激波诱导环形SF<sub>6</sub>气柱演化的机理

郑纯; 何勇; 张焕好; 陈志华

doi:10.11883/bzycj-2022-0226

激波诱导环形SF₆气柱演化的机理

doi: 10.11883/bzycj-2022-0226

郑纯^1,,
何勇¹,
张焕好²,
陈志华^2, ,

1.
南京理工大学机械工程学院，江苏南京 210094
2.
南京理工大学瞬态物理重点实验室，江苏南京 210094

基金项目: 国家自然科学基金（12072162, 12102196）；中国博士后科学基金（2022M711642）；江苏省自然科学基金（BK20210322）

详细信息

作者简介:
郑　纯（1992－　），男，博士，博士后，Chun9211@njust.edu.cn

通讯作者:
陈志华（1967－　），男，博士，教授，chenzh@njust.edu.cn

中图分类号: O354.5
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- 文章访问数: 371
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- 被引次数: 0
出版历程
- 收稿日期: 2022-05-26
- 修回日期: 2022-10-24
- 网络出版日期: 2022-11-02
- 刊出日期: 2023-01-05

On the evolution mechanism of the shock-accelerated annular SF₆ cylinder

1.
School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China
2.
Key Laboratory of Transient Physics, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu, China

摘要

摘要: 基于可压缩多组分Navier-Stokes控制方程，结合5阶加权本质无振荡格式以及网格自适应加密技术和level-set方法，数值模拟了平面激波（Ma=1.23）与环形SF₆气柱（内外半径分别为8和17.5 mm）界面的相互作用过程。相比于之前的实验结果，数值模拟结果揭示了入射激波在界面内4次透射过程中的复杂波系结构，观察到透射激波在内部界面传播时形成自由前导折射结构并向自由前导冯诺依曼折射结构转换的波系演变过程；另外，界面内的复杂激波结构诱导内部下游界面上的涡量发生了3次反向；在界面演化后期，内部界面形成的“射流”结构与下游界面相互作用，诱导界面形成一对主涡、一对次级涡以及一个反向“射流”结构。定量分析了环形界面长度、宽度、位移、环量以及混合率的变化情况，结果表明，内部气柱的存在减弱了前期小涡结构合并形成大涡结构过程中对界面高度与长度的影响，同时提高了重质气体与环境气体的混合率。
- 激波 /
- 环形气柱 /
- Richtmyer-Meshkov不稳定性 /
- 涡流
Abstract: Based on the compressible multicomponent Navier-Stokes equations, the interaction of a planar shock wave (Ma=1.23) with an annular SF₆ cylinder whose inner and outer radii were set as 8 and 17.5 mm respectively was numerically studied. The simulation was conducted based on the finite volume method. For capturing the complex shock and vortex structures as well as the interfaces, the adaptive mesh refinement method, level set method, and fifth-order weighted essentially non-oscillatory scheme were used for the simulation. The adaptive mesh refinement method dynamically refined the uniform Cartesian grids around the multiple moving shocks and accelerated interfaces. The level set method tracked the interface, while the fifth-order weighted essentially non-oscillatory scheme captured discontinuities such as shock waves and contact surfaces. Time advancement was achieved with the third-order strong-stability-preserving Runge-Kutta method. Compared with the previous experimental results, numerical results revealed the complex evolution of shock wave structures generated in the process of four shock transmissions in the annular cylinder. It is found that the transition from free precursor refraction to free precursor von Neumann refraction occurs when the transmitted shock wave passes through the inner cylinder. In addition, the complex shock structures that developed between the inner and outer downstream interfaces cause the pressure gradient direction to reverse several times on the inner downstream interface, which eventually leads to three reversals of vorticity on the inner downstream interface. In the later stage, the “jet” structure formed on the inner cylinder would impact the downstream interfaces, and finally induces the interfaces to generate a pair of primary vortices, a pair of secondary vortices and a reverse “jet”. Quantitative analyses of the variation of the length, width, displacement, the circulation and mixing rate of the annular cylinder were conducted. The results demonstrate that the presence of the inner cylinder attenuates the influence on the height and length of the annular cylinder during the process of small vortexes merging into the large vortexes in the early stage, and increases the mixing rate of the heavy gas and the ambient gas.
- shock wave /
- annular gas cylinder /
- Richtmyer-Meshkov instability /
- vortex

HTML全文

图 1 平面激波冲击圆形和环形SF₆气柱界面的实验和数值密度纹影对比

Figure 1. Comparison of experimental and numerical density schlieren seqences of shock-accelerated circular and annular SF₆ cylinder interface

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图 2 圆形SF₆气柱界面特征点位移的实验（圆点）和数值（实线）结果定量对比

Figure 2. Quantitative comparison of experimental (dots) and numerical (lines) diagrams of the characteristic points on the shocked SF₆ cylinder

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图 3 计算模型示意图

Figure 3. Illustration of the computational model

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图 4 网格收敛性验证

Figure 4. Grid convergence validation

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图 5 平面激波冲击环形SF₆界面演化过程的密度纹影图

Figure 5. Density schlieren sequences of the evolution process of the shock-accelerated annular SF₆ interface

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图 6 环形SF₆气柱界面内上激波结构演化过程中的密度纹影图（上）和压力云图（下）

Figure 6. Density schlieren (upper) and pressure contour (lower) of the shock wave structure evolution in the annular SF₆ interface

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图 7 界面的长度和高度

Figure 7. Histories of the length and height of interfaces

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图 8 界面位移

Figure 8. Histories of displacement of interfaces

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图 9 环形SF₆界面上涡量$ \omega $的演化云图

Figure 9. Evolution of the vorticity $ \omega $ on the annular SF₆ interface

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图 10 界面上总环量和环量绝对值随时间变化

Figure 10. Histories of the total circulation and the absolute value of the circulation of the interfaces

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图 11 上半部分界面总环量、正环量和负环量随时间变化

Figure 11. Histories of the total circulation, the positive circulation and the negative circulation of the upper half part interfaces

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图 12 气体混合率随时间的变化情况

Figure 12. Histories of the gas mixing rate

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表 1 气体参数

Table 1. Gas parameters

气体名称比热比摩尔质量/（g·mol⁻¹）密度/（kg·m⁻³）

空气 1.399 28.967 1.23
SF₆ 1.103 128.491 5.45

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