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| Titel |
Mechanics of submerged granular flows driven by gravity |
| VerfasserIn |
Aronne Armanini, Michele Larcher, Elena Nucci, Michael Dumbser |
| Konferenz |
EGU General Assembly 2013
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 15 (2013) |
| Datensatznummer |
250084884
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| Zusammenfassung |
| This work presents a model for gravity driven granular flows saturated with water,
particularly suited for modeling of debris flows.
To describe these natural phenomena a two–phase approach is necessary: the liquid-phase
(the interstitial fluid), which usually is water treated with a Newtonian rheology, and the solid
phase (the granular fluid). Here we will consider only the rheology of a mixture
of a liquid and a granular fluid without cohesion. The rheology of granular fluid
depends of the type of interaction among particles. In this respect, it is possible
to identify two different behavior: the collisional regime, where the contacts are
instantaneous, and the frictional regime with long lasting contacts. The model is based on
the observation that the two regimes are not stratified but coexist in a large part of
the flow depth [2]. The kinetic theory of dense gas is adopted as rheology for the
collisional regime [4], while we propose a new rheological formulation and a new
equation of state for the frictional regime. This rheological formulation boils down
to the Coulombian condition on the static, loose bed and extinguishes gradually
its influence, while approaching the free surface region dominated by collisional
contacts.
In particular, we propose an heuristic rheological model for the frictional regime based on
dimensional considerations of the forces involved, which end up with the introduction of the
Savage numbers as a significant dimensionless group: Is = Ïs(dpËγ)2- pg. Ïs is the
material density of the grains, Ëγ the shear rate, dp the diameter of the particles and
pg the granular pressure. We will then integrate the set of mass, momentum and
energy equations in steady uniform 2D flow [3] and compare these results with the
experimental data [1]. Finally, we will analyze in detail the balance of the total kinetic
energy of the granular flow and the balance of the kinetic energy of the collisional
component. We highlight the mechanism of transfer of energy between the two
regimes.
Bibliography
[1] Armanini, A., Capart, H., Fraccarollo, L. and Larcher, M., 2005 a. Rheological
stratification in experimental free-surface flows of granular-liquid mixtures. J. Fluid Mech.
532 , 269–319.
[2] Armanini, A., Larcher, M., Fraccarollo, L., 2009. Intermittency of rheological regimes
in uniform liquid-granular flows. Phys. Rev. E 79, 051306.
[3] Armanini A., Dumbser M., Nucci E. & Larcher M., 2013, Dynamics of submerged
gravitational granular flows in: Numerical methods for Hyperbolic Equations: Theory and
applications. Editors: E. Vàzquez-Cendòn, A. Hidalgo, P. Garcìa-Navarro and L. Cea; CRC
Press Taylor and Francis Group; pp. 157-163.
[4] Lun, C.K.K., Savage, S.B., Jeffrey, D.J. and Chepurniy N., 1984, Kinetic theories for
granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general
flow field. J. Fluid Mech., 140, 223-256. |
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