复杂两相流动的动态网格自适应连续表面力方法

罗双双; 杨翊仁; 孙建伟; 陈浩

doi:10.3969/j.issn.0258-2724.20240263

复杂两相流动的动态网格自适应连续表面力方法

doi: 10.3969/j.issn.0258-2724.20240263

罗双双^{1, 2,},
杨翊仁^{1, 2},
孙建伟³,
陈浩^{1, 2, ,}

1.
西南交通大学力学与航空航天学院，四川成都 611756
2.
西南交通大学先进结构材料力学行为与服役安全四川省重点实验室，四川成都 611756
3.
华北油田第四采油厂，河北廊坊 065000

基金项目: 国家自然科学基金项目（12172311）

详细信息

作者简介:
罗双双（1981—），男，工程师，博士研究生，研究方向为液滴飞溅现象的数值仿真，E-mail：double@swjtu.edu.cn

通讯作者:
陈浩（1983—），男，讲师，博士，研究方向为计算流体动力学，E-mail： chenhao@swjtu.edu.cn

中图分类号: O359.1
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- 文章访问数: 43
- HTML全文浏览量: 61
- PDF下载量: 2
- 被引次数: 0
出版历程
- 收稿日期: 2024-05-31
- 修回日期: 2025-01-08
- 网络出版日期: 2026-03-25

Adaptive Mesh Refinement and Continuum Surface Force Method for Complex Two-Phase Flows

LUO Shuangshuang^{1, 2
,},
YANG Yiren^{1, 2},
SUN Jianwei³,
CHEN Hao^{1, 2
, ,}

1.
Sichuan Province Key Laboratory of Advanced Structural Materials Mechanical Behavior and Service Safety, Southwest Jiaotong University, Chengdu 611756, China
2.
School of Mechanics and Aerospace Engineering, Southwest Jiaotong University, Chengdu 611756, China
3.
The Fourth Exploit Factory Huabei Oilfield Company, Langfang 065000, China

摘要

摘要:
针对具有复杂气液界面拓扑变化的两相流动问题，构建一种能够兼顾计算效率与界面解析精度的数值模拟方法. 首先，采用具有树状数据结构的四叉树/八叉树笛卡尔网格进行空间离散，利用其层级结构实现动态网格自适应；其次，在自适应网格框架下实现连续表面力（CSF）模型，通过对体积分数进行两次卷积模糊化处理，平滑地将表面张力分布至界面邻域，并结合分段线性界面重构技术准确追踪气液界面；随后，建立网格加密准则，同时考虑基于流场速度小波分析的离散误差和界面处的曲率分布，以实现对流场剧烈变化区域及相界面的动态加密；最后，通过经典气液两相流算例验证算法的准确性与可靠性. 研究表明：在表面张力Laplace律验证中，采用界面曲率为细化准则时，其内外压力差计算误差仅为3.0%，远优于基于体积分数准则的7.5%～24.0%误差，且精度与均匀细网格相当；所提方法较均匀细网格可降低约一个数量级的计算耗时；在表面张力波计算中，数值解与正则模态理论解的均方根误差可低至10⁻⁵量级；在双元液滴正碰模拟中，准确复现了实验中观测到的哑铃形与菱形变形序列，并捕捉到气膜破裂及微小气泡形成等复杂界面拓扑演化细节.
- 两相流动 /
- 四叉树/八叉树数据结构 /
- 连续表面力方法 /
- 自适应网格
Abstract:
To address two-phase flow problems with complex gas-liquid interface topology variation, a numerical simulation method capable of balancing computational efficiency and interface resolution accuracy was proposed. First, quadtree/octree Cartesian meshes with tree data structures were employed for spatial discretization. Adaptive mesh refinement was developed by leveraging the mesh’s hierarchical structures. Second, the continuum surface force (CSF) model was implemented within the adaptive mesh framework. By applying double convolution blurring to the volume fraction, the surface tension was smoothly distributed to the interface neighborhood, and the piecewise linear interface reconstruction technique was utilized to track the gas-liquid interface accurately. Subsequently, a mesh refinement criterion was established, and both the discrete error based on wavelet analysis of flow field velocity and the interface curvature distribution were considered, thereby achieving dynamic refinement in regions with sharp flow field variations and phase boundaries. Finally, the accuracy and reliability of the algorithm were validated through numerical examples of classic gas-liquid two-phase flow. The results show that in the verification of the Laplace law of surface tension, when the interface curvature is adopted as the refinement criterion, the computational error of internal and external pressure difference is only about 3.0%, which is significantly superior to the error range from 7.5% to 24% when using the volume fraction as the criterion, and its accuracy is consistent with that of uniform fine meshes. The proposed method can reduce the computational time consumption by approximately one order of magnitude compared with uniform fine meshes. In the numerical examples of surface tension waves, the root mean square error between the numerical solution and the theoretical solutions of regular modal can be reduced to the order of 10⁻⁵. In the simulation of a head-on collision between binary droplets, the experimentally observed dumbbell-shaped and diamond-shaped deformation sequences are reproduced, and the complex interface topology evolution details such as gas film rupture and the formation of tiny bubbles are captured.
- two-phase flow /
- quadtree/octree data structure /
- continuum surface force method /
- adaptive mesh

HTML全文

图 1 四叉树网格和树状数据结构

Figure 1. Quadtree mesh and tree data structure

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图 2 虚拟网格及双线性插值

Figure 2. Virtual meshes and bilinear interpolation

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图 3 相界面参数位置

Figure 3. Position of phase interface parameters

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图 4 自适应网格及局部放大图

Figure 4. Adaptive mesh and local zoom

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图 5 3种计算模型下的自适应网格数

Figure 5. Adaptive mesh number of three computational models

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图 6 相界面相对平衡位置的振幅随时间演化

Figure 6. Evolution of amplitude at relative equilibrium position of phase interface with time

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图 7 双元液滴碰撞

Figure 7. Binary droplet collision

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图 8 气膜演化过程

Figure 8. Evolution process of gas film

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图 9 液滴碰撞时网格总数的变化

Figure 9. Variation of total number of meshes during droplet collision

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图 10 液滴附近的自适应网格

Figure 10. Adaptive mesh near droplet

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表 1 二维液滴压力差

Table 1. Pressure difference in two-dimensional droplet

层格层级	细化准则	压力差	压力差误差/%
5～8	体积分数	2.48	24.0
6～8	体积分数	2.47	23.5
7～8	体积分数	2.15	7.5
5～8	曲率	2.06	3.0

下载: 导出CSV

表 2 三维液滴压力差

Table 2. Pressure difference in three-dimensional droplet

网格层级与细化准则	5～8， f	6～8， f	7～8， f	5～8， $\kappa $
压力差	4.43	4.45	4.41	3.93
误差/%	21.5	22.5	20.5	3.5

下载: 导出CSV

表 3 网格数与CPU时间

Table 3. Number of meshes and CPU time

计算模型	网格层级	网格数	CPU 时间/s
二维	5～8	5194	2.92
二维	8～8	65536	14.48
轴对称	5～8	3070	2.50
轴对称	8～8	65536	15.97
三维	5～8	385064	940.71
三维	8～8	16777216	6417.03

下载: 导出CSV

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