Robustness of the Leading Edge Vortex on Rotating Wings to Unsteady Perturbations

The vast majority of research works on low aspect ratio rotating wings report that, at high angle of attack, the leading edge vortex that forms on the upper surface of the wing is stable. This ‘trick’ is used by insects and auto-rotating seeds, for example, to achieve the desirable amount of lift. Yet, a few experimental studies suggest that leading edge vortices might be unstable under similar, low Rossby number, conditions. While it is unclear what causes vortex shedding in these studies, the present communication explores the sensitivity of leading edge vortex attachment to perturbations of the rotating speed and demonstrates that shedding can be triggered even for very small perturbations, corresponding to wing tip displacements lower than 1% of the wing chord.

     

Lift enhancement through flexibility of plunging wings at low Reynolds numbers

In this paper the combined effect of two mechanisms for lift enhancement at low Reynolds numbers are considered, wing oscillations and wing flexibility. The force, deformation and flow fields of rigid and flexible low aspect ratio (AR=3) and high aspect ratio (AR=6) wings oscillating at a fixed post-stall angle of attack of 15° and amplitude of 15% of chord are measured. The force measurements show that flexibility can increase the time-averaged lift coefficient significantly. For low aspect ratio wings the maximum lift coefficient across all Strouhal numbers was C_l=1.38 for the rigid wing as opposed to C_l=2.77 for the flexible wing. Very similar trends were observed for the high aspect ratio wings. This increase is associated with significant deformation of the wing. The root is sinusoidally plunged with small amplitude but this motion is amplified along the span resulting in a larger tip motion but with a phase lag. The amount it is amplified strongly depends on Strouhal number. A Strouhal number of Sr_c=1.5 was selected for detailed flow field measurements due to it being central to the high-lift region of the flexible wings, producing approximately double the lift of the rigid wing. For this Strouhal number the rigid wings exhibit a Leading Edge Vortex (LEV) ring. This is where the clockwise upper-surface LEV pairs with the counter-clockwise lower-surface LEV to form a vortex ring that self-advects upstream and away from the wing's upper surface. Conversely the deformation of the flexible wings inhibits the formation of the LEV ring. Instead a strong upper-surface LEV forms during the downward motion and convects close to the airfoil upper surface thus explaining the significantly higher lift. These measurements demonstrate the significant gains that can be achieved through the combination of unsteady aerodynamics with flexible structures.     

Experimental investigation of a circular radially deforming cylinder near wake using an infrared technique

The present experimental study aims at developing a method to control the circular cylinder near wake by radial deformation and understand the underlying physics. Using an infra-red camera, we examine the temperature distribution of the near wake center line of a sinusoidal law radially deforming circular cylinder. From these measurements, the near wake is characterized by the length of the recirculation zone, the vortex formation zone length, the temperature fluctuation maximum intensity and the vortex street shedding frequency. For several deformations frequencies, we study the radial deformation influence on the near wake characteristics. It is noted that the wake structure is strongly affected by the deformation frequency. Among other things, we note the recirculation zone length reduction and the vortex formation zone length reduction when the radial vibrations are close to the “Lock-in” fundamental range. It is also noted that the variations of the vortex shedding frequency depend on the deformation frequency.     

On vortex shedding from low aspect ratio dual step cylinders

A dual-step cylinder is comprised of two cylinders of different diameters. A large diameter cylinder (D) with low aspect ratio (L/D) is attached to the mid-span of a small diameter cylinder (d). The present study investigates the effect of Reynolds number (Re_D) and L/D on dual step cylinder wake development for D/d=2, 0.2≤L/D≤3, and two Reynolds numbers, Re_D=1050 and 2100. Experiments have been performed in a water flume facility utilizing flow visualization, Laser Doppler Velocimetry (LDV), and Particle Image Velocimetry (PIV). The results show that vortex shedding occurs from both the large and small diameter cylinders for 1≤L/D≤3 at Re_D=2100 and 2≤L/D≤3 at Re_D=1050. At these conditions, large cylinder vortices predominantly form vortex loops in the wake and small cylinder vortices form half-loop vortex connections. At lower aspect ratios, vortex shedding from the large cylinder ceases, with the dominant frequency in the large cylinder wake attributed to the passage of vortex filaments connecting small cylinder vortices. At these lower aspect ratios, the presence of the large cylinder induces periodic vortex dislocations. Increasing L/D increases the frequency of occurrence of vortex dislocations and decreases the dominant frequency in the large cylinder wake. The identified changes in wake topology are related to substantial variations in the location of boundary layer separation on the large cylinder, and, consequently, changes in the size of the vortex formation region. The results also show that the Reynolds number has a substantial effect on wake vortex shedding frequency, which is more profound than that expected for a uniform cylinder.     

An experimental investigation of flow past a dual step cylinder

Flow development in the wake of a dual step cylinder has been investigated experimentally using Laser Doppler Velocimetry and flow visualization. The dual step cylinder model is comprised of a large diameter cylinder (D) mounted at the mid-span of a small diameter cylinder (d). The experiments have been performed for a Reynolds number (Re _D ) of 1,050, a diameter ratio (D/d) of 2, and a range of large cylinder aspect ratios (L/D). The results show that the flow development is highly dependent on L/D. The following four distinct flow regimes can be identified based on vortex dynamics in the wake of the large cylinder: (1) for L/D ≥ 15, three vortex shedding cells form in the wake of the large cylinder, one central cell bounded by two cells of lower frequency, (2) for 8 < L/D ≤ 14, a single vortex shedding cell forms in the wake of the large cylinder, (3) for 2 < L/D ≤ 6, vortex shedding from the large cylinder is highly three-dimensional. When spanwise vortices are shed, they deform substantially and attain a hairpin shape in the near wake, (4) for 0.2 ≤ L/D ≤ 1, the large cylinder induces vortex dislocations between small cylinder vortices. The results show that for Regimes I to III, on the average, the frequency of vortex shedding in the large cylinder wake decreases with L/D, which is accompanied by a decrease in coherence of the shed vortices. In Regime IV, small cylinder vortices connect across the large cylinder wake, but these connections are interrupted by vortex dislocations. With decreasing L/D, the frequency of dislocations decreases and the dominant frequency in the large cylinder wake increases toward the small cylinder shedding frequency.     

Influence of rounding corners on the wake of a finite-length cylinder: An experimental study

This study aims to investigate experimentally the influence of rounding corners (r) as well as aspect ratio (AR) on the flow structures of a surface-mounted finite cylinder. The cylinders with sharp (r* = r/D = 0) and rounded corners (r*=0.167, 0.25 and 0.5) and aspect ratio or height-to-width/diameter ratio (AR = H/D) between 2 and 7 are utilized. The experiments are based on the five-hole probe and hot-wire measurements as well as the oil flow visualization. Wake measurements are made in an open return wind tunnel at the Reynolds number, Re = 1.6 × 10⁴, where Re is defined based on the side width/diameter (D) of the cylinder cross-section and the freestream velocity. It is found that r* and AR have significant effects on the flow structure from the perspective of wake topology, strength of streamwise vortices, and vortex shedding frequency. For all r* considered, the wake is characterized by a quadrupole type (both the tip and base vortices are present) at AR = 7, while a dipole type occurs for AR = 2 and 4 (the base vortices are absent). The strength (circulation) of the streamwise vortex structures is affected by r*. For all AR examined in the present study, the strengths of tip and base vortex structures decrease with increasing r*. The oil flow visualization demonstrates that the features of the horseshoe vortex are sensitive to r* and AR. With increasing r*, the location of the separation line moves downstream and the distance between horseshoe vortex legs decreases. Velocity measurements reveal that the downwash flow enhances with increasing r*. It is also found that the Strouhal number increases progressively by 60% as r* increases from 0 to 0.5, regardless of AR.     

Resonance in flow past oscillating cylinder under subcritical conditions

Flow around an oscillating cylinder in a subcritical region are numerically studied with a lattice Boltzmann method(LBM). The effects of the Reynolds number,oscillation amplitude and frequency on the vortex wake modes and hydrodynamics forces on the cylinder surface are systematically investigated. Special attention is paid to the phenomenon of resonance induced by the cylinder oscillation. The results demonstrate that vortex shedding can be excited extensively under subcritical conditions, and the response region of vibration frequency broadens with increasing Reynolds number and oscillation amplitude. Two distinct types of vortex shedding regimes are observed. The first type of vortex shedding regime(VSR I) is excited at low frequencies close to the intrinsic frequency of flow, and the second type of vortex shedding regime(VSR II)occurs at high frequencies with the Reynolds number close to the critical value. In the VSR I, a pair of alternately rotating vortices are shed in the wake per oscillation cycle,and lock-in/synchronization occurs, while in the VSR II, two alternately rotating vortices are shed for several oscillation cycles, and the vortex shedding frequency is close to that of a stationary cylinder under the critical condition. The excitation mechanisms of the two types of vortex shedding modes are analyzed separately.     

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.     

Numerical simulation of two-degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary

Two-degree-of-freedom vortex-induced vibrations (VIV) of a circular cylinder close to a plane boundary are investigated numerically. The Reynolds-Averaged Navier-Stokes (RANS) equations are solved using the Arbitrary Lagrangian Eulerian (ALE) scheme with a k-ω turbulence model closure. The numerical model is validated against experimental data of VIV of a cylinder in uniform flow and VIV of a cylinder close to a plane boundary at low mass ratios. The numerical results of the vibration mode, vibration amplitude and frequency agree well with the experimental data. VIV of a circular cylinder close to a plane boundary is simulated with a mass ratio of 2.6 and gap ratios of e/D=0.002 and 0.3 (gap ratio is defined as the ratio of gap between the cylinder and the bed (e) to cylinder diameter (D)). Simulations are carried out for reduced velocities ranging from 1 to 15 and Reynolds numbers ranging from 1000 to 15 000. It is found that vortex-induced vibrations occur even if the initial gap ratio is as small as e/D=0.002, although reported research indicated that vortex shedding behind a fixed circular cylinder is suppressed at small gap ratios (e/D<0.3 or 0.2). It was also found that vibration amplitudes are dependant on the bouncing back coefficient when the cylinder hits the plane boundary. Three vortex shedding modes are identified according to the numerical results: (i) single-vortex mode where the vortices are only shed from the top of the cylinder; (ii) vortex-shedding-after-bounce-back mode; (iii) vortex-shedding-before-bounce-back mode. It was found that the vortex shedding mode depends on the reduced velocity.     

Vortex-induced oscillations at low Reynolds numbers: Hysteresis and vortex-shedding modes

Results are presented for the numerical simulation of vortex-induced vibrations (VIVs) of a cylinder at low Reynolds numbers (Re). A stabilized space–time finite-element formulation is utilized to solve the incompressible flow equations in primitive variables. The cylinder, of low nondimensional mass (m^*=10), is free to vibrate in, both, the transverse and in-line directions. To investigate the effect of Re and reduced natural frequency, F_n, two sets of computations are carried out. In the first set of computations the Reynolds number is fixed (=100) and the reduced velocity (U^*=1/F_n) is varied. Hysteresis, in the response of the cylinder, is observed at the low- as well as high-end of the range of reduced velocity for synchronization/lock-in. In the second set of computations, the effect of Reynolds number (50Re500) is investigated for a fixed reduced velocity (U^*=4.92). The effect of the Reynolds number is found to be very significant for VIVs. While the vortex-shedding mode at low Re is 2S (two single vortices shed per cycle), at Re300 and larger, the P+S mode of vortex shedding (a single vortex and one pair of counter-rotating vortices are released in each cycle of shedding) is observed. This is the first time that the P+S mode has been observed for a cylinder undergoing free vibrations. This change of vortex-shedding mode is hysteretic in nature and results in a very large increase in the amplitude of in-line oscillations. Since the flow ceases to remain two-dimensional beyond Re200, it remains to be seen whether the P+S mode of shedding can actually be observed in reality for free vibrations.     

An experimental study of the unsteady vortex structures in the wake of a root-fixed flapping wing

An experimental study was conducted to characterize the evolution of the unsteady vortex structures in the wake of a root-fixed flapping wing with the wing size, stroke amplitude, and flapping frequency within the range of insect characteristics for the development of novel insect-sized nano-air-vehicles (NAVs). The experiments were conducted in a low-speed wing tunnel with a miniaturized piezoelectric wing (i.e., chord length, C = 12.7 mm) flapping at a frequency of 60 Hz (i.e., f = 60 Hz). The non-dimensional parameters of the flapping wing are chord Reynolds number of Re = 1,200, reduced frequency of k = 3.5, and non-dimensional flapping amplitude at wingtip h = A/C = 1.35. The corresponding Strouhal number (Str) is 0.33, which is well within the optimal range of 0.2 < Str < 0.4 used by flying insects and birds and swimming fishes for locomotion. A digital particle image velocimetry (PIV) system was used to achieve phased-locked and time-averaged flow field measurements to quantify the transient behavior of the wake vortices in relation to the positions of the flapping wing during the upstroke and down stroke flapping cycles. The characteristics of the wake vortex structures in the chordwise cross planes at different wingspan locations were compared quantitatively to elucidate underlying physics for a better understanding of the unsteady aerodynamics of flapping flight and to explore/optimize design paradigms for the development of novel insect-sized, flapping-wing-based NAVs.     

On the vortex dynamics in the wake of a finite surface-mounted square cylinder

The shedding process in the near wake of a surface-mounted, square cross-section cylinder of height-to-width aspect ratio 4 at a Reynolds number of 12,000 based on free-stream velocity and the obstacle width was investigated. The boundary layer thickness was 0.18 obstacle heights based on 99% free-stream velocity. The study is performed using planar high frame-rate particle image velocimetry synchronized with pressure measurements and hot-wire anemometry. Spatial cross-correlation, instantaneous phase relationships, and phase-averaged velocity data are reported. Two dominant vortex-shedding regimes are observed. During intervals of high-amplitude pressure fluctuations on the obstacle side faces, alternate formation and shedding of vortices is observed (regime A) similar to the von Kármán process. Regime B is characterized by two co-existing vortices in the obstacle lee throughout the shedding cycle and is observed within low-amplitude pressure fluctuation intervals. Despite the coexisting vortices in the base region, opposite sign vorticity is still shed out-of-phase downstream of this vortex pair giving rise to a staggered arrangement of counter-rotating vortices downstream. While the probability of occurrence of Regime B increases toward the free end, the amplitude modulation remains coherent along the obstacle height. Conditionally phase-averaged reconstructions of the flow field are consistent with the spatial distribution of the phase relationships and their probability density function. Earlier observations are reconciled showing that the symmetric shedding of vortices is a rare occurrence.     

Cavity induced vibration of flexible hydrofoils

The objective of this work is to investigate the influence of cavity-induced vibrations on the dynamic response and stability of a NACA66 hydrofoil at 8° angle of attack at Re=750 000 via combined experimental measurements and numerical simulations. The rectangular, cantilevered hydrofoil is assumed to be rigid in the chordwise direction, while the spanwise bending and twisting deformations are represented using a two-degrees-of-freedom structural model. The multiphase flow is modeled with an incompressible, unsteady Reynolds Averaged Navier–Stokes solver with the k–ω Shear Stress Transport (SST) turbulence closure model, while the phase evolutions are modeled with a mass-transport equation based cavitation model. The numerical predictions are compared with experimental measurements across a range of cavitation numbers for a rigid and a flexible hydrofoil with the same undeformed geometries. The results showed that foil flexibility can lead to: (1) focusing – locking – of the frequency content of the vibrations to the nearest sub-harmonics of the foil׳s wetted natural frequencies, and (2) broadening of the frequency content of the vibrations in the unstable cavitation regime, where amplifications are observed in the sub-harmonics of the foil natural frequencies. Cavitation was also observed to cause frequency modulation, as the fluid density, and hence fluid induced (inertial, damping, and disturbing) forces fluctuated with unsteady cavitation.     

Effect of pre-strain and excess length on unsteady fluid–structure interactions of membrane airfoils

Aerodynamic characteristics of two-dimensional membrane airfoils were experimentally investigated in a wind tunnel. The effects of the membrane pre-strain and excess length on the unsteady aspects of the fluid–structure interaction were studied. The deformation of the membrane as a function of angle of attack and free-stream velocity was measured using a high-speed camera. These measurements were complemented by the measurements of unsteady velocity field with a high frame-rate Particle Image Velocimetry (PIV) system as well as smoke visualization. Membrane airfoils with excess length exhibit higher vibration modes, earlier roll-up of vortices, and smaller separated flow regions, whereas the membranes with pre-strain generally behave more similarly to a rigid airfoil. Measured frequencies of the membrane vibrations suggest a possible coupling with the wake instabilities at high incidences for all airfoils.     

Spanwise correlations in the wake of a circular cylinder and a trapezoid placed inside a circular pipe

The spanwise correlation of a circular cylinder and a trapezoidal bluff body placed inside a circular pipe in fully developed turbulent regime is studied using hotwire anemometer. The present configuration possesses complex fluid structure interaction owing to the following features: high blockage effect; low aspect ratio of the body; upstream turbulence and interaction of axisymmetric flow with a two dimensional bluff body. The spatial correlation of such configuration is seldom reported in the literature. Results are presented for Reynolds number of Re_D=1×10⁵. Three different blockage ratios (0.14, 0.19 and 0.28) are considered in the present study. Correlation coefficient is observed to improve with increase in blockage ratio. Compared to a circular cylinder, a trapezoidal bluff body possesses high correlation length. The near wall effects tend to increase the phase drift, which is reflected in low correlation coefficients close to the pipe wall. The results show that the simultaneous effect of curvature, low aspect ratio and upstream turbulence reduces the correlation coefficients significantly as compared to unconfined and confined (parallel channel) flows. The low frequency modulations with a circular cylinder are higher for lower blockage ratios. The three-dimensionality of vortex shedding for trapezoid with a blockage ratio of 0.28 was observed to be lower compared to circular cylinder and all other blockage ratios. Low frequency modulations were found to be responsible for weak vortex shedding from a circular cylinder compared to a trapezoidal bluff body. The vortex shedding is observed to be nearly two dimensional in case of a trapezoidal bluff body of blockage ratio 0.28.     

Aerodynamics and mechanisms of elementary morphing models for flapping wing in forward flight of bat

Large active wing deformation is a significant way to generate high aerodynamic forces required in bat's flapping flight. Besides the twisting, elementary morphing models of a bat wing are proposed, including wing-bending in the spanwise direction, wing-cambering in the chordwise direction, and wing area-changing. A plate of aspect ratio 3 is used to model a bat wing, and a three-dimensional unsteady panel method is used to predict the aerodynamic forces. It is found that the cambering model has great positive influence on the lift, followed by the area-changing model and then the bending model. Further study indicates that the vortex control is a main mechanism to produce high aerodynamic forces. The mechanisms of aerodynamic force enhancement are asymmetry of the cambered wing and amplification effects of wing area-changing and wing bending. Lift and thrust are generated mainly during downstroke, and they are almost negligible during upstroke by the integrated morphing model-wing.     

Experimental investigation of the effect of chordwise flexibility on the aerodynamics of flapping wings in hovering flight

Ornithopters or mechanical birds produce aerodynamic lift and thrust through the flapping motion of their wings. Here, we use an experimental apparatus to investigate the effects of a wing's twisting stiffness on the generated thrust force and the power required at different flapping frequencies. A flapping wing system and an experimental set-up were designed to measure the unsteady aerodynamic and inertial forces, power usage and angular speed of the flapping wing motion. A data acquisition system was set-up to record important data with the appropriate sampling frequency. The aerodynamic performance of the vehicle under hovering (i.e., no wind) conditions was investigated. The lift and thrust that were produced were measured for different flapping frequencies and for various wings with different chordwise flexibilities. The results show the manner in which the elastic deformation and inertial flapping forces affect the dynamical behavior of the wing. It is shown that the generalization of the actuator disk theory is, at most, only valid for rigid wings, and for flexible wings, the power P varies by a power of about 1.0  of the thrust T. This aerodynamic information can also be used as benchmark data for unsteady flow solvers.     

Self-sustained global oscillations in a jet in crossflow

A jet in crossflow with an inflow ratio of 3, based on the maximum velocity of the parabolic jet profile, is studied numerically. The jet is modeled as an inhomogeneous boundary condition at the crossflow wall. We find two fundamental frequencies, pertaining to self-sustained oscillations in the flow, using full nonlinear direct numerical simulation (DNS) as well as a modal decomposition into global linear eigenmodes and proper orthogonal decomposition (POD) modes; a high frequency which is characteristic for the shear-layer vortices and the upright vortices in the jet wake, and a low frequency which is dominant in the region downstream of the jet orifice. Both frequencies can be related to a region of reversed flow downstream of the jet orifice. This region is observed to oscillate predominantly in the wall-normal direction with the high frequency, and in the spanwise direction with the low frequency. Moreover, the steady-state solution of the governing Navier?CStokes equations clearly shows the horseshoe vortices and the corresponding wall vortices further downstream, and the emergence of a distinct counter-rotating vortex pair high in the free stream. It is thus found that neither the inclusion of the jet pipe nor unsteadiness is necessary to generate the characteristic counter-rotating vortex pair.     

The dynamic character of the hemisphere-cylinder wake

 The dynamic character of the hemisphere-cylinder wake was studied over the entire range of angles of attack, i.e. α=0° to 90°. The work was carried out in two wind tunnel facilities, using hot-wire anemometry. Velocity auto- and cross-spectra in the wake reveal that the leeward vortices exhibit periodic motions, with multiple dominant frequencies for 24°<α<42°, one single dominant frequency for 15°<α<22°, while no periodic activity is detected for α<15°. In the regime 15°<α<42°, a new periodic heaving motion of the vortices is documented. Vortex heaving transitions to the more classical vortex shedding periodicity in the neighborhood of α=45°. Above α=55°, vortex shedding occurred at a single Strouhal number of 0.15. The limiting case α=90° was investigated in detail for semi-infinite and finite hemisphere-cylinder models and comparisons were made to axisymmetric bodies with different nose shapes. Received: 2 March 1998 / Accepted: 22 October 1998     

Symmetric vortex shedding in the near wake of a circular cylinder due to streamwise perturbations

Symmetric perturbations imposed on cylinder wakes may result in a modification of the vortex shedding mode from its natural antisymmetric, or alternating, to a symmetric one where twin vortices are simultaneously shed from both sides of the cylinder. In this paper, the symmetric mode in the wake of a circular cylinder is induced by periodic perturbations imposed on the in-flow velocity. The wake field is examined by PIV and LDV for Reynolds numbers about 1200 and for a range of perturbation frequencies between three and four times the natural shedding frequency of the unperturbed wake. In this range, a strong competition between symmetric and antisymmetric vortex shedding occurs for the perturbation amplitudes employed. The results show that symmetric formation of twin vortices occurs close to the cylinder synchronized with the oscillatory component of the flow. The symmetric mode rapidly breaks down and gives rise to an antisymmetric arrangement of vortex structures further downstream. The downstream wake may or may not be phase-locked to the imposed oscillation. The number of cycles for which the symmetric vortices persist in the near wake is a probabilistic function of the perturbation frequency and amplitude. Finally, it is shown that symmetric shedding is associated with positive energy transfer from the fluid to the cylinder due to the fluctuating drag.