球形汇聚-反射激波作用下湍动能方程的模化

Modeling of turbulent kinetic equation in converging-reflecting spherical shock-turbulence interaction

球形激波与湍流间的相互作用在惯性约束聚变(ICF)、超新星爆发、冲击波碎石等许多工程问题中有重要意义.本文通过直接数值模拟,研究了球形激波的汇聚与反射诱导的湍流及其相互作用问题,分析了这一流动的特点和湍流的产生机制.重点讨论了该流动的湍动能系综平均方程中各项的作用和起主导作用的物理机制,发现传统的剪切湍流的产生机制和黏性项量级普遍偏小,激波才是诱发湍流的主要因素,因而在湍动能方程中起主导作用.由于激波的主导作用,压力脉动对湍动能方程有重要影响,与压力脉动有关的各个项在湍动能方程中均起重要作用.一些在一般湍流中可以忽略的项,例如质量流量项、压力体胀项等,在球形汇聚-反射激波与湍流相互作用问题中起重要作用.本文还探讨了涡黏性模式的有效性,发现满足可实现性原理的涡黏性模式可以较好地模拟雷诺应力.同时,本文揭示了现有湍动能方程封闭模式在本问题的应用中存在很大误差,并尝试对这些项提出新的封闭模式.

The interaction between spherical shock and turbulence is very important in inertial confinement fusion(ICF),supernova explosion,shock wave lithotripsy and other engineering problems.In this work,the interaction between convergingreflecting spherical shock and isotropic turbulence is studied through direct numerical simulation.The characteristics of the flow and the mechanism of turbulence generation are analyzed in detail.Research attention has mainly focused on the behavior of turbulent kinetic equation and the physical mechanisms that play important roles in the flow.It is found that the traditional mechanisms for shear-driven turbulent flows are weak and viscous terms in the turbulent kinetic equation can even be neglected.Shock wave is attributed as the main factor inducing turbulence and plays a leading role in the turbulent kinetic equation.It is particularly observed that the pressure fluctuation induced by the shock has a dominant influence on the turbulent kinetic equation.Terms related to pressure fluctuation play important role in turbulence generation.Some terms that were normally ignored in shear-driven turbulence,such as mass flux and pressure dilatation terms,exhibit large magnitudes in the interaction of converging-reflecting spherical shock with turbulence.The validity of the eddy viscosity model is also discussed in this work.It is illustrated that the eddy viscosity model satisfying the realizability principle can deliver much better simulations of Reynolds stresses than the standard k-εtwo-equation model.It is also revealed here that the traditional closure models of the unknown terms in the turbulent kinetic equation are remarkably erroneous when applied to the present problem.Attempts have made to propose new closure models for the mass flux and pressure dilatation terms in the turbulent kinetic equation.