A numerical method based upon the immersed boundary technique for the
fluid-solid coupling and on a soft-sphere approach for solid-solid contact is
used to perform direct numerical simulation of the flow-induced motion of a
thick bed of spherical particles in a horizontal plane channel. The collision
model features a normal force component with a spring and a damper, as well as
a damping tangential component, limited by a Coulomb friction law. The standard
test case of a single particle colliding perpendicularly with a horizontal wall
in a viscous fluid is simulated over a broad range of Stokes numbers, yielding
values of the effective restitution coefficient in close agreement with
experimental data. The case of bedload particle transport by laminar channel
flow is simulated for 24 different parameter values covering a broad range of
the Shields number. Comparison of the present results with reference data from
the experiment of Aussillous et al. (J. Fluid Mech. 2013) yields excellent
agreement. It is confirmed that the particle flow rate varies with the third
power of the Shields number once the known threshold value is exceeded. The
present data suggests that the thickness of the mobile particle layer
(normalized with the height of the clear fluid region) increases with the
square of the normalized fluid flow rate.Comment: accepted for publication in Int. J. Multiphase Flow, more data
available at http://www.ifh.kit.edu/dns_data/particles/bedload
