Numerical Investigation On Water Entry Problems Based On Smoothed Particle Hydrodynamics Method

The study on the response of deformable structure when it enters into the water is crucial for the stability and safety evaluation of the structure.However,the large slamming force may lead to intense spray with the entrapped air on the water surface.This further increases the complexity of the fluid-structure interaction,which brings great challenges to the numerical method.As a Lagrangian particle method,Smooth Particle Hydrodynamics(SPH)method has unique advantages in dealing with the free surface,large deformation and fragmentation.In this paper,SPH method is enhanced and applied to the FSI(Fluid-Structure Interaction)problem to study the dynamic response of the structure under the water load and to provide a reference for the structural design in the engineering.In chapter 2,the SPH basic theory and its numerical techniques are introduced.Base on the high-order kernel estimation,the DFPM(Discontinuous Finite Particle Method)and the DSFPM(Discontinuous Simplified Finite Particle Method)methods are deduced in consideration of the discontinuous interface.The autonomous programming of the DFPM and DSFPM methods are used in collision examples with the different deformations to show that they can solve the unstable stress and velocity field.Meanwhile,the adaptive transformation algorithm of the DFPM and DSFPM is demonstrated to adapt the structure with the different deformation degrees.The third chapter studies the interface,the tensile instability and the adaption problems existed in the traditional SPH.For the three-phase coupling problem,the contact algorithms of the fluid-solid and gas-liquid are given respectively.The interaction between particles is transformed into the Riemann problem.The solid stress Riemann method and dynamic virtual particle method are proposed.Next,aiming at the pressure oscillation,numerical fracture and cavity issues,the Low-dissipation GSPH,the total Lagrangian SPH with four-particles selection and the pressure relaxation are presented respectively.The above methods are verified by the dam break and uniaxial tension examples.Finally,the adaptive SPH is realized in the FSI problem.This chapter proposes the two-phases split criterion for the first time.The split strategy also is introduced,including the splitting form,the interaction between coarse and fine particles,the position correction of particles,and the selection of splitting parameters.Finally,the particle dynamic refinement is applied to a water entry problem to test its advantages in the cost and accuracy.Based on the theoretical and numerical improvements in the first two chapters,the fourth chapter studies the fluid-elastomer interaction problem.Firstly,the water entry of the elastic wedge is simulated,and the advantage of the contact algorithm based on the Riemann solution is proved.Furthermore,the Low-dissipation GSPH method and the total Lagrangian SPH with four-particles selection proposed in the third chapter for fluid and solid are illustrated in improving the pressure fluctuation and the numerical instability.The influences of parameters on the structural response are also discussed.Besides,the variable resolution is developed for the deformable structure,which greatly improves the local resolution.When the structure enters the water,it is often accompanied by the air cushion and entrainment.The coupling of the deformable structure and the multiphase flow is studied for the first time in this chapter.The gas phase is added to the water entry model,and the influence of air on the response of elastic structure is discussed.The pressure relaxation method for gas phase is further explained.On this basis,the responses of the structure under different Reynolds number and Mach number are given.When the structure enters the water with large velocity,the material would enter into the plastic stage.In the fifth chapter,the material is extended to the elastic-plastic material,and SPH model with elastic-plastic material is constructed.Considering the tensile instability in the solid,the total Lagrangian SPH with four-particles selection mode is combined with the elasticplastic constitutive model.The high-speed impact example is simulated to show effectiveness.On this basis,the elastic structure in Chapter 4 is changed to the elastoplastic body.The twophase and three-phase models are studied respectively.The yield position,the slamming force and the deflection of the structure at different times are given.The difference between the elastoplastic and elastic materials is revealed,and the influence of different parameters on the structural response of elastoplastic materials are studied.In the last chapter,the FSI problem involving large deformation of structure in engineering is firstly simulated to illustrate the ability and accuracy of the algorithm.Furthermore,the C program is transplanted into the CUDA framework to realize the large-scale calculation.The two-dimensional water entry model is extended to the three-dimensional model to study the three-dimensional effect of the elastic body when it enters the water.Moreover,the air effect of two/three-dimension is compared to show the rationality of the autonomous program.