Hydrodynamic Stability of Flow Through Compliant Channels and Tubes

Kumaran, V.

doi:10.1007/978-94-017-0415-1_5

Cited by 12 publications

(6 citation statements)

References 32 publications

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“…However, we note that axial motion of the free surface can lead to modes of instability not possible in the current configuration. 7,44 For later use, the energy equation associated with Eq. ͑1͒ is given by…”

Section: The Modelmentioning

confidence: 99%

Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer

2010

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We examine the linear stability of two-dimensional Poiseuille flow in a long channel confined by a rigid wall and a massless damped-tensioned membrane. We seek solutions that are periodic in the streamwise spatial direction and time, solving the homogeneous eigenvalue problem using a Chebyshev spectral method and asymptotic analysis. Several modes of instability are identified, including Tollmien-Schlichting ͑TS͒ waves and traveling-wave flutter ͑TWF͒. The eigenmode for neutrally stable downstream-propagating TWF in the absence of wall damping is shown to have a novel asymptotic structure at high Reynolds numbers, not reported in symmetric flexible-walled channels, involving a weak but destabilizing critical layer at the channel centerline where the wave speed is marginally greater than the maximum Poiseuille flow speed. We also show that TS instabilities along the lower branch of the neutral curve are modified remarkably little by wall compliance, but can be either stabilized or destabilized by wall damping. We discuss the energy budget underlying TWF and briefly describe the structure of other flow-induced surface instabilities.

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Section: The Modelmentioning

confidence: 99%

Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer

2010

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“…Several strategies have been proposed for enhancing the mixing rates, including patterning grooves in channel walls (Stroock et al 2002), electro-osmotic flows (Bazant & Squires 2004), multiple bends and converging sections, etc. One method for inducing an instability is to replace the rigid walls of the microtube with a sufficiently soft material (Kumaran 2003). The instability due to flexible walls has been theoretically well studied, but it is fair to say that there is not, as yet, any experimental evidence for the applicability in real systems.…”

Section: Introductionmentioning

confidence: 97%

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

Verma

Kumaran

2011

J. Fluid Mech.

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A flow-induced instability in a tube with flexible walls is studied experimentally. Tubes of diameter 0.8 and 1.2 mm are cast in polydimethylsiloxane (PDMS) polymer gels, and the catalyst concentration in these gels is varied to obtain shear modulus in the range 17-550 kPa. A pressure drop between the inlet and outlet of the tube is used to drive fluid flow, and the friction factor f is measured as a function of the Reynolds number Re. From these measurements, it is found that the laminar flow becomes unstable, and there is a transition to a more complicated flow profile, for Reynolds numbers as low as 500 for the softest gels used here. The nature of the f -Re curves is also qualitatively different from that in the flow past rigid tubes; in contrast to the discontinuous increase in the friction factor at transition in a rigid tube, it is found that there is a continuous increase in the friction factor from the laminar value of 16/Re in a flexible tube. The onset of transition is also detected by a dye-stream method, where a stream of dye is injected into the centre of the tube. It is found that there is a continuous increase of the amplitude of perturbations at the onset of transition in a flexible tube, in contrast to the abrupt disruption of the dye stream at transition in a rigid tube. There are oscillations in the wall of the tube at the onset of transition, which is detected from the laser scattering off the walls of the tube. This indicates that the coupling between the fluid stresses and the elastic stresses in the wall results in an instability of the laminar flow.

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“…Fluid-structure-interaction (FSI) studies span a vast and diverse range of applications -from natural phenomenon such as the fluttering of flags (Shelley & Zhang 2011), phonation (Heil & Hazel 2011), blood flow in arteries (Freund 2014), path of rising bubbles (Ern et al 2012), to the more engineering applications of aircraft stability (Dowell & Hall 2001), vortex induced vibrations (Williamson & Govardhan 2004), compliant surfaces (Riley, Gad-el Hak & Metcalfe 1988;Kumaran 2003) etc. The phenomena that emerge out of an FSI problem often exhibit a highly nonlinear, dynamically rich and complex behaviour with different flow regimes such as fluttering and tumbling of plates falling under gravity (Mittal, Seshadri & Udaykumar 2004), or the unsteady path of rising bubbles (Mougin & Magnaudet 2001;Ern et al 2012).…”

Section: Introductionmentioning

confidence: 99%

On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems

2020

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Hydrodynamic Stability of Flow Through Compliant Channels and Tubes

Cited by 12 publications

References 32 publications

Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer

Local instabilities of flow in a flexible channel: Asymmetric flutter driven by a weak critical layer

A dynamical instability due to fluid–wall coupling lowers the transition Reynolds number in the flow through a flexible tube

On the linear global stability analysis of rigid-body motion fluid–structure-interaction problems

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