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Chinese Journal of Ship Research, Volume. 17, Issue 2, 81(2022)

Numerical simulation analysis of liquid sloshing in tank under random excitation

Shengchao JIANG1, Bo XU2, and Zihao WANG1
Author Affiliations
  • 1School of Naval Architecture Engineering, Dalian University of Technology, Dalian 116024, China
  • 2Marine Design and Research Institute of China, Shanghai 200011, China
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    AbstractGet PDFGet PDF(in Chinese)
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    References (11)
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    Equations(17)
    $ \frac{{\partial \rho {u_i}}}{{\partial {x_i}}} = 0 $(1)

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    $ \frac{{\partial \rho {u_i}}}{{\partial t}} + \frac{{\partial \left( {\rho ({u_i} - u_i^{\rm{m}}){u_j}} \right)}}{{\partial {x_j}}} = - \frac{{\partial p}}{{\partial {x_i}}} + \mu \frac{\partial }{{\partial {x_j}}}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right) + {f_i} $(2)

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    $ \varphi =\left\{ \begin{aligned} & \varphi =0,\qquad\quad\;\; 空气中\\& 0 < \varphi < 1,\qquad 自由面\\& \varphi =1,\qquad\quad\;\;\; 水中 \end{aligned}\right.$(3)

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    $ \frac{{\partial \varphi }}{{\partial t}} + \left( {{u_i} - u_i^{\rm{m}}} \right)\frac{{\partial \varphi }}{{\partial {x_i}}} = 0 $(4)

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    $ \begin{split} & \rho = \varphi {\rho _{\rm{w}}} + (1 - \varphi ){\rho _{\rm{a}}} \\& \mu = \varphi {\mu _{\rm{w}}} + (1 - \varphi ){\mu _{\rm{a}}} \end{split}$(5)

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    $ \Delta t < \mathrm{min}\left\{\frac{Cr\times \Delta x}{{u}_{\mathrm{max}}},\;\frac{Cr\times \Delta y}{{v}_{\mathrm{max}}},\;\frac{Cr\times \Delta {\textit{z}}}{{w}_{\mathrm{max}}}\right\} $(6)

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    $ x = A\sin \omega t $(7)

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    $ S(\omega ) = \alpha {g^2}\frac{1}{{{\omega ^2}}}\exp \left[ { - \frac{5}{4}{{\left( {\frac{{{\omega _{\text{p}}}}}{\omega }} \right)}^4}} \right]{\gamma ^{\exp \left[ { - {{{{\left( {{{{\omega _{\text{p}}}} /\omega }} \right)}^2}} /{\left( {2{\sigma ^2}\omega _{\text{p}}^2} \right)}}} \right]}} $(8)

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    $ \gamma {\text{ = }}3.3,\;{\sigma _{\text{a}}}{\text{ = }}0.07,\;{\sigma _{\text{b}}} = 0.09 $()

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    $ \alpha {\text{ = }}0.076{(\overline X )^{ - 0.22}},\;\overline X {\text{ = }}gX/{U^2} $()

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    $ U{\text{ = }}k{X^{ - 0.615}}H_{\rm{s}}^{1.08},\;k = 83.7 $()

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    $ {\omega _{\text{p}}} = 22(g/U){(\overline X )^{ - 0.33}} $()

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    $ \eta (t) = \sum\limits_{i = 1}^{{N_\omega }} {{A_i}} \sin ({\omega _i}t + {\varphi _i}) $(9)

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    $ {A_i} = \sqrt {2S(\omega )\Delta \omega } $(10)

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    $ x(t) = \sum\limits_{i = 1}^{{N_\omega }} {{A_i}} \sin ({\omega _i}t + {\varphi _i}) $(11)

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    $ {R}_{\text{m}}=\left\{ \begin{aligned} & \frac{1}{2}\left[1-\mathrm{cos}\left(\frac{{\text{π}} t}{{T}_{\text{m}}}\right)\right],\;\;\;\;\;t < {T}_{\text{m}}\\& \qquad\quad 1,\;\qquad\qquad\; t > {T}_{\text{m}} \end{aligned}\right. $(12)

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    $ {\lambda _3} = \frac{1}{{{\sigma ^3}}}\frac{1}{n}{\sum\limits_{i = 1}^n {\left( {{\eta _i} - \overline \eta } \right)} ^3} $(13)

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    Shengchao JIANG, Bo XU, Zihao WANG. Numerical simulation analysis of liquid sloshing in tank under random excitation[J]. Chinese Journal of Ship Research, 2022, 17(2): 81

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    Paper Information

    Category: Ship Design and Performance

    Received: Nov. 15, 2020

    Accepted: --

    Published Online: Mar. 24, 2025

    The Author Email:

    DOI:10.19693/j.issn.1673-3185.02183

    Topics

    laser devices and laser physics
    Lasers and Laser Optics
    Laser physics
    laser manufacturing
    Instrumentation, Measurement and Metrology