Streamwise evolution of an inclined cylinder wake

The streamwise evolution of an inclined circular cylinder wake was investigated by measuring all three velocity and vorticity components using an eight-hotwire vorticity probe in a wind tunnel at a Reynolds number Re_d of 7,200 based on free stream velocity (U _∞) and cylinder diameter (d). The measurements were conducted at four different inclination angles (α), namely 0°, 15°, 30°, and 45° and at three downstream locations, i.e., x/d = 10, 20, and 40 from the cylinder. At x/d = 10, the effects of α on the three coherent vorticity components are negligibly small for α ≤ 15°. When α increases further to 45°, the maximum of coherent spanwise vorticity reduces by about 50%, while that of the streamwise vorticity increases by about 70%. Similar results are found at x/d = 20, indicating the impaired spanwise vortices and the enhancement of the three-dimensionality of the wake with increasing α. The streamwise decay rate of the coherent spanwise vorticity is smaller for a larger α. This is because the streamwise spacing between the spanwise vortices is bigger for a larger α, resulting in a weak interaction between the vortices and hence slower decaying rate in the streamwise direction. For all tested α, the coherent contribution to [`(v<sup>2</sup>)] \overline{{v^{2}}} is remarkable at x/d = 10 and 20 and significantly larger than that to [`(u²)] \overline{{u^{2}}} and [`(w<sup>2</sup>)]. \overline{{w^{2}}}. This contribution to all three Reynolds normal stresses becomes negligibly small at x/d = 40. The coherent contribution to [`(u²)] \overline{{u^{2}}} and [`(v²)] \overline{{v^{2}}} decays slower as moving downstream for a larger α, consistent with the slow decay of the coherent spanwise vorticity for a larger α.     

Thermal characteristics of the wake shear layers from a slightly heated circular cylinder

In this paper, we investigate the thermal characteristics of wake shear layers generated by a slightly heated circular cylinder. Measurements of the fluctuating temperature were made in the region x/d = 0.6 to x/d = 3 (where x is the downstream distance from the cylinder axis and d is the cylinder diameter) using a single cold-wire probe. The Reynolds number Re was varied in the range 2,600–8,600. For Re = 5,500, simultaneous measurements were made with a rake of 16 cold wires, aligned in the direction of the mean shear, at x/d = 2 and 3. The results indicate that the passive temperature can be an effective marker of various instabilities of the wake shear layers, including the Kelvin–Helmholtz (KH) instability. The temperature data have confirmed the approximate Re ^m dependence of the KH instability frequency (f _KH) with different values of m over different ranges of Re, as reported previously in the literature. However, it is found that this power-law dependence is not exact, and a third-order polynomial dependence appears to fit the data well over the full range of Re. Importantly, it is found that the wake shear-layer instabilities can be grouped into three categories: (1) one with frequencies much smaller than the Bénard–Kármán-vortex shedding frequency, (2) one associated with the vortex shedding and (3) one related to the KH instability. The low-frequency shear-layer instabilities from both sides of the cylinder are in-phase, in contrast to the anti-phase high-frequency KH instabilities. Finally, the observed streamwise decrease in the mean KH frequency provides strong support for the occurrence of vortex pairing in wake shear layers from a circular cylinder, thus implying that both the wake shear layer and a mixing layer develop in similar fashion.     

Momentum and heat transport in a finite-length cylinder wake

This paper reports an experimental study of turbulent momentum and heat transport in the wake of a wall-mounted finite-length square cylinder, with its length-to-width ratio L/d = 3–7. The cylinder was slightly heated so that heat produced could be considered as a passive scalar. A moveable three-wire probe (a combination of an X-wire and a cold wire) was used to measure velocity and temperature fluctuations at a Reynolds number of 7,300 based on d and the free-stream velocity. Measurements were performed at 10 and 20d downstream of the cylinder at various spanwise locations. Results indicate that L/d has a pronounced effect on Reynolds stresses, temperature variance and heat fluxes. The downwash flow from the free end of the cylinder acts to suppress spanwise vortices and, along with the upwash flow from the cylinder base, makes the finite-length cylinder wake highly three-dimensional. Reynolds stresses, especially the lateral normal stress, are significantly reduced as a result of suppressed spanwise vortices at a small L/d. The downwash flow acts to separate the two rows of spanwise vortices further apart from the wake centerline, resulting in a twin-peak distribution in temperature variance. While the downwash flow entrains high-speed fluid into the wake, responsible for a small deficit in the time-averaged streamwise velocity near the free end, it does not alter appreciably the distribution of time-averaged temperature. It has been found that the downwash flow gives rise to a counter-gradient transport of momentum about the central region of the wake near the free end of the cylinder, though such a counter-gradient transport does not occur for heat transport.     

Secondary wake instabilities of a blunt trailing edge profiled body as a basis for flow control

Flow in the wake of a blunt trailing edge profiled body, comprised of an elliptical leading edge and a rectangular trailing edge, has been investigated experimentally, to identify and characterize the secondary instabilities accompanying the von Kármán vortices. The experiments, which involve laser-induced fluorescence for visualization and particle image velocimetry for quantitative measurement of the wake instabilities, cover Reynolds numbers ranging from 250 to 2,150 based on thickness of the body, to include the wake transition regime. The dominant secondary instability appears as spanwise undulations in von Kármán vortices, which evolve into pairs of counter-rotating vortices, with features resembling the instability mechanism predicted by Ryan et al. (J Fluid Mech 538:1–29, 2005). Feasibility of a flow control approach based on interaction with the secondary instability using a series of discrete trailing edge injectors has also been investigated. The control approach mitigates the adverse effects of vortex shedding in certain conditions, where it is able to amplify the secondary instability effectively.     

Numerical simulation of flapping‐wing insect hovering flight at unsteady flow

A computational fluid dynamics (CFD) analysis was conducted to study the unsteady aerodynamics of a virtual flying bumblebee during hovering flight. The integrated geometry of bumblebee was established to define the shape of a three‐dimensional virtual bumblebee model with beating its wings, accurately mimicking the three‐dimensional movements of wings during hovering flight. The kinematics data of wings documented from the measurement to the bumblebee in normal hovering flight aided by the high‐speed video. The Navier–Stokes equations are solved numerically. The solution provides the flow and pressure fields, from which the aerodynamic forces and vorticity wake structure are obtained. Insights into the unsteady aerodynamic force generation process are gained from the force and flow‐structure information. The CFD analysis has established an overall understanding of the viscous and unsteady flow around the virtual flying bumblebee and of the time course of instantaneous force production, which reveals that hovering flight is dominated by the unsteady aerodynamics of both the instantaneous dynamics and also the past history of the wing. A coherent leading‐edge vortex with axial flow and the attached wingtip vortex and trailing edge vortex were detected. The leading edge vortex, wing tip vortex and trailing edge vortex, which caused by the pressure difference between the upper and the lower surface of wings. The axial flow, which include the spanwise flow and chordwise flow, is derived from the spanwise pressure gradient and chordwise pressure gradient, will stabilize the vortex and gives it a characteristic spiral conical shape. Copyright © 2006 John Wiley & Sons, Ltd.     

Stereoscopic and tomographic PIV of a pitching plate

This paper applies particle image velocimetry (PIV) to a simplified, canonical, pitch-hold-return problem of a pitching plate in order to gain some understanding of how three dimensionality develops in such flows. Data from a progression of PIV studies, from stereoscopic PIV yielding three-component, two-dimensional (3C-2D) data to tomographic PIV yielding three-component, three-dimensional (3C-3D) data are presented thus providing progressively more detailed information. A comparison of results is made between the two techniques. The PIV study is performed in a water tunnel facility with cross-sectional area 500 × 500 mm, and involves a full-span (nominally two-dimensional) plate, suspended between a wall end boundary condition and a free surface, pitching at a dimensionless pitch rate of K _c  = 0.93 in flow at Re = 7,500. Results demonstrate the existence of spanwise flows in both the leading edge and trailing edge vortices, but with strong directionality in the leading edge vortex towards the wall end boundary condition. Observations of instantaneous flow patterns suggest also the existence of three-dimensional coherent vortex filament structures in the outer regions of the leading edge vortex.     

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.     

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re _c  = 10⁴), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re _c  = 10⁴), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re _c  = 4 × 10⁴, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For Re _c = 4.85 × 10⁴, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.     

Effects of the corner radius on the near wake of a square prism

The near wake of square cylinders with different corner radii was experimentally studied based on particle imaging velocimetry (PIV), laser doppler anemometry (LDA) and hotwire measurements. Four bluff bodies, i.e., r/d=0 (square cylinder), 0.157, 0.236, 0.5 (circular cylinder), where r is corner radius and d is the characteristic dimension of the bluff bodies, were examined. A conditional sampling technique was developed to obtain the phase-averaged PIV data in order to characterize quantitatively the effect of corner radii on the near-wake flow structure. The results show that, as r/d increases from 0 to 0.5, the maximum strength of shed vortices attenuates, the circulation associated with the vortices decreases progressively by 50%, the Strouhal number, St, increases by about 60%, the convection velocity of the vortices increases along with the widening of the wake width by about 25%, the vortex formation length and the wake closure length almost double in size. Meanwhile, both the vortex wavelength, λ _x , and the lateral spacing, λ _y , decrease as r/d increases, but the ratio of λ _y to λ _x is approximately 0.29, irrespective of r/d, which is close to the theoretical value of 0.281 for a stable Karman vortex street. The decrease in wavelength is probably responsible for the change in the flow structure from the approximately circular-shaped vortex at r/d=0 to the laterally stretched vortex at r/d=0.5. The leading edge corner radius is more important than the trailing one in influencing the near wake structure since it determines to a great extent the behavior of the streamlines, the separation angle and the base pressure. It is further found that the ratio of the mean drag coefficient to the total shed circulation, C _d/Γ₀, approaches a constant, about 0.25 for different bluff bodies in the subcritical flow regime. The streamwise evolution of vortices and the streamwise fluctuating velocity along the centerline for rounded cylinders are also discussed.     

Approach to local axisymmetry in a turbulent cylinder wake

The objective of this experimental study is to characterise the small-scale turbulence in the intermediate wake of a circular cylinder using measured mean-squared velocity gradients. Seven of the twelve terms which feature in ε, the mean dissipation rate of the turbulent kinetic energy, were measured throughout the intermediate wake at a Reynolds number of Re _d  ≈ 3000 based on the cylinder diameter (d). Earlier measurements of the nine major terms of ε by Browne et al. (J Fluid Mech 179: 307–326 1987) at a downstream distance (x) of x = 420d and Re _d  ≈ 1170 are also used. Whilst departures from local isotropy are significant at all locations in the wake, local axisymmetry of the small-scale turbulence with respect to the mean flow direction is first satisfied approximately at x = 40d. The approach towards local axisymmetry is discussed in some detail in the context of the relative values of the mean-squared velocity gradients. The data also indicate that axisymmetry is approximately satisfied by the large scales at x/d ≥ 40, suggesting that the characteristics of the small scales reflect to a major extent those of the large scales. Nevertheless, the far-wake data of Browne et al. (1987) show a discernible departure from axisymmetry for both small and large scales.     

Base drag reduction by control of the three-dimensional unsteady vortical structures

The present paper deals with the wake of a 2D body equipped with a drag reduction device. The device is a 3D trailing edge consisting of alternate segments of blunt base and spanwise cavity. The aerodynamic mechanisms acting on the near wake are studied in a water tunnel from schlieren observations by thermally marking large scale structures. The results show that the efficiency of the device is directly related to the presence of longitudinal vortices. An optimization of the shapes in subsonic compressible flow had led to a decrease of more than 40% of the total drag of the profile.     

Aerodynamic forces and flow fields of a two-dimensional hovering wing

This paper reports the results of an experimental investigation on a two-dimensional (2-D) wing undergoing symmetric simple harmonic flapping motion. The purpose of this investigation is to study how flapping frequency (or Reynolds number) and angular amplitude affect aerodynamic force generation and the associated flow field during flapping for Reynolds number (Re) ranging from 663 to 2652, and angular amplitudes (α _A) of 30°, 45° and 60°. Our results support the findings of earlier studies that fluid inertia and leading edge vortices play dominant roles in the generation of aerodynamic forces. More importantly, time-resolved force coefficients during flapping are found to be more sensitive to changes in α _A than in Re. In fact, a subtle change in α _A may lead to considerable changes in the lift and drag coefficients, and there appears to be an optimal mean lift coefficient around α _A = 45°, at least for the range of flow parameters considered here. This optimal condition coincides with the development a reverse Karman Vortex street in the wake, which has a higher jet stream than a vortex dipole at α _A = 30° and a neutral wake structure at α _A = 60°. Although Re has less effect on temporal force coefficients and the associated wake structures, increasing Re tends to equalize mean lift coefficients (and also mean drag coefficients) during downstroke and upstroke, thus suggesting an increasing symmetry in the mean force generation between these strokes. Although the current study deals with a 2-D hovering motion only, the unique force characteristics observed here, particularly their strong dependence on α _A, may also occur in a three-dimensional hovering motion, and flying insects may well have taken advantage of these characteristics to help them to stay aloft and maneuver. An erratum to this article can be found at     

Flow structure of wake behind a rotationally oscillating circular cylinder

Flow around a circular cylinder oscillating rotationally with a relatively high forcing frequency has been investigated experimentally. The dominant parameters affecting this experiment are the Reynolds number (Re), oscillation amplitude (θ_A), and frequency ratio F_R=f_f/f_n, where f_f is the forcing frequency and f_n is the natural frequency of vortex shedding. Experiments were carried out under conditions of Re=4.14×10³, 0°θ_A60° and 0.0F_R2.0. Rotational oscillation of the cylinder significantly modified the flow structure in the near-wake. Depending on the frequency ratio F_R, the cylinder wake showed five different flow regimes, each with a distinct wake structure. The vortex formation length and the vortex shedding frequency were greatly changed before and after the lock-on regime where vortices shed at the same frequency as the forcing frequency. The lock-on phenomenon always occurred at F_R=1.0 and the frequency range of the lock-on regime expanded with increasing oscillation amplitude θ_A. In addition, the drag coefficient was reduced when the frequency ratio F_R was less than 1.0 (F_R<1.0) while fixing the oscillation amplitude at θ_A=30°. When the oscillation amplitude θ_A was used as a control parameter at a fixed frequency ratio F_R=1.0 (lock-on regime), the drag reduction effect was observed at all oscillation amplitudes except for the case of θ_A=30°. This type of active flow control method can be used effectively in aerodynamic applications while optimizing the forcing parameters.     

A numerical investigation of the effects of the spanwise length on the 3-D wake of a circular cylinder

The numerical prediction of vortex-induced vibrations has been the focus of numerous investigations to date using tools such as computational fluid dynamics. In particular, the flow around a circular cylinder has raised much attention as it is present in critical engineering problems such as marine cables or risers. Limitations due to the computational cost imposed by the solution of a large number of equations have resulted in the study of mostly 2-D flows with only a few exceptions. The discrepancies found between experimental data and 2-D numerical simulations suggested that 3-D instabilities occurred in the wake of the cylinder that affect substantially the characteristics of the flow. The few 3-D numerical solutions available in the literature confirmed such a hypothesis. In the present investigation the effect of the spanwise extension of the solution domain on the 3-D wake of a circular cylinder is investigated for various Reynolds numbers between 40 and 1000. By assessing the minimum spanwise extension required to predict accurately the flow around a circular cylinder, the infinitely long cylinder is reduced to a finite length cylinder, thus making numerical solution an effective way of investigating flows around circular cylinders. Results are presented for three different spanwise extensions, namely πD/2, πD and 2πD. The analysis of the force coefficients obtained for the various Reynolds numbers together with a visualization of the three-dimensionalities in the wake of the cylinder allowed for a comparison between the effects of the three spanwise extensions. Furthermore, by showing the different modes of vortex shedding present in the wake and by analysing the streamwise components of the vorticity, it was possible to estimate the spanwise wavelengths at the various Reynolds numbers and to demonstrate that a finite spanwise extension is sufficient to accurately predict the flow past an infinitely long circular cylinder.     

Dependence of the wake on inclination of a stationary cylinder

Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot wire vorticity probe over a streamwise range of x/d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°). The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean velocity which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values of the streamwise (u) and spanwise (w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity (v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number (St _N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ _u and ρ _v of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ _u and ρ _v decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ _w of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake.     

Dependence of flow classification on the Reynolds number for a two-cylinder wake

This work aims to investigate the dependence of flow classification on the Reynolds number (Re) for the wake of two staggered cylinders. The Re examined ranges from 1.5×10³ to 2.0×10⁴. The pitch ratio, P^⁎=P/d examined is 1.2–6.0 (d is the cylinder diameter), and angle (α) is 0–90°, where P is the center-to-center spacing between two cylinders and α is the angle between the incident flow and the line through the cylinder centers. Two single hotwires were used to measure simultaneously the fluctuating streamwise velocities (u) in the vortex streets generated by the two cylinders. The power spectral density functions and the Strouhal numbers were then obtained from the u signals, based on which the flow structure pattern or mode could be determined. Over two hundred configurations of two staggered cylinders have been examined for each Re. It is found that Re has an appreciable effect on the dependence of the flow mode on P^⁎ and α. The observation is connected to the Re effect on the generic features of a two-cylinder wake such as flow separation, boundary layer thickness, gap flow deflection and vortex formation length.     

Two-dimensionality of a cantilevered-cylinder wake in the presence of an oscillating upstream cylinder

The effect of a longitudinally oscillating cylinder on the two-dimensionality of flow around a downstream cylinder is studied based on a two-point correlation measured using two hot-wires. The oscillation amplitude is A/d=0.472 and the oscillation frequency f_e/f_s=0.0372 and 0.186, where d is the cylinder diameter and f_s the frequency of natural vortex shedding from an isolated stationary cylinder. Three centre-to-centre spacing (L) ratios of the two cylinders were examined, i.e., L/d=1.8, 2.5 and 4.8, representing three typical flow regimes. The experiment was conducted at a Reynolds number (Re) of 5920, based on d and the free-stream velocity. It is found that the spanwise correlation of the flow depends on not only the oscillation but also the flow regimes. At L/d=1.8, the correlation is strongest among the three regimes, but worst in the co-shedding regime (L/d=4.8). The upstream cylinder oscillation improves the spanwise correlation of the flow in the gap of the cylinders, irrespective of regimes, especially for L/d=1.8 and 2.5, but impairs that behind the cylinders for L/d=1.8 and 2.5 due to a change in the flow regime. A theoretical analysis based on the boundary vorticity theory indicates that the oscillation increases the vorticity flux, in particular, in the spanwise direction between the cylinders, resulting in a significantly improved spanwise correlation, though this increase is negligibly small behind the downstream cylinder.     

PIV–LES analysis of channel flow rotating about the streamwise axis

The flow field of a channel rotating about the streamwise axis is analyzed experimentally and numerically. The current investigations were carried out at a bulk velocity based Reynolds number of Re_m = 2850 and a friction velocity based Reynolds number of Re_τ = 180, respectively. Particle-image velocimetry (PIV) measurements are compared with large-eddy simulation data to show earlier direct numerical simulation findings to generate too large a reverse flow region in the center region of the spanwise flow. The development of the mean spanwise velocity distribution and the influence of the rotation on the turbulent properties, i.e., the Reynolds stresses and the two-point correlations of the flow, are confirmed in both investigations. The rotation primarily influences those components of the Reynolds shear stresses, which contain the spanwise velocity component. The size of the correlation areas and thus the length scales of the flow generally grow in all three coordinate directions leading to longer structures. Furthermore, experimental results of the same channel flow at a significantly lower bulk Reynolds number of Re_{m, l} = 665, i.e., a laminar flow in a non-rotating channel, are introduced. The experiments show the low Reynolds number flow to become turbulent under rotation and to develop the same characteristics as the high Reynolds number flow.     

Investigation of flow field of clap and fling motion using immersed boundary coupled lattice Boltzmann method

This paper deals with the investigation of flow field due to clap and fling mechanism using immersed boundary coupled with lattice Boltzmann method. The lattice Boltzmann method (LBM), an alternative to Navier–Stokes solver, is used because of its simplicity and computational efficiency in solving complex moving boundary problems. Benchmark problems are simulated to validate the code, which is then used for simulating flow over two elliptic wing of aspect ratio 5 performing clap and fling flapping motion for different flow parameters such as Reynolds number (Re=75, 100, 150), advance ratio (J=10E−3.10E−2,0.2) and frequency (f=0.05 Hz, 0.25 Hz). Numerical simulation is able to capture typical low Reynolds number unsteady phenomena such as, ׳wake vortex wing interaction׳, ׳Kramer effect׳ and ׳delayed stall׳. The results are both qualitatively and quantitatively consistent with experimental observation. The parametric study involving different combinations of Re, f and J depict distinctly different aerodynamic performances providing physical insights into the flow physics. It is observed that a combination of low f, low J and high Re flow results in better aerodynamic performance. Pronounced lift enhancement via leading edge vortices are obtained in unsteady regime (J<1) compared to quasi-steady regime (J>1). The role of leading edge vortices in enhancing lift are investigated by studying the size and strength of these vortices for different flow conditions. For a given Re, the magnitude of maximum lift coefficient decreases with increasing f irrespective of the value of J; while the same is enhanced with the increasing Re.     

Self-sustained aeroelastic oscillations of a NACA0012 airfoil at low-to-moderate Reynolds numbers

A wind tunnel experimental investigation of self-sustained oscillations of an aeroelastic NACA0012 airfoil occurring in the transitional Re regime is presented. To the authors’ knowledge this is the first time that aeroelastic limit cycle oscillations (LCOs) associated with low Re effects have been systematically studied and reported in the public literature. While the aeroelastic apparatus is capable of two-degree-of-freedom pitch-plunge motion, the present work concerns only the motion of the airfoil when it is constrained to rotate in pure pitch. The structural stiffness is varied as well as the position of the elastic axis; other parameters such as surface roughness, turbulence intensity and initial conditions are also briefly discussed. In conjunction with the pitch measurements, the flow is also recorded using hot-wire anemometry located in the wake at a distance of one chord aft of the trailing edge. It is observed that for a limited range of chord-based Reynolds numbers, 4.5×10⁴Re_c1.3×10⁵, steady state self-sustained oscillations are observed. Below and above that range, these oscillations do not appear. They are characterized by a well-behaved harmonic motion, whose frequency can be related to the aeroelastic natural frequency, low amplitude (θ_max<5.5°) and some sensitivity to flow perturbations and initial conditions. Furthermore, hot-wire measurements for the wing held fixed show that no periodicity in the undisturbed free-stream nor in the wake account for the oscillations. Overall, these observations suggest that laminar separation plays a role in the oscillations, either in the form of trailing edge separation or due to the presence of a laminar separation bubble.