Numerical Method Of Compressible Multi-Medium Flow And Dynamics Of Dense Particle Cloud

Compressible multiphase flows can be widely seen in nature,industry and national defense,and thus are of great importance in scientific research and applications.Be-cause of the wide range of scales in space and time involved,there are challenges for theoretical modeling and numerical simulations of these problems.In particular,it is crucial to develop high-resolution,robust conservative sharp interface methods.In this thesis,two kinds of sharp-interface methods have been proposed:One is to simulate the interaction between shocks and particle cloud with second-order accuracy,and the other is for compressible generalized three-phase flows.Based on the proposed numeri-cal methods,we.investigate the migration of dense particles in high-speed airflows.The main works are briefly summarized as follows:(1)We present a second-order accurate conservative sharp interface method capable of simulating particles motion in compressible inviscid flows.We implement a cut cell algorithm to resolve moving particles of arbitrary shape on a Cartesian mesh,thereby generating unstructured body-fitted meshes near the particle surfaces and structured meshes away from the particles.A second-order finite volume method in the arbitrary Lagrange-Eulerian framework is used for the discretization of the Euler equations,so that exact conservation of mass,momentum and energy is enforced for the flow computations,even in the presence of moving particles.The boundary condition at the particle surfaces is enforced by solving a local Riemann problem,and the movement.of a particle is affected by the forces exerted by the surrounding fluid and its collisions with other particles.A hard sphere collision model is proposed to deal with multi-body collisions in dense particle clouds and to ensure the conservation of momentum and energy during collisions.The accuracy and robustness of this method is validated by comparing against benchmark solutions or experimental data available in the literature.(2)We propose a conserved sharp interface method for simulating two-dimensional compressible generalized three-phase flow.By using the regional Level-Set func-tion to track the interface,we store the interface information of three phases,and avoid the occurrence of cavities and overlapping areas near the interface.We pro-pose a ternary-phase cut cell method to reconstruct the interface on the Cartesian grid,and use different interfacial conditions to deal with the general three-phase flow problem.The method is able to not only deal with the three-phase fluid flow effectively,but also accurately simulate the two-phase flow with complex solid wall.Compared with the previous two-phase cut cell method,the method can effectively handles the situation that three phases coexist in one mesh.Numerical examples show that the method can successfully deal with compressible three-phase flows with three-phase points,large density ratios and interface topology changes.(3)We numerically study the problem of the migration of dense particles in high-speed airflows.The migration of particle cloud with different volume fraction under two configurations of particle distribution(regular and staggered)is studied system-atically.It is found that the intensity of reflected shock wave and transmitted wave which are generated in the upstream and downstream of the particle cloud respectively are closely related to the initial configuration and volume fraction of the particle cloud.After the shock wave impacts onto the particle group,it is observed that the last two rows of particles in the downstream of the parti-cle group move more rapidly than the particles in the upstream front row,and consequently separate from the particle cloud.Based on the detailed evolution of particle cloud and flow field,we interpret the mechanism of the rapid expan-sion of particle cloud and the apparent peeling of the two downstream particle rows.Finally,we obtain the theoretical predictions of the diffusion thickness of the particle cloud with regular and staggered arrangements based on the pressure difference model according to the fractal theory,and the theoretical predictions are in good agreement with the numerical simulation results.