University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
NASA Langley Research Center, Hampton, Virginia 23666, USA.
J Chem Phys. 2017 Aug 7;147(5):054107. doi: 10.1063/1.4996654.
A novel reduced-order method is presented for modeling reacting flows characterized by strong non-equilibrium of the internal energy level distribution of chemical species in the gas. The approach seeks for a reduced-order representation of the distribution function by grouping individual energy states into macroscopic bins, and then reconstructing state population using the maximum entropy principle. This work introduces an adaptive grouping methodology to identify and lump together groups of states that are likely to equilibrate faster with respect to each other. To this aim, two algorithms have been considered: the modified island algorithm and the spectral clustering method. Both methods require a measure of dissimilarity between internal energy states. This is achieved by defining "metrics" based on the strength of the elementary rate coefficients included in the state-specific kinetic mechanism. Penalty terms are used to avoid grouping together states characterized by distinctively different energies. The two methods are used to investigate excitation and dissociation of N (Σg+1) molecules due to interaction with N(Su4) atoms in an ideal chemical reactor. The results are compared with a direct numerical simulation of the state-specific kinetics obtained by solving the master equations for the complete set of energy levels. It is found that adaptive grouping techniques outperform the more conventional uniform energy grouping algorithm by providing a more accurate description of the distribution function, mole fraction and energy profiles during non-equilibrium relaxation.
一种新的降阶方法被提出用于模拟反应流，其特点是化学物种的内部能级分布具有强烈的非平衡。该方法通过将单个能量状态分组到宏观箱中，寻求分布函数的降阶表示，然后使用最大熵原理重建状态种群。本工作引入了一种自适应分组方法，以识别和组合可能相对于彼此更快达到平衡的状态组。为此，考虑了两种算法：改进的岛屿算法和谱聚类方法。这两种方法都需要在内部能量状态之间进行相似性度量。这是通过基于包含在特定于状态的动力学机制中的基本速率系数的强度来定义“度量”来实现的。惩罚项用于避免将具有明显不同能量的状态组合在一起。这两种方法用于研究 N(Σg+1)分子由于与理想化学反应器中的 N(Su4)原子相互作用而激发和离解。将结果与通过求解完整能级主方程获得的特定于状态的动力学的直接数值模拟进行比较。结果表明，自适应分组技术通过在非平衡弛豫期间提供分布函数、摩尔分数和能量分布的更准确描述，优于更传统的均匀能量分组算法。
