Effect of vortex shedding in unsteady aerodynamic forces for a low Reynolds number stationary wing at low angle of attack

This study elucidates the relation between wake vortex shedding and aerodynamic force fluctuations for a low Reynolds number wing from time resolved particle image velocimetry (TR-PIV) experimental measurements. The results reveal a periodic lift and drag variation within the shedding cycle and resolve the frequencies of those fluctuations from a proper orthogonal decomposition (POD) and power spectral density (PSD) analysis. To show the effect of vortex shedding on the body force fluctuations, the evolution of instantaneous aerodynamic forces is compared to the pressure field of the fluid flow and to the vortical structures in the wake of the airfoil. A six step model describing the vortex-force relation is proposed. It shows that changes in lift such as maximum lift and minimum lift are associated with the detachment of a vortex. It also shows that the minimum or local minimum drag value is obtained at the onset formation of a vortex on the airfoil wake. Similarly, the maximum or local maximum drag is obtained at the onset formation of the saddle on the airfoil wake. The model further explains the asymmetry observed in the unsteady drag force evolution. The model can be used to optimize flow control and fluid-structure interaction applications.     

Transverse motions of a single sphere in hanging or swing configurations under a longitudinal flow

As a result of the reporting of casual observations of the oscillation or rotation of the beacons in transmission line guard cables, some attention has been paid to the stability of the guard cables with beacons.The relatively more frequent observation of these motions has been explained in recent papers dealing with the elastic part of the problem as a consequence of the increasing number of resonant frequencies (one for each additional beacon) that can be excited by appropriate aerodynamic loads. But a model that could explain the aerodynamic forces that can give rise to this motion is still lacking.In this paper we consider the transverse motions of a single sphere in two simplified configurations, (1) hanging (tethered at one point), and (2) swing (tethered at two points) under a longitudinal flow, performing small amplitude swinging oscillations or circular-orbit autorotation about an axis parallel to the main flow direction. The dynamic model here presented is based on the motion equations, which also include a model for the aerodynamic lift and drag forces on the sphere in transverse motion, which considers the effect of changes of flow around the sphere due to the cable interference. These forces are contained in the symmetry plane of the flow relative to the sphere, and, when projected on the lateral direction, give rise to a lateral force, which can explain the existence of the azimuthal motion even at a large reduced velocity, outside the vortex induced vibration (VIV) range The conditions for stable small oscillation motion and circular-orbit autorotation of a sphere in a swing configuration are given.The results for the aerodynamic loads in transverse motion have also been applied to the case of a circular-orbit autorotation of a hanging sphere (spherical pendulum) under a vertical flow. The angular rotation speed and the orbit radius (or cable angle) have been determined as a function of aerodynamic coefficients and configuration parameters.     

Unsteady response of airfoils due to small-scale pitching motion with considerations for foil thickness and wake motion

Unsteady pressures, forces, and pitching moments generated by foils experiencing vibratory motion in an incompressible, attached flow configuration are studied within this work. Specifically, two-dimensional, unsteady potential flow and unsteady Reynolds-Averaged Navier–Stokes calculations are performed on various Joukowski foils undergoing sinusoidal, variable amplitude, small-scale pitching motion at a chord-based Reynolds number of 10${}^6$ over a range of reduced frequencies between 0.01–100. These calculated results from both approaches are compared directly to predictions from implementing the Theodorsen model, which treats foils as infinitely thin, flat plates that shed a planar sheet of vorticity. The effects of relaxing these seemingly strict conditions are explored, and the particular terms which control the unsteady responses are identified and discussed. For increasing pitch amplitudes and reduced frequencies the shed wake is seen to become quite non-planar and to form coherent vortex structures. Despite this wake behavior, the normalized airfoil responses at the disturbance reduced frequency are seen to be largely unaffected. However, non-negligible responses are generated across a wide range of other frequencies. Potential flow calculations for symmetric Joukowski foils show that there is marginal effect of foil thickness at reduced frequencies less than one. For higher reduced frequency conditions however, the unsteady lift response is seen to experience both an amplification of level and a phase shift relative to the Theodorsen model. A specific augmenting expression is developed for this behavior through analysis within the potential flow framework.     

Hydrodynamics of a tandem fish school with asynchronous undulation of individuals

We perform numerical simulations using immersed boundary method for flow over a single and two fish in tandem performing traveling wave like motion for a range of Strouhal numbers. We investigate the hydrodynamic performance of single- and tandem-fish configurations using unsteady profiles of lateral side-force and drag coefficients, their time-averaged values, and wake behind these bodies. We present the spectra of hydrodynamic forces and find that the nature of these forces for a single fish resembles to those of stationary/oscillating bluff bodies and oscillating airfoils. For tandem cases, we vary the phase speed of undulatory motion of the rear fish while keeping the free-stream velocity constant. We show that hydrodynamic forces of the upstream and rear fish contain harmonics which are produced by nonlinear interaction of the oscillation frequencies of both fish. We find that the wake and time-averaged drag of the upstream fish remain almost independent of the undulating frequency of the rear fish at a certain Strouhal number. We also relate this observation with the absence of oscillation frequency of the rear fish in the Fourier spectra of hydrodynamic forces of the upstream fish. For the complete range of parameters, it is inferred that swimming in a tandem configuration seems more beneficial for the upstream fish. It happens due to wake-splitting effect of the rear fish that causes an enhancement of pressure in its wake. For the rear fish, it gains an advantage of drafting under certain conditions and its performance deteriorates at Strouhal numbers greater than 0.40.     

Numerical modelling of the entrainment of particles in inviscid supersonic flow

The interaction between particles situated in close proximity and moving at supersonic speeds is investigated computationally. The simplest case of the motion of a single particle travelling behind a lead particle is used to elucidate the role of aerodynamic forces in the motion of a group of particles. The effect of the following parameters on the drag and lift forces acting on each of two particles of equal diameter in proximity is investigated: the free-stream Mach number, and the axial and lateral displacements of the trailing particle. The two-dimensional flow field is numerically simulated using an unsteady Euler CFD code to find the steady-state drag and lift coefficients for both particles. Three static zones of aerodynamic influence in the wake of the lead particle are identified, which are denoted as the entrainment, lateral attraction, and ejection zones. A non-dimensional representation of the zones of influence is given. It is shown that the dynamic entrainment of particles can occur even when the path of the trailing particle originates outside the entrainment and lateral attraction zones.     

Drag reduction of motor vehicles by active flow control using the Coanda effect

A test facility has been constructed to realistically simulate the flow around a two dimensional car shaped body in a wind tunnel. A moving belt simulator has been employed to generate the relative motion between model and ground. In a first step, the aerodynamic coefficients c _L and c _D of the model are determined using static pressure and force measurements. LDA-measurements behind the model show the large vortex and turbulence structures of the near and far wake. In a second step, the ambient flow around the model is modified by way of an active flow control which uses the Coanda effect, whereby the base-pressure increases by nearly 50% and the total drag can be reduced by 10%. The recirculating region is completely eliminated. The current work reveals the fundamental physical phenomena of the new method by observing the pressure forces on the model surface as well as the time averaged velocities and turbulence distributions for the near and far wake. A theory resting on this empirical information is developed and provides information about the effectiveness of the blowing method. For this, momentum and energy equations were applied to the flow around the vehicle to enable a validation of the theoretical results using experimental values. Received: 9 June 1998 / Accepted: 20 July 1999     

An aerodynamic ROM of the blade subjected to wake based on Fourier method for flow

A reduced-order model (ROM) is presented based on Fourier method for flow to predict aerodynamic forces of blades subjected to periodic time-varying upstream wakes. In the method, a time-varying wake is decomposed into harmonic waves by fast Fourier transformation. Using the Fourier method for flow and neglecting the cross-coupling between harmonics, the aerodynamic forces caused by the wake are represented by a linear combination of harmonics with the same frequencies as the wake. The coefficients of the aerodynamic force harmonics are interpolated at the per-fitted curves of the normalized Fourier coefficients (coefficients of aerodynamic forces harmonics corresponding to a unit simple harmonic excitation)–frequency relationship. A blade example is used to show the ability of the proposed method. The results indicate that the ROM method can predict the aerodynamic forces of blades caused by wakes efficiently and accurately. The amplitude levels of wakes have a linear impact on the accuracy of the ROM. Neglecting the higher-order cross-coupling between the harmonics in the ROM method is acceptable.     

Development of models correlating vibration excitation forces to dynamic characteristics of two-phase flow in a tube bundle

Recent experiments revealed significant quasi-periodic forces in both the drag and lift directions in a rotated triangular tube bundle subjected to two-phase cross-flow. The quasi-periodic drag forces were found to be related to the momentum flux fluctuations in the main flow path between the cylinders. The quasi-periodic lift forces, on the other hand, are mostly correlated to the oscillation in the wake of the cylinders. In this paper, we develop semi-analytical models for correlating vibration excitation forces to dynamic characteristics of two-phase flow in a rotated triangular tube bundle for a better understanding of the nature of vibration excitation forces. The relationships between the lift or drag forces and the dynamic characteristics of two-phase flow are established through fluid mechanics momentum equations. A model has been developed to correlate the void fraction fluctuation in the main flow path and the dynamic drag forces. A second model has been developed for correlating the oscillation in the wake of the cylinders and the dynamic lift forces. Although still preliminary, each model can predict the corresponding forces relatively well.     

定常流作用于波浪形边界附近的圆柱上的水动力

本文介绍在水洞中做的作用于波浪形边界附近的水动力特性的实验研究。在基于圆柱模型直径的 R_c=10~4～1.9×10~4 范围内,测量了圆柱在波谷、波峰和不同距离上的阻力、升力脉动变化的频率。流谱显示实验揭示了尾流结构随距离-直径比 G/D 的变化情况及圆柱与边界相互作用的机制。     

Aerodynamic drag reduction of a simplified squareback vehicle using steady blowing

A large contribution to the aerodynamic drag of a vehicle arises from the failure to fully recover pressure in the wake region, especially on squareback configurations. A degree of base pressure recovery can be achieved through careful shape optimisation, but the freedom of an automotive aerodynamicist to implement significant shape changes is limited by a variety of additional factors such styling, ergonomics and loading capacity. Active flow control technologies present the potential to create flow field modifications without the need for external shape changes and have received much attention in previous years within the aeronautical industry and, more recently, within the automotive industry. In this work the influence of steady blowing applied at a variety of angles on the roof trailing edge of a simplified ? scale squareback style vehicle has been investigated. Hot-wire anemometry, force balance measurements, surface pressure measurements and PIV have been used to investigate the effects of the steady blowing on the vehicle wake structures and the resulting body forces. The energy consumption of the steady jet is calculated and is used to deduce an aerodynamic drag power change. Results show that overall gains can be achieved; however, the large mass flow rate required restricts the applicability of the technique to road vehicles. Means by which the mass flow rate requirements of the jet may be reduced are discussed and suggestions for further work put forward.     

DYNAMIC SIMULATION OF MARINE RISERS MOVING RELATIVE TO EACH OTHER DUE TO VORTEX AND WAKE EFFECTS

This article presents a time domain simulator which simulates the dynamic interaction of two adjacent cylindrical risers moving relative to each other in an ambient steady flow. The main objective of the simulator is to assess whether adjacent marine risers moving in each other's wake will collide or not. The simulator named Time domain RIser Collision Evaluation (TRICE) uses drag and lift coefficients as well as excitation frequencies computed by an in-house developed numerical Navier–Stokes equation solver (CFD). The CFD program computes lift and drag forces, the standard deviation of the excitation forces and the dominant vortex shedding frequency as a function of the relative position of two cylinders restrained from motion. We propose, based on analysis and observations during experiments, that the wake induced oscillation (WIO) behaviour determines if the risers collide or not, and that the U001vortex-induced vibration (VIV) behaviour determines most of the energy in the collision. That is, the wake behaviour controls the gross motions of the risers relative to each other. The current version is limited to handle two cylindrical risers in staggered and tandem configurations. The results from the simulations are successfully compared with experimental data. TRICE predicts the minimum current when collisions occur with a deviation typically better than 8% for both tandem and staggered arrangements.     

Active decoupling of the axisymmetric body wake response to a pitching motion

Controlled interactions between fluidic actuators and the cross flow over the aft end of a wire-mounted axisymmetric wind tunnel bluff body model (Re_D=2.3·10⁵) are exploited for modification of the near wake dynamics, and the consequent global aerodynamic loads. Actuation is effected using an array of four aft-facing synthetic jet modules through narrow, azimuthally-segmented slots that are equally distributed around the perimeter of the tail end. The model is supported by eight wires, each including a miniature inline force transducer for measurements of the time-resolved tension. The model’s position is varied in a prescribed trajectory by synchronous activation of shape memory alloy (SMA) segments in each of the mounting wires, and the aerodynamic forces and moments are manipulated over a range of pitch attitude. The effectiveness of the flow control approach is demonstrated by decoupling of the wake response from the body’s pitch motion at a low pitch frequency (k=0.013). It is shown that, under the active control, the wake symmetry can be restored or its asymmetry can be amplified.     

Bluff-body drag reduction by passive ventilation

The drag of a sphere at highRe can be reduced to more than half its value by passive ventilation from the stagnation region to the base. Simultaneously, the flow field around the base is stabilized and made symmetric, leading to reduction of unsteady aerodynamic forces. At highRe, the vent flow breaks through the dead water region associated with the near wake and aerodynamically streamlines the base. The streamlining is done by virtue of a base-vortex-ring beyond the point of turbulent boundary layer separation. A mean flow model for the flow around the vented sphere is proposed.Smoke flow visualized on a laser light screen placed at two diameters behind the base of the sphere shows the effectiveness of the method in suppressing the flow oscillations.The drag reduction achieved is very sensitive to the quality of the external surface and relatively insensitive to disturbances in the internal flow. Surface roughness or boundary layer tripping wire on the external flow can completely offset the benefit obtained.     

探测器对超音速刚性盘-缝-带型降落伞系统的影响

研究了流体初始马赫数为 2.0 时, 探测器的存在与否对刚性盘-缝-带型降落伞系统气动减速性能以及流场流体结构特性的影响. 对于非定常可压缩流体的数值模拟, 流场采用了三层块结构自适应网格加密技术, 配合混合形式的TCD (tuned center difference)和WENO (weighted essentially non-oscillatory)计算格式以及基于拉伸涡亚格子模型的大涡模拟方法来处理超音速流中的激波以及大尺度湍流旋涡结构等. 结果表明: 无探测器时, 降落伞系统的流场结构稳定, 扰动较小; 有探测器存在时, 探测器后端的湍流尾迹和伞衣内部逆向运动溢出的流体与伞衣前端的弓形激波周期性的相互作用, 使得激波位置发生前移、激波倾角变小, 伞衣内部流场难以达到平衡稳定状态. 这加剧了降落伞系统的气动阻力振荡脉动变化, 降低了降落伞系统气动阻力系数, 同时也使得降落伞系统流场尾迹结构更加复杂.      

Experimental investigation of a flapping wing model

The main objective of this research study was to investigate the aerodynamic forces of an avian flapping wing model system. The model size and the flow conditions were chosen to approximate the flight of a goose. Direct force measurements, using a three-component balance, and PIV flow field measurements parallel and perpendicular to the oncoming flow, were performed in a wind tunnel at Reynolds numbers between 28,000 and 141,000 (3–15 m/s), throughout a range of reduced frequencies between 0.04 and 0.20. The appropriateness of quasi-steady assumptions used to compare 2D, time-averaged particle image velocimetry (PIV) measurements in the wake with direct force measurements was evaluated. The vertical force coefficient for flapping wings was typically significantly higher than the maximum coefficient of the fixed wing, implying the influence of unsteady effects, such as delayed stall, even at low reduced frequencies. This puts the validity of the quasi-steady assumption into question. The (local) change in circulation over the wing beat cycle and the circulation distribution along the wingspan were obtained from the measurements in the tip and transverse vortex planes. Flow separation could be observed in the distribution of the circulation, and while the circulation derived from the wake measurements failed to agree exactly with the absolute value of the circulation, the change in circulation over the wing beat cycle was in excellent agreement for low and moderate reduced frequencies. The comparison between the PIV measurements in the two perpendicular planes and the direct force balance measurements, show that within certain limitations the wake visualization is a powerful tool to gain insight into force generation and the flow behavior on flapping wings over the wing beat cycle.     

On the unsteady motion and stability of a heaving airfoil in ground effect

This study explores the fluid mechanics and force generation capabilities of an inverted heaving airfoil placed close to a moving ground using a URANS solver with the Spalart-Allmaras turbulence model. By varying the mean ground clearance and motion frequency of the airfoil, it was possible to construct a frequency-height diagram of the various forces acting on the airfoil. The ground was found to enhance the downforce and reduce the drag with respect to freestream. The unsteady motion induces hysteresis in the forces’ behaviour. At moderate ground clearance, the hysteresis increases with frequency and the airfoil loses energy to the flow, resulting in a stabilizing motion. By analogy with a pitching motion, the airfoil stalls in close proximity to the ground. At low frequencies, the motion is unstable and could lead to stall flutter. A stall flutter analysis was undertaken. At higher frequencies, inviscid effects overcome the large separation and the motion becomes stable. Forced trailing edge vortex shedding appears at high frequencies. The shedding mechanism seems to be independent of ground proximity. However, the wake is altered at low heights as a result of an interaction between the vortices and the ground.     

Large aerodynamic forces on a sweeping wing at low Reynolds number

The aerodynamic forces and flow structure of a model insect wing is studied by solving the Navier-Stokes equations numerically. After an initial start from rest, the wing is made to execute an azimuthal rotation (sweeping) at a large angle of attack and constant angular velocity. The Reynolds number (Re) considered in the present note is 480 (Re is based on the mean chord length of the wing and the speed at 60% wing length from the wing root). During the constant-speed sweeping motion, the stall is absent and large and approximately constant lift and drag coefficients can be maintained. The mechanism for the absence of the stall or the maintenance of large aerodynamic force coefficients is as follows. Soon after the initial start, a vortex ring, which consists of the leading-edge vortex (LEV), the starting vortex, and the two wing-tip vortices, is formed in the wake of the wing. During the subsequent motion of the wing, a base-to-tip spanwise flow converts the vorticity in the LEV to the wing tip and the LEV keeps an approximately constant strength. This prevents the LEV from shedding. As a result, the size of the vortex ring increases approximately linearly with time, resulting in an approximately constant time rate of the first moment of vorticity, or approximately constant lift and drag coefficients. The variation of the relative velocity along the wing span causes a pressure gradient along the wingspan. The base-to-tip spanwise flow is mainly maintained by the pressure-gradient force. The project supported by the National Natural Science Foundation of China (10232010)     

On the development of lift and drag in a rotating and translating cylinder

The two-dimensional flow around a rotating cylinder is investigated numerically using a vorticity forces formulation with the aim of analyzing quantitatively the flow structures, and their evolutions, that contribute to the lift and drag forces on the cylinder. The Reynolds number considered, based on the cylinder diameter and steady free stream speed, is Re=200, while the non-dimensional rotation rate (ratio of the surface speed and free stream speed) selected was α=1 and 3. For α=1 the wake behind the cylinder for the fully developed flow is oscillatory due to vortex shedding, and so are the lift and drag forces. For α=3 the fully developed flow is steady with constant (high) lift and (low) drag. Each of these cases is considered in two different transient problems, one with angular acceleration of the cylinder and constant speed, and the other one with translating acceleration of the cylinder and constant rotation. We characterize quantitatively the contributions of individual fluid elements (vortices) to aerodynamic forces, explaining and quantifying the mechanisms by which the lift is generated in each case. In particular, for high rotation (when α=3), we explain the relation between the mechanisms of vortex shedding suppression and those by which the lift is enhanced and the drag is almost suppressed when the fully developed flow is reached.     

The influence of the wake of a flapping wing on the production of aerodynamic forces

The effect of the wake of previous strokes on the aerodynamic forces of a flapping model insect wing is studied using the method of computational fluid dynamics. The wake effect is isolated by comparing the forces and flows of the starting stroke (when the wake has not developed) with those of a later stroke (when the wake has developed). The following has been shown. (1) The wake effect may increase or decrease the lift and drag at the beginning of a half-stroke (downstroke or upstroke), depending on the wing kinematics at stroke reversal. The reason for this is that at the beginning of the half-stroke, the wing ``impinges' on the spanwise vorticity generated by the wing during stroke reversal and the distribution of the vorticity is sensitive to the wing kinematics at stroke reversal. (2) The wake effect decreases the lift and increases the drag in the rest part of the half-stroke. This is because the wing moves in a downwash field induced by previous half-stroke's starting vortex, tip vortices and attached leading edge vortex (these vortices form a downwash producing vortex ring). (3) The wake effect decreases the mean lift by 6%–18% (depending on wing kinematics at stroke reversal) and slightly increases the mean drag. Therefore, it is detrimental to the aerodynamic performance of the flapping wing. The project supported by the National Natural Science Foundation of China (10232010) and the National Aeronautic Science Fund of China(03A51049) The English text was polished by Xing Zhang     

Numerical investigation on aerodynamic performance of a bionic flapping wing

This paper numerically studies the aerodynamic performance of a bird-like bionic flapping wing. The geometry and kinematics are designed based on a seagull wing,in which flapping, folding, swaying, and twisting are considered. An in-house unsteady flow solver based on hybrid moving grids is adopted for unsteady flow simulations. We focus on two main issues in this study, i.e., the influence of the proportion of down-stroke and the effect of span-wise twisting. Numerical results show that the proportion of downstroke is closely related to the efficiency of the flapping process. The preferable proportion is about 0.7 by using the present geometry and kinematic model, which is very close to the observed data. Another finding is that the drag and the power consumption can be greatly reduced by the proper span-wise twisting. Two cases with different reduced frequencies are simulated and compared with each other. The numerical results show that the power consumption reduces by more than 20%, and the drag coefficient reduces by more than 60% through a proper twisting motion for both cases. The flow mechanism is mainly due to controlling of unsteady flow separation by adjusting the local effective angle of attack. These conclusions will be helpful for the high-performance micro air vehicle(MAV) design.