Avalanche simulation - École Polytechnique Fédérale de...
1
Avalanche simulation M. Rentschler, Ch. Ancey, S. Cochard Environemental hydraulics laboratory, EPFL, Switzerland [email protected] LABORATOIRE YDRAULIQUE NVIRONNEMENTALE E H Abstract To tackle the delicate issue of avalanche simulation we are investigating the dynamics of this kind of phenomena on the lab scale, which enables us to make reproducible experiments under well-controled laboratory conditions. More specifically we focus our attention on the motion of an avalanching mass flowing down an inclined plane (channelized or not), with a significant slope change in its lower part. Velocity (front and free surface) and the flow depth can be accurately measured at any point using image processing techniques. In the meantime, we extend numerical tools (three-dimensional Navier-Stokes solver) to model this experiment. The final objective is to understand the dynamics of complex fluids far from equilibrium (no steady regime is achieved) and develop governing equations that are more appropriate to that purpose than the classical shallow-water equations. 1. Natural Phenomena Figure 1: Avalanche in the test field of the SLF in the Vall´ ee de la Sionne(Valais). (Courtesy of SLF) Very expensive Experiments (Costs of about 60000 SFr ) Not reproducible Uncertainties on the initial conditions Large number of involved processed Few parameters that can be conveniently measured 2. Isolated process: Viscoplastic flow ( a ) Carbopol deposit ( b ) Avalanche deposit Viscoplastic flow Avalanche deposits on an inclined terrain (plastic behavior) Avalanche flows like a viscoplastic fluid Carbopol Yield-stress τ 0 No Thixotropy Reproducible and stable Easy to handle: No melting, not poisonous... Rheological properties of the Carbopol τ 0 Viscosity μ Shear Stress τ 0 20 40 60 80 100 120 140 160 180 200 10 -5 10 -4 10 -3 0.01 0.1 1 10 100 1 10 100 1000 10 4 10 5 10 6 Shear Stress τ [Pa] Shear-rate ˙ γ [1/s] Viscosity μ [Pa/s] Figure 3: Rheometrical measurements for a Carbopol sample. The lines represent the fitted Herschel-Bulkley model. Herschel-Bulkley model If |τ | <τ 0 : ˙ γ =0, If |τ | >τ o : τ = τ 0 + K | ˙ γ | 1 n 3. Experimental device Inclined plane Figure 4: The inclined plane with Steve Cochard. Variable inclination Various geometries Very short time to open the gate Measuring the free surface Camera Projector Inclined plan Fluid Reservoir Dam (open) Figure 5: Measuring the free-surface evolution using image processing techniques. Pattern projection Recording the deformation of the pattern Calculating the position of the free surface (a) (b) (c) Figure 6: (a) Projection on the plane, (b) same projection on the surge, (c) resulting free surface height. 4. Numerical Simulation Numerical treatment Algorithm: Semi implicit incompressible Navier-Stokes solver Finite Volume on rectangular staggered grid Level-Set representation of the free surface Turbulence model via turbulent viscosity Parallel computing Model: Shear rate dependent viscosity function: For the Herschel-Bulkley model: μ = τ 0 + | ˙ γ | 1 n | ˙ γ | Surface tension Numerical results 0.01 1.0 Viscosity [Pas] Figure 7: Dam break of viscoplastic material. Snapshot showing the collapse and spreading of a viscoplastic fluid along a horizon- tal plane. 5. Conclusion We developed a framework that is a first stab at modeling rapid gravity-driven mass movements (such as snow avalanches) on the laboratory scale. The objective is to gain insight into the dynamics of complex (nonlinear) fluids in non-steady flows and to propose governing equations that overcome the current lim- itations of flow-dynamics models, which are usually based on the shallow-flow approximation and near-equilibrium regime as- sumption. For that purpose, we work in two complementary di- rections: We built an experimental facility (inclined planes), which can be operated to create fluid avalanches in the laboratory (finite volume of material instantaneously released). Specific image processing techniques have been developed to measure the free-surface evolution and track the front position and velocity. On the short term, additional parameters such as the velocity profile inside the flowing material could be probed, still using image processing techniques. We extend a Navier-Stokes solver primarily developed at the University of Bonn (NaSt3D) to cope with nonlinear rheologies. The front and free-surface boundaries conditions pose serious problems from the numerical point of view. On the short term, we should be able to use this code for simulating avalanches on the lab scale. On the long term, we are thinking about a mix numerical code, which combines both two-dimensional (flow-depth averaged) and three-dimensional capacities within a single tool. References [1]C. Ancey. Powder-snow avalanches: approximation as non- Boussinesq clouds with a Richardson-number-dependent entrainment function. Journal of Geophysical Research, 109(F01005), 2004. [2]C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler. Existence and features of similarity solutions for non- Boussinesq gravity currents. submitted to Physica D, 2006. [3]C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler. Front dynamics of supercritical non-Boussinesq gravity cur- rents. Water Resources Research, 42, W08424, 2006., 42(W08424), 2006. [4] C. Ancey and M. Meunier. Estimating bulk rheological prop- erties of flowing snow avalanches from field data. Journal of Geophysical Research, 109(F01004), 2004. [5]S. Cochard and C. Ancey. Accurate measurements of free- surface in the dam-break problem. In A.H. Cardoso, ed- itor, River Flow 2006 - International Conference on Flu- vial Hydraulics, volume 2, pages 1863–1872, Lisbon, 2006. Balkema. [6]R. Croce, M. Griebel, and M. A. Schweitzer. A Parallel Level- Set Approach for Two-Phase Flow Problems with Surface Tension in Three Space Dimensions. Preprint 157, Sonder- forschungsbereich 611, Universit¨ at Bonn, 2004. submitted. SGR 2006, Annual Meeting of the Swiss Group of Rheology, 20th October, 2006, University Fribourg, Switzerland In Cooperation with:
Transcript of Avalanche simulation - École Polytechnique Fédérale de...
Avalanche simulationM. Rentschler, Ch. Ancey, S. Cochard
Environemental hydraulics laboratory, EPFL, [email protected]
LABORATOIREYDRAULIQUE
NVIRONNEMENTALEEH
Abstract
To tackle the delicate issue of avalanche simulation we are investigating the dynamics of this kind of phenomena on the lab scale, which enables us to make reproducible experiments under well-controledlaboratory conditions. More specifically we focus our attention on the motion of an avalanching mass flowing down an inclined plane (channelized or not), with a significant slope change in its lower part. Velocity(front and free surface) and the flow depth can be accurately measured at any point using image processing techniques. In the meantime, we extend numerical tools (three-dimensional Navier-Stokes solver) tomodel this experiment. The final objective is to understand the dynamics of complex fluids far from equilibrium (no steady regime is achieved) and develop governing equations that are more appropriate to thatpurpose than the classical shallow-water equations.
1. Natural Phenomena
Figure 1: Avalanche in the test field of the SLF in the Vallee dela Sionne(Valais). (Courtesy of SLF)
Very expensive Experiments (Costs of about 60000 SFr)
Not reproducible
Uncertainties on the initial conditions
Large number of involved processed
Few parameters that can be conveniently measured
2. Isolated process: Viscoplastic flow
( a ) Carbopol deposit ( b ) Avalanche deposit
Viscoplastic flow
Avalanche deposits on an inclined terrain (plastic behavior)Avalanche flows like a viscoplastic fluid
Carbopol
Yield-stress τ0
No ThixotropyReproducible and stableEasy to handle: No melting, not poisonous...
Rheological properties of the Carbopol
τ0
ViscosityµShear Stressτ
0
20
40
60
80
100
120
140
160
180
200
10−5 10−4 10−3 0.01 0.1 1 10 1001
10
100
1000
104
105
106
She
arS
tres
sτ[P
a]
Shear-rateγ [1/s]
Vis
cosi
tyµ
[Pa/
s]
Figure 3: Rheometrical measurements for a Carbopol sample.The lines represent the fitted Herschel-Bulkley model.
Herschel-Bulkley model
If |τ | < τ0: γ = 0,
If |τ | > τo: τ = τ0 + K|γ|1n
3. Experimental device
Inclined plane
Figure 4: The inclined plane with Steve Cochard.
Variable inclination
Various geometries
Very short time to open the gate
Measuring the free surface
Camera
Projector
Inclined plan
Fluid
Reservoir
Dam(open)
Figure 5: Measuring the free-surface evolution using imageprocessing techniques.
Pattern projection
Recording the deformation of the pattern
Calculating the position of the free surface
( a ) ( b ) ( c )
Figure 6: (a) Projection on the plane, (b) same projection onthe surge, (c) resulting free surface height.
4. Numerical Simulation
Numerical treatment
Algorithm:
Semi implicit incompressible Navier-Stokes solver
Finite Volume on rectangular staggered grid
Level-Set representation of the free surface
Turbulence model via turbulent viscosity
Parallel computing
Model:
Shear rate dependent viscosity function:For the Herschel-Bulkley model:
µ =τ0 + |γ|
1n
|γ|
Surface tension
Numerical results
0.01 1.0Viscosity [Pa s]
Figure 7: Dam break of viscoplastic material. Snapshot showingthe collapse and spreading of a viscoplastic fluid along a horizon-tal plane.
5. Conclusion
We developed a framework that is a first stab at modeling rapidgravity-driven mass movements (such as snow avalanches) onthe laboratory scale. The objective is to gain insight into thedynamics of complex (nonlinear) fluids in non-steady flows andto propose governing equations that overcome the current lim-itations of flow-dynamics models, which are usually based onthe shallow-flow approximation and near-equilibrium regime as-sumption. For that purpose, we work in two complementary di-rections:
We built an experimental facility (inclined planes), which canbe operated to create fluid avalanches in the laboratory (finitevolume of material instantaneously released). Specific imageprocessing techniques have been developed to measure thefree-surface evolution and track the front position and velocity.On the short term, additional parameters such as the velocityprofile inside the flowing material could be probed, still usingimage processing techniques.
We extend a Navier-Stokes solver primarily developed at theUniversity of Bonn (NaSt3D) to cope with nonlinear rheologies.The front and free-surface boundaries conditions pose seriousproblems from the numerical point of view. On the short term,we should be able to use this code for simulating avalancheson the lab scale. On the long term, we are thinking abouta mix numerical code, which combines both two-dimensional(flow-depth averaged) and three-dimensional capacities withina single tool.
References
[1] C. Ancey. Powder-snow avalanches: approximation as non-Boussinesq clouds with a Richardson-number-dependententrainment function. Journal of Geophysical Research,109(F01005), 2004.
[2] C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler.Existence and features of similarity solutions for non-Boussinesq gravity currents. submitted to Physica D, 2006.
[3] C. Ancey, S. Cochard, S. Wiederseiner, and M. Rentschler.Front dynamics of supercritical non-Boussinesq gravity cur-rents. Water Resources Research, 42, W08424, 2006.,42(W08424), 2006.
[4] C. Ancey and M. Meunier. Estimating bulk rheological prop-erties of flowing snow avalanches from field data. Journal ofGeophysical Research, 109(F01004), 2004.
[5] S. Cochard and C. Ancey. Accurate measurements of free-surface in the dam-break problem. In A.H. Cardoso, ed-itor, River Flow 2006 - International Conference on Flu-vial Hydraulics, volume 2, pages 1863–1872, Lisbon, 2006.Balkema.
[6] R. Croce, M. Griebel, and M. A. Schweitzer. A Parallel Level-Set Approach for Two-Phase Flow Problems with SurfaceTension in Three Space Dimensions. Preprint 157, Sonder-forschungsbereich 611, Universitat Bonn, 2004. submitted.
SGR 2006, Annual Meeting of the Swiss Group of Rheology, 20th October, 2006, University Fribourg, Switzerland In Cooperation with:
