369700 The Role of Granular Temperature in Turbulent Gas-Particle Flows
Fluid-particle flows are ubiquitous in engineering and environmental applications, and are often turbulent. In systems with heavy particles and significant mass loading, momentum coupling between the phases leads to the spontaneous generation of dense clusters that result in cluster-induced turbulence (CIT). To aid in the development of turbulence models for gas-particle flows, we have performed detailed simulations of homogeneous and vertical wall-bounded CIT. These simulations use an Eulerian-Lagrangian framework with inelastic particle-particle and particle-wall collisions. Special care is taken during interphase exchange to decouple the particle-diameter-to-mesh-size ratio using a two-step filter. The two phases are coupled via resolved contributions from the fluid stress and the sub-filtered contribution is modeled using Stokes drag.
Using a novel filtering approach, a length-scale separation between the correlated particle velocity field and the uncorrelated granular temperature field is observed. This separation allows us to extract the instantaneous Eulerian particle-phase volume fraction, velocity and granular temperature fields from the Lagrangian particle data. Direct comparisons can thus be made with hydrodynamic models derived using the kinetic theory of granular flows (KTGF). In particular, we can accurately decompose the total fluctuating energy of the particle phase into correlated and uncorrelated components, which correspond, respectively, to the particle-phase turbulent kinetic energy and the mean granular temperature.
In homogeneous CIT, we observe from the instantaneous granular temperature fields that the maximum granular temperature occurs on the downstream side of dense clusters, and thus acts to reduce the cluster fall velocity due to the higher granular pressure. Furthermore, the simulation data for the local particle-particle collision frequency follows the KTGF prediction when the granular temperature – as opposed to the total fluctuating energy – is used to estimate the collision velocity. In the wall-bounded CIT simulations, we find that the granular temperature levels are generally low compared to the fluctuating energy generated by the coupling of dense clusters with the correlated particle velocity field. For this reason, turbulent momentum transport – rather than KTGF viscous transport – dominates, except in the viscous layer near the wall. Finally, based on the simulation data, we shall comment on the perspective of using classical turbulence closures for homogeneous and wall-bounded CIT.
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