TVD格式在水滴流场数值模拟中的应用

王昭力; 曾涛; 周志宏; 陈宇

doi:10.7527/S1000-6893.2022.27010

航空学报 >

2022 , Vol. 43 >Issue 12: 627010 - 627010

DOI: https://doi.org/10.7527/S1000-6893.2022.27010

临近空间高速飞行器数值模拟技术专栏

TVD格式在水滴流场数值模拟中的应用

王昭力 ,
曾涛 ,
周志宏 ,
陈宇

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1. 四川大学建筑与环境学院, 成都 610065;
2. 宜宾四川大学产业技术研究院, 宜宾 644000

收稿日期: 2022-01-28

修回日期: 2022-03-07

网络出版日期: 2022-05-19

基金资助

国家自然科学基金（12072213）；国家科技重大专项（J2019-III-0010-0054）；国家数值风洞工程（NNW2019-JT01-023）

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Application of TVD scheme in numerical simulation of water droplet field

WANG Zhaoli ,
ZENG Tao ,
ZHOU Zhihong ,
CHEN Yu

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1. College of Architecture and Environment, Sichuan University, Chengdu 610065, China;
2. Yibin Industrial Technology Research Institute of Sichuan University, Yibin 644000, China

Received date: 2022-01-28

Revised date: 2022-03-07

Online published: 2022-05-19

Supported by

National Natural Science Foundation of China (12072213); National Science and Technology Major Project (J2019-III-0010-0054); National Numerical Windtunnel Project (NNW2019-JT01-023)

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摘要

结冰会严重影响飞机的飞行安全，而数值模拟是研究飞机结冰的重要手段，在使用欧拉法求解水滴流场时，由于液态水含量分布存在间断以及欧拉法速度的单值性特性，会导致飞机结冰数值计算中的水滴流场迭代求解过程容易发散。针对这一问题，考虑双曲型守恒律方程，给出了水滴流场计算的5种TVD型有限体积方法，主要思想是在一阶单调格式的基础上，在每一个单元上对变量作单调线性重构函数。其中，时间离散采用四阶Runge-Kutta方法。通过计算，分析了该方法的精度和收敛性，通过对NACA0012翼型、NACA23012翼型以及30P30N三段翼的计算结果表明该方法是成功的。提高了欧拉法求解水滴流场的空间精度，也为TVD格式在两相流中的应用提供有益参考。

关键词： 结冰; 水滴撞击; 欧拉法; 对流项离散; TVD格式; 通量限制器

本文引用格式

王昭力 , 曾涛 , 周志宏 , 陈宇 . TVD格式在水滴流场数值模拟中的应用[J]. 航空学报, 2022 , 43(12) : 627010 -627010 . DOI: 10.7527/S1000-6893.2022.27010

Abstract

Aircraft icing endangers the safety of aviation, while numerical calculation is a major method to research icing. The iterative solving process of the water droplet field in the numerical calculation of aircraft icing tends to easily diverge due to the discontinuity in the distribution of water content and the singularity of the velocity in the Euler method. Aiming at this problem and considering the hyperbolic conservation law equation, we present five TVD schemes for the calculation of the water droplet field. The main idea is to develop a monotonic linear reconstruction function for the variables on each unit based on the first-order upwinding scheme, and the time discretization adopts the fourth-order Runge-Kutta method. The accuracy and convergence of the method are analyzed by calculation, and the calculation results of the NACA0012 airfoil, NACA23012 airfoil and three-element airfoil 30P30N show that the method is successful. It improves the spatial accuracy in solving the water droplets field using Eulerian method and provides reference for the application of TVD scheme in two-phase flow.

Key words： icing; droplet impingement; Euler method; discretion of convection; TVD scheme; flux limiter

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