rGFM和level-set方法在水柱群和喷管流场计算中的应用

doi:10.19596/j.cnki.1001-246x.7842

计算物理 ›› 2019, Vol. 36 ›› Issue (2): 165-174.DOI: 10.19596/j.cnki.1001-246x.7842

rGFM和level-set方法在水柱群和喷管流场计算中的应用

丁生荣¹, 徐胜利², 卢键方³, 张梦萍¹

1. 中国科学技术大学数学学院, 安徽合肥 230026;
2. 清华大学航空航天学院, 北京 100084;
3. 北京计算科学研究中心, 北京 100193

收稿日期:2018-02-07 修回日期:2018-05-16 出版日期:2019-03-25 发布日期:2019-03-25
通讯作者: 徐胜利,E-mail:slxu@mail.tsinghua.edu.cn;张梦萍,E-mail:mpzhang@ustc.edu.cn
作者简介:丁生荣(1992-),女,博士,从事激波与多相流相互作用等运动界面问题的研究,E-mail:dsr9208@mail.ustc.edu.cn
基金资助:
中国运载火箭技术研究院基金（CALT201601）和清华大学自主课题（20161080102）资助

Moving Shock Interacting with Cylindrical Water Columns and a Nozzle Flow Field: rGFM and Level-Set Method

DING Shengrong¹, XU Shengli², LU Jianfang³, ZHANG Mengping¹

1. School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, China;
2. School of Aerospace Engineering, Tsinghua University, Beijing 100084, China;
3. Beijing Computational Science Research Center, Beijing 100193, China

Received:2018-02-07 Revised:2018-05-16 Online:2019-03-25 Published:2019-03-25

摘要/Abstract

摘要： 计算平面运动激波和水柱群相互作用以及喷管流场.在Descartes网格中利用level-set方法分别追踪气/水和气/固界面，采用rGFM方法处理气/水和气/固界面边界条件.将喷管内壁简化为气/固界面并施加固壁边界条件，内壁型线数据拟合采用三次样条插值.采用5阶WENO格式分别求解Euler方程、level-set方程和界面重新初始化方程.给出激波和水柱群相互作用流场密度纹影图和指定点p-t曲线以及喷管流场压力、密度云图和速度场.改进界面法线确定方法可提高Riemann问题构造精度.可分辨运动激波和水柱群作用产生的复杂激波波系，表明激波在各水柱界面的透射和反射、在列和行水柱界面的多次反射和透射.水柱群下游区域的激波波后压力下降，表明激波加热水柱群附近气流和反向运动的反射激波造成了激波衰减.喷管流场数值解和理论解相符.

关键词: 激波, 界面, WENO格式, level-set方法, GFM方法

Abstract: Flow field induced by a moving shock interacted with cylindrical water columns and a nozzle flow field was numerically investigated. Fixed Cartesian grids are used and level-set method combined with revised real ghost fluid method (rGFM) is applied for tracking gas-water and gas-solid interfaces. Fifth order WENO schemes are employed for solving Eulerian and level-set equations as well as reinitialization equations. Nozzle contours are simplified as gas-solid interface, and nozzle contour profiles are expressed by splines for ease of obtaining normal vector. In the case of shock interacting with water columns, schlieren images and pressure time histories at specified points are shown to describe shock evolution and mitigation downstream. It indicates that complex shock structures are distinguished accurately by the method, and shock transmission and reflection occur on gas-water interfaces of neighboring columns in a row and in a column respectively. In addition, pressure, density contours and velocity of nozzle flow field is in agreement with inviscid solution by gas dynamics theory, which demonstrates effectiveness and robustness of level-set method coupling with rGFM for computing flow field in a complex geometry involving gas-water and gas-solid interfaces.

Key words: shockwave, interface, WENO schemes, level-set, GFM

中图分类号:

丁生荣, 徐胜利, 卢键方, 张梦萍. rGFM和level-set方法在水柱群和喷管流场计算中的应用[J]. 计算物理, 2019, 36(2): 165-174.

DING Shengrong, XU Shengli, LU Jianfang, ZHANG Mengping. Moving Shock Interacting with Cylindrical Water Columns and a Nozzle Flow Field: rGFM and Level-Set Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2019, 36(2): 165-174.

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rGFM和level-set方法在水柱群和喷管流场计算中的应用

Moving Shock Interacting with Cylindrical Water Columns and a Nozzle Flow Field: rGFM and Level-Set Method

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