| Multi-media Riemann problem becomes a hot issue in recently years. The main difficulty of this problem lies in the discontinuous interfaces. As the fluids show differences in state and property at two sides of interface, it is hard to simulate of the fluids motion near the interface, especially for the interface of medias with complex equation of states (EOS). Although a lot of numerical models are developed for such a discontinuous interface problem, many of them describe the media with EOS in which constant-parameter are used. The development of numerical solver for variable-parameter EOS is still very slow because it is hard to maintain the pressure equilibrium among different medias. At present, the equilibrium condition of pressure are always carried up by using additional procedures in calculation. The additional procedures, however, make the computation complex, especially for fluids which contain three or more medias. For these reasons, we made a lot of works to seek a simple and effective to solve the multi-media interface problem.An improved Mie-Gruneisen mxiture model based on mass fraction is presented here. The model expresses the general EOS in a Mie-Gruneisen form which contains variable parameters. The Mie-Gruneisen EOS use thermodynamical parameters which vary with density, that make the EOS flexible in application, but the drawback of Mie-Gruneisen EOS is that the expression is a bit complex. To simplify the computation process, the variable parameters in Mie-Gruneisen EOS are taken as independent variables and introduced in calculation, and new auxiliary equations are added to compute these variables. So the Riemann problem can be solved by a combination of the original Euler equations and new auxiliary equations. For multi-media fluids, it is very effective to consider the fluids mixture as an entire fluid, and use color functions to make a distinction of the fluid components. In our works, mass fraction is chosen as color function and the multi-media problem is still solved by the Euler equations and other corresponding auxiliary equations. Considering that the fluids mixture contains different medias, the auxiliary equations are constructed by establishing a diffused balance among different medias here. The diffused balance is based on an approximation of fluid mixture model which connects its medias by mass fraction. The role of mass fraction is replacing the discountinous jumping by smooth transition and guaranteeing a non-oscillation solution near the interface. To make the system completed, transport equations, in terms of mass fraction, are added in the equations system. The whole equations system of the Mie-Griineisen mass fraction model includes three parts:original Euler equations for the whole fluids, auxiliary equations of new created variables, and transport equations. The Mie-Griineisen mass fraction model is in a simple style and can be easily extend to Riemann problem with three or more medias.The strong gas-water Riemann problem is studied with the help of Mie-Griineisen mass fraction model. For strong shock problem of gas-water interaction in underwater explosion, the different reference states are considered here. For compressed water, shock-Hugoniot curve is taken as reference state; while for expanding water, it is replaced by Murnagham isentropic curve. Therefore, the EOS for water is in a piecewise form with respect to density. For such a piecewise EOS of water, there’s a crucial point that the state estimation relies on density of water. As the mixture model based on mass fraction is used here, the density of water can be directly deduced and there’s no need to use other additional condition. And some numerical tests about gas-water problem are present here. The comparisons of calculated and experimental data show that the Mie-Griineisen mass fraction model gives accuracy solutions for strong shock gas-water flow.The Mie-Griineisen mass fraction model is applied to the fluid-structure interaction in underwater explosion. The impact effects of explosion shock wave on rigid and elastic body are both studied here. For rigid body, the edge of body are taken as boundary, the boundary conidition is set as total reflection condition. The condition is satisfied by setting illusion points at inner region the rigid body. While for elastic body, it is modeled by a Mie-Griineisen EOS, which taking Hugoniot curve as reference state. The feasibility of elastic body model is tested and verified by detonation shock tube tests. Then the model is applied to the simulation of some2D underwater explosion problems. In the simulation, deformation of structure under explosion loads, as well as second shock wave, are specially studied here.The protection effects of mitigation layer against shock wave in underwater explosion are investigated here. By using uniform Mie-Griineisen EOS to model explosive charge, water and mitigation layer, as well as other elastic structure, it is easy and effective for Mie-Gruneisen mass fraction model to simulate the interaction among different medias. Then an investigation about the effects of mitigation layer is given here. In this investigation, it is found that when structure is covered by mitigation layer, the impact of explosion wave produces second shock wave or rarefaction wave on structure. The property of the second wave depends on the shock impedance of layer, if this shock impedance higher than water, it generates shock wave; or else, it generates rarefaction wave. And the protection effects only occur when the impedance of layer is smaller than water. In addition, the compressible structure can also be protected by mitigation layer. The deformation will be reduced when mitigation layer is used. For structure mitigated by low impedance layer, the affection of layer thickness and explosive-structure distance is studied here. It is concluded that they mainly affect the protection effects on second shock while almost don’t affect the protection effects on main shock. |
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