固体炸药爆轰与惰性介质相互作用的一种扩散界面模型

提出一种保持热力学一致性的扩散界面模型，用来数值模拟固体炸药爆轰与惰性介质的相互作用问题。基于混合网格内各组分物质间可以达到力学平衡状态而不能达到热学平衡状态的假设，由混合网格能量守恒以及压力相等条件，推导出每种组分物质的体积分数演化方程。由此获得的扩散界面模型包括组分物质的质量守恒方程、混合物质的动量及总能量守恒方程，同时包括组分物质的体积分数演化方程和混合物质的压力演化方程。该扩散界面模型的主要特点是考虑了化学反应以及热学非平衡的影响。提出的扩散界面模型在物质界面附近不会出现物理量的非物理振荡现象、适用于任意表达形式的物质状态方程以及任意数目的惰性介质。

An improved diffuse interface model for the numerical simulation of interaction between solid explosive detonation and inert media

In the article a thermodynamically consistent diffuse interface model is proposed in order to numerically simulate the interaction between solid explosive detonation and compressible inert media. The chemical reaction of detonation course in solid explosive is simplified as the solid-phase reactant changing into the gas-phase product, thus the mixture within a control volume is regarded to be composed by three kinds of components: solid-phase reactant, gas-phase product and inert media, and all components are thought to be in mechanical equilibrium and thermal nonequilibrium because of their having distinct thermodynamic properties or equations of state. The starting point based on the energy conservation of the mixture and pressure equivalence among components within the control volume is adopted to derive the evolution equation for volume fraction of every component, in which the equation for energy conservation of the mixture is decomposed into a family of equations for energy conservation of the all components with the heat exchange resulting from thermal nonequilibrium. Thus, the governing equations of proposed diffuse interface model include: the conservation equation for mass of every component and the conservation equations for momentum and total energy of the mixture, and the evolution equations for volume fraction of every component and for pressure of the mixture. The important character of the present model is that the mass transfer due to chemical reaction and the heat exchange due to thermal nonequilibrium are involved. In this model, pressure is solved directly from the governing equations instead of computed next from the obtained conservative variables. The present model may apply to arbitrary expression of equation of state and allow for any number of inert media. The partially differential governing equations of the diffuse interface model are numerically solved by a temporal-spatial second-order Godunov-type finite volume scheme with wave propagation algorithm. From numerical examples, the proposed diffuse interface model can eliminate the unphysical oscillations near the material interfaces, and obtain the agreeable results with the physical mechanism.