TVD格式在水滴流场数值模拟中的应用

Application of TVD scheme in numerical simulation of water droplet field

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。

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 30 P30 N 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.