基于VOF模型的相界面面积和形心计算方法

于鹏飞; 张蒙; 刘虎; 车得福

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基于VOF模型的相界面面积和形心计算方法

更新时间：2025-11-18

- 基于VOF模型的相界面面积和形心计算方法
- Algorithms to calculate interface area and centroid based on the VOF model
- 西安交通大学学报 2025年
- 作者机构：
  
  西安交通大学动力工程多相流国家重点实验室,陕西省西安市710049
- 作者简介：
  
  于鹏飞（1995—），男，博士生
- 基金信息：
  
  耦合LOHC催化析氢反应的微通道内气液两相流动传热特性及不稳定性研究(xzy012024028)
- DOI：
  中图分类号： TK124
- 收稿：2025-07-14，
  
  修回：2025-09-11，
  
  录用：2025-09-29，
- 稿件说明：
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于鹏飞, 张蒙, 刘虎, 等. 基于VOF模型的相界面面积和形心计算方法[J/OL]. 西安交通大学学报, 2025.

YU Pengfei, ZHANG Meng, LIU Hu, et al. Algorithms to calculate interface area and centroid based on the VOF model[J/OL]. JOURNAL OF XI’AN JIAOTONG UNIVERSITY, 2025.
于鹏飞, 张蒙, 刘虎, 等. 基于VOF模型的相界面面积和形心计算方法[J/OL]. 西安交通大学学报, 2025. DOI：

YU Pengfei, ZHANG Meng, LIU Hu, et al. Algorithms to calculate interface area and centroid based on the VOF model[J/OL]. JOURNAL OF XI’AN JIAOTONG UNIVERSITY, 2025. DOI：

摘要

为提升相间传质数值模拟精度，本研究在VOF模型框架内提出了一个集成速度拓展的界面面积和形心计算方法。该方法由多边形切割算法和质量源分配算法两部分构成，具有准确度高、计算开销低、鲁棒性好等优点。多边形切割算法将网格内的相界面近似为平面多边形，从多边形的任一顶点出发将其分割成若干三角形，进而给出相界面的面积和形心。质量源分配算法利用亥姆霍兹方程，将传质引起的体积膨胀项转移到主相内，使得次相速度场无散，从而确保体积分数方程精确求解。测试发现：无相间传质时，多边形切割算法计算液滴表面积的相对误差在±1%以内；发生相间传质（传质速率

m''

= 10 kg·m

-2

·s

-1

）时，单独使用多边形切割算法导致结果失真。当两个算法协同应用时，模拟结果与液滴理论生长曲线呈现良好的一致性：液滴表面积最大绝对百分比误差为0.89%，液滴体积最大绝对百分比误差为0.28%。

Abstract

In order to enhance the accuracy of numerical simulation of interphase mass transfer

a method integrated with velocity extension was proposed

whereby the interface area and centroid are calculated within the framework of the VOF model. The method comprises a polygon-cutting algorithm and a mass source distribution algorithm

offering the advantages of high accuracy

low computational cost

and good robustness. The polygon-cutting algorithm works under the assumption that the interface in a grid is a planar polygon. The polygon is then cut into several triangles from a vertex

thereby calculating the area and centroid of the interface. The mass source distribution algorithm utilizes the Helmholtz equation to shift the volume expansion term caused by mass transfer to the primary phase

ensuring that the secondary-phase velocity field is divergence-free and the volume fraction equation is solved accurately. Results show that

in the absence of interphase mass transfer

the polygon-cutting algorithm can calculate the surface area of the droplet with relative errors within ±1%. However

the algorithm cannot offer reasonable results once interphase mass transfer occurs (mass transfer rate

m''

= 10 kg·m

-2

·s

-1

). As the two algorithms were applied synergistically

results exhibit good agreement with the theoretical growth curves of the droplet: the maximum absolute percentag

e error was 0.89% for surface area

and the maximum absolute percentage error was 0.28% for volume.

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