球坐标系下多介质混合物模型的数值模拟

吴宗铎; 赵勇; 严谨; 宗智; 高云

doi:10.11883/bzycj-2018-0075

球坐标系下多介质混合物模型的数值模拟

doi: 10.11883/bzycj-2018-0075

吴宗铎^1,,
赵勇^2, ,,
严谨¹,
宗智³,
高云⁴

1.
广东海洋大学海洋工程学院，广东湛江 524088
2.
大连海事大学交通运输工程博士后流动站，辽宁大连 116026
3.
大连理工大学船舶工程学院，辽宁大连 116024
4.
西南石油大学油气藏地质及开发工程国际重点实验室，四川成都 610500

基金项目: 国家自然科学基金（11702066，51679021，51609206，51679037）；广东省自然科学基金（2017A030313275）

详细信息

作者简介:
吴宗铎（1984－　），男，博士，讲师，wuzongduo0@aliyun.com

通讯作者:
赵　勇（1981－　），男，博士，副教授，fluid@126.com

中图分类号: O.382; O359+.1
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- 文章访问数: 5541
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- PDF下载量: 38
- 被引次数: 0
出版历程
- 收稿日期: 2018-03-12
- 修回日期: 2018-06-27
- 刊出日期: 2019-05-01

Numerical simulation about the multi-component mixture model under spherical coordinate system

WU Zongduo^1
,,
ZHAO Yong^{2
, ,},
YAN Jin¹,
ZONG Zhi³,
GAO Yun⁴

1.
College of Ocean Engineering, Guangdong Ocean University, Zhanjiang 524088, Guangdong, China
2.
Transportation Engineering postdoctoral research station, Dalian Maritime University, Dalian 116026, Liaoning, China
3.
Department of Naval Architecture, Dalian University of Technology, Dalian 116024, Liaoning, China
4.
State Key Laboratory of Oil and Gas Reservoir Gelogy and Exploration, Southwest Petroleum University,
Chengdu 610500, Sichuan, China

摘要

摘要: 利用多介质混合模型在求解球坐标系下的Riemann问题时，需要考虑界面处压力平衡性弱、奇点处理、状态方程复杂等多个难点。本文将原始基于体积分数的Mie-Grüneisen多介质混合模型扩展到球坐标系下，并对多个细节进行了修正和改进，包括：在界面处对热力学参数进行修正、采用质量分数导出新输送方程、利用质量分数加权计算偏导数、采用相邻网格点的物理量定义奇点等。经过改进后的计算模型，可以得到无振荡的数值解，而且可以准确捕捉到冲击波和界面的位置。另外，使用改进后的质量分数模型比原始的体积分数模型得到的计算结果更准确。
- 多介质 /
- 混合模型 /
- Mie-Grüneisen模型界面的位置方程 /
- 球坐标
Abstract: The aim of the paper is to extend the Mie-Grüneisen mixture model to spherical coordinate. As the multi-component mixture model is applied to the Riemann problem under spherical coordinate, many problems need to be taken into account: weak equilibrium, singular point treatment, complex equations of states and so on. In the article, the research work starts from the Mie-Grüneisen mixture model, then extend to the revision and modification about many details, include: revision of the thermo dynamical parameters at interface, deduction of new transport equation by mass fraction, weighting evaluation of partial derivatives by mass fraction, definition of physical parameters by the adjacent grid for singular point and other so on. The seriously modified numerical model, can not only obtain non-oscillation solutions, but also catch the positions of shock wave and interface clearly. In addition, the modified mass fraction model, can get more accurate results than the original model with mass fraction.
- multi-component /
- mixture model /
- Mie-Grüneisen equation /
- spherical coordinate

HTML全文

图 1 平面冲击波界面处p的数值特征

Figure 1. The numerical property of p at the interfacefor plane shock wave

下载: 全尺寸图片幻灯片

图 2 冲击波与界面位置随时间的变化

Figure 2. Time evolutions of position of shock wave and interface

下载: 全尺寸图片幻灯片

图 3 冲击波到达3倍R₀时，压力与速度的分布

Figure 3. The distributions of pressure and velocity when shock wave reaches 3R₀

下载: 全尺寸图片幻灯片

图 4 冲击波到达不同位置处的压力曲线

Figure 4. Pressure curves at the time instants when the shock wave reaches different positions

下载: 全尺寸图片幻灯片

图 5 冲击波在不同位置处的压力峰值变化

Figure 5. Peak value variation of pressure of the shock wave at different positions

下载: 全尺寸图片幻灯片

图 6 不同计算模型下压力随时间变化曲线

Figure 6. Time evolutions of pressure for different numerical models

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表 1 状态方程参数

Table 1. Coefficients of EOS

材料	ρ₀/(kg·m⁻³)	A/GPa	B/GPa	R₁	R₂	ω
TNT炸药	1 630	371.2	3.21	4.15	0.95	0.35

下载: 导出CSV

材料	ρ₀/(kg·m⁻³)	a₁/GPa	a₂/GPa	a₃/GPa	b₀	b₁	b₂	b₃
水	1 000	2.19	9.224	8.767	0.394	1.393 7	0	0

下载: 导出CSV

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