Enhancing the absolute instability of a boundary layer by adding a far-away plate

2007 ◽  
Vol 579 ◽  
pp. 29-61 ◽  
Author(s):  
J. J. HEALEY
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Piecewise Linear ◽  
Saddle Points ◽  
Absolute Instability ◽  
Infinite Domain ◽  
Unstable Flow ◽  
Order Of Magnitude ◽  
The Absolute ◽  
Layer Flow

When a solid plate, with a boundary condition of no normal flow through it, is introduced parallel to a shear layer it is normally expected to exert a stabilizing influence on any inviscid linearly unstable waves. In this paper we present an example of an absolutely unstable boundary-layer flow that can be made more absolutely unstable by the addition of a plate parallel to the original flow and far from the boundary layer itself. In particular, the addition of the plate is found to increase the growth rate of the absolute instability of the original boundary-layer flow by an order of magnitude for long waves. This phenomenon is illustrated using piecewise-linear inviscid basic-flow profiles, for which analytical dispersion relations have been derived. Long-wave stability theories have been developed in several limits clarifying the mechanisms underlying the behaviour and establishing its generic nature. The class of flows expected to exhibit this phenomenon includes a class found recently to have an exponential growth of disturbances in the wall-normal direction, owing to the approach of certain saddle-points to certain branch-cuts in the complex-wavenumber plane. The theory also suggests that a convectively unstable flow in an infinite domain can be converted, in some circumstances, into an absolutely unstable flow when the domain is made finite by the addition of a plate, however far away the plate is.

An experimental study of absolute instability of the rotating-disk boundary-layer flow

1996 ◽  
Vol 314 ◽  
pp. 373-405 ◽  
Author(s):  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Wave Packet ◽  
Boundary Layer Flow ◽  
Critical Reynolds Number ◽  
Linear Stability Theory ◽  
Absolute Instability ◽  
Unstable Flow ◽  
Average Value ◽  
Layer Flow

In this paper, the results of experiments on unsteady disturbances in the boundary-layer flow over a disk rotating in otherwise still air are presented. The flow was perturbed impulsively at a point corresponding to a Reynolds numberRbelow the value at which transition from laminar to turbulent flow is observed. Among the frequencies excited are convectively unstable modes, which form a three-dimensional wave packet that initially convects away from the source. The wave packet consists of two families of travelling convectively unstable waves that propagate together as one packet. These two families are predicted by linear-stability theory: branch-2 modes dominate close to the source but, as the packet moves outwards into regions with higher Reynolds numbers, branch-1 modes grow preferentially and this behaviour was found in the experiment. However, the radial propagation of the trailing edge of the wave packet was observed to tend towards zero as it approaches the critical Reynolds number (about 510) for the onset of radial absolute instability. The wave packet remains convectively unstable in the circumferential direction up to this critical Reynolds number, but it is suggested that the accumulation of energy at a well-defined radius, due to the flow becoming radially absolutely unstable, causes the onset of laminar–turbulent transition. The onset of transition has been consistently observed by previous authors at an average value of 513, with only a small scatter around this value. Here, transition is also observed at about this average value, with and without artificial excitation of the boundary layer. This lack of sensitivity to the exact form of the disturbance environment is characteristic of an absolutely unstable flow, because absolute growth of disturbances can start from either noise or artificial sources to reach the same final state, which is determined by nonlinear effects.

Stability of Blasius Boundary-Layer Flow Interacting With a Compliant Panel

2014 ◽  
Author(s):  
Konstantinos Tsigklifis ◽  
Anthony D. Lucey
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Travelling Wave ◽  
Unstable Flow ◽  
Blasius Boundary Layer ◽  
Compliant Wall ◽  
Plate Spring ◽  
Difference Form ◽  
Tollmien Schlichting ◽  
Layer Flow

We develop a model to study the fluid-structure interaction (FSI) of a compliant panel with a Blasius boundary-layer flow. We carry out a two-dimensional global linear stability analysis modeling the flow using a combination of vortex and source boundary-element sheets on a computational grid while the dynamics of a plate-spring compliant wall are represented in finite-difference form. The system is then couched as an eigenvalue problem and the eigenvalues of the various flow- and wall-based instabilities are analyzed for two distinct sets of system parameters. Key findings are that coalescence — or resonance — of a structural eigenmode with either the most unstable flow-based Tollmien-Schlichting Wave (TSW) or wall-based travelling-wave flutter (TWF) modes can occur. This renders the convective nature of these instabilities to become global for a finite compliant wall, a phenomenon that has not hitherto been reported in the literature.

Experimental study of rotating-disk boundary-layer flow with surface roughness

2015 ◽  
Vol 786 ◽  
pp. 5-28 ◽  
Author(s):  
Shintaro Imayama ◽  
P. Henrik Alfredsson ◽  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Excellent Agreement ◽  
Boundary Layer Flow ◽  
Rotating Disk ◽  
Absolute Instability ◽  
Turbulent Transition ◽  
Artificial Surface ◽  
Layer Flow ◽  
Laminar Turbulent Transition

Rotating-disk boundary-layer flow is known to be locally absolutely unstable at $R>507$ as shown by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) and, for the clean-disk condition, experimental observations show that the onset of transition is highly reproducible at that Reynolds number. However, experiments also show convectively unstable stationary vortices due to cross-flow instability triggered by unavoidable surface roughness of the disk. We show that if the surface is sufficiently rough, laminar–turbulent transition can occur via a convectively unstable route ahead of the onset of absolute instability. In the present work we compare the laminar–turbulent transition processes with and without artificial surface roughnesses. The differences are clearly captured in the spectra of velocity time series. With the artificial surface roughness elements, the stationary-disturbance component is dominant in the spectra, whereas both stationary and travelling components are represented in spectra for the clean-disk condition. The wall-normal profile of the disturbance velocity for the travelling mode observed for a clean disk is in excellent agreement with the critical absolute instability eigenfunction from local theory; the wall-normal stationary-disturbance profile, by contrast, is distinct and the experimentally measured profile matches the stationary convective instability eigenfunction. The results from the clean-disk condition are compared with theoretical studies of global behaviours in spatially developing flow and found to be in good qualitative agreement. The details of stationary disturbances are also discussed and it is shown that the radial growth rate is in excellent agreement with linear stability theory. Finally, large stationary structures in the breakdown region are described.

A Comparison of the Influence of Mechanical and Acoustical Vibrations on Free Convections From a Horizontal Cylinder

1962 ◽  
Vol 84 (3) ◽  
pp. 268-268 ◽  
Author(s):  
R. M. Fand ◽  
E. M. Peebles
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Experimental Investigation ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Boundary Layer Flow ◽  
Horizontal Cylinder ◽  
Mechanical Vibrations ◽  
Order Of Magnitude ◽  
Layer Flow

This technical brief reports the results of an experimental investigation of the influence of horizontal transverse mechanical vibrations (frequency order of magnitude: 100 cps) upon the rate of convective heat transfer from a horizontal cylinder. The results of the experiments are compared with earlier findings. It is shown that, in spite of a tenfold difference in frequency (and amplitude), the heat-transfer correlations previously obtained for the case of horizontal acoustical vibrations [1] are also valid for horizontal mechanical vibrations, and that the character of the boundary-layer flow is the same (thermoacoustic streaming [2]) for these two cases.

An experimental study of edge effects on rotating-disk transition

2013 ◽  
Vol 716 ◽  
pp. 638-657 ◽  
Author(s):  
Shintaro Imayama ◽  
P. Henrik Alfredsson ◽  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Global Instability ◽  
Global Mode ◽  
Turbulent Transition ◽  
Layer Flow

AbstractThe onset of transition for the rotating-disk flow was identified by Lingwood (J. Fluid. Mech., vol. 299, 1995, pp. 17–33) as being highly reproducible, which motivated her to look for absolute instability of the boundary-layer flow; the flow was found to be locally absolutely unstable above a Reynolds number of 507. Global instability, if associated with laminar–turbulent transition, implies that the onset of transition should be highly repeatable across different experimental facilities. While it has previously been shown that local absolute instability does not necessarily lead to linear global instability: Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) has shown, using the linearized complex Ginzburg–Landau equation, that if the finite nature of the flow domain is accounted for, then local absolute instability can give rise to linear global instability and lead directly to a nonlinear global mode. Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) also showed that there is a weak stabilizing effect as the steep front to the nonlinear global mode approaches the edge of the disk, and suggested that this might explain some reports of slightly higher transition Reynolds numbers, when located close to the edge. Here we look closely at the effects the edge of the disk have on laminar–turbulent transition of the rotating-disk boundary-layer flow. We present data for three different edge configurations and various edge Reynolds numbers, which show no obvious variation in the transition Reynolds number due to proximity to the edge of the disk. These data, together with the application (as far as possible) of a consistent definition for the onset of transition to others’ results, reduce the already relatively small scatter in reported transition Reynolds numbers, suggesting even greater reproducibility than previously thought for ‘clean’ disk experiments. The present results suggest that the finite nature of the disk, present in all real experiments, may indeed, as Healey (J. Fluid. Mech., vol. 663, 2010, pp. 148–159) suggests, lead to linear global instability as a first step in the onset of transition but we have not been able to verify a correlation between the transition Reynolds number and edge Reynolds number.

The stability of rotating-disc boundary-layer flow over a compliant wall. Part 2. Absolute instability

1997 ◽  
Vol 350 ◽  
pp. 261-270 ◽  
Author(s):  
A. J. COOPER ◽  
PETER W. CARPENTER
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Transition To Turbulence ◽  
Control Technique ◽  
Absolute Instability ◽  
Rotating Disc ◽  
Compliant Wall ◽  
Wall Compliance ◽  
Layer Flow ◽  
The Stability

A numerical study has been undertaken of the influence of a compliant boundary on absolute instability. In a certain parameter range absolute instability occurs in the boundary layer on a rotating disc, thereby instigating rapid transition to turbulence. The conventional use of wall compliance as a laminar-flow control technique has been to lower growth rates of convective instabilities. This has the effect of reducing amplification of disturbances as they propagate downstream. For absolute instability, however, only the suppression of its onset would be a significant gain. This paper addresses the question of whether passive wall compliance can be advantageous when absolute instability exists in a boundary layer.A theoretical model of a single-layer viscoelastic compliant wall was used in conjunction with the sixth-order system of differential equations which govern the stability of the boundary-layer flow over a rotating disc. The absolute/convective nature of the flow was ascertained by using a spatio-temporal analysis. Pinch-point singularities of the dispersion relation and a point of zero group velocity identify the presence of absolute instability. It was found that only a low level of wall compliance was enough to delay the appearance of absolute instability to higher Reynolds numbers. Beyond a critical level of wall compliance results suggest that complete suppression of absolute instability is possible. This would then remove a major route to transition in the rotating-disc boundary layer.

Absolute instability of the boundary layer on a rotating disk

1995 ◽  
Vol 299 ◽  
pp. 17-33 ◽  
Author(s):  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Turbulent Flow ◽  
Rotating Disk ◽  
Absolute Instability ◽  
Average Value ◽  
Streamline Curvature ◽  
Curvature Effects ◽  
Coriolis Effects ◽  
The Absolute ◽  
Layer Flow

This paper is concerned with the theoretical behaviour of the boundary-layer flow over a disk rotating in otherwise still fluid. The flow is excited impulsively at a certain radius at timet= 0. This paper analyses the inviscid stability of the flow and the stability with viscous, Coriolis and streamline curvature effects included. In both cases, within a specific range of the parameter space, it is shown that the flow isabsolutelyunstable, i.e. disturbances grow in time at every fixed point in space. Outside this range, the flow is convectively unstable or stable. The absolute or convective nature of the instabilities is determined by examining the branch-point singularities of the dispersion relation. Absolute instability is found for Reynolds numbers above 510. Experimentally observed values for the onset of transition from laminar to turbulent flow have an average value of 513. It is suggested that absolute instability may cause the onset of transition to turbulent flow. The results from the inviscid analysis show that the absolute instability is not caused by Coriolis effects nor by streamline curvature effects. This indicates that this mechanism may be possible on swept wings, where Coriolis effects are not present but the boundary layers are otherwise similar.

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