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.     

Unsteady panel method for flapping foil

A computer program based on a potential-flow panel method was developed to evaluate the hydrodynamic forces acting on a harmonically heaving and pitching two-dimensional rigid foil. A new formulation of the unsteady Kutta condition, postulating a finite pressure difference at the trailing edge of the oscillating foil, is proposed and implemented in the numerical procedure. A comparison with published experimental data [Anderson JM, Streitlien K, Barrett DS, Triantafyllou MS. Oscillating foils of high propulsive efficiency. J Fluid Mech 1998;360(1):41–72; Read DA, Hover FS, Triantafyllou MS. Forces on oscillating foils for propulsion and maneuvering. J Fluids Struct 2003;17(1):163–83; Schouveiler L, Hover FS, Triantafyllou MS. Performance of flapping foil propulsion. J Fluids Struct 2005;20(7):949–59] showed good agreement with the computational results. The analysis of the experimental results indicates clearly that robust computational procedures are necessary for reliable data processing in terms of calibration, noise removal, correction factors, etc. The proposed two-dimensional approach to the problem is currently being developed as a three-dimensional procedure that will address the unsteady flow effects such as inertia-related ones that are currently omitted.     

Influence of the wake model on the thrust of oscillating foil

Trust generation by flapping wing is a complex fluid phenomenon involving unsteady effects. The work discusses a Boundary Element Method (BEM) based computer model for the analysis of hydrodynamic forces on flapping foil. The specific focus is on the wake model and its effects on the generated thrust. An unsteady formulation of the Kutta condition, assuming finite pressure difference at the trailing edge of the moving foil, was implemented in the numerical procedure to account for the shedding of trailing-edge vortical structures. It is shown that the numerical results depend strongly on the choice of the wake model, especially at large oscillation frequencies. However, the model of the thrust-producing jet (due to the trailing-edge pressure differences) predicts accurately the thrust trend as a function of the oscillation frequency. In other words, the numerical results show the need of experimental data in order to choose the appropriate wake model. An experimental validation of the numerical method is proposed on the basis of recent experimental results that clearly show the time lag between the foil vertical acceleration and generated thrust as predicted by the model. This proves the point that the unsteady BEM approach to these problems is physically sound.     

Numerical Study on the Suppression of the Oscillating Wake of a Square Cylinder by a Traveling Wave Wall

Traveling waves generated on the side surfaces of a square cylinder are employed to suppress the oscillating wake for improving the flow behavior around a square cylinder; this method is termed the traveling wave wall (TWW) method. This study aimed to evaluate the influence of the key parameters of TWW on the control of aerodynamic forces and the oscillating wake of the flow around a square cylinder. Unsteady numerical analyses at a low Reynolds number (Re) of 100 were performed using a two-dimensional CFD simulation. First, the grid independence and time step independence tests of the simulation were conducted to verify the rationality of the solving parameter settings, and the validation of flow around the fixed square cylinder at Re =100 was carried out. Subsequently, the lift and drag coefficients and the vortex shedding modes under different combinations of three TWW control parameters, including wave velocity, wave amplitude, and wavenumber, were analyzed in detail. The results show that TWW can remarkably reduce the mean value of drag coefficient and the RMS value of the lift coefficient by more than 12% compared to the method involving a standard square cylinder. Two peaks occur in the lift coefficient spectrum, with the low frequency corresponding to the vortex shedding frequency in the wake of the flow around the square cylinder and the high frequency corresponding to the traveling wave frequency. The vorticity contours show that the alternating vortices in the wake of the square cylinder are not completely suppressed under the selected control parameters.     

Computational study of unsteady viscous flow around a transversely and longitudinally oscillating circular cylinder in a uniform flow at high reynolls numbers

A finite difference simulation method for the time dependent viscous incompressible flow around a transversely and longitudinally oscillating circular cylinder at Reynolds numbers of Re=4×10³ and 4×10⁴ is presented. The Navier-Stokes equations in finite difference form are solved on a moving grid system, based on a time dependent coordinate transformation. Solution of the vortex street development behind the cylinder is obtained when the cylinder remains stationary and also when it is oscillating. Time eholution of the flow configuration is studied by means of stream lines, pressure contours and vorticity contours. The computer results predict the lock-in phenomenon which occurs when the oscillation frequency is close to the vortex shedding frequency in the transverse mode or around double the vortex shedding frequency in the longitudinal mode. The time dependent lift and drag coefficients are obtained by the integration of the pressure and shear forces around the body. The drag, lift and the displacement relations are also discussed.     

倒角化处理对于矩形高层建筑风荷载特性的影响机理研究

通过风洞测压试验,对比不同风向下、不同倒角半径的矩形高层建筑表面风压分布、整体风力及斯托罗哈数St;采用PIV试验,给出建筑的近尾流流动特性,并从流场作用角度,揭示倒角化处理对于矩形高层建筑风荷载特性的影响机理。研究表明:临界风向下,在建筑一侧分离的剪切层发生流动再附,形成分离泡;此时,建筑的阻力达谷值,升力和St达最大值。相比而言,倒角化矩形高层建筑的临界风向小于无气动措施的工况。St主要受到横风向投影宽度和尾流涡对间距的影响,在一定的风向范围内,当倒角半径达一定数值,St将有所增大。在建筑的整体阻力方面,倒角化处理将使得建筑尾流涡对尺寸减小;涡对横向流速增大,涡量掺混运动加剧,旋涡强度减弱。在此作用下,建筑整体阻力降低。在建筑的整体升力方面,采用倒角化处理后,旋涡脱落的不规则性和随机性增大,脱落强度减弱,这促使建筑整体升力减小;但倒角化处理对于升力的减小效应并非见于所有风向。     

Aeroelastic response of 2-D lifting surfaces to gust and arbitrary explosive loading signatures

The aeroelastic response to time-dependent external excitation of a two-dimensional rigid/elastic-lifting surface in incompressible flow field featuring plunging – pitching coupled motion is addressed in this paper. The expressions of the unsteady aerodynamic lift and moment in the time domain are given in terms of the Wagner's function, while the gust loads are given in terms of the Küssner's function. Numerical simulations of the aeroelastic response to gust and blast pressure signatures and comparisons with the solution obtained for an airfoil featuring plunging motion alone, are supplied. The concepts of the alleviation factor envelope and of the one- and two-degrees-of-freedom rigid/elastic-lifting surfaces, considered in conjunction with the aeroelastic response, are investigated and pertinent conclusions are outlined.     

Hydrodynamics numerical investigation of hoistable masts for underwater vehicles

Hoistable masts are key systems of underwater vehicles. The hoistable mast enables a underwater vehicle to penetrate the sea surface and exchange information with little risk of being detected. It is very important for researching the hydrodynamic behaviour of flow pass hoistable masts in order to reduce the production of visible, electro-optic, infrared, radar cross section wake and hydroacoustics signatures. Using the unsteady incompressible Navier-Stokes equation as the governing equation, the large eddy simulation (LES) model is implemented to investigate the shedding of vortices, the flow pattern of turbulence, the unsteady pressure fluctuation and the time history of the lift coefficient and drag coefficient of hoistable masts with various mast shapes and various arrangements in this paper. Combining the FFT, combined time-frequency transform and wavelet power spectrum analysis, the characteristics of unsteady pressure can be obtained in both time and frequency domain. It shows that the main frequency of pressure fluctuation is near the frequency of vortex shedding in time domain using the FFT method. It can be inferred from the combined time-frequency transform that the unsteady pressure fluctuation has obviously the peak value and second peak value in time domain. It could indicate that the fluctuation power varies from the fluctuation frequency through the power spectrum analysis. By the data analysis, it shows that the vortex shedding is the dominant cause of the periodically pressure fluctuation. And the interaction pattern of wake and interplay between wake and the walls of masts under different arrangements are also discussed in this paper.     

柔性扑翼气动性能的数值研究

国内外对扑翼飞行的气动特性进行了大量研究,这些研究大多基于简谐扑动的刚性翼,然而大量观察发现鸟或昆虫飞行时,翅膀存在明显的柔性变形,这种变形对其气动性能具有显著的影响。该文针对一简化的二维柔性扑翼模型,采用数值求解N-S方程并耦合扑翼柔性变形方程的计算方法,研究了扑翼柔性变形对其气动性能的影响。结果显示扑翼的柔性变形改变了扑翼周围的涡结构,从而影响扑翼的气动性能;适当的柔性变形能延迟前缘涡的脱落,从而有效地改善扑翼的推进效率,但同时减弱了扑翼在低雷诺数环境中产生高升力的尾迹捕捉机制。     

Rapid plunging of a body partly submerged in water

The water flow is studied when a thin body, part-submerged in originally still water, is plunged vertically downward. The rapid motion is at medium-to-large Reynolds number. The flow structure consists mainly of two viscous nonlinear layers, namely the unsteady boundary layer on the plunging body and unsteady wake along the trailing free surface, and one inviscid linear region in the bulk of the water. The former produce unsteady displacements which force the motion in the inviscid bulk, along with mixed boundary conditions, and control the evolutions of the wake-side and upper free surfaces. Other regions present are also considered. Analytical and numerical solutions are described, including the effects of the high Froude number and of contact slippage, and the time to bubble formation on the body.     

Shear flow past a square cylinder near a wall

A numerical study on the wake behind a square cylinder placed parallel to a wall has been made. The cylinder is considered to be within the boundary layer of the wall, so that the outside flow is taken to be due to uniform shear. Flow has been investigated in the laminar Reynolds number (based on the cylinder height) range. The interaction of wall boundary layer on the vortex shedding at Reynolds number up to 1400.0 has been investigated for cylinder to wall gap height 0.5 and 0.25 times the cylinder height. The gap flow between the cylinder and wall during a period of vortex shedding has been obtained. The governing unsteady Navier–Stokes equations are discretised through the finite volume method on staggered grid system. An algorithm SIMPLE has been used to compute the discretised equations iteratively. Our results show that at the gap height 0.5 times the cylinder height the vortex shedding occurs at a Strouhal number greater than for an isolated cylinder. Vortex shedding suppression occurs and wake becomes steady up to a certain value of Reynolds number at gap height 0.25 time the cylinder height. At higher Reynolds number the formation of a single row of negative vortices behind the cylinder when it is in close proximity to wall is noteworthy. Due to the shear, the drag experienced by the cylinder is found to decrease with the reduction of gap height.     

Aerodynamic forces and flow structures of an airfoil in some unsteady motions at small Reynolds number

Summary The aerodynamic forces and flow structures of a NACA 0012 airfoil in some unsteady motions at small Reynolds number (Re=100) are studied by numerically solving the Navier-Stokes equations. These motions include airfoil acceleration and deceleration from one translational speed to another and rapidly pitching up in constant freestream (equivalent to pitching up during translational motion at constant speed). It is shown that at small Reynolds number (Re=100), when the airfoil is performing fast acceleration or deceleration from one speed to another, a large aerodynamic force can be generated during and for a time period after the acceleration or deceleration; a large aerodynamic force can also be generated when the airfoil is performing a fast pitching motion in a constant freestream. In these fast unsteady motions, an airfoil in low Re flow can produce a large aerodynamic force as effective as in large Re flow, or the effect of unsteady motion dominates the Reynolds number effect. During the fast unsteady motion of the airfoil, new layers of strong vorticity are formed near the upper and lower surfaces of the airfoil under the previously existing thick vorticity layers, and it is the generation and motion of the new vorticity layers that is mainly responsible for the generation of the large aerodynamic force; the large-scale structure and movement of the newly produced vorticity layers are similar to that of high Re flow.     

海底管道悬跨段流致振动实验研究及涡激力模型修正

对输送液体的模型管道进行了涡激振动试验研究,试验结果表明:当理论涡脱频率与管道的固有频率不一致时,作用在振荡管道上的涡激力并非简谐扰力,而是具有一定带宽的窄带随机扰力。因此,管道的涡激振动响应也是一个随机过程。当理论涡脱频率与管道的固有频率接近时,管道的涡激振动响应逼近简谐振动。试验结果也表明:作用在振荡圆柱体上的涡激力频率不仅是流速和圆柱体直径的函数,也是圆柱体固有频率的函数。     

扑动轨迹对扑翼气动特性影响的数值研究

国内外对扑翼飞行的气动性能进行了大量研究,这些研究大多针对特定运动轨迹下的扑翼,然而大量观察发现,昆虫在飞行时其翅膀会出现各种不同的运动形式,这些不同的翅膀运动方式必定对其气动性能产生重要影响。该文基于对昆虫的实验和数值模拟中常用的几种扑动轨迹模型分析,建立了三种具有相同准稳态气动力的扑翼扑动轨迹,并采用数值求解N-S 方程的方法,研究了前飞状态下不同扑动轨迹对扑翼气动特性产生的影响。结果显示扑动和转动均为简谐函数轨迹形式的扑翼具有较高的升举效率和推进效率。进一步通过对不同扑动轨迹扑翼流场分析得出,扑动轨迹不能改变扑翼产生的尾流性质,但可以影响涡的强度,从而使扑翼产生不同的气动性能。     

风力机翼型在复合运动下的动态失速数值分析

现代大型风力机在工作时叶片经历大变形与振动,将会对其周围的动态流场产生影响,从而导致气动力的改变。因此有必要深入研究风力机翼型在复合运动情况下的动态失速气动特性,以正确预测大型风力机运行时的载荷。该文应用计算流体力学方法,对S809翼型在不同运动形式下的动态失速特性进行了二维数值分析。首先对翼型在作俯仰运动下的轻失速和深失速情况分别结合S-A、SST k-ω和RSM三种湍流模型进行了动态失速数值模拟,结果表明S-A、SST k-ω和RSM三种湍流模型都能有效地计算出翼型的气动力。然后采用SST k-ω模型仿真了翼型在挥舞运动、俯仰摆振耦合运动下的动态失速气动特性,并与相同工况条件下翼型作俯仰运动时的气动特性进行了对比分析。发现翼型在挥舞运动下的动态失速虽然弱于俯仰运动,但其强度不容忽视;而翼型在作俯仰与摆振耦合运动时比单纯作俯仰运动时的失速程度更深。因此在风力机设计阶段为获得保守的气动载荷预测,有必要将叶片截面在挥舞与摆振方向的运动转换成等效攻角,叠加在主攻角上进行动态失速气动力计算。     

Fin sweep angle does not determine flapping propulsive performance

The importance of the leading-edge sweep angle of propulsive surfaces used by unsteady swimming and flying animals has been an issue of debate for many years, spurring studies in biology, engineering, and robotics with mixed conclusions. In this work, we provide results from three-dimensional simulations on single-planform finite foils undergoing tail-like (pitch-heave) and flipper-like (twist-roll) kinematics for a range of sweep angles covering a substantial portion of animals while carefully controlling all other parameters. Our primary finding is the negligible 0.043 maximum correlation between the sweep angle and the propulsive force and power for both tail-like and flipper-like motions. This indicates that fish tails and mammal flukes with similar range and size can have a large range of potential sweep angles without significant negative propulsive impact. Although there is a slight benefit to avoiding large sweep angles, this is easily compensated by adjusting the fin’s motion parameters such as flapping frequency, amplitude and maximum angle of attack to gain higher thrust and efficiency.     

矩形柱二维尾流的稳定性研究

采用实验和数值模拟两种方法对长宽比为3∶1的矩形柱尾流进行了稳定性研究.实验发现当雷诺数接近临界值时,未加扰动的矩形柱尾流呈二维定常状态.当在柱体上游一定位置和下游靠近柱体的位置上沿垂直于来流方向施加一个宽度很小的短时脉冲射流扰动以后,扰动随时间放大,并出现旋涡脱落现象,并且这种扰动激发的旋涡脱落可以持续很长时间,不会衰减.而在下游较远处施加同样的扰动时,扰动将会衰减,不能激发出持续的旋涡脱落.数值模拟再现了上述实验结果,并且表明,当扰动强度(脉冲射流出口速度)较小时,不会出现持续的规则旋涡脱落,只有当扰动强度达到一定阈值时,旋涡脱落才能被激发.     

A proportional-integral-differential control of flow over a circular cylinder

In the present study, we apply proportional (P), proportional-integral (PI) and proportional-differential (PD) feedback controls to flow over a circular cylinder at Re=60 and 100 for suppression of vortex shedding in the wake. The transverse velocity at a centreline location in the wake is measured and used for the feedback control. The actuation (blowing/suction) is provided to the flow at the upper and lower slots on the cylinder surface near the separation point based on the P, PI or PD control. The sensing location is varied from 1d to 4d from the centre of the cylinder. Given each sensing location, the optimal proportional gain in the sense of minimizing the sensing velocity fluctuations is obtained for the P control. The addition of I and D controls to the P control certainly increases the control performance and broadens the effective sensing location. The P, PI and PD controls successfully reduce the velocity fluctuations at sensing locations and attenuate vortex shedding in the wake, resulting in reductions in the mean drag and lift fluctuations. Finally, P controls with phase shift are constructed from successful PI controls. These phase-shifted P controls also reduce the strength of vortex shedding, but their results are not as good as those from the corresponding PI controls.