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Title: Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability

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 viscoelastic 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. more »« less

Currier, Todd M.; Carleton, Adrian G.; Modarres-Sadeghi, Yahya(
, Journal of Fluid Mechanics)

null
(Ed.)

We present the dynamics of a hydrofoil free to oscillate in a plane as it interacts with vortices that are shed from a cylinder placed upstream. We consider cases where the cylinder is (i) fixed, (ii) forced to rotate constantly in one direction or (iii) forced to rotate periodically. When the upstream cylinder is fixed, at lower reduced velocities, the hydrofoil oscillates with a frequency equal to the frequency of vortices shed from the cylinder, and at higher reduced velocities with a frequency equal to half of the shedding frequency. When we force the cylinder to rotate in one direction, we control its wake and directly influence the response of the hydrofoil. When the rotation rate goes beyond a critical value, the vortex shedding in the cylinder's wake is suppressed and the hydrofoil is moved to one side and remains mainly static. When we force the cylinder to rotate periodically, we control the frequency of vortex shedding, which will be equal to the rotation frequency. Then at lower rotation frequencies, the hydrofoil interacts with one of the vortices in its oscillation path in the positive crossflow (transverse) direction, and with the second vortex in the negative crossflow direction, resulting in a 2:1 ratio between its inline and crossflow oscillations and a figure-eight trajectory. At higher rotation frequencies, the hydrofoil interacts with both shed vortices on its positive crossflow path and again in its negative crossflow path, resulting in a 1:1 ratio between its inline and crossflow oscillations and a linear trajectory.

Hughes, Michael; Gopalarathnam, Ashok; Bryant, Matthew(
, Proceedings of the Online Symposium on Aeroelasticity, Fluid-Structure Interaction, and Vibrations)

Periodic upstream flow disturbances from a bluff body have recently been shown to be able to modulate and annihilate limit cycle oscillations (LCOs) in a downstream aeroelastic wing section under certain conditions. To further investigate these phenomena, we have implemented a controllable wind tunnel disturbance generator to enable quantification of the parameter ranges under which these nonlinear interactions can occur. This disturbance generator, consisting of a pitch-actuated cylinder with an attached splitter plate, can be oscillated to produce a von Karman type wake with vortex shedding frequency equal to the oscillation frequency over a range of frequencies around the natural shedding frequency of the cylinder alone. At vortex shedding frequencies away from the LCO frequency of the wing, forced oscillations were observed in the wing, but the wing did not enter self-sustaining LCOs. However, when disturbances were introduced near the LCO frequency, the initially static downstream wing entered self-sustaining oscillations in the presence of the incoming vortices, and these LCOs persisted when the disturbance generator was stopped. Annihilation of the wing LCOs was also observed disturbance vortices were introduced upstream of the wing in LCO.

The rising global trend to reduce dependence on fossil fuels has provided significant
motivation toward the development of alternative energy conversion methods
and new technologies to improve their efficiency. Recently, oscillating energy harvesters
have shown promise as highly efficient and scalable turbines, which can be
implemented in areas where traditional energy extraction and conversion are either
unfeasible or cost prohibitive. Although such devices are quickly gaining popularity,
there remain a number of hurdles in the understanding of their underlying fluid
dynamics phenomena.
The ability to achieve high efficiency power output from oscillating airfoil energy
harvesters requires exploitation of the complexities of the event of dynamic stall.
During dynamic stall, the oncoming flow separates at the leading edge of the airfoil
to form leading ledge vortex (LEV) structures. While it is well known that LEVs
play a significant role in aerodynamic force generation in unsteady animal flight
(e.g. insects and birds), there is still a need to further understand their spatiotemporal
evolution in order to design more effective energy harvesting enhancement
mechanisms.
In this work, we conduct extensive experimental investigations to shed-light
on the flow physics of a heaving and pitching airfoil energy harvester operating
at reduced frequencies of k = fc=U1 = 0.06-0.18, pitching amplitude of 0 = 75
and heaving amplitude of h0 = 0:6c. The experimental work involves the use
of two-component particle image velocimetry (PIV) measurements conducted in
a wind tunnel facility at Oregon State University. Velocity fields obtained from
the PIV measurements are analyzed qualitatively and quantitatively to provide a
description of the dynamics of LEVs and other flow structures that may be present
during dynamic stall. Due to the difficulties of accurately measuring aerodynamic
forces in highly unsteady flows in wind tunnels, a reduced-order model based on
the vortex-impulse theory is proposed for estimating the aerodynamic loadings
and power output using flow field data. The reduced-order model is shown to be
dominated by two terms that have a clear physical interpretation: (i) the time
rate of change of the impulse of vortical structures and (ii) the Kutta-Joukowski
force which indirectly represents the history effect of vortex shedding in the far
wake. Furthermore, the effects of a bio-inspired flow control mechanism based on
deforming airfoil surfaces on the flow dynamics and energy harvesting performance
are investigated.
The results show that the aerodynamic loadings, and hence power output, are
highly dependent on the formation, growth rate, trajectory and detachment of the
LEV. It is shown that the energy harvesting efficiency increases with increasing
reduced frequency, peaking at 25% when k = 0.14, agreeing very well with published
numerical results. At this optimal reduced frequency, the time scales of the
LEV evolution and airfoil kinematics are matched, resulting in highly correlated
aerodynamic load generation and airfoil motion. When operating at k > 0:14, it
is shown that the aerodynamic moment and airfoil pitching motion become negatively
correlated and as a result, the energy harvesting performance is deteriorated.
Furthermore, by using a deforming airfoil surface at the leading and trailing edges,
the peak energy harvesting efficiency is shown to increase by approximately 17%
and 25% relative to the rigid airfoil, respectively. The performance enhancement
is associated with enhanced aerodynamic forces for both the deforming leading
and trailing edges. In addition, The deforming trailing edge airfoil is shown to
enhance the correlation between the aerodynamic moment and pitching motion at
higher reduced frequencies, resulting in a peak efficiency at k = 0:18 as opposed
to k = 0:14 for the rigid airfoil.

Dey, Anita A.; Modarres-Sadeghi, Yahya; Rothstein, Jonathan P.(
, Journal of Fluid Mechanics)

It is well known that when a flexible or flexibly mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices. Here, we show for the first time that fluid–structure interactions can also be observed when the fluid is viscoelastic. For viscoelastic fluids, a flexible structure can become unstable in the absence of fluid inertia, at infinitesimal Reynolds numbers, due to the onset of a purely elastic flow instability. Nonlinear periodic oscillations of the flexible structure are observed and found to be coupled to the time-dependent growth and decay of viscoelastic stresses in the wake of the structure.

Abstract Large-eddy simulations (LES) are employed to investigate the role of time-varying currents on the form drag and vortex dynamics of submerged 3D topography in a stratified rotating environment. The current is of the form U c + U t sin(2 πf t t ), where U c is the mean, U t is the tidal component, and f t is its frequency. A conical obstacle is considered in the regime of low Froude number. When tides are absent, eddies are shed at the natural shedding frequency f s , c . The relative frequency is varied in a parametric study, which reveals states of high time-averaged form drag coefficient. There is a twofold amplification of the form drag coefficient relative to the no-tide ( U t = 0) case when lies between 0.5 and 1. The spatial organization of the near-wake vortices in the high drag states is different from a Kármán vortex street. For instance, the vortex shedding from the obstacle is symmetric when and strongly asymmetric when . The increase in form drag with increasing stems from bottom intensification of the pressure in the obstacle lee which we link to changes in flow separation and near-wake vortices.

Dey, Anita A., Modarres-Sadeghi, Yahya, Lindner, Anke, and Rothstein, Jonathan P. Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability. Retrieved from https://par.nsf.gov/biblio/10198027. Soft Matter 16.5 Web. doi:10.1039/C9SM01794A.

Dey, Anita A., Modarres-Sadeghi, Yahya, Lindner, Anke, & Rothstein, Jonathan P. Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability. Soft Matter, 16 (5). Retrieved from https://par.nsf.gov/biblio/10198027. https://doi.org/10.1039/C9SM01794A

Dey, Anita A., Modarres-Sadeghi, Yahya, Lindner, Anke, and Rothstein, Jonathan P.
"Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability". Soft Matter 16 (5). Country unknown/Code not available. https://doi.org/10.1039/C9SM01794A.https://par.nsf.gov/biblio/10198027.

@article{osti_10198027,
place = {Country unknown/Code not available},
title = {Oscillations of a cantilevered micro beam driven by a viscoelastic flow instability},
url = {https://par.nsf.gov/biblio/10198027},
DOI = {10.1039/C9SM01794A},
abstractNote = {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 viscoelastic 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.},
journal = {Soft Matter},
volume = {16},
number = {5},
author = {Dey, Anita A. and Modarres-Sadeghi, Yahya and Lindner, Anke and Rothstein, Jonathan P.},
}

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