Extended kinetic theory applied to inclined granular flows: role of boundaries

Extended kinetic theory applied to inclined granular flows: role of boundaries We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Granular Matter Springer Journals

Extended kinetic theory applied to inclined granular flows: role of boundaries

Loading next page...
 
/lp/springer_journal/extended-kinetic-theory-applied-to-inclined-granular-flows-role-of-afosWzAEGz
Publisher
Springer Berlin Heidelberg
Copyright
Copyright © 2017 by Springer-Verlag GmbH Germany
Subject
Physics; Soft and Granular Matter, Complex Fluids and Microfluidics; Engineering Fluid Dynamics; Materials Science, general; Geoengineering, Foundations, Hydraulics; Industrial Chemistry/Chemical Engineering; Engineering Thermodynamics, Heat and Mass Transfer
ISSN
1434-5021
eISSN
1434-7636
D.O.I.
10.1007/s10035-017-0738-1
Publisher site
See Article on Publisher Site

Abstract

We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction.

Journal

Granular MatterSpringer Journals

Published: Jul 8, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off