Abstract
The twodimensional water entry of a rigid symmetric body with account for cavity formation on the body surface is studied. Initially the liquid is at rest and occupies the lower half plane. The rigid symmetric body touches the liquid free surface at a single point and then starts suddenly to penetrate the liquid vertically with a timevarying speed. We study the effect of the body deceleration on the pressure distribution in the flow region. It is shown that, in addition to the high pressures expected from the theory of impact, the pressure on the body surface can later decrease to subatmospheric levels. The creation of a cavity due to such low pressures is considered. The cavity starts at the lowest point of the body and spreads along the body surface forming a thin space between a new free surface and the body. Within the linearised hydrodynamic problem, the positions of the two turnover points at the periphery of the wetted area are determined by Wagner’s condition. The ends of the cavity’s free surface are modelled by the Brillouin–Villat condition. The pressure in the cavity is assumed to be a prescribed constant, which is a parameter of the model. The hydrodynamic problem is reduced to a system of integral and differential equations with respect to several functions of time. Results are presented for constant deceleration of two body shapes: a parabola and a wedge. The general formulation made also embraces conditions where the body is free to decelerate under the total fluid force. Contrasts are drawn between results from the present model and a simpler model in which the cavity formation is suppressed. It is shown that the expansion of the cavity can be significantly slower than the expansion of the corresponding zone of subatmospheric pressure in the simpler model. For forced motion and cavity pressure close to atmospheric, the cavity grows until almost complete detachment of the fluid from the body. In the problem of free motion of the body, cavitation with vapour pressure in the cavity is achievable only for extremely large impact velocities.
Original language  English 

Pages (fromto)  155174 
Number of pages  20 
Journal  Journal of Engineering Mathematics 
Volume  96 
Issue number  1 
Early online date  1 May 2015 
DOIs  
Publication status  Published  Feb 2016 
Keywords
 Cavitation
 Solid–liquid impact
 Wagner model
 Water entry
Profiles

Mark Cooker
 School of Mathematics  Honorary Associate Professor
 Fluid and Solid Mechanics  Member
Person: Honorary, Research Group Member

Alexander Korobkin
 School of Mathematics  Professor in Applied Mathematics
 Fluid and Solid Mechanics  Member
Person: Research Group Member, Academic, Teaching & Research