Predicting the high-angle-of-attack characteristics of an airfoil for micro/unmanned aerial vehicle applications

In recent years, there has been increasing use of micro and unmanned aerial vehicles (MAVs and UAVs), with UAVs in particular playing essential roles in high-definition remote sensing,^1–6 infrastructure surveillance,^7–9 three-dimensional mapping,^10–13 and photogrammetry.^14–19 This has lead to significant advances in aerodynamic research, especially in elucidating the behavior at high angles of attack (AoAs) of airfoils designed for these vehicles. A thorough investigation of such behavior is necessary to meet the specific operating needs of MAVs and UAVs, which include improved maneuverability, efficiency, and stability in a variety of flight situations. MAVs and UAVs are often built to fly efficiently at higher AoAs than larger aircraft. Although the exact values may differ, many MAV/UAV designs can attain AoAs that exceed 30° and reach up to 45° or even higher under specific maneuvering or aerodynamic circumstances.

MAVs and UAVs rely on airfoils developed for low Reynolds numbers. Such airfoils are also essential components of small-scale wind turbines (SSWTs), which make an important contribution to reducing electrical grid demands and emissions of greenhouse gases.^20–23 These airfoils need to be custom-made for each application in order for them to work as efficiently as possible. Artificial neural networks, evolutionary algorithms, and surrogate modeling are among the tools that have been widely used for optimizing airfoil design.^24–28 

Lian et al.²⁹ investigated the flow-induced vibration of a wind turbine airfoil at a 90° AoA using fluid–structure interaction (FSI) simulation. The unsteady aerodynamic force causes chordwise vibration, leading to high-amplitude vortex-induced vibration (VIV) and frequency lock-in. A dynamic mode decomposition (DMD) technique was used to investigate the mechanism of bifurcation from an energy balance perspective. It was concluded from the reconstructed Lissajous curves that energy transfer mainly occurred in modes, and the original time-domain Lissajous curves were found to agree well with this result.

Mahapatra et al.³⁰ investigated two-dimensional flow over a NACA 0012 airfoil at various AoAs and inlet velocities using the k-ω shear stress transport (SST) model and focusing on the case of an AoA over 20° and significant inlet velocity. They concluded that the results revealed unsteady flow behavior and vortex formation, with a transition to a highly unstable state between 40° and 50°.

Ali et al.³¹ analyzed the pressure distribution on airfoil surfaces, lift and drag forces, and mean velocity profiles. They observed that higher AoAs resulted in higher pressure coefficients on the lower surface, leading to a higher lift coefficient. However, the pressure distribution on the upper surface did not change significantly with ground clearance for higher AoAs. It was concluded that upper surface suction causes an adverse pressure gradient, leading to a thicker wake and higher drag. Cambered airfoils can generate lift at zero AoAs, resulting in curved streamlines and higher average velocity on the upper surface.

Much research on rotorcraft aims to increase flight speed or alleviate adverse physical phenomena by expanding the Mach/AoA envelope in which rotor blades operate. In this context, prediction of airfoil characteristics has been improved by the use of computational fluid dynamics (CFD) codes capable of quantifying airfoil behavior at high and reverse AoAs. The application of hybrid Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) turbulence methods has increased the accuracy of such predictions.³² 

Gonzaga-Bermeo et al.³³ investigated the efficiency of a submerged asymmetric NACA 1412 airfoil in extracting energy from incoming water flow, focusing on the impact of the effective AoA α and feathering parameter χ on efficiency and power extracted, and aiming at achieving an efficiency of over 15%. Employing ANSYS Fluent as the simulation tool, they formulated a dedicated C programming code and implemented it to facilitate oscillatory motion on the airfoil. Hujare et al.³⁴ carried out a study with the aim of reducing the time taken to finalize the design parameters during the process of wing design. An appropriate AoA was found to be crucial for proper flow separation in the face of incoming winds. In the multiple-wing configuration that was investigated, each wing was strategically positioned behind the previous one to maximize lift and minimize drag forces. The front wing was taken to consist of two wing elements, three parametric optimization parameters were considered, and 25 models with different combinations of parameters were studied. Numerical simulation gave a C_L/C_D ratio for the optimized model (model X₅) of 15.78, while an experimental test gave a 15.32 ratio for this model.

Previous studies have investigated high-AoA flow dynamics using numerical approaches such as CFD and experimental setups such as wind tunnel tests. However, many of these studies have been limited by constraints on the Reynolds number or by difficulties in accurately capturing flow separation. There remains a significant gap in the understanding of detailed turbulence characteristics, such as skin friction and viscosity variations, at extreme AoAs for low-Reynolds-number airfoils, which are critical for MAV/UAV applications operating in diverse conditions such as urban monitoring, disaster response, and military reconnaissance. This study addresses these gaps by conducting a high-AoA analysis from 0° to 90° using the k-ω SST turbulence model in ANSYS Fluent, thereby providing insights into turbulence effects, flow separation, and aerodynamic performance that should be helpful in optimizing MAV/UAV airfoil design.

A numerical investigation was conducted using ANSYS Fluent software to predict the aerodynamic characteristics at higher AoA, i.e., 0°–90°, over a low-Reynolds-number airfoil for MAV/UAV applications. Specifically, the k-ω SST turbulence model was employed to analyze aerodynamic characteristics at higher AoAs. The k-ω SST model was chosen for its superior accuracy in predicting boundary layer behavior, robust handling of adverse pressure gradients and flow separation, adaptability to low Reynolds numbers, and proven reliability in high-AoA aerodynamic studies. The study focused on flight scenarios pertinent to MAVs operating at low Reynolds numbers, typically between 12 and 15 m/s. For this analysis, a flight speed of 12 m/s was considered.

The computational approach utilized a coupled scheme with a least squares cell-based second-order upwind method. Standard initialization procedures were applied, and convergence criteria were set at 10⁻³ to ensure accurate results and stable simulations. To predict the turbulence intensity near the airfoil surface, y⁺ was taken as 0.9893 (y⁺ < 1), which was sufficient to achieve turbulent flow near the airfoil surface.

A airfoil that had been newly designed especially for MAV/UAV applications was used.³⁵ The far-field incoming air had a velocity of 12 m/s, giving a chord-based (c = 0.301 m) Reynolds number of Re = 2.4 × 10⁵. The computational domain was extended by 20 chord lengths from the airfoil’s leading edge and 20 chord lengths from its trailing edge, as shown in Fig. 1.

The computational domain was carefully constructed to ensure minimal boundary effects on the flow solution, with the airfoil at a sufficient distance from domain boundaries. Mesh quality was assessed to ensure smooth transitions and minimize skewness. A grid-independence test was performed, the results of which are shown in Fig. 2 and Table I. A fine mesh with a total of 85 295 elements and 84 695 nodes (fine mesh_1 in Table I) was chosen for subsequent simulations, since the this resolution offered an optimal balance between computational cost and accuracy of results. An initial spacing of 0.03 mm was adopted.

As already mentioned, the k-ω SST turbulence model was selected for this study because of its proven efficacy in high-AoA simulations, particularly for the low-Reynolds-number flows typical of MAV/UAV operations. Its advantages include superior accuracy in predicting boundary layer behavior and flow separation, which are critical at high AoAs. By blending the k-ω model’s precision in near-wall regions with the k-ε model’s robustness in the free stream, the SST model ensures reliable predictions across diverse flow regimes. It effectively handles adverse pressure gradients and flow transition phenomena, which are prevalent at extreme AoAs. Furthermore, its adaptability to low Reynolds numbers makes it particularly suitable for MAV/UAV airfoil studies.

However, the model has limitations, such as increased computational cost compared with simpler turbulence models, and it may require fine mesh resolution near the wall to maintain accuracy. Additionally, although it performs well in capturing large-scale flow features and separation, its accuracy in resolving small-scale turbulence may be slightly constrained. Despite these limitations, the k-ω SST model provides the best balance between accuracy and computational feasibility for high-AoA simulations, making it the optimal choice for this study.

From Fig. 3, it can be seen that the lift coefficient increases almost linearly from 1.2981 at 0° AoA to a peak value of 2.2473 at 14°. There is a notable decrease in lift coefficient to 1.3496 at 15° AoA, followed by a slow rise and then a decrease again up to 30°. This suggests that the airfoil is experiencing complex flow phenomena. The onset of flow separation or stall, common in high-AoA conditions, could be the cause of this fall and rise. The lift coefficient remains relatively constant, oscillating between 1.3911 and 1.543 across the high-AoA range from 35° to 90°. This suggests that the airfoil reaches a plateau in lift generation, potentially reaching a near-stall state where it maximizes lift but does not significantly increase, despite the higher AoA.

From Fig. 4, it can be seen that the drag coefficient exhibits a gradual increase from 0.0222 at 0° AoA to 0.3572 at 12°. This trend reflects typical behavior as the AoA increases, with the drag increasing as a consequence of increased flow separation and pressure drag. At 14° AoA, the drag coefficient significantly peaks at 0.4892. This peak corresponds to the maximum lift coefficient and indicates a critical point where flow separation and induced drag are at their highest, leading to a dramatic rise in drag. After the peak at 14°, the drag coefficient decreases consistently, reaching a minimum of 0.0467 at 90°. This decrease suggests improved flow conditions or reduced turbulence and separation at these high angles, which might be due to a more streamlined or stable flow as the airfoil maintains lift even at extreme angles.

According to Fig. 5, the L/D ratio is extremely high at low AoAs, peaking at 58.47 at 0°. This indicates excellent aerodynamic efficiency in these conditions. However, as the AoA increases, the ratio drops significantly owing to rising drag and relatively stable lift. The L/D ratio decreases significantly, from 18.78 at 4° to 4.59 at 14°. The large drop around 14° is associated with the peak in drag coefficient, reflecting a significant loss in aerodynamic efficiency as the airfoil approaches critical flow conditions. After the sharp drop, the L/D ratio begins to increase from 7.64 at 15° to a high of 32.33 at 90°. This indicates that despite increased drag, the airfoil achieves a much higher efficiency at extreme AoAs. This suggests improved lift-to-drag characteristics in these high-AoA conditions.

Figure 6 shows that at 0° AoA, the center of pressure CP is −46.7, indicating a high-suction or low-pressure region on the airfoil. This is typical for low AoAs, where the airfoil experiences a strong pressure differential. As the AoA increases from 2° to 12°, CP becomes less negative and moves toward positive values. This transition indicates a reduction in suction as the airfoil starts to experience more positive pressures due to the increased flow angle. The CP fluctuates between AoAs of 13° and 14°, with a notable drop to 1.62 at 14°, indicating a region of increased pressure on the airfoil. This drop is consistent with the peak in drag and a significant decrease in L/D ratio, indicating flow separation or stall. Beyond 14°, from 15° to 90°, CP increases steadily to 17.22 at 90°, indicating progressively higher pressure on the airfoil. This trend suggests a high-pressure build-up at extreme AoAs, possibly due to the airfoil’s stalling behavior as the flow pattern becomes more stabilized.

Analysis of turbulence intensity data at the leading and trailing edges reveals key insights into flow behavior across various AoAs. From Fig. 7, it can be seen that at 0°, the relatively low turbulence intensity at the leading edge (0.067) suggests a stable and laminar flow regime. As the AoA increases to 20°, the rise in turbulence intensity to 0.074 indicates the onset of flow disturbances caused by the steeper inclination of the airfoil. The peak at 30° (0.130 28) highlights a critical point where significant flow separation or unsteady vortices dominate, adversely affecting aerodynamic performance. Beyond 30°, the sharp decline in turbulence intensity to 0.016 159 at 50° and further to 0.008 236 at 60° indicates either flow reattachment or stabilization of the separation zone. The slight increase to 0.010 583 at 90° suggests a shift in the flow pattern, possibly due to the fully stalled regime and consistent flow separation.

By contrast, the turbulence intensity at the trailing edge remains relatively low and stable, ranging from 0.009 927 2 at 0° AoA to 0.021 809 at 90°. This limited sensitivity of the trailing edge to changes in the AoA indicates that the trailing edge plays a less significant role in dictating the overall turbulence effects compared with the leading edge. For instance, an increase in turbulence at the leading edge affects boundary layer separation, directly influencing lift reduction and drag increase, particularly near stall conditions. Similarly, stable turbulence at the trailing edge may contribute to maintaining smoother wake dynamics, influencing drag behavior.

From Fig. 8, it can be seen that at 0° AoA, the maximum wall shear stress at the leading edge is 2.5655, decreasing to 2.5033 at 20°. This suggests a relatively stable shear stress, with minor fluctuations as AoA increases. The shear stress at the leading edge peaks at 4.1378 at 30°, indicating higher frictional forces, possibly due to flow separation or increased turbulence. At 40°, the shear stress decreases slightly to 3.9029, but it remains high. At high AoAs, from 50° to 90°, the shear stress at leading edge decreases, falling to 1.4759 by 90°. Although flow separation may stabilize, the observed lower wall shear stress suggests a more uniform flow pattern at high AoAs. The trailing edge wall shear stress increases from 1.5809 at 0° to 2.1896 at 20°, reflecting increasing frictional forces likely due to changing flow conditions. From 30° to 90°, the shear stress continues to rise, peaking at 3.4766 at 90°. This steady increase suggests that frictional forces at the trailing edge are more sensitive to AoA changes and remain high even at extreme angles.

Analysis of the turbulence viscosity ratio from Fig. 9 highlights key trends in the flow dynamics around the airfoil at various AoAs. At the leading edge, the turbulence viscosity ratio begins at a value of 0.1683 at 0°, reflecting a relatively stable flow with moderate turbulence effects. As the AoA increases, the ratio rises to 0.2646 at 20°, indicating that the effects of turbulence start to dominate over those of viscosity, which is consistent with the onset of boundary layer instability. The significant peak of 0.5586 at 30° represents a critical point where turbulent forces greatly exceed viscous forces, likely corresponding to flow separation and increased aerodynamic instability. Beyond this peak, the ratio drops dramatically to 0.0125 at 50°, suggesting reduced turbulence dominance, possibly owing to flow reattachment or the establishment of a different flow regime. At very high AoAs (60°–90°), the turbulence viscosity ratio stabilizes at minimal values (around 0.004 at 90°), indicating that viscous forces are now dominant, corresponding to stable flow separation or a fully stalled regime.

At the trailing edge, the turbulence viscosity ratio is significantly lower throughout, starting at 0.0036 at 0° and increasing steadily to 0.0159 at 30°, indicating growing turbulence relative to viscosity, but at a much smaller magnitude compared with the leading edge. The ratio continues to rise to 0.0214 at 50°, suggesting a late-stage increase in turbulence effects at the trailing edge, before stabilizing around 0.0146 at 90°. This trend highlights the comparatively minor but still increasing role of turbulence at the trailing edge, especially at higher AoAs. For instance, the peak in the viscosity ratio at the leading edge (30°) correlates with the peak turbulence intensity and likely marks a point of maximum lift reduction and drag increase due to separation. Similarly, the stabilization of the ratio at high AoAs (60°–90°) suggests that viscous forces dominate, contributing to a fully separated flow regime with diminished lift and reduced L/D ratio.

From Fig. 10, it can be seen that the maximum skin friction coefficient found at 0.029 089 at 0° decreases slightly to 0.028 381 at 20°. This indicates that the frictional drag at the leading edge decreases with increasing AoA, likely because of changes in flow characteristics affecting the boundary layer. The skin friction coefficient increases to a peak of 0.046 918 at 30°, reflecting higher frictional drag, possibly due to increased turbulence or flow separation. It then decreases to 0.023 777 at 50°, suggesting that the effect of turbulence or separation reduces, and the boundary layer may stabilize or transition. The skin friction coefficient decreases further to around 0.016 705 at 80° and remains nearly constant at 0.016 729 at 90°. The lower values indicate reduced frictional drag at high AoAs, possibly due to a more stable or less turbulent boundary layer.

At the trailing edge, the maximum skin friction coefficient is 0.017 927 at 0° and rises to 0.026 837 4 at 30°. This indicates that frictional drag increases with increasing AoA, likely due to the growing effect of the boundary layer and potential turbulence. The skin friction coefficient continues to rise, reaching 0.039 426 2 at 90°. This consistent increase suggests that the trailing edge experiences ongoing frictional drag as the AoA increases, again likely due to stronger turbulence or boundary layer growth.

Figure 11 depicts the flow pathlines, illustrating the flow trajectories around the airfoil. The smooth flow lines over the leading edge transition into separation at the upper trailing edge, indicating a loss of streamlined flow. This pattern highlights the effects of flow detachment and reattachment, which significantly affect lift and drag characteristics. The trajectory divergence near the trailing edge is consistent with increased turbulence and vorticity, especially at high AoAs.

Figure 12 shows the static pressure distribution around the airfoil. A region of high pressure is visible on the lower surface of the airfoil, while the upper surface experiences a lower-pressure zone, contributing to lift generation. Near the trailing edge, a gradual pressure recovery is evident, but the leading-edge pressure peak and separation zone highlight the effects of adverse pressure gradients, a precursor to stall phenomena at higher AoAs.

Figure 13 shows the velocity magnitude around the airfoil. It highlights a high-speed flow region over the upper surface due to low pressure and accelerated airflow, a characteristic feature of lift generation. The flow deceleration on the lower surface indicates relatively higher pressure. At the leading edge, flow separation zones and reattachment can be observed, which are particularly significant at higher AoAs, leading to turbulence and flow instability.

Figure 14 depicts the velocity magnitude distribution around the airfoil, visualized by velocity contours and flow vectors. High velocities (red regions) are observed over the upper surface near the leading edge, corresponding to low pressure, while low velocities (blue regions) indicate high pressure on the lower surface. The flow pattern indicates a smooth airflow at lower AoAs, while at higher AoA, signs of turbulence and flow separation appear near the trailing edge, significantly affecting aerodynamic performance.

Figure 15 shows the pressure coefficient C_p distribution along the chord length of the airfoil for AoAs of 10°, 30°, 60°, and 90°. At lower AoAs (10° and 30°), the pressure distribution is smooth, with a higher pressure on the lower surface and a lower pressure on the upper surface, indicating efficient lift generation. As the AoA increases to 60° and 90°, the pressure difference diminishes, and the curves become more symmetric, indicating reduced lift and increased drag due to flow separation and potential stall.

A comparison between the present study and data from Ref. 39 shows a generally consistent trend in the lift coefficient C_L across the tested AoAs, with percentage variations ranging from 6.98% to 19.16%,as shown in Fig. 16. At 0° AoA, the present study predicts a C_L of 1.29, which is 6.98% higher than the value of 1.2 in Ref. 39. This minor deviation could result from differences in turbulence modeling. At 4° AoA, the percentage variation increases to 19.16%, indicating a more significant overprediction by the present study (C_L = 1.67 compared with 1.35 in Ref. 39). This might be due to enhanced sensitivity of the k-ω SST model to flow attachment and near-wall behavior at low AoAs.

At 12° AoA, the percentage variation is 11.5%, with the present study predicting C_L = 2.0, compared with 1.77 in Ref. 39, demonstrating reasonable agreement while slightly overestimating lift. Finally, at 16° AoA, the present study predicts C_L = 2.24, which is 9.82% lower than the value of 2.46 in Ref. 39, possibly because of the prediction of earlier flow separation by the k-ω SST model.

Overall, the present study captures the trends of increasing and decreasing C_L with increasing AoA, validating the use of the k-ω SST model for high-AoA simulations. However, the observed variations highlight the impact of model assumptions, mesh resolution, and turbulence behavior on simulation accuracy, emphasizing the need for refinement to reduce discrepancies further.

Variations in experimental wind tunnel facilities and differences in atmospheric conditions play a significant role in the data collection and evaluation process, which ultimately could result in the discrepancy between experimental and simulation data.

This study has presented a detailed analysis of the aerodynamic performance of a low-Reynolds-number airfoil across a wide range of high AoAs from 0° to 90°. The findings provide both quantitative and qualitative insights into the airfoil’s behavior, which are crucial for optimizing designs for MAV and UAV applications.

1. The lift coefficient C_L increases from 1.2981 at 0° AoA to a maximum of 2.034 at 11°, then decreases to 1.51 at 90°. At moderate AoAs, the airfoil provides effective lift generation, but it faces challenges at extreme angles due to flow separation or stall, which affects lift.

2. The drag coefficient C_D increases significantly from 0.0222 at 0° AoA to a peak of 0.3572 at 12°, then decreases to 0.0467 at 90°. The observed trend in C_D shows that higher AoAs cause more turbulence and flow separation at first, but then high AoAs make the flow more stable.

3. The lift-to-drag (L/D) ratio reaches a maximum of 32.334 at 90° AoA, showing that aerodynamic efficiency improves at high AoAs despite the increased drag. This high L/D ratio indicates that the airfoil performs efficiently at extreme AoAs, making it advantageous for certain UAV applications.

4. The maximum skin friction coefficient C_f at the leading edge is 0.046 918 at 30° AoA, while at the trailing edge it peaks at 0.039 426 2 at 90°. These values reveal the locations where frictional drag is most important. There are strong frictional forces at the leading edge because of turbulence or flow separation, and there is more drag at the trailing edge because the boundary layer is growing.

5. The turbulence viscosity ratio at the leading edge peaks at 0.5586 at 30° AoA, indicating high turbulence relative to viscosity, and decreases to 0.004 at 90°. At the trailing edge, this ratio consistently increases, reaching 0.039 426 2 at 90°, suggesting more pronounced turbulence effects at higher AoAs.

These insights are essential for optimizing airfoil designs to enhance performance and efficiency for MAV and UAV applications. Further research into boundary layer behavior and turbulence management could provide additional improvements in aerodynamic design.

The authors have no conflicts to disclose.

V. Somashekar: Investigation (lead). L. Vinod: Methodology (supporting); Writing – original draft (supporting).

The data that supports the findings of this study are available within the article.