147_add_Added Masses of Ship Structures.pdf - 136 5 Added Masses of Bodies Moving Close to a Free Surface If on a free surface we have the boundary

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136 5 Added Masses of Bodies Moving Close to a Free Surface If on a free surface we have the boundary condition ∂ϕ ∂z z = 0 = 0 (see ( 5.19 )) in the limit k 0 0, one can continue function ϕ(x,y,z,t) to the upper half-space as an even function: ϕ(x,y,z,t) = ϕ(x,y, z,t), which implies for velocities: v x (x,y,z,t) = v x (x,y, z,t) ; v y (x,y,z,t) = v y (x,y, z,t) ; v z (x,y,z,t) = − v z (x,y, z,t). (5.21) Formulas ( 5.21 ) show that the flow around the duplicated hull under the motion along the x and y axes is the same as the flow around the single hull along the same axis. However, the motion of the duplicated hull along the z -axis gives the same picture as the motion of the single hull if two halfs of the duplicated hull move in opposite directions. Therefore, the added masses λ 11 , λ 22 , λ 26 , λ 66 of the hull can be computed under the boundary condition ( 5.19 ) as halfs of corresponding added masses of the duplicated hull moving in an infinite fluid. Therefore, in computation of added masses of the hull one should consider the following problems: 1. Computation of added masses of the duplicated hull moving in an infinite fluid (in this way one can compute added masses). If the case of boundary condition

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• Fall '09
• Fluid Dynamics, Boundary value problem, free surface, Added Masses

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