Granular Flows From the Laboratory to the Ski Jump

Transcription

1 Granular Flows From the Laboratory to the Ski Jump Jim McElwaine Department of Earth Sciences Durham University

2 Acknowledgments Betty Sovilla Barbara Turnbull Kouichi Nishimura Christophe Ancey Dieter Issler Takahiro Ogura Eckart Meiburg Shane Byrne Nathalie Vriend

3 Plan of Talk Introduction to Avalanches Granular Levees Direct Numerical Simulations Integral Models and Field Obervations Shallow Models and Field Obervations Mars

4 Powder Avalanche on K2 Pierre Beghin

5 Head of Powder Snow Avalanche Cemagref

6 Slab Avalanche Fracture Line

7 Skier in Slab Avalanche Debris Cemagref

8 Patreksfjörður 1983, a Slush Flow Killed 3 People

9 Destroyed House at Saint Colomban Les Villars

10 Test Chute in Davos film

11 Destroyed Buildings at La Morte Cemagref

12 Damage by a flood wave at Súgandafjörður

13 Current Avalanche Research Huge variety: speeds km/h densities kg/m 3 masses kg Three dimensional terrain and structure Snow properties are complicated and ill-defined Unpredictable, destructive, unreproducible Current theories are phenomenological Genesis of powder snow avalanches not understood

14 Ping-Pong Avalanches

15 Levee Formation in Natural Flows Phys. Rev. E 83: (2011) Types Avalanches Rock Slides Debris Flows Effects Increased Runout Changed Hazard Zones

16 Levee Formation at Vallée de la Sionne film

17 Deposit thickness hstop as a function of slope angle θ h stop d = a tanθ tanθ 1

18 Theoretical Motivation An empirical law for the steady granular flow from experiments and simulations u h Fr = = α+β gh cosθ hstop(θ), u velocity h flow depth hstop deposit depth g gravity θ slope angle Fr h

19 Experimental setup film Phys. Rev. E (83):031306, Gran. Mat. (2012)

20 Regime diagram for Sand Q mass flow rate

21 Evolution of the surface velocity Ballotini Q = 10 g/s, θ = 25 Sand Q = 104 g/s, θ = 32

22 Surface Measurements with Particle Image Velocimetry (PIV) Ballotini Sand u (mm/s) x (mm) u (mm/s) x (mm)

23 Surface height and velocity of sand z (mm) u (mm/s) Clear Surface t=2min t=10min t=30min t=40min base y (mm) Surface Height t=2min t=10min t=30min t=40min z (mm) u (mm/s) Covered surface t=3min t=5min t=12min t=20min base y (mm) Surface Height t=3min t=5min t=12min t=20min y (mm) Surface Velocity y (mm) Surface Velocity Covered surface Speeds up convergence, steady states are identical

24 Centre height and velocity against flow rate h (mm) u (mm/s) Q (g/s)

25 Characteristic width of the flowing region Q = ρhu(w W 0 ) W = W 0 + Q ρhu ρ density, H depth, U velocity, Q mass flux, W width

26 Speed against height Speed against position u / (gh) 1/ g/s 50 g/s 75 g/s h / h stop Speed against height u h = α+β gh cosθ hstop(θ) +ν h 2 2 u gh cosθ z 2

27 Granular Solitons film z (mm) time (s) Surface height Measured in the middle of the slope Avalanche profiles

28 Dry-mixed avalanche artificially released at the Vallée da la Sionne

29 Deposit showing a homogeneous snow depth distribution

30 Riegl LMS-Q240i laser scanner Specs time of flight principle points per second horizontal resolution 500 mm vertical resolution 100 mm high density of points inertial measurement GPS

31 Snow depths variations h δ FMCW and Pylon! m m m m m m m m m m m m m m m m m Meters

32 Bunker Rescue

33 Average snow depth variation h δ Average snow depth variation (cm) Domain 816 Domain Slope angle ( )

34 Cohesion-Frictional Model ρgd f sinθ = c +µρgd f cosθ d f = c ρg(sinθ µ cosθ) ρ density g gravity d f flow depth θ slope angle c cohesion µ friction #816 c = 123±25N m 2 µ = 0.35±0.02 #817 c = 146±26N m 2 µ = 0.36±0.02

35 Deposit depth d f = h d cosθ #816 Deposition depth (m) best fit range best fit range Slope angle ( )

36 Chutes A Granular Rheometers J. Fluid. Mech. 710:35 (2012) Previous chutes have been built but low mass fluxes only steady flows studied limited slope angles limited boundary conditions limited measurement systems

37 Our Chute Return Chute Screw Conveyor Bucket Lift Feed Hopper Chute Equipment Traverse Overflow Chute

38 Our Chute 20 kg s 1 Flux rate 2000 kg Capacity 0.25 m Chute width 4 m Chute length 0 60 slope angle instrumentation traverse complete surface velocity and height

39 Chute Components

40 Velocity for Rough and Smooth Bases Smooth, 40 Rough, Velocity Velocity Distance Distance

41 Height for Rough and Smooth Bases Smooth, 40 Rough, Height Height Distance Distance

42 Transverse Velocity Profiles Smooth Base 50, 7.6 kg s 1 40, 7.6 kg s Velocity Velocity Cross Chute Cross Chute

43 Transverse Velocity Profiles Rough Base 50, 7.6 kg s 1 40, 7.6 kg s Velocity Velocity Cross Chute Cross Chute

44 µ(i) Friction Law µ(i) = µ 1I 0 +µ 2 I I 0 + I 18 µ hstop /d I θ ( ) h stop /d as a function of the inclination over the bumpy base. Fitting gives µ 1 = 0.54 and µ 2 = 0.68.

45 Macroscopic Friction coefficient (µ) 0.62 µ(i) Smooth Base Smooth Perspex Red Steep, Blue Shallow 0.9 µ(i) Rough Base Grade 40 Sandpaper Red Steep, Blue Shallow mu Inclination mu Inclination I I γ u d = I = u gh cosθ γ u h = I = ud gh 3 cosθ

46 µ(i) at fixed inclination (40 ) 0.85 Plain data Model 1 - plain mu Wall contribution subtracted 0.8 Model 1 - mu adjusted u du dx = g sinθ Constant wall friction ( h µ(i)+µ w 2w 0.4 ) g cosθ µ 1 = 0.05,µ 2 = 0.93, I 0 = 0.16 µ w = 2.6

47 µ(i) at fixed flux High flow rate 17.8 kg s 1 Grade 40 Sandpaper Flux: kg/s Medium flow rate 10.2 kg s 1 Grade 40 Sandpaper Flux: kg/s mu mu I dµ di = µ 1 µ 2 I=0 I I

48 Terminal velocity on a bumpy surface uterm gd θ ( ) Iterm q (kgs 1 ) ˆq θ ( ) Each line represents the terminal velocities at a given inclination as the flux varies.

49 Onset of Turbulence Velocity Velocity Cross Chute 40 at 3.3 kg s 1 and 5.3 kg s Cross Chute

50 Lateral Instability Velocity Velocity Cross Chute Cross Chute Velocity Cross Chute

51 Lateral Instability Develops Down the Chute Inelastic collapse?

52 Roll Wave Instability Spacetime plots of surface height

53 Leidenfrost effect 6 large mixed 5 small 4 l θ Height of the low density layer at the basal surface in DEM simulations

54 Conclusions Phase diagram q/ρwd gd q/ρwd gd θ ( ) θ ( ) Flat Base Bumpy Base ( ) Constant velocity flows, ( ) Accelerating, Dense Flows, (+) Flows with separation at walls, ( ) Low density flows, ( ) Superstable heap formation

55 Conclusions Extrapolated Phase diagram Steady ñ Unknown, high q Low q Separated Dilute θ ( )

56 CO 2 Avalanche on Mars from HiRise Aspect: W WSW SW S Four simultaneous avalanches with a range of Slope azimuths south is up and left Speeds measured in ten of m s 1

57 Helene moon of Saturn Helene moon of Saturn 7P Churyumov comet

58 Thanks!

59 Publications Turnbull, B. and J.N. McElwaine, Experiments on the non-boussineq Flow of Self-Igniting Suspension Currents on a Steep Open Slope., J. Geophys. Res., 113(F01003), doi: /2007jf Turnbull, B., J.N. McElwaine and Ancey, C., The Kulikovskiy Sveshnikova Beghin Model of Powder Snow Avalanches: Development and Application, J. Geophys. Res., 112(F01004), doi: /2006jf Turnbull, B., and J.N. McElwaine, A Comparison of Powder Snow Avalanches at Vallée de la Sionne with Plume Theories, J. Glaciol., 53(30) J.N. McElwaine, and Turnbull, B.,2006. Plume Theories Versus Compact Models for Powder Snow Avalanches, Sixth International Symposium on Stratified Flows, Perth, December 11-14, McElwaine, J.N., Rotational flow in gravity current heads, Phil. Trans. R. Soc. Lond., 363, , /rsta McElwaine, J.N. and Turnbull, B., Air Pressure Data from the Vallée de la Sionne Avalanches of 2004, J. Geophys. Res., 110(F03010), doi: /2004jf McElwaine, J.N. and Nishimura, K Particulate Gravity Currents, Blackwell Science, chap. Ping-pong Ball Avalanche Experiments, no. 31 in Special Publication of the International Association of Sedimentologists,