Wavy Airfoil Research Articles

Analysis of wavy leading-edge noise reduction and source mechanism in rod-airfoil interactions

Inspired by the wings of owls and the tubercles present on humpback whales' flippers, leading-edge serrations have demonstrated the potential to mitigate airfoil–turbulence interaction noise. To deepen our understanding of the underlying mechanisms driving this noise reduction, we conducted compressible large-eddy simulations on a rod-airfoil configuration equipped with wavy leading edges (WLEs) of varying amplitudes. All tested serrations exhibited some degree of noise reduction, with the amplitude of the WLE exerting a significant influence on the overall noise reduction effect. Notably, the wavy airfoil with the largest amplitude demonstrated the most substantial noise reduction in the mid-frequency range, achieving a remarkable decrease in up to 2.2 dB in noise levels. Applying multi-process acoustic theory, we delved into sound production on surfaces and near-field structures responsible for generating noise sources. Our findings underscore a crucial mechanism contributing to noise reduction—the source cutoff effects manifested through the significant weakening of noise sources at hill regions along the serrations' surface. Stronger source cutoff effects were observed with larger WLE amplitudes. Furthermore, our study reveals that destructive relationships among sources also play a pivotal role in reducing flow noise. The reduction in mid-frequency noise results from a synergy of the source cutoff effect and destructive source relationships induced by WLEs, while the decrease in low-frequency noise primarily emanates from the source cutoff effect.

Effect of wavy leading edges on airfoil tonal noise

This work presents numerical studies on the effect of wavy leading edges on airfoil instability tonal noise. Large eddy simulations are conducted for NACA0012 (National Advisory Committee for Aeronautics) airfoils with straight and wavy leading edges. The far-field aerodynamic noise is predicted using the Ffowcs Williams and Hawkings acoustic analogy theory. The inflow Mach number is approximately 0.17 with an angle of attack of 4.3°, and the chord based Reynolds number is 600 000. The present numerical method is first validated by existing numerical results and a semi-empirical model for the straight baseline airfoil. Then, the effects of wavy leading edges on the aerodynamic performance, aeroacoustic performance, and noise reduction mechanisms are discussed in detail. The wavy leading edge is found to be detrimental to the mean aerodynamic performance with a decreased lift and increased drag. However, the lift fluctuations are significantly reduced. The instability tonal noise and its harmonic are totally removed by the wavy leading edges, while an extra broadband hump appears at the middle frequency. The low frequency and high frequency noise are also increased by the wavy airfoil. The laminar separation bubble is removed, and the flow separation is decreased by the wavy airfoil in the vicinity of the trailing edge. The pressure fluctuations around the trailing-edge are considerably diminished, and the spanwise coherence spectra are also significantly reduced by the wavy airfoil. Furthermore, it is noteworthy that the coherence reduction spectrum at the source is almost consistent with the far-field noise reduction spectrum.

Experimental Study on Wind Turbine Airfoil Trailing Edge Noise Reduction Using Wavy Leading Edges

Aerodynamic noise produced by the rotating blade is an important hindrance for the rapid development of modern wind turbines. Among the various noise sources, the airfoil trailing edge noise contributes a lot to the wind turbine noise. The control of wind turbine airfoil trailing edge self-noise by bio-inspired sinusoidal wavy leading edges is experimentally studied in a semi-anechoic chamber. The noise radiated by the baseline NACA 0012 airfoil and various wavy airfoils is measured using a planar microphone array consisting of fifty-two microphones. The noise source identifications are achieved by using the CLEAN-SC method. The effects of velocity and angle of attack on noise radiation of the baseline airfoil are analyzed in detail. The noise control law of the wavy amplitude and wavelength on airfoil trailing edge noise is explored. Based on the acoustic beamforming results, the noise control effects of the wavy leading edges are intuitively demonstrated. In general, the wavy leading edge with a larger amplitude and smaller wavelength has a better effect on the airfoil trailing edge noise reduction. The maximum sound pressure level reduction can be up to 33.9 dB. The results of this study are expected to provide important information for wind turbine aerodynamic noise control.

Optimization of configuration of corrugated airfoil using deep reinforcement learning and transfer learning

An optimization method combining deep reinforcement learning (DRL) and computational fluid dynamics (CFD) was developed, and its effectiveness and limitations are investigated. As a target to apply the method, an optimization problem to find geometry parameters of the wavy airfoil that maximizes the lift–drag ratio is set. Twin delayed deep deterministic policy gradient (TD3) is adopted as the DRL algorithm. The CFD code based on the standard scheme for viscous incompressible flows is used for the calculation of the lift–drag ratio. The neural networks learn a policy for improving the lift–drag ratio by changing the geometry parameters of the airfoil at the fixed angle of attack (AoA) of 0° and successfully achieve a maximum lift–drag ratio: the obtained final shape is almost the same as that acquired by the gradient method. However, when the global optimal solution is near the penalized region, the DRL has the disadvantage of tending to fall into local optima. The effects of several parameters of DRL, such as the reward function and the number of sample points in random exploration, are investigated. Moreover, by using a trained neural network at an AoA of 0°, a converged solution can be obtained more quickly for an AoA different from those of the trained case if an appropriate reward function is set. This indicates the possibility of transfer learning.

Modeling of the compartmentalization effect induced by leading-edge tubercles

As a passive flow control technique, the use of leading-edge tubercles inspired by humpback whale flippers has attracted much interest. It is believed that one of the flow control mechanisms of leading-edge tubercles is compartmentalization, which is similar to the way in which wing fences act. However, to date, there has been no direct evidence for this belief. In view of this, the present work aims to verify and quantitatively describe the compartmentalization effect induced by leading-edge tubercles. Numerical simulation is performed to investigate the flow structures on a wavy airfoil with leading-edge tubercles, and the results reveal the presence of typical biperiodic flow patterns when a critical angle of attack is exceeded. Based on the flow characteristics of the wavy airfoil, special fences paired in a diverging configuration are designed and positioned on the baseline airfoil. A modeling method is developed to determine the main parameters of the fence configurations. It is found that the fenced airfoils designed using this method are able to reproduce the typical flow characteristics of the wavy airfoil under different inflow conditions. The spanwise distributions of the sectional airfoil performance under flow control by leading-edge tubercles and by the specially designed fences are very similar. A combined mechanism mainly including the lifting-line theory and the compartmentalization theory is proposed to provide a more comprehensive picture of the flow dynamic of leading-edge tubercles. This work provides strong evidence to confirm the compartmentalization mechanism of action of leading-edge tubercles, as well as developing a quantitative modeling method, both of which are important for fully understanding the underlying mechanism and guiding further optimization of this passive flow control technique.

Investigation of leading-edge protuberances for the performance improvement of thick wind turbine airfoil1

An effective flow separation control method is urgently needed to improve the aerodynamic performance of the thick wind turbine airfoil. The purpose of the present study is to explore the effect of leading-edge protuberances (LEPs) on the aerodynamic performances for thick wind turbine airfoil during stall region. A direct force measurement technique employing three-component force balance was used to analyze the aerodynamic characteristics of airfoils with LEPs at a Reynolds number of Re = 2 × 105 through the wind tunnel experiment. Particle Image Velocimetry measurement was also performed to understand the effects of LEPs on flow separation and to correlate these effects with the aerodynamic performances of airfoil. The mean velocity and vorticity results indicate that the LEPs can effectively suppress flow separation for the thick airfoil in the stall region, moreover the airfoil with smaller amplitudes and wavelengths tends to perform significantly better in flow separation control. The LEPs method promotes the wavy airfoil with a better flow separation characteristics, which can effectively improve the aerodynamic performance and reduce the intensity of aerodynamic fluctuations for the thick airfoil. In addition, the stall process of the wavy airfoil is much gentler without sharp deterioration. Therefore, the LEPs method can help maintain high aerodynamic performance and prevent structural problems for the inboard region of wind turbine blades.

Mitigation of transonic shock buffet on a supercritical airfoil through wavy leading edges

Mitigation of the shock buffet phenomenon over a supercritical airfoil by means of wavy leading edges (WLEs) is analyzed with implicit large eddy simulations. A Dassault Aviation's V2C airfoil is simulated in a transonic flow with Re∞=5.0×105 and M∞=0.7 at α=7.0°. This airfoil profile is designed for transonic flows, delaying the onset of wave drag and decreasing the skin friction drag. The results of this upstream flow condition on a straight airfoil are a large oscillation of lift and drag coefficients. In the first part, time-averaged aerodynamic characteristics over a straight leading edge (SLE) airfoil and three modified airfoils with different wavy amplitudes are compared. The results show that overall WLE airfoils are more efficient than SLE ones, and the airfoil with the lowest amplitude (h = 0.0075) is the most efficient, increasing the lift coefficient and decreasing the drag coefficient. Flow unsteadiness plays a key role for airfoils in transonic flows at moderate and high angles of attack. Hence, the second part of the paper is a detailed unsteady analysis of flow phenomena. The starting point is an investigation of unsteady aerodynamic performance. It is observed that WLE airfoils are capable of significantly decreasing low-frequency oscillations' amplitude, identified with shock buffet. The best performance is obtained with h = 0.0125 where a high-frequency oscillation becomes the dominant unsteady phenomenon. High-frequency oscillations are identified through the application of a frequency filtering method to the flow field. It is proved that the oscillation on the SLE airfoil is related to vortex shedding, while the one on WLE airfoils is related to laminar separation bubble (LSB) breathing. Overall, the unsteady analysis shows a connection between shock buffet and LSB breathing phenomena on wavy airfoils and identifies the WLE amplitude as a key parameter to control this relation and mitigate the shock buffet.

Aerodynamic performance and wake development of airfoils with wavy leading edges

A comprehensive numerical investigation is performed to study the aerodynamic performance and wake development of a NACA0012 airfoil with wavy leading edges (WLE). The WLEs are in the form of sinusoidal profiles with two design parameters of amplitude and wavelength. Parametric studies of the amplitude and wavelength are conducted to better understand the effect of WLEs. The chord length based Reynolds number is 400 000 and the angle of attack varies from 0° to 20°. For angles of attack less than the stall angle, steady Reynolds-averaged Navier–Stokes (RANS) computations are carried out using the SST (Shear Stress Transportation) k–ω turbulence model. For the post-stall angles of attack, unsteady simulations are carried out using the SST–SAS (Scale-Adaptive Simulation) model to solve the transient separation flow. The numerical results indicate that the aerodynamic performance of the wavy airfoil is sensitive to both the amplitude and wavelength of the WLEs. The WLE with a larger amplitude and smaller wavelength results in a worse aerodynamic performance. The drag coefficient is decreased significantly by the WLEs in the post-stall region. In addition, the wavy airfoils possess a soft stall process without the abrupt loss of the lift when the amplitude is large enough. The wake profiles for the wavy airfoils differ significantly from those for a conventional airfoil, especially for high angles of attack. In the post-stall regime of the baseline airfoil, the wavy airfoils have a higher wake deficit compared to the baseline airfoil, but the turbulence kinetic energy is reduced significantly. The leading edge separation vortex generated by the baseline airfoil is broken down into small vortices by the wavy modification, leading to a reduced lift and drag fluctuations.

Aerodynamic load control on a dynamically pitching wind turbine airfoil using leading-edge protuberance method

The aerodynamic loads of wind turbine blades are substantially affected by dynamic stall induced by the variations of the angle of attack of local airfoil sections. The purpose of the present study is to explore the effect of leading-edge protuberances on the fluctuation of the aerodynamic performances for wind turbine airfoil during dynamic stall. An experimental investigation is carried out by a direct force measurement technique employing force balance at a Reynolds number Re = 2 × 105. The phase-averaged and instantaneous aerodynamic loads of the pitching airfoil, including the baseline and the wavy airfoil, are presented and analyzed. The phase-averaged results indicate that the effects of dynamic stall for the wavy airfoil can be delayed or minimized compared to the baseline airfoil, and the negative damping area of the wavy airfoil is significant decreased in full-stall condition. These effects of leading-edge protuberances are more notable at a higher reduced frequency. For the instantaneous aerodynamic loads of the wavy airfoil, there is an observable reduction in fluctuations compared with baseline case. Furthermore, spectral analysis is applied to quantitatively undercover the nonstationary features of the instantaneous aerodynamic loads. It is found that the leading edge protuberances can reduce the harmonics of the aerodynamic force signal, and enhance the stability of the aerodynamic loads under different reduced frequencies. In conclusion, leading-edge protuberances are found effective to reduce the fluctuation characteristics of the aerodynamic loads during the dynamic stall process, and help to improve the stability and prolong the service life of the wind turbine blades.

Aerodynamic Shape Optimization of a Wavy Airfoil for Ultra-Low Reynolds Number Regime in Gliding Flight

The effect of the number of waves and the width of the ridge and valley in chord direction for a wavy airfoil was investigated at the angle of attack of 0 ∘ and Reynolds number of 10 3 through using the two-dimensional direct numerical simulation for four kinds of wavy airfoil shapes. A new method for parameterizing a wavy airfoil was proposed. In comparison with the original corrugated airfoil profile, the wavy airfoils that have more distinct waves show a lower aerodynamic efficiency and the wavy airfoils that have less distinct waves show higher aerodynamic performance. For the breakdown of the lift and drag concerning the pressure stress and friction stress contributions, the pressure stress component is significantly dominant for all wavy airfoil shapes concerning the lift. Concerning the drag, the pressure stress component is about 75 % for the wavy airfoils that have more distinct waves, while the frictional stress component is about 70 % for the wavy airfoils that have less distinct waves. From the distribution of pressure isoline and streamlines around wavy airfoils, it is confirmed that the pressure contributions of the drag are dominant due to high pressure on the upstream side and low pressure on the downside; the frictional contribution of the drag is dominant due to large surface areas of the airfoil facing the external flow. The effect of the angle of attack on the aerodynamic efficiency for various wavy airfoil geometries was studied as well. Aerodynamic shape optimization based on the continuous adjoint approach was applied to obtain as much as possible the highest global aerodynamic efficiency wavy airfoil shape. The optimal airfoil shape corresponds to an increase of 60 % and 62 % over the aerodynamic efficiency and the lift from the initial geometry, respectively, when optimal airfoil has an approximate drag coefficient compared to the initial geometry. Concerning an fixed angle of attack, the optimal airfoil is statically unstable in the range of the angle of attack from − 1 ∘ to 6 ∘ , statically quasi-stable from − 6 ∘ to − 2 ∘ , where the vortex is shedding at the optimal airfoil leading edge. Concerning an angle of attack passively varied due to the fluid force, the optimal airfoil keeps the initial angle of attack value with an initial disturbance, then quickly increases the angle of attack and diverges in the positive direction.

Flow control on wind turbine airfoil affected by the surface roughness using leading-edge protuberance

In recent years, leading-edge protuberances have attracted plenty of attention as a passive method to manipulate flow separation on wind turbine blades. In this paper, an experimental investigation is carried out to explore the effect of leading-edge protuberances on the aerodynamic performance of wind turbine airfoils with and without surface roughness. A direct force measurement technique with the application of three-component balance is applied, and a hot-wire anemometer is used to measure the boundary layer flow to understand the governing mechanism for the flow regulation of the leading-edge protuberances. The current results confirm that the surface roughness leads to a decreased lift-to-drag ratio and an increased aerodynamic fluctuation of the baseline airfoil, which may cause severe losses in wind power capture. For the wavy airfoil, the leading-edge protuberance has facilitated the suppression of flow separation and the improvement of the airfoil aerodynamic performance in the poststall region. The results of the velocity measurement indicate that the leading-edge protuberances weaken the vortex shedding on the airfoil, which has a significant impact on the fluctuation of the aerodynamic force. For airfoils with a rough surface, the vortex shedding energy close to the trailing edge is evidently weakened for the wavy airfoil, which contributes effectively to the suppression of the shedding of the separated vortex and improve the stability of the aerodynamic force, compared to the baseline case. The effectiveness of leading-edge protuberances in the improvement of the performance stability may facilitate the service life of the blade and the ability of wind power capture.

Aerodynamic Control of Low-Reynolds-Number Airfoil with Leading-Edge Protuberances

This paper presents an experimental investigation of the control of airfoil aerodynamics at a low Reynolds number of within a wide range of attack angle using a leading-edge-protuberance technique. The essence of the technique is to manipulate flow around the airfoil by replacing the straight leading edge of a baseline airfoil with a sinusoidal wavy airfoil. Whereas the lift and drag forces and the lift-to-drag ratio were measured using a three-component force balance, the flow was mainly measured using a particle-image velocimetry. The sinusoidal protuberances effectively suppressed airfoil stall, and the corresponding aerodynamic performance was impaired to some extent. Meanwhile, control significantly improved the airfoil aerodynamics in the poststall region, for example, , leading to a maximum 25.0 and 39.2% increase in lift coefficient and lift-to-drag ratio, respectively, and a maximum 20.0% decrease in drag coefficient. The protuberances may influence control performance in a similar way with low-profile vortex generators. The flow physics behind the observations were discussed in detail.

Numerical study of flows past airfoils with wavy surfaces

The paper presents three-dimensional numerical studies on the aerodynamic characteristics of two different modified NACA0012 airfoils with different wavy surfaces using the large eddy simulations. Two types of wavy airfoils are investigated with wavy airfoil-A having a sinusoidal waviness on upper and lower surfaces with a constant chord length, while wavy airfoil-B having sinusoidal variation in both of the leading and trailing edges as well as on the upper and lower surfaces along the spanwise direction. The force characteristics and the flow structures are captured and compared with a corresponding standard NACA0012 airfoil with a Reynolds number of Re=1.6×105. The flow structures and surface pressure distributions on wavy airfoils were found to be significantly different from those on a conventional NACA0012 airfoil. For angles of attack less than the baseline stall angle of a NACA0012 airfoil, a slight decrease of lift coefficient was observed for both types of wavy airfoils, while the lift coefficient for the wavy airfoil-B increases up to 20% greater than that of a NACA0012 airfoil when the angle of attack is larger than the baseline stall angle of 13°. The flow over the leading edge of wavy airfoil-B remained attached at post stall angles of attack. In general, the wavy airfoil-A just exhibits a suppression the airfoil’s fluctuation force, while the wavy airfoil-B demonstrates an advantageous aerodynamic effect on the control of loss of lift in the post stall regime of a conventional NACA0012 airfoil.

Numerical Investigation of Flow past a Wavy Airfoil

The effect of the wavy surface on the aerodynamic characteristics of an airfoil is studied using the large eddy simulations. A more gentle lift characteristic is obtained during stall. For angles of attack less than the baseline stall angle of a NACA0012 airfoil, a lift coefficient reduction was observed for the wavy airfoils, while the lift coefficient increases up to 23% greater than that of a NACA0012 airfoil when the angle of attack is larger than the baseline stall angle of the NACA0012 airfoil.