在直角坐标系用NGFM模拟复杂计算域水下高压气泡膨胀问题

史汝超; 张亚军; 徐胜利

doi:10.11858/gywlxb.2014.06.009

在直角坐标系用NGFM模拟复杂计算域水下高压气泡膨胀问题

doi: 10.11858/gywlxb.2014.06.009

史汝超^1,,
张亚军²,
徐胜利^1,*, ,

1.
中国科学技术大学近代力学系，安徽合肥 230027
2.
中国工程物理研究院流体物理研究所，四川绵阳 621999

基金项目: 国家自然科学基金项目(10902110)

详细信息

作者简介:
史汝超(1982—), 男，博士，主要从事水下爆炸研究.E-mail:rcshi@mail.ustc.edu.cn

通讯作者:
徐胜利(1965—), 男，博士，教授，主要从事水下爆炸研究.E-mail:slxu@ustc.edu.cn

中图分类号: O382.1
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出版历程
- 收稿日期: 2013-01-28
- 修回日期: 2013-04-26

Simulation of Expansion of High Pressure Bubble under Water in Complex Calculation Region using NGFM in Cartesian Coordinate System

1.
Department of Modern Mechanics, USTC, Hefei 230027, China
2.
Institute of Fluid Physics, CAEP, Mianyang 621999, China

摘要

摘要: 采用NGFM(New version of Ghost Fluid Method)处理复杂计算域的固壁边界，用RGFM(Real Ghost Fluid Method)求解气-水界面附近网格节点的状态参数，从而在直角坐标系下对复杂计算域的水下高压气泡膨胀问题进行数值模拟。流场控制方程选用Euler方程，用五阶WENO格式离散空间导数项，二阶Runge-Kutta法离散时间导数项；气-水界面追踪使用Level Set方法，对Level Set方程，用五阶HJ-WENO(Hamilton-Jacobi WENO)和三阶Runge-Kutta法求解。将计算结果与任意坐标系下的结果进行对比，验证了NGFM在笛卡尔网格中处理复杂形状固壁边界的可行性。得到了水下流场压力等值线图、高压气泡的演变过程以及特定点处的压力-时间曲线。计算结果表明，高压气泡在固壁反射激波的作用下，膨胀过程受到抑制；强激波在固壁的反射会导致固壁附近出现大范围的空化流动。
- 高压气泡膨胀 /
- 任意坐标系 /
- 复杂计算域 /
- Level Set方法 /
- Ghost Fluid方法
Abstract: We adopted a new version of ghost fluid method (NGFM) to treat the wall boundary in a complex calculation region in Cartesian coordinate system, and real ghost fluid method (RGFM) to predict the flow states at grid nodes just next to the gas-liquid interface.Flow field was solved by Euler equation with 5th-order WENO spatial discretization and 2nd-order Runge-Kutta (R-K) time discretization.We used the level set method to keep track of gas-liquid interface.Level set function was discretized by 5th-order Hamilton-Jacobi WENO and 3rd-order R-K method.We verified that NGFM was easy to extend and could be applied to treat complex wall boundary in Cartesian grid by comparing with results in arbitrary coordinate system.We carried out pressure contours, the change process of bubble shape and pressure history at some given points.The numerical results demonstrate that the expansion of high pressure bubble is restricted by the reflected shock wave from the wall.It is also shown that the reflection of strong shock wave from wall can lead to extensive cavitation flow.
- high pressure bubble expanding /
- arbitrary coordinate system /
- complex calculation domain /
- level set method /
- ghost fluid method

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图 1 RGFM中气-水界面附近节点赋值示意图(一维模型)

Figure 1. Updating the real and ghost nodes bordering the gas-liquid interface in RGFM (1D)

下载: 全尺寸图片幻灯片

图 2 NGFM中流-固界面附近节点赋值示意图(一维模型)

Figure 2. Updating the real and ghost nodes next to the liquid-solid interface in NGFM (1D)

下载: 全尺寸图片幻灯片

图 3 t=0.210 ms时，用NGFM处理固壁边界的数值解和理论解的比较

Figure 3. Comparison of results using NGFM to treat the wall boundary with the theoretical results at t=0.210 ms

下载: 全尺寸图片幻灯片

图 4 t=0.270 ms时，用NGFM处理固壁边界的数值解和理论解的比较

Figure 4. Comparison of the results using NGFM to treat the wall boundary with the theoretical results at t=0.270 ms

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图 5 计算域的尺寸和建模示意图

Figure 5. Schematics of the size and modeling of calculation domain

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图 6 激波传播和高压气泡变化过程(蓝色虚线表示高压气泡，红色虚线表示空化区域；Δp为相邻压力等值线间的压差)

Figure 6. Shock wave propagation and change process of high pressure bubble (Blue dashed line indicates high pressure bubble, red dashed line indicates cavitation region; Δp indicates the pressure difference between adjacent isolines)

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图 7 NGFM计算结果和任意坐标系下计算结果的比较

Figure 7. Comparison of the results using NGFM to treat wall boundary with the results in arbitrary coordinate system

下载: 全尺寸图片幻灯片

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