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Research Papers: Fundamental Issues and Canonical Flows

Analysis of Flow Past Oscillatory Cylinders Using a Finite Element Fixed Mesh Formulation

[+] Author and Article Information
Felipe A. González

Departamento de Ingeniería Mecánica,
Universidad de Santiago de Chile,
Av. Bdo. O′Higgins 3363,
Santiago 8320000, Chile

Marcela A. Cruchaga

Departamento de Ingeniería Mecánica,
Universidad de Santiago de Chile,
Av. Bdo. O′Higgins 3363,
Santiago 8320000, Chile
e-mail: marcela.cruchaga@usach.cl

Diego J. Celentano

Departamento de Ingeniería
Mecánica y Metalúrgica,
Pontificia Universidad Católica de Chile,
Av. V. Mackenna 4860,
Santiago 8320000, Chile

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 25, 2016; final manuscript received February 20, 2017; published online May 18, 2017. Assoc. Editor: Elias Balaras.

J. Fluids Eng 139(8), 081202 (May 18, 2017) (16 pages) Paper No: FE-16-1628; doi: 10.1115/1.4036247 History: Received September 25, 2016; Revised February 20, 2017

In this work, we propose a fixed mesh finite element formulation to solve the fluid dynamic on an Eulerian mesh dealing with immersed bodies in motion. The study is focused on the computation of the fluid dynamic forces acting on immersed bodies which strongly depend on the evolution of the vortex shedding. The frequency of vortex detachment for flow past cylinder problems can be modified when the cylinder moves, promoting the modification of the wake of vortices. Synchronization phenomena appear when the frequencies of the resulting flow pattern coincide with the frequency of the imposed body motion. To study this problem, we propose to describe the immersed body surface by a collection of markers that moves according to the imposed body motion. The markers are updated using a Lagrangian scheme. In this framework, a distinct aspect of the present work is the imposition of the body velocity as an internal immersed boundary condition for the fluid dynamic analysis. To transfer the body velocity to the fluid along the fluid–solid interface, a restriction on the flow velocity is added into the weak form of the Navier–Stokes equations by means of a penalty technique. This work encompasses the study of flows past a crossflow, streamwise, and rotational oscillating cylinders. The results are satisfactorily compared with numerical data reported in the literature, showing a proper behavior for the analysis of long-term vibrating systems at low Reynolds numbers.

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Figures

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Fig. 1

Sketch of the numerical approach: body surface defined by markers (a), velocity imposition at edge level (b), and extended markers to compute the hydrodynamics forces (c)

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Fig. 2

Flow past a cylinder problem description: geometry and boundary conditions (a), crossflow oscillating cylinder (b), streamwise oscillating cylinder (c), and rotationally oscillating cylinder (d)

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Fig. 3

Time variation of the drag coefficient (a) and lift coefficient (b); power spectral density (PSD) of the lift coefficient (c) and phase diagram (d) for F = 0.5

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Fig. 4

Vorticity contours of the flow around an oscillatory cylinder in a crossflow over one forced period T0 for F = 0.5

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Fig. 5

Time variation of the drag coefficient (a) and lift coefficient (b); PSD of the lift coefficient (c) and phase diagram (d) for F = 0.9

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Fig. 6

Time variation of the drag coefficient (a) and lift coefficient (b); PSD of the lift coefficient (c) and phase diagram (d) for F = 1.1

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Fig. 7

Vorticity contours of the flow around an oscillatory cylinder in a crossflow over one forced period T0 for F = 1.1

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Fig. 8

Time variation of the drag coefficient (a) and lift coefficient (b); PSD of the lift coefficient (c) and phase diagram (d) for F = 1.5

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Fig. 9

Drag coefficient (a), lift coefficient (b), spectral power density of the CL (c), and phase diagram (d) for a frequency ratio F = 1.0

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Fig. 10

Vorticity field every two forced oscillation periods T0, for F = 1.0

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Fig. 11

Evolution of the aerodynamic drag (a) and lift (b) coefficients, spectral frequency density of the CL (c), and phase diagram (d) for a frequency ratio F = 1.5

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Fig. 12

Drag coefficient (a), lift coefficient (b), spectral power density of the CL (c), and phase diagram (d) for a frequency ratio F = 2.0

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Fig. 13

Vorticity outline in two forced oscillation periods T0, for F = 2.0

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Fig. 14

Evolution of the aerodynamic drag (a) and lift (b) coefficients, spectral frequency density of the CL (c), and phase diagram (d) for a frequency ratio F = 2.5

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Fig. 15

Evolution of the aerodynamic drag (a) and lift (b) coefficients, spectral density of the frequency of the CL (c), and phase diagram (d) for a frequency ratio F = 1.5

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Fig. 16

Drag (a) and lift (b) coefficients, spectral power density of the CL (c), and phase diagram (d) for a frequency ratio F = 3.8

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Fig. 17

Vorticity field in a forced oscillation period T0, for F = 3.8

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Fig. 18

Evolution of the aerodynamic drag (a) and lift (b) coefficients, spectral density of the frequency of the CL (c), and phase diagram (d) for a frequency ratio F = 6.4

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Fig. 19

Vorticity field for multiple forced oscillation periods T0, at F = 6.4

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Fig. 20

Drag (a) and lift (b) coefficients, spectral power density of the CL (c), and phase diagram (d) for a frequency ratio F = 8.5

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