# Water entry problem in the presence of another floating or submerged body

Al Khulayf, Amer (2024) Water entry problem in the presence of another floating or submerged body. Doctoral thesis, University of East Anglia.

## Abstract

Water entry problems are important for those who work in the naval sector. Water impacts of practical rigid bodies in the presence of a submerged circular cylinder or floating flat plates are studied in this thesis. The presence of these bodies nearby the impact place can significantly change the water impact process or cause a crash.

These two problems are two-dimensional. The gravity and surface tension effects are neglected due to the impacting body is large and the acceleration of the fluid particles during the impact are much greater than the gravitational acceleration. The fluids in both problems are incompressible and inviscid. The flows caused by impact are potential with with the velocity potentials of the flows being solutions of the Laplace equation. The hydrodynamic pressure in the flow regions are described by the Bernoulli’s equation, where the hydrostatic pressure is neglected because the dynamic pressure components much higher than the hydrostatic components in the water impact problems. Water impacts of problems in the presence of a submerged circular cylinder or floating flat plates are studied using Wagner model of water impact.

Both problems are boundary value problems with mixed boundary conditions. Such problems are difficult to solve because of singularity of the solution at the points where the boundary conditions change their type. The problems are solved using conformal mappings of the flow regions onto a ring for the problem of impact in the presence of a submerged body, and onto a circle for the problem with several floating plates.

The mixed boundary value problems are reduced to coupled singular integral equations on the boundaries of the flow regions. The integral equations are formulated in terms of the distributions of the velocity potentials along the solid boundaries. The problems are studied with the submerged or floating bodies being either stationary or free to move.

The solutions of the integral equations are obtained in the form of Fourier series with unknown coefficients, which are solutions of linear algebraic equations. The systems of the algebraic equations are carefully analysed with obtaining asymptotic behaviour of the matrices of the system for limiting cases. The numerical distributions of the velocity potentials were compared with approximate analytical solutions for the cases where floating or submerged bodies are far away of the impact place.

Item Type: Thesis (Doctoral) Faculty of Science > School of Mathematics Chris White 11 Jun 2024 08:59 11 Jun 2024 08:59 https://ueaeprints.uea.ac.uk/id/eprint/95529