Direct Numerical Simulation of Rotating Ellipsoidal Particles using Moving Nonconforming Schwarz-Spectral Element Method

Abstract

We present application of a highly-scalable overlapping grid-based nonconforming Schwarz-spectral element method (Schwarz-SEM) to study the dynamics of rotating ellipsoidal particles. The current study is one of the first to explore the effect of rotation on ellipsoidal particles using fully resolved simulations (direct numerical simulation). The rotating ellipsoidal particles show substantial difference in the dynamics of the flow, when compared against non-rotating particles. The difference is primarily due to periodic attachment and separation of the flow to the surface of the particle for the rotating cases, which results in a higher drag on the particles when compared to the corresponding non-rotating cases. The dynamics is also different from a rotating spherical particle, where a steady shear layer develops near the surface of the sphere. For the rotating ellipsoidal particles, this mechanism results in a phase-difference between the position of observed maximum and minimum drag, and the position of expected maximum and minimum drag (i.e., maximum and minimum projected area). A similar phase-difference is also observed for the lift acting on the rotating ellipsoidal particles. The results presented here demonstrate the importance of explicitly modeling the shape and rotation of particles when we study the dynamics of non-spherical particles. Finally, the study also validates the use of nonconforming Schwarz-SEM for tackling problems in fully resolved particulate flow dynamics.

Multirate Timestepping for the Incompressible Navier-Stokes Equations in Overlapping Grids

“…The singlerate timestepping scheme is most efficient when P c = 1024 = P f /4, which is in agreement with (36) since E c ≈ E f /4. As P c is decreased, the time to solution increases as expected.…”

“…In [1], we further demonstrated that Q = 0 is sufficient from an accuracy point of view for basic statistics (e.g., mean or rms) of turbulent flows. This predictorcorrector approach has been used in the Schwarz-SEM framework [34,35,36] to demonstrate that it maintains the spatial and temporal convergence of the underlying monodomain SEM framework, and is effective for solving highly turbulent flow phenomenon in complex domains using an arbitrary number of overlapping grids.…”