The lift on a disc immersed in a rotating granular bed

Abstract

The discrete element method has been used to study the lift F L on a stationary disc immersed coaxially in a slowly rotating cylinder containing a granular material. In a tall granular column, F L rises with the immersion depth h, but reaches a roughly constant asymptote at large h, in agreement with previous studies. Our results indicate that the argument in some earlier studies that F L is proportional to the static stress gradient is incorrect. Instead, our results show that the lift is caused by an asymmetry in the dilation and shear rate between the regions above and below the disc. We argue that the cause of the lift is similar to that in fluids, namely that it arises as a result of the disturbance in the velocity and density fields around the body due to its motion relative to the granular bed.Positive and negative values of ðz2hÞ correspond to the regions below and above the disc, respectively. Here the data of (a) and (b) correspond to H562 d p and H5222 d p , respectively, for a disc of thickness t510 d p and different depths of immersionh. Panel (c) shows the difference in the solids fraction (averaged in the same manner) between the lower and upper surfaces of the disc; the blue triangles and red asterisks are data for the short and tall columns, respectively. [Color figure can be viewed at wileyonlinelibrary.com] AIChE Journal

Comparison of the compressible class of models and non-local models with the discrete element method for steady fully developed flow of cohesionless granular materials through a vertical channel

“…There are six parameters in the model for the contact forces between particles: the spring constants and , the damping constants and , the coefficient of interparticle friction and the coefficient of particle–wall friction . Following Debnath, Rao & Nott (2017), we choose , , , and , where and are the density and the diameter of the particle, respectively, and is the acceleration due to gravity. It is widely acknowledged that should be a few orders of magnitude larger for materials such as aluminium, stainless steel, brass and glass beads (see e.g.…”

“…The time step used is 1.2 × 10 −4 d p /g. Debnath et al (2017) estimated the lift on a disc immersed in a rotating bed of granular material, and found that modest changes in the value of k n by a factor of 10 do not affect the normal stresses exerted on the disc significantly. The value of k t /k n is commonly used; it is obtained by considering an elastic collision between a sphere and a flat surface, assuming that the time periods for normal and tangential collisions are equal (Shäfer et al 1996).…”

Different shear regimes in the dense granular flow in a vertical channel

“…As the computational time step is proportional to , a large value of makes the simulations computationally expensive. Hence the value of is chosen in the range , and is set to (Debnath, Rao & Nott 2017). The damping coefficient is chosen so that normal coefficient of restitution for the interaction between two particles, , is set equal to .…”