A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

Sen, Pratima; Carpenter, Peter W.; Hegde, S.; Davies, Christopher

doi:10.1017/s0022112008005545

Cited by 5 publications

(5 citation statements)

References 31 publications

(73 reference statements)

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“…Flow through channels composed of multiple compliant compartments (or over multiple compliant plates) also has potential application in turbulent-drag reduction, where it has been hypothesized that arranging several compliant panels in series could be used as part of a device to delay the onset of laminar-turbulent transition [8,9,37], based on initial experiments conducted by Kramer in the 1960s [24].…”

Section: Introductionmentioning

confidence: 99%

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Stewart¹,

Foss²

2019

ANZIAM J.

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We consider a theoretical model for the flow of Newtonian fluid through a long flexible-walled channel which is formed from four compliant and rigid compartments arranged alternately in series. We drive the flow using a fixed upstream flux and derive a spatially one-dimensional model using a flow profile assumption. The compliant compartments of the channel are assumed subject to a large external pressure, so the system admits a highly collapsed steady state. Using both a global (linear) stability eigensolver and fully nonlinear simulations, we show that these highly collapsed steady states admit a primary global oscillatory instability similar to observations in a single channel. We also show that in some regions of the parameter space the system admits a secondary mode of instability which can interact with the primary mode and lead to significant changes in the structure of the neutral stability curves. Finally, we apply the predictions of this model to the flow of blood through the central retinal vein and examine the conditions required for the onset of self-excited oscillation. We show that the neutral stability curve of the primary mode of instability discussed above agrees well with canine experimental measurements of the onset of retinal venous pulsation, although there is a large discrepancy in the oscillation frequency.

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Section: Introductionmentioning

confidence: 99%

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Stewart¹,

Foss²

2019

ANZIAM J.

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“…Having outlined the model ( § 2), in § 3.1 we solve Orr-Sommerfeld problems to characterize the full spectra of local modes in both the rigid and compliant channel segments, without making any long-wavelength or high-frequency approximations. We then build truncated modal expansions in each segment, matching these across junctions using a formalism proposed by Manuilovich (2004); this is better suited to the present problem than the wave-driver approach of Sen et al (2009). In addition to recovering small-amplitude, high-frequency sloshing, we use this approach in § 4 to track the mode 1 neutral curve to relatively low Reynolds numbers (and low frequencies), demonstrating how hydrodynamic modes contribute increasingly to the global instability.…”

Section: Introductionmentioning

confidence: 99%

Sloshing and slamming oscillations in a collapsible channel flow

et al. 2010

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We consider laminar high-Reynolds-number flow through a finite-length planar channel, where a portion of one wall is replaced by a thin massless elastic membrane that is held under longitudinal tension T and subject to a linear external pressure distribution. The flow is driven by a fixed pressure drop along the full length of the channel. We investigate the global stability of two-dimensional Poiseuille flow using a method of matched local eigenfunction expansions, which is compared to direct numerical simulations. We trace the neutral stability curve of the primary oscillatory instability of the system, illustrating a transition from high-frequency 'sloshing' oscillations at high T to vigorous 'slamming' motion at low T . Small-amplitude sloshing at high T can be captured using a low-order eigenmode truncation involving four surface-based modes in the compliant segment of the channel coupled to Womersley flow in the rigid segments. At lower tensions, we show that hydrodynamic modes increasingly contribute to the global instability, and we demonstrate a change in the mechanism of energy transfer from the mean flow, with viscous effects being destabilizing. Simulations of finite-amplitude oscillations at low T reveal a generic slamming motion, in which the flexible membrane is drawn close to the opposite rigid wall before recovering rapidly. A simple model is used to demonstrate how fluid inertia in the downstream rigid channel segment, coupled to membrane curvature downstream of the moving constriction, together control slamming dynamics.

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“…They have shown good agreement between their results and those obtained from the direct numerical simulation (DNS) results of Davies and Carpenter [2]. The method developed by Sen et al [3] is fairly generic, and, the same methodology is applied here across the junction between rigid and porous panels. Furthermore, Fransson and Alfredsson [4] have given the stability analysis for channel flow but they have not reported any porous developing region.…”

Section: Introductionmentioning

confidence: 65%

“…(14) is solved using a procedure described in a companion paper by Sen et al [5]. The jump in the amplitude at the rigid-porous junction is calculated by using a procedure discussed by Sen et al [3].…”

Section: Developing Flow Region On a Porous Wallmentioning

confidence: 99%

Stability of Flow Past Alternate Rigid and Porous Panels in Boundary Layer Flow and in Channel Flow

Paul

Sen

Hegde

2015

Procedia Engineering

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Propagation of two-dimensional small amplitude Tollmien-Schlichting (TS) waves has been investigated over a rigid panel followed by a porous panel in the presence of cross-flow. In the present work boundary layer flow over alternate rigid-porous panels in which suction is applied through the porous panel is investigated.Also investigated is the problem of flow past alternate rigid and porous panels with cross flow. A general space marching solution has been discussed for calculating the mean velocity profile for the above case, in the developing region of mean flow in the porous panel, following the rigid-porous junction. Numerical solutions are obtained using a finite difference method for the suitably simplified Navier Stokes equations, using appropriate boundary conditions. Detailed two-dimensional analyses have been done for the disturbance waves using both the quasi-parallel (QP) approximation, and more accurately, using the non-parallel (NP) approach. The non-parallel approach has been carried out over the developing mean-flow region of the porous panel, following the rigid-porous junction.Numerical solutions have been obtained by finite difference procedures. In some of the cases results have been validated with the available literature. Finally, the jumps in the amplitude of the disturbance waves across the rigidporous junction were calculated using the theory of Sen et al. [6].The important outcome from this work is in optimizing the length of the porous panel, following the rigid-porous junction. It is seen that, as compared to the length required to approach the asymptotic mean flow state to within 99%, only a very short porous panel length is sufficient to stabilize the disturbances.Hence, it is foreseen that alternate long rigid panels, with in-between short porous panels, could be a very effective way of stabilizing the disturbances, and thus delaying laminar to turbulent transition. c 2015 Published by Elsevier Ltd. Peer-review under repsonsibility of organising committee of the 6th BSME International Conference on Thermal Engineering (ICTE 2014)

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A wave driver theory for vortical waves propagating across junctions with application to those between rigid and compliant walls

Cited by 5 publications

References 31 publications

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Self-Excited Oscillations in a Collapsible Channel With Applications to Retinal Venous pulsation

Sloshing and slamming oscillations in a collapsible channel flow

Stability of Flow Past Alternate Rigid and Porous Panels in Boundary Layer Flow and in Channel Flow

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