竖直平面激波与水平热层作用后流场的理论计算方法研究

贾雷明; 田宙

doi:10.11883/bzycj-2018-0510

竖直平面激波与水平热层作用后流场的理论计算方法研究

doi: 10.11883/bzycj-2018-0510

贾雷明^{1, 2,},
田宙²

1.
清华大学工程物理系，北京 100084
2.
西北核技术研究院，陕西西安 710024

详细信息

作者简介:
贾雷明（1989－　），男，博士研究生，jialeiming@nint.ac.cn

中图分类号: O354.5
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出版历程
- 收稿日期: 2018-12-21
- 修回日期: 2019-05-20
- 刊出日期: 2019-12-01

On the theoretical calculation method for interaction between the vertical plane shock wave and the horizontal thermal layer

JIA Leiming^{1, 2
,},
TIAN Zhou²

1.
Department of Engineering Physics, Tsinghua University, Beijing 100084, China
2.
Northwest Institute of Nuclear Technology, Xi’an 710024, Shaanxi, China

摘要

摘要: 围绕竖直平面激波与固壁附近水平热层作用问题，提出了流动进入准自相似阶段后固壁附近流场参量的理论计算方法。与已有的Mirels方法相比，本文的方法在下列三个方面进行了改进：（1）舍弃“热层内激波速度与入射激波速度相等”的假定，分析了热层内激波的传播过程，并基于几何激波动力学理论计算热层内激波强度；（2）假定在与入射激波后流体而非入射激波阵面固连的坐标系中，波后流体在定常等熵波作用下，形成沿固壁运动的“活塞”，驱动其前方的热层气体运动；（3）“活塞”内流体与其毗邻的热层气体满足压力和速度连续，不再引入速度比例系数。利用改进后的方法，对于马赫数为2.00的竖直平面激波，在不同热层密度条件下进行计算。本文方法得到的热层内激波强度以及物质界面处的压力、速度和密度等参量，与数值模拟结果偏差均小于10%，优于Shreffler和Mirels计算方法。对于马赫数为1.36的竖直平面激波，当其传播速度小于热层内气体声速时，Shreffler和Mirels计算方法不再适用，而本文中提出的方法得到的计算结果与数值模拟结果和已有实验数据基本吻合，最大偏差约20%。上述结果表明，本文中提出的理论计算方法提高了现有方法的合理性，扩大了适用范围。
- 激波 /
- 热层 /
- 准自相似 /
- 流场参量
Abstract: In this paper we presented a theoretical calculation method for the physical quantities of flow filed after entering the quasi-self-similar stage concerning the interaction between the vertical planar shock wave and the horizontal thermal layer near the rigid wall. Compared with the existing Mirels’ theoretical method, ours has improved in the following three aspects: (1) the propagation process of the shock in the thermal layer is analyzed, and the shock intensity is calculated following the theory of geometrical shock dynamics, whereas the assumption that the propagation speed of the shock in the thermal layer is equal to that of the incident shock is abandoned; (2) an assumption is made that in the coordinate system fixed with the fluid behind the incident shock instead of the incident shock itself, the fluid behind the incident shock evolves into a " piston” under the action of steady isentropic wave, which moves along the wall and drives the thermal layer gas in front of it; and (3) the fluid in the " piston” and its adjacent thermal layer gas satisfy the continuity of pressure and velocity without introducing the velocity proportional coefficient. Our improved method is employed in the cases involving a Mach number 2.00 incident shock and different thermal layer densities, and gives the shock strength in the thermal layer and the field pressure, velocity and density on each side of the material interface. The deviation between the theoretical results and numerical results is below 10% in different thermal layer densities, which is much better than those of the Shreffler’s and Mirels’ methods. For a Mach number 1.36 incident shock with a propagation speed less than the speed of sound in the thermal layer, Shreffler’s and Mirels’ methods are no longer applicable, whereas the above mentioned theoretical mothod could still work and produce results that accord well with experimental data and numerical results, and the maximum deviation is about 20%, indicating that the above improved theoretical method is more reasonable and applicable than the existing theoretical calculation methods.
- shock wave /
- thermal layer /
- quasi-self-similar /
- flow field quantity

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图 1 竖直平面激波与热层作用示意图

Figure 1. Illustration of the interaction of a vertical planar shock with a thermal layer

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图 2 波T沿界面的非正规折射（D_P1＞D_I）

Figure 2. Irregular refraction of wave T at the horizontal material interface (D_P1＞D_I)

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图 3 波T沿界面的非正规折射（D_P1＜D_I）

Figure 3. Irregular refraction of wave T at the horizontal material interface (D_P1＜D_I)

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图 4 热层内激波传播

Figure 4. Shock propagation with time in the thermal layer

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图 5 固壁附近流场区域划分示意图

Figure 5. Illustration of flow field division near the wall

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图 6 不同工况条件下压力p和水平速度u沿固壁的分布

Figure 6. Profiles of pressure and horizontal velocity along the wall in different cases

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图 7 t=0.5 ms，不同工况下的压力等值线图

Figure 7. Pressure contour lines at t =0.5 ms in different cases

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图 8 t=13.0 ms，流场密度云图分布（ρ_tl=0.50 kg/m³）

Figure 8. Density contour at t=13.0 ms with ρ_tl=0.50 kg/m³

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图 9 不同时刻，物理量沿固壁分布（ρ_tl=0.50 kg/m³）

Figure 9. Parameters vs. x along the wall at different time instants with ρ_tl=0.50 kg/m³

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图 10 不同理论方法的计算结果(Ma_I=2.00)

Figure 10. Results from various theoretical methods with Ma_I=2.00

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图 11 不同理论方法的计算结果(Ma_I=1.36)

Figure 11. Results from various theoretical methods with Ma_I=1.36

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表 1 流场中激波结构类型

Table 1. Wave structure types above material interface

ρ_tl / (kg·m⁻³)	p_T / MPa	D_P1 / (m·s⁻¹)	p_T' / MPa	波系类型
0.10	0.219	1 607.83	0.191	W1
0.20	0.268	1 244.74	0.233
0.30	0.304	1 077.95	0.265
0.40	0.333	975.25	0.291
0.50	0.359	903.08	0.313
0.60	0.381	848.39	0.333
0.70	0.401	804.86	0.351
0.80	0.419	768.98	0.368
0.90	0.435	738.67	0.419	W2

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表 2 不同工况条件下固壁附近流场参量

Table 2. Parameter values near the rigid wall for different cases

ρ_tl/(kg·m⁻³)	t^*/ms	p₄/MPa			u₄/(m·s⁻¹)			ρ_4L/(kg·m⁻³)			ρ_4R/(kg·m⁻³)			p₅/MPa
ρ_tl/(kg·m⁻³)	t^*/ms	TA	NS	ε/%	TA	NS	ε/%	TA	NS	ε/%	TA	NS	ε/%	TA	NS	ε/%
0.1	10.0	0.195	0.183	6.51	968.88	941.81	2.87	1.47	1.44	1.87	0.16	0.15	7.38	0.112	0.118	4.92
0.2	12.5	0.239	0.231	3.32	910.17	857.25	6.17	1.70	1.67	1.51	0.37	0.36	3.20	0.151	0.156	3.30
0.3	13.5	0.282	0.275	2.52	852.07	820.68	3.82	1.91	1.87	2.11	0.62	0.60	4.00	0.192	0.193	0.76
0.4	15.0	0.320	0.312	2.67	798.33	787.34	1.40	2.09	2.05	2.04	0.90	0.88	2.75	0.228	0.228	0.10
0.5	16.0	0.354	0.349	1.58	746.68	755.16	1.12	2.25	2.27	0.93	1.20	1.17	2.91	0.261	0.261	0.12
0.6	16.5	0.383	0.383	0.06	697.86	706.73	1.26	2.38	2.37	0.32	1.51	1.49	1.61	0.290	0.295	1.85
0.7	17.0	0.405	0.415	2.49	655.55	653.82	0.26	2.47	2.53	2.29	1.82	1.81	0.70	0.312	0.333	6.35
0.8	18.0	0.434	0.437	0.63	577.03	588.04	1.87	2.60	2.62	0.77	2.15	2.11	1.92	0.364	0.366	0.67
0.9	18.0	0.447	0.447	0.02	515.82	525.43	1.83	2.65	2.66	0.24	2.43	2.40	1.12	0.409	0.408	0.30

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