Showing papers on "Starting vortex published in 2009"

On vortex shedding from an airfoil in low-Reynolds-number flows

Abstract: Development of coherent structures in the separated shear layer and wake of an airfoil in low-Reynolds-number flows was studied experimentally for a range of airfoil chord Reynolds numbers, 55 × 10 3 ≤ Re c ≤ 210 × 10 3 , and three angles of attack, α = 0°, 5° and 10°. To illustrate the effect of separated shear layer development on the characteristics of coherent structures, experiments were conducted for two flow regimes common to airfoil operation at low Reynolds numbers: (i) boundary layer separation without reattachment and (ii) separation bubble formation. The results demonstrate that roll-up vortices form in the separated shear layer due to the amplification of natural disturbances, and these structures play a key role in flow transition to turbulence. The final stage of transition in the separated shear layer, associated with the growth of a sub-harmonic component of fundamental disturbances, is linked to the merging of the roll-up vortices. Turbulent wake vortex shedding is shown to occur for both flow regimes investigated. Each of the two flow regimes produces distinctly different characteristics of the roll-up and wake vortices. The study focuses on frequency scaling of the investigated coherent structures and the effect of flow regime on the frequency scaling. Analysis of the results and available data from previous experiments shows that the fundamental frequency of the shear layer vortices exhibits a power law dependency on the Reynolds number for both flow regimes. In contrast, the wake vortex shedding frequency is shown to vary linearly with the Reynolds number. An alternative frequency scaling is proposed, which results in a good collapse of experimental data across the investigated range of Reynolds numbers.

MTV measurements of the vortical field in the wake of an airfoil oscillating at high reduced frequency

Abstract: We present an experimental investigation of the flow structure and vorticity field in the wake of a NACA-0012 airfoil pitching sinusoidally at small amplitude and high reduced frequencies. Molecular tagging velocimetry is used to quantify the characteristics of the vortex array (circulation, peak vorticity, core size, spatial arrangement) and its downstream evolution over the first chord length as a function of reduced frequency. The measured mean and fluctuating velocity fields are used to estimate the mean force on the airfoil and explore the connection between flow structure and thrust generation.Results show that strong concentrated vortices form very rapidly within the first wavelength of oscillation and exhibit interesting dynamics that depend on oscillation frequency. With increasing reduced frequency the transverse alignment of the vortex array changes from an orientation corresponding to velocity deficit (wake profile) to one with velocity excess (reverse Karman street with jet profile). It is found, however, that the switch in the vortex array orientation does not coincide with the condition for crossover from drag to thrust. The mean force is estimated from a more complete control volume analysis, which takes into account the streamwise velocity fluctuations and the pressure term. Results clearly show that neglecting these terms can lead to a large overestimation of the mean force in strongly fluctuating velocity fields that are characteristic of airfoils executing highly unsteady motions. Our measurements show a decrease in the peak vorticity, as the vortices convect downstream, by an amount that is more than can be attributed to viscous diffusion. It is found that the presence of small levels of axial velocity gradients within the vortex cores, levels that can be difficult to measure experimentally, can lead to a measurable decrease in the peak vorticity even at the centre of the flow facility in a flow that is expected to be primarily two-dimensional.

Three-dimensional vorticity patterns of cylinder wakes

Abstract: The vortex organization of cylinder wakes is experimentally studied by time-resolved tomographic Particle Image Velocimetry at Reynolds numbers ranging from 180 to 5,540. Time resolved measurements are performed at Re = 180, 360 and 540, whereas the transitional (Re = 1,080) and turbulent regimes (Re = 5,540) are investigated by snapshots separated in phase by more than π/4. The vortex structure evolution is visualized by the 3D vorticity field, revealing a regular shedding at the lowest Reynolds, whereas at Re > 500 the Benard-Karman vortex street exhibits counter-rotating stream-wise vortex pairs (characteristic of Mode B) dominating the 3D motion. The regime at Re = 360 produces a transitional pattern where the counter-rotating vortex pairs (Mode B), coexist with profoundly distorted shedding of oblique elements forming a chain of rhombus-like vortex cells. In the turbulent flow regime (Re = 5,540) a large increase in the range of flow scales is directly observed with the appearance of Kelvin-Helmholtz type vortices in the separated shear layer consistently with what is abundantly reported in literature. The statistical description of the secondary structures is inferred from a 3D autocorrelation analysis yielding two span-wise wavelengths for the counter-rotating pairs, an inner length given by (twice) the distance between counter-rotating elements and an outer one given by the distance between pairs. The uncertainty analysis of the present tomographic PIV experiments reveals that this approach is suited for the investigation of vortex wakes with a typical error of 2 and 10% on the velocity and vorticity vectors, respectively.

High-Fidelity Simulation of Transitional Flows Past a Plunging Airfoil

Abstract: This investigation addresses the simulation of the unsteady separated flows encountered by a plunging airfoil under low-Reynolds-number conditions (Rec 6 ◊ 10 4 ). The flow fields are computed employing a previously developed and extensively validated high-fidelity implicit large-eddy simulation (ILES) approach. In order to permit comparison with available experimental measurements, calculations are performed first for an SD7003 airfoil section at an angle of attack o = 4 plunging with reduced frequency k = 3.93 and nondimensional amplitude ho = 0.05. Under these conditions, it is demonstrated that for Rec = 10 4 , transitional effects are not significant and that the dynamic-stall vortices remain fairly coherent as they propagate along the airfoil. For Rec = 4 ◊ 10 4 , 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. A detailed description of this transition process near the leading edge is provided. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. As a second example, the suppression of static stall at high angle of attack ( o = 14 ) is investigated using high-frequency small-amplitude vibrations (k = 10,ho = 0.005). At Rec = 6 ◊ 10 4 , separation is completely eliminated in a time-averaged sense, and the mean drag is reduced by approximately 40%. The instantaneous flow is characterized by the periodic generation of dynamic-stall vortices near the leading edge and by their subsequent transition as they convect close to the airfoil. For Rec = 10 4 , significant reduction of the timeaveraged separation region is still possible with transitional effects present in the aft-portion of the airfoil. For larger forcing amplitude (ho = 0.04,Rec = 10 4 ), a very intriguing regime emerges. The dynamic stall vortex moves around and in front of the leading edge and experiences a dramatic breakdown as it impinges against the airfoil. As a result, the phased-averaged flow displays no coherent vortices propagating along the airfoil upper surface. This new flow structure is also characterized in the mean by the existence of a strong jet in the near wake which manifests in a high value of net thrust. The present study demonstrates the importance of transitional effects for low-Reynolds-number maneuvering airfoils, as well as the suitability of the ILES approch for exploring such flow regime.

The influence of airfoil kinematics on the formation of leading-edge vortices in bio-inspired flight

Abstract: The formation process of leading-edge vortices has been investigated experimentally using Particle Image Velocimetry. Various airfoil kinematics have been tested, including asymmetric and peak-shifted plunging motions, and are evaluated for Re = 30,000 and a reduced frequency range of 0.2 ≤ k ≤ 0.33. By measuring the growth in the leading-edge vortex during the dynamic-stall process, the vortex pinch-off process is examined based on the concept of an optimal vortex formation time. The various kinematics are then evaluated with respect to their associated vortex strength, timing and convection into the wake.

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

Abstract: 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 timeaveraged 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 \((Re_c = 10^4)\), 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 motioninduced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stalllike vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number \((Re_c = 10^4)\), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For \(Re_c = 4 \times 10^4\), 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 \(Re_c = 4.85 \times 10^4\), it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.

The numerical comparison of flow patterns and propulsive performances for the hydromedusae Sarsia tubulosa and Aequorea victoria.

Abstract: SUMMARY The thrust-generating mechanism of a prolate hydromedusa Sarsia tubulosa and an oblate hydromedusa Aequorea victoria was investigated by solving the incompressible Navier–Stokes equations in the swirl-free cylindrical coordinates. The calculations clearly show the vortex dynamics related to the thrust-generating mechanism, which is very important for understanding the underlying propulsion mechanism. The calculations for the prolate jetting hydromedusa S. tubulosa indicate the formation of a single starting vortex ring for each pulse cycle with a relatively high vortex formation number. However, the calculations for the oblate jet-paddling hydromedusa A. victoria indicate shedding of the opposite-signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction as the vortices move away from the hydromedusa in the wake. In addition to this jet propulsion mechanism, the hydromedusa9s bell margin acts like a paddle and the highly flexible bell margin deforms in such a way that the low pressure leeward side of the bell margin has a projected area in the direction of motion. This thrust is particularly important during refilling of the subumbrella cavity where the stopping vortex causes significant pressure drag. The swimming performances based on our numerical simulations, such as swimming velocity, thrust, power requirement and efficiency, were computed and support the idea that jet propulsion is very effective for rapid body movement but is energetically costly and less efficient compared with the jet-paddling propulsion mechanism.

Numerical Study of an Oscillating Airfoil in Transonic Buffeting Flows

Abstract: Numerical simulations are conducted to compute the aerodynamic flowfield response that is observed for a NACA0012 airfoil that undergoes prescribed harmonic oscillation at transonic Mach numbers. Large shock oscillations are observed for certain combinations of Mach number and steady mean angle of attack. These are termed as buffet in this paper. Prescribing an airfoil oscillation about the buffeting flowfield reveals a nonlinear interaction between the flowfields induced by the buffet and airfoil motion, respectively. At low airfoil-oscillation amplitudes, the time histories of the aerodynamic coefficients exhibit two frequencies, that of the buffet and that of the oscillating airfoil. As the airfoil amplitude increases, the flowfield response at the buffet frequency decreases. Beyond a certain level of airfoil amplitude, lock-in occurs: the flowfield response at the buffet frequency vanishes, and the flow system response predominantly assumes the frequency of the airfoil motion. The airfoil amplitude that will cause lock-in is dependent on the ratio between the frequency of the airfoil oscillation and the buffet frequency. The closer these frequencies are, the smaller the airfoil-oscillation amplitude that will cause lock-in. There is a broad analogy between this flow phenomenon and the flowfield of the von Karman vortex street found behind a cylinder with the cylinder undergoing a prescribed oscillation. This paper reviews that phenomenon, suggests an aerodynamic gain-phase model for the lock-in region, and suggests a possible relation between this flow mechanism and limit-cycle oscillation.

Effects of Vortex Generators on an Airfoil at Low Reynolds Numbers

Abstract: A low-speed wind-tunnel investigation is presented detailing the effects of vortex generators on an airfoil at low Reynolds numbers (80,000 and 160,000) Six different static vortex generator layouts were tested In addition, an oscillatory (or active) vortex generator was designed and tested Force balance measurements were recorded and interpreted with the aid of surface flow visualization The data suggest that the static vortex generators function similarly to those at higher Reynolds numbers; increasing the maximum lift coefficient and increasing the stall angle Different static vortex generator configurations appear preferable at the two tested Reynolds number ranges The oscillating vortex generator did not appear effective in its present configuration

Helical structure of longitudinal vortices embedded in turbulent wall-bounded flow

Abstract: Embedded vortices in turbulent wall-bounded flow over a flat plate, generated by a passive rectangular vane-type vortex generator with variable angle β to the incoming flow in a low-Reynolds-number flow (Re=2600 based on the inlet grid mesh size L =0.039 m and free stream velocity U ∞ = 1.0 m s -1 ), have been studied with respect to helical symmetry. The studies were carried out in a low-speed closed-circuit wind tunnel utilizing stereoscopic particle image velocimetry (SPIV). The vortices have been shown to possess helical symmetry, allowing the flow to be described in a simple fashion. Iso-contour maps of axial vorticity revealed a dominant primary vortex and a weaker secondary one for 20° ≤ β ≤ 40°. For angles outside this range, the helical symmetry was impaired due to the emergence of additional flow effects. A model describing the flow has been utilized, showing strong concurrence with the measurements, even though the model is decoupled from external flow processes that could perturb the helical symmetry. The pitch, the vortex core size, the circulation and the advection velocity of the vortex all vary linearly with the device angle β. This is important for flow control, since one thereby can determine the axial velocity induced by the helical vortex as well as the swirl redistributing the axial velocity component for a given device angle β. This also simplifies theoretical studies, e.g. to understand and predict the stability of the vortex and to model the flow numerically.

Long lasting modifications to vortex shedding using a short plasma excitation.

Abstract: A unique phenomenon in flow control is described, where the lift and drag on a circular cylinder could be modified for over eight vortex shedding cycles by a short pulse of dielectric-barrier-discharge plasma. This is equivalent to flow control for over 150 times the pulse duration, which seems to be due to a secondary vortex initiated by plasma that interacts with the von Karman vortex formation and temporarily amplifies or suppresses the vortex street. Depending on the pulse timing, the drag and lift fluctuations could be increased by 22% and 50% or reduced by 8% and 40%, respectively, with a power saving ratio over 1000.

Formation, survival, and destruction of vortices in accretion disks

Abstract: Two-dimensional hydrodynamical disks are nonlinearly unstable to the formation of vortices. Once formed, these vortices essentially survive forever. What happens in three dimensions? We show with incompressible shearing box simulations that in three dimensions, a vortex in a short box forms and survives just as in two dimensions. But a vortex in a tall box is unstable and is destroyed. In our simulation, the unstable vortex decays into a transient turbulent-like state that transports angular momentum outward at a nearly constant rate for hundreds of orbital times. The three-dimensional instability that destroys vortices is a generalization of the two-dimensional instability that forms them. We derive the conditions for these nonlinear instabilities to act by calculating the coupling between linear modes, and thereby derive the criterion for a vortex to survive in three dimensions as it does in two dimensions: the azimuthal extent of the vortex must be larger than the scale height of the accretion disk. When this criterion is violated, the vortex is unstable and decays. Because vortices are longer in azimuthal than in radial extent by a factor that is inversely proportional to their excess vorticity, a vortex with given radial extent will only survive in a three-dimensional disk if it is sufficiently weak. This counterintuitive result explains why previous three-dimensional simulations always yielded decaying vortices: their vortices were too strong. Weak vortices behave two-dimensionally even if their width is much less than their height because they are stabilized by rotation, and behave as Taylor-Proudman columns. We conclude that in protoplanetary disks, weak vortices can trap dust and serve as the nurseries of planet formation. Decaying strong vortices might be responsible for the outward transport of angular momentum that is required to make accretion disks accrete.

High-Amplitude Pitch of a Flat Plate: An Abstraction of Perching and Flapping

Abstract: We compare water tunnel experiment and 2D vortex-particle computation for a generalization of the classical problem of flat-plate constant-rate pitch and related motions, at frequencies and Reynolds numbers relevant to Micro Air Vehicle applications. The motivation is problems of maneuvering, perching and gust response. All of the examined flows evince a strong leading edge vortex. Increasing pitch rate tends to tighten the leading edge vortex and to produce a trailing-edge vortex system dominated by a counter-rotating pair. Pitch pivot point location is crucial to the leading edge vortex size and formation history, and to its subsequent behavior in convecting over the airfoil suction-side. Despite the respective limitations of the experiment and computations, agreement in vorticity fields between the two at an overlapping case at Re = 10,000 is good, whence it is possible to use the computation to obtain integrated force data unavailable in the experiment. These were studied for Re= 100 and 1000. Lift pr...

Turbulent vortex shedding from a blunt trailing edge hydrofoil

Abstract: Placed in a fluid stream, solid bodies can exhibit a separated flow that extends to their wake. The detachment of the boundary layer on both upper and lower surfaces forms two shear layers which generate above a critical value of Reynolds number a periodic array of discrete vortices termed von Karman street. The body experiences a fluctuating lift force transverse to the flow caused by the asymmetric formation of vortices. The structural vibration amplitude is significantly amplified when the vortex shedding frequency lies close to a resonance frequency of the combined fluid-structure system. For resonance condition, fatigue cracks are likely to occur and lead to the premature failure of the mechanical system. Despite numerous and extensive studies on the topic, the periodic vortex shedding is considered to be a primary damage mechanism. The wake produced by a streamlined body, such as a hydrofoil, is an important issue for a variety of applications, including hydropower generation and marine vessel propulsion. However, the current state of the laboratory art focuses mainly in the wakes produced by hydraulically smooth bluff bodies at low Reynolds numbers. The present work considers a blunt trailing edge symmetric hydrofoil operating at zero angle of attack in a uniform high speed flow, Reh = 16.1·103 - 96.6·103 where the reference length h is the trailing edge thickness. Experiments are performed in the test section of the EPFL-LMH high speed cavitation tunnel. With the help of various measurement devices including laser Doppler vibrometer, particle image velocimetry, laser Doppler velocimetry and high speed digital camera, the effects of cavitation on the generation mechanism of the vortex street are investigated. Furthermore, the effects of a tripped turbulent boundary layer on the wake characteristics are analyzed and compared with the condition of a natural turbulent transition. In cavitation free regime and according to the Strouhal law, the vortex shedding frequency is found to vary quasi-linearly with the free-stream velocity provided that no hydrofoil resonance frequency is excited, the so-called lock-off condition. For such regime, the shed vortices exhibit strong span-wise instabilities and dislocations. A direct relation between vortex span-wise organization and vortex-induced vibration amplitude is found. In the case of resonance, the coherence of the vortex shedding process is significantly enhanced. The eigen modes are identified so that the lock-in of the vortex shedding frequency on a free-stream velocity range occurs for the first torsional mode. In the case of liquid flows, when the pressure falls below the vapor pressure, cavitation occurs in the vortex core. For lock-off condition, the cavitation inception index is linearly dependent on the square root of the Reynolds number which is in accordance with former models. For lock-in, it is significantly increased and makes clear that the vortex roll-up is amplified by the phase locked vibrations of the trailing edge. For the cavitation inception index and considering the trailing edge displacement velocity, a new correlation relationship that encompasses the lock-off and the lock-in conditions is proposed and validated. In addition, it is found that the transverse velocity of the trailing edge increases the vortex strength linearly. Therefore, the displacement velocity of the hydrofoil trailing edge increases the fluctuating forces on the body and this effect is additional to any increase of vortex span-wise organization, as observed for the lock-in condition. Cavitation developing in the vortex street cannot be considered as a passive agent for the visualization of the turbulent wake flow. The cavitation reacts on the wake as soon as it appears. At early stage of cavitation development, the vortex-induced vibration and flow velocity fluctuations are significantly increased. For fully developed cavitation, the vortex shedding frequency increases up to 15%, which is accompanied by the increase of the vortex advection velocity and reduction of the stream-wise and cross-stream inter-vortex spacings. These effects are addressed and thought to be a result of the increase of the vorticity by cavitation. Besides, it is shown that the cavitation does not obviously modify the vortex span-wise organization. Moreover, hydro-elastic couplings are found to be enabled/disabled by permitting a sufficient vortex cavitation development. The effects on the wake characteristics of a tripped turbulent boundary layer, as opposed to the natural turbulent transition, are investigated. The foil surface is hydraulically smooth and a fully effective boundary-layer tripping at the leading edge is achieved with the help of a distributed roughness. The vortex shedding process is found to be strongly influenced by the boundary-layer development. The tripped turbulent transition promotes the re-establishment of organized vortex shedding. In the context of the tripped transition and in comparison with the natural one, significant increases in the vortex span-wise organization, the induced hydrofoil vibration, the wake velocity fluctuations, the wake energies and the vortex strength are revealed. The vortex shedding process intermittency is decreased and the coherence is increased. Although the vortex shedding frequency is decreased, a modified Strouhal number based on the wake width at the end of the vortex formation region is constant and evidences the similarity of the wakes. This result leads to an effective estimation of the vortex shedding frequency.

Near wake vortex dynamics of a hovering hawkmoth

Abstract: Numerical investigation of vortex dynamics in near wake of a hovering hawkmoth and hovering aerodynamics is conducted to support the development of a biology-inspired dynamic flight simulator for flapping wing-based micro air vehicles. Realistic wing-body morphologies and kinematics are adopted in the numerical simulations. The computed results show 3D mechanisms of vortical flow structures in hawkmoth-like hovering. A horseshoe-shaped primary vortex is observed to wrap around each wing during the early down- and upstroke; the horseshoe-shaped vortex subsequently grows into a doughnut-shaped vortex ring with an intense jet-flow present in its core, forming a downwash. The doughnut-shaped vortex rings of the wing pair eventually break up into two circular vortex rings as they propagate downstream in the wake. The aerodynamic yawing and rolling torques are canceled out due to the symmetric wing kinematics even though the aerodynamic pitching torque shows significant variation with time. On the other hand, the time-varying the aerodynamics pitching torque could make the body a longitudinal oscillation over one flapping cycle.

Airfoil Stall Suppression by Use of a Bubble Burst Control Plate

Abstract: To suppress the stall on an NACA 0012 airfoil, a thin plate (hereafter referred to as a burst control plate) was attached on the airfoil to delay the burst of laminar separation bubbles formed at the stall angle. The burst control plate is used to enhance the vortical structures in the separated shear layer. Wind-tunnel tests were conducted at a chord Reynolds number of 1.3 x 10 5 . Flow visualization tests and surface pressure measurements showed that the burst control plate placed on the airfoil suppresses the bubble burst at a wide range of angle of attack and therefore, both the stall angle and the maximum lift coefficient are increased. The particle image velocimetry measurements indicated that when the angle of attack of the airfoil with the burst control plate is set higher than the stall angle of the original airfoil, a similar flow structure of the original airfoil was observed.

Aerodynamic and Aeroacoustic Properties of a Flatback Airfoil: An Update

Abstract: Results from an experimental study of the aerodynamic and aeroacoustic properties of a atback version of the TU Delft DU97-W-300 airfoil are presented for a chord Reynolds number of 3 10 6 . The data were gathered in the Virginia Tech Stability Wind Tunnel, which uses a special aeroacoustic test section to enable measurements of airfoil self-noise. Corrected wind tunnel aerodynamic measurements for the DU97-W-300 are compared to previous solid wall wind tunnel data and are shown to give good agreement. Aeroacoustic data are presented for the atback airfoil, with a focus on the amplitude and frequency of noise associated with the vortex-shedding tone from the blunt trailing edge wake. The effect of a splitter plate attachment on both drag and noise is also presented. Computational Fluid Dynamics predictions of the aerodynamic properties of both the unmodied DU97-W-300 and the atback version are compared to the experimental data. Technical risks associated with the use of atback airfoils for the inboard region of wind turbine blades include increased aerodynamic noise and increased aerodynamic drag. Both of these penalties are the result of the blunt trailing edge shape and the wake that is produced by this shape. The relatively low pressure at the blunt base results in a much larger drag force than for a conventional airfoil shape. The effect of this drag penalty on rotor thrust and torque coefcient for typical inboard twist angles is not severe, and in fact can be offset by the additional lift that a atback airfoil generates. 3 Consideration of drag reducing devices such as splitter plates or trailing edge serrations may be desireable to further boost performance, however. The increased noise from the atback is due primarily to the vortex shedding phenomenon associated with bluff- body wakes. The vortex shedding often leads to tonal noise, similar to the Aeolian tones of o w past circular cylinders. The intensity of bluff-body vortex shedding tones at low Mach number scales with the sixth power of the relative o w velocity. Broadband aeroacoustic noise sources associated with turbulent boundary layer-trailing edge interaction scale with the fth power of the relative o w velocity. Since outboard o w velocities are much higher than those encoun- tered inboard, the overall aerodynamic noise levels of a rotor incorporating inboard atback shapes will likely continue to be dominated by outboard trailing edge noise. However, two aspects of the atback noise source may be cause for concern. First, the vortex-shedding noise from atbacks is likely to be contained in a relatively low-frequency band (50-200 Hz). Some community noise regulations have separate low-frequency noise standards apart from considera- tion of A-weighted sound, which emphasize higher frequencies to which the human ear is more sensitive. Second, the

Circulation Generation and Vortex Ring Formation by Conic Nozzles

Abstract: Vortex rings are one of the fundamental flow structures in nature. In this paper, the generation of circulation and vortex rings by a vortex generator with a static converging conic nozzle exit is studied numerically. Conic nozzles can manipulate circulation and other flow invariants by accelerating the flow, increasing the Reynolds number, and by establishing a two-dimensional flow at the exit. The increase in the circulation efflux is accompanied by an increase in the vortex circulation. A novel normalization method is suggested to differentiate between two contributions to the circulation generation: a one-dimensional slug-type flow contribution and an inherently two-dimensional flow contribution. The one-dimensional contribution to the circulation increases with the square of the centerline exit velocity, while the two-dimensional contribution increases linearly with the decrease in the exit diameter. The two-dimensional flow contribution to the circulation production is not limited to the impulsive initiation of the flow only (as in straight tube vortex generators), but it persists during the entire ejection. The two-dimensional contribution can reach as much as 44% of the total circulation (in the case of an orifice). The present study offers evidences on the importance of the vortex generator geometry, and in particular, the exit configuration on the emerging flow, circulation generation, and vortex ring formation. It is shown that both total and vortex ring circulations can be controlled to some extent by the shape of the exit nozzle.

Short-wavelength stability analysis of a helical vortex tube?

Abstract: The stability of a helical vortex tube is studied by short-wavelength stability analysis. The ratio ϵ of the core to the curvature radius is assumed to be small but finite. The base flow of the helical vortex tube is obtained by perturbation expansion which exhibits rotational and translational motions as a whole. It is shown that the helical vortex tube is subject to curvature instability, which was first found for the vortex ring. The growth rates of the curvature instability are obtained both analytically and numerically. The effects of torsion and rotation are investigated. Both torsion and rotation appear as second-order correction to the growth rate of the curvature instability which is first order in ϵ. They break symmetry so that the maximal growth rates are larger than the vortex ring of which all the parameters but torsion and rotation are the same.

On the prolong attachment of leading edge vortex on a flapping wing

Abstract: In this paper, we take a fundamental approach to investigate the effect of spanwise flow on the prolonged attachment of leading edge vortex (LEV) on a flapping wing. By imposing a constant acceleration-constant velocity flow on elliptic wings of various sweep angles and angles of attack, our experimental and numerical results show that while spanwise flow per se has negligible influence on the prolong attachment of the LEV, vortex stretching can significantly delay detachment of the LEV, even for a small spanwise flow.

Motion of a vortex ring in a simple shear flow

Abstract: The motion and deformation of a vortex ring in a linear or simple shear flow have been simulated numerically by using the lattice Boltzmann method with multiple relaxation times. The study is motivated by a recent experiment [T. T. Lim, K. B. Lua, and K. Thet, Phys. Fluids 20, 051701 (2008)], which shows that a vortex ring propagating in a uniform cross flow does not experience Kutta lift and undergo tilting and deformation. The focus of the present study is to examine the effect of a simple shear in a cross flow on the motion of a vortex ring. Numerical approach is adopted here because a truly simple shear flow is difficult to generate experimentally. Our computation shows that a vortex ring tilts and deforms in a simple shear flow, and the tilting can be attributed to the modification of the vorticity distribution of the vortex ring as a result of the entrainment of background vorticity by the vortex core. It is further shown that although the shear in the flow has the tendency to elongate the vortex ri...