Roe格式在水滴欧拉方程数值求解中的应用

Application of Roe Scheme in Numerical Solution of Euler Equation for Water Droplets

目前普遍采用欧拉法求解水滴运动控制方程以模拟结冰表面水滴撞击特性。水滴欧拉方程近似没有压力项的空气欧拉方程,但已应用于空气欧拉方程的空间离散格式多数不能直接应用于水滴欧拉方程,有研究者将经典Roe格式应用于水滴欧拉方程时出现了奇点问题。通过对水滴欧拉方程进行形式改造,基于中心格式验证改造方法的有效性,并应用Roe格式结合线性重构与限制器函数实现对水滴欧拉方程二阶精度的求解。将NACA23012翼型计算结果与FENSAP ICE软件进行对比,两者水滴收集系数分布基本一致。

At present,the Euler method is widely used to solve the governing equation of water droplet movement to simulate droplet impingement characteristics on icing surface.The water droplet Euler equation is similar to the air Euler equation without pressure term,but most of the spatial discretization schemes that have been applied to the air Euler equation cannot be directly applied to the water droplet Euler equation,and some researchers have encountered singularity problem when applying the classical Roe scheme to the water droplet Euler equation.Through the formal transformation of water droplet Euler equation,the effectiveness of the transformation method is verified based on the central scheme,and then the Roe scheme is applied and the second order accuracy of the water droplet Euler equation is solved by combining linear reconstruction and limiter function.The results of NACA23012 airfoil were compared with FENSAP ICE software,and the distribution of water droplet collection coefficient was basically the same.