Computational Method Study On Shock Mitigation Coatings Subjected To Underwater Explosion

Coating shock mitigation coatings on naval vessels is a new trend for underwater shock load mitigation.Predicting the response of shock mitigation coatings subjected to underwater explosion accurately and efficiently is the basis of shock mitigation coatings design.The underwater explosion problem can be divided into different categories: far-field underwater explosion problems and near-field underwater explosion problems according to the different explosive distances and structural responses;early-time response problems and mid/late-time response problems based on the different time scales and features of the structural responses.To obtain high accuracy and high efficiency,different computational methods need to be employed for different categories of underwater explosion problems.For far-field underwater explosion problem,computational methods for the acoustic fluid are usually used.For near-field,early-time response underwater explosion problems,computational methods for the compressible fluid are usually employed.For near-field,mid/late-time response underwater explosion problem,computational methods for the incompressible fluid are commonly applied.In recent years,the research on the computational methods for underwater explosion and the protective mechanism of shock mitigation coatings have made great improvements.However,due to the complexity of the problem of shock mitigation coatings subjected to underwater explosion,the accuracy and efficiency of the computational methods for underwater explosion and the optimal design of the shock mitigation coatings needs to be improved further.For this reason,this thesis reviewed the protective mechanism of shock mitigation coatings subjected to underwater explosion and the computational methods for underwater explosion.It is found that in the past research,for far-field underwater explosion problems,the longitudinal elasticity of the soft shock mitigation coatings along the direction of shock wave propagation is seldom studied,and there is no analytical methods with high efficiency and high accuracy;for near-field,early-time response problems,the modified ghost fluid method(MGFM)for fluid-structure interaction is lack of flexibility and difficult to extend to the problem considering rather various kinds of materials of the shock mitigation coatings,since the MGFM needs to construct different Riemann problems for different kinds of coating materials;for near-field,total-time response problems,the existing numerical methods are inefficient or in low accuracy;for the optimal design of the shock mitigation coatings,the analysis of graded effects of the coatings subjected to near-field underwater explosion are not comprehensive.Based on the existing problem in the current research,to provide basic theoretical supports for the design of the shock mitigation coatings,this thesis have conducted the studies of wave theory based computational method for shock mitigation coatings subjected to farfield underwater explosion,coupling Runge-Kutta discontinuous Galerkin(RKDG)method and finite element method(FEM)(RKDG-FEM)for the near-field,early-time response underwater explosion,coupling RKDG,boundary element method(BEM)and FEM(RKDG-BEM-FEM)for the near-field,total-time response underwater explosion and the graded effects of shock mitigation coatings subjected to near-field underwater explosion.The specific research contents and conclusions are given as follows:(1)For the shock mitigation coating in far-field underwater explosion problems,assuming that the fluid is the acoustic fluid controlled by wave equations,this thesis presents a theoretical computational method for onedimensional shock waves propagating in one or two mediums with airbacked/rigid-backed conditions which includes the effects of cavitation and large deformation.Taking the elasticity in the longitudinal direction into account,the theoretical computational method can accurately predict the pressure at the interface between different medium.Comparing with traditional FEM,the proposed method improves the accuracy and efficiency.The investigations in the elasticity of the shock mitigation coatings indicate that the elasticity have a significant effect on the fluid cavitation.According to elastic feature of the coatings,the response of the fluid cavitation is divided into different regimes which are provided in the thesis.In addition,in the thesis,the non-dimensional peak pressure and transmitted momentum as a function of the non-dimensional impedance and transit time are quantitatively given to reveal the influence of the coating elasticity on the load on the coating.(2)For the shock mitigation coating in near-field,early-time response underwater explosion problems,assuming that the fluid(gas and water)is compressible,inviscid and with no heat transfer,controlled by Eulerian equations,this thesis develops RKDG-FEM and the corresponding codes,where the fluid response is solved by RKDG,the structural response is solved by Abaqus/Explicit,and the coupling interface is realized by a fortran subroutine.Within the code,the level set method is used to capture the gaswater and water-structure interface.The MGFM with special designed for RKDG is used to treat the gas-water interfaces.For the coupling of the fluid and solid interface,this thesis improved the MGFM for the fluid-structure interaction problem.Directly using Lagrangian interface velocity as the velocity solution of the constructed Riemann problem,the interface pressure and the fluid density are obtained by solving the modified fluid-solid Riemann problem.The obtained interface pressure then serves as boundary conditions to the Lagrangian domain.The improved method do not need to construct different Riemann problems for different kinds of coating materials,and can impose the boundary conditions for the Lagrangian domain and Eulerian domain at the same time,which improve the flexibility of the computational method for fluid-structure interaction and preserve the computational accuracy.Case studies are performed to verify the correctness of RKDG-FEM and demonstrate that the numerical solver is able to capture the non-linear fluid-structure interaction involving the strong shocks,the gas bubble dynamics,the cavitation inception and collapse,and the complex stress and deformation fields of deformable sandwich structures.(3)For the shock mitigation coating in near-field,total-time response underwater explosion problems,assuming that the fluid is incompressible and controlled by Laplace equations in the near-field,mid/late-time response,this thesis develops RKDG-BEM-FEM and the corresponding codes to deal with the low efficiency of RKDG-FEM in solving the mid/latetime response,where RKDG-FEM solves the early-time response characterized by shock wave phase,BEM-FEM solves the mid/late-time response characterized by bubble pulse phase,and the coupling between RKDG-FEM and BEM-FEM is realized by a coupling interface.Compared with solely using the compressible fluids solvers for the total-time response,RKDG-BEM-FEM can greatly reduce the computation time;compared with solely using the incompressible fluids solvers such as BEM for the totaltime response,RKDG-BEM-FEM takes the effects of the shock wave into account,which increases the accuracy.In addition,when the flow status is transformed from the RKDG solver to the BEM solver,the proposed method can predict the period and the maximum radius of the explosion bubble with high accuracy,even if the fluid mesh is not fine enough in the RKDG solver.The developed RKDG-BEM-FEM solver is then applied to calculate the response of bare steel plates,rubber coated steel plates,and foam coated plates subjected to near-field underwater explosion.The calculations by RKDG-BEM-FEM are compared with experimental results and indicate that RKDG-BEM-FEM can accurately and efficiently predict the early-time shock wave phase and mid/late-time bubble pulse phase of the structures coated with shock mitigation coatings.(4)The developed RKDG-FEM solver is then applied to study the effects of cores grading of shock mitigation coatings.The effects of face sheets and different core configurations,including “low/medium/high”,“high/medium/low” and “medium/medium/medium”(relative density from close to the explosive to far from the explosive),are taken into considerations.The results show that the shock resistance ability of the cores is codetermined by the effects of fluid-structure interactions and the efficiency of the energy absorption of the cores.The total work done by the fluids is dependent on the strength of the foam cores adjacent to the water.The amount of the total work done will be smaller for the softer foam core.For the case of relatively strong cores and the outer face sheet with low stiffness or soft cores and the outer face sheet with high stiffness,the core arrangement of “low/medium/high” has the best performance to shock loadings;on the other hand,for the case of intermediate core strengths and stiffness of the outer face sheet,the configuration of “high/medium/low” has the best performance.