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.

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.

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 The influence of moderate angle-of-attack variation on disturbances evolution and transition to turbulence in supersonic boundary layer on swept wing

2019 ◽  
Vol 234 (1) ◽  
pp. 96-101
Author(s):  
Alexander Kosinov ◽  
Nikolai Semionov ◽  
Yury Yermolaev ◽  
Boris Smorodsky ◽  
Gleb Kolosov ◽  
...  
Keyword(s):  
Boundary Layer ◽  
Theoretical Study ◽  
Angle Of Attack ◽  
Reynolds Numbers ◽  
Supersonic Boundary Layer ◽  
Linear Stability Theory ◽  
Transition To Turbulence ◽  
Computational Results ◽  
Swept Wing ◽  
Turbulent Transition

The paper is devoted to an experimental and theoretical study of effect of moderate angle-of-attack variation on disturbances evolution and laminar-turbulent transition in a supersonic boundary layer on swept wing at Mach 2. Monotonous growth of the transition Reynolds numbers with angle of attack increasing from −2° to 2.7° is confirmed. For the same conditions, calculations based on linear stability theory are performed. The experimental and computational results show a favourable comparison.

scholarly journals Transition to turbulence in the rotating disk boundary layer of a rotor–stator cavity

2018 ◽  
Vol 848 ◽  
pp. 631-647 ◽  
Author(s):  
Eunok Yim ◽  
J.-M. Chomaz ◽  
D. Martinand ◽  
E. Serre
Keyword(s):  
Boundary Layer ◽  
Similarity Solution ◽  
Rotating Disk ◽  
Transition To Turbulence ◽  
Mean Flow ◽  
Self Similarity ◽  
Mean Velocity ◽  
Global Mode ◽  
Spatial Growth ◽  
The Mean

The transition to turbulence in the rotating disk boundary layer is investigated in a closed cylindrical rotor–stator cavity via direct numerical simulation (DNS) and linear stability analysis (LSA). The mean flow in the rotor boundary layer is qualitatively similar to the von Kármán self-similarity solution. The mean velocity profiles, however, slightly depart from theory as the rotor edge is approached. Shear and centrifugal effects lead to a locally more unstable mean flow than the self-similarity solution, which acts as a strong source of perturbations. Fluctuations start rising there, as the Reynolds number is increased, eventually leading to an edge-driven global mode, characterized by spiral arms rotating counter-clockwise with respect to the rotor. At larger Reynolds numbers, fluctuations form a steep front, no longer driven by the edge, and followed downstream by a saturated spiral wave, eventually leading to incipient turbulence. Numerical results show that this front results from the superposition of several elephant front-forming global modes, corresponding to unstable azimuthal wavenumbers $m$, in the range $m\in [32,78]$. The spatial growth along the radial direction of the energy of these fluctuations is quantitatively similar to that observed experimentally. This superposition of elephant modes could thus provide an explanation for the discrepancy observed in the single disk configuration, between the corresponding spatial growth rates values measured by experiments on the one hand, and predicted by LSA and DNS performed in an azimuthal sector, on the other hand.

scholarly journals Transition to turbulence in the rotating-disk boundary-layer flow with stationary vortices

2017 ◽  
Vol 836 ◽  
pp. 43-71 ◽  
Author(s):  
E. Appelquist ◽  
P. Schlatter ◽  
P. H. Alfredsson ◽  
R. J. Lingwood
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Low Frequency ◽  
Rotating Disk ◽  
High Amplitude ◽  
Transition To Turbulence ◽  
Navier Stokes ◽  
Absolute Instability ◽  
Global Instability ◽  
Roughness Elements

This paper proposes a resolution to the conundrum of the roles of convective and absolute instability in transition of the rotating-disk boundary layer. It also draws some comparison with swept-wing flows. Direct numerical simulations based on the incompressible Navier–Stokes equations of the flow over the surface of a rotating disk with modelled roughness elements are presented. The rotating-disk flow has been of particular interest for stability and transition research since the work by Lingwood (J. Fluid Mech., vol. 299, 1995, pp. 17–33) where an absolute instability was found. Here stationary disturbances develop from roughness elements on the disk and are followed from the linear stage, growing to saturation and finally transitioning to turbulence. Several simulations are presented with varying disturbance amplitudes. The lowest amplitude corresponds approximately to the experiment by Imayama et al. (J. Fluid Mech., vol. 745, 2014a, pp. 132–163). For all cases, the primary instability was found to be convectively unstable, and secondary modes were found to be triggered spontaneously while the flow was developing. The secondary modes further stayed within the domain, and an explanation for this is a proposed globally unstable secondary instability. For the low-amplitude roughness cases, the disturbances propagate beyond the threshold for secondary global instability before becoming turbulent, and for the high-amplitude roughness cases the transition scenario gives a turbulent flow directly at the critical Reynolds number for the secondary global instability. These results correspond to the theory of Pier (J. Engng Maths, vol. 57, 2007, pp. 237–251) predicting a secondary absolute instability. In our simulations, high temporal frequencies were found to grow with a large amplification rate where the secondary global instability occurred. For smaller radial positions, low-frequency secondary instabilities were observed, tripped by the global instability.

scholarly journals The effects of mass transfer on the global stability of the rotating-disk boundary layer

2010 ◽  
Vol 663 ◽  
pp. 401-433 ◽  
Author(s):  
CHRISTIAN THOMAS ◽  
CHRISTOPHER DAVIES
Keyword(s):  
Boundary Layer ◽  
Mass Transfer ◽  
Rotating Disk ◽  
Disk Surface ◽  
Reynolds Numbers ◽  
Base Flow ◽  
Absolute Instability ◽  
Unstable Region ◽  
Global Behaviour ◽  
Simulation Results

Numerical simulations were conducted to investigate the effects of surface suction and injection on the global behaviour of linear disturbances in the rotating-disk boundary layer. This extends earlier work, which considered the case with no mass transfer. For disturbances in the genuine base flow, where radially inhomogeneity is retained, mass injection at the disk surface led to behaviour that remained qualitatively similar to that which was found when there was no mass transfer. The initial development of disturbances within the absolutely unstable region involved temporal growth and upstream propagation, as should be anticipated for an absolute instability. However, this did not persist indefinitely. Just as for the case without mass transfer, the simulation results suggested that convective behaviour would eventually dominate, for all the Reynolds numbers investigated. In marked contrast, the results obtained for flows with mass suction indicate a destabilization due to the effects of the base-flow radial inhomogeneity. It was possible to identify disturbances excited within the absolutely unstable region that grew continually, with a temporal growth rate that increased as the disturbance evolved. The strong locally stabilizing effect of suction on the absolute instability, which gives rise to large increases in critical Reynolds numbers, appears to be obtainable only at the expense of introducing a new form of global instability. Analogous forms of global behaviour can be found in impulse solutions of the linearized complex Ginzburg–Landau equation. These solutions were deployed to interpret and make comparisons with the numerical simulation results. They illustrate how the long-term behaviour of a disturbance can be determined by the precise balance between radial increases in temporal growth rates, corresponding shifts in temporal frequencies and diffusion/dispersion effects. This balance provides some insight into why disturbances that are absolutely unstable, for the homogenized version of the rotating-disk boundary-layer flow, may become, in the genuine radially inhomogeneous flow, either globally stable or globally unstable, depending on the level of mass transfer that is applied at the disk surface.

Boundary-layer transition and the behaviour of spiral vortices on rotating spheres

1983 ◽  
Vol 137 ◽  
pp. 153-164 ◽  
Author(s):  
Y. Kohama ◽  
R. Kobayashi
Keyword(s):  
Boundary Layer ◽  
Reynolds Numbers ◽  
Boundary Layer Transition ◽  
Transition Regime ◽  
Sphere Surface ◽  
Layer Transition ◽  
Turbulent Transition ◽  
Vortex Axis ◽  
Laminar Turbulent Transition

The mechanism of boundary-layer transition and the behaviour of spiral vortices on spheres rotating in otherwise undisturbed fluid were investigated experimentally. Critical and transition Reynolds numbers which determine the laminar-turbulent transition regime on the sphere surface were measured. In addition the number of spiral vortices on the sphere and the direction of the vortex axis were clarified.

scholarly journals Transition delay in a boundary layer flow using active control

2013 ◽  
Vol 731 ◽  
pp. 288-311 ◽  
Author(s):  
Onofrio Semeraro ◽  
Shervin Bagheri ◽  
Luca Brandt ◽  
Dan S. Henningson
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Linear Control ◽  
Transition To Turbulence ◽  
Stream Velocity ◽  
Spanwise Direction ◽  
Turbulent Transition ◽  
Transition Delay ◽  
Strong Control ◽  
Laminar Turbulent Transition

AbstractActive linear control is applied to delay the onset of laminar–turbulent transition in the boundary layer over a flat plate. The analysis is carried out by numerical simulations of the nonlinear, transitional regime. A three-dimensional, localized initial condition triggering Tollmien–Schlichting waves of finite amplitude is used to numerically simulate the transition to turbulence. Linear quadratic Gaussian controllers based on reduced-order models of the linearized Navier–Stokes equations are designed, where the wall sensors and the actuators are localized in space. A parametric analysis is carried out in the nonlinear regime, for different disturbance amplitudes, by investigating the effects of the actuation on the flow due to different distributions of the localized actuators along the spanwise direction, different sizes of the actuators and the effort of the controllers. We identify the range of parameters where the controllers are effective and highlight the limits of the device for high amplitudes and strong control action. Despite the fully linear control approach, it is shown that the device is effective in delaying the onset of laminar–turbulent transition in the presence of packets characterized by amplitudes $a\approx 1\hspace{0.167em} \% $ of the free stream velocity at the actuator location. Up to these amplitudes, it is found that a proper choice of the actuators positively affects the performance of the controller. For a transitional case, $a\approx 0. 20\hspace{0.167em} \% $, we show a transition delay of $\Delta {\mathit{Re}}_{x} = 3. 0\times 1{0}^{5} $.

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