A fast Chebyshev method for simulating flexible-wing propulsion

Moore, Nicholas J.

doi:10.1016/j.jcp.2017.05.052

Cited by 24 publications

(53 citation statements)

References 89 publications

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“…Various groups have conducted numerical simulations of the Navier-Stokes equations coupled to an immersed body's dynamics, and have thus studied flapping wings [51][52][53][54][55] and deformable bodies with more realistic fish-like kinematics [56][57][58][59][60][61][62][63]. Hemelrijk et al [64] and Daghooghi et al [65] modeled a fish school by numeri-cally simulating a swimmer with doubly-periodic boundary conditions in 2D and 3D, respectively, and found that swimmers move faster in schools than in isolation.…”

Section: Introductionmentioning

confidence: 99%

Lattices of Hydrodynamically Interacting Flapping Swimmers

2019

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Fish schools and bird flocks exhibit complex collective dynamics whose self-organization principles are largely unknown. The influence of hydrodynamics on such collectives has been relatively unexplored theoretically, in part due to the difficulty in modeling the temporally long-lived hydrodynamic interactions between many dynamic bodies. We address this through a novel discrete-time dynamical system (iterated map) that describes the hydrodynamic interactions between flapping swimmers arranged in one-and two-dimensional lattice formations. Our 1D results exhibit good agreement with previously published experimental data, in particular predicting the bistability of schooling states and new instabilities that can be probed in experimental settings. For 2D lattices, we determine the formations for which swimmers optimally benefit from hydrodynamic interactions. We thus obtain the following hierarchy: while a side-by-side single-row "phalanx" formation offers a small improvement over a solitary swimmer, 1D in-line and 2D rectangular lattice formations exhibit substantial improvements, with the 2D diamond lattice offering the largest hydrodynamic benefit. Generally, our self-consistent modeling framework may be broadly applicable to active systems in which the collective dynamics is primarily driven by a fluid-mediated memory. arXiv:1904.13045v2 [cond-mat.soft] 1 Nov 2019 II. SIMPLE MODEL OF AN IN-LINE FORMATIONWe first consider the simplest model for a school: an infinite line of swimmers modeled as heaving rigid wings driven periodically with prescribed vertical po-

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Section: Introductionmentioning

confidence: 99%

Lattices of Hydrodynamically Interacting Flapping Swimmers

2019

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“…Here, the setup and assumptions are the same as in Moore [2017]. Consider a two-dimensional, inextensible elastic plate of length L and thickness d. The plate is thin (d L), and is transversely deflected a small amount Y from its neutral position, with its slope Y x 1.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…where C T S is the leading edge suction force (formula given in Moore [2017]), and the power input is…”

Section: Problem Descriptionmentioning

confidence: 99%

Distributed flexibility in inertial swimmers

Floryan

Rowley

2020

J. Fluid Mech.

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We study a linear inviscid model of a passively flexible swimmer with distributed flexibility, calculating its propulsive performance and optimal distributions of flexibility. The frequencies of actuation and mean stiffness ratios we consider span a large range, while the mass ratio is fixed to a low value representative of swimmers. We present results showing how the trailing edge deflection, thrust coefficient, power coefficient, and efficiency vary with frequency, mean stiffness, and stiffness distribution. Swimmers with distributed flexibility have the same qualitative features as those with uniform flexibility. Significant gains in thrust can be made, however, by tuning the stiffness such that a resonant response is triggered, or by concentrating stiffness towards the leading edge if resonance cannot be triggered. To minimize power, the opposite is true. Meaningful gains in efficiency can be made at low frequencies by concentrating stiffness away from the leading edge, since doing so induces efficient travelling wave kinematics. We also consider the effects of a finite Reynolds number in the form of streamwise drag. The drag adds an offset to the net thrust produced by the swimmer, causing efficiency-maximizing distributions of flexibility to tend towards thrust-maximizing ones, representative of what is found in nature.

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“…Here, the setup and assumptions are the same as in Moore (2017). Consider a twodimensional, inextensible elastic plate of length L and thickness d. The plate is thin (d L), and is transversely deflected a small amount Y from its neutral position, with its slope Y x 1.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…The leading edge suction force used in Moore (2017) is the limit of the suction force on a leading edge of small but finite radius of curvature, in the limit that the radius tends to zero. The leading edge suction force is a reasonable model of the actual flow when it is attached (Saffman 1992), so we have chosen to include it.…”

Section: Problem Descriptionmentioning

confidence: 99%

Clarifying the relationship between efficiency and resonance for flexible inertial swimmers

Floryan¹,

Rowley²

2018

J. Fluid Mech.

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We study a linear inviscid model of a passively flexible swimmer, calculating its propulsive performance, eigenvalues, and eigenfunctions with an eye towards clarifying the relationship between efficiency and resonance. The frequencies of actuation and stiffness ratios we consider span a large range, while the mass ratio is mostly fixed to a low value representative of swimmers. We present results showing how the trailing edge deflection, thrust coefficient, power coefficient, and efficiency vary in the stiffness-frequency plane. The trailing edge deflection, thrust coefficient, and power coefficient show sharp ridges of resonant behaviour for mid-to-high frequencies and stiffnesses, whereas the efficiency does not show resonant behaviour anywhere. For low frequencies and stiffnesses, the resonant peaks smear together and the efficiency is high. In this region, flutter modes emerge, inducing travelling wave kinematics which make the swimmer more efficient. We also consider the effects of a finite Reynolds number in the form of streamwise drag. The drag adds an offset to the net thrust produced by the swimmer, causing resonant peaks to appear in the efficiency (as observed in experiments in the literature).

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A fast Chebyshev method for simulating flexible-wing propulsion

Cited by 24 publications

References 89 publications

Lattices of Hydrodynamically Interacting Flapping Swimmers

Lattices of Hydrodynamically Interacting Flapping Swimmers

Distributed flexibility in inertial swimmers

Clarifying the relationship between efficiency and resonance for flexible inertial swimmers

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