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

New regimes and phase transitions in channeled

granular flowsRenaud Delannay

P. RichardA. ValanceN. Brodu

Newton Institute Dense Granular Flows 2013

Flat Frictional Channels

=

Common andimportant setup

for granular flows

Glass beads on aluminum base

•q < 15.5°=θmin: no flow

•15.5°< q < 20°: steady fully developed (SFD) flows

•q > 20°=θmax: 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 grains Friction at the boundaries

Introduction of flat frictionnal walls PRE Brodu et al. 2013

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 H: (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

OscillationsUnidirectionalStopped

→ We recover the experimental angular range (q [15°, 20°]) of SFD flows

Accelerated regimes in experiments = not long enough chute facility

The maximum inclination angle of exp. observed SFD flows, qm, 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(μgp

)

Whith lateral walls → other friction forces

SFD flows for θ > atan(μgp

) 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

tancos

sin

N

S

gpN

S

Nmg

S

q

Stationary states (H: = 4)

Velocity profiles : <V(y,z)>y (q [12°,32°])

Velocity profiles : <V(y,z)>z (q [12°,32°])

D

B ↔ experiments

E

Transverse (Y)

Hig

ht (Z

)

B-D Transition: Velocity field in the transv. plane

UnidirectionalFlow

GranularConvection (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 » velocityVs mean velocity just above the basal grains

Bagnold profile

New origin on the basal layer: H’ and z’ taken from this origin.

V’x = Vx - Vs (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 : <V(y,z)>y (q [12°,32°])

Velocity profiles : <V(y,z)>z (q [12°,32°])

D

E

D-E Transition: the « supported » regime !

Volume fraction

Convection regime

Transition

Dense core supportedby 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 H: =4

Volume fractions4° increments, 24 ≤ θ ≤ 88°Steady Fully Developed flows

Transition toward granular gas at H: =4, bumpy boundaries

Volume fractions4° increments, 24 ≤ θ ≤ 88°Steady Fully Developed flows

Supported regime: mass effect

Packing fraction vertical profile.

● : center of massĤ

© Angle : 42°, H: ↑ from 3 to 20

Effective Friction decreases with more massLift 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 H: =11, θ=50°

Kinetic Energy

Time

Oscillations

Stacked rolls : new! q = 24°, H: = 15

Velocity in thetransverse section

Packing fraction

ordered grainswith shear bandsbetween some layers

Ordered based and side rolls θ=18°, H: =13

Despite the variety of the regimes, approximate law holds:

Final velocity ∝ Ĥ¼ sin θ

Note that mass flow rate Q V * H� H� 5/4