Numerical simulation of extended particles in a fluid flow

Abstract

Fully resolved flow simulations of finite-size particles with a hybrid Spectral/Immersed-Boundary method, PHYSALIS, are presented. An important quantity for modeling the effect of particles on the turbulent kinetic energy budget is the viscous dissipation occurring near the particles as a consequence of the no-slip condition. This quantity is studied by considering one or several spheres fixed against a uniform or a turbulent flow stream, for particle Reynolds number Re = 80 and turbulence intensities I = 16% and 27%.

Near the particle surfaces, the dissipation field has the mean thickness of the boundary layer as characteristic scale, and can be roughly estimated from the statistics of the hydrodynamic force on the particles. The wake perturbation induced by the free-stream turbulence determines shedding of compact vorticity patches. By this process, which seems to be an essential feature of finite-size particles, small flow structures are produced, and the wake turbulent dissipation is consequently enhanced. Our results cast doubt on the possibility of using the hydrodynamic force to estimate the wake dissipation.

Hydrodynamic interactions between spheres placed side-by-side on a regular, plane lattice perpendicular to the mean flow are dominated by the flow blockage which increases the velocity in the gap between the spheres. It seems that when the turbulence integral scale is comparable to the inter-particle separation, the free-stream turbulence structures can pass through the gaps between the particles being subject only to minor distortion.

Results for a simulation of 1024 spheres sedimenting at a finite Reynolds number are also analyzed. PHYSALIS captures the mean sedimentation velocity observed in experiments. The velocity fluctuations compare reasonably well with results presented in the literature. The suspension microstructure is characterized by a prevalence of horizontally-aligned particle pairs at close distance. When the probability of occurrence of horizontal pairs instantaneously decreases, the average sedimentation velocity increases since vertical pairs settle faster.

In numerical methods based on structured Cartesian grids, the computed hydrodynamic force acting on each moving particle is known to present spurious numerical oscillations. An explanation for this phenomenon is presented, which involves the pressure response to small discontinuities in the velocity at the numerical boundary.