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.

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.

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.

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.

Application of IITM-RANS3D to free-fall water entry of prismatic and non-prismatic finite wedges

High-speed watercraft and ships undergo coupled motions which make the front portion of the hull exit and violently re-enter water.This induces short-term slamming loads that may compromise the structural integrity of the hull.The slamming of the bow can be modeled as straight wedges of different deadrise angles(DRAs)falling into water from different heights.The advent of computational fluid dynamics has allowed the problem of wedge-slamming to be simulated using the full Navier-Stokes equations thus complementing the pioneering studies based on experiments.Recently,most researchers are opting to use commercial software to simulate the wedge-impact problem as it allows access to overset meshing algorithms which are robust in modeling the wedge as a moving body.Embedded boundary methods(EBMs)offer some advantages over overset meshing in that the mesh only needs to be generated once and Cartesian mesh-based solvers can be implemented.However,the application of EBMs to wedge-impact has been limited in the literature and merits further development.In this context,we investigate the applicability of the fast-fictitious-domain(FFD)based embedded boundary treatment to simulate the violent water-entry of wedges.We extend our in-house Navier-Stokes model IITM-RANS3D to handle floating bodies through integration of a rigid-body dynamics solver and an algorithm to embed three-dimensional stereolithography(STL)geometries as solids over a Cartesian mesh.The proposed algorithm is extensively benchmarked against variable DRA wedge-slamming experiments reported in the literature as well as constant DRA wedge-slamming experiments performed in-house.Very good agreement is reported in terms of the time-history of hydrodynamic impact pressures measured at various locations on the hull as well as the wedge motion responses thus demonstrating the suitability of FFD for simulating the coupled hydrodynamics of slamming for simplified hull geometries.

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 AND THEORETICAL STUDY ON THE HIGH-SPEED HORIZONTAL WATER ENTRY BEHAVIORS OF CYLINDRICAL PROJECTILES

In this article,the horizontal water-entry of flat-nose projectiles of two different lengths at impact velocities of 400 m/s-600 m/s is studied experimentally and theoretically.Based on the solution of the Rayleigh-Besant problem,a set of projectile dynamic equations are derived and a cavity model is built to describe the projectile＇s water entry dynamics.A parameter in the cavity model is determined by employing the principle of energy conservation.The results indicate that the flat-nose projectiles enjoy a good stability of trajectory,the drag coefficient and the velocity decay coefficient are dependent on the cavitation number,and increase along the penetration distance but with a relatively small variation.The maximum cavity radius decreases monotonically with the penetration distance.Projectiles with the same nose shapes at different initial velocities have a basically consistent cavity dimension before the deep pinching off phenomenon occurs.Good agreements are observed between results obtained by the analytical model and the experimental results.

WATER ENTRY OF A WEDGE BASED ON SPH MODEL WITH AN IMPROVED BOUNDARY TREATMENT

The hydrodynamic problem of a two-dimensional wedge entering water is studied based on Smoothed Particle Hydrodynamics （SPH） model. A non-reflection boundary treatment for SPH method is proposed to reduce the reflection of sound waves. The boundary pressure is obtained using an improved coupling boundary treatment approach, which is validated by comparing the simulation results with experimental and analytical results in literature. A series of cases with different initial entering velocities are simulated. The maximum force on the wedge and the corresponding time required to reach it for the different cases of initial entering velocities of the wedge are obained and fitted into formulas against the initial entering velocity of the wedge. The maximum drag coefficients of the wedge for the different cases with Froude number greater than 2 are all near the value of 0.91.

Two-phase SPH simulation of vertical water entry of a two-dimensional structure

In view of the fact that the SPH model is easy to handle the flows with the free surface of large deformation, a 2-D flow induced by vertical water entry of a 2-D structure is simulated using the two-phase SPH model. The local pressure of the boundary particles is obtained by pressure of the fluid particles nearby through a modified kernel approximation. To evaluate the accuracy of the method, water entry of a 2-D symmetric wedge with fixed separation point of the free surface on the wedge surface is simulated. The pressure distribution of the wedge at the initial stage agrees well with the analytical results available. Evolution of the free surface and the air flow in the cavity induced by the water entry are obtained. A higher speed air jet is found at the neck of the cavity when the neck of the cavity becomes smaller. For the case of a horizontal cylinder entering the water with an unknown separation point of flow on the model surface, the early stage of the water entry is simulated for the rigid body with different density. Evolution of the free surface deformation of the half-buoyant cylinder and neutrally buoyant cylinder water entry is compared with the experimental data. The effects of the density ratio and Froude number on the pinch-off of the cavity are discussed. It is found that the pinch-off time remains almost constant for different density ratio and Froude number. Meanwhile, for a given Froude number, the dimensionless pinch-off depth and the location of the cylinder at the time of pinch-off increase with the density ratio. Further, for a given density ratio, these two parameters increase with the Froude number and, however, the relative cavity shape appears to be a self-similar shape when Fr ≥8.35.

Numerical simulation of the effect of waves on cavity dynamics for oblique water entry of a cylinder

The water entry process associated with complicated unsteady structures,with consideration of the influence of the waves,is not well studied.In the present work,the oblique water entry of a cylinder under different regular waves is numerically investigated.The volume of fluid(VOF)method and the sub-grid scale(SGS)stress model based on the large eddy simulation(LES)method are adopted for the 3-D simulation with six degrees of freedom.The present numerical model is based on a wave model,and as shown by the previous work that the predicted cavity evolution in the calm water agrees well with the experimental results.The present model is validated and it is shown that it could be used to predict the correct wave periods and fluctuations.The cavity evolution mechanism,the dynamic characteristics and the vortex structures are analyzed.The cavity of the water entry with waves closes more quickly than in the calm water case.Finally,several parametric studies of the water entry with different wave heights and water entry locations are carried out.The results provide insights into the effects of the waves on the cavity dynamics for oblique water entry problems.

Effects of Froude number and geometry on water entry of a 2-D ellipse

By using the finite volume method with volume of fluid model and global dynamic mesh technique, the effects of Froude number and geometry on the water entry process of a 2-D ellipse are investigated numerically. For the time history of the vertical force, the computational fluid dynamics（CFD） results match the experimental data much better than the classical potential-flow theories due to the consideration of the viscosity, turbulence, surface tension, gravity, and compressibility. The results show that the position of peak pressure on ellipse shifts from the spray root to the bottom of ellipse at a critical time. The critical time changes with the geometry and Froude number. By studying the vertical force, the ellipse water entry process can be divided into the initial and late stages based on the critical dimensionless time of about 0.1. The geometry of the ellipse plays a dominant role in the initial stage, while the Froude number is more important in the late stage of entry. The classical Wagner theory is extended to the ellipse water entry, and the predicted maximum value of vertical force coefficient in the initial stage is 4？a/b that matches the CFD results very well, where a and b are the horizontal axis and vertical axis of the ellipse parallel and perpendicular to the initial calm water surface, respectively.

Water entry and exit of axisymmetric bodies by CFD approach

The water impact and subsequent entry of three rigid axisymmetric bodies,a sphere and two cones,in the early phase are simulated using CFD utilizing a VOF scheme to track the free surface and the results compared with the recent experimental results available in the literature.The penetration depth,vertical velocity and vertical acceleration time histories have been reproduced well by CFD with a wide choice of mesh density,whereas the peak pressure on impact required a much finer mesh and appropriate choice of the time step.Delineating an interaction region around the trajectory of the body with fine mesh and an adaptive time stepping strategy has worked well to capture the peak impact pressure accurately with reasonable computational effort.The‘full’motion of the sphere,which is buoyant,has also been simulated using CFD allowing its 6-dof motion for several cycles of entry and exit phases.The features of the behavior,especially the loss of symmetry of the trajectory,are discussed.

Numerical simulation of water entry problems considering air effect using a multiphase Riemann-SPH model

The water entry is a classic fluid-structure interaction problem in ocean engineering.The prediction of impact loads on structure during the water entry is critical to some engineering applications.In this paper,a multiphase Riemann-SPH model is developed to investigate water entry problems.In this model,a special treatment,a cut-off value for the particle density,is arranged to avoid the occurrence of negative pressure.A remarkable advantage of the present multiphase SPH model is that the real speed of sound in air can be allowed when simulating water-air flows.In the present work,considering the air effect,several typical water entry problems are studied,and the evolution of multiphase interface,the motion characteristic of structure and complex fluid-structure interactions during the water entry are analyzed.Compared with the experimental data,the present multiphase SPH model can obtain satisfactory results,and it can be considered as a reliable tool in reproducing some fluid-structure interaction problems.

Water entry of decelerating spheres simulations using improved ISPH method

In this paper, we simulated the vertical impact of spheres on a water surface using three-dimensional incompressible smoothed particle hydrodynamics(3-D ISPH) method. The sphere motion is taken to be a rigid body motion and it is modeled by ISPH method. The governing equations are discretized and solved numerically using ISPH method. A stabilized incompressible SPH method by relaxing the density invariance condition is adopted. Here, we computed the motions of a rigid body by direct integration of the fluid pressure at the position of each particle on the body surface. The equations of translational and rotational motion were integrated in time domain to update the position of the rigid body at each time step. In this study, we improved the boundary treatment between fluid and fixed solid boundary by using virtual marker technique. In addition, an improved algorithm based on the virtual marker technique for the boundary particles is proposed to treat the moving boundary of the rigid body motion. The force exerted on the moving rigid boundary particles by the surrounding particles, is calculated by the SPH approximation at the virtual marker points. The applicability and efficiency of the current ISPH method are tested by comparison with reference experimental results.

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.

A Level Set Immersed Boundary Method for Water Entry and Exit

The interaction between free surface flow and structure is investigated using a new level set immersed boundary method.The incorporation of an improved immersed boundary method with a free surface capture scheme implemented in a Navier-Stokes solver allows the interaction between fluid flow with free surface and moving body/bodies of almost arbitrary shape to be modelled.A new algorithm is proposed to locate exact forcing points near solid boundaries,which provides an accurate numerical solution.The discretized linear system of the Poisson pressure equation is solved using the Generalized Minimum Residual(GMRES)method with incomplete LU preconditioning.Uniform flow past a cylinder at Reynolds number Re=100 is modelled using the present model and results agree well with the experiment and numerical data in the literature.Water exit and entry of a cylinder at the prescribed velocity is also investigated.The predicted slamming coefficient is in good agreement with experimental data and previous numerical simulations using a ComFlow model.The vertical slamming force and pressure distribution for the free falling wedge is also studied by the present model and comparisons with available theoretical solutions and experimental data are made.

Numerical study on the dynamic characteristics of water entry of cavity body using two-phase SPH method

The air usually has a major influence on the water entry of a typical cavity body(cavity body is a hollow,cylindrical,semiclosed structure),which not only lowers the slamming load but also affects the dynamic characteristics of water entry.In this paper,a two-phase smoothed particle hydrodynamics(SPH)model for simulating the water entry of cavity body is presented.The SPH model combined with Riemann solver is improved to deal with the two-phase flows with the discontinuous quantities across the interface.One-sided Riemann problem is used to impose the fluid–structure interaction and a switchfunction-based Riemann solver dissipation is formulated to improve the interfacial instability owing to the strong impact.The motion equations of rigid body are incorporated into two-phase SPH model to describe the motion of cavity body.The proposed model is validated by research on the test cases in the published literature.Finally,this work presents a study of water entry of cavity body by experiment and this two-phase SPH method.The dynamics phenomena in the coupling process between cavity body and two-phase flow are investigated.And the effects of air,mass,the sizes and incline angles of cavity body on the dynamic characteristics of cavity body and two-phase flows are shown.