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ZHANG Teng, REN Jun-sheng, MEI Tian-long. Mathematical model of ship motions in regular waves based on Froude-Krylov force nonlinear method[J]. Journal of Traffic and Transportation Engineering, 2020, 20(2): 77-87. doi: 10.19818/j.cnki.1671-1637.2020.02.007
Citation: ZHANG Teng, REN Jun-sheng, MEI Tian-long. Mathematical model of ship motions in regular waves based on Froude-Krylov force nonlinear method[J]. Journal of Traffic and Transportation Engineering, 2020, 20(2): 77-87. doi: 10.19818/j.cnki.1671-1637.2020.02.007
shu

Mathematical model of ship motions in regular waves based on Froude-Krylov force nonlinear method

doi: 10.19818/j.cnki.1671-1637.2020.02.007
  • 1.

    Navigation College, Dalian Maritime University, Dalian 116026, Liaoning, China

  • 2.

    School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai 200240, Chin

Funds:

National High-tech Research and Development Program of China 2015AA016404

National Natural Science Foundation of China 51779029

Special Foundation for Basic Scientific Research of Central Colleges of China 313204330

More Information
  • Author Bio:

    ZHANGTeng(1991-), male, PhD, E-mail: 13342284962@163.com

  • Received Date: 2019-08-01
  • Publish Date: 2020-04-25
    Abstract
  • To accurately predict the ship motions in regular waves, the adaptive mesh method based on the quad-tree division was proposed to generate the instantaneous wet hull surface. The Froude-Krylov(F-K) force and hydrostatic restoring force were calculated on the instantaneous wet hull surface. For the F-K force fluctuating violently at the wave profile, the quad-tree division method was adopted to further divide the panels interacted with the wave profile. Based on the linear theory, the perturbation forces were calculated on the mean wet hull surface by using the instantaneous free surface Green function. To avoid the serious numerical error caused by the violent fluctuation of instantaneous free surface Green function near the free liquid surface, the waterline integral term of boundary integral equation satisfied by the perturbation potential was excluded. The numerical computation was carried out for the Wigley Ⅰ hull with a forward speed against waves at a Froude number of 0.2. Calculation result shows that for the hull under the instantaneous wave profile, the quantity of panel required by the F-K force nonlinear method is less, being 1/4-1/8 of the fine mesh method. Except for irregular frequencies, the relative errors of hydrodynamic coefficients obtained by the methods with and without waterline term are less than 33.4% and 54.8%, respectively, comparing with the experimental result. Therefore, the hydrodynamic coefficient computational result obtained with the waterline term is closer to the experimental result. When the incident wave amplitude is 0.018 m, and the ratio of wave length to ship length is 1.25, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 3.2% and 17.0%, respectively, lower than the experimental value. When the ratio of wave length to ship length is 2.00, the pitch response amplitude operators obtained by the F-K force nonlinear method and the linear method are 6.7% and 13.5%, respectively, lower than the experimental value. Thus, the F-K force nonlinear method can accurately simulate the ship motions in regular waves.

     

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