Three-dimensional boundary-layer instability and separation induced by small-amplitude streamwise vorticity in the upstream flow

1993 ◽  
Vol 246 ◽  
pp. 21-41 ◽  
Author(s):  
M. E. Goldstein ◽  
S. J. Leib
Keyword(s):  
Boundary Layer ◽  
Small Amplitude ◽  
Three Dimensional ◽  
Cross Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
Linear Perturbation ◽  
Streamwise Vorticity ◽  
Dimensional Boundary ◽  
Layer Flow

We consider the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. We show how the initially linear perturbation, ultimately leads to a small-amplitude but nonlinear cross-flow far downstream from the leading edge. This motion is imposed on the boundary-layer flow and eventually causes the boundary layer to separate. The streamwise velocity profiles within the boundary layer become inflexional in localized spanwise regions just upstream of the separation point. The flow in these regions is therefore susceptible to rapidly growing inviscid instabilities.

The three-dimensional laminar boundary layer on a flat plate

1965 ◽  
Vol 22 (3) ◽  
pp. 587-598 ◽  
Author(s):  
L. Sowerby
Keyword(s):  
Boundary Layer ◽  
Flat Plate ◽  
Three Dimensional ◽  
Leading Edge ◽  
Main Stream ◽  
Dimensional Parameter ◽  
Stress Components ◽  
Dimensional Boundary ◽  
Layer Flow ◽  
Limiting Streamlines

A series expansion is derived for the three-dimensional boundary-layer flow over a flat plate, arising from a general main-stream flow over the plate. The series involved are calculated as far as terms of order ξ2, where ξ is a non-dimensional parameter defining distance measured from the leading edge of the plate. The results are applied to an example in which the main stream arises from the disturbance of a uniform stream by a circular cylinder mounted downstream from the leading edge of the plate, the axis of the cylinder being normal to the plate. Calculations are made for shear stress components on the plate, and for the deviation of direction of the limiting streamlines from those in the main stream.

Receptivity mechanisms in three-dimensional boundary-layer flows

2009 ◽  
Vol 618 ◽  
pp. 209-241 ◽  
Author(s):  
LARS-UVE SCHRADER ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Free Stream ◽  
Three Dimensional ◽  
Leading Edge ◽  
Nonlinear Process ◽  
Transition To Turbulence ◽  
Boundary Layer Flows ◽  
Free Stream Turbulence ◽  
Dimensional Boundary ◽  
Layer Flow

Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.

The long-time behaviour of incompressible swept-wing boundary layers subject to impulsive forcing

1998 ◽  
Vol 355 ◽  
pp. 359-381 ◽  
Author(s):  
M. J. TAYLOR ◽  
N. PEAKE
Keyword(s):  
Boundary Layer ◽  
Flow Direction ◽  
Three Dimensional ◽  
Cross Flow ◽  
Leading Edge ◽  
Rotating Disk ◽  
Linear Stability Theory ◽  
Swept Wing ◽  
Long Time ◽  
Layer Flow

The long-time limit of the response of incompressible three-dimensional boundary layer flows on infinite swept wedges and infinite swept wings to impulsive forcing is examined using causal linear stability theory. Following the discovery by Lingwood (1995) of the presence of absolute instabilities caused by pinch points occurring in the radial direction in the boundary layer flow of a rotating disk, we search for pinch points in the cross flow direction for both the model Falkner–Skan–Cooke profile of a swept wedge and for a genuine swept-wing configuration. It is shown in both cases that, within a particular range of the parameter space, the boundary layer does indeed support pinch points in the wavenumber plane corresponding to the crossflow direction. These crossflow-induced pinch points do not constitute an absolute instability, as there is no simultaneous pinch occurring in the streamwise wavenumber plane, but nevertheless we show here how they can be used to find the maximum local growth rate contained in a wavepacket travelling in any given direction. Lingwood (1997) also found pinch points in the chordwise wavenumber plane in the boundary layer of the leading-edge region of a swept wing (i.e. at very high flow angles). The results presented in this paper, however, demonstrate the presence of pinch points for a much larger range of flow angles and pressure gradients than was found by Lingwood, and indeed describe the flow over a much greater, and practically significant, portion of the wing.

Effect on a laminar boundary layer of small-amplitude streamwise vorticity in the upstream flow

2001 ◽  
Vol 426 ◽  
pp. 229-262 ◽  
Author(s):  
DAVID W. WUNDROW ◽  
M. E. GOLDSTEIN
Keyword(s):  
Reynolds Number ◽  
Small Amplitude ◽  
Experimental Studies ◽  
Leading Edge ◽  
Transition Process ◽  
Streamwise Velocity ◽  
Shear Layers ◽  
Linear Perturbation ◽  
Streamwise Vorticity ◽  
Upstream Flow

This paper is a generalization of a previous analysis of the effects of a small-amplitude, steady, streamwise vorticity field on the flow over an infinitely thin flat plate in an otherwise uniform stream. That analysis, which is given in Goldstein & Leib (1993), required that the disturbance Reynolds number (i.e. the Reynolds number based on the disturbance velocity and length scale) be infinite while the present paper considers the more general case where this quantity can be finite. The results show how an initially linear perturbation of the upstream flow ultimately leads to a small-amplitude but nonlinear cross-flow far downstream from the leading edge. This flow can, under certain conditions, cause the streamwise velocity profiles to develop distinct shear layers in certain localized spanwise regions. These shear layers, which are remarkably similar to the ones that develop in Tollmien–Schlichting-wave transition (Kovasznay, Komoda & Vasudeva 1962), are highly inflectional and can therefore support the rapidly growing inviscid instabilities that are believed to break down into turbulent spots (Greenspan & Benney 1963, and, subsequently, many others). Numerical computations are carried out for input parameters which approximate the flow conditions of some recent experimental studies of the so-called Klebanoff-mode phenomenon. The results are used to explain some of the experimental observations, and, more importantly, to explain why the averaged quantities usually reported in these experiments do not correlate well with the turbulent-spot formation and therefore with the overall transition process.

Structure of a streamwise-oriented vortex incident upon a wing

2017 ◽  
Vol 816 ◽  
pp. 306-330 ◽  
Author(s):  
C. McKenna ◽  
M. Bross ◽  
D. Rockwell
Keyword(s):  
Root Mean Square ◽  
Cross Flow ◽  
Leading Edge ◽  
Streamwise Velocity ◽  
Mean Square ◽  
Swirl Ratio ◽  
Streamwise Vorticity ◽  
Image Velocimetry ◽  
Unsteady Loading ◽  
Drag Ratio

Impingement of a streamwise-oriented vortex upon a fin, tail, blade or wing represents a fundamental class of flow–structure interaction that extends across a range of applications. It can give rise to unsteady loading known as buffeting and to changes of the lift to drag ratio. These consequences are sensitive to parameters of the incident vortex as well as the location of vortex impingement on the downstream aerodynamic surface, generically designated as a wing. Particle image velocimetry is employed to determine patterns of velocity and vorticity on successive cross-flow planes along the vortex, which lead to volume representations and thereby characterization of the streamwise evolution of the vortex structure as it approaches the downstream wing. This evolution of the incident vortex is affected by the upstream influence of the downstream wing, and is highly dependent on the spanwise location of vortex impingement. Even at spanwise locations of impingement well outboard of the wing tip, a substantial influence on the structure of the incident vortex at locations significantly upstream of the leading edge of the wing was observed. For spanwise locations close to or intersecting the vortex core, the effects of upstream influence of the wing on the vortex are to: decrease the swirl ratio; increase the streamwise velocity deficit; decrease the streamwise vorticity; increase the azimuthal vorticity; increase the upwash; decrease the downwash; and increase the root-mean-square fluctuations of both streamwise velocity and vorticity. The interrelationship between these effects is addressed, including the rapid attenuation of axial vorticity in presence of an enhanced defect of axial velocity in the central region of the vortex. When the incident vortex is aligned with, or inboard of, the tip of the wing, the swirl ratio decreases to values associated with instability of the vortex, thereby giving rise to enhanced values of azimuthal vorticity relative to the streamwise (axial) vorticity, as well as relatively large root-mean-square values of streamwise velocity and vorticity.

Experimental and Theoretical Investigation of the Supersonic Boundary Layer Stability on the Swept Wing

2008 ◽  
Vol 3 (3) ◽  
pp. 34-38
Author(s):  
Sergey A. Gaponov ◽  
Yuri G. Yermolaev ◽  
Aleksandr D. Kosinov ◽  
Nikolay V. Semionov ◽  
Boris V. Smorodsky
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Leading Edge ◽  
Supersonic Boundary Layer ◽  
Mean Flow ◽  
Swept Wing ◽  
Wing Model ◽  
Dimensional Boundary ◽  
The Stability ◽  
Good Agreement

Theoretical and an experimental research results of the disturbances development in a swept wing boundary layer are presented at Mach number М = 2. In experiments development of natural and small amplitude controllable disturbances downstream was studied. Experiments were carried out on a swept wing model with a lenticular profile at a zero attack angle. The swept angle of a leading edge was 40°. Wave parameters of moving disturbances were determined. In frames of the linear theory and an approach of the local self-similar mean flow the stability of a compressible three-dimensional boundary layer is studied. Good agreement of the theory with experimental results for transversal scales of unstable vertices of the secondary flow was obtained. However the calculated amplification rates differ from measured values considerably. This disagreement is explained by the nonlinear processes observed in experiment

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