Research Papers: Structures and Safety Reliability

Linear and Nonlinear Sectional Loads With Potential and Field Methods

[+] Author and Article Information
Alexander von Graefe

University Duisburg-Essen,
Bismarckstrasse 69,
Duisburg 47057, Germany
e-mail: alexander.von-graefe@dnvgl.com

Ould el Moctar

University Duisburg-Essen,
Bismarckstrasse 69,
Duisburg 47057, Germany
e-mail: ould.el-moctar@uni-due.de

Jan Oberhagemann

Brooktorkai 18,
Hamburg 20457, Germany
e-mail: jan.oberhagemann@dnvgl.com

Vladimir Shigunov

Brooktorkai 18,
Hamburg 20457, Germany
e-mail: vladimir.shigunov@dnvgl.com

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 June 18, 2013; final manuscript received February 11, 2014; published online April 1, 2014. Assoc. Editor: Dominique Roddier.

J. Offshore Mech. Arct. Eng 136(3), 031602 (Apr 01, 2014) (9 pages) Paper No: OMAE-13-1057; doi: 10.1115/1.4026885 History: Received June 18, 2013; Revised February 11, 2014

A Rankine source method is applied to predict linear and weakly nonlinear sectional loads of a modern container ship. The method uses solution in the frequency domain, linearized with respect to wave amplitude about the nonlinear steady flow due to forward speed, which accounts for the nonlinear free-surface conditions, ship wave, and dynamic trim and sinkage. Weak nonlinearity of the sectional loads in waves (e.g., hogging-sagging asymmetry) is taken into account by pressure extrapolation and integration up to the estimated actual water line. The sectional forces obtained with this method are compared with the results of other methods, including (1) linear Rankine panel method, where flow due to waves is linearized about the double-body flow, (2) linear zero-speed Green function method with correction for forward speed, (3) fully nonlinear simulations based on field-based solution of Reynolds-averaged Navier–Stokes (RANS) equations, and (4) model tests. Comparison with RANS solution and model tests shows, that the proposed method can accurately predict sectional loads for small to moderate wave heights.

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Fig. 1

Vertical bending moment at Lpp/2; experimental data and simulation results with RANS method, using four different grids with 2.5 × 105 to 1.8 × 106 cells

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Fig. 2

Ship motions in head waves

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Fig. 3

Ship motions in following waves

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Fig. 6

Vertical bending moment at Lpp/2 from simulations with RANS method for varying wave height (top) and in comparison with low-pass filtered and unfiltered experimental results [18] (bottom)

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Fig. 7

Nonlinear loads in head waves at 5.0 knots forward speed

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Fig. 8

Nonlinear loads in following waves at 5.0 knots forward speed

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Fig. 4

Linear loads in head waves at various forward speeds

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Fig. 5

Linear loads in following waves at 5.0 knots forward speed



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