Unstructured MEL modelling of non linear 3D Ship hydrodynamics

Abstract

In the present work the investigations of non linear effects, in the context of potential flow theory, are investigated. These effects are caused by three main reasons, namely: the changes of the wetted geometry of the floating body, the water line dynamics and the fully non linear nature of the free surface boundary conditions. In order to understand the importance of tackling the non linear effects, a three dimensional frequency study of the S175 conteinership is carried out, at different Froude numbers, using linear frequency domain methods and a partly non linear time domain method.

A time domain analysis, with the aid of an unstructured mixed Eulerian Lagrangian (MEL) description of the fluid flow, is implemented aiming in exploring potential low non linear effects. In this framework, the mixed boundary value problem of the Eulerian phase of the MEL scheme is tackled by means of a Boundary Element Method using constant elements (or a direct Rankine panel method). At given time step, on Neumann boundaries the impervious boundary condition is specified whereas, on Dirichlet boundaries, the potential on the free surface is prescribed. The solution of the Boundary Value problem yields the potential on the Neumann boundaries and its normal derivative on Dirichlet boundaries. In the Lagrangian phase, the free surface boundary conditions are then integrated in time. This method was used to solve the linear time domain radiation, i.e by applying linearized free surface boundary conditions on the exact free surface and solving the mixed boundary value problem on the mean undisturbed free surface, for the case of forced motions of a hemisphere and a Wigley hull. In addition, the linear time domain method is also extended to the unified hydroelastic analysis in time domain for the cases of 2 and 3 nodes bending. Results are presented for the Wigley hull, undergoing prescribed forced oscillations for both rigid and flexible mode shapes.

The extension of the MEL scheme to a numerical tool capable of addressing several degrees of non linearities (from body nonlinear to fully nonlinear) is also discussed. In this context, two numerical formulations to calculate the time derivative of the velocity potential are implemented, namely: a backward finite scheme and an exact calculation based in the time harmonic property of the velocity potential. In latter case, a second boundary value problem is constructed and solved for the time derivative of the potential on Neumann boundaries and for the normal acceleration on Dirichlet boundaries. Results of both approaches are compared for the case of a sphere undergoing force oscillations in heave are compared to results obtained by other time domain methods. Moreover, after the boundary value problem is solved, a radial basis function representation of the velocity potential and free surface elevation is constructed, this approach allows for the estimation of the gradient of the velocity potential (body nonlinear and fully nonlinear simulations) and free surface steepness (fully nonlinear simulations). The results of the body non linear analysis, for large amplitude of oscillation in heave, are presented for the both the sphere and Wigley hull. For the latter, body non linear results of the coupling between heave into the first distortion mode (2-node) are also presented. The results of the fully non linear simulations are presented for the case of a sphere.

An investigation of the suitability of two unstructured meshing libraries is also performed in the context of the MEL simulation scheme. Practical issues related to (re)meshing at each time step, the representation of ship like geometries, free surface evolution and numerical stability are highlighted for both libraries.

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Identifiers

ORCID for Pandeli Temarel: orcid.org/0000-0003-2921-1242

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