态-态模型下的CO<sub>2</sub>系统热非平衡过程数值研究

段欣葵; 曾明; 王辉; 王东方

doi:10.7638/kqdlxxb-2023.0140

态-态模型下的CO₂系统热非平衡过程数值研究

国防科技大学空天科学学院，长沙　410073

基金项目: 国家自然科学基金（11927803）

详细信息

作者简介:
段欣葵（2001—），女，湖南永州人，硕士研究生，研究方向：高温气体动力学. E-mail：duan_xk@163.com

通讯作者:
曾明^*（1971—），女，湖南娄底人，教授，研究方向：高温气体动力学. E-mail: ming_z@163.com

中图分类号: V211.22
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出版历程
- 收稿日期: 2023-08-28
- 修回日期: 2023-11-08
- 录用日期: 2023-11-21
- 网络出版日期: 2023-12-07
- 发布日期: 2023-12-10
- 刊出日期: 2024-06-24

Numerical study of thermal nonequilibrium process in CO₂ system with state-to-state model

College of Aerospace Science and Engineering, National University of Defense Technology, Changsha　410073, China

摘要

摘要:
以火星大气条件下飞行器非平衡流场研究为背景，采用态-态模型对定容静止CO₂系统自30 km火星大气条件（181 K）瞬时升温后的热非平衡过程开展数值模拟。考虑CO₂分子的对称拉伸、弯曲和非对称拉伸三个振动模态共201个振动能级，微观过程包括：振动-平动（VT）能量交换过程引起的同一模态内部的和不同模态间的振动能级跃迁，振动-振动（VV）能量交换过程引起的同一模态内部振动能级跃迁。分析不同振动模态的能级分布演化特点，并考察对应微观过程细节探究内在原因，结果表明：VT过程起支配作用，对由初始低温突然升温后保持定温的气体非平衡过程，VV过程的贡献可以忽略；CO₂分子的弯曲振动模态具有最快的激发速率，平衡时也具有最高的粒子数占比，升温至2000 K情况下，对称拉伸和非对称拉伸模态的松弛时间约为弯曲模态的2.2倍和46.1倍；更高温度下振动能级跃迁速率加大，升温至5000 K情况达到平衡的平均松弛时间比2000 K情况低了2个量级。
- 热非平衡 /
- 态-态模型 /
- CO₂ /
- 数值模拟 /
- 振动能级分布
Abstract:
With the background of research on nonequilibrium flow field outside Mars probe, the thermal nonequilibrium process after temperature increase of a stationary CO₂ system from Martian atmospheric condition at an altitude of 30 km (181 K) is studied with state-to-state model. The system with initial condition of Martian atmosphere is heated suddenly to a high temperature and then is kept at constant temperature and volume. Three vibrational modes (symmetric stretching, bending and asymmetric stretching modes) and totally 201 vibrational energy levels are considered. The microscopic processes include: vibration-translation (VT) energy exchange processes that cause transitions between energy levels of the same or different modes, vibration-vibration (VV) energy exchange processes that cause transitions within the same mode. The time evolution of vibrational distribution for the three modes and the specifics of the corresponding microscopic processes are analyzed. The results show that: (1) VT processes are dominant, the contribution of VV processes can be ignored for such sudden increase and then constant temperature case. (2) Among the three vibrational modes, the bending mode has the fastest excitation rate and the largest equilibrium population. For the case of temperature rise to 2000 K, the relaxation time for the symmetric and asymmetric stretching modes is respectively about 2.2 times and 46.1 times of that for the bending mode. (3) As the transition rates increase with temperature, the average relaxation time for 5000 K case is lower than that for 2000 K by two orders of magnitude.
- thermal nonequilibrium /
- state-to-state model /
- carbon dioxide /
- numerical simulation /
- vibrational population distribution

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图 9 升温至T = 2000 K和T = 5000 K两种情况下三种模态粒子数占比随时间的变化

Figure 9. Particle population fractions of three modes under two temperature conditions

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图 1 CO₂的3种振动模态

Figure 1. Three vibration modes of CO₂

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图 2 CO₂分子三种模态振动能级图

Figure 2. Vibrational energy levels in three modes of CO₂

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图 3 非平衡过渡过程中若干时刻的振动能级分布（T = 2000 K）

Figure 3. Vibration energy level distributions at several moments in nonequilibrium transient process (T = 2000 K)

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图 4 三种模态粒子数占比随时间的变化（T = 2000 K）

Figure 4. Proportion of particle population in three modes (T = 2000 K)

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图 5 三种模态具有相近振动能的能级松弛过程对比（T = 2000 K）

Figure 5. Comparison of relaxation process of vibrational levels with similar energy in three modes (T = 2000 K)

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图 6 有无VV过程作用的若干时刻振动能级分布对比（T = 2000 K）

Figure 6. Comparison of vibration energy level distribution with or without VV process at several moments in nonequilibrium transient process (T = 2000 K)

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图 7 向v₁ = 1与v₂ = 2两个振动能级（振动能约为0.165 eV）的跃迁过程

Figure 7. Transitions to v₁ = 1 and v₂ = 2 with vibration energy about 0.165 eV

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图 8 非平衡过渡过程中若干时刻的振动能级分布（T = 5000 K）

Figure 8. Vibration energy level distribution at several moments in nonequilibrium transient process (T = 5000 K)

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表 1 初始时刻V₁和V₂模态粒子数密度（T = 2000 K）

Table 1 Population of V₁ and V₂ modes at the initial moment (T = 2000 K)

State	$n_{{v_i}}^0$ /m^–3
v₀	1.20×10²³
v₁ = 1	2.99×10¹⁸
v₂ = 1	1.19×10²¹
v₂ = 2	5.90×10¹⁸

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表 2 初始时刻V₁和V₂模态跃迁速率（T = 2000 K）

Table 2 Transition rates of V₁ and V₂ modes at the initial moment (T = 2000 K)

Process	k_f /（m³·s^–1）	k_b /（m³·s^–1）	${{{\text{d}}{n_{{v_i}}}} \mathord{\left/ {\vphantom {{{\text{d}}{n_{{v_i}}}} {{\text{d}}t}}} \right. } {{\text{d}}t}}$ /（m^–3·s^–1）	Total ${{{\text{d}}{n_{{v_i}}}} \mathord{\left/ {\vphantom {{{\text{d}}{n_{{v_i}}}} {{\text{d}}t}}} \right. } {{\text{d}}t}}$ /（m^–3·s^–1）
${v_{{1_{}}(0 \to 1)}}$	2.87×10^–22	–7.49×10^–22	4.18×10²⁴	4.18×10²⁴
${v_{{2_{}}(0 \to 2)}}$	2.85×10^–21	–3.73×10^–21	4.15×10²⁵	2.12×10²⁶
${v_{{2_{}}(1 \to 2)}}$	1.19×10^–18	–1.93×10^–18	1.71×10²⁶	2.12×10²⁶
注：k_f表示正向跃迁速率系数，k_b表示逆向跃迁速率系数。

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表 3 升温至T = 2000 K和T = 5000 K两种情况下平衡时基态及三种模态粒子数占比

Table 3 Fractions of equilibrium particle population in ground state and three modes under two temperature conditions

T/K	${n_{{v}_0}}\Big/n$	${n_{{\mathrm{V}}_1}}\Big/n$	${n_{{\mathrm{V}}_2}}\Big/n$	${n_{{\mathrm{V}}_3}}\Big/n$
2000	23.9%	14.9%	55.9%	5.3%
5000	8.2%	17.8%	65.6%	8.4%

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