含重力多相流系统的离散玻尔兹曼建模

Discrete Boltzmann Modeling of Multiphase Flow Systems With Gravity

本文提出了适用于含重力多相流系统的离散玻尔兹曼模型(DBM)。该模型基于动理学理论,使用形式统一的离散Boltzmann方程描述多相流的演化过程。在方程右侧,加入相变源项用于描述相变现象,同时引入了外力项,用于描述重力场的影响。该DBM使用二维33速模型,此速度模型是基于Hermite多项式理论建立的。通过Chapman-Enskog多尺度分析可以证明,该DBM除了能够恢复包含分子间相互作用和外力的Navier-Stokes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,通过四个数值算例(自由落体,气液共存曲线,Sod激波管,气泡融合)验证DBM的正确性。

A discrete Boltzmann model(DBM)for multiphase flow systems with gravity is proposed.Based on the theory of kinetics,the discrete Boltzmann equations in a uniform form are employed to describe the evolution of multiphase flows.On the right-side of the equations,the phase transition source term is added to describe the phase transition phenomenon,and the external force term is introduced to describe the influence of gravity field.Based on the Hermite polynomial theory,a two-dimensional 33-velocities model is introduced.Via the chapman-enskog analysis,it is demonstrated that the DBM can not only recover the Navier-Stokes equations involving the intermolecular interaction and external force,but also describe some thermodynamic non-equilibrium behaviors.Finally,this DBM is verified by four numerical benchmarks,including the free-falling process,gas-liquid coexistence curve,Sod shock tube,and bubble coalesence.