New regimes and phase transitions in channeled granular flows Renaud Delannay P. RichardA. ValanceN....

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Transcript of New regimes and phase transitions in channeled granular flows Renaud Delannay P. RichardA. ValanceN....

  • Slide 1
  • New regimes and phase transitions in channeled granular flows Renaud Delannay P. RichardA. ValanceN. Brodu Newton Institute Dense Granular Flows 2013
  • Slide 2
  • Flat Frictional Channels = Common and important setup for granular flows
  • Slide 3
  • Glass beads on aluminum base < 15.5= min : no flow 15.5< < 20: steady fully developed (SFD) flows > 20= 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)
  • Slide 4
  • Some values of limit angles (flat base) MD (Linear Spring-Dashpot) simulations with periodic BC min (& max) do not match experimental values with periodic BC Friction between grainsFriction at the boundaries
  • Slide 5
  • 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
  • Slide 6
  • 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)
  • Slide 7
  • 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. Michels experiments : the length L ( 3m) corresponds to 1 on the figure.
  • Slide 8
  • Simulation / Experiment comparison Without lateral walls (ex : simulations with PBC along Y) Necessary condition for SFD flows : (Coulomb) Accelerated flows for > atan( gp ) Whith lateral walls other friction forces SFD flows for > atan( 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
  • Slide 9
  • Stationary states (H = 4) Velocity profiles : y ( [12,32]) Velocity profiles : z ( [12,32]) D B experiments E
  • Slide 10
  • Transverse (Y) Hight (Z) B-D Transition : Velocity field in the transv. plane Unidirectional Flow Granular Convection (rolls)
  • Slide 11
  • 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.
  • Slide 12
  • 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)
  • Slide 13
  • Volume fraction ( 0.59) almost constant with structuration in layers (B) inverted density profile disparition des couches (D) B-D transition : packing fraction profiles
  • Slide 14
  • D-E Transition Velocity profiles : y ( [12,32]) Velocity profiles : z ( [12,32]) D E
  • Slide 15
  • 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
  • Slide 16
  • Transition toward granular gas at H=4 Volume fractions 4 increments, 24 88 Steady Fully Developed flows
  • Slide 17
  • Transition toward granular gas at H=4, bumpy boundaries Volume fractions 4 increments, 24 88 Steady Fully Developed flows
  • Slide 18
  • Supported regime: mass effect Packing fraction vertical profile. : center of mass Angle : 42, H from 3 to 20 Effective Friction decreases with more mass Lift increases with more mass Consistent with the long runout hypothesis !
  • Slide 19
  • Larger mass holdups: many new regimes! Experiments This talk so far
  • Slide 20
  • Symmetry breaking & oscillations Mass holdup H=11, =50 Kinetic Energy Time Oscillations
  • Slide 21
  • Stacked rolls : new! = 24 , H = 15
  • Slide 22
  • Velocity in the transverse section Packing fraction ordered grains with shear bands between some layers Ordered based and side rolls =18, H=13
  • Slide 23
  • Despite the variety of the regimes, approximate law holds: Final velocity sin Note that mass flow rate Q V * H H 5/4