(716c) Sine-Squared Scaling of Drag Coefficient for Different Non-Spherical Particles

Different industrial applications involve wide range of non-spherical particles. The present work
investigates a simplified drag model that can be used for larger scale Euler-Lagrangian
fluidization simulations. The flow around different prolate (needle-like) and oblate (disc-like)
spheroids is studied using a multi-relaxation-time lattice Boltzmann method. We compute the
mean drag coefficient C_D,ϕ at different incident angles ϕ for a wide range of Reynolds numbers
(Re). We show that the sine-squared drag law C_D,ϕ = C_D,ϕ=0^∘ + (C_D,ϕ=90^∘−C_D,ϕ=0^∘)sin²ϕ
holds up to large Reynolds numbers Re = 2000. The sine-squared dependence of C_D occurs at
Stokes flow (very low Re) due to linearity of the flow fields. We explore the physical origin
behind the sine-squared law at high Re, and reveal that surprisingly, this does not occur
due to linearity of flow fields. Instead, it occurs due to an interesting pattern of
pressure distribution contributing to the drag, at higher Re, for different incident
angles.

The present results demonstrate that it is possible to perform just two simulations at
ϕ = 0^∘ and ϕ = 90^∘ for a given Re and obtain particle shape specific C_D at arbitrary
incident angles. Similarly, we find that the equivalent theoretical equation of lift
coefficient C_L can provide a decent approximation, even at high Re, for prolate
spheroids. Such a drag and lift law valid for needle-like prolate spheroids is very
useful for Euler-Lagrangian fluidization simulations of non-spherical particles. The
drag law has limited applicability to flatter oblate spheroids, which do not exhibit
the sine-squared interpolation, even for Re = 100, due to stronger wake-induced
drag.