高速可压反应流的二维简化离散玻尔兹曼模型

Simplified two-dimensional discrete Boltzmann model of high-speed compressible reactive flows

如何有效模拟高速反应流现象是当前航空航天、能源与动力工程等领域的难点和热点。为此,本文提出了适用于超声速可压缩反应流的简化离散玻尔兹曼模型(DBM)。该模型基于动理学方法,使用形式统一的离散玻尔兹曼方程描述化学反应流的演化过程。在方程右侧,通过化学反应项将化学反应与多物理场自然耦合。该DBM使用二维九速模型,其离散速度分为三组,每组大小独立可调。为了描述分子转动和振动对应的额外自由度,引入了三组独立可调的参数用于描述额外自由度部分的内能。由此,该DBM具备了模拟比热比可调的反应流系统的功能。另外,平衡态离散速度分布函数与化学反应项各自满足九个独立的矩关系,其表达式都可以通过矩阵求逆的方式获得。通过ChapmanEnskog多尺度分析可以证明,该DBM除了能够在连续性极限条件下恢复描述化学反应流的Euler方程组之外,还具有描述一定热力学非平衡行为的功能。最后,通过数值算例表明,该DBM的数值结果与理论解吻合。

How to investigate high-speed reactive flows effectively is an important open issue in the fields of aerospace,energy,and power engineering,etc.For this purpose,a simplified discrete Boltzmann model(DBM) is proposed for supersonic compressible reactive flows.Based on the kinetic method,this model uses a unified discrete Boltzmann equation to describe the evolution of reactive flows.The chemical reaction is naturally coupled with multi-physics fields through the reaction term on the right-hand side of the discrete Boltzmann equation.A two-dimensional nine-velocity model is proposed with the velocities divided into three groups,and the speed of each group is independently adjustable.To describe extra degrees of freedom corresponding to molecular rotation and/or oscillation,three groups of independently adjustable parameters are employed to describe the internal energies in extra degrees of freedom.Therefore,DBM is suitable for reactive flows with adjustable specific heat ratios.In addition,both the equilibrium discrete distribution functions and reaction terms satisfy nine independent moment relations,and their expressions can be obtained by the matrix inversion method.Through Chapman-Enskog multiscale analysis,it is proved that DBM not only can recover the reactive Euler equations in the continuum limit,but also has the capability of describing some thermodynamic nonequilibrium behaviors.Finally,three benchmarks,including the homogeneous reaction,Sod tube,and detonation wave,are employed to verify and validate DBM.It turns out that results of DBM agree well with theoretical solutions.