Analysis of stability of a thin layer of granular material moving on an inclined plane

1998 ◽  
Vol 39 (6) ◽  
pp. 918-921
Author(s):  
Yu. A. Berezin ◽  
L. A. Spodareva
Keyword(s):  
Granular Material ◽  
Thin Layer ◽  
Inclined Plane ◽  
Analysis Of Stability

Improved two-equation model for thin layer fluid flowing down an inclined plane problem

2007 ◽  
Vol 19 (9) ◽  
pp. 098106 ◽  
Author(s):  
H. Ait Abderrahmane ◽  
G. H. Vatistas
Keyword(s):  
Thin Layer ◽  
Plane Problem ◽  
Equation Model ◽  
Inclined Plane

scholarly journals Granular jets and hydraulic jumps on an inclined plane

2011 ◽  
Vol 675 ◽  
pp. 87-116 ◽  
Author(s):  
C. G. JOHNSON ◽  
J. M. N. T. GRAY
Keyword(s):  
Granular Material ◽  
Numerical Solutions ◽  
Slope Angle ◽  
Three Dimensional ◽  
Breaking Wave ◽  
Hydraulic Jumps ◽  
Inclined Plane ◽  
Steady Regime ◽  
Diverse Range ◽  
The Impact

A jet of granular material impinging on an inclined plane produces a diverse range of flows, from steady hydraulic jumps to periodic avalanches, self-channelised flows and pile collapse behaviour. We describe the various flow regimes and study in detail a steady-state flow, in which the jet generates a closed teardrop-shaped hydraulic jump on the plane, enclosing a region of fast-moving radial flow. On shallower slopes, a second steady regime exists in which the shock is not teardrop-shaped, but exhibits a more complex ‘blunted’ shape with a steadily breaking wave. We explain these regimes by consideration of the supercritical or subcritical nature of the flow surrounding the shock. A model is developed in which the impact of the jet on the inclined plane is treated as an inviscid flow, which is then coupled to a depth-integrated model for the resulting thin granular avalanche on the inclined plane. Numerical simulations produce a flow regime diagram strikingly similar to that obtained in experiments, with the model correctly reproducing the regimes and their dependence on the jet velocity and slope angle. The size and shape of the steady experimental shocks and the location of sub- and supercritical flow regions are also both accurately predicted. We find that the physics underlying the rapid flow inside the shock is dominated by depth-averaged mass and momentum transport, with granular friction, pressure gradients and three-dimensional aspects of the flow having comparatively little effect. Further downstream, the flow is governed by a friction–gravity balance, and some flow features, such as a persistent indentation in the free surface, are not reproduced in the numerical solutions. On planes inclined at a shallow angle, the effect of stationary granular material becomes important in the flow evolution, and oscillatory and more general time-dependent flows are observed. The hysteretic transition between static and dynamic friction leads to two phenomena observed in the flows: unsteady avalanching behaviour, and the feedback from static grains on the flowing region, leading to levéed, self-channelised flows.

An ultrastructural study of postmeiotic development in the megasporocarp of Azolla microphylla

1986 ◽  
Vol 64 (4) ◽  
pp. 822-833 ◽  
Author(s):  
Y. R. Herd ◽  
E. G. Cutter ◽  
I. Watanabe
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Granular Material ◽  
Thin Layer ◽  
Middle Region ◽  
Azolla Microphylla ◽  
Transmission Electron ◽  
Storage Products ◽  
Functional Megaspore ◽  
And Storage

The development of megasporocarps of Azolla microphylla, after the retention of a single functional megaspore within the megasporangium, was studied by light and transmission electron microscopy, using material grown under controlled conditions. The young megaspore contained a thin layer of cytoplasm with various organelles and was bounded by a thin exine. It was surrounded by a dense periplasmodial tapetum, which consisted of a peripheral vacuolate region, containing degenerated megaspores, a middle region containing nuclei and large organelles such as amyloplasts and mitochondria, and an inner zone, invaginated round the spore, comprising microtubules, ribosomes, and coated vesicles. At a later stage the exine increased in thickness, and greater vacuolation occurred at the periphery of the periplasmodium. The endoperine was formed by deposition of granular material between the exine and the periplasmodium, and further granular material deposited in small vacuoles gave rise to the exoperine. The floats were formed from three (tapetal) membrane-bounded chambers, in which granular material gradually became organised to form the pseudocells. Characteristic exoperinal filaments were formed in channels in the periplasmodium, which was eventually completely used up in the formation of floats, collar, and megaspore wall, in which sporopollenin was probably present. The megaspore itself became engorged with cytoplasm and storage products such as lipid and starch. Cells of Anabaena with relatively thick walls were present between the megasporangial wall and the indusium.

scholarly journals A two-phase two-layer model for fluidized granular flows with dilatancy effects

2016 ◽  
Vol 801 ◽  
pp. 166-221 ◽  
Author(s):  
François Bouchut ◽  
Enrique D. Fernández-Nieto ◽  
Anne Mangeney ◽  
Gladys Narbona-Reina
Keyword(s):  
Granular Material ◽  
Thin Layer ◽  
Pore Pressure ◽  
Friction Force ◽  
Excess Pore Pressure ◽  
Layer Model ◽  
Two Phase ◽  
Two Layer Model ◽  
Two Phases ◽  
Averaged Model

We propose a two-phase two-thin-layer model for fluidized debris flows that takes into account dilatancy effects, based on the closure relation proposed by Roux & Radjai (Physics of Dry Granular Media, 1998, Springer, pp. 229–236). This relation implies that the occurrence of dilation or contraction of the granular material depends on whether the solid volume fraction is respectively higher or lower than a critical value. When dilation occurs, the fluid is sucked into the granular material, the pore pressure decreases and the friction force on the granular phase increases. On the contrary, in the case of contraction, the fluid is expelled from the mixture, the pore pressure increases and the friction force diminishes. To account for this transfer of fluid into and out of the mixture, a two-layer model is proposed with a fluid layer on top of the two-phase mixture layer. Mass and momentum conservation are satisfied for the two phases, and mass and momentum are transferred between the two layers. A thin-layer approximation is used to derive average equations, with accurate asymptotic expansions. Special attention is paid to the drag friction terms that are responsible for the transfer of momentum between the two phases and for the appearance of an excess pore pressure with respect to the hydrostatic pressure. For an appropriate form of dilatancy law we obtain a depth-averaged model with a dissipative energy balance in accordance with the corresponding three-dimensional initial system.

The motion of a finite mass of granular material down a rough incline

1989 ◽  
Vol 199 ◽  
pp. 177-215 ◽  
Author(s):  
S. B. Savage ◽  
K. Hutter
Keyword(s):  
Granular Material ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Similarity Solutions ◽  
The Other ◽  
Continuum Approximation ◽  
Finite Difference Schemes ◽  
Finite Mass ◽  
Inclined Plane ◽  
Numerical Predictions

Rock, snow and ice masses are often dislodged on steep slopes of mountainous regions. The masses, which typically are in the form of innumerable discrete blocks or granules, initially accelerate down the slope until the angle of inclination of the bed approaches the horizontal and bed friction eventually brings them to rest. The present paper describes an initial investigation which considers the idealized problem of a finite mass of material released from rest on a rough inclined plane. The granular mass is treated as a frictional Coulomb-like continuum with a Coulomb-like basal friction law. Depth-averaged equations of motion are derived; they bear a superficial resemblance to the nonlinear shallow-water wave equations. Two similarity solutions are found for the motion. They both are of surprisingly simple analytical form and show a rather unanticipated behaviour. One has the form of a pile of granular material in the shape of a parabolic cap and the other has the form of anM-wave with vertical faces at the leading and trailing edges. The linear stability of the similarity solutions is studied. A restricted stability analysis, in which the spread is left unperturbed shows them to be stable, suggesting that mathematically both are possible asymptotic wave forms. Two numerical finite-difference schemes, one of Lagrangian, the other of Eulerian type, are presented. While the Eulerian technique is able to reproduce theM-wave similarity solution, it appears to give spurious results for more general initial conditions and the Lagrangian technique is best suited for the present problem. The numerical predictions are compared with laboratory experiments of Huber (1980) involving the motion of gravel released from rest on a rough inclined plane. Although in these experiments the continuum approximation breaks down at large times when the gravel layer is only a few particle diameters thick, the general features of the development of the gravel mass are well predicted by the numerical solutions.

Experimental study of collisional granular flows down an inclined plane

1999 ◽  
Vol 400 ◽  
pp. 199-227 ◽  
Author(s):  
EMMANUEL AZANZA ◽  
FRANÇOIS CHEVOIR ◽  
PASCAL MOUCHERONT
Keyword(s):  
Experimental Study ◽  
Kinetic Theory ◽  
Granular Material ◽  
Solid Fraction ◽  
Particle Flux ◽  
Inclined Plane ◽  
Mean Velocity ◽  
Hydrodynamic Description ◽  
Rough Plane ◽  
Complete Measurement

The collisional flow of a slightly inelastic granular material down a rough inclined plane is usually described by kinetic theories. We present an experimental study aimed at analysing the assumptions and the quantitative predictions of such theories. A two-dimensional channel coupled to a model granular material and image analysis allow detailed and complete measurement of the kinematics and structure of the flows. We determine the range of inclination and particle flux for which the flow is stationary and uniform. The characteristic profiles of solid fraction, mean velocity and granular temperature are systematically measured. Both the true collisional and the dilute kinetic regimes are examined. We show that a quasi-hydrodynamic description of these regimes seems relevant, and that the pressure and the viscosity terms are in good qualitative agreement with the prediction of the kinetic theory. The profiles are well described by the kinetic theory near the top of the flow, at low solid fraction. Conversely there are large discrepancies near the rough plane, where the material is structured in layers.

Sign in / Sign up

Export Citation Format

Share Document