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.

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.

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.

Effect of Reynolds number on drag reduction in turbulent boundary layer flow over liquid–gas interface

2020 ◽  
Vol 32 (12) ◽  
pp. 122111
Author(s):  
Hongyuan Li ◽  
SongSong Ji ◽  
Xiangkui Tan ◽  
Zexiang Li ◽  
Yaolei Xiang ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Turbulent Boundary Layer ◽  
Drag Reduction ◽  
Boundary Layer Flow ◽  
Turbulent Boundary Layer Flow ◽  
Layer Flow

Two-dimensional global low-frequency oscillations in a separating boundary-layer flow

2008 ◽  
Vol 614 ◽  
pp. 315-327 ◽  
Author(s):  
UWE EHRENSTEIN ◽  
FRANÇOIS GALLAIRE
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Perturbation Analysis ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Low Frequency ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Optimal Perturbation ◽  
Layer Flow

A separated boundary-layer flow at the rear of a bump is considered. Two-dimensional equilibrium stationary states of the Navier–Stokes equations are determined using a nonlinear continuation procedure varying the bump height as well as the Reynolds number. A global instability analysis of the steady states is performed by computing two-dimensional temporal modes. The onset of instability is shown to be characterized by a family of modes with localized structures around the reattachment point becoming almost simultaneously unstable. The optimal perturbation analysis, by projecting the initial disturbance on the set of temporal eigenmodes, reveals that the non-normal modes are able to describe localized initial perturbations associated with the large transient energy growth. At larger time a global low-frequency oscillation is found, accompanied by a periodic regeneration of the flow perturbation inside the bubble, as the consequence of non-normal cancellation of modes. The initial condition provided by the optimal perturbation analysis is applied to Navier–Stokes time integration and is shown to trigger the nonlinear ‘flapping’ typical of separation bubbles. It is possible to follow the stationary equilibrium state on increasing the Reynolds number far beyond instability, ruling out for the present flow case the hypothesis of some authors that topological flow changes are responsible for the ‘flapping’.

scholarly journals Stability Analysis on Nonequilibrium Supersonic Boundary Layer Flow with Velocity-Slip Boundary Conditions

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 142
Author(s):  
Xin He ◽  
Kai Zhang ◽  
Chunpei Cai
Keyword(s):  
Boundary Layer ◽  
Stability Analysis ◽  
Boundary Conditions ◽  
Boundary Layer Flow ◽  
Velocity Slip ◽  
Linear Stability Theory ◽  
Resonance Phenomenon ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Layer Flow

This paper presents our recent work on investigating velocity slip boundary conditions’ effects on supersonic flat plate boundary layer flow stability. The velocity-slip boundary conditions are adopted and the flow properties are obtained by solving boundary layer equations. Stability analysis of two such boundary layer flows is performed by using the Linear stability theory. A global method is first utilized to obtain approximate discrete mode values. A local method is then utilized to refine these mode values. All the modes in these two scenarios have been tracked upstream-wisely towards the leading edge and also downstream-wisely. The mode values for the no-slip flows agree well with the corresponding past results in the literature. For flows with slip boundary conditions, a stable and an unstable modes are detected. Mode tracking work is performed and the results illustrate that the resonance phenomenon between the stable and unstable modes is delayed with slip boundary conditions. The enforcement of the slip boundary conditions also shortens the unstable mode region. As to the conventional second mode, flows with slip boundary conditions can be more stable streamwisely when compared with the results for corresponding nonslip flows.

Flow Characteristics around Circular Cylinders with a Normal Slit

2017 ◽  
Vol 379 ◽  
pp. 48-57 ◽  
Author(s):  
Cheng Hsiung Kuo ◽  
Hwa Wei Lin ◽  
Chih Tao Chai ◽  
Fred Cheng
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
Rear Surface ◽  
Flow Characteristics ◽  
Boundary Layer Separation ◽  
Circular Cylinders ◽  
Flow Structures ◽  
Phase Lock ◽  
Layer Flow

Alterations of boundary layer separation along the upper-rear surface of a baseline and slit cylinder and the formation of a vortex in the near-wake are investigated by particle image velocimetry (PIV) at Reynolds number 1000. The slit ratio (S/D) is 0.3. The phase-lock flow structures are referred to the time-dependent volume flux at the slit exit and are achieved by the modified phase-averaged technique. The alterations and the evolution of boundary-layer flow along the upper-rear surface are demonstrated by the phase-lock flow structures. It is found that the alternate blowing and suction at the slit exit serves as a perturbation to the boundary layer near the shoulder of the slit cylinder leading to a significant delay of flow separation and the flow reattachment of boundary-layer flow along the upper-rear surface of the cylinder. After perturbation, the vortex street behind a slit cylinder is more organized and stronger than that behind a baseline cylinder at Reynolds number 1000.

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