Modeling Of Turbulent Kinetic Equation In Converging-Reflecting Spherical Shock-Turbulence Interaction

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-e two-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.