The Discontinuous Galerkin Method For Compressible Gas-Solid Two-Phase Flow

Multiphase flow phenomenon are widespread in nature and in modern industrial processes.Many industrial applications such as chemical engineering,energy power,metallurgy and weapon physics involve multiphase flow problems.Multiphase flows are more complex than single-phase flows in various forms.However,they all follow the basic laws of mass,momentum and energy conservation in essence.It is the existence of these commonalities that makes it possible to study their motion rules.A new branch of fluid Inechanics,multiphase fluid mechanics(dynamics),has been formed.Although the discipline of multiphase(two-phase)flow has developed rapidly in recent decades,many experiences have been accumulated,many theories have been put forward,and many production and living problems have been solved.However,due to the complexity of multiphase flows,many phenomena,mechanisms and processes of multiphase flows are not well understood.The models ot two-phase flow are complex and various,their mathematical properties and numerical methods are different,and they are still advancing in their respective directions.Unlike general industrial applications,in high-tech fields such as aerospace and weapons,gas-solid two-phase flow is often accompanied by sharp changes in pressure and density,especially in the presence of compressible phenomena such as shock waves.The existence of particle phase has a huge impact on the compression effect of gas.Discontinuous Galerkin method(DG method)is an efficient and flexible tool for solving partial differential equations.It has been widely used in natural science and engineering.In this paper,the DG method is extended to solve the governing equations of' compressible gas-solid two-phase flow.This paper begins with the introduction of the basic concepts related to gas-solid two-phase flow,reviews the development history of two-phase flow research,and introduces the physical and mathematical models of various two-phase flows.The governing equations of the two-fluid model for the dilute gas-solid two-phase flow are derived and its mathematical properties are analyzed.The dilute gas-solid two-phase flow in the dusty gas shock tube and solid rocket engine nozzle is solved by DG method,and the influence of particle phase on gas motion is analyzed in detail.It is found that in compressible gas-solid two-phase flow,?the mass ratio and particle size of the particle phase are the key parameters affecting the flow structure.The particle mass ratio determines the equilibrium state of the two-phase flow,and the particle size determines the process of two-phase relaxation.The governing equations of the two-fluid model for dense gas-solid two-phase flow are derived based on the kinetic theory of granular flow.According to the characteristics of compressible flow,a set of strict hyperbolic conservation laws are simplified to make it suitable for discretization by RKDG method.The feasibility of dense flow calculation is verified by the calculation of implosion compression process of high concentration dusty gas.