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Simplified models of Water entry and exit

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The two-dimensional problem of a symmetric wedge which enters water and exits from it thereafter at a time-dependent speed is considered. The pressure distribution along the wetted part of the wedge and the total hydrodynamic force acting on the wedge are calculated by three simplified models: the Original Wagner Model (OWM) of water entry and the Linearized Model of water exit (LME), the Modified Logvinovich Model (MLM) of entry and exit, and Generalized Wagner Model (GWM) of entry and exit.

Computational Fluid Dynamics (CFD) simulations are also used to generate reference results for the development and elaboration of the water exit models with large displacements. A custom solver (CFD1) built on the open-source finite-volume CFD library OpenFOAM is employed to solve the Navier-Stokes equations governing the air-water flow. To start with the exit models, one needs to ensure that the entry stage is well predicted by both CFD and simplified models. However, the hydrodynamic forces and the pressure distributions predicted by the GWM and by the MLM were found to be rather different from those predicted by the CFD during the entry stage. To examine why the force predictions are so different, only vertical motions of a symmetric wedge with the deadrise angle of 45 degrees were considered in detail, and special attention was paid to the end of the entry stage, where the wedge speed is small.

The accuracy of the CFD results was confirmed by running each case of the wedge motions twice by the OpenFOAM solvers developed by Piro and Maki (2013, CFD1 ) and by Seng et al. (2014, CFD2 ). It was found that both OpenFOAM solvers provide close results. The obtained results demonstrate that the gravity provides an important contribution to the force at the end of the entry stage. The gravity effects were included in the symplified models of water entry/exit.

(In collaboration with T.I. Khabakhpasheva, Kevin J. Maki and Sopheak Seng)

This talk is part of the Applied Mathematics Seminar Series series.

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