摘要
本文依据国家自然科学基金项目《激波与可燃堆积粉尘相互作用》(批准号：19772018)和《流动及其机理的DSMC／EPSM混合算法研究》(批准号：19902021)以及国家高技术研究发展计划863项目《稀薄气体及过渡区RCS射流对气动的干扰特性研究》(批准号：2002AA726050)赋予的研究内容，在对国内外相关非均相非平衡流动建模与算法研究调研的基础上，选择了非均相流中的气固两相流和气体热化学非平衡流两类具有代表性的流动，用以探索满足Boltzmann方程输运特性的非均相非平衡可压流的流动规律，旨在寻求对这类复杂流动研究行之有效的模型和数值求解方法。
首先，针对连续介质范畴的可压稠密气固两相流的特点，引入颗粒粒化温度概念，构建适合于可压两相流的双流体模型，建立了统一的气固两相流控制方程。尔后从分析颗粒相在真空等情况下的波系传播特征着手，推导了颗粒相的近似黎曼算子，构造出能用于可压稠密气固两相非等熵流动的分步Roe格式，数值模拟了激波在一定厚度的惰性堆积粉尘床中传播及诱导粉尘颗粒运动的过程，给出了流场细致结构和流场的动态过程。同时将计算结果与实验进行比较，证实模型与算法的有效性，为解决可压稠密气固且存在间断界面的两相流问题提供了有效的研究途径。
其次，针对高空稀薄条件下过渡区气固两相流的流动特征以及DSMC方法的要求，通过宏观物理量的细观表达和气固两相本质一致的速度分布函数，建立了基于宏观物理量描述的气固相互作用与单个模拟粒子运动状态之间的联系，构建了适用于DSMC方法的气固相互作用的热力学模型和颗粒碰撞模型。并通过引入颗粒粒化温度，给出了颗粒相的来流和固壁边界条件的数学描述。在此基础上，对有气固两相横向喷流干扰的二维有限平板高超声速流场进行了数值模拟。由于DSMC方法的物理模拟本质使其能够较为容易地引入更真实的模型实现对复杂的物理化学过程的描述，因此本文工作为应用DSMC方法解决过渡区含化学反应等传质传热现象的气固两相流动提供了新的研究方法。
再者，鉴于DSMC方法和EPSM方法所具有的粒子模拟本质以及各自在计算包含稀薄与连续混合流动时所表现的优势和不足，本文应用Knudsen(克努森)数和Bird定义的连续介质模型失效参数作为流态控制参数，给出了复杂流场中稀薄／连续不同流态的判断依据，研究了稀薄区使用DSMC方法、连续流区使用EPSM方法的合理性，自动高效地实现了稀薄／连续复杂流场的DSMC／EPSM分区计算。应用DSMC／EPSM混合算法，数值模拟了无厚度有限平板的横向喷流干扰、有厚度有限平板的横向喷流干扰和轴对称平头圆柱的逆向喷流干扰流场，分析了不同来流克努森数和喷流马赫数下的流场结构及气动干扰特性，揭示了过渡区喷流干扰的稀薄气体效应。
最后，本文发展了仅适用于整数自由度能量分布的EPSM算法，使其不但能处理振动能不完全激发状念下的热力学非平衡问题，还能处理化学反应流动问题。同时，应用改进的DSMC／EPSM混合算法，数值模拟了稀薄流过渡区有横向喷流干扰的二维有限平板和有逆向喷流干扰的平头圆柱高超声速化学反应流场，探讨了高温气体化学反应效应对流场结构及喷流气动干扰特性的影响。
According to the requirements of the NSFC Project (Grant No. 19772018) and (Grant No. 19902021) and the National 863 Program (Grant No.2002AA726050), and based on the investigation of models and algorithms about inhomogeneous and non-equilibrium flows, two typical kinds of these flows: gas-solid two-phase flows and thermal chemical non-equilibrium gas flows, are chosen to study the properties of compressible inhomogeneous and non-equilibrium flows which are governed by the Boltzmann equation for trying to find the feasible models and numerical methods to solve these complicated flow problems.Firstly, the two-fluid model and the unified governing equations for dense compressible gas-solid flows are established on the concept of granular temperature which is used to represent the properties of this flow. Approximate Riemann solver of solid phase is deduced from the characteristics of wave propagating in the varied conditions including the vacuum, and the algorithm of Roe's fractional step scheme is constructed to solve non-isentropic dense compressible gas-solid flows. Numerical simulation of the shock-induced fluidization of inert powder layers is performed, the results show the detailed structure and the evolving process of the flow field. It is also experimentally proved that the model and the algorithm are valid, so the work of this paper can supply an effective method to describe the dense compressible two-phase flow with strong discontinuity surfaces.Secondly, analyzing the properties of gas-solid flow in the transitional region of rarefied gas and the requirements of the direct simulation Monte Carlo (DSMC) method, the relationship is set up between the gas-solid interaction based on the macro physical parameters and the single simulation particle's kinetic states via the micro-expression of the macro physical parameters, each coherent velocity distribution function of gas phase and solid phase is given in the unified form. The mechanical and thermal models of gas-solid interaction and the models of particle-particle collision are also constructed. The numerical disposition of the boundary conditions of solid phase is performed in the form of the granular temperature. Numerical solutions are obtained for the case of gas-solid transverse jet from a two-dimensional flat plate interacting with rarefied external hypersonic flows. As the more real model can be easily inducted to the DSMC method for solving physical chemical flow due to the physical simulation essence of the DSMC method, the work of this paper may provide a new approach to describe the gas-solid flow with chemical reactions in the transitional region.Thirdly, considering the particle simulation essential characteristics of the DSMC method and the equilibrium particle simulation method (EPSM), and each advantage and disadvantage in simulating mixed rarefied and continuum flows, the local Knudsen number Kn and Bird's
breakdown parameter P are adopted as the physical and numerical criteria that identify the boundary between continuum and rarefied computational domains. Rationality that the DSMC method is implemented in rarefied region, and the EPSM method in continuum region is verified, the hybrid DSMC/EPSM code is presented to automatically divide zones in continuum/rarefied flows using the controlling parameters Kn and P. Simulations are performed for the cases of transverse jet from two-dimensional flat plate with non-thickness and thickness, inverse jet from flat-nosed cylinder interacting with rarefied external flows. The structure of flow field and the aerodynamic properties along with the varied Knudsen number and jet Mach number are analyzed in details, and the rarefied gas effects of the jet interaction are embodied in the transitional region.Lastly, the EPSM code, that is initially only used for integral degrees of free
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