Unsteady loading on an airfoil of arbitrary thickness

The unsteady loading on an airfoil of arbitrary thickness is evaluated by using the generalized form of Blasius theorem and a conformal mapping that maps the airfoil surface onto a circle. For a blade vortex interaction the results show that the time history of the unsteady loading is determined by the passage of the vortex relative to the leading edge singularity in the circle plane. The singularity lies inside the circle and moves to a smaller radius as the thickness is increased, causing the unsteady loading pulse to be smoothed. The effect of angle of attack is to move the stagnation point relative to the leading edge singularity and this significantly increases the unsteady lift if the vortex passes on the suction side of the airfoil. These characteristics are different for a step upwash gust, which is considered as a simplified model of a large scale turbulent gust. It is shown that the time history of the magnitude of the unsteady loading is almost completely unaltered by angle of attack for the step gust, but it's direction of action rotates forward by an angle equal to the angle of attack, extending an earlier result by Howe for a flat plate in a turbulent flow to airfoils of arbitrary thickness. However spectral analysis of the gust shows that the high frequency blade response is reduced as the thickness of the airfoil is increased.     

Symbolic regression modeling of noise generation at porous airfoils

Based on data sets from previous experimental studies, the tool of symbolic regression is applied to find empirical models that describe the noise generation at porous airfoils. Both the self noise from the interaction of a turbulent boundary layer with the trailing edge of an porous airfoil and the noise generated at the leading edge due to turbulent inflow are considered. Following a dimensional analysis, models are built for trailing edge noise and leading edge noise in terms of four and six dimensionless quantities, respectively. Models of different accuracy and complexity are proposed and discussed. For the trailing edge noise case, a general dependency of the sound power on the fifth power of the flow velocity was found and the frequency spectrum is controlled by the flow resistivity of the porous material. Leading edge noise power is proportional to the square of the turbulence intensity and shows a dependency on the fifth to sixth power of the flow velocity, while the spectrum is governed by the flow resistivity and the integral length scale of the incoming turbulence.     

Effect of relative camber on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification

In this paper, the aerodynamic performance of the S series of wind turbine airfoils with different relative cambers and their modifications is numerically studied to facilitate a greater understanding of the effects of relative camber on the aerodynamic performance improvement of asymmetrical blunt trailing-edge modification. The mathematical expression of the blunt trailing-edge modification profile is established using the cubic spline function, and S812, S816 and S830 airfoils are modified to be asymmetrical blunt trailing-edge airfoils with different thicknesses. The prediction capabilities of two turbulence models, the k-ω SST model and the S-A model, are assessed. It is observed that the k-ω SST model predicts the lift and drag coefficients of S812 airfoil more accurately through comparison with experimental data. The best trailing-edge thickness and thickness distribution ratio are obtained by comparing the aerodynamic performance of the modifications with different trailing-edge thicknesses and distribution ratios. It is, furthermore, investigated that the aerodynamic performance of original airfoils and their modifications with the best thickness of 2% c and distribution ratio being 0:4 so as to analyze the increments of lift and drag coefficients and lift–drag ratio. Results indicate that with the increase of relative camber, there are relatively small differences in the lift coefficient increments of airfoils whose relative cambers are less than 1.81%, and the lift coefficient increment of airfoil with the relative camber more than 1.81% obviously decreases for the angle of attack less than 6.3°. The drag coefficient increment of S830 airfoil is higher than that of S816 airfoil, and those of these two airfoils mainly decrease with the angle of attack. The average lift–drag ratio increment of S816 airfoil with the relative camber of 1.81% at different angles of attack ranging from 0.1° to 20.2° is the largest, closely followed by S812 airfoil. The lift–drag ratio increment of S830 airfoil is negative as the angle of attack exceeds 0.1°. Thus, the airfoil with medium camber is more suited to the asymmetrical blunt trailing-edge modification.     

An experimental investigation of unsteady surface pressure on an airfoil in turbulence—Part 2: Sources and prediction of mean loading effects

An experimental investigation into the response of an airfoil in turbulence was undertaken and the results are presented in a two part series of papers. The effects of mean loading on the airfoil response are investigated in Part 1 with the likely origins discussed in this paper (Part 2). Unsteady pressure measurements were made on the surface of a NACA 0015 airfoil immersed in grid turbulence (λ/c=13%) for angles of attack α=0-20°. This paper (Part 2) presents the causes of the low-frequency reduction and high-frequency increase observed in measured lift and pressure spectral levels. Scaling lift spectra on the mean lift reveals the increase in lift spectral level for reduced frequencies greater than 10 is closely related to the airfoils mean pressure field. Based on analysis of the chordwise and spanwise pressure correlation length scale, the reduction in lift spectral level at low reduced frequency appears to result from distortion of the inflow by the mean velocity field. A possible model is developed that accurately predicts mean loading effects on lift spectra. This model uses a circular cylinder fit to the airfoil to compute effects of distortion on the inflow turbulence. The distorted inflow velocity spectrum is then used with Amiet's theory to predict the unsteady loading. This model successfully captures the reduction observed in measured lift spectra at low reduced frequencies. Furthermore, it is shown that the angle of attack effects arising from inflow distortion are significant only when the relative scale of the inflow turbulence to airfoil chord is sufficiently small (λ/c=13% for present experiment).     

Panel methods for airfoils in turbulent flow

This paper describes how panel methods can be used to calculate the unsteady loading and radiated noise from airfoils in incompressible turbulent flow, while completely accounting for the mean flow distortion of the turbulence in the vicinity of the blade. Formulations based on the velocity and on the stagnation enthalpy are discussed. In three-dimensional flows, care must be taken with the velocity-based formulation to avoid singular behavior associated with vortex stretching by the mean flow. The velocity-based method is implemented in two dimensions to illustrate application of these methods, and is validated against Amiet's theory. Calculations showing the effect of blade thickness and angle of attack on the unsteady loading spectra are given. It is concluded that airfoil angle of attack has only a small effect on the unsteady loading, but that blade thickness reduces the spectral levels at high frequencies.     

An experimental study of airfoil instability tonal noise with trailing edge serrations

This paper presents an experimental study of the effect of trailing edge serrations on airfoil instability noise. Detailed aeroacoustic measurements are presented of the noise radiated by an NACA-0012 airfoil with trailing edge serrations in a low to moderate speed flow under acoustical free field conditions. The existence of a separated boundary layer near the trailing edge of the airfoil at an angle of attack of 4.2 degree has been experimentally identified by a surface mounted hot-film arrays technique. Hot-wire results have shown that the saw-tooth surface can trigger a bypass transition and prevent the boundary layer from becoming separated. Without the separated boundary layer to act as an amplifier for the incoming Tollmien–Schlichting waves, the intensity and spectral characteristic of the radiated tonal noise can be affected depending upon the serration geometry. Particle Imaging Velocimetry (PIV) measurements of the airfoil wakes for a straight and serrated trailing edge are also reported in this paper. These measurements show that localized normal-component velocity fluctuations that are present in a small region of the wake from the laminar airfoil become weakened once serrations are introduced. Owing to the above unique characteristics of the serrated trailing edges, we are able to further investigate the mechanisms of airfoil instability tonal noise with special emphasis on the assessment of the wake and non-wake based aeroacoustic feedback models. It has been shown that the instability tonal noise generated at an angle of attack below approximately one degree could involve several complex mechanisms. On the other hand, the non-wake based aeroacoustic feedback mechanism alone is sufficient to predict all discrete tone frequencies accurately when the airfoil is at a moderate angle of attack.     

The prediction of broadband noise from wind turbines

This paper describes a broadband noise prediction scheme for wind turbines. The source mechanisms included in the method are unsteady lift noise, unsteady thickness noise, trailing edge noise and the noise from separated flow. Special methods have been developed to model the inflow turbulence from the atmospheric boundary layer and acoustic radiation to the geometric near field of the rotor. Predictions are compared with measurements on 20 m and 80 m diameter wind turbines. The results show that the turbulence length scale in the atmospheric boundary layer is too large to give the measured noise levels. Very good agreement is obtained between predictions and measurements if the turbulence length scale is taken to be equal to the blade chord.     

A frequency domain numerical method for airfoil broadband self-noise prediction

This paper describes a numerical approach, based in the frequency domain, for predicting the broadband self-noise radiation due to an airfoil situated in a smooth mean flow. Noise is generated by the interaction between the boundary layer turbulence on the airfoil surface and the airfoil trailing edge. Thin airfoil theory is used to deduce the unsteady blade loading. In this paper, the important difference with much of the previous work dealing with trailing edge noise is that the integration of the surface sources for computation of the radiated sound field is evaluated on the actual airfoil surface rather than in the mean-chord plane. The assumption of flat plate geometry in the calculation of radiation is therefore avoided. Moreover, the solution is valid in both near and far fields and reduces to the analytic solution due to Amiet when the airfoil collapses to a flat plate with large span, and the measurement point is taken to the far field.Predictions of the airfoil broadband self-noise radiation presented here are shown to be in reasonable agreement with the predictions obtained using the Brooks approach, which are based on a comprehensive database of experimental data. Also investigated in this paper is the effect on the broadband noise prediction of relaxing the ‘frozen-gust’ assumption, whereby the turbulence at each frequency comprises a continuous spectrum of streamwise wavenumber components. It is shown that making the frozen gust assumption yields an under-prediction of the noise spectrum by approximately 2dB compared with that obtained when this assumption is relaxed, with the largest occurring at high frequencies.This paper concludes with a comparison of the broadband noise directivity for a flat-plat, a NACA 0012 and a NACA 0024 airfoil at non-zero angle of attack. Differences of up to 20 dB are predicted, with the largest difference occurring at a radiation angle of zero degrees relative to the airfoil mean centre line.     

Flow control of the semicircular airfoil with a vortex cell at slot suction of air and its blowout into the near wake

In the vicinity of a semicircular airfoil with slot suction of air provided with a 0.2-diameter (chord) vortex cell installed on the backside of the wing, at low speeds and zero angle of attack the pattern of the unsteady separated air-flow undergoes substantial changes, those changes being accompanied with the displacement of flow separation point toward the trailing edge. The slot suction of air and its blowout into the near wake in such an airfoil is organized using a discharge channel with a fan; from this channel, the air jet is discharged into atmosphere tangentially to the airfoil base, with the pressure drop in the fan being equal to twice the pressure head. Under such conditions, the integral force characteristics of the wing show dramatic changes: the lift force, initially being ultra-low negative, becomes positive, and the drag decreases two-fold. The static pressure decreases by two or three times on the upper arch of the profile, and it increases by two times on the lower part of the airfoil, the level of pressure pulsations decreasing by more than ten times.     

An experimental investigation of unsteady surface pressure on an airfoil in turbulence—Part 1: Effects of mean loading

An experimental investigation into the response of an airfoil in turbulence is undertaken and the results are presented in a two part series of papers. The effects of mean loading on the airfoil response are investigated in this paper (Part 1) with the likely sources discussed in Part 2. Unsteady surface pressure measurements were made on a NACA 0015 immersed in grid turbulence (λ/c=13%) for angles of attack, α=0-20°, with a dense array of pressure transducers. These measurements reveal a reduction of up to 5 dB in pressure spectral level as the angle of attack is increased for reduced frequencies less than 5. This observed mean-loading effect has never before been measured or shown to occur theoretically. Lift spectra computed from pressure measurements show a similar result. Furthermore, the reduction in lift spectral level appears to have an α² dependence. Also, for small angles of attack (α<8°) Amiet's zero-mean-loading theory may be useful for predicting the airfoil response since the reduction in spectral level is less than 1 dB here. Based on comparisons at α=0°, Amiet's theory predicts with reasonable accuracy (within 4 dB at low frequency) pressure and lift spectral levels. This theory successfully predicts the shape of both pressure and lift spectra and the decrease in pressure spectral level moving away from the airfoil leading edge. Additionally, Reba and Kerschen's theory, which accounts for non-zero-mean loading using Rapid Distortion Theory, predicts large increases in pressure and lift spectral levels not shown to occur in the measurement. The predicted rise in spectral level appears to result from the flat-plate model with leading-edge singularity which does not fully account for the distortion of the inflow.     

钝尾缘翼型非定常气动特性及机理

钝尾缘翼型气动特性受到尾涡脱落的影响,在翼型DU 91-W2-250的基础上对称加厚得到了新钝尾缘翼型DU91-W2-250_6,利用密网格进行了非定常气动特性的数值研究。在各个攻角下钝尾缘翼型气动特性都具有周期性的特点,具体的波动特征如波动幅值及周期等则受脱落涡的大小、脱落位置及尾迹宽度的影响,而升力系数波峰、波谷则分别出现在顺时针涡及逆时针涡脱落的时刻。     

柔性旋涡发生器对翼型前缘分离的自适应控制

采用边长为10 mm的三角形柔性和刚性旋涡发生器,安装在二维NACA0018翼型上翼面前缘不同弦长处,用于控制翼型前缘分离流动.实验在低速直流式风洞中进行,以翼型弦长为特征长度的Reynolds数Re=1.1×105,采用单丝热线风速仪测量尾流速度剖面.分别研究柔性和刚性两种材料的三角形旋涡发生器对翼型前缘分离的控制效果.实验结果表明,与刚性旋涡发生器相比,柔性旋涡发生器利用来流能量实现自适应控制,使剪切层下移,从而明显抑制前缘分离.      

Free stream turbulence effect on the flow structure over the finite span straight wing

Flow visualization tests have been performed to examine the structure of the near-wall flow over a low-aspect ratio straight wing installed at various angles of attack a and chord Reynolds numberRe _c=U_∞c/ν=1.76×10⁵. The experiments were carried out at two free-stream turbulence levels, ε=0.1% and ε=1%, the latter one having been achieved using a baffling grid. To visualize the flow, termochromic cholesteric liquid crystals and digital processing of video images were used. At the low turbulence level and α=27°, a flow stall on the lee side of the wing was observed, with a pair of largescale vortices rotating in the wing plane. Simultaneously, no vortex structures were observed on the windward wing surface. It was found the flow patterns on either side of the wing significantly changed with increasing free-stream turbulence level. A separation bubble appeared near the leading edge on the lee side of the airfoil at ε=1%, and large-scale stationary longitudinal vortices originated over the wing windward surface. The number and sizes of the longitudinal structures were found to be dependent on the angle of attack.     

基于等离子体环量控制的翼型气动特性

为了研究等离子体环量控制对翼型的影响特性,采用基于唯象学的等离子体气动激励数学模型和二维雷诺平均N-S方程,选取NCCR 1510-7067N环量控制翼型,数值模拟后缘半径对升力和效费比的影响规律,并进行优化。设计最佳后缘半径模型进行低速风洞实验,获得迎角-4~12,速度6,10,15 m/s下的压力分布和升力特性。研究表明:后缘半径过大或过小都不利于Coanda效应的产生,确定最佳后缘半径与弦长的比值为0.048,效费比97.69。低雷诺数下,随着迎角的增加,出现了层流长泡分离和短泡分离,等离子体射流不仅改善了尾部流场,还通过环量增加抑制层流分离,提高了升力。     

水平轴风力机专用翼型族试验分析及优化设计

对水平轴风力机专用翼型族—CAS-W1-XXX薄翼型族试验结果进行了分析,并将其与国外同等厚度翼型进行对比。试验结果表明,与国外同等厚度翼型相比CAS-W1-XXX薄翼型具有良好的前缘粗糙不敏感性、高的最大升力系数、设计升力系数和良好的失速特性。为进一步提高翼型的气动特性,在试验结果的基础上对CAS-W1-XXX薄翼型族进行再次优化。根据XFOIL计算结果,优化后翼型的最大升阻比得到提高,并且与DU翼型相比具有良好的气动特性。同时对CAS-W1-XXX厚翼型中出现的小攻角失速现象进行了优化改进。     

On the generation of side-edge flap noise

A theory is proposed for estimating the noise generated at the side edges of part span trailing edge flaps in terms of pressure fluctuations measured just in-board of the side edge on the upper surface of the flap. Asymptotic formulae are developed in the opposite extremes of Lorentz contracted acoustic wavelength large/small compared with the chord of the flap. Interpolation between these limiting results enables the field shape and its dependence on subsonic forward flight speed to be predicted over the whole frequency range. It is shown that the mean width of the side edge gap between the flap and the undeflected portion of the airfoil has a significant influence on the intensity of the radiated sound. The results indicate that the noise generated at a single side edge of a full scale part span flap can exceed that produced along the whole of the trailing edge of the flap by 3 dB or more.     

前缘旋转的风力机翼型气动性能研究

本文通过数值计算,研究了一种前缘为可转动圆柱的二维S809翼型的气动性能.研究表明,通过驱动前缘圆柱旋转,可有效抑制翼型吸力面的流动分离,使得翼型在较大攻角下具有良好的气动性能,提高了翼型的最大升力系数与升阻比.该流动控制方法具有简单有效、花费代价小等优点.     

Noise due to turbulent flow past a trailing edge

A theoretical method [I] for calculating far field noise from an airfoil in an incident turbulent flow is extended to apply to the case of noise produced by turbulent flow past a trailing edge, and some minor points of the theory in reference [1] are clarified. For the trailing edge noise, the convecting surface pressure spectrum upstream of the trailing edge is taken to be the appropriate input. The noise is regarded as generated almost totally by the induced surface dipoles near the trailing edge and thus equal, but anticorrelated, noise is radiated into the regions above and below the airfoil wake, respectively. The basic assumption of the analysis, from which these concepts of appropriate input and dominance of dipole sources follow, is that the turbulence remains stationary in the statistical sense as it moves past the trailing edge. The results show that such trailing edge noise often is quite small, compared say to that produced by typical oncoming turbulence levels of one percent, but that it might be appreciable for an airfoil with a flow separation, or for a blown flap.     

Measurement of aerodynamic noise and unsteady flow field around a symmetrical airfoil

The purpose of this paper is to study the physics of aerodynamic noise generation from the symmetrical airfoil of NACA 0018 in a uniform flow. The relationship between the noise spectrum and the unsteady flow field around the airfoil is studied in an acoustic wind tunnel using flow visualization and PIV analysis. The discrete frequency noise was generated from the airfoil inclined at small angle of attack to the free stream. The flow visualization result indicates the presence of attached boundary layer over the suction side and the separated shear layer over the rear pressure side of the airfoil, when the discrete frequency noise is observed. It is found from the PIV analysis that a large magnitude of vorticity is generated periodically from the pressure side of the trailing edge and it develops into an asymmetrical vortex street in the wake of the airfoil. The periodicity of the shedding vortices was found to agree with that of the frequency of the generated noise.