient way to improve the aerodynamic performance of airfoils and suppress the LSB in energy and aviation applications.

Acknowledgement: The authors would like to acknowledge funding from the Scientific Research Projects Unit of Erciyes University.

Funding Statement: The authors are grateful to the Scientific Research Projects Unit of Erciyes University under contract no: FDS-2022-11532 and FOA-2025-14773.

Author Contributions: The authors confirm contribution to the paper as follows: Conceptualization: Mustafa Serdar Genç, Halil Hakan Açıkel, Mustafa Özden; methodology: Mustafa Serdar Genç, Halil Hakan Açıkel, Mustafa Özden; software: Mustafa Özden, Eren Anıl Sezer, Muhammed Hatem; validation: Mustafa Serdar Genç, Halil Hakan Açıkel, Eren Anıl Sezer, Sinem Keskin; formal analysis: Mustafa Serdar Genç, Halil Hakan Açıkel, Eren Anıl Sezer, Sinem Keskin, Muhammed Hatem, Mustafa Özden; investigation: Eren Anıl Sezer, Sinem Keskin, Muhammed Hatem; data curation: Mustafa Serdar Genç, Eren Anıl Sezer, Mustafa Özden, Sinem Keskin, Muhammed Hatem; writing—original draft preparation: Mustafa Serdar Genç, Mustafa Özden, Sinem Keskin, Muhammed Hatem; writing—review and editing: Mustafa Serdar Genç, Halil Hakan Açıkel; visualization: Mustafa Serdar Genç, Halil Hakan Açıkel, Mustafa Özden, Eren Anıl Sezer, Sinem Keskin, Muhammed Hatem; supervision: Mustafa Serdar Genç, Halil Hakan Açıkel, Mustafa Özden; project administration: Mustafa Serdar Genç; funding acquisition: Mustafa Serdar Genç. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials: Data available on request from the authors. The data that support the findings of this study are available from the corresponding author, Mustafa Serdar Genç, upon reasonable request.

Ethics Approval: Not applicable.

Conflicts of Interest: The authors declare no conflicts of interest.

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