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Research Papers: CFD and VIV

Linear Dynamic Stability Analysis of a Surface-Piercing Plate Advancing at High Forward Speed

[+] Author and Article Information
Babak Ommani

MARINTEK,
Trondheim 7052, Norway,
e-mail: babak.ommani@marintek.sintef.no

Odd M. Faltinsen

Centre for Autonomous Marine Operations
and Systems (AMOS),
Department of Marine Technology,
Norwegian University of Science
and Technology,
Trondheim 7491, Norway
e-mail: odd.faltinsen@ntnu.no

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received January 26, 2014; final manuscript received September 6, 2015; published online October 5, 2015. Assoc. Editor: Thomas Fu.

J. Offshore Mech. Arct. Eng 137(6), 061802 (Oct 05, 2015) (9 pages) Paper No: OMAE-14-1004; doi: 10.1115/1.4031578 History: Received January 26, 2014; Revised September 06, 2015

The dynamic stability of a surface-piercing plate, advancing with high forward speed in the horizontal plane, is investigated in the scope of linear theory. The hydrodynamic forces on the plate in sway and yaw are presented in terms of frequency and forward speed-dependent added mass and damping coefficients. Flow separation from the trailing edge of the plate is considered. A time-domain boundary integral method using linear distribution of Rankine sources and dipoles on the plate, free surface, and vortex sheet is used to calculate these hydrodynamic coefficients numerically. Comparison between the current numerical results and previous numerical and experimental results is presented. Using linear dynamic stability analysis, the influence of hydrodynamic coefficients on the plate's stability is investigated as a simplified alternative to a semidisplacement vessel.

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References

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Lavis, D. R. , 1980, “ The Development of Stability Standards for Dynamically Supported Craft, a Progress Report,” High Speed Surface Craft Exhibition and Conference, Kalerghi Publications, Brighton, Sussex, UK, pp. 384–394.
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Ommani, B. , and Faltinsen, O. M. , 2011, “ Study on Linear 3D Rankine Panel Method for Prediction of Semi-Displacement Vessels' Hydrodynamic Characteristics at High Speed,” 11th International Conference on Fast Sea transportation (FAST 2011), Honolulu, HI, pp. 138–144.
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Xü, H. , 1991, “ Potential Flow Solution for a Yawed Surface-Piercing Plate,” J. Fluid Mech., 226, pp. 291–317. [CrossRef]
Ommani, B. , and Faltinsen, O. M. , 2014, “ Viscous and Potential Forces on an Advancing Surface-Piercing Flat Plate With a Fixed Drift Angle,” J. Mar. Sci. Technol., 20(2), pp. 278–291. [CrossRef]
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Figures

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Fig. 1

Schematic view of the problem and definition of the coordinate systems: (a) a plate advancing in the negative X-direction and (b) a ship advancing in the negative X-direction (FS: free surface, Body: plate, and VS: vortex sheet)

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Fig. 2

Comparison of A22, B22, A66, and B66 for a surface-piercing plate with forward speed Fn = 0.3 and aspect ratio Λ = H/L = 0.2 (Exp.: experimental data, 2D + t: Chapman's 2D + t method, and Pro.1. and Pro.2.: procedures 1 and 2), all from Ref. [12].

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Fig. 3

Comparison of the nondimensional added mass in sway and yaw of a surface-piercing plate with forward speed, aspect ratio Λ = H/L = 0.1

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Fig. 4

Comparison of the nondimensional damping in sway and yaw of a surface-piercing plate with forward speed, aspect ratio Λ = H/L = 0.1

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Fig. 5

Sway–yaw dynamic stability graph: white area: stable (stable every where), dashed lines: computation domain, and circles: free-system's response frequencies

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Fig. 6

Root-locus plot for the sway–yaw system; s: root of the dynamic system's characteristic equation; and Froude numbers are shown on the curve

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Fig. 7

Influence of the hydrodynamic coefficients on the dynamic stability in sway–yaw: black squares: unstable systems and white squares: stable systems

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Fig. 8

Influence of B66 on the root-locus plot for a coupled sway–yaw dynamic system, s: root of the dynamic system's characteristic equation

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Fig. 9

Dynamic stability graph obtained by reducing B66 by 60%: black area: unstable, white area: stable, dashed lines: computation domain, and circles: free-system's response frequencies

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Fig. 10

Influence of x′G on the root-locus plot for a coupled sway–yaw dynamic system, s: root of the dynamic system's characteristic equation

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Fig. 11

Dynamic stability graph obtained by increasing x′G/L to 0.22. Black area: unstable, white area: stable, dashed lines: computation domain, circles: free-system's response frequencies, and pluses: the imaginary part of the unstable roots.

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