Multisensor Hot Wire Vorticity Probe Measurements of the Formation Field of Two Corotating Vortices

Experimental evidence is reported, regarding the formation of a pair of co-rotating tip vortices by a split wing configuration, consisting of two half wings at equal and opposite angles of attack. Simultaneous measurements of the three-dimensional vector fields of velocity and vorticity were conducted on a cross plane at a downstream distance corresponding to 0.3 cord lengths (near wake), using an in-house constructed 12-sensor hot wire anemometry vorticity probe. The probe consists of three closely separated orthogonal 4-wire velocity sensor arrays, measuring simultaneously the three-dimensional velocity vector at three closely spaced locations on a cross plane of the flow filed. This configuration makes possible the estimation of spatial velocity derivatives by means of a forward difference scheme of first order accuracy. Velocity measurements obtained with an X-wire are also presented for comparison. In this near wake location, the flow field is dictated by the pressure distribution established by the flow around the wings, mobilizing large masses of air and leading to the roll up of fluid sheets. Fluid streams penetrating between the wings collide, creating on the cross plane flow a stagnation point and an “impermeable” line joining the two vortex centres. Along this line fluid is directed towards the two vortices, expanding their cores and increasing their separation distance. This feeding process generates a dipole of opposite sign streamwise mean vorticity within each vortex. The rotational flow within the vortices obligates an adverse streamwise pressure gradient leading to a significant streamwise velocity deficit characterizing the vortices. The turbulent flow field is the result of temporal changes in the intensity of the vortex formation and changes in the position of the cores (wandering).     

Effect of mini-flaps on the structure of the near wake behind a model half-wing

The effect of mini-flaps on the vortex structure of the near wake flow behind a model of a half-wing, rectangular in plan, is investigated. In a subsonic wind tunnel the time-average flow parameters are measured in several sections behind a model with flaps mounted on both upper and lower surfaces near the trailing edge. The wake flow parameters are compared with those for a model with no flaps. The considerable effect of the flaps on the flow structure in the viscous core of a tip vortex formed behind the model half-wing is established.     

Experimental investigation on tip vortices and aerodynamics

The tip vortices and aerodynamics of a NACA0012 wing in the vicinity of the ground were studied in a wind tunnel. The wing tip vortex structures and lift/drag forces were measured by a seven-hole probe and a force balance, respectively. The evolution of the flow structures and aerodynamics with a ground height were analyzed. The vorticity of tip vortices was found to reduce with the decreasing of the ground height, and the position of vortex-core moved gradually to the outboard of the wing tip. Therefore, the down-wash flow induced by the tip vortices was weakened. However, vortex breakdown occurred as the wing lowered to the ground. From the experimental results of aerodynamics, the maximum lift-to-drag ratio was observed when the angle of attack was 2.5° and the ground clearance was 0.2.     

Application of a vortex lattice numerical model in the calculation of inviscid incompressible flow around delta wings

The flow over a flat plate delta wing at incidence and in sideslip is studied using vortex lattice models based on streamwise penelling. For the attached flow problem the effect of sideslip is simulated by modifying the standard vortex lattice model for zero sideslip by aligning the trailing vortices aft of the wing along the resultant flow direction. For the separated flow problem a non-linear vortex lattice model is developed for both zero and non-zero sideslip angles in which the shape and position of the leading edge separation vortices are calculated by an iterative procedure starting from an assumed initial shape. The theoretical values are compared with available theoretical and experimental results.     

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)     

Time-resolved scanning tomography PIV measurements around a flapping wing

The three-dimensional flow that develops around a finite flapping wing is investigated using a tomographic scanning PIV technique. The acquisition and correlation processes employed to achieve such measurements have been carefully validated. Issues regarding the relevant timescales of the flow and the spanwise space-resolution are addressed. Results obtained on a hovering flapping wing whose plunging phase is described by a rectilinear motion highlight the influence of the free end condition and the formation of the tip vortex on the leading edge vortices behavior, wing/wake interactions, and wake stabilization.     

Volumetric three-component velocimetry measurements of the turbulent flow around a Rushton turbine

Volumetric three-component velocimetry measurements have been taken of the flow field near a Rushton turbine in a stirred tank reactor. This particular flow field is highly unsteady and three-dimensional, and is characterized by a strong radial jet, large tank-scale ring vortices, and small-scale blade tip vortices. The experimental technique uses a single camera head with three apertures to obtain approximately 15,000 three-dimensional vectors in a cubic volume. These velocity data offer the most comprehensive view to date of this flow field, especially since they are acquired at three Reynolds numbers (15,000, 107,000, and 137,000). Mean velocity fields and turbulent kinetic energy quantities are calculated. The volumetric nature of the data enables tip vortex identification, vortex trajectory analysis, and calculation of vortex strength. Three identification methods for the vortices are compared based on: the calculation of circumferential vorticity; the calculation of local pressure minima via an eigenvalue approach; and the calculation of swirling strength again via an eigenvalue approach. The use of two-dimensional data and three-dimensional data is compared for vortex identification; a ‘swirl strength’ criterion is less sensitive to completeness of the velocity gradient tensor and overall provides clearer identification of the tip vortices. The principal components of the strain rate tensor are also calculated for one Reynolds number case as these measures of stretching and compression have recently been associated with tip vortex characterization. Vortex trajectories and strength compare favorably with those in the literature. No clear dependence of trajectory on Reynolds number is deduced. The visualization of tip vortices up to 140° past blade passage in the highest Reynolds number case is notable and has not previously been shown.     

PIV analysis of flow around a container ship model with a rotating propeller

The flow characteristics of the propeller wake behind a container ship model with a rotating propeller were investigated using a two-frame PIV (Particle Image Velocimetry) technique. Ensemble-averaged mean velocity fields were measured at four different blade phases and ensemble-averaged to investigate the flow structure in the near-wake region. The mean velocity fields in longitudinal planes show that a velocity deficit is formed in the regions near the blade tips and hub. As the flow develops in the downstream direction, the trailing vortices formed behind the propeller hub move upward slightly due to the presence of the hull wake and free surface. Interaction between the bilge vortices and the incoming flow around the hull causes the flow structure to be asymmetric. Contour plots of the vorticity give information on the radial distribution of the loading on the blades. The radial velocity profiles fluctuate to a greater extent under the heavy (J=0.59) and light loading (J=0.88) conditions than under the design loading condition (J=0.72). The turbulence intensity has large values around the tip and trailing vortices. As the wake develops in the downstream direction, the strength of the vorticity diminishes and the turbulence intensity increases due to turbulent diffusion and active mixing between the tip vortices and the adjacent wake flow.     

Stereo PIV measurement of a finite, flapping rigid plate in hovering condition

Qualitative and quantitative flow visualizations were performed on a flapping rigid plate to establish a quantitative method for flow observation and evaluation of the force in the near field of a flapping wing. Flow visualization was performed qualitatively with dye visualization and quantitatively with velocity measurements using stereo particle image velocimetry (PIV) on three planes near the tip of the plate along its chord and oriented normally. By ensemble averaging the velocity fields of the same phase angles, they represent a portion of the volume near the tip. Measurements were conducted with two flapping frequencies to compare the flow structure. The second invariant of the deformation tensor visualized the leading edge and mid-chord vortices around the plate appearing due to flow separation behind the plate while other vortical structures were visualized by streamlines. These structures appear to be related to the dynamics of the leading edge vortex. Force analysis by integrating the phase-averaged velocity field within a chosen control volume showed increases in the maxima of the magnitudes of the non-dimensional unsteady force terms on the edge of the plate at the angles after the end of each stroke. The non-dimensional phase-averaged momentum flux was similar for both flapping frequencies.     

The temporal evolution of a pair of streamwise vortices

A detailed investigation of the velocity and vorticity fields of a pair of vortices growing over a 75°-sweep delta wing is carried out through LDV measurements of three components of velocity and vorticity. Data are obtained along one of the vortices. The wing is undergoing a ramp-like pitch-up motion. The evolution of the flow field in four planes normal to the free-stream velocity is captured at 100 time instants through the wing motion. The delta wing is pitched through angles of attack ranging from 28° to 68°. From the velocity data at each incidence, the corresponding vorticity field is calculated. Hysteresis effects on vortex development and breakdown are studied through axial velocity and vorticity contours. The topologies of streamlines and vortex lines are compared with the corresponding topologies of the steady case. It is found that vortex breakdown can be detected first by a drastic reduction of the axial velocity. This phenomenon is developing in a non-axisymmetric fashion, beginning at the inboard side of the vortex. This is followed by a reduction of the axial vorticity component and finally by a reversal of the azimuthal vorticity component.This work was supported by the Air Force Office of Scientific Research, Project No. AFOSR-91-0310 and was monitored by Major Daniel Fant.     

High-speed stereo DPIV measurement of wakes of two bat species flying freely in a wind tunnel

Previous studies on wake flow visualization of live animals using DPIV have typically used low repetition rate lasers and 2D imaging. Repetition rates of around 10 Hz allow ~1 image per wingbeat in small birds and bats, and even fewer in insects. To accumulate data representing an entire wingbeat therefore requires the stitching-together of images captured from different wingbeats, and at different locations along the wing span for 3D-construction of wake topologies. A 200 Hz stereo DPIV system has recently been installed in the Lund University wind tunnel facility and the high-frame rate can be used to calculate all three velocity components in a cube, whose third dimension is constructed using the Taylor hypothesis. We studied two bat species differing in body size, Glossophaga soricina and Leptonycteris curasoa. Both species shed a tip vortex during the downstroke that was present well into the upstroke, and a vortex of opposite sign to the tip vortex was shed from the wing root. At the transition between upstroke/downstroke, a vortex loop was shed from each wing, inducing an upwash. Vorticity iso-surfaces confirmed the overall wake topology derived in a previous study. The measured dimensionless circulation, Γ/Uc, which is proportional to a wing section lift coefficient, suggests that unsteady phenomena play a role in the aerodynamics of both species.     

Evolution of vortices in the wake of an ARJ21 airplane: Application of the lift-drag model

Wake separation is crucial to aircraft landing safety and is an important factor in airport operational efficiency. The near-ground evolution characteristics of wake vortices form the foundation of the wake separation system design. In this study, we analysed the near-ground evolution of vortices in the wake of a domestic aircraft ARJ21 initialised by the lift-drag model using large eddy simulations based on an adaptive mesh. Evolution of wake vortices formed by the main wing, flap and horizontal tail was discussed in detail. The horizontal tail vortices are the weakest and dissipate rapidly, whereas the flap vortices are the strongest and induce the tip vortex to merge with them. The horizontal tail and flap of an ARJ21 do not significantly influence the circulation evolution, height change and movement trajectory of the wake vortices. The far-field evolution of wake vortices can therefore be analysed using the conventional wake vortex model.     

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     

An analytic approach to theoretical modeling of highly unsteady viscous flow excited by wing flapping in small insects

Numerous studies on the aerodynamics of insect wing flapping were carried out on different approaches of flight investigations, model experiments, and numerical simulations, but the theoretical modeling remains to be explored. In the present paper, an analytic approach is presented to model the flow interactions of wing flapping in air for small insects with the surrounding flow fields being highly unsteady and highly viscous. The model of wing flapping is a 2-D flat plate, which makes plunging and pitching oscillations as well as quick rotations reversing its positions of leading and trailing edges, respectively, during stroke reversals. It contains three simplified aerodynamic assumptions: (i) unsteady potential flow; (ii) discrete vortices shed from both leading and trailing edges of the wing; (iii) Kutta conditions applied at both edges. Then the problem is reduced to the solution of the unsteady Laplace equation, by using distributed singularities, i.e., sources/sinks, and vortices in the field. To validate the present physical model and analytic method proposed via benchmark examples, two elemental motions in wing flapping and a case of whole flapping cycles are analyzed, and the predicted results agree well with available experimental and numerical data. This verifies that the present analytical approach may give qualitatively correct and quantitatively reasonable results. Furthermore, the total fluid-dynamic force in the present method can be decomposed into three parts: one due to the added inertial (or mass) effect, the other and the third due to the induction of vortices shed from the leading-and the trailing-edge and their images respectively, and this helps to reveal the flow control mechanisms in insect wing flapping. The project supported by the National Natural Science Foundation of China (10072066) and the Chinese Academy of Sciences (KJCX-SW-LO4, KJCX2-SW-L2)     

Effect of apex strake incidence-angle on the vortex development and interaction of a double-delta wing

The vortex flow characteristics of a sharp-edged delta wing with an apex strake was investigated through the visualization and particle image velocimetry (PIV) measurement of the wing-leeward flow region, and the wing-surface pressure measurement. The wing model was a flat-plate, and 65°-sweep cropped-delta wing with sharp leading edges. The apex strake was also a flat-plate wing with a cropped-delta shape of 65°/90° sweep, and it can change its incidence angle. The flow Reynolds number was 2.2 × 10⁵ for the flow visualization and 8.2 × 10⁵ for the PIV and wing-surface pressure measurements. The physics of the vortex flow in the wing-leeward flow region and the suction-pressure distribution on the wing upper-surface were interrelated and analyzed. The effect of a positive (negative) strake incidence-angle was the upward movement of the strake and wing vortices away from (downward movement of the strake and wing vortices toward) the wing-upper surface and the delayed (enhanced) coiling interaction between them. This change of vortex flow characteristics projected directly on the suction pressure distribution on the wing upper-surface.     

Flow-induced vibrations of low aspect ratio rectangular membrane wings

An experimental study of a low aspect ratio rectangular membrane wing in a wind tunnel was conducted for a Reynolds number range of 2.4×10⁴–4.8×10⁴. Time-accurate measurements of membrane deformation were combined with the flow field measurements. Analysis of the fluctuating deformation reveals chordwise and spanwise modes, which are due to the shedding of leading-edge vortices as well as tip vortices. At higher angles of attack, the second mode in the chordwise direction becomes dominant as the vortex shedding takes place. The dominant frequencies of the membrane vibrations are similar to those of two-dimensional membrane airfoils. Measured frequency of vortex shedding from the low aspect ratio rigid wing suggests that membrane vibrations occur at the natural frequencies close to the harmonics of the wake instabilities. Vortex shedding frequency from rigid wings shows remarkably small effect of aspect ratio even when it is as low as unity.     

Three-dimensional vortex formation on a heaving low-aspect-ratio wing: Computations and experiments

This paper addresses by means of high-resolution numerical simulations and experimental quantitative imaging the three-dimensional unsteady separation process induced by large-amplitude heaving oscillations of a low-aspect-ratio wing under low-Reynolds-number conditions. Computed results are found to be in good agreement with experimental flow visualizations and PIV measurements on selected cross-flow planes. The complex unsteady three-dimensional flow structure generated during dynamic stall of the low-aspect-ratio wing is elucidated. The process is characterized by the generation of a leading-edge vortex system which is pinned at the front corners of the plate and which exhibits intense transverse flow toward the wing centerline during its initial stages of development. This vortex detaches from the corners and evolves into an newly found arch-type structure. The legs of the arch vortex move along the surface toward the wing centerline and reconnect forming a ring-like structure which is shed as the next plunging cycle begins. Vortex breakdown, total collapse and reformation of the wing tip vortices are also observed at various stages of the heaving motion. At the relatively high value of reduced frequency considered, these basic flow elements of the complex three-dimensional dynamic stall process are found to persist over a range of Reynolds numbers.     

Three-component velocity field measurements of propeller wake using a stereoscopic PIV technique

A stereoscopic PIV (Particle Image Velocimetry) technique was used to measure the three-dimensional flow structure of the turbulent wake behind a marine propeller with five blades. The out-of-plane velocity component was determined using two CCD cameras with an angular displacement configuration. Four hundred instantaneous velocity fields were measured for each of four different blade phases, and ensemble averaged in order to find the spatial evolution of the propeller wake in the region from the trailing edge up to one propeller diameter (D) downstream. The influence of propeller loading conditions on the wake structure was also investigated by measuring the velocity fields at three advance ratios (J=0.59, 0.72 and 0.88). The phase-averaged velocity fields revealed that a viscous wake formed by the boundary layers developed along the blade surfaces. Tip vortices were generated periodically and the slipstream contracted in the near-wake region. The out-of-plane velocity component and strain rate had large values at the locations of the tip and trailing vortices. As the flow moved downstream, the turbulence intensity, the strength of the tip vortices, and the magnitude of the out-of-plane velocity component at trailing vortices all decreased due to effects such as viscous dissipation, turbulence diffusion, and blade-to-blade interaction.     

Calculation of aerodynamic characteristics of a wing profile with discharge of a controllable jet into the external flow

A wing profile of infinite span, whose lower surface is replaced by a system of guide vanes, is placed in a flow of an ideal incompressible fluid. Fluid flows out through the system of guide vanes from the internal cavity of the wing into the external stream, forming a jet in the wake (Fig. 1). The total pressure in the wing cavity and in the jet differs from the total pressure in the outer free stream. The jet boundaries are streamlines extending to infinity, along which there is a discontinuity of the velocity value. The flow of fluid in the internal wing cavity is simulated by a flow caused by a system of suitably located sources, and the system of guide vanes is replaced by discrete vortices.The form of the profile arc is selected so that the fluid flow from the sources in the direction which is nearly opposite the direction of the freestream velocity is restrained by the segment of the contour with high curvature in the vicinity of the leading edge. We consider the flow regime about the profile with an exhausting jet for which the two ends of the arc the points of detachment of the stream and the velocity discontinuity line (profile arc, jet boundary) is a smooth curve, which imposes an additional condition on the magnitude of the circulation. As the model for the study of the flow about a profile with jet blowing we take the arc of a logarithmic spiral.Formulas are obtained for determining the over-all characteristics of the stream forces acting on the profile in the presence of the jet and the total pressure discontinuity. On the basis of the calculations made for a thin wing a qualitative analysis is made for the stream force acting on the profile.The authors wish to thank S. A. Khristianovich for formulating the problem and for his advice.     

The Dean instability in power-law and Bingham fluids in a curved rectangular duct

The laminar flow of power-law and yield-stress fluids in 180° curved channels of rectangular cross section was studied experimentally and numerically in order to understand the effect of rheological fluid behavior on the Dean instability that appears beyond a critical condition in the flow. This leads to the apparition of Dean vortices that differ from the two corner vortices created by the channel wall curvature.Flow visualizations showed that the Dean vortices develop first in the near-wall zone on the concave (outer) wall, where the shear rate is higher and the viscosity weaker; then they penetrate into the centre of the channel cross section where power-law fluids have high viscosity and Bingham fluids are unyielded in laminar flow. Based on the complete formation on the concave wall of the new pairs of counter-rotating vortices (Dean vortices), the critical value of the Dean number decreases as the power-law index increases for the power-law fluids, and the Bingham number decreases for the Bingham fluids. For power-law fluids, a diagram of critical Dean numbers, based on the number of Dean vortices formed, was established for different axial positions. For the same flow conditions, the critical Dean number obtained using the axial velocity gradient criterion was smaller then that obtained with the visualization technique.