Dynamics of tethered membranes in inviscid flow

Mavroyiakoumou, Christiana; Alben, Silas

doi:10.1016/j.jfluidstructs.2021.103384

Cited by 8 publications

(9 citation statements)

References 61 publications

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“…if the membrane shape does not change much in the limit , as seems to occur in the first and third columns. However, if the membrane becomes ever wavier as decreases, the frequency may also diverge, consistent with the 2-D tethered membrane data in Mavroyiakoumou & Alben (2021 a ) and the closely related problem of a fixed–free flag with bending rigidity (Alben 2022). The fourth and second columns, respectively, are similar to these cases.…”

Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...supporting

confidence: 83%

“…Unlike the amplitude, the membranes’ shapes and frequencies do not vary much with . In most cases with large () and some cases with moderate (), the frequency approximately scales as , as in the large-amplitude 2-D studies Mavroyiakoumou & Alben (2020, 2021 a ). The scaling can be explained in two or three dimensions by balancing the term in the membrane equation with the other terms, which are independent of .…”

Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...mentioning

confidence: 66%

“…At small the frequency typically plateaus here (in the first and third columns). A different behaviour was seen in 2-D simulations of tethered membranes in Mavroyiakoumou & Alben (2021 a ) which were similar to the 2-D free–free case. There, the frequencies scaled as at small and the shapes had very sharp spatial features that required hundreds of points in the streamwise direction to resolve, much higher resolution than we use here in three dimensions.…”

Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...mentioning

confidence: 80%

“…Section 2 describes our large-amplitude membrane-vortex-sheet model. Unlike our previous work (Mavroyiakoumou & Alben 2020, 2021 b , a ), here, we consider a membrane surface held in a 3-D inviscid flow with 12 different sets of boundary conditions. We solve this nonlinear model using Broyden's method and an unsteady vortex-lattice algorithm.…”

Section: Introductionmentioning

confidence: 99%

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Membrane flutter in three-dimensional inviscid flow

Mavroyiakoumou

Alben

2022

J. Fluid Mech.

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We develop a model and numerical method to study the large-amplitude flutter of rectangular membranes (of zero bending rigidity) that shed a trailing vortex-sheet wake in a three-dimensional (3-D) inviscid fluid flow. We apply small initial perturbations and track their decay or growth to large-amplitude steady-state motions. For 12 combinations of boundary conditions at the membrane edges we compute the stability thresholds and the subsequent large-amplitude dynamics across the three-parameter space of membrane mass density, pretension and stretching rigidity. With free side edges we find good agreement with previous 2-D results that used different discretization methods. We find that the 3-D dynamics in the 12 cases naturally forms four groups based on the conditions at the leading and trailing edges. The deflection amplitudes and oscillation frequencies have scalings similar to those in the 2-D case. The conditions at the side edges, although generally less important, may have small or large qualitative effects on the membrane dynamics – e.g. steady vs unsteady, periodic vs chaotic or the variety of spanwise curvature distributions – depending on the group and the physical parameter values.

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Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...supporting

confidence: 83%

Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...mentioning

confidence: 66%

Section: Membrane Dynamics Across Parameter Space For 12 Boundary Con...mentioning

confidence: 80%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Membrane flutter in three-dimensional inviscid flow

Mavroyiakoumou

Alben

2022

J. Fluid Mech.

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“…We also assume that the motion of the bubble is assigned a priori and does not depend on the fluid dynamics. In a more realistic scenario, the bubble surface deformation would be influenced by the fluid motion, resulting in a two-way coupling as in fluid/membrane interaction problems [31,32].…”

Section: Introductionmentioning

confidence: 99%

A finite-difference ghost-point multigrid method for multi-scale modelling of sorption kinetics of a surfactant past an oscillating bubble

Astuto¹,

Coco²,

Russo³

2022

Preprint

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We propose a method for the numerical solution of a multiscale model describing sorption kinetics of a surfactant around an oscillating bubble. The evolution of the particles is governed by a convection-diffusion equation for the surfactant concentration c, with suitable boundary condition on the bubble surface, which models the action of the short range attractive-repulsive potential acting on them when they get sufficiently close to the surface [1]. In the domain occupied by the fluid, the particles are transported by the fluid motion generated by the bubble oscillations.The method adopted to solve the equation for c is based on a finite-difference scheme on a uniform Cartesian grid and implemented in 2D and 3D axisymmetric domains. We use a level-set function to define the region occupied by the bubble, while the boundary conditions are discretized by a ghost-point technique to guarantee second order accuracy at the curved boundary. The sparse linear system is finally solved with a geometric multigrid technique designed ad-hoc for this specific problem. Several accuracy tests are provided to prove second order accuracy in space and time.The fluid dynamics generated by the oscillating bubble is governed by the Stokes equation solved with a second order accurate method based on a monolithic approach, where the momentum and continuity equations are solved simultaneously. Since the amplitude of the bubble oscillations are very small, a simplified model is presented where the computational bubble is actually steady and its oscillations are represented purely with time-dependent boundary conditions. A numerical comparison with the moving domain model confirms that this simplification is perfectly reasonable for the class of problems investigated in this paper.

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