用于非平衡热等离子体数值模拟的物理数学模型

Physical-mathematical Model Used for Simulations of Non-equilibrium Thermal Plasmas

准确的物理数学模型,包括基本控制方程及与其相应的等离子体热力学与输运性质计算公式,是采用数值模拟方法深入研究非平衡热等离子体体系中传热、流动及其他复杂物理化学过程的基础。为此从Boltzmann方程出发,首先推导出描述等离子体中不同组分质量守恒、动量守恒和能量守恒方程以及电流连续性方程等基本控制方程,然后采用修正的Chapman-Enskog方法推导出等离子体输运性质参数,包括扩散系数、粘性系数、电子和重粒子平动热导率和电导率等的表达式。不仅在保证等离子体体系质量、动量、能量和电荷通量自洽的前提下封闭了控制方程,而且与现有广泛采用的描述平衡态热等离子体特性的模型间的自洽性也得到了保证。另外,采用所提出的方法推导出的非平衡热等离子体物理数学模型可以避免对目前仍存在争议的定压比热、反应热导率等参数的定义和计算。

Development of an accurate physical-mathematical model,including the basic governing equations and the corresponding computational formulas of the thermodynamic and transport properties,is a fundamental requirement for investigating the heat transfer,fluid flow,and other complicated processes in a non-equilibrium thermal plasma system.Therefore,firstly,on the basis of the Boltzmann equation,we obtained basic governing equations,including the species mass,momentum,energy conservation equations and the current continuity equation.Then,the expressions for the transport properties,including the diffusion coefficients,viscosity,translational thermal conductivities of electrons and heavy species,and electrical conductivity,were derived using the modified Chapman-Enskog method.The obtained physical-mathematical model not only ensures the self-consistency of the mass,momentum,and energy fluxes as well as the current flow in the governing equations and the corresponding transport coefficients,but also ensures the self-consistency of treatments used for modeling the equilibrium and non-equilibrium thermal plasmas.In addition,it is shown that the definition of the specific heat at constant pressure and the reactive thermal conductivity of the non-equilibrium thermal plasmas are not necessary in this self-consistent theory.