scholarly journals Global vorticity shedding for a vanishing wing

2012 ◽  
Vol 695 ◽  
pp. 112-134 ◽  
Author(s):  
M. S. Wibawa ◽  
S. C. Steele ◽  
J. M. Dahl ◽  
D. E. Rival ◽  
G. D. Weymouth ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Tip Vortex ◽  
Spanwise Direction ◽  
Streamwise Vorticity ◽  
Biologically Inspired ◽  
Cross Sectional ◽  
Image Velocimetry ◽  
Moving Body ◽  
Surrounding Fluid

AbstractIf a moving body were made to vanish within a fluid, its boundary-layer vorticity would be released into the fluid at all locations simultaneously, a phenomenon we call global vorticity shedding. We approximate this process by studying the related problem of rapid vorticity transfer from the boundary layer of a body undergoing a quick change of cross-sectional and surface area. A surface-piercing foil is first towed through water at constant speed, $U$, and constant angle of attack, then rapidly pulled out of the fluid in the spanwise direction. Viewed within a fixed plane perpendicular to the span, the cross-sectional area of the foil seemingly disappears. The rapid spanwise motion results in the nearly instantaneous shedding of the boundary layer into the surrounding fluid. Particle image velocimetry measurements show that the shed layers quickly transition from free shear layers to form two strong, unequal-strength vortices, formed within non-dimensional time ${t}^{\ensuremath{\ast} } = 0. 03$, based on the foil chord and forward velocity. These vortices are connected to, and interact with, the foil’s tip vortex through additional streamwise vorticity formed during the rapid pulling of the foil. Numerical simulations show that two strong spanwise vortices form from the shed vorticity of the boundary layer. The three-dimensional effects of the foil removal process are restricted to the tip of the foil. This method of vorticity transfer may be used for quickly introducing circulation to a fluid to provide forcing for biologically inspired flow control.

Distortion of the stagnation-point flow due to cross-stream vorticity in the external flow

1995 ◽  
Vol 352 (1700) ◽  
pp. 443-452 ◽  
Keyword(s):  
Boundary Layer ◽  
Stagnation Point ◽  
Three Dimensional ◽  
External Flow ◽  
Stagnation Point Flow ◽  
Spanwise Direction ◽  
Two Dimensional ◽  
Streamwise Vorticity ◽  
Flow Reynolds Number ◽  
Vortical Disturbance

The structure of the stagnation-point flow in the presence of weak steady cross-stream vorticity in the external flow is investigated. A specific case of the two-dimensional basic forward stagnation-point flow past a circular cylinder is considered with the external three-dimensional vortical disturbance taken to be periodic in the spanwise direction with a wavelength λ*≤λ* N =π D /( Re D ) 1/2 , where D is the diameter of the cylinder and Re D is the flow Reynolds number. It is shown that the presence of weak but finite streamwise vorticity, with λ*≤λ* N in the external flow, can be supported by the flow in the stagnation zone, leading to a substructure of counterrotating streamwise eddies in the boundary layer. The magnitude of the streamwise vorticity in the boundary layer is found to match with that in the external flow for A* ^ X*N; it is of much smaller order for λ* > λ* N , which corresponds to a disturbance of the type considered by Hammerlin (1955).

scholarly journals Buoyancy-driven algebraic (localised) boundary-layer disturbances

2021 ◽  
Vol 132 (1) ◽  
Author(s):  
S. M. Edwards ◽  
R. E. Hewitt
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Boundary Region ◽  
Dominant Mode ◽  
Spanwise Direction ◽  
Pressure Gradients ◽  
Cross Sectional ◽  
Gradient Parameter ◽  
Sectional Plane ◽  
Downstream Flow

AbstractWe show that a new class of steady linear eigenmodes exist in the Falkner–Skan boundary layer, associated with an algebraically developing, thermally coupled three-dimensional perturbation that remains localised in the spanwise direction. The dominant mode has a weak temperature difference that decays (algebraically) downstream, but remains sufficient (for favourable pressure gradients that are below a critical level) to drive an algebraically growing disturbance in the velocity field. We determine the critical Prandtl number and pressure gradient parameter required for downstream algebraic growth. We also march the nonlinear boundary-region equations downstream, to demonstrate that growth of these modes eventually gives rise to streak-like structures of order-one aspect ratio in the cross-sectional plane. Furthermore, this downstream flow can ultimately become unstable to a two-dimensional Rayleigh instability at finite amplitudes.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Large- and small-scale vortical motions in a shear layer perturbed by tabs

1999 ◽  
Vol 382 ◽  
pp. 307-329 ◽  
Author(s):  
JUDITH K. FOSS ◽  
K. B. M. Q. ZAMAN
Keyword(s):  
Shear Layer ◽  
Pitch Angle ◽  
Large Scale ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Streamwise Vorticity ◽  
Cross Sectional ◽  
Scale Population

The large- and small-scale vortical motions produced by ‘delta tabs’ in a two-stream shear layer have been studied experimentally. An increase in mixing was observed when the base of the triangular shaped tab was affixed to the trailing edge of the splitter plate and the apex was pitched at some angle with respect to the flow axis. Such an arrangement produced a pair of counter-rotating streamwise vortices. Hot-wire measurements detailed the velocity, time-averaged vorticity (Ωx) and small-scale turbulence features in the three-dimensional space downstream of the tabs. The small-scale structures, whose scale corresponds to that of the peak in the dissipation spectrum, were identified and counted using the peak-valley-counting technique. The optimal pitch angle, θ, for a single tab and the optimal spanwise spacing, S, for a multiple tab array were identified. Since the goal was to increase mixing, the optimal tab configuration was determined from two properties of the flow field: (i) the large-scale motions with the maximum Ωx, and (ii) the largest number of small-scale motions in a given time period. The peak streamwise vorticity magnitude [mid ]Ωx−max[mid ] was found to have a unique relationship with the tab pitch angle. Furthermore, for all cases examined, the overall small-scale population was found to correlate directly with [mid ]Ωx−max[mid ]. Both quantities peaked at θ≈±45°. It is interesting to note that the peak magnitude of the corresponding circulation in the cross-sectional plane occurred for θ≈±90°. For an array of tabs, the two quantities also depended on the tab spacing. An array of contiguous tabs acted as a solid deflector producing the weakest streamwise vortices and the least small-scale population. For the measurement range covered, the optimal spacing was found to be S≈1.5 tab widths.

The Three-Dimensional Interaction of a Shock Wave with a Turbulent Boundary Layer

1966 ◽  
Vol 17 (3) ◽  
pp. 231-252 ◽  
Author(s):  
A. McCabe
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Reasonable Agreement ◽  
Three Dimensional ◽  
Side Wall ◽  
Approximate Theory ◽  
Streamwise Vorticity ◽  
Supersonic Wind Tunnel ◽  
Dimensional Interaction

SummaryExperiments are described on the interaction of the shock wave generated by a wedge in a supersonic wind tunnel with the turbulent boundary layer on the side wall. It is shown that the onset of separation appears to be largely affected by the action of streamwise vorticity in the interaction region. A simple approximate theory based on this concept shows reasonable agreement with the experimental results. Comparisons have been made with two-dimensional interactions of normal shocks and boundary layers, but they did not produce any conclusive results.

Water Synthetic Jet Driven by a Piezoelectric Actuator – LIF and PIV Experiments

2015 ◽  
Vol 1104 ◽  
pp. 45-50 ◽  
Author(s):  
Zuzana Broučková ◽  
Shu Shen Hsu ◽  
An Bang Wang ◽  
Zdeněk Trávníček
Keyword(s):  
Reynolds Number ◽  
Particle Image Velocimetry ◽  
Piezoelectric Actuator ◽  
Particle Image ◽  
Three Dimensional ◽  
Laser Induced Fluorescence ◽  
Synthetic Jet ◽  
Fluid Exchange ◽  
Image Velocimetry ◽  
Surrounding Fluid

A synthetic jet (SJ) is a fluid jet flow generated from fluid oscillations during a periodical fluid exchange between an actuator cavity and surrounding fluid. A water synthetic jet was generated from submerged piezoelectric-driven SJ actuator. The actuator slot width was 0.36 mm. The experiments were performed using laser induced fluorescence (LIF) flow visualization and particle image velocimetry (PIV) techniques, both in a phase locked setup. The LIF visualization was used to demonstrate three-dimensional nature of the SJ formation process and to estimate SJ velocity. The PIV experiment quantified SJ velocity cycles in chosen plans. The driven frequency was adjusted near the resonance at approximately 46 Hz. It was evaluated theoretically and confirmed experimentally by means of LIF visualization. The time-mean orifice velocity and the Reynolds number were estimated asU0= 0.07–0.10 m/s andRe= 100–150, respectively.

An experimental insight into the effect of confinement on tip vortex cavitation of an elliptical hydrofoil

1999 ◽  
Vol 390 ◽  
pp. 1-23 ◽  
Author(s):  
OLIVIER BOULON ◽  
MATHIEU CALLENAERE ◽  
JEAN-PIERRE FRANC ◽  
JEAN-MARIE MICHEL
Keyword(s):  
Boundary Layer ◽  
Lift Coefficient ◽  
Three Dimensional ◽  
Tangential Velocity ◽  
Velocity Profiles ◽  
Tip Clearance ◽  
Tip Vortex ◽  
Flat Plates ◽  
Tip Vortex Cavitation ◽  
Cavitation Inception

The present paper is devoted to an analysis of tip vortex cavitation under confined situations. The tip vortex is generated by a three-dimensional foil of elliptical planform, and the confinement is achieved by flat plates set perpendicular to the span, at an adjustable distance from the tip. In the range of variation of the boundary-layer thickness investigated, no significant interaction was observed between the tip vortex and the boundary layer which develops on the confinement plate. In particular, the cavitation inception index for tip vortex cavitation does not depend significantly upon the length of the plate upstream of the foil. On the contrary, tip clearance has a strong influence on the non-cavitating structure of the tip vortex and consequently on the inception of cavitation in its core. The tangential velocity profiles measured by a laser-Doppler velocimetry (LDV) technique through the vortex, between the suction and the pressure sides of the foil, are strongly asymmetric near the tip. They become more and more symmetric downstream and the confinement speeds up the symmetrization process. When the tip clearance is reduced to a few millimetres, the two extrema of the velocity profiles increase. This increase results in a decrease of the minimum pressure in the vortex centre and accounts for the smaller resistance to cavitation observed when tip clearance is reduced. For smaller values of tip clearance, a reduction of tip clearance induces on the contrary a significant reduction in the maxima of the tangential velocity together with a significant increase in the size of the vortex core estimated along the confinement plate. Hence, the resistance to cavitation is much higher for such small values of tip clearance and in practice, no tip vortex cavitation is observed for tip clearances below 1.5 mm. The cavitation number for the inception of tip vortex cavitation does not correlate satisfactorily with the lift coefficient, contrary to classical results obtained without any confinement. Owing to the specificity introduced by the confinement, the usual procedure developed in an infinite medium to estimate the vortex strength from LDV measurements is not applicable here. Hence, a new quantity homogeneous to a circulation had to be defined on the basis of the maximum tangential velocity and the core size, which proved to be better correlated to the cavitation inception data.

Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge

2010 ◽  
Vol 653 ◽  
pp. 245-271 ◽  
Author(s):  
L.-U. SCHRADER ◽  
L. BRANDT ◽  
C. MAVRIPLIS ◽  
D. S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Free Stream ◽  
Three Dimensional ◽  
Low Frequency ◽  
Leading Edge ◽  
Sound Waves ◽  
Streamwise Vorticity ◽  
Low Frequencies ◽  
Free Stream Turbulence

Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien–Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.

scholarly journals Role of the tip vortex in the force generation of low-aspect-ratio normal flat plates

2007 ◽  
Vol 581 ◽  
pp. 453-468 ◽  
Author(s):  
MATTHEW J. RINGUETTE ◽  
MICHELE MILANO ◽  
MORTEZA GHARIB
Keyword(s):  
Aspect Ratio ◽  
Vortex Formation ◽  
Three Dimensional ◽  
Unsteady Motion ◽  
Tip Vortex ◽  
Flat Plates ◽  
Low Aspect Ratio ◽  
Start Up ◽  
Image Velocimetry

We investigate experimentally the force generated by the unsteady vortex formation of low-aspect-ratio normal flat plates with one end free. The objective of this study is to determine the role of the free end, or tip, vortex. Understanding this simple case provides insight into flapping-wing propulsion, which involves the unsteady motion of low-aspect-ratio appendages. As a simple model of a propulsive half-stroke, we consider a rectangular normal flat plate undergoing a translating start-up motion in a towing tank. Digital particle image velocimetry is used to measure multiple perpendicular sections of the flow velocity and vorticity, in order to correlate vortex circulation with the measured plate force. The three-dimensional wake structure is captured using flow visualization. We show that the tip vortex produces a significant maximum in the plate force. Suppressing its formation results in a force minimum. Comparing plates of aspect ratio six and two, the flow is similar in terms of absolute distance from the tip, but evolves faster for aspect ratio two. The plate drag coefficient increases with decreasing aspect ratio.

Dynamics of laminar separation bubbles at low-Reynolds-number aerofoils

2009 ◽  
Vol 630 ◽  
pp. 129-153 ◽  
Author(s):  
R. HAIN ◽  
C. J. KÄHLER ◽  
R. RADESPIEL
Keyword(s):  
Reynolds Number ◽  
Particle Image ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Transition Process ◽  
Spanwise Direction ◽  
Time Resolved ◽  
Laminar Separation ◽  
Image Velocimetry ◽  
Dominant Frequencies

The laminar separation bubble on an SD7003 aerofoil at a Reynolds numberRe= 66000 was investigated to determine the dominant frequencies of the transition process and the flapping of the bubble. The measurements were performed with a high-resolution time-resolved particle image velocimetry (TR-PIV) system. Contrary to typical measurements performed through conventional PIV, the different modes can be identified by applying TR-PIV. The interaction between the shed vortices is analysed, and their significance for the production of turbulence is presented. In the shear layer above the bubble the generation and amplification of vortices due to Kelvin–Helmholtz instabilities is observed. It is found that these instabilities have a weak coherence in the spanwise direction. In a later stage of transition these vortices lead to a three-dimensional breakdown to turbulence.

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