Numerical study on the cavity dynamics for vertical water entries of twin spheres

In this study, a three dimensional(3D) numerical model of six-degrees-of-freedom(6DOF) is applied to simulate the water entries of twin spheres side-by-side at different lateral distances and time intervals.The turbulence structure is described using the shear-stress transport k-ω(SST k-ω) model, and the volume of fluid(VOF) method is used to track the complex air-liquid interface. The motion of spheres during water entry is simulated using an independent overset grid. The numerical model is verified by comparing the cavity evolution results from simulations and experiments. Numerical results reveal that the time interval between the twin water entries evidently affects cavity expansion and contraction behaviors in the radial direction. However, this influence is significantly weakened by increasing the lateral distance between the two spheres. In synchronous water entries, pressure is reduced on the midline of two cavities during surface closure, which is directly related to the cavity volume. The evolution of vortexes inside the two cavities is analyzed using a velocity vector field, which is affected by the lateral distance and time interval of water entries.

Experimental observation on water entry of a sphere in regular wave

This paper presents a novel experiment to observe the whole water entry process of a free-falling sphere into a regular wave.A time-accurate synchronizing system modulates the moment elaborately to ensure the sphere impacting onto the water surface at the desirable wave phase.Four high-speed cameras focus locally to measure the high-precision size of the cavity evolution.Meanwhile,the aggregated field view of the camera array covers both the splash above the free surface and the entire cavity in the wave.The detailed methodologies are described and verified for the hardware set-up and the image post-processing.The theoretical maximum deviation is 1.7%on the space scale.The integral morphology of the cavity is captured precisely in the coordinate system during the sphere penetrates through the water at four representative wave phases and the still water.The result shows that the horizontal velocity of the fluid particle in the wave impels the cavity and changes the shape distinctly.Notably,the wave motion causes the cavity to pinch offearlier at the wave trough phase and later at the wave crest phase than in the still water.The wave motion influences the falling process of the sphere slightly in the present parameters.

UNDERWATER ACOUSTICS AND CAVITATING FLOW OF WATER ENTRY

The fluid mechanics of water entry is studied through investigating the underwater acoustics and the supercavitation.Underwater acoustic signals in water entry are extensively measured at about 30 different positions by using a PVDF needle hydrophone.From the measurements we obtain (1)the primary shock wave caused by the impact of the blunt body on free surface;(2)the vapor pressure inside the cavity;(3)the secondary shock wave caused by pulling away of the cavity from free surface;and so on.The supercavitation induced by the blunt body is observed by using a digital high-speed video camera as well as the single shot photography.The periodic and 3 dimensional motion of the supercavitation is revealed.The experiment is carried out at room temperature.

HYDRODYNAMIC BEHAVIOR OF AN UNDERWATER MOVING BODY AFTER WATER ENTRY

An experimental study was conducted to investigate the water entry phenomenon. A facility was designed to carry out the tests with the entry veloci- ties of around 352 m/s. Visualization, pressure ineasurement, velocity measurement and underwater impact test were performed to investigate the hydroballistic behav- ior of the underwater moving body, the underwater flow field, the supercavitation, etc.. This study shows that the motion of a high-speed underwater body is strongly three-dimensional and chaotic. Furthermore, it is found that the distribution of the trajectory deflection of the underwater projectile depends on the depth of water. It is also found by measuring the deformation on a witness plate submerged in water, that the impact energy of an underwater projectile is reduced as it penetrates deeper into water.

Study on the Effect of Two-Dimensional Helicopter V-buoy’s Way of Water Entry on Water Impact

To analyze the effect of the way of water entry on water impact, the FLUENT software was adopted to simulate a two-dimensional (2D) helicopter V-buoy’s free fall and forced fall at a constant velocity.Combining with the UDF program and the dynamic mesh model, the standard k-ε turbulence model was used and the VOF technique was adopted to capture free surface.The physical parameters such as velocity and force were calculated and compared with those results of boundary element method with good agreement obtained.It was found that the force of 2D V-buoy at a constant velocity was much greater than that in free fall motion.Meanwhile, the maximum pressure coefficients C p max in both cases were almost equal and the dimensionless water-entry depths y' corresponding to C p max were also similar.

Numerical simulation of calm water entry of flatted-bottom seafloor mining tool

The hydrodynamic problem of a two-dimensional model of seafloor mining tool entering still water vertically at constant speed was analyzed based on the velocity potential theory. For the assumption that the water entry occurs with very short time interval, the viscosity and gravity of fluid were neglected. Considering the characteristic shape of it, the seafloor mining tool was simplified as a flat-bottom body. The governing equations were the Reynolds time-averaged equations and the k-e model. Finite element analysis was undertaken using the CFD software, Fluent. The impact pressures on the bottom of the mining tool were computed based on the improved volume of fuid method （VOF）. The pressure distribution, the maximum impact pressure, and the impact duration time during the water entry of mining tool are presented at various deploying velocities, the two peak pressures in the impact process are observed, and the relationship between the maximum impact pressure and the deploying velocity is obtained. The results are compared with those based on other prediction theories and methods.

Experimental Investigation of Water-Entry Phenomenon

In order to investigate the cavity shape and velocity attenuation of steel spheres after high-speed water entry, the high-speed water entry of different water entry angles were performed. The cavity shapes were recorded using high-speed photo recorder, and the velocities after water entry were measured. The diameters of equivalent disk of steel spheres after water entry were obtained from the processing of cavity images. Based on the steady and uncompressing flow assumption, a theoretical model for velocity attenuation of steel spheres with cavity was proposed and calculated results were in good agreement with the experimental results. The second cavity breaking off phenomenon, which has not been reported before, was discovered. The established theoretical model provides a reference for other relative researches.

Numerical Simulation for Water Entry of a Wedge at Varying Speed by a High Order Boundary Element Method

A high order boundary element method was developed for the complex velocity potential problem. The method ensures not only the continuity of the potential at the nodes of each element but also the velocity. It can be applied to a variety of velocity potential problems. The present paper, however, focused on its application to the problem of water entry of a wedge with varying speed. The continuity of the velocity achieved herein is particularly important for this kind of nonlinear free surface flow problem, because when the time stepping method is used, the free surface is updated through the velocity obtained at each node and the accuracy of the velocity is therefore crucial. Calculation was made for a case when the distance S that the wedge has travelled and time t follow the relationship s=Dtα, where D and α are constants, which is found to lead to a self similar flow field when the effect due to gravity is ignored.

A Numerical Study on the Asymmetric Water Entry of A Wedge Section

The effect of the asymmetric water entry over a submerged part of a ship on the hydrodynamic impact is investigated numerically. A wedge body is considered and the problem is assumed to be two-dimensional. The results of symmetric and asymmetric impacts are compared. The effect is found significant in the numerical simulation. The maximum hydrodynamic pressure at a heel angle of 10 degrees becomes about 95% more than that of the symmetric entry. The result of the present work proves the importance of asymmetrical hydrodynamic impact loading for structural design of a ship. Besides, the numerical procedure is not limited to a wedge type cross section and it is possible to apply it for any real geometry of ships and high-speed craft.

Numerical Simulation of the Water Entry of a Structure in Free Fall Motion

To solve the problems concerning water entry of a structure, the RANS equations and volume of fluid （VOF） method are used. Combining the user-defined function （UDF） procedure with dynamic grids, the water impact on a structure in free fall is simulated, and the velocity, displacement and the pressure distribution on the structure are investigated. The results of the numerical simulation were compared with the experimental data, and solidly consistent results have been achieved, which validates the numerical model. Therefore, this method can be used to study the water impact problems of a structure.

Numerical investigation of water-entry of flatted-bottom seafloor mining tool in ocean waves

A numerical wave load model based on two-phase(water-air) Reynolds-Averaged Navier Stokes(RANS) type equations is used to evaluate hydrodynamic forces exerted on flatted-bottom seafloor mining tool during its entering ocean waves of deploying process.The discretization of the RANS equations is achieved by a finite volume approach(FV).The volume of fluid method(VOF) is employed to track the complicated free surface.A numerical wave tank is built to generate the ocean waves which are suitable for deploying seafloor mining tool.A typical deploying condition is employed to reflect the process of flatted-bottom body impacting with waves,and the pressure distribution of bottom is also presented.Four different lowering velocities are applied to obtain the time histories of maximum pressure of bottom,and it can be concluded that the pressure coefficient decreases with water velocity increasing,which is similar with ordinary water entry case.The numerical results clearly demonstrate the characteristics of flatted-bottom body entering ocean waves.

An Essential Solution of Water Entry Problems and its Engineering Applications

For solving water entry problems, a numerical method is presented, which is a CFD method based on free surface capturing method and Cartesian cut cell mesh.In this approach, incompressible Euler equations for a variable density fluid are numerically calculated by the finite volume method.Then artificial compressibility method, dual time-stepping technique and Roe's approximate Riemann solver are adopted in the numerical scheme.Finally, some application cases are designed to show the ability of the current method to cope with water entry problems in ocean engineering.

Evolution of three-dimensional cavitation following water entry of an inclined cylinder

The water entry of an inclined cylinder is firstly studied experimentally for low Froude number. The cylinder is 50 mm in diameter and 200 mm in length, with a moderate length to diameter ratio. As it is submerged below the water surface, the cavity is fully three-dimensional. Due to the rotation of the cylinder caused by the initial inclined impact, the cavity evolution is quite complicated and a new phenomenon is revealed. The cylinder moves along a curved trajectory in water, which greatly affects the evolution of the cavities. The cavity breaks up into two sub-cavities, and finally collapses because of hydrostatic pressure.

Vertical Water-Entry of Bullet-Shaped Projectiles

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.

Cavity formation during water entry of heated spheres

We experimentally study the cavity formation when heated spheres impact onto water at low and high subcooling.The observations present that the formation and appearance of the cavity are affected by the boiling modes and the heat transfer intensity. In the nucleate-boiling regime, a rough cavity can be formed at a rather low impact velocity, while at the same velocity, the cavity formed in the film-boiling regime may have a very smooth interface with a stable vapor layer around the sphere. We discuss the effects of the impact speed, water and sphere temperatures on the stability of the vapor layer. For low subcooled water, the stable vapor layer will be disturbed when increasing the impact velocity, leading to a disturbed cavity. For high subcooled water, the film boiling has a particular boiling model in which the vapor layer around the sphere cannot keep its stability. In this particular film-boiling regime, no cavities can be formed at low impact velocities and only broken cavities can be formed at high impact velocities.

Numerical Simulation of Water Entry of Wedges in Waves Using A CIPBased Model

In this study,the water entry of wedges in regular waves is numerically investigated by a two-dimensional in-house numerical code.The numerical model based on the viscous Navier−Stokes(N−S)equations employs a high-order different method—the constrained interpolation profile(CIP)method to discretize the convection term.A Volume of Fluid(VOF)-type method,the tangent of hyperbola for interface capturing/slope weighting(THINC/SW)is employed to capture the free surface/interface,and an immersed boundary method is adopted to treat the motion of wedges.The momentum source function derived from the Boussinesq equation is applied as an internal wavemaker to generate regular waves.The accuracy of the numerical model is validated in comparison with experimental results in the literature.The results of water entry in waves are provided in terms of the impact force of wedge,velocity and pressure distributions of fluid.Considerable attention is paid to the effects of wave parameters and the position of wedge impacting the water surface.It is found that the existence of waves significantly influences the velocity and pressure field of fluid and impact force on the wedges.

Numerical Investigation on the Deformation of the Free Interface During Water Entry and Exit of a Circular Cylinder by Using the Immersed Boundary-Multiphase Lattice Boltzmann Flux Solver

In this work,the deformation of free interface during water entry and exit of a circular cylinder is investigated numerically by using the two-dimensional(2D)immersed boundary-multiphase lattice Boltzmann flux solver(IB-MLBFS).The fluid domain is discretized by finite volume discretization,and the flux on the grid interface is evaluated by lattice Boltzmann equations.Both the implicit velocity correction and the surface flux correction are implemented by using the immersed boundary-method to consider the fluid-structure interaction and the contact interface between the multiphase fluids and the structure.First,the water entry of a circular cylinder is simulated and the results are compared with the experiment,which considered the length-diameter ratio of the circular cylinder.The reliability of 2D simulation is verified and the deformation of the free interface is well investigated.Afterward,the water exit of a circular cylinder with constant velocity is simulated,which is less researched.In addition,the results show the advantage of present IB-MLBFS to some extent.Finally,the water exit and re-entry of a circular cylinder are presented,and the results present the complex deformation of the free interface and the dynamic response of the moving structure.Based on the numerical results,the free interface of the multiphase fluids is well captured,and the contact interface on the boundary of the moving structure is accurately presented by the IB-MLBFS.

Two-dimensional Numerical Simulation of an Elastic Wedge Water Entry by a Coupled FDM-FEM Method

Hydroelastic behavior of an elastic wedge impacting on calm water surface was investigated. A partitioned approach by coupling finite difference method （FDM） and finite element method （FEM） was developed to analyze the fluid structure interaction （FSI） problem. The FDM, in which the Constraint Interpolation Profile （CIP） method was applied, was used for solving the flow field in a fixed regular Cartesian grid system. Free surface was captured by the Tangent of Hyperbola for Interface Capturing with Slope Weighting （THINC/SW） scheme. The FEM was applied for calculating the structural deformation. A volume weighted method, which was based on the immersed boundary （IB） method, was adopted for coupling the FDM and the FEM together. An elastic wedge water entry problem was calculated by the coupled FDM-FEM method. Also a comparison between the current numerical results and the published results indicate that the coupled FDM-FEM method has reasonably good accuracy in predicting the impact force.

Boundary Element Analysis of Two Dimensional Structure Water Entry Based on Attached Water Quality

Combining nonlinear boundary conditions of free liquid surface, the impact force of wedge shape profile and the change of free liquid surface were calculated and analyzed based on the solving ideas of Von Karman T. The results were compared with the results of the existing literature, and the results were in good agreement with the existing results. In addition, the impact forces of U profile and the external drift profile were calculated, and the impact load of two kinds of profiles were analyzed through time evolution.

Numerical Simulation of High-Speed Water Entry of Cone-Cylinder

Numerical method by solving Reynolds-averaged Navier-Stokes equations is presented to solve the vertical high-speed water entry problem of a cone-cylinder. The results of the trajectory and cavity shape agree well with the results obtained by the analytical model from literatures. The velocity of the projectile decays rapidly during the penetration,which is about 90% losing in 80D penetration depth. Pressure distributions are also discussed and the results show that the largest pressure appears on the tip of the cone and the lowest pressure occurs inside the cavity and causes vapor generation. For inside the cavity,there is always a supplement of air from outside before the splash closed,after that,the cavity is mainly filled with vapor.