Time-Domain Analysis Of Water Entry Of A Two Dimensional Finite Width Wedge With Flow Detachment

Fluid and structure impact is very common in the field of marine technology,such as the ship bow reentering water,green water on deck,resonant sloshing in ship tanks and water slamming on a platform.The effect of water slamming on structure is twofold: on the one hand,it can cause serious structural damage.On the other hand,it may seriously affect the globe ship behavior seriously.Water entry is a kind of typical slamming problem,and the nonlinear effect always takes the dominant position.The strong nonlinear effect makes it very difficult to predict the slamming load on structures and the coupling motion between structures and fluids.The review of the previous study on water entry of two-dimensional wedges is divided into two parts according to whether wedges enter water in a given speed or in free fall.The two parts are reviewed from two aspects of theoretical study and numerical simulation.The study on water entry of an infinite-width wedge is introduced in each aspect as well as a finite-width wedge.The boundary element method and the mixed Euler-Lagrange method to track free surface are used for studying water entry problem of a finite-width wedge.The mathematical model and the boundary integral equation which satisfy the completely nonlinear boundary condition are established.A modified fourth-order Runge-Kutta scheme is used for time stepping.A cubic spline approximation and least square method are respectively used to regrid and smooth the new free surface.To treat the intersection between the free surface and the body surface,normal derivative of velocity potential at the intersection can be divided into two parts before flow detachment,and after flow detachment a velocity continuous condition is used at the point.The jet is treated by shallow water equation before flow detachment,and by momentum equation after flow detachment.The stretched coordinate system is used properly,and the auxiliary function method is used to decouple the mutual motion between the fluid and the structure.A finite-width wedge entering water obliquely at a prescribed speed is considered.The numerical model includes the effects of the asymmetry of the body shape,horizontal speed,gravity and flow detachment.Through time step and element length convergence study and comparison with existing numerical and experimental results,the numerical method in the present paper has been verified and the numerical results are stable and reliable.For vertical water entry of symmetrical wedges,entry of wedges with different deadrise angles and with different initial vertical velocities are studied.It is found that when wedges with different deadrise angles enter water,for the wedge with a smaller deadrise angle,the difference of the pressure distribution on body surface between before and after flow detachment is more significant,and the pressure will reduce more after flow detachment.The gravity effect is unimportant within a short time,or when a wedge enters water with a larger velocity.Asymmetric water entry of wedges with different heel angles,horizontal velocities and rotational velocities are also studied.The flow will cross the tip of the wedge when water entry is asymmetric,and it will cause that the pressure varies rapidly near the tip.When the relative direction of the main flow is along the symmetry line,the discontinuity of the pressure at the tip gradually disappears as time progresses.A two-dimensional finite wedge entering water obliquely in freefall with three degrees of freedom is considered.The mathematical model is established and the auxiliary function method is used to decouple the mutual motion between the fluids and the structures.The present model and numerical method have been verified in several aspects through convergence study and the comparison results for both symmetric and asymmetric water entry with existing results.When a body enters water vertically,the acceleration rapidly changes its direction and its magnitude can be much larger than acceleration due to gravity.As a result,the entry speed is reduced sharply.Oblique entry of an asymmetrical body with rotational velocity is studies,in which the fluid force will set the body into motion of three degrees of freedom.The effect of the location of the centre of the body mass has been studies.Water entry of a finite-width wedge with influence of a free floating body is considered.The portion of the fluid domain disturbed by the water entry increases as the body moves into the water.The whole process of water entry can be divided into two stages according to whether the fluid around the free floating body is disturbed.At the first stage,the single wedge entering water is studied in the stretched coordinate,and at the second stage both the freefall in three degrees of a finite-width wedge and the motion of the free floating body are studied in Cartesian space coordinate.The motion and force of the floating body effected by a symmetric wedge vertically entering water is studied,and the influence of wedges with different speeds,deadrise angles and distances from the free floating body is investigated.The coupled motion between a finite-width wedge in freefall in three degrees and the free floating body is considered,and the influence of water entry of wedges with different initial heel angles,initial horizontal velocities and initial rotational velocities is studied.