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Influence of Velocity Slip on Turbulent Features of a Drygranular Dense Flow

Published online by Cambridge University Press:  11 August 2015

C. Fang
C. Fang*
Affiliation:
Department of Civil Engineering, National Cheng Kung University, Tainan, Taiwan
*
* Corresponding author ([email protected])
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Abstract

A zero-order turbulence closure model of a dry granular dense flow is proposed, with the boundary considered an energy source and sink of the turbulent kinetic energy of the grains. Muller-Liu entropy principle is carried out to derive the equilibrium closure relations, with their dynamic responses postulated from the experimental calibrations. A gravity-driven flow with incompressible grains down an inclined moving plane is studied to investigate the influence of velocity slip near solid boundary on the turbulent features of the flow. While the calculated mean porosity and velocity correspond to the experimental outcomes, increasing velocity slip on the boundary tends to enhance the turbulent dissipation nearby. The distribution of the turbulent dissipation shows a similarity with that of conventional Newtonian fluids in turbulent boundary layer flows. Boundary as an energy sink is more apparent in the zero-order model.

Keywords

Dry granular dense flowTurbulence closure modelVelocity slip
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 4 , August 2015 , pp. 457 - 465
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2015 

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References

1.Aranson, I. S. and Tsimring, L. S., Granular Patterns, Oxford University Press, Oxford (2009).Google Scholar
2. GDR MiDi, “On Dense Granular Flows,” European Physics Journal E, 14, pp. 341–365 (2004).CrossRefGoogle Scholar
3.Rao, K. K. and Nott, P. R., Introduction to Granular Flows, Cambridge University Press, London (2008).Google Scholar
4.Batchelor, G. K., The Theory of Homogeneous Turbulence, Cambridge University Press, Cambridge (1993).Google Scholar
5.Tsinober, A., An Informal Conceptual Introduction to Turbulence, Springer, Heidelberg (2009).CrossRefGoogle Scholar
6.Hanes, D. M. and Inman, D., “Observations of Rapidly Flowing Granular-Fluid Materials,” Journal of Fluid Mechanics, 150, pp. 357–380 (1985).Google Scholar
7.Hui, K., Haff, P. K. and Ungar, J. E., “Boundary Conditions for High-Shear Grain Flows,” Journal of Fluid Mechanics, 145, pp. 223–233 (1984).CrossRefGoogle Scholar
8.Richman, M. W., “Boundary Conditions Based Upon a Modified Maxwellian Velocity Distribution for Flows if Identical, Smooth, Nearly Elastic Spheres,” Acta Mechanica, 75, pp. 227–240 (1988).Google Scholar
9.Savage, S. B., “Mechanics of Granular Flows,” Continuum Mechanics in Environmental Sciences and Geophysics, Hutter, K., Ed. Springer, Heidelberg, pp. 467–522 (1993).Google Scholar
10.Campbell, C. S., “Stress-Controlled Elastic Granular Shear Flows,” Journal of Fluid Mechanics, 539, pp. 273–297 (2005).CrossRefGoogle Scholar
11.Daniel, R. C., Poloski, A. P. and Saez, A. E., “A Continuum Constitutive Model for Cohesionless Granular Flows,” Chemical Engineering Science, 62, pp. 1343–1350 (2007).Google Scholar
12.Faccanoni, G. and Mangeney, A., “Exact Solution for Granular Flows,” International Journal for Numerical and Analytical Methods in Geomechanics, 37, pp. 1408–1433 (2013).CrossRefGoogle Scholar
13.Fang, C., Wang, Y. and Hutter, K., “Shearing Flows of a Dry Granular Material-Hypoplastic Constitutive Theory and Numerical Simulations,” International Journal for Numerical and Analytical Methods in Geomechanics, 30, pp. 1409–1437 (2006).Google Scholar
14.Fang, C., “Gravity-Driven Dry Granular Slow Flows Down an Inclined Moving Plane: A Comparative Study Between Two Concepts of the Evolution of Porosity,” Rheologica Acta, 48, pp. 971–992 (2009).Google Scholar
15.Fang, C., “Rheological Characteristics of Solid-Fluid Transition in Dry Granular Dense Flows: A Thermodynamically Consistent Constitutive Model with a Pressure-Ratio Order Parameter,” International Journal for Numerical and Analytical Methods in Geomechanics, 34, pp. 881–905 (2010).Google Scholar
16.Jenkins, J. T. and Savage, S. B., “A Theory for the Rapid Flow of Identical, Smooth, Nearly Elastic, Spherical Particles,” Journal of Fluid Mechanics, 130, pp. 187–202 (1983).Google Scholar
17.Johnson, P. C. and Jackson, R., “Frictional-Collisional Constitutive Relations for Granular Materials, with Applications to Plane Shearing,” Journal of Fluid Mechanics, 176, pp. 67–93 (1987).Google Scholar
18.Jop, P., “Hydrodynamic Modeling of Granular Flows in a Modified Couette Cell,” Physics Review E, 77, p. 032301 (2008).Google Scholar
19.Jop, P., Forterre, Y. and Pouliquen, O., “A Constitutive Law for Dense Granular Flows,” Nature, 411, pp. 727–730 (2006).Google Scholar
20.Kirchner, N., “Thermodynamically Consistent Modeling of Abrasive Granular Materials. I: Non-Equilibrium Theory,” Proceeding of Royal Society London A, 458, pp. 2153–2176 (2002).Google Scholar
21.Lun, K. K., Savage, S. B., Jeffery, D. J. and Chepurny, N., “Kinetic Theories for Granular Flow: Inelastic Particles in Couette Flow and Slightly Inelastic Particles in a General Flow Field,” Journal of Fluid Mechanics, 140, pp. 223–256 (1984).Google Scholar
22.Wang, Y. and Hutter, K., “A Constitutive Theory of Fluid-Saturated Granular Materials and its Application in Gravitational Flows,” Rheologica Acta, 38, pp. 214–223 (1999).Google Scholar
23.Ahmadi, G., “A Turbulence Model for Rapid Flows of Granular Materials. Part I. Basic Theory,” Powder Technology, 44, pp. 261–268 (1985).Google Scholar
24.Ahmadi, G. and Shahinpoor, M., “Towards a Turbulent Modeling of Rapid Flow of Granular Materials,” Powder Technology, 35, pp. 241–248 (1983).Google Scholar
25.Luca, I., Fang, C. and Hutter, K., “A Thermodynamic Model of Turbulent Motions in a Granular Material,” Continuum Mechanics and Thermodynamics, 16, pp. 363–390 (2004).Google Scholar
26.Ma, D. and Ahmadi, G., “A Turbulence Model for Rapid Flows of Granular Materials. Part II. Simple Shear Flows,” Powder Technology, 44, pp. 269–279 (1985).CrossRefGoogle Scholar
27.Wilmanski, K., “Porous Media at Finite Strains. The New Model with the Balance Equation of Porosity,” Archives of Mechanics, 48, pp. 591–628 (1996).Google Scholar
28.Fang, C. and Wu, W., “On the Weak Turbulent Motions of an Isothermal Dry Granular Dense Flow with Incompressible Grains: Part I. Equilibrium Turbulence Closure Models,” Acta Geotechnica, 9, pp. 725–738 (2014).Google Scholar
29.Hutter, K., Laloui, L. and Vulliet, L., “Thermodynamically Based Mixture Models of Saturated and Unsaturated Soils,” Mechanics of Cohesive and Frictional Materials, 4, pp. 295–338 (1999).Google Scholar
30.Svendsen, B. and Hutter, K., “On the Thermodynamics of a Mixture of Isotropic Materials with Constraints,” International Journal of Engineering Sciences, 33, pp. 2021–2054 (1999).CrossRefGoogle Scholar
31.Hutter, K. and Johnk, K., Continuum Methods of Physical Modeling, Springer, Heidelberg, Berlin (2004).Google Scholar
32.Muller, I., Thermodynamics, Pitmann, New York (1985).Google Scholar
33.Goldhirsch, I., “Introduction to Granular Temperature,” Powder Technology, 182, pp. 130–136 (2008).Google Scholar
34.Vescovi, D., di Prisco, C. and Berzi, D., “From Solid to Granular Gases: The Steady State for Granular Materials,” International Journal for Numerical and Analytical Methods in Geomechanics, 37, pp. 2937–2951 (2013).Google Scholar
35.Wang, Y. and Hutter, K., “Granular Material Theories Revisited,” Geomorphological Fluid Mechanics, Balmforth, N. J. and Provenzale, A. Eds., Springer, Heidelberg, pp. 79–107 (2001).Google Scholar
36.Kirchner, N. and Teufel, A., “Thermodynamically Consistent Modeling of Abrasive Granular Materials. II: Thermodynamic Equilibrium and Applications to Steady Shear Flows,” Proceeding of Royal Society London A, 458, pp. 3053–3077 (2002).Google Scholar
37.Passman, S. L., Nunziato, J. W. and Walsh, E. K., “A Theory of Multiphase Mixtures,” Rational Thermodynamics, Truesdell, C. Ed., Springer, Heidelberg, pp. 287–325 (1984).Google Scholar
38.Fang, C. and Wu, W., “On the Weak Turbulent Motions of an Isothermal Dry Granular Dense Flow with Incompressible Grains: Part II. Complete Closure Models and Numerical Simulations,” Acta Geotechnica, 9, pp. 739–752 (2014).Google Scholar
39.Fellin, W., “Extension to Barodesy to Model Void Ratio and Stress Dependency of the K0 Value,” Acta Geotecnica, 8, pp. 561–565 (2013).Google Scholar
40.Fuentes, W., Triantaftllidis, T. and Lizcano, A., “Hypoplastic Model for Sands with Loading Surface,” Acta Geotechnica, 7, pp. 177–192 (2012).Google Scholar
41.Wu, W. and Kolymbas, D., “Hypoplasticity Then and Now,” Constitutive Modeling of Granular Materials, Kolymbas, D. Ed., Springer Verlag, Heidelberg, Berlin, pp. 57–105 (2000).Google Scholar
42.Ai, J., Langston, P. A. and Yu, H.-S., “Discrete Element Modeling of Material Non-Coaxiality in Simple Shear Flows,” International Journal for Numerical and Analytical Methods in Geomechanics, 38, pp. 615–635 (2013).Google Scholar
43.Bauer, E. and Herle, I., “Stationary States in Hypoplasticity,” Constitutive Modeling of Granular Materials, Kolymbas, D. Ed., Springer Verlag, Heidel-bergm, Berlin, pp. 167–192 (2000).Google Scholar
44.Herle, I. and Gudehus, G., “Determination of Parameters of a Hypoplastic Constitutive Model From Properties of Grain Assemblies,” Mechanics of Cohesive and Frictional Materials, 4, pp. 461–485 (1999).Google Scholar
45.Marcher, Th., Vermeer, P. A. and Wolffersdorf, P.-A., “Hypoplastic and Elastoplastic Modeling—A Comparison with Test Data,” Constitutive Modeling of Granular Materials, Kolymbas, D. Ed., Springer Verlag, Heidelberg, Berlin, pp. 353–371 (2000).Google Scholar
46.Buscamera, G., “Uniqueness and Existence in Plastic Models for Unsaturated Soils,” Acta Geotechnica, 9, pp. 313–327 (2014).Google Scholar
47.Perng, A. T. H., Capart, H. and Chou, H. T., “Granular Configurations, Motions, and Correlations in Slow Uniform Flows Driven by an Inclined Conveyor Belt,” Granular Matter, 8, pp. 5–17 (2006).CrossRefGoogle Scholar
48.Wendt, J. F., Computational Fluid Dynamics: An Introduction, Springer, Heidelberg, Berlin (2009).Google Scholar
49.Fang, C., “A; κ-ε Turbulent Closure Model of an Isothermal Dry Granular Dense Matter, Part I: Equilibrium Closure Relations,” Acta Mechanica (in review) (2015).Google Scholar
50.Fang, C., “A κ-ε Turbulent Closure Model of an Isothermal Dry Granular Dense Matter, Part II: Closure Model and Numerical Simulations,” Acta Mechanica (in review) (2015).Google Scholar