Global instability analysis of a boundary layer flow over a small cavity

2019 ◽  
Author(s):  
Marlon Mathias ◽  
Marcello F. Medeiros
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Global Instability ◽  
Instability Analysis ◽  
Small Cavity ◽  
Layer Flow

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.

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.

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