New regimes and phase transitions in channeled granular flows Renaud Delannay P. RichardA. ValanceN. Brodu Newton Institute Dense Granular Flows 2013

Flat Frictional Channels = Common and important setup for granular flows

Glass beads on aluminum base  < 15.5°=θ min : no flow 15.5°<  < 20°: steady fully developed (SFD) flows  > 20°=θ max : accelerated flows (+ oscillations) M. Y. Louge and S. C. Keast, Physics of fluids 13,5 (2001) - Min/max angles for SFD flows seems independent of H (contrary to bumpy base). - Presence of fluctuations (waves)‏

Some values of limit angles (flat base) MD (Linear Spring-Dashpot) simulations with periodic BC θmin (& θmax) do not match experimental values with periodic BC Friction between grainsFriction at the boundaries

Introduction of flat frictionnal walls PRE Brodu et al Parameters (material, contacts...) are set to these from Louge & Keast (2001). Bounded on each side, same width between lateral walls : W = 68D Shallow flows with identical mass holdup H̃ (number of grains / unit area) + periodic only along the flow direction

Transients and stationary states Kinetic energy over time, translation & rotation (insert)‏ for angles between 13° and 31°. All inclination angles larger than 15° lead to stationary states (even for very large angles not represented here)

Simulation / Experiment comparison Oscillations Unidirectional Stopped → We recover the experimental angular range (   [15°, 20°]) of SFD flows Accelerated regimes in experiments = not long enough chute facility The maximum inclination angle of exp. observed SFD flows,  m, is limited by the length L of the setup. Michel’s experiments : the length L (≈ 3m) corresponds to 1 on the figure.

Simulation / Experiment comparison Without lateral walls (ex : simulations with PBC along Y) Necessary condition for SFD flows : (Coulomb)  Accelerated flows for θ > atan(μ gp ) Whith lateral walls → other friction forces SFD flows for θ > atan(μ gp ) are possible Experiments: -There are always lateral boundaries which exert friction forces. -At the beginning, if these forces are too small to balance the difference between the weight and the basal friction, the flows accelerates. -The lateral friction increases and, if the chute is long enough, becomes large enough to balance the difference, leading to SFD flows N mgmg S 

Stationary states (H̃ = 4) Velocity profiles : y (   [12°,32°]) Velocity profiles : z (   [12°,32°]) D B ↔ experiments E

Transverse (Y) Hight (Z) B-D Transition : Velocity field in the transv. plane Unidirectional Flow Granular Convection (rolls)

B-D transition : velocity profiles Shearing layer (induced by walls) (B) Plug flow in the centre Sheared through the whole width (D) due to secondary rolls « Sliding » at the base : basal layer of rolling and bumping grains can be interpreted as an effective bumpy base for the main bulk of the flow on top of it.

Flows on flat frictional surfaces can be decomposed into a rolling basal layer, above which the main bulk of the flow follows the Bagnold scaling B-D transition : Bagnold profiles « sliding » velocity V s mean velocity just above the basal grains Bagnold profile New origin on the basal layer: H’ and z’ taken from this origin. V’ x = V x - V s (velocity relatively to the basal layer)

Volume fraction (ν ≈0.59) almost constant with structuration in layers (B) inverted density profile disparition des couches (D) B-D transition : packing fraction profiles

D-E Transition Velocity profiles : y (   [12°,32°]) Velocity profiles : z (   [12°,32°]) D E

D-E Transition : the « supported » regime ! Volume fraction Convection regime Transition Dense core supported by a granular gas! Granular Leidenfrost effect C. Campbell (1989) suggests this regime as a possible scenario for long run-out avalanches (reduced friction at the base). Granular temperature

Transition toward granular gas at H̃=4 Volume fractions 4° increments, 24 ≤ θ ≤ 88° Steady Fully Developed flows

Transition toward granular gas at H̃=4, bumpy boundaries Volume fractions 4° increments, 24 ≤ θ ≤ 88° Steady Fully Developed flows

Supported regime: mass effect Packing fraction vertical profile. ● : center of mass ĤĤ © Angle : 42°, H̃ ↑ from 3 to 20 Effective Friction decreases with more mass Lift increases with more mass ⇒ Consistent with the long runout hypothesis !

Larger mass holdups: many new regimes! Experiments This talk so far…

Symmetry breaking & oscillations Mass holdup H̃=11, θ=50° Kinetic Energy Time Oscillations

Stacked rolls : new!  = 24 °, H̃ = 15

Velocity in the transverse section Packing fraction ordered grains with shear bands between some layers Ordered based and side rolls θ=18°, H̃=13

Despite the variety of the regimes, approximate law holds: Final velocity ∝ Ĥ ¼ sin θ Note that mass flow rate Q  V * H̃  H̃ 5/4