Theoretical and experimental studies of wave diffraction and radiation loads on a horizontally submerged perforated plate
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- Institutt for marin teknikk 
Interactions of free-surface waves and submerged perforated structures are far less understood than the interactions of waves and conventional impermeable structures. This motivates the present research to investigate major hydrodynamic properties of submerged perforated structures, especially horizontally submerged perforated plates. Studies carried out in present thesis are mainly in the framework of potential flow theory. However, the local detailed viscous caused flow around each single perforation on the plate influences the global wave forces on the plate. The viscous effects of plate perforations are represented by applying a quadratic pressure-loss condition. The effect of perforation on the global wave forces, as well as the resulting amplitude or the Keulegan-Carpenter (KC) number characteristic added mass and damping coefficients are examined numerically and experimentally. We show in theory that the amplitude or KC number dependent hydrodynamic coefficients come from the quadratic pressureloss condition. The quadratic pressure-loss condition relates the pressure loss between the two plate sides to the square of relative velocity between the water particle through perforation and the plate. Further, the non-dimensional flow quantities’ dependence on plate perforation ratio and KC number can be combined and expressed with one single parameter, namely the perforation-effect KC number. Numerical works are carried out in both two and three dimensions. In two-dimensional semi-analytical studies, the existence of a horizontally submerged perforated plate is represented by a vortex distribution. The quadratic pressure-loss condition is equivalently linearized on the mean plate position in the frequency domain studies. The wave excitation loads, added mass and damping coefficients when the plate is forced to heave or roll, as well as the far-field wave transmission and reflection coefficients are extensively discussed by varying the incident wave parameters and the plate lengths, submergence, perforation ratios and motion amplitudes. In addition, new experiments are performed in three dimensions to examine the added mass and damping coefficients of heaving perforated plates, as well as the free-surface effects. The same scenarios are numerically studied by a three-dimensional boundary element method (BEM) in the frequency domain. In the BEM, a cylindrical control surface is introduced, which divides the water domain into inner and outer sub-domains. On the control surface, the velocity potential is formulated analytically and is matched with the inner domain BEM. In the inner domain BEM the linear free-surface conditions, as well as the equivalent linearized pressure-loss condition on an arbitrarily shaped plate are taken into account. Further, the satisfaction of the pressure-loss condition requires the iterations of solving boundary integral equations in inner domain for both velocity potential and flow velocities on the plate. Total forces on the plate are obtained after the convergence of BEM. The plate perforation will affect the vortex shedding at the plate edges. The associated cross flow drag forces are empirically calculated by a drag term as in the Morison equation, with a reasonable modification of cross flow velocity in order to take plate perforation into account. The empirical drag forces influence both the added mass and damping coefficients. Linear free-surface effects, KC numbers, perforation ratios, submergence, as well as the sensitivity studies of empirical drag forces are discussed. Reasonable agreement between numerical results and experiments are presented. We emphasize that for the smaller KC numbers, damping effects from plate perforations play an important role. For larger KC numbers, the empirical drag forces, which depend on plate edges and free-surface effects, need to be correctly adjusted. In the last part of the thesis, a two-dimensional fully nonlinear time-domain numerical wave tank with a submerged plate is formulated without flow separation from the plate edges. Nonlinear effects from free-surface conditions, as well as the quadratic pressureloss condition on the instantaneous plate positions are examined. Numerical results are only successful for submerged solid plate cases. Wave decompositions due to small plate submergence are shown. When the plate is perforated, the quadratic pressure-loss condition is used to update the velocity potential drop between the two plate sides as an evolutionary equation. The numerical difficulties are believed to come from the singularities at the two plate ends for a non-separated flow condition. No converged results are obtained in a standard fourth-order Runge-Kutta time-stepping process and a linear BEM. Possible solutions and extensions of present work for submerged perforated plates are discussed in a time domain perspective.