3.1. Aerodynamic Performance
The calculated lift coefficients of both smooth and rough airfoils are compared to experimental results by Van Rooij et al. [
17], as illustrated in
Figure 4. The comparison shows that the numerical results closely match the experimental data, thereby confirming the reliability of the numerical methods used in this research. For the smooth airfoil, the lift coefficient increases linearly around an AOA of 0°. When the AOA exceeds 8°, the lift coefficient curve begins to deviate from this linear trend, indicating the onset of trailing edge separation on the upper surface of the airfoil. In contrast, the rough airfoil’s lift coefficient curve exhibits a distinctive “N” shape. Initially, the lift coefficient rises from 0 to 0.6 as the AOA increases from −10° to 0°. Between AOAs of 0° and 5°, a segment with a negative slope in the lift curve is observed. Beyond an AOA of 5°, the lift coefficient continues to rise but at a relatively low rate. The flow pattern and underlying mechanisms responsible for this unique “N” shape in the lift performance of the rough airfoil will be explored in the subsequent subsections.
Some discrepancies between the numerical and experimental results, particularly in the near-stall region, can be observed in
Figure 4. These differences may be attributed to the turbulence model used in this study (the four-equation transition SST model), which assumes turbulence is isotropic and may not perform well under conditions of massive flow separation. To achieve greater accuracy in the near-stall and post-stall regions, more advanced numerical methods, such as Large Eddy Simulation (LES), Detached Eddy Simulation (DES), or Scale-Adaptive Simulation (SAS), may yield better results. However, this research primarily focuses on the effects of leading-edge roughness, particularly on the nonlinear lift performance around a 0° angle of attack (AOA). The influence of leading-edge roughness is relatively minor in the post-stall region, where large-scale leading-edge separation vortices dominate. Additionally, one of the objectives of this study is to develop a practical numerical method that can be applied to large-scale wind turbine blades to estimate the impact of leading-edge roughness. For modern large-scale wind turbines equipped with pitch control systems, the blade sections typically operate at relatively low angles of attack. Given these considerations, the current numerical method is deemed sufficient for capturing the primary characteristics induced by leading-edge roughness.
Figure 5 displays the calculated drag coefficients for both smooth and rough airfoils. The smooth airfoil exhibits its lowest drag coefficient, approximately 0.01, at an AOA of 0°. The drag coefficient increases as the AOA deviates from 0°, either increasing or decreasing. For AOAs greater than 8°, the drag coefficient rises sharply, attributed to the onset of trailing edge separation on the upper surface and the consequent increase in pressure drag. In contrast, the rough airfoil consistently exhibits a higher drag coefficient curve compared to the smooth airfoil. At AOAs near 0°, where friction drag predominates, the difference in drag coefficient is approximately 0.03, likely due to the increased friction drag caused by the leading-edge roughness. As the AOAs increase, the difference in drag coefficient grows, which may be attributed to changes in the separation condition induced by the roughness at the leading edge, leading to a more significant pressure drag. Notably, there is a slight decrease in the drag coefficient between AOAs of 2° and 4°. The reasons behind this decrease will be examined in the following subsections.
3.2. Flow Patterns
Figure 6 illustrates the contour of turbulence intensity around the smooth airfoil at an AOA of 0°. The boundary layer flow is laminar before reaching halfway along the chord, exhibiting relatively low turbulence intensity. As the flow passes around the mid-chord, the thickness of the region with high turbulence intensity gradually increases, indicating a transition to a turbulent boundary layer.
Figure 7 presents the nondimensional streamwise wall shear at this condition, defined by
where
is the streamwise wall shear. The value of
is positive if the flow is attached and negative for reversed flow, providing an intuitive depiction of the laminar separation bubble and turbulent separation point positions. According to
Figure 7, the laminar separation bubble is located around 46% of the chord on the lower surface and around 38% of the chord on the upper surface. Beyond these points, the flows reattach and the boundary layer becomes turbulent. This indicates that the turbulence model used in this research can simulate the free-transition condition of airfoils effectively. Additionally, a small trailing-edge separation vortex is observed at around 75% of the chord on the lower surface, while turbulent separation is absent on the upper surface. This phenomenon is due to the higher adverse pressure gradient from the maximum thickness position to the trailing edge on the lower surface.
Figure 8 and
Figure 9 display the contours of turbulence intensity and the nondimensional streamwise wall shear of the rough airfoil at 0° AOA, respectively. Due to the influence of leading-edge roughness, the boundary layer on the rough airfoil is fully turbulent, with regions of high turbulence intensity covering the entire airfoil surface, as seen in
Figure 8. This complete transition eliminates the presence of a laminar separation bubble, as observed in
Figure 9. This indicates that the primary effect of the leading-edge roughness is to establish a fixed-transition condition, resulting in a turbulent boundary layer over most of the airfoil surface.
Figure 9 also reveals that the wall shear around the leading edge of the rough airfoil is significantly higher than that of the smooth airfoil, contributing to the higher drag coefficient seen in
Figure 5. When the flow passes the end of the leading-edge roughness, at approximately 2% of the chord (c) on the upper surface and 10% of the chord on the lower surface, there is an abrupt drop in wall shear. The turbulent separation point on the lower surface moves upstream to around 52% of the chord, compared to the smooth airfoil. Additionally, the scale of the trailing-edge separation vortex increases, accompanied by high turbulence intensity. The flow on the upper surface remains attached, similar to the smooth airfoil.
The streamlines around the smooth and rough airfoils at different AOAs are shown in
Figure 10 and
Figure 11, respectively. For the smooth airfoil, the flow remains fully attached at AOAs of 0° and 4°, where the lift coefficient curve increases linearly. A trailing-edge separation vortex appears on the lower surface at an AOA of −6°, and on the upper surface at an AOA of 14°, where the lift coefficient curve deviates from its linear increase. These flow patterns are similar to those observed on traditional thin airfoils of combined trailing-edge and leading-edge stall types.
For the rough airfoil, a separation vortex is evident on the lower surface at an AOA of −6°, with the separation point located around the maximum thickness position. The separation vortex is significantly larger compared to the smooth airfoil. As the AOA increases to 0°, the separation point on the lower surface remains near the maximum thickness position, while the scale of the separation vortex reduces. With a further increase in AOA to 4°, the separation point on the lower surface moves downstream to about 2/3 of the chord, and the size of the separation vortex further decreases. Additionally, trailing-edge separation begins to develop on the upper surface, matching the scale of the separation vortex on the lower surface. At an AOA of 14°, the flow is fully attached to the lower surface, while the separation vortex on the upper surface grows significantly, extending to the entire scale of the airfoil and creating a secondary vortex downstream of the trailing edge. Overall, the flow separation patterns of the rough airfoil differ substantially from those of the smooth airfoil, particularly at AOAs of 0° and 4° within the negative-slope lift region. The formation mechanism of the negative-slope lift will be further explored in the following subsection.
3.3. Mechanism Discussion on the Nonlinear Lift Performance
To elucidate the formation mechanism of the negative-slope lift performance of the rough airfoil around 0° AOA, the pressure contours and streamlines at 0° and 4° AOA are compared, as shown in
Figure 12. The characteristic streamlines between the main stream and the separation vortex were extracted and marked in the figure. Given that the normal pressure variation is minimal in the separation region, the airfoil profile combining these characteristic streamlines can be considered as an enclosed control body, which approximately conforms to potential flow theory. For the lower surface, as the AOA increases from 0° to 4°, the characteristic streamline rises while the trailing-edge separation vortex diminishes. Consequently, the adverse pressure gradient from the maximum thickness position to the trailing-edge confluence increases, resulting in a stronger negative pressure around the maximum thickness on the lower surface. In contrast, on the upper surface, the characteristic streamline also rises but the trailing-edge separation vortex enlarges. This causes a reduction in the adverse pressure gradient from the maximum thickness position to the trailing-edge confluence, leading to a weaker negative pressure around the maximum thickness position. The resulting pressure coefficient distribution is shown in
Figure 13. The combined effect of the enhanced negative pressure peak on the lower surface and the weakened negative pressure peak on the upper surface causes a significant drop in airfoil lift as the AOA increases from 0° to 4°, thereby demonstrating a distinct negative-slope lift performance.
3.4. Effect of Roughness Height
The aerodynamic performance of smooth and rough airfoils differs significantly, as detailed in the previous subsections. This raises the question of whether a critical state exists between these two performance regimes. To explore this, the effect of roughness height (RH) on airfoil performance is further analyzed, as illustrated in
Figure 14. At low roughness heights (RH ≤ 0.05 mm), the lift coefficient curve closely mirrors that of a smooth airfoil, with both the lift slope and post-stall lift gradually decreasing as RH increases. This suggests that at low RH, the aerodynamic characteristics are only marginally affected, exhibiting a performance similar to that of a smooth airfoil, albeit with a slight decline. Conversely, at high roughness heights (RH ≥ 0.30 mm), the lift coefficient curve adopts a distinctive “N” shape, showing minimal variation with further increases in RH. This indicates that at high RH, aerodynamic performance is predominantly governed by the roughness, leading to a significantly altered and less efficient lift behavior that stabilizes in this new regime. For medium roughness heights (0.07 mm ≤ RH ≤ 0.10 mm), an intermediate condition emerges, characterized by unstable flow behavior as the angle of attack (AOA) increases, resulting in multiple saltation points in the lift curve. This reflects a transitional state where aerodynamic performance is neither fully smooth nor fully rough, leading to fluctuating and unstable lift characteristics.
According to the continuity and smoothness of the lift coefficient curves in
Figure 14, four distinct flow regimes can be identified, as illustrated in
Figure 15. The classification of these flow regimes under varying roughness heights is summarized in
Figure 16. The primary characteristics of these flow regimes are detailed as follows:
The Type 1 Flow Regime primarily occurs on relatively smooth airfoils (RH ≤ 0.05 mm). The flow patterns with increasing AOA are similar to those observed on traditional thin airfoils, as depicted in
Figure 10. As the AOA increases from −6° to 18°, the flow undergoes a transition from trailing-edge separation on the lower surface to full attachment and finally to trailing-edge separation on the upper surface. The value of the lift coefficient decreases with increasing roughness, which is also similar to the behavior observed on traditional thin airfoils.
The Type 2 Flow Regime is mainly observed at small negative angles on rough airfoils (RH ≥ 0.30 mm). The trailing-edge separation vortex on the lower surface is relatively stable. As the AOA increases, the adverse pressure gradient on the upper surface increases, leading to a corresponding rise in the lift coefficient, as depicted in
Figure 11a,b. The lift coefficient in this regime is relatively insensitive to variations in roughness height.
The Type 3 Flow Regime is mainly observed at positive angles on rough airfoils (RH ≥ 0.30 mm). The trailing-edge separation vortex on the upper surface enlarges with increasing AOA (
Figure 11c,d), which plays a dominant role in lift performance. The scale of the separation vortex is larger than that at a same AOA in the Type 1 Flow Regime, leading to a relatively low lift coefficient. The Type 3 Flow Regime typically follows the Type 2 Flow Regime, with an abrupt transition between the two, giving rise to the characteristic “N” shape in the lift coefficient curve.
The Type 4 Flow Regime is primarily observed on airfoils with medium roughness heights (0.07 mm ≤ RH ≤ 0.10 mm). The overall trend of the lift curve is similar to Type 3 but slightly higher. This difference is attributed to the flow on the lower surface not being fully turbulent, as confirmed by wall shear analysis in
Figure 17. It is shown that the flow is fully turbulent for RH = 0.3 mm, while an evident transition can be observed around half the chord on the lower surface for RH = 0.1 mm.
These four flow regimes illustrate how varying roughness heights influence the aerodynamic performance of airfoils, resulting in distinct lift characteristics under different conditions.