Center for Combustion Energy; Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China.
Department of Mechanical Engineering, University College London, Torrington Place, London WC1E 7JE, United Kingdom.
Phys Rev E. 2019 Jan;99(1-1):012142. doi: 10.1103/PhysRevE.99.012142.
A multiple-relaxation-time discrete Boltzmann model (DBM) is developed for compressible thermal reactive flows. A unified Boltzmann equation set is solved for hydrodynamic and thermodynamic quantities as well as higher order kinetic moments. The collision, reaction, and force terms are uniformly calculated with a matrix inversion method, which is physically accurate, numerically efficient, and convenient for coding. Via the Chapman-Enskog analysis, the DBM is demonstrated to recover reactive Navier-Stokes (NS) equations in the hydrodynamic limit. Both specific heat ratio and Prandtl number are adjustable. Moreover, it provides quantification of hydrodynamic and thermodynamic nonequilibrium effects beyond the NS equations. The capability of the DBM is demonstrated through simulations of chemical reactions in the free falling process, sound wave, thermal Couette flow, and steady and unsteady detonation cases. Moreover, nonequilibrium effects on the predicted physical quantities in unsteady combustion are quantified via the DBM. It is demonstrated that nonequilibrium effects suppress detonation instability and dissipate small oscillations of fluid flows.
开发了一种多松弛时间离散玻尔兹曼模型（DBM），用于可压缩热反应流。通过矩阵反演方法统一求解了用于计算流体力学和热力学量以及更高阶动力学矩的统一玻尔兹曼方程组。碰撞、反应和力项都通过矩阵反演方法进行统一计算，这种方法物理上准确、数值上高效、便于编写代码。通过Chapman-Enskog 分析，证明 DBM 在流体力学极限下可以恢复反应性纳维-斯托克斯（NS）方程。比热比和普朗特数都是可调的。此外，它还提供了超越 NS 方程的流体力学和热力学非平衡效应的量化。通过自由落体过程、声波、热库埃特流以及稳态和非稳态爆轰情况中的化学反应模拟，证明了 DBM 的能力。此外，通过 DBM 量化了非平衡效应对非稳态燃烧中预测物理量的影响。结果表明，非平衡效应抑制了爆轰不稳定性并耗散了流体流动的小振荡。
