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Research Papers

Fluid–Structure Interaction Simulation of Vortex-Induced Vibration of a Flexible Hydrofoil

[+] Author and Article Information
Abe H. Lee

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802
e-mail: abelee5084@gmail.com

Robert L. Campbell, Brent A. Craven

Applied Research Laboratory;Department of Mechanical and
Nuclear Engineering,
The Pennsylvania State University,
University Park, PA 16802

Stephen A. Hambric

Applied Research Laboratory,
The Pennsylvania State University,
University Park, PA 16802

1Corresponding author.

2Current address: Division of Applied Mechanics, Office of Science and Engineering Laboratories, Center for Devices and Radiological Health, U.S. Food and Drug Administration, Silver Spring, MD.

Contributed by the Noise Control and Acoustics Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received December 13, 2015; final manuscript received April 5, 2017; published online 30 May, 2017. Assoc. Editor: Marco Amabili.

J. Vib. Acoust 139(4), 041001 (May 30, 2017) (12 pages) Paper No: VIB-15-1521; doi: 10.1115/1.4036453 History: Received December 13, 2015; Revised April 05, 2017

Abstract

Fluid–structure interaction (FSI) is investigated in this study for vortex-induced vibration (VIV) of a flexible, backward skewed hydrofoil. An in-house finite element structural solver finite element analysis nonlinear (FEANL) is tightly coupled with the open-source computational fluid dynamics (CFD) library openfoam to simulate the interaction of a flexible hydrofoil with vortical flow structures shed from a large upstream rigid cylinder. To simulate the turbulent flow at a moderate computational cost, hybrid Reynolds-averaged Navier–Stokes–large eddy simulation (RANS–LES) is used. Simulations are first performed to investigate key modeling aspects that include the influence of CFD mesh resolution and topology (structured versus unstructured mesh), time-step size, and turbulence model (delayed-detached-eddy-simulation and $k−ω$ shear stress transport-scale adaptive simulation). Final FSI simulations are then performed and compared against experimental data acquired from the Penn State-ARL 12 in water tunnel at two flow conditions, 2.5 m/s and 3.0 m/s, corresponding to Reynolds numbers of 153,000 and 184,000 (based on the cylinder diameter), respectively. Comparisons of the hydrofoil tip-deflections, reaction forces, and velocity fields (contours and profiles) show reasonable agreement between the tightly coupled FSI simulations and experiments. The primary motivation of this study is to assess the capability of a tightly coupled FSI approach to model such a problem and to provide modeling guidance for future FSI simulations of rotating propellers in crashback (reverse propeller operation).

Figures

Fig. 1

Top: schematic of the Penn State ARL 12 in water tunnel test section. Bottom: schematic of the water tunnel with walls removed around the test section to show the cylinder and downstream hydrofoil.

Fig. 2

Partitioned FSI algorithm based on a fixed-point iteration and under-relaxation for tightly coupled solutions [6]. u is the structure’s displacement, ω is the under-relaxation coefficient, and ε is the convergence criterion.

Fig. 3

FE model of the hydrofoil and load cell: left: FE model and right: the fundamental in-vacuo mode at 35.7 Hz obtained from FE modal analysis. The fundamental mode acts like cantilevered bending in the y-direction (lift direction). This is the dominant mode excited by the shed vortices in the wake of the upstream cylinder.

Fig. 4

Setup of the overlay mesh motion model inside the water tunnel test section. Tunnel walls are removed to show the overlay model and hydrofoil.

Fig. 5

Contours of instantaneous velocity magnitude with UTunnel = 2.5 m/s using the 20 M cell unstructured mesh: top: DDES and bottom: k−ω SST–SAS

Fig. 6

Force coefficient time histories on the cylinder from DDES and k−ω SST–SAS simulations using the 20 M cell unstructured mesh at UTunnel=2.5 m/s

Fig. 7

Force time histories on the hydrofoil from DDES and k−ω SST–SAS simulations using the 20 M cell unstructured mesh at UTunnel=2.5 m/s

Fig. 8

Contours of instantaneous velocity magnitude (in units of m/s) from unstructured meshes: 20 M and 40 M cells. Tunnel inlet flow speed is 2.5 m/s.

Fig. 9

Contours of instantaneous velocity magnitude (in units of m/s) from structured meshes: 3.9 M, 10 M, and 15 M cells. Tunnel inlet flow speed is 2.5 m/s.

Fig. 10

Contours of the magnitude of time-averaged velocity (in units of m/s) from unstructured meshes: 20 M and 40 M cells. Tunnel inlet flow speed is 2.5 m/s. ΔT is the duration of time-averaging.

Fig. 11

Contours of the magnitude of time-averaged velocity (in units of m/s) from structured meshes: 3.9 M, 20 M, and 40 M cells. Tunnel inlet flow speed is 2.5 m/s. ΔT is the duration of time-averaging.

Fig. 12

Visualization of instantaneous velocity magnitude (m/s) and von Mises stress (Pa) on the hydrofoil surface and load cell at time t = 2.5 s with UTunnel  = 3.0 m/s

Fig. 13

Time-averaged velocity magnitude (in units of m/s). Top: UTunnel = 2.5 m/s and bottom: UTunnel = 3.0 m/s. Duration of time-averaging is approximately 2.4 s.

Fig. 14

Time histories of the applied fluid force integrated over the wetted surface of the hydrofoil. Top: UTunnel = 2.5 m/s and bottom: UTunnel = 3.0 m/s.

Fig. 15

Time histories of the hydrofoil tip deflection in the y (lift) direction: top: UTunnel = 2.5 m/s and bottom: UTunnel = 3.0 m/s. Note that the second y-axis (on the right) is the tip deflection normalized by the hydrofoil chord length.

Fig. 16

Time histories of the reaction force at the root of the load cell. Top: UTunnel = 2.5 m/s and bottom: UTunnel = 3.0 m/s.

Fig. 17

Top: static pressure probe locations in the water tunnel test section (viewed from the top) from CFD simulations; x = 0.225 m, 0.329 m, and 0.538 m correspond to the probe locations used in the experiments. Bottom: schematic of the water tunnel test section including the cylinder, tunnel wall, and hydrofoil viewed from the top. Particle image velocimetry (PIV) measurements were acquired at z = 188 mm (hydrofoil midspan) within the dashed box, and the dots are the locations where velocity time traces were recorded.

Fig. 18

Contour plots of the time-averaged streamwise (x) velocity on a horizontal plane at z = 0.188 m (midspan of the hydrofoil). Top: FSI simulation scaled by UTunnel = 3.00 m/s and bottom: PIV data scaled by UTunnel = 2.83 m/s. Note that, in the bottom-right region of the hydrofoil plot, PIV data are missing due to a shadow in the experiment.

Fig. 19

Contour plots of the RMS of the fluctuating component of the cross-stream velocity on a horizontal plane at z = 0.188 m (midspan of the hydrofoil). Top: FSI simulation scaled by UTunnel = 3.00 m/s and bottom: PIV data scaled by UTunnel = 2.83 m/s. Note that, in the bottom-right region of the hydrofoil plot, PIV data are missing due to a shadow in the experiment.

Fig. 20

Mean component of the time-averaged streamwise velocity profiles. Top: FSI simulation scaled by UTunnel = 3.00 m/s and bottom: averaged LDV data from all flow conditions (UTunnel = 1.86, 2.30, 2.56, 2.65, and 2.83 m/s). The LDV data were normalized by the corresponding tunnel flow speed before obtaining the average results.

Fig. 21

Fluctuating component of the time-averaged cross-stream velocity profiles. Top: FSI simulation scaled by UTunnel = 3.00 m/s and bottom: averaged LDV data from all flow conditions (UTunnel = 1.86, 2.30, 2.56, 2.65, and 2.83 m/s). The LDV data were normalized by the corresponding tunnel flow speed before obtaining the average results.

Fig. 22

Tip deflection time histories from FSI simulations at UTunnel = 2.5 and 3.0 m/s

Fig. 23

Tip deflection time histories from experimental data [22] at UTunnel = 2.26 and 2.68 m/s

Fig. 24

Computed force time histories from FSI simulations

Fig. 25

Measured force time histories from load cell experimental data [22]

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