Modeling And Research Of Non-equilibrium Flows And Multi-phase Flows

Non-equilibrium and multiphase flows widely exist in nature and engineering fields,such as supernova explosion,supersonic flight,inertial confinement fusion,micro-electromechanicals system and microfluidic control technology,oil and gas exploitation,and the mixing and combustion of fuel in an engine,etc.Research on these kinds of flows not only has important scientific significance,but also can provide effective guidance for engineering practice.At the same time,non-equilibrium and multiphase flow problems usually possesses complex spatio-temporal multi-scale and strong nonlinear characteristics.Research on these kind of problems needs both reliable physical model and pratical data analysis and information extraction techniques.In this dissertation,several typical non-equilibrium and multiphase flow problems are investigated from two aspects: physical modeling and numerical simulation.In terms of physical modeling,a series of reliable kinetic models suitable for non-equilibrium flow with high-Knudsen number are constructed based on discrete Boltzmann method(DBM);In terms of simulation research,the behavior characteristics and formation mechanism of nonequilibrium and multi-phase complex flow processes are studied from multiple perspectives based on the new DBM combined with a variety of complex physical field analysis techniques.The main contents of the study are as follows:First,a Maxwell-type kinetic boundary condition for DBM is developed,thus the application scope of DBM is successfully extended to slip flow.The tangential momentum accommodation coefficient is introduced in the new boundary condition on the basis of complete diffuse reflection boundary,which can be used to characterize the roughness of different wall surfaces.Combined with the new boundary condition,DBM can accurately capture the slip velocity and the nonlinear distribution of the velocity in the Knudsen layer near the wall.Second,the DBM of transition flow is constructed based on Ellipsoidal statistical BGK model.The new model can break through the limitation of the fixed Prandtl number in the single relaxation time DBM.In addition to being consistent with the macroscopic fluid equations at the Burnett level under the corresponding conditions,the new model can also provide some thermal non-equilibrium behavior characteristics that are most closely related to macroscopic flows.The relationship between the non-equilibrium effects provided by DBM near the shock front and the viscous stress and heat flux terms in Burnett equations is studied.Based on the multi-scale expansion technique,a new method for quantitatively recovering the main characteristics of molecular velocity distribution function is presented.Third,the general framework of the discrete Boltzmann modeling for the thermal nonequilibrium flow is presented based on the Shakhov model combined with the Hermite polynomial expansion.The new model not only has the adjustable specific heat ratio and the Prandtl number,but also can be directly expanded to any higher order.It can capture the nonequilibrium characteristics near the boundary and in the main flow area at the same time.The accuracy of the new model in describing non-equilibrium flows is verified by comparing with the analytical solutions of slip flow and DSMC results.Fourth,in the study of hydrodynamic instability,Kelvin-Helmholtz instability is taken as an example to analyze the non-equilibrium characteristics near the fluid interface.A new interface capture technique is proposed based on the newly defined non-equilibrium strength measure.It shows that the non-equilibrium strength provided by DBM can be readily used to obtain the fluid interface with higher resolution.Finally,the phase separation process is investigated based on multi-phase flow DBM and in combination with the complex physical field analysis method.For the first time,an analytical relation between entropy production rate and non-equilibrium characteristics in multi-phase flow system is obtained.Based on this relation,the main mechanism of entropy increase and its relative importance in the process of system evolution can be conveniently studied.A new physical criterion for dividing the two stages,spinodal decomposition and domain growth,of phase separation is proposed based on the rate of entropy production.The effects of heat flux,viscosity and surface tension on the entropy production during the phase separation process are carefully examined and the corresponding physical explanations are given.In addition,the competition and cooperation between the two mechanisms of entropy production under various heat flux,viscosity,and surface tension are compared and analyzed,respectively.