Abstract
In this paper, an improved potential flow model is proposed for the hydrodynamic analysis of ships advancing in waves. A desingularized Rankine panel method, which has been improved with the added effect of nonlinear steady wave-making (NSWM) flow in frequency domain, is employed for 3D diffraction and radiation problems. Non-uniform rational B-splines (NURBS) are used to describe the body and free surfaces. The NSWM potential is computed by linear superposition of the first-order and second-order steady wave-making potentials which are determined by solving the corresponding boundary value problems (BVPs). The so-called mj terms in the body boundary condition of the radiation problem are evaluated with nonlinear steady flow. The free surface boundary conditions in the diffraction and radiation problems are also derived by considering nonlinear steady flow. To verify the improved model and the numerical method adopted in the present study, the nonlinear wave-making problem of a submerged moving sphere is first studied, and the computed results are compared with the analytical results of linear steady flow. Subsequently, the diffraction and radiation problems of a submerged moving sphere and a modified Wigley hull are solved. The numerical results of the wave exciting forces, added masses, and damping coefficients are compared with those obtained by using Neumann–Kelvin (NK) flow and double-body (DB) flow. A comparison of the results indicates that the improved model using the NSWM flow can generally give results in better agreement with the test data and other published results than those by using NK and DB flows, especially for the hydrodynamic coefficients in relatively low frequency ranges.
Highlights
Over the last decades, the rapid development of computing power and the emergence of more sophisticated numerical methods have promoted the applications of numerical methods in ship hydrodynamics problems
One can find that the results based on the nonlinear steady wave-making (NSWM) flow and other two methods based on the NK and DB flows do not show evident differences, the reasons can be explained as follows: on one hand, though the effect of nonlinear steady flow is considered in the free surface boundary condition Equation (24), the interaction has no relation with the diffraction potential in the body surface boundary condition Equation (25); on the other hand, the small differences can be attributed to the predominant proportion of the Froude–Krylov force in the wave exciting force
A desingularized Rankine panel method based on the NSWM flow is applied for analysis of the hydrodynamic problems of a ship advancing in waves
Summary
The rapid development of computing power and the emergence of more sophisticated numerical methods have promoted the applications of numerical methods in ship hydrodynamics problems. The mean second-order wave force was evaluated by Rankine panel method using NK or DB linearization, which was treated as the input force in the equations for predicting maneuvering behavior These two linearization methods, as described in [4], can be justified in the case of a slender ship, but they are not suitable for blunt bodies or ships moving at high speeds [9]. The second-order or even higher-order derivatives of the velocity potential can be directly evaluated without complicated numerical treatments to eliminate the singularities in the integral equation; the method is faster and easier to implement In recent years, this method has been extended and applied in the analysis of 2D wave-body interaction problems, such as Feng et al [18,19,20]. The BVP for the second-order steady velocity potential is given as:
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