Numerical analysis of particle-turbulence interaction in high-speed gas flows
Final Report Abstract
High-speed gas flows with dispersed solid particles are encountered in various environments associated with geophysics, astrophysics, and engineering. Examples include explosive volcanic eruptions, the formation of interstellar clouds and protoplanetary disks, and cold spraying for surface coating. These multiphase systems are characterized by a complex interplay of gasphase turbulence, particle dynamics, heat transfer, and compressibility effects such as shock waves. Despite their relevance, the fundamental mechanisms of particle-turbulence interaction in these flows are still poorly understood. In this project, novel highly-resolved simulations of compressible turbulence were therefore conducted. The distinct feature of highly compressible turbulence is the formation of embedded shock waves, called eddy shocks, that can substantially impact the energy balance and trajectory of solid particles. The analyses in this project suggest a reevaluation of previously accepted estimates for the eddy shock strength and thickness. In particular, eddy shocks were found to be about four times stronger than reported. The shocks are also significantly thicker than previously estimated or than shock theory would imply, highlighting the distinct role of turbulence in modifying the shock structure. A new procedure for the detection of eddy shock waves thus was proposed and demonstrated to be substantially more accurate than the state-of-the-art algorithm. Moreover, novel analysis in a Lagrangian reference frame demonstrates a subset of these compressive structures to be steepening waves rather than regular shock waves. Based on the new shock detection scheme, the hydrodynamic drag of inertial particles in highspeed turbulence was investigated, most importantly, during the passing of particles through eddy shock waves. Based on the data, a new charateristic time scale was defined, describing the average time interval after which a particle encounters the next eddy shock wave. This time scale suggests a new classification of particle-turbulence interaction: in contrast to light particles, particles with higher inertia are unable to “relax” to the ambient flow before they travel through another shock. In other words, such particles always remain in a “shocked” state and are ballistic with respect to the relevant flow scales. Next, the footprint of the particles in the kinetic energy balance of the fluid phase was investigated. Particles absorb energy in expansion regions and release energy in compressive regions. The compressive effect substantially increases near eddy shocks: due to their inertia, particles strongly accelerate the ambient fluid when passing into the post-shock region, thereby increasing the fluid kinetic energy. These findings suggest that heavy particles in compressible turbulence can behave ballistic in a way which is distinct from ballistic behavior in incompressible turbulence. The analyses also evidence Taylor’s weak shock solution to be a reliable ansatz function to reconstruct eddy shock profiles. This makes Taylor’s solution a viable candidate for the statistical modelling of eddy shocks; their increased thickness could be modeled in terms of an artificial (eddy) viscosity, to reproduce the statistical distribution of shock thicknesses compared to regular shocks. This approach may give rise to a new class of particle-drag models for compressible turbulence.
