Self-propulsion of a counter-rotating cylinder pair in a viscous fluid

Rees, Wim M. van; Novati, Guido; Koumoutsakos, Petros

doi:10.1063/1.4922314

Cited by 15 publications

(7 citation statements)

References 21 publications

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“…Increase of both the center velocity and the jet thrust due to the widening gap are also shown in a previous study (Figures 5 and 6 in Ref. 13). One implication of this result is the reversal of the overall thrust direction for the cylinder pair.…”

Section: Flow Behaviorsupporting

confidence: 85%

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An Analytical Approximation for the Local Flow Between Counter-Rotating Cylinder Pair

Ogretim

2020

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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Flow around a pair of cylinders is of interest for various applications. Especially with the development of self-propelled, autonomous vehicles, this topic has gained further importance. There have been experimental, numerical and, to a much less extent, theoretical studies of this flow and its implications on the cylinders. However, the complexity of the problem does not allow a general solution, and case-by-case solutions have been produced. In this study, a theoretical approach was embraced, in which differential geometry is employed to model the local flow between a pair of counter-rotating cylinders. In order to obtain practical formulae for a steady, laminar, incompressible flow, Navier-Stokes equations were simplified and expressed in a new, parabolic coordinate system. Then, further simplifications due to the symmetrical nature of the problem were applied. Finally, boundary conditions were imposed while performing the integrals, and the desired equations for velocity and pressure were reached. Unlike the previous studies that are limited to very slow flows, the equations obtained in this study are applicable in the entire incompressible, laminar regime, albeit only between the cylinders. Using these equations, the effects of the rotation speed, cylinder spacing and cylinder radius were studied and presented graphically.

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Section: Flow Behaviorsupporting

confidence: 85%

“…Van Rees et al [13] performed a very detailed study of the self-propulsion of the counter-rotating cylinder pair in stationary fluid. Although they imposed no free stream flow velocity, their study also revealed the two different mechanisms of self-propulsion, depending on the distance between the cylinders and the rotational speed.…”

Section: Introductionmentioning

confidence: 99%

An Analytical Approximation for the Local Flow Between Counter-Rotating Cylinder Pair

Ogretim

2020

Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler

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“…22,28,29 A number of studies have relied on this technique for coupling simulations of self-propelled swimmers with machine learning algorithms, 30 and for design-optimization of swimmer morphology and kinematics. [31][32][33][34] These studies demonstrate the capability of the penalization algorithm to handle multiple, complex, and deforming geometries with relative ease. Nonetheless, these studies have not overcome the difficulty of determining pointwise forces exerted on a solid surface.…”

mentioning

confidence: 79%

Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization

Verma

Abbati

Novati

et al. 2017

Numerical Methods in Fluids

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Summary The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self‐propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body‐fitted grids are used. Alternatively, such simulations may use penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow‐induced forces on the surface of both rigid and deforming bodies, in simulations using remeshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree‐code algorithm. The viscous forces are determined by evaluating the strain‐rate tensor on the surface of deforming bodies, and on a “lifted” surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow‐induced surface forces. The capabilities of our method are demonstrated using simulations of self‐propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.

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“…Beyond this work, we believe that the simplicity of the 3D cylinder pair, both in its geometry and actuation, makes it an attractive model system for both theoretical studies and practical applications of low Reynolds number applications. Different extensions can be easily examined, such as investigating unsteady gaits in the inertial regime 13 , employing three or more cylinders and analyzing their optimal configuration in 3D, and broadening to applications beyond locomotion, by using the flow induced by the counter-rotating cylinders for sensing and mixing.…”

Section: Discussionmentioning

confidence: 99%

“…By changing the reference frame, this result can also be found in the century-old work by Jeffery 12 . The behavior of the counter-rotating cylinder pair in Reynolds numbers of O(10)-O(100) was undertaken in van Rees, Novati, and Koumoutsakos 13 by numerically solving the Navier-Stokes equations.…”

Section: Introductionmentioning

confidence: 99%

Locomotion of a rotating cylinder pair with periodic gaits at low Reynolds numbers

Rees

2020

Physics of Fluids

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We consider the periodic gaits of a microswimmer formed by two rotating cylinders, placed apart at a fixed width. Through a combination of theoretical arguments and numerical simulations, we derive semi-analytic expressions for system's instantaneous translational and rotational velocities, as a function of the rotational speeds of each cylinder. We can then integrate these relations in time to find the speed and efficiency of the swimmer for any imposed gait. Here we focus particularly on identifying the periodic gaits that lead to the highest efficiency. To do so, we consider three stroke parametrizations in detail: alternating strokes, where only one cylinder rotates at a time; titled rectangle strokes, that combine co-and counter-rotation phases; and smooth strokes represented through a set of Fourier series coefficients. For each parametrization we compute maximum efficiency solutions using a numerical optimization approach. We find that the parameters of the global optimum, and the associated efficiency value, depend on the average mechanical input power. The efficiency asymptotes towards that of a steadily counter-rotating cylinder pair as the input power increases. Finally, we address a possible three-dimensional extension of this system by evaluating the efficiency of a counterrotating three-dimensional (3D) cylinder pair with spherical end caps. We conclude that the counter-rotating cylinder pair combines competitive efficiency values and offer high versatility with simplicity of geometry and actuation, and thus could be a possible basis for engineered microswimmers.

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Self-propulsion of a counter-rotating cylinder pair in a viscous fluid

Cited by 15 publications

References 21 publications

An Analytical Approximation for the Local Flow Between Counter-Rotating Cylinder Pair

An Analytical Approximation for the Local Flow Between Counter-Rotating Cylinder Pair

Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization

Locomotion of a rotating cylinder pair with periodic gaits at low Reynolds numbers

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