Effect of the bottom material capture and the non-Newtonian rheology on the dynamics of turbulent downslope flows. (English. Russian original) Zbl 1347.76005
Fluid Dyn. 51, No. 3, 299-310 (2016); translation from Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 2016, No. 3, 3-15 (2016).
Summary: The paper is devoted to the mathematical modeling of naturally occurring downslope flows, such as snow avalanches, mudflows, and rapid landslides. The medium in motion is modeled as a non-Newtonian fluid, the non-Newtonian fluids of different types corresponding to different-in-nature flows. It is taken into account that the downslope flows capture the slope material and entrain it into the motion. The flow is assumed to be turbulent and the Lushchik-Pavel’ev-Yakubenko three-equation turbulence model is used. It is so generalized that it allows for flow unsteadiness, complicated rheological properties, the presence of a free boundary, and the mass transfer at the lower flow boundary. The effect of the bottom material capture and the nonlinear rheological properties of the medium in motion on the flow dynamics is numerically investigated.
Keywords:
downslope flows; turbulence; non-Newtonian fluids; slope material entrainment; mathematical modelingReferences:
| [1] | Eglit, M. E., Theoretical Approaches to the Calculations of the Snow Avalanche Motion, 60 (1968) |
| [2] | M. E. Eglit and K. S. Demidov, “Mathematical Modeling of Snow Entrainment in Avalanche Motion,” Cold Regions Sci. Technol. 43, 10 (2005). · doi:10.1016/j.coldregions.2005.03.005 |
| [3] | B. Sovilla, P. Burlando, and P. Bartelt, “Field Experiments and Numerical Modeling ofMass Entrainment in Snow Avalanches,” J. Geophys. Res. 111(F03007), 1 (2006). |
| [4] | O. Hungr, S. McDougall, and M. Bovis, Entrainment of Material by Debris Flows, Springer, Berlin (2005). · doi:10.1007/3-540-27129-5_7 |
| [5] | W. H. Herschel and R. Bulkley, “Ü ber die Viskosität und Elastizität von Solen,” Ann. Soc. Testing Mater. 26, 621 (1923). |
| [6] | P. Coussot, Mudflow Rheology and Dynamics, Balklema Publ., Rotterdam (1997). · Zbl 0949.76001 |
| [7] | X. Huang and M. H. Garcia, “AHerschel-BulkleyModel for Mud Flowdown a Slope,” J. FluidMech. 374, 305 (1998). · Zbl 0928.76011 · doi:10.1017/S0022112098002845 |
| [8] | Issler, D.; Hutter, K. (ed.); Kirchner, N. (ed.), Experimental Informations on SnowAvalanches, 109 (2003) · doi:10.1007/978-3-540-36565-5_4 |
| [9] | M. Kern, F. Tiefenbacher, and J. McElwaine, “The Rheology of Snow in Large Chute Flows,” Cold Regions Sci. Technol. 39, 181 (2004). · doi:10.1016/j.coldregions.2004.03.006 |
| [10] | E. Bovet, C. Chiaia, and L. Preziosi, “A New Model for Snow Avalanche Dynamics Based on Non-Newtonian Fluids,” Meccanica 45, 753 (2010). · Zbl 1258.74007 · doi:10.1007/s11012-009-9278-z |
| [11] | N. J. Balmforth, A. S. Burbidge, R. V. Craster, J. Salzig, and A. Shen, “Visco-plastic Models of Isothermal Lava Domes,” J. Fluid Mech. 403, 37 (2000). · Zbl 0957.76003 · doi:10.1017/S0022112099006916 |
| [12] | M. E. Eglit and A. E. Yakubenko, “Numerical Modeling of Slope Flows Entraining BottomMaterial,” Cold Regions Sci. Technol. 108, 139 (2014). · doi:10.1016/j.coldregions.2014.07.002 |
| [13] | Eglit, M. E.; Yakubenko, A. E.; Yakubenko, T. A., Numerical Modeling of an Unsteady Flow of a Nonlinear Viscous Fluid, 218 (2013) |
| [14] | D. Issler and M. Pastor Pérez, “Interplay of Entrainment and Rheology in Snow Avalanches; a Numerical Study,” Annals of Glaciology 52, 143 (2011). · doi:10.3189/172756411797252031 |
| [15] | D. Issler, “Dynamically Consistent Entrainment Laws for Depth-Averaged Avalanche Models,” J. Fluid Mech. 759, 701 (2014). · doi:10.1017/jfm.2014.584 |
| [16] | P. T. Slatter, “Modeling the Turbulent Flow of Non-Newtonian Slurries,” R & D Journal, 12 2, 68 (1996). |
| [17] | R. P. Chhabra and J. F. Richardson, Non-Newtonian Flow and Applied Rheology, Elsevier, Oxford (2008). |
| [18] | M. Rudman and H. M. Blackburn, “Direct Numerical Simulation of Turbulent Non-Newtonian Flow Using a Spectral Element Method,” Apl. Math. Modeling 30, 1229 (2006). · Zbl 1375.76016 · doi:10.1016/j.apm.2006.03.005 |
| [19] | M. Nakamura and T. Sawada, “A k-e Model for Turbulent Analysis of Bingham Plastic Fluid in a Pipe,” Trans. Jap. Soc. Mech. Eng. B 52 479, 2544 (1986). · doi:10.1299/kikaib.52.2544 |
| [20] | V. G. Lushchik, A. A. Pavel’ev, and A. E. Yakubenko, “Three-Parameter Model of Shear Turbulence,” Fluid Dynamics 13 3, 350 (1978). · Zbl 0443.76057 · doi:10.1007/BF01050525 |
| [21] | V. G. Lushchik, A. A. Pavel’ev, and A. E. Yakubenko, “Three-Parameter Model of Turbulence: Heat Transfer Calculations,” Fluid Dynamics 21 2, 200 (1986). · Zbl 0386.76038 · doi:10.1007/BF01050170 |
| [22] | V. G. Lushchik and A. E. Yakubenko, “Comparative Analysis of Turbulence Models for Calculating a Near-Wall Boundary Layer,” Fluid Dynamics 33 1, 36 (1998). · Zbl 0922.76222 · doi:10.1007/BF02698159 |
| [23] | V. G. Lushchik and A. E. Yakubenko, “Friction and Heat Transfer in the Boundary Layer on a Permeable Surface in the Case of Foreign Gas Injection,” Teplofiz. Vys. Temp. 43, 880 (2005). |
| [24] | A. I. Leontiev, V. G. Lushchik, and A. E. Yakubenko, “A Heat-Insulated Permeable Wall with Suction in a Compressible Gas Flow,” Int. J. Heat Mass Transfer 52 (17-18), 4001 (2009). · Zbl 1167.80346 · doi:10.1016/j.ijheatmasstransfer.2008.10.029 |
| [25] | T. E. Lang and J. D. Dent, “ScaleModeling of Snow Avalanche Impact on Structures,” J. Glaciology 26 94, 189 (1980). |
| [26] | M. Naaim, F. Naaim-Bouvet, T. Faug, and A. Bouchet, “Dense Snow AvalancheModeling: Flow, Erosion, Deposition and Obstacle Effects,” Cold Regions Sci. Technol. 39, 193 (2004). · doi:10.1016/j.coldregions.2004.07.001 |
| [27] | E. A. Vedeneeva, “Lava Spreading during Volcanic Eruptions on the Condition of Partial Slip along the Underlying Surface,” Fluid Dynamics 50 2, 203 (2015). · Zbl 1325.76061 · doi:10.1134/S0015462815020040 |
| [28] | J. D. Dent and T. E. Lang, “Modeling of Snow Flow,” J. Glaciology 26 94, 131 (1980). |
| [29] | J. D. Dent and T. E. Lang, “Experiments on the Mechanics of Flowing Snows,” Cold Regions Sci. Technol. 5 3, 253 (1982). · doi:10.1016/0165-232X(82)90018-0 |
| [30] | K. Nishimura and N. Maeno, “Contribution of Viscous Forces to Avalanche Dynamics,” Annals of Glaciology, 13, 202 (1989). |
| [31] | J. D. Dent, K. J. Burrel, D. S. Schmidt, M. Y. Louge, E. E. Adams, and T. G. Jazbutis, “Density, Velocity and Friction Measurements in Dry-Snow Avalanche,” Annals of Glaciology, 26, 247 (1998). |
| [32] | T. Juha-Pekka, R. Huhtanen, and J. Karvinen, “Interaction of Non-Newtonian Fluid Dynamics and Turbulence on the Behavior of Pulp Suspension Flows,” Annual Transactions of the Nordic Rheology Society, 13, 177 (2005). |
| [33] | A. A. Gavrilov and V. Ya. Rudyak, “A Model of AveragedMolecularViscosity for Turbulent Flow of Non-Newtonian Fluids,” J. Siberian Federal Univ. Math. & Phys. 7 1, 46 (2014). · Zbl 1522.76004 |
| [34] | J. Khorshidi, S. Niazi, H. Davari, M. Abyaneh, and A. Mahmoodzadeh, “TurbulentModeling for Non-Newtonian Fluid in an Eccentric Annulus,” Canadian J. Pure Appl. Science, 7, 2425 (2013). |
| [35] | A. E. Yakubenko, “Development of the Three-EquationDifferential Turbulence Model and Investigation of Flows of Liquids, Gases, and Electroconducting Media on its Basis” [in Russian], Moscow State Univ., Dissertation (1991). |
| [36] | K. Hanjalic and B. E. Launder, “Contribution towards a Reynolds-Stress Closure for Low-Reynolds-Number Turbulence,” J. Fluid Mech. 74, 593 (1976). · Zbl 0325.76067 · doi:10.1017/S0022112076001961 |
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