摘要
空化流动问题本质上是可压缩流动,应用可压缩方法开展数值模拟研究更符合物理实际。气体和液体压缩性的显著差别使得低速空化流动数值模拟的刚性问题非常突出,通过引入预处理技术解决低速问题中由于特征值量值不一致导致的收敛刚性问题,提高收敛速度。同时,以预处理后的特征值构造Roe格式耗散项,提高低速流动计算精度。鉴于自然空化流动中气液组分转换现象和物质输运现象并存,且气体和液体的密度在常温状态下存在显著差别,预处理后的源项雅克比矩阵的特征值与无粘通量雅克比矩阵的特征值存在量级的差异,这会使得求解过程不稳定或收敛速度极慢,即出现"源项刚性"问题。为此,本文系统推导了预处理框架下的气液两相流隐式求解方法,采用点隐式方法处理源项,通过直接求逆的方式增强算法的稳定性。研究中分别考察了三种不同的算子分裂方式在LU-SGS(Lower-Upper Symmetric-Gauss-Seidel)隐式迭代中的模拟效果,并提出适用于DDADI(Diagonally Dominant Alternating Direction Implicit)的算子分裂方式,在NACA0015水翼空化算例模拟中综合比较了上述四种隐式迭代方式对低速空化问题收敛性的影响。最后,应用本方法对三维尖锥自然空化算例进行了考核模拟,捕捉到自然空泡流场中的主要特征,计算结果与试验测量结果吻合。
Thc cavitation flow is cssentially com prcSble,so thc compressible method is morc appropriatc for thc physical cssentials.The difference of gas and liquid in compressibility intensively deteriorates the stiffness issue in low speed cavitation flow simulation.A compressible solver is adopted to numerically investigate this kind of two-phase flow with precondition technique,to shrink the convergence course by dealing with the issue of imbalance of eigenvalues in low speed flow.Meanwhile,the dissipative term of R oe's scheme is rebuild on the basis of preconditioned system to improve the accuracy under low speed flow.Moreover,the phase transition and the material convection coexist in natural cavitation flow,and the fluids of gas and liquid vary much in density at normal temperature,these two factors are consequently followed by that the eigenvalues of source Jacobian matrix and inviscid flux Jacobian matrix differs in order of magnitude.This phenomenon is the“source stiffenes”problem and results in the unstability of the solver.The Point implicit method is applied to treat the source item,and the stability of method is enhanced by directly inversing the matrix.Three different operator splitting schemes are investigated in LU-SGS(Lower-Upper Symmetric-Gauss-Seidel)implicit iteration,and anoperator splitting scheme suited for DDADI(Diagonally Dominant Alternating Direction Implicit)is developed.A comparison between the four implicit schemes is drew in NACA0015hydrofoil ow-speed cavitation case,to study the influence of different schemes on convergence.At the lastpart,the natural cavitation case of3-D(three-dimension)cone is simulated by the current m ethod,capturing the main characteristic of the natural cavity flow field,and attaining a group of simulating data that matches well with the experiment data.
作者
牟斌
江雄
王建涛
Mou Bin;Jiang Xiong;Wang Jiantao(Computational Aerodynamics Institute of Chines .Aerodynam ic Development and Research Centera 621000,China)
出处
《空气动力学学报》
CSCD
北大核心
2017年第1期27-32,共6页
Acta Aerodynamica Sinica
关键词
空化
预处理
隐式求解
数值模拟
原项
cavitation
precondition
implicit method
numerical sim ulation
source item
作者简介
牟斌（1974 -)，男，四川什邡人，研究员，博士，研究方向：水汽两相流.E-mail:809970229@qq.com;通信作者：王建涛* (1982-)，研究方向：水汽两相流. E-niail:jtwang@utc.edu
