scholarly journals Segregation-induced finger formation in granular free-surface flows

2016 ◽  
Vol 809 ◽  
pp. 168-212 ◽  
Author(s):  
J. L. Baker ◽  
C. G. Johnson ◽  
J. M. N. T. Gray
Keyword(s):  
Granular Flows ◽  
Free Surface Flows ◽  
Pyroclastic Flows ◽  
Coarse Grained ◽  
Momentum Balance ◽  
Large Particles ◽  
Averaged Model ◽  
Well Posed ◽  
Dense Granular Flows ◽  
New System

Geophysical granular flows, such as landslides, pyroclastic flows and snow avalanches, consist of particles with varying surface roughnesses or shapes that have a tendency to segregate during flow due to size differences. Such segregation leads to the formation of regions with different frictional properties, which in turn can feed back on the bulk flow. This paper introduces a well-posed depth-averaged model for these segregation-mobility feedback effects. The full segregation equation for dense granular flows is integrated through the avalanche thickness by assuming inversely graded layers with large particles above fines, and a Bagnold shear profile. The resulting large particle transport equation is then coupled to depth-averaged equations for conservation of mass and momentum, with the feedback arising through a basal friction law that is composition dependent, implying greater friction where there are more large particles. The new system of equations includes viscous terms in the momentum balance, which are derived from the $\unicode[STIX]{x1D707}(I)$-rheology for dense granular flows and represent a singular perturbation to previous models. Linear stability calculations of the steady uniform base state demonstrate the significance of these higher-order terms, which ensure that, unlike the inviscid equations, the growth rates remain bounded everywhere. The new system is therefore mathematically well posed. Two-dimensional simulations of bidisperse material propagating down an inclined plane show the development of an unstable large-rich flow front, which subsequently breaks into a series of finger-like structures, each bounded by coarse-grained lateral levees. The key properties of the fingers are independent of the grid resolution and are controlled by the physical viscosity. This process of segregation-induced finger formation is observed in laboratory experiments, and numerical computations are in qualitative agreement.

scholarly journals Segregation of large particles in dense granular flows suggests a granular Saffman effect

2018 ◽  
Vol 3 (7) ◽  
Author(s):  
K. van der Vaart ◽  
M. P. van Schrojenstein Lantman ◽  
T. Weinhart ◽  
S. Luding ◽  
C. Ancey ◽  
...  
Keyword(s):  
Granular Flows ◽  
Large Particles ◽  
Dense Granular Flows

Finite element simulation of complex dense granular flows using a well-posed regularization of the μ(I)-rheology

2019 ◽  
Vol 188 ◽  
pp. 102-113 ◽  
Author(s):  
Linda Gesenhues ◽  
José J. Camata ◽  
Adriano M.A. Côrtes ◽  
Fernando A. Rochinha ◽  
Alvaro L.G.A. Coutinho
Keyword(s):  
Finite Element ◽  
Finite Element Simulation ◽  
Granular Flows ◽  
Element Simulation ◽  
Well Posed ◽  
Dense Granular Flows

scholarly journals Compressibility regularizes the 𝜇(I)-rheology for dense granular flows

2017 ◽  
Vol 830 ◽  
pp. 553-568 ◽  
Author(s):  
J. Heyman ◽  
R. Delannay ◽  
H. Tabuteau ◽  
A. Valance
Keyword(s):  
Friction Coefficient ◽  
Acoustic Waves ◽  
Compressible Flows ◽  
Granular Flows ◽  
Potential Candidate ◽  
Volume Changes ◽  
Ill Posed ◽  
The Stability ◽  
Well Posed ◽  
Dense Granular Flows

The $\unicode[STIX]{x1D707}(I)$-rheology was recently proposed as a potential candidate to model the incompressible flow of frictional grains in the dense inertial regime. However, this rheology was shown to be ill-posed in the mathematical sense for a large range of parameters, notably in the low and large inertial number limits (Barker et al., J. Fluid Mech., vol. 779, 2015, pp. 794–818). In this rapid communication, we extend the stability analysis of Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) to compressible flows. We show that compressibility regularizes the equations, making the problem well-posed for all parameters, with the condition that sufficient dissipation be associated with volume changes. In addition to the usual Coulomb shear friction coefficient $\unicode[STIX]{x1D707}$, we introduce a bulk friction coefficient $\unicode[STIX]{x1D707}_{b}$, associated with volume changes and show that the problem is well-posed if $\unicode[STIX]{x1D707}_{b}>1-7\unicode[STIX]{x1D707}/6$. Moreover, we show that the ill-posed domain defined by Barker et al. (J. Fluid Mech., vol. 779, 2015, pp. 794–818) transforms into a domain where the flow is unstable but remains well-posed when compressibility is taken into account. These results suggest the importance of taking into account dynamic compressibility for the modelling of dense granular flows and open new perspectives to investigate the emission and propagation of acoustic waves inside these flows.

scholarly journals Asymmetric breaking size-segregation waves in dense granular free-surface flows

2016 ◽  
Vol 794 ◽  
pp. 460-505 ◽  
Author(s):  
P. Gajjar ◽  
K. van der Vaart ◽  
A. R. Thornton ◽  
C. G. Johnson ◽  
C. Ancey ◽  
...  
Keyword(s):  
Particle Motion ◽  
Wave Structure ◽  
Free Surface Flows ◽  
Pyroclastic Flows ◽  
Breaking Wave ◽  
Size Segregation ◽  
Small Particles ◽  
Flux Function ◽  
Large Particles ◽  
Over The Top

Debris and pyroclastic flows often have bouldery flow fronts, which act as a natural dam resisting further advance. Counter intuitively, these resistive fronts can lead to enhanced run-out, because they can be shouldered aside to form static levees that self-channelise the flow. At the heart of this behaviour is the inherent process of size segregation, with different sized particles readily separating into distinct vertical layers through a combination of kinetic sieving and squeeze expulsion. The result is an upward coarsening of the size distribution with the largest grains collecting at the top of the flow, where the flow velocity is greatest, allowing them to be preferentially transported to the front. Here, the large grains may be overrun, resegregated towards the surface and recirculated before being shouldered aside into lateral levees. A key element of this recirculation mechanism is the formation of a breaking size-segregation wave, which allows large particles that have been overrun to rise up into the faster moving parts of the flow as small particles are sheared over the top. Observations from experiments and discrete particle simulations in a moving-bed flume indicate that, whilst most large particles recirculate quickly at the front, a few recirculate very slowly through regions of many small particles at the rear. This behaviour is modelled in this paper using asymmetric segregation flux functions. Exact non-diffuse solutions are derived for the steady wave structure using the method of characteristics with a cubic segregation flux. Three different structures emerge, dependent on the degree of asymmetry and the non-convexity of the segregation flux function. In particular, a novel ‘lens-tail’ solution is found for segregation fluxes that have a large amount of non-convexity, with an additional expansion fan and compression wave forming a ‘tail’ upstream of the ‘lens’ region. Analysis of exact solutions for the particle motion shows that the large particle motion through the ‘lens-tail’ is fundamentally different to the classical ‘lens’ solutions. A few large particles starting near the bottom of the breaking wave pass through the ‘tail’, where they travel in a region of many small particles with a very small vertical velocity, and take significantly longer to recirculate.

scholarly journals Self-diffusion scalings in dense granular flows

Soft Matter ◽  
2021 ◽  
Author(s):  
Riccardo Artoni ◽  
Michele Larcher ◽  
James T. Jenkins ◽  
Patrick Richard
Keyword(s):  
Shear Rate ◽  
Solid Fraction ◽  
Granular Flows ◽  
The Self ◽  
Granular Temperature ◽  
Restitution Coefficient ◽  
Self Diffusion ◽  
Diffusivity Tensor ◽  
Dense Granular Flows

The self-diffusivity tensor in homogeneously sheared dense granular flows is anisotropic. We show how its components depend on solid fraction, restitution coefficient, shear rate, and granular temperature.

Shock waves in dense granular flows down a chute

Shock Waves ◽  
2007 ◽  
Vol 17 (5) ◽  
pp. 337-349 ◽  
Author(s):  
Piroz Zamankhan
Keyword(s):  
Shock Waves ◽  
Granular Flows ◽  
Dense Granular Flows

Shear induced diffusion in dense granular flows

2010 ◽  
Author(s):  
Ashish V. Orpe ◽  
Chris H. Rycroft ◽  
Arshad A. Kudrolli ◽  
Joe Goddard ◽  
Pasquale Giovine ◽  
...  
Keyword(s):  
Granular Flows ◽  
Dense Granular Flows
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