含激波、旋涡和声波的复杂多尺度流动的直接数值模拟

本文主要报道了我们近年来在银河并行机上采用五阶WENO格式所做的一系列直接数值模拟研究,主要包括激波与单旋涡相互作用、激波与旋涡对相互作用、激波与三维纵向旋涡的相互作用,以及可压缩各向同性湍流。研究的主要目的是揭示激波与旋涡间相互作用中的激波动力学特性、旋涡变形、旋涡破裂和声波的产生机理,以及湍流等多尺度复杂流动的流场结构和流动机理。研究表明,高阶WE-NO格式具有很好的分辨率和稳定性,是研究上述包含强间断与复杂流场结构的流动的理想数值方法。研究发现,激波与强旋涡相互作用具有多级特征,即激波与初始旋涡的相互作用、反射激波与变形旋涡的相互作用、小激波与变形旋涡的相互作用。激波与旋涡对相互作用中产生的声波包含两个区域:线性区和非线性区。在线性区,激波与旋涡对相互作用产生的声波是激波分别与每个旋涡单独作用产生的声波的线性叠加;而在非线性区则与激波和耦合旋涡对的作用有关。在激波与纵向旋涡的相互作用过程中,发现旋涡破裂区存在多螺旋结构。在高初始湍流马赫数的各向同性湍流脉动场中,也发现了广泛报导的"小激波"的存在,这是可压缩湍流有别于不可压缩湍流的显著结构特征。

A Direct Numerical Simulation of the Complex Multi-Scale Flow with Shock,Vortex and Sound Wave

In this paper,we offer an overview of our recent DNS studies on the interaction between a shock wave and a single planar vortex,apair of planarvortices or a longitudinal vortex,compressible isotropic turbulence through directly solving the two and three dimensional unsteady compressible Navier-Stokes equations using a fifth order weighted essentially non-oscillatory(WENO)finite difference scheme based on the YH parallel computer.The main purpose of these studies is to reveal the feature of shock dynamics,vortex deformation or vortex breakdown and the mechanism of sound generation in the interaction between a shock wave and vortices,as well as to explore the flow structure and mechanism of turbulence.These studies have demonstrated the excellent resolution and stability properties of the high order WENO schemes,making such schemes an ideal numerical tool for the study of shock vortex interactions in which both strong discontinuities and complex flow structures coexist.Through these studies, it is found that there is a multistage feature in the interaction between a shock wave and a strong vortex, which contains the interaction of the shock wave and the initial vortex,of the reflected shock wave and the deformed vortex and of the shocklets and the deformed vortex.The sound generated by the interaction between a shock wave and a vortex pair contains two regimes:the linear regime and the nonlinear regime.In the linear regime,the sound wave generated by the interaction of a shock wave and a vortex pair equals to the linear combination of the sound wave generated by the interactions between the same shock wave and each vortex.The second regime corresponds to the shock interaction with a coupled vortex pair.In the interaction between the shock and a longitudinal vortex,we find that there is a multi-helix structure in the region of vortex breakdown.Our simulation of the compressible isotropic turbulence also confirms the existence of shocklets at sufficiently high turbulent Mach number,which is the most noticeable influence of compressibility on the structure of turbulence.