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Research Papers: Ocean Engineering

Low-Dimensional Components of Flows With Large Free/Moving-Surface Motion

[+] Author and Article Information
Yi Zhang

Metrum Research Group,
Tariffville, CT 06081
e-mail: yiz@metrumrg.com

Solomon C. Yim

School of Civil and Construction Engineering,
Oregon State University,
Corvallis, OR 97331
e-mail: solomon.yim@oregonstate.edu

1Corresponding author.

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received September 18, 2014; final manuscript received July 27, 2018; published online October 1, 2018. Assoc. Editor: Thomas Fu.

J. Offshore Mech. Arct. Eng 141(2), 021101 (Oct 01, 2018) (13 pages) Paper No: OMAE-14-1131; doi: 10.1115/1.4041016 History: Received September 18, 2014; Revised July 27, 2018

Flow systems with highly nonlinear free/moving surface motion are common in engineering applications, such as wave impact and fluid-structure interaction (FSI) problems. In order to reveal the dynamics of such flows, as well as provide a reduced-order modeling (ROM) for large-scale applications, we propose a proper orthogonal decomposition (POD) technique that couples the velocity flow field and the level-set function field, as well as a proper normalization for the snapshots data so that the low-dimensional components of the flow can be retrieved with a priori knowledge of equal distribution of the total variance between velocity and level-set function data. Through numerical examples of a sloshing problem and a water entry problem, we show that the low-dimensional components obtained provide an efficient and accurate approximation of the flow field. Moreover, we show that the velocity contour and orbits projected on the space of the reduced basis greatly facilitate understanding of the intrinsic dynamics of the flow systems.

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Figures

Grahic Jump Location
Fig. 5

Free surface profiles from the sloshing problem h = 0.40L, η = 0.10L. Solid line: free surface based on POD modes. Dash line: free surface based on FEM.

Grahic Jump Location
Fig. 6

Horizontal flow velocity time history during the last period of the tank oscillation at node 1, located near the right wall at the bottom of the tank

Grahic Jump Location
Fig. 1

Flow domain in the sloshing problem

Grahic Jump Location
Fig. 2

Singular values of the first 100 POD pressure modes of the sloshing problem

Grahic Jump Location
Fig. 3

Free surface profiles from the sloshing problem h = 0.12L, η = 0.01L. Solid line: free surface based on POD modes. Dash line: free surface based on FEM.

Grahic Jump Location
Fig. 4

Free surface profiles from the sloshing problem h = 0.12L, η = 0.10L. Solid line: free surface based on POD modes. Dash line: free surface based on FEM.

Grahic Jump Location
Fig. 7

Flow velocity contours for the first four POD modes of the sloshing problem h = 0.12L, η= 0.01L

Grahic Jump Location
Fig. 10

Orbits on the wi–wj plane in the sloshing problem h = 0.12L, η = 0.01L

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Fig. 8

Flow velocity contours for the first four POD modes of the sloshing problem h = 0.12L, η= 0.10L

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Fig. 9

Flow velocity contours for the first four POD modes of the sloshing problem h = 0.40L, η = 0.10L

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Fig. 18

Projected orbits of the cylinder water entry problem

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Fig. 11

Projected orbits in the sloshing problem h = 0.12L, η = 0.01L

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Fig. 12

Projected orbits in the sloshing problem h = 0.40L, η = 0.10L

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Fig. 13

Flow domain in the cylinder water entry problem

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Fig. 14

Singular values of the first 30 POD pressure modes of the water entry problem

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Fig. 15

Free surface at the near field during initial stage of the water entry. Solid line: free surface based on POD modes. Dash line: free surface based on FEM.

Grahic Jump Location
Fig. 16

Free surface at the far field at the later stage of the water entry. Solid line: free surface based on POD modes. Dash line: free surface based on FEM.

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Fig. 17

The first 5 velocity POD modes of the cylinder water entry problem

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