The hydrodynamic stability of flow over Kramer-type compliant surfaces. Part 2. Flow-induced surface instabilities

Abstract

The flow-induced surface instabilities of Kramer-type compliant surfaces are investigated by a variety of theoretical approaches. This class of instability includes all those modes of instability for which the mechanism of generation involves essentially inviscid processes. The results should be applicable to all compliant surfaces that could be modelled theoretically by a thin elastic plate, with or without applied longitudinal tension, supported on a springy elastic foundation. with or without a viscous fluid substrate; material damping is also taken into account through the viscoelastic properties of the solid constituents of the coatings.The simple case of a potential main flow is studied first. The eigenmodes for this case are subjected to an energy analysis following the methods of Landahl (1962). Instabilities that grow both in space and time are then considered, and absolute and convective instabilities identified and analysed.The effects of irreversible processes on the flow-induced surface instabilities are investigated. The shear flow in the boundary layer gives rise to a fluctuating pressure component which is out of phase with the surface motion. This leads to an irreversible transfer of energy from the main stream to the compliant surface. This mechanism is studied in detail and is shown to be responsible for travelling-wave flutter. Simple results are obtained for the critical velocity, wavenumber and stability boundaries. These last are shown to be in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation. An analysis of the effects of a viscous fluid substrate and of material damping is then carried out. The simpler inviscid theory is shown to predict values of the maximum growth rate which are, again, in good agreement with the results obtained by the numerical integration of the Orr–Sommerfeld equation provided that the instability is fairly weak.Compliant surfaces of finite length are analysed in the limit as wave-length tends to zero. In this way the static-divergence instability is predicted. Simple formulae for critical velocity and wavenumber are derived. These are in exact agreement with the results of the simpler infinite-length theory. But, whereas a substantial level of damping is required for the instability on a surface of infinite length, static divergence grows fastest in the absence of damping on a surface of finite length.

Flutter in a quasi-one-dimensional model of a collapsible channel

“…Similar instabilities are readily observed in experimental collapsible-tube systems, such as the Starling resistor [1], but are yet to be fully understood in all flow regimes [2]. Moreover, although collapsible channels are inherently global systems with self-excited oscillations often being driven or considerably modified by the presence of finite boundaries [3], they are undoubtedly linked to the local instabilities in homogeneous domains with flexible walls [4][5][6][7]. In the simplest collapsible channel model, a finite-Reynolds-number fluid flow is driven through a two-dimensional channel that has a finite segment of one of the walls replaced with a prestretched elastic membrane under external pressure.…”

Propagation of Small Disturbance Waves in a Fluid Flow across the Junctions between Rigid and Compliant Panels

“…If the plate is driven at a frequency, 13 and if it is above cutoff frequency i.e, 13>.JK / m , then waves will propagate along the plate. Further, generally d =0 and the four fundamental solutions of Eqn (1) are: (4) \jJ{y,x,t) =j{y,x) e-…”

Using Bio-Replicated Forming Technologies to Fabricate Shark-Skin Surface

“…Therefore, these micro-replication methods can be improved further. The elastic matrix of a non-smooth shark-skin is similar to that of the smooth skin of a dolphin and may reduce drag because of its excellent transition-delaying properties [Carpenter and Garrad 1986]. In the bio-replicated forming method, polymeric materials can be used as highly elastic substrates because of their excellent processability, ease of moulding and demoulding, and a wide spectrum of other physical and mechanical properties.…”