关键词:热化学非平衡;直接蒙特卡罗方法;反应模型;微观分析 Abstract The non-equilibrium phenomenon of thermochemical coupling has been a difficult problem in high temperature aerothermal dynamics, and hinders to analyze phenomena such as cell structure of detonation wave and ignition speed of low temperature combustion. In this paper, typical chemical reaction models (TCE, VFD, QK models) employed in the direct simulation Monte Carlo (DSMC) simulation are analyzed using two examples (namely, N dissociation at high temperature, and chain displacement reaction in H? O combustion) from microscopic reaction probability, vibrational state specific reaction rates, total reaction rate under thermal nonequilibrium condition, and post-collision redistribution of internal energy. It is found that the probability distribution of vibrational energy of reacted molecules deviates from the equilibrium Boltzmann distribution for both the high temperature dissociation reaction having high activation energy and the chain displacement reaction having low activation energy. The VFD model with strong vibrational favored contribution can predict well the high temperature dissociation reaction, whereas the TCE model (a special case of VFD model) and QK model are better for the chain displacement reaction. Besides, the post-collision redistribution of internal energy should follow the principle of detailed balance, as small deviations may cause inequality between the translational and vibrational energy under final equilibrium state. The DSMC simulation results also show that the vibrational favor of chemical reactions has an obvious effect on the thermochemical coupling process. Particularly, because molecules having high vibrational energy are more easily to have chemical reactions, the decrease of the average vibrational energy of the gas will affect the subsequent chemical reactions.
在高温时(>15 000 K)由于氮气的离解和振动松弛的特征时间比较接近, 会导致再入激波附近的非平衡区域存在所谓的振动与离解耦合现象(CVD). 这一现象对飞行再入中的高温流场有重要影响, 但由于存在复杂的微观物理和苛刻的高温环境, 实际流动问题的数值模拟结果和实验结果都存在一定误差, 二者在定量上的准确对比目前还有困难[26]. 本节的主要目的是通过空间均匀的热化学耦合问题对反应模型的动力学性质开展应用评估. DSMC模拟的初始条件为数密度为 的纯净氮气, 其平动、转动、振动温度分别为30 000 K, 20 000 K, 5 000 K, 初始模拟粒子总数为 . DSMC模拟所需的转动能和振动能的松弛碰撞数 和 由特征松弛时间 转化得到, 转换中都引入了相应的DSMC 微观修正[35]. 此外振动能的特征松弛时间 还考虑了高温修正[7]. 为了突出离解前期的振动与离解耦合过程, 只考虑了单向的离解反应, 忽略了对前期影响很小的复合反应. 另外由于QK模型和TCE模型的动力学性质比较接近, DSMC模拟只选择了TCE 和VFD模型进行评估比较. 计算结果如图7所示, 其中图7(a)给出了反应过程的 浓度变化, 图7(b)为平动温度和振动温度变化, 而转动温度很快和平动温度达到平衡并未在图中给出. 在反应前期, 振动温度明显低于平动温度, VFD模型预测的离解反应速率明显低于TCE模型结果, 反应吸热相对少, 因此系统整体温度高. 比较结果显示在同一时刻VFD和TCE模型预测的温度相差可达1000 K以上, 表明化学模型细节差异对于实际应用的重要性. 显示原图|下载原图ZIP|生成PPT 图7离解过程中的浓度和温度变化 ||||(a) 浓度随时间的变化;(b) 温度随时间的变化 -->Fig.7Evolution of concentration and temperature during dissociation |||| (a)Evolution of concentration;(b) Temperature history -->
通过微观模拟还可以分析化学反应对系统热力学状态的影响. 图8为采用VFD模型的算例在8.3955 ns 时分子的振动能概率分布. 与相同振动温度(12 698 K)的平衡态Boltzmann分布相比, 模拟结果在低振动能级与平衡态基本一致, 但高振动能级的概率明显降低. 原因是离解反应在短时间内消耗了超出平衡的高振动能级的分子, 而热松弛过程(非弹性碰撞)尚未补充恢复. 这说明即使采用双温反应速率的宏观化学反应模型, 在计算热化学耦合问题时仍会带来一定的误差, 而微观粒子模拟或态指定的反应速率求解方法则能包含更多反应细节、模拟结果更为可信. 显示原图|下载原图ZIP|生成PPT 图8VFD模型计算的离解过程中振动能级的瞬时概率分布 -->Fig.8Vibrational energy distribution of during dissociation with VFD model -->
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