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.

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.

Is Tollmien-Schlichting wave necessary for transition of zero pressure gradient boundary layer flow?

2019 ◽  
Vol 31 (3) ◽  
pp. 031701 ◽  
Author(s):  
Prasannabalaji Sundaram ◽  
Tapan K. Sengupta ◽  
Soumyo Sengupta
Keyword(s):  
Boundary Layer ◽  
Pressure Gradient ◽  
Boundary Layer Flow ◽  
Tollmien Schlichting ◽  
Layer Flow

scholarly journals Magnetohydrodynamic cross-field boundary layer flow

1982 ◽  
Vol 5 (2) ◽  
pp. 377-384 ◽  
Author(s):  
D. B. Ingham ◽  
L. T. Hildyard
Keyword(s):  
Magnetic Field ◽  
Boundary Layer ◽  
Asymptotic Solution ◽  
Boundary Layer Flow ◽  
Leading Edge ◽  
Field Boundary ◽  
Boundary Layer Equations ◽  
Mhd Boundary Layer ◽  
Blasius Boundary Layer ◽  
Layer Flow

The Blasius boundary layer on a flat plate in the presence of a constant ambient magnetic field is examined. A numerical integration of the MHD boundary layer equations from the leading edge is presented showing how the asymptotic solution described by Sears is approached.

Homoclinic bifurcation in Blasius boundary‐layer flow

1995 ◽  
Vol 7 (6) ◽  
pp. 1282-1291 ◽  
Author(s):  
Uwe Ehrenstein ◽  
Werner Koch
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Homoclinic Bifurcation ◽  
Blasius Boundary Layer ◽  
Layer Flow

scholarly journals On the Asymptotic Approach to Thermosolutal Convection in Heated Slow Reactive Boundary Layer Flows

2008 ◽  
Vol 2008 ◽  
pp. 1-15
Author(s):  
Stanford Shateyi ◽  
Precious Sibanda ◽  
Sandile S. Motsa
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Chemical Species ◽  
Reynolds Numbers ◽  
Thermosolutal Convection ◽  
Boundary Layer Flows ◽  
Instability Waves ◽  
Tollmien Schlichting ◽  
Layer Flow ◽  
Negative Buoyancy

The study sought to investigate thermosolutal convection and stability of two dimensional disturbances imposed on a heated boundary layer flow over a semi-infinite horizontal plate composed of a chemical species using a self-consistent asymptotic method. The chemical species reacts as it diffuses into the nearby fluid causing density stratification and inducing a buoyancy force. The existence of significant temperature gradients near the plate surface results in additional buoyancy and decrease in viscosity. We derive the linear neutral results by analyzing asymptotically the multideck structure of the perturbed flow in the limit of large Reynolds numbers. The study shows that for small Damkohler numbers, increasing buoyancy has a destabilizing effect on the upper branch Tollmien-Schlichting (TS) instability waves. Similarly, increasing the Damkohler numbers (which corresponds to increasing the reaction rate) has a destabilizing effect on the TS wave modes. However, for small Damkohler numbers, negative buoyancy stabilizes the boundary layer flow.

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.

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