Particle-laden flows around a circular obstacle: numerical simulations of the wake instability.*

We investigated particle-laden flows around a circular obstacle. The fluid flow is seeded with solid finite-size spherical particles of varying density from neutrally-buoyant to highly inertial material for granular flows. As particles interact with the fluid and the obstacle placed in a wide 3D domain the onset and the dynamics of the wake is strongly modified. The size ratio between the particle to cylinder diameter is either 10 or 5. We have investigated a range of parameters (Reynolds and Stokes numbers) that spans from steady attached flow, wake formation and unsteady vortex shedding.

Our numerical approach is fully-coupled, such that fluid-particles (10 grid cells per particle diameter) and particle-particle interactions (discrete element model of collisions and friction) plus the feedback effect of particles on the fluid flow are resolved. The simulations of suspension flows are based on modern simulation methods to generate highly efficient and scalable Lattice Boltzmann Method calculations. The code used for this study is waLBerla, an open-source C++ multiphysics software framework, which was designed for high-performance computing on massively parallel clusters. Simulations of particle resolved dynamics with up to 4,800 million grid cells and 1.8 million spherical particles are carried out for different flow regimes and particle concentrations from dilute (5%) to semi-dilute regime (20% volume concentration). 

The flow response is described by characteristic parameters such as dimensionless vortex shedding or wake recirculation length. Flow regimes with neutrally-buoyant particles can be rationalized by means of mixture material properties while we observe a progressive transition to granular flow for inertial particles. Drag and lift forces acting onto the cylinder are commented. and the physical analysis is based on the respective hydrodynamic and particle collision contributions.