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.

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.

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.

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 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.

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.

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.

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.

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.

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 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.

A Modified Logvinovich Model For Hydrodynamic Loads on an Asymmetric Wedge Entering Water with a Roll Motion

The water entry problem of an asymmetric wedge with roll motion was analyzed by the method of a modified Logvinovich model (MLM). The MLM is a kind of analytical model based on the Wagner method, which linearizes the free surface condition and body boundary condition. The difference is that the MLM applies a nonlinear Bernoulli equation to obtain pressure distribution, which has been proven to be helpful to enhance the accuracy of hydrodynamic loads. The Wagner condition in this paper was generalized to solve the problem of the water entry of a wedge body with rotational velocity. The comparison of wet width between the MLM and a fully nonlinear numerical approach was given, and they agree well with each other. The effect of angular velocity on the hydrodynamic loads of a wedge body was investigated.

Experimental Study of a Sphere Bouncing on the Water

In this paper,the fow physics and impact dynamics of a sphere bouncing on a water surface are studied experimentally.During the experiments,high-speed camera photography techniques are used to capture the cavity and free surface evolution when the sphere impacts and skips on the water surface.The infuences of the impact velocity(v_(1))and impact angle(θ_(1))of the sphere on the bouncing fow physics are also investigated,including the cavitation evolution,motion characteristics,and bounding law.Regulations for the relationship between v_(1)andθ_(1)to judge whether the sphere can bounce on the water surface are presented and analyzed by summarizing a large amount of experimental data.In addition,the efect ofθ_(1)on the energy loss of the sphere is also analyzed and discussed.The experiment results show that there is a ftted curve of v_(1)=17.5θ_(1)−45.5 determining the relationship between the critical initial velocity and angle whether the sphere bounces on the water surface.

Experimental investigation of clam water impact on flatted-bottom seafloor mining tool

A test rig for constant velocity water entry experiments was developed that drives a flatted-bottom section attached on six degree of freedom(6-DOF) platform to enter the water vertically at near constant velocity.The experiment system,which consists of drive and actuation system,water pool,model test sections,load cell,and control system,was presented.Water entry forces of different velocities were measured during impact process,and for each test case,three runs were performed with the same motion program to check the repeatability of the force readings.The experiment results are compared with two-dimensional(2D) CFD simulation methods for flatted-bottom rigid bodies with constant entry velocity.Experimental results indicate that the impact forces mainly depend on water entry velocities.It is concluded that the feasibility and accuracy of simulation methods has been validated.

Analysis of particle dispersion and cavity formation during bulk particle water entry using fully coupled CFD-DEM-VOF approach

This paper presents the development and validation of a fully coupled computational fluid dynamics—discrete element method—volume of fluid(CFD-DEM-VOF)model to simulate the complex behavior of particle-laden flows with free surfaces.The coupling between the fluid and particle phases is established through the implemented continuity,momentum,and alpha transport equation.The coupled particle forces such as drag,pressure gradient,dense virtual mass,viscous,and interface forces are also integrated,with drag and dense virtual mass forces being dependent on local porosity.The integrated conservative alpha transport equation ensures phase volume conservation during interactions between particles and water.Additionally,we have implemented a trilinear interpolation method designed to operate on unstructured hexahedral meshes.This method has been tested for its ability to properly resolve the coupling effects in the numerical simulations,particularly in cases with a relatively low cell-size ratio.The model is validated through three distinct test cases:single particle water entry,dam break with particles,and water entry of a group of particles case.The experimental setup is built to study the dynamics of the water entry of a group of particles,where three key flow features are analyzed:the evolution of average particle velocity,cavity shape,and particle dispersion cloud profiles in water.The tests involve four different scenarios,including two different water levels(16.1 and 20.1 cm)and two different particle densities(2650 and 4000 kg/m3).High-speed videometry and particle tracking velocimetry(using ImageJ/TrackMate)methods are employed for experimental data acquisition.It is demonstrated that numerical results are in excellent agreement with theoretical predictions and experimental data.The study highlights the significance of vortices in cavity shaping and particle dispersion.The validated CFD-DEM-VOF model constitutes a robust tool for simulating particle-laden flows,contributing valuable insights into the complex interplay between particles and fluids.