Particle-laden turbulent flows are important features of many environmental and industrial
processes. However, the large range of scales, from the boundary layers of individual particles, to
the macro-scale dynamics of particle clusters, presents a challenge to developing feasible and
accurate simulations. In addition, single phase approaches to model reduction cannot capture the
relevant physics for engineering and scientific purposes. In this talk, we will discuss our work
towards addressing these challenges.

Previous work has introduced the concept of cluster-induced turbulence (CIT) wherein coupling
between a fluid phase and a dispersed solid phase,  falling under gravity,  leads to the generation
of turbulent-like fluctuations. CIT is reminiscent of many physical flows, displaying common characteristics such as particle clustering, jet bypassing, and particle phase compressibility. Towards understanding particle-laden flow behavior near walls, we apply homogeneous shear to CIT. We present a phenomenon observed in Eulerian-Lagrangian (EL) simulations of sheared CIT, that above a certain shear Stokes numbers, clusters disintegrate.

Next we will present an Eulerian-Eulerian (EE) method for simulating particle-laden flows.
Eulerian- Eulerian (EE) methods can offer computational savings over EL methods as particles do not need to be tracked individually.  Traditionally, EE methods cannot accurately simulate
particle-laden flows in regions  of high particle Knudsen number.  The multi-valued nature of the
particle velocity field must be treated  with a polykinetic description. Quadrature-based moment
methods (QBMM) approximate the full kinetic description by solving for a set of moments of the
particle velocity distribution function (VDF) and providing closures for the higher order moments
using Gaussian quadrature. A conditional hyperbolic quadrature method of moment (CHyQMOM) has been developed that also preserves the hyperbolicity of the kinetic equations. We present simulation
comparisons between CHyQMOM and EL in the context of particle-laden
homogeneous isotropic turbulence and CIT.