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.

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.

On the laminar–turbulent transition of the rotating-disk flow: the role of absolute instability

2014 ◽  
Vol 745 ◽  
pp. 132-163 ◽  
Author(s):  
Shintaro Imayama ◽  
P. Henrik Alfredsson ◽  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Secondary Instability ◽  
Transition To Turbulence ◽  
Absolute Instability ◽  
Nonlinear Saturation ◽  
Global Mode ◽  
Turbulent Transition ◽  
Laminar Turbulent Transition

AbstractThis paper describes a detailed experimental study using hot-wire anemometry of the laminar–turbulent transition region of a rotating-disk boundary-layer flow without any imposed excitation of the boundary layer. The measured data are separated into stationary and unsteady disturbance fields in order to elaborate on the roles that the stationary and the travelling modes have in the transition process. We show the onset of nonlinearity consistently at Reynolds numbers, $R$, of $\sim $510, i.e. at the onset of Lingwood’s (J. Fluid Mech., vol. 299, 1995, pp. 17–33) local absolute instability, and the growth of stationary vortices saturates at a Reynolds number of $\sim $550. The nonlinear saturation and subsequent turbulent breakdown of individual stationary vortices independently of their amplitudes, which vary azimuthally, seem to be determined by well-defined Reynolds numbers. We identify unstable travelling disturbances in our power spectra, which continue to grow, saturating at around $R=585$, whereupon turbulent breakdown of the boundary layer ensues. The nonlinear saturation amplitude of the total disturbance field is approximately constant for all considered cases, i.e. different rotation rates and edge Reynolds numbers. We also identify a travelling secondary instability. Our results suggest that it is the travelling disturbances that are fundamentally important to the transition to turbulence for a clean disk, rather than the stationary vortices. Here, the results appear to show a primary nonlinear steep-fronted (travelling) global mode at the boundary between the local convectively and absolutely unstable regions, which develops nonlinearly interacting with the stationary vortices and which saturates and is unstable to a secondary instability. This leads to a rapid transition to turbulence outward of the primary front from approximately $R=565$ to 590 and to a fully turbulent boundary layer above 650.

413 Effects of the Orbital Motion on the Boundary Layer Flow over a Rotating Disk under Orbital Motion at High Reynolds Number

2015 ◽  
Vol 2015.68 (0) ◽  
pp. 153-154
Author(s):  
Yasuhiro OKUMURA ◽  
Shinnosuke FUJIKAWA ◽  
Mizue MUNEKATA ◽  
Hiroyuki YOSHIKAWA ◽  
Kazuyuki KUDO
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Boundary Layer Flow ◽  
High Reynolds Number ◽  
Orbital Motion ◽  
Rotating Disk ◽  
Layer Flow ◽  
High Reynolds

The linear stability of boundary-layer flow over compliant walls: effects of boundary-layer growth

1994 ◽  
Vol 280 ◽  
pp. 199-225 ◽  
Author(s):  
K. S. Yeo ◽  
B. C. Khoo ◽  
W. K. Chong
Keyword(s):  
Boundary Layer ◽  
Reynolds Number ◽  
Linear Stability ◽  
Boundary Layer Flow ◽  
Reynolds Numbers ◽  
Travelling Wave ◽  
Layer Growth ◽  
Local Flow ◽  
Low Reynolds ◽  
Layer Flow

The linear stability of boundary-layer flow over compliant or flexible surfaces has been studied by Carpenter & Garrad (1985), Yeo (1988) and others on the assumption of local flow parallelism. This assumption is valid at large Reynolds numbers. Non-parallel effects due to growth of the boundary layer gain in significance and importance as one gets to lower Reynolds number. This is especially so for a compliant surface, which can sustain a variety of wall-related instabilities in addition to the Tollmien—Schlichting instabilities (TSI) that are found over rigid surfaces. The present paper investigates the influence of boundary-layer non-parallelism on the TSI and wall-related travelling-wave flutter (TWF) on compliant layers. Corrections to the growth rate of locally parallel theory for boundary-layer non-parallelism are obtained through a multiple-scale analysis. The results indicate that flow non-parallelism has an overall destabilizing influence on the TSI and TWF. Flow non-parallelism is also found to have a very strong destabilizing effect on the branch of TWF that stretches to low Reynolds number. The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers.

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.

scholarly journals The interaction of Blasius boundary-layer flow with a compliant panel: global, local and transient analyses

2017 ◽  
Vol 827 ◽  
pp. 155-193 ◽  
Author(s):  
Konstantinos Tsigklifis ◽  
Anthony D. Lucey
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Travelling Wave ◽  
Navier Stokes ◽  
Global Instability ◽  
Blasius Boundary Layer ◽  
Layer Flow ◽  
High Level

We study the fluid–structure interaction (FSI) of a compliant panel with developing Blasius boundary-layer flow. The linearised Navier–Stokes equations in velocity–vorticity form are solved using a Helmholtz decomposition coupled with the dynamics of a plate-spring compliant panel couched in finite-difference form. The FSI system is written as an eigenvalue problem and the various flow- and wall-based instabilities are analysed. It is shown that global temporal instability can occur through the interaction of travelling wave flutter (TWF) with a structural mode or as a resonance between Tollmien–Schlichting wave (TSW) instability and discrete structural modes of the compliant panel. The former is independent of compliant panel length and upstream inflow disturbances while the specific behaviour arising from the latter phenomenon is dependent upon the frequency of a disturbance introduced upstream of the compliant panel. The inclusion of axial displacements in the wall model does not lead to any further global instabilities. The dependence of instability-onset Reynolds numbers with structural stiffness and damping for the global modes is quantified. It is also shown that the TWF-based global instability is stabilised as the boundary layer progresses downstream while the TSW-based global instability exhibits discrete resonance-type behaviour as Reynolds number increases. At sufficiently high Reynolds numbers, a globally unstable divergence instability is identified when the wavelength of its wall-based mode is longer than that of the least stable TSW mode. Finally, a non-modal analysis reveals a high level of transient growth when the flow interacts with a compliant panel which has structural properties capable of reducing TSW growth but which is prone to global instability through wall-based modes.

Model for unstable global modes in the rotating-disk boundary layer

2010 ◽  
Vol 663 ◽  
pp. 148-159 ◽  
Author(s):  
J. J. HEALEY
Keyword(s):  
Boundary Layer ◽  
Landau Equation ◽  
Rotating Disk ◽  
Reynolds Numbers ◽  
Absolute Instability ◽  
Global Mode ◽  
Ginzburg Landau ◽  
Varying Coefficients ◽  
Unstable Medium ◽  
Spatially Varying

Recent simulations and experiments appear to show that the rotating-disk boundary layer is linearly globally stable despite the existence of local absolute instability. However, we argue that linear global instability can be created by local absolute instability at the edge of the disk. This argument is based on investigations of the linearized complex Ginzburg–Landau equation with weakly spatially varying coefficients to model the propagation of a wavepacket through a weakly inhomogeneous unstable medium. Therefore, this mechanism could operate in a variety of locally absolutely unstable flows. The corresponding nonlinear global mode has a front at the radius of onset of absolute instability when the disk edge is far from the front. This front moves radially outwards when the Reynolds number at the disk edge is reduced. It is shown that the laminar–turbulent transition front also behaves in this manner, possibly explaining the scatter in observed transitional Reynolds numbers.

scholarly journals Inviscid Modes within the Boundary-Layer Flow of a Rotating Disk with Wall Suction and in an External Free-Stream

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2967
Author(s):  
Bashar Al Saeedi ◽  
Zahir Hussain
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Axial Flow ◽  
Rotating Disk ◽  
Disk Surface ◽  
Inviscid Fluid ◽  
Turbulent Transition ◽  
Boundary Layer Instability ◽  
Layer Flow ◽  
High Reynolds

The purpose of this paper is to investigate the linear stability analysis for the laminar-turbulent transition region of the high-Reynolds-number instabilities for the boundary layer flow on a rotating disk. This investigation considers axial flow along the surface-normal direction, by studying analytical expressions for the steady solution, laminar, incompressible and inviscid fluid of the boundary layer flow due to a rotating disk in the presence of a uniform injection and suction. Essentially, the physical problem represents flow entrainment into the boundary layer from the axial flow, which is transferred by the spinning disk surface into flow in the azimuthal and radial directions. In addition, through the formation of spiral vortices, the boundary layer instability is visualised which develops along the surface in spiral nature. To this end, this study illustrates that combining axial flow and suction together may act to stabilize the boundary layer flow for inviscid modes.

scholarly journals Low Reynolds number k-ε modeling by using the direct numerical simulation (DNS) data

2008 ◽  
pp. 48-65
Keyword(s):  
Numerical Simulation ◽  
Boundary Layer ◽  
Reynolds Number ◽  
Direct Numerical Simulation ◽  
Boundary Layer Flow ◽  
Low Reynolds Number ◽  
Reynolds Numbers ◽  
Damping Function ◽  
Layer Flow ◽  
Near Wall

The constant C and the near-wall damping function f in the eddyviscosityrelation of the k-ε model are evaluated from direct numerical simulation (DNS) data for developed channel and boundary-layer flow, eachat two Reynolds numbers. Various existing

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