In the present study, we experimentally investigate water surface deformation due to the impact of rounded cylindrical projectiles with different aspect ratios (1.0–8.0). The subsequent jet and splash formation is closely related to the dynamics of an underwater cavity. To control the cavity formation, two kinds of surface conditions (smooth and rough) are applied to the front parts of the projectiles, and two impact speeds are considered. The Froude, Reynolds and Weber numbers are in the ranges of 32–90, and 1700–5000, respectively. When the front is smooth, the water film rises up along the body surface immediately after impact, and the temporal variation of its height is analytically estimated. The film converges at the rear pole to create an apex jet at lower aspect ratios and simply rises up and falls with the body at higher aspect ratios. The jets could be further distinguished as thin and thick jets, whose breakdown is found to be a function of the viscous force and surface tension, i.e. the Ohnesorge number. On the other hand, when the front is rough, the water film cannot rise up along the body surface, and instead early separation occurs to make the splash above a free surface. The splash size is quantified to assess the effects of the aspect ratio and impact speed. Upon splash formation, a cavity is created under the free surface, which emanates from the nose of the projectile. As the body sinks, the cavity pinch-off occurs due to the imbalance between the hydrostatic pressure and air pressure inside the cavity. At higher aspect ratios, cavity pinch-off occurs on the side wall of the projectile and leaves a portion of the cavity bubble on it. When the surface is smooth, no underwater cavity forms. Finally, we compare the hydrodynamic force acting on the sinking bodies with and without cavity formation, based on the underwater trajectory of each projectile. It is found that the underwater cavity reduces the drag force on the sinking body when it fully encapsulates the body; however, if the air bubbles are partially attached to the body after pinch-off, they tend to detach irregularly or impose additional drag on the body.

Water entry of rounded cylindrical bodies with different aspect ratios and surface conditions

Experimental investigation of oblique water entry of high-speed truncated cone projectiles: Cavity dynamics and impact load

Numerical investigations on the oblique water entry of high-speed projectiles

Improvement of cavity shape modeling in water-entry of circular cylinders by considering the cavity memory effect

Solid object water entry is a common problem in various natural, industrial and military applications, which involves large deformation of free surfaces and violent fluid–structure interactions. In computational fluid dynamics (CFD), this is a type of problem that tests the robustness and capacity of any CFD numerical algorithm. In this work, the newly-developed updated Lagrangian particle hydrodynamics (ULPH) method, which is a fluid version of peridynamics, is enhanced and applied to simulate solid object water entry problems. ULPH method is Lagrangian meshfree particle method that can ensure the specific free surface conditions automatically satisfied. The density filter and artificial viscosity diffusion are adopted in the ULPH scheme to stabilize and smooth the pressure field. In the process of a rigid body entering water, it may induce negative pressure in some areas of impact region, which can cause spurious tensile instability in some meshfree particle simulations, such as SPH and ULPH. A tensile instability control technique based on the ULPH framework has been developed to overcome the numerical instability. To validate the stability and accuracy of the ULPH approach in simulating water entry problems, several 2D and 3D examples of water entry have been carried out in this work. The necking and cavity pinch-off phenomena are visible in the numerical results. The simulation results of the ULPH method are well compared with experimental data and other numerical solutions. The water crown, cavity shapes and stream pattern formed around the rigid body entering the water can be well captured. The computation results show that the ULPH method has the ability to simulate the complex solid object water entry precess accurately.

Updated Lagrangian particle hydrodynamics (ULPH) modeling of solid object water entry problems

The vertical water-entry behavior of bullet-shaped projectiles was experimentally and theoretically studied. Particular attention was given to characterizing projectile dynamics, the resultant evolution of air cavity and particularly surface closure before deep closure in the moderate speed. We developed equations for the projectile motion with significant and negligible gravitational effects. Based on the solution to the Rayleigh-Besant problem, a theoretical model was developed to describe the evolution of the cavity shape, including the time evolution of the cavity on fixed locations and its location evolutions at fixed times. The gravitation effects during the initial stage of the impact of the projectile on the water can be ignored, but those during the later stage should be considered, many literatures do not have the report of this aspect. The theoretical predictions were consistent with the experimental observations. The evolution of air cavity had a significant effect on ballistic stability.

https://file.scirp.org/pdf/JAMP_2014051614043646.pdf

Xi’an

Papers

Vertical Water-Entry of Bullet-Shaped Projectiles