The stability of plane Poiseuille flow in the presence of elastic boundaries

Korotkin, Alexandr I.

doi:10.1016/0021-8928(65)90019-5

Cited by 4 publications

(1 citation statement)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…They numerically integrated the Orr-Sommerfeld equation in order to substantiate, albeit for a simpler flow, the predictions made earlier by Benjamin (1960) for Tollmien-Schlichting waves in a Blasius boundary layer over a compliant surface. Korotkin (1965) later developed the analytic theory for the compliant channel problem, but formulated the boundary conditions incorrectly. † Green & Ellen (1972) presented numerical results showing that, for sufficiently compliant walls, the neutral stability curve for the Tollmien-Schlichting mode could become deformed so as to include an additional region of instability at higher wavenumbers.…”

Section: Earlier Workmentioning

confidence: 99%

Instabilities in a plane channel flow between compliant walls

1997

View full text Add to dashboard Cite

The stability of plane channel flow between compliant walls is investigated for disturbances which have the same symmetry, with respect to the channel centreline, as the Tollmien–Schlichting mode of instability. The interconnected behaviour of flow-induced surface waves and Tollmien–Schlichting waves is examined both by direct numerical solution of the Orr–Sommerfeld equation and by means of an analytic shear layer theory. We show that when the compliant wall properties are selected so as to give a significant stability effect on Tollmien–Schlichting waves, the onset of divergence instability can be severely disrupted. In addition, travelling wave flutter can interact with the Tollmien–Schlichting mode to generate a powerful instability which replaces the flutter instability identified in studies based on a potential mean-flow model. The behaviour found when the mean-flow shear layer is fully accounted for may be traced to singularities in the wave dispersion relation. These singularities can be attributed to solutions which represent Tollmien–Schlichting waves in rigid-walled channels. Such singularities will also be found in the dispersion relation for the case of Blasius flow. Thus, similar behaviour can be anticipated for Blasius flow, including the disruption of the onset of divergence instability. As a consequence, it seems likely that previous investigations for Blasius flow will have yielded very conservative estimates for the optimal stabilization that can be achieved for Tollmien–Schlichting waves for the purposes of laminar-flow control.

show abstract

Section: Earlier Workmentioning

confidence: 99%