Surface vorticity modeling of flow around airfoils

A surface vorticity method based on the new Kutta condition has been developed for solving the steady flow around an airfoil and unsteady separated flow past airfoil with a spoiler. In a discussion of the Kutta condition, it is argued that the appropriate Kutta condition is required to obtain a satisfactory solution. In this paper, two new methods of satisfying the Kutta condition incorporated in the surface vorticity method are described. The first method, which is based on results from flow visualization, is to introduce an additional control point at a short distance downstream of the trailing edge. In order to account for the fact that the velocity above the trailing edge is different from that below as in the real flow, the second method is to add a finite segment of vortex sheet downstream of the trailing edge. The present Kutta conditions are incorporated into the surface vorticity method and extend to solve unsteady flow around an airfoil with a spoiler. The computational results are in reasonable agreement with other computation as well as experiments.     

大跨屋盖表面旋涡的PIV试验研究

该文通过风洞流场显示试验,观察了大跨平屋盖和马鞍屋盖表面的分离泡和锥形涡现象,给出了不同风向、不同屋盖表面的旋涡流线和涡量场分布;分析了风向角、屋盖曲率对于旋涡形态的影响。试验结果表明,当风向垂直于平屋盖迎风前缘时,屋盖表面将形成典型的分离泡现象,且分离泡的涡核位置恰好对应了涡量场的负向峰值。在斜向风作用下,平屋盖和以高点作为迎风点的马鞍屋盖表面将出现锥形涡。观察旋涡的平均流线和涡量场分布图,发现当来流沿两种屋盖对角线时,锥形涡截面形状接近圆形;当来流偏离屋盖对角线时,在靠近来流的一侧,锥形涡截面形状接近椭圆形;流场内负向涡量分布于壁面上,峰值集中在迎风前缘附近和旋涡周围。在相同的风向角下,曲率较大的马鞍表面锥形涡涡轴与屋盖迎风前缘所成角度较大,曲率较小的马鞍表面锥形涡涡轴与迎风前缘所成角度较小。此外,旋涡的瞬时流线图表明,锥形涡是一种瞬时变化的流体现象,其形态和位置在每个瞬时都不相同。     

Vortex motion in the early stages of unsteady flow around a circular cylinder

In this paper, processes in the early stages of vortex motion and the development of flow structure behind an impulsively-started circular cylinder at high Reynolds number are investigated by combining the discrete vortex model with boundary layer theory, considering the separation of incoming flow boundary layer and rear shear layer in the recirculating flow region. The development of flow structure and vortex motion, particularly the formation and development of secondary vortex and a pair of secondary vortices and their effect on the flow field are calculated. The results clearly show that the flow structure and vortices motion went through a series of complicated processes before the symmetric main vortices change into asymmetric: development of main vortices induces secondary vortices; growth of the secondary vortices causes the main vortex sheets to break off and causes the symmetric main vortices to become “free” vortices, while a pair of secondary vortices is formed; then the vortex sheets, after breaking off, gradually extend downstream and the structure of a pair of secondary vortices becomes relaxed. These features of vortex motion look very much like the observed features in some available flow field visualizations. The action of the secondary vortices causes the main vortex sheets to break off and converts the main vortices into free vortices. This should be the immediate cause leading to the instability of the motion of the symmetric main vortices. The flow field structure such as the separation position of boundary layer and rear shear layer, the unsteady pressure distributions and the drag coefficient are calculated. Comparison with other results or experiments is also made. This work was presented at the First Asian Congress of Fluid Mechanics, Bangalore in December 1980.     

A numerical study on pressure drop and separation efficiency of a new swirl tube cleaner

In this paper, a new design of Swirl Tube Cleaner (STC) was introduced. The performance of an STC in terms of the separation efficiency and pressure drop was numerically investigated for different vane angles, vane lengths, and inlet velocities. The Reynolds stress turbulence model was used to detect the main flow structures of the highly swirling flow inside the STC. The discrete phase model that employs the Lagrangian frame of reference was utilized for particle tracking. The results are in good agreement with experimental data available in the literature. For all cases under investigation, the main flow characteristics of the STC consist of a hub vortex flow downstream of the back cone and tip vortices in the wake flow of the vanes. Around the initiation point of the vortex flow, the centrifugal accelerations are one order of magnitude higher than that of the upstream flow around vanes. The results show that the overall separation efficiency with the specified particle size distribution can reach 88% at a pressure drop lower than 250 [Pa] for the highest flow rate. Compared to traditional STCs, the new STC decreases the pressure drop by about 50% while enhancing overall separation efficiency by approximately 2%, considering the numerical accuracy.     

Flow visualization studies of vortices

An actual vortex in the Kármán vortex street downstream of a circular cylinder has a core of finite dimension which increases downstream. The circulation of the vortex is nearly constant. The ratiob/a which is 0.281 according to the theory of Kármán, grows from 0.2 to 0.4 in the near wake. In the flow about a circular cylinder rotating in a uniform flow, a Kármán vortex street, Görtler-type vortices and Taylor vortices are generated at the same time. In the flow about a circular cylinder impulsively started with a constant velocity, the primary twin vortices behind the cylinder induce secondary twin vortices near the separation point. At the beginning of the motion, the separation does not occur even though a reverse flow is observed in the boundary layer. Mutual slip-through of a pair of vortex rings was achieved by increasing the Reynolds number. A vortex ring rebounds from a plane surface due to the separation of the flow on the surface induced by the vortex ring, and the secondary vortex ring is formed from the separated shear layer.     

基于PIV技术的平屋盖表面分离泡流动结构研究

该文利用粒子图像测速技术,通过风洞流场显示试验,观察了大跨平屋盖表面的分离泡现象,给出了不同来流工况下多个可视化平面的旋涡流线和涡量场分布。试验结果表明,当风向垂直于平屋盖迎风前缘时,屋盖顶面将出现典型的分离泡现象,涡量场的负向峰值出现在迎风前缘处,屋面风压力随离迎风前缘距离的增加而减小。均匀流场下流动将在迎风边缘产生分离而后再附,再附长度近乎横跨整个屋盖;而湍流场中的小尺度湍流促使分离剪切层较早地再附形成分离泡,且湍流度越大,旋涡再附长度越短。运用FLUENT模拟了平屋盖表面的分离泡,与流动显示试验结果吻合较好。通过多个可视化平面的综合分析得到分离泡的三维形态特征,建立了旋涡的演化、涡核位置与建筑物表面压力分布的内在联系,获得了若干有价值的结论。     

Boundary element simulation of inviscid flow around an oscillatory foil with vortex sheet

The dynamic performance of a rigid foil with harmonic vertical and rotational motions in fluid flow has been studied through velocity potential theory. A boundary element based time stepping scheme is introduced to simulate the flow around the foil and the vortex wake. The body surface condition is satisfied on the exact foil surface and the motion and deformation of the wake sheet shed at the trailing edge is tracked. Kelvin condition is satisfied and a Kutta condition for the unsteady motion is proposed to circumvent the singularity at the trailing edge. Point vortex, which is reduced from wake vortex dipole, is introduced to approximate the vorticity. The performance of foil NACA0012 with harmonic vertical and rotational motions are studied extensively; the propulsion/swimming mode, energy harvesting mode and the flying mode are analysed in detail.     

Oscillating cascade unsteady aerodynamics including separated flow effects

A mathematical model is developed to predict the effect of flow separation on the unsteady aerodynamic lift and moment acting on a two-dimensional flat plate cascade which is harmonically oscillating in a subsonic flow field. The unsteady flow is considered to be a small perturbation to the uniform steady flow, with the steady flow assumed to separate at a specified fixed position on the airfoil suction surface. This formulation does not require the difference in the upwash velocity across the airfoil in the separated flow region to be determined before calculating the unsteady pressure difference across the chordline of the airfoils, thereby eliminating the assumption that the upwash difference is zero at the trailing edge when the steady flow is separated. Results obtained demonstrate that although flow separation decreases bending mode stability, it does not result in bending mode flutter. However, flow separation can result in torsion mode flutter, with this instability being a function of the location of both the separation point and the elastic axis.     

On unsteady airfoil-vortex interaction

Summary An experimental investigation on unsteady airfoil-vortex interaction has been done. The incident vortex, to interact with a downstream airfoil (NACA 0018, chord lengthc=20 mm), is generated by a square cylinder (side lengthD=20 mm). The square cylinder and airfoil are arranged in tandem and the spacing ratioL/D of the central distance to the side length is set a constant value of 4.625. The free stream Mach numbers are varied between 0.153 and 0.750, whereas the free stream Reynolds numbers (based on the side lengthD) are varied between 0.713×10⁵ and 3.44×10⁵.It is found that as the incident vortex approaches the airfoil, the circulation and scale are decreased until it arrives at a position near the leading edge of the airfoil. During this stage, some circulation of the incident vortex is transferred to the secondary vortex generated on the airfoil opposite to the surface that the incident vortex approaches. Thus, circulation and scale of the secondary vortex are increased. However, after the incident vortex goes further downstream, no circulation of the incident vortex is transferred to the secondary vortex effectively. As the result, both of the incident vortex and secondary vortex decay due to the viscous dissipation through the interaction with the boundary layer of the airfoil. The locus of the incident vortex is deviated in such a way that it goes away from the airfoil. The streamwise position of the secondary vortex is adjusted by the incident vortex, orvice versa, so as to meet each other just behind the trailing edge of the airfoil.With 8 Figures     

Separated flow past three-dimensional bodies as a singular perturbation problems

This paper proposes a method for computing steady wake flows of an inviscid fluid over a three-dimensional body with polygonal cross-section and arbitrary plan-form. The method is based on the technique of matched asymptotic expansions, assuming a large aspect ratio. The far-field velocity potential is given essentially by a lifting line and a line source. The near-field, treated as two-dimensional, is solved by a suitable version of Tulin's double spiral vortex model which incorporates a downwash correction and an underpressure in the near-wake. The latter is related to the Reynolds number of the corresponding real flow using recent results by Tulin and Hsu and the authors. Numerical results for a few prototype problems (flat-plate airfoil with separation at both the leading edge and the upper surface, flat-plate win with full or partial spoiler) are presented. The method can be efficiently implemented on a parallel computer.     

翼型动态风洞试验洞壁效应研究

翼型动态失速导致气动非线性特征突出,与洞壁效应耦合给风洞试验数据带来极大的不确定性,该文通过试验和数值手段揭示了翼型动态试验洞壁效应产生机理和影响规律,结果表明:相比于静态试验,由于洞壁的存在,动态试验翼型的尾流区的总压和静压分布更不均匀,动态试验翼型在相同迎角下的洞壁干扰更严重,表现为翼型在大迎角段,洞壁干扰导致模型中间截面附近和端部截面附近的速度分布和压力分布差异更明显,且相比于压力面,吸力面流动的二维性变得较差。侧壁干扰抑制了翼型中间截面附近的流向分离,诱导了端部附近的展向分离流。上洞壁和下洞壁的非定常压力系数随翼型实时迎角变化也呈迟滞环曲线,迟滞环方向相反,且脉动一阶主频率与翼型俯仰振荡频率一致。风洞洞壁干扰下,翼型动态失速三维涡结构呈“Ω”型。风洞上下壁干扰使得翼型线性段的升力系数和升力线斜率均增加,诱导翼型提前失速;在负行程,则使得翼型升力系数降低。侧壁干扰在负行程诱导了翼型表面的展向流动、减小了翼型弦向流动速度,引起翼型升力系数减小,正行程范围则影响较小,且翼型失速延迟。FL-11风洞翼型动态试验的上下壁干扰效应为主导因素;但是侧壁干扰不可忽略,特别是在翼型振荡周期的大迎角和负行程范围。     

Simulating three-dimensional vortex motion by a vortex blob method

A three-dimensional vortex blob method was applied to calculate several vortex motions: the deformation of pseudo-elliptic vortex rings, the jet issuing from the pseudo-elliptic nozzle into flow of uniform velocity, the unsteady separated flow around a circular disk with an angle of attack, and the interaction of several vortex rings which approximately reproduced the Kolmogorov spectrum. In the first three cases, the viscous diffusion of vorticity was included. The pseudo-elliptic vortex rings experienced axis switching and split into a few deformed vortex rings. Rolling-up vortices in the pseudo-elliptic jet had a symmetric arrangement in the minor-axis plane and an antisymmetric arrangement in the major-axis plane in the developing region; further downstream, the vortices were arranged antisymmetrically in both planes. The wake behind the disk normal to the main flow reproduced the spiral and columnar modes of instability. A problem in the three-dimensional vortex method is that vorticity tends to diverge at a stage of evolution of the vortex motions. An approximate method of avoiding the divergence of vorticity is proposed.     

马鞍屋盖表面锥形涡流动模型研究

该文基于大跨平屋盖和马鞍屋盖表面锥形涡流动显示试验,对现有的兰金涡模型进行改进,在其涡核区与势流区之间添加过渡区,从而建立了简化的二维锥形涡流动模型,给出了旋涡上部流速、旋涡内部流线曲率以及屋面涡核吸力之间的定量关系。据此流动模型,分析了旋涡强度的影响因素即为旋涡内部流线曲率和旋涡流速:旋涡内部流线曲率越大,旋涡转速越快,旋涡强度越大。基于流动显示试验和测压试验所得平屋盖以及马鞍屋盖表面各旋涡参数之比,以平屋盖表面锥形涡为基准,量化了各风向下马鞍屋盖表面的锥形涡强度。通过加入考虑旋涡效应对传统准定常理论进行修正,给出了锥形涡涡核吸力(均值、峰值)的计算公式,并将计算值与马鞍屋盖刚性模型风洞测压试验数据进行对比,验证了锥形涡流动模型对于预测马鞍表面锥形涡涡核吸力的有效性。     

Wind pressure features of large-span flat roof in different wind fields induced by conical vortex

The wind pressure features on a large-span flat roof in uniform flow field and turbulent field induced by conical vortex were studied, through wind tunnel tests. From the comparison of the mean and fluctuating wind pressure distributions on a flat roof in different wind fields induced by conical vortex, results indicate that the mean suction dominates in the smooth flow, whereas the fluctuating suction is more obvious in the turbulent flow. The probability density function for the pressure fluctuations under different approaching flows is analyzed. The two-peaked distribution, peculiar to turbulent flow field, is observed on the curve of probability density. The fluctuating pressures at reattachment points are larger under the turbulent flow. This indicates a more intense reattachment, which may cause overturning moment for roof-mounted items. Point vortex, RanKine vortex, and simplified Cook expression are applied to fit the pressure profiles beneath conical vortices, respectively. The results have shown that the RanKine vortex model and simplified Cook expression were applicable to forecast the wind pressure profiles beneath conical vortices, while point vortex underestimated the real wind suction. The wind pressure distributions in turbulent fields induced by different wind angles were contrasted, when the approaching flow is along the diagonal of the roof, the intensity of the vortex pairs is almost equal, with obvious reattachment. When the approaching flow deviate from the diagonal of the roof, the lateral turbulent component spins the vortex more quickly; this induces larger mean suctions beneath windward vortices. Smaller suctions are observed beneath the leeward vortex, due to less vorticity being converted to vortex motion from the freestream.     

混流式水轮机小开度下导水机构内湍流特性和叶道涡结构研究

为准确捕捉小开度流动的瞬态湍流特性,充分了解流场结构,采用滑移网格技术以及基于Vreman亚格子模型的全局动态大涡模拟方法,不仅得到混流式水轮机全流道内速度、压力以及涡量的分布,同时捕捉到了活动导叶周围独特的流动形式和叶道涡的时空演化。计算结果表明:当高转速、小开度工况时,流道内流体的圆周速度占有绝对优势,加强了导叶后尾迹涡的相互影响,致使流道中发生更为剧烈和复杂的漩涡、脱流等各种水力不稳定现象。从蜗壳到转轮室的压力脉动均以低频为主,主要的频率能量成分基本相同,说明小开度低频异常振动与压力波的传递有关。叶道涡是致使叶片疲劳破坏的主要因素。     

Quantitative simulation of gas-particle two phase plane mixing layer using discrete vortex method

The gas and particle phase in a two-phase plane mixing layer flow are numerically simulated using the discrete vortex method and a trajectory tracking method. It is shown that the number of vortex elements contained in two semi-infinite discrete vortex sheet and the method of generating control volumes for statistical calculation of the particle phase have important effects on the predicted results of particle phase, especially for quantitative prediction. By adopting different number of vortex elements for two semi-infinite discrete vortex sheet and overlapping the control volumes, predicted results including streamwise velocity, fluctuating velocity and Reynolds shear stress of both phases are obtained and agree well with experimental measurements quantitatively. It shows that the discrete vortex method can achieve the accurate quantitative simulation of two-phase flow.     

仿生翼型对半主动扑翼捕能性能的影响

为了分析仿生翼型对半主动扑翼捕能性能的影响,该文在Fluent流体求解器的基础上,通过二次开发,编制了一套可有效求解流体流动、扑翼主动转动和被动往复扑动的计算程序。在此基础上,研究仿蜻蜓翼型、仿海鸥翼型、NACA0012和NACA0015四种翼型的捕能性能,结果表明采用仿生翼型的扑翼具有更好的捕能性能。进一步通过对不同外形扑翼的流场分析发现,采用仿生翼型可使扑翼在被动往复扑动过程中产生更强的涡流,并且在俯仰运动过程中可延缓涡流从扑翼表面脱落,从而使扑翼具有较好的捕能性能。     

直径30cm圆柱的气动力参数和绕流特性研究

为研究光滑圆柱的气动力系数和绕流特性,在均匀流中进行不同风速下的测压风洞试验,试验获得了阻力系数、升力系数、表面风压分布、风压相关性系数、斯托罗哈数等随雷诺数的变化特征,并将试验结果与以往结果进行比较。研究表明:升力系数的脉动值大于阻力系数的脉动值,说明涡脱造成的横风向激励比顺风向紊流激励剧烈;雷诺数位于临界区域时,圆柱表面风压分布呈现出对称-不对称-对称的变化过程,反映了由层流分离转化为湍流分离的全过程;在雷诺数为352000时呈现一侧为层流分离、另一侧为湍流分离的临界流态,风压呈现出左右不对称的单边泡形式;获得层流分离和湍流分离时的表面风压相关性分布特征,层流分离时圆柱同一侧的风压测点均呈较强的正相关,而湍流分离时在分离点前的区域相关性较强,分离点之后的区域相关性较弱;层流分离的升力系数谱有显著的峰值,表明尾流是规则的漩涡脱落,而湍流分离的升力系数谱没有明显峰值,表明尾流是随机的漩涡脱落。     

Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder

Summary Effects of an airfoil and shock waves on vortex shedding process behind a square cylinder have been examined experimentally at a Mach number of about 0.91 and at a Reynolds number (based on the side lengthD of the square cylinder) of about 4.2×10⁵. The main experimental parameter is the spacing ratioL/D, and is varied from 1.125 to 5.5, whereL is the spacing between the square cylinder and the airfoil.It is found that similarly to the case at subcritical Mach numbers at the supercritical Mach number there exist three patterns of the flow around the square cylinder and airfoil arranged in tandem depending upon the spacing ratioL/D: In the first flow pattern with small spacing ratio, the downstream airfoil is enclosed completely in the vortex formation region of the square cylinder. In the second flow pattern, the shear layers separating from the square cylinder reattach to the airfoil. In the third flow pattern with large spacing the shear layers roll up upstream of the airfoil. The Strouhal number at the supercritical Mach number is higher than that at the subcritical Mach numbers. Shock waves hasten the vortex shedding behind the square cylinder by decreasing the area of asymmetrical part of the vortex formation region with respect to the wake axis, and let the streamwise length of the separating shear layers longer than otherwise.With 8 Figures     

Inviscid separated flows of finite extent

Two-dimensional, inviscid, incompressible flow is considered when the flow region contains a separation bubble of finite length. Within the separation bubble a slender-eddy approximation is employed, whilst outside it small disturbance theory is used to solve the potential-flow equations. The solution is completed by matching the pressure across the vortex sheet that divides the two regions of flow. Solutions are presented for the flow past smooth indentations in an otherwise plane boundary.