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Register a new userAeroelastic instability of cantilevered flexible plates in uniform flow
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We address the flutter instability of a flexible plate immersed in an axial flow. This instability is similar to flag flutter and results from the competition between destabilising pressure forces and stabilising bending stiffness. In previous experimental studies, the plates have always appeared much more stable than the predictions of two-dimensional models. This discrepancy is discussed and clarified in this paper by examining experimentally and theoretically the effect of the plate aspect ratio on the instability threshold. We show that the two-dimensional limit cannot be achieved experimentally because hysteretical behaviour and three-dimensional effects appear for plates of large aspect ratio. The nature of the instability bifurcation (sub- or supercritical) is also discussed in the light of recent numerical results.
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The interaction of flexible structures with viscoelastic flows can result in very rich dynamics. In this paper, we present the results of the interactions between the flow of a viscoelastic polymer solution and a cantilevered beam in a confined microfluidic geometry. Cantilevered beams with varying length and flexibility were studied. With increasing flow rate and Weissenberg number, the flow transitioned from a fore-aft symmetric flow to a stable detached vortex upstream of the beam, to a time-dependent unstable vortex shedding. The shedding of the unstable vortex upstream of the beam imposed a time-dependent drag force on the cantilevered beam resulting in flow-induced beam oscillations. The oscillations of the flexible beam were classified into two distinct regimes: a regime with a clear single vortex shedding from upstream of the beam resulting in a sinusoidal beam oscillation pattern with the frequency of oscillation increasing monotonically with Weissenberg number, and a regime at high Weissenberg numbers characterized by 3D chaotic flow instabilities where the frequency of oscillations plateaued. The critical onset of the flow transitions, the mechanism of vortex shedding and the dynamics of the cantilevered beam response are presented in detail here as a function of beam flexibility and flow viscoelasticity.
We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler-Bernoulli equation. A constant flux of liquid is supplied at one end of the beam, which is clamped horizontally, while the other end of the beam is free. As the liquid film spreads, its weight causes the beam deflection to increase, which in turn enhances the spreading rate of the liquid. This feedback mechanism causes the front position ${sigma}$(t) and the deflection angle at the front ${phi}$(t) to go through a number of different power-law behaviours. For early times, the liquid spreads like a horizontal gravity current, with ${sigma}$(t) = $t^{4/5}$ and ${phi}$(t) = $t^{13/5}$. For intermediate times, the deflection of the beam leads to rapid acceleration of the liquid layer, with ${sigma}$(t) = $t^4$ and ${phi}$(t) = $t^9$. Finally, when the beam has sagged to become almost vertical, the liquid film flows downward with ${sigma}$(t) = $t$ and ${phi}$(t) ~ ${pi}$/2. We demonstrate good agreement between these theoretical predictions and experimental results.
In a shear flow particles migrate to their equilibrium positions in the microchannel. Here we demonstrate theoretically that if particles are inertial, this equilibrium can become unstable due to the Saffman lift force. We derive an expression for the critical Stokes number that determines the onset of instable equilibrium. We also present results of lattice Boltzmann simulations for spherical particles and prolate spheroids to validate the analysis. Our work provides a simple explanation of several unusual phenomena observed in earlier experiments and computer simulations, but never interpreted before in terms of the unstable equilibrium.
We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive force theory. Deformation of helices by viscous flow is well-described by non-linear finite extensibility. Under distributed loading, the pitch distribution is non-uniform and from this, we identify both linear and non-linear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at high flow rate.
This paper presents a theoretical derivation of the empirical Blasius power law correlation for the friction factor. The coefficients in this correlation are shown to be dependent on the Reynolds number. Published experimental data is well correlated. Key words: Blasius, friction factor, turbulence, power law, log-law, wall layer
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