Numerical investigation of the vertical plunging force of a spherical intruder into a prefluidized granular bed

Abstract

The plunging of a large intruder sphere into a prefluidized granular bed with various constant velocities and various sphere diameters is investigated using a state-of-the-art hybrid discrete particle and immersed boundary method, in which both the gas-induced drag force and the contact force exerted on the intruder can be investigated separately. We investigate low velocities, where velocity dependent effects first begin to appear. The results show a concave-to-convex dependence of the plunging force as a function of intruder depth. In the concave region the force fits to a power law with an exponent around 1.3, which is in good agreement with existing experimental observations. Our simulation results further show that the force exerted on the frontal hemisphere of the intruder is dominant. At larger intruder velocities, friction with the granular medium causes a velocity-dependent drag force. As long as the granular particles have not yet closed the gap behind the intruder, this drag force is independent of the actual intruder depth. In this regime, the drag force experienced by intruders of different diameter moving at different velocities all fall onto a single master curve if plotted against the Reynolds number, using a single value for the effective viscosity of the granular medium. This master curve corresponds well to the Schiller-Naumann correlation for the drag force between a sphere and a Newtonian fluid. After the gap behind the intruder has closed, the drag force increases not only with velocity but also with depth. We attribute this to the effect of increasing hydrostatic particle pressure in the granular medium, leading to an increase in effective viscosity.

The role of initial speed in projectile impacts into light granular media

“…Figs.2 and 3 show the vertical position z(t) and speed v i (t) of the intruder, obtained experimentally and numerically, respectively. For the experimental cases, the initial speed is estimated from a parabolic fit of the intruder trajectory before impact together with the initial falling height H. As noted, in all cases the intruder dynamics predicted numerically is in very good quantitative agreement with the experimental results and in line with previous findings 20,[32][33][34] .…”

Support of modified Archimedes' law theory in granular media

“…Many experiments and simulations show that, at steady state (see below) F z (z) = kz α , but there is no consensus on the value of α. Hill et al, 23 and Peng et al 24 found α = 1.3 while Hou et al 25 , Durian et al 12,19,26 , Lohse et al 27 and Kang et al 28 measured α = 1 experimentally, although the latter also showed and discussed an initial regime for z < z c . Simulations by Xu et al 16 also support α = 1.0.…”

Resistance Force on a Spherical Intruder in Fluidized Bed

“…The main aim of this sub-section is to benchmark the simulation code by calculating the granular drag force in packed bed. In literature (Lohse et al 2004); Katsuragi and Durian 2007;Xu et al 2014), this problem is reasonably studied and the relation for modeling granular drag force can be written as: , In some work, is included in rather than as a separate term (Katsuragi & Durian 2007). For intruders with relatively smaller velocities (i.e.…”

“…(this value of for ignoring and the relation for in Eq. 14are obtained from literature (Lohse et al 2004;Katsuragi & Durian 2007;Xu et al 2014;Hou et al 2005;Hill et al 2005) (16) Lohse et al (2004) proposed the value of =13.3 0.5 N/m and =1 using experiments of free fall of large object in loosely packed sand. Hill et al (2005) using the plunging and retraction experiments of intruders into granular material proposed the value of =15 3 N/m and =1.3.…”