New regimes and phase transitions in channeled
granular flowsRenaud Delannay
P. RichardA. ValanceN. Brodu
Newton Institute Dense Granular Flows 2013
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!
Velocity in thetransverse section
Packing fraction
ordered grainswith shear bandsbetween some layers
Ordered based and side rolls θ=18°, H: =13
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