Abstract
Prandtl’s mixing length method and the k‐epsilon method are introduced into the Moving Particle Semi‐Implicit (MPS) method for the purpose of modeling turbulence effects associated with water entries of two‐dimensional (2D) bow flare section. The presented numerical method is validated by comparing its numerical prediction with experimental data and other numerical results obtained from the Boundary Element Method (BEM). The time histories of the pressure and the vertical slamming force acting on the dropping ship section subjected to various conditions with different dropping velocity and inclined angles are analyzed. The results show that both the pressure and the vertical slamming force are in good agreement with the experimental data.
Highlights
For container ships the bow flare slamming can happen in rough seas; the slamming impact may lead to a series of instantaneous vibration and structure damage.The slamming calculation theory is firstly proposed by Von Karman [1] and Wagner [2], which is mainly used to solve the 2D water entry problem
Marintek Sintef Group used a 30∘ dead rise angle wedge to accomplish the water entry impact experiment; the slamming impact is recorded in time domain; the results show that the pressure reached the maximum value before the flow separation, and after the flow separation the pressure rapidly attenuated at the separation point
Moving Particle Semi-Implicit Method is firstly presented by Koshizuka [17] to calculate incompressible fluid flow problem, which is a meshless numerical method based on Lagrange particles
Summary
For container ships the bow flare slamming can happen in rough seas; the slamming impact may lead to a series of instantaneous vibration and structure damage. In order to solve arbitrary shape water entry problem, Zhao et al [5] proposed Boundary Element Method (BEM) to realize the practical numerical analysis; the slamming pressure is calculated by solving the nonlinear Bernoulli equation This method can satisfy the moving boundary condition accurately when calculating the velocity potential. Moving Particle Semi-Implicit Method is firstly presented by Koshizuka [17] to calculate incompressible fluid flow problem, which is a meshless numerical method based on Lagrange particles. Alam et al [33] used MPS method to solve the unsteady Navier-Stokes equation for incompressible fluid flows with and without the surface tension effect; equilateral prism-shaped object models were simulated to fall onto the free surface of the water; the hydrodynamic behaviors of water splash with and without the surface tension effect were presented to show the comparison and differences. The modified method is based on the equations updated by Khayyer et al [42] to provide more stability and accuracy; the results are compared with those obtained by BEM method and experiment data to verify the feasibility of this proposed method
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