摘要
提出了一种改进的虚拟单元浸没边界法,并与一种高阶格式的有限差分算法相结合,运用于求解超声速复杂几何绕流问题.该算法的核心思想在于在固体边界的内部和外部分别施加满足边界关系的作用点,使得几何边界离散更加细化,起到了壁面附近网格局部加密的作用.采用源空间内流体点作为反距离插值算法的重构点,有效避免了插值点数目过少而与作用点相重合情况.通过对二维激波反射现象(马赫数为2.81)和三维超声速球体绕流问题(马赫数为1.2)的数值模拟,与实验结果对比表明,本文改进算法相对一般的虚拟边界法来说能显著提高数值精度,减小计算误差.计算结果揭示了球体绕流中剪切层、压缩波系和尾迹的相互作用导致自由剪切层失稳的机理.剪切层厚度和湍流雷诺脉动经历了线性增长、大幅度震荡和小幅度波动三个阶段,导致剪切层表面褶皱因子变化呈指数规律增长.其湍流结构表现出明显的各向异性,具体在流向雷诺正应力在湍流脉动中占主导地位,激波的压缩作用对不同方向雷诺正应力的影响存在空间迟滞效应.
An improved ghost-cell immersed boundary method proposed in this paper, coupled with a high order finite difference solver, is applied to simulate the supersonic compressive flows around the complex obstacles. The main improvement of this algorithm is the treatment of the solid boundary that both ghost points inside the solid domain and forcing points inside the fluid domain due to the extension of the boundary are chosen to reconstruct the flow information considering the effect of solid wall on fluid. This brings refined boundary with discrete points and strengthens the wall conditions, which plays the role of local mesh refinement. The fluid points are limited in a certain source space as the interpolating points of the inverse distance algorithm, which effectively avoids the fact that the interpolating points are too few to possibly lead to coincide with the forcing points. Two problems of two dimensional shock reflection （Ma=2.81） and three dimensional flow around the smooth sphere （Ma=1.2） demonstrate the significant improvement of the numerical accuracy compared to the general ghost cell method. The results reveal the instability mechanism of the free shear layer as a result of the interaction between the shear layer, the compression wave system and the wake. The thickness and Reynolds fluctuation of the shear layer experience three regimes of linear growth, large amplitude oscillation and small amplitude fluctuation, resulting in an exponential growth of wrinkling factor. The turbulent structure near the shear layer shows obvious anisotropy because the streamwise Reynolds normal stress is dominant and a spatial hysteresis exists in the effect of the tail shock on Reynolds normal stresses in different directions.
作者
张阳
邹建锋
郑耀
Zhang Yang;Zou Jianfeng;Zheng Yao(College of Aeronautics and Astronautics,Zhejiang University,Hangzhou 310027,China)
出处
《力学学报》
EI
CSCD
北大核心
2018年第3期538-552,共15页
Chinese Journal of Theoretical and Applied Mechanics
基金
国家自然科学基金资助项目(11372276
11432013)
关键词
虚拟单元边界法
剪切层
超声速流动
ghost cell immersed boundary method
shear layer
supersonic flow
