High-speed granular chute flows

Geophysical granular flows, such as snow avalanches and debris flows, represent a great hazard to man and infrastructures. These natural phenomena are characterized by the rapid flow of a granular solid phase, embedded in an ambient fluid. Since such events occur with little warning, in addition to investigating the triggering conditions, it is of crucial interest to predict their propagation and run-out distances. The main purpose of the present research is to better understand the flow dynamics of dry granular flows, in the presence of no-slip bottom boundary conditions, and predict their propagation by using a depth-averaged approach. In this case, a stratification of different flow regimes, such as quasi-static and dense collisional, occurs and makes the utilization of the classical single layer depth-averaged models insufficient, because of important uncertainties about the velocity and shear stress distributions along the flow depth. In the first part of the present work, an experimental-numerical study on dam-break flows of dry granular material is reported. It has been found that a modification to the formula, proposed in the Savage-Hutter model for calculating the earth-pressure coefficient, leads to an improved agreement with experimental data, in presence of no-slip bottom conditions. In the second part, an experimental study on steady state velocity profiles of dry granular flows is reported. The granular material, used in this experimental research, was Ottawa sand (ASTM C-778 20/30). The velocity profiles at the side walls and free surfaces have been obtained, through granular PIV techniques. The measurements are in accordance with other experimental works on different granular materials and suggest the occurrence of a rheological stratification along the flow depth, in case of no-slip bottom condition. In order to better describe such a complex flow dynamics, a two-layer depth-averaged model has been proposed. The dynamics of the two layers, ideally corresponding to dense-collisional and quasi-static regimes, have been considered independently. As well, mass exchanges between the layers have calculated through a physically based closure equation. The well-known mathematical issue of the hyperbolicity loss in two-layer models has been carefully addressed. In order to overcome it, a local modification of source terms of the original mathematical model has been proposed. Such a treatment consists of introducing an extra resistance at the interface, if necessary, to avoid the hyperbolicity loss. This approach has been found to be robust and yields reasonable results, as long as the asymptotic steady state solution and boundary conditions fulfil the hyperbolicity requirements of the original model. Through comparisons with experimental data, the two-layer approach turns out to be very promising to describe the complex flow dynamics in case of no-slip bottom boundary conditions, although a more detailed description of the basal shear stress seems to be required. In the third part of the present dissertation, the same two-layer approach has been used in order to rewrite the mathematical model in a curvilinear coordinates system, attached to the interface between the two layers. The model equations have been obtained, by using the same approach proposed in Tai and Kuo (2008). In the model derivation, the physically negligible quantities are identified in a more rational way than the previous model, by means of a scaling approximation.

In a recent article (Forterre & Pouliquen 2001), we have reported a new instability observed in rapid granular flows down inclined planes that leads to the spontaneous formation of longitudinal vortices. From the experimental observations, we have proposed an instability mechanism based on the coupling between the flow and the granular temperature in rapid granular flows. In order to investigate the relevance of the proposed mechanism, we perform in the present paper a three-dimensional linear stability analysis of steady uniform flows down inclined planes using the kinetic theory of granular flows. We show that in a wide range of parameters, steady uniform flows are unstable under transverse perturbations. The structure of the unstable modes is in qualitative agreement with the experimental observations. This theoretical analysis shows that the kinetic theory is able to capture the formation of longitudinal vortices and validates the instability mechanism.

Granular materials are characterized by large collections of discrete particles, where the particle-particle interactions are significantly more important than the particle-fluid interactions. The current kinetic theory captures fairly accurately the granular flow behavior in the dilute case, when only binary interactions are significant, but is not accurate at all in the dense flow regime, where multi-particle interactions and contacts must be modeled. To improve the kinetic theory results for granular flows in the dense flow regime, we propose a Modified Kinetic Theory (MKT) model that utilizes the contact duration or cutoff time to account for the complex particle-particle interactions in the dense regime. The contact duration model, also called TC model, was originally proposed by Luding and McNamara [“How to handle the inelastic collapse of a dissipative hard-sphere gas with the TC model,” Granular Matter 1, 113 (1998)] to solve the inelastic collapse issue existing in the inelastic hard sphere model. This model defines a cutoff time tc such that dissipation is not counted if the time between two consecutive contacts is less than tc. As shown in their study, the use of a cutoff time tc can also reduce the dissipation during multi-particle contacts. In this paper we relate the TC model with the Discrete Element Method (DEM) by choosing the cutoff time tc to be the duration of contact calculated from the linear-spring-dashpot soft-sphere model of the DEM. We examine two types of granular flows, simple shear flow and the plane shear flow, and compare the results of the classical kinetic theory model, the present MKT model, and the DEM model. We show that the MKT model entails a significant improvement over the kinetic theory model for simple shear flows at inertial regimes. With the MKT model the calculations are close to the DEM results at solid fractions as high as 0.57. Even for the plane shear flows, where shear rate and solid fraction are inhomogeneous, the results of the MKT model agree very well with the DEM results.

Three-dimensional physics-based cellular automata model for granular shear flow

Über Den Böschungswinkel Von Schutthalden

Many contributions on the modelling of granular flow and the solving of such models numerically restrict themselves either to fast, dilute or to dense, quasi‐static granular flow. In many engineering applications both regimes appear at the same time in different parts of the simulations or consecutively at different stages of flow. We numerically investigate a continuum model for granular flow, which covers the regime of fast dilute flow as well as slow dense flow down to vanishing velocity. Our model is at small and intermediate densities equivalent to the model used by Bocquet et al.. [1], An inherent instability in this model for vanishing granular temperature and vanishing velocities is removed by a cross over from a kinetic pressure to an athermal yield pressure at densities close to random close packing. Also the model for the viscosity is modified such that it diverges for small granular temperatures analogous to the diverging viscosities of liquids close to the glass transition. The presented model is a simplified version of a model of Savage [2], which nevertheless recovers many aspects of dense granular flow. We solve the system of the strongly nonlinear singular hydrodynamic equations with the help of a newly developed nonlinear predictor corrector algorithm together and a finite volume space discretisation. To validate our numerical approach we solve a Couette problem to demonstrate the existence of shear bands and simulate the formation of sandpiles with angle of repose consistent with the analytically estimated internal friction angle of the model.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation V. Kumaran; The hard‐particle model for a dense granular flow down an inclined plane. AIP Conference Proceedings 5 May 2010; 1227 (1): 58–71. https://doi.org/10.1063/1.3435421 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

Formation and movement of multiple fire whirls

To model submarine flows of granular materials we propose an extension of the drift-flux approach. The extended model is able to represent dilute suspensions as well as dense granular flows. The dense granwular flow is modelled as a Herschel–Bulkley fluid, with a yield stress that depends on the dispersed phase pressure. Qualitative numerical experiments show that the model is able to correctly reproduce the stability of submerged sand heaps with different internal angles of friction and initial slopes. When initially starting with heaps with an angle smaller than the internal angle of friction, the heaps are stable. When starting with heaps with angles larger than the internal angle of friction, a flow of solid material is initiated. The flow later stops when the bed is at an angle smaller than the internal angle of friction.

A continuum description of granular flows would be of considerable help in predicting natural geophysical hazards or in designing industrial processes. However, the constitutive equations for dry granular flows, which govern how the material moves under shear, are still a matter of debate. One difficulty is that grains can behave like a solid (in a sand pile), a liquid (when poured from a silo) or a gas (when strongly agitated). For the two extreme regimes, constitutive equations have been proposed based on kinetic theory for collisional rapid flows, and soil mechanics for slow plastic flows. However, the intermediate dense regime, where the granular material flows like a liquid, still lacks a unified view and has motivated many studies over the past decade. The main characteristics of granular liquids are: a yield criterion (a critical shear stress below which flow is not possible) and a complex dependence on shear rate when flowing. In this sense, granular matter shares similarities with classical visco-plastic fluids such as Bingham fluids. Here we propose a new constitutive relation for dense granular flows, inspired by this analogy and recent numerical and experimental work. We then test our three-dimensional (3D) model through experiments on granular flows on a pile between rough sidewalls, in which a complex 3D flow pattern develops. We show that, without any fitting parameter, the model gives quantitative predictions for the flow shape and velocity profiles. Our results support the idea that a simple visco-plastic approach can quantitatively capture granular flow properties, and could serve as a basic tool for modelling more complex flows in geophysical or industrial applications.

A scalable parallel computing SPH framework for predictions of geophysical granular flows

Geophysical granular flows, like avalanches and debris flows, are hazardous phenomena for infrastructures and human activities. The complex dynamics of granular systems, involved in these phenomena, poses important challenges to their reliable mathematical modelling. In this context, laboratory investigations on granular flows and non-invasive optical measuring methods are irreplaceable tools for getting a deeper insight into the granular dynamics, as they provide useful information for model calibration and validation. Frictional and collisional momentum flux exchanges coexist in dense granular flows. These resistance mechanisms and their complex interplay with the boundary conditions generate non-negligible fluxes of translational and fluctuation energies along the flow domain, which also influence the kinematics of the free surface. In this work we study steady granular flows in a chute geometry over a fixed bed, specifically focusing on the spatial fluctuations of the free surface. Several tests have been carried out by systematically varying the mass flow rate, the chute inclination and the basal roughness. The experimental apparatus, consisting of a narrow Plexiglas flume, is equipped with a load cell to measure the mass flow rate and a high-speed camera to get non-invasive optical measurements of the free surface fluctuations. A harmonic analysis, employing the Welch method, is performed on a time-series signal obtained from suitably binarized digital images of the free surface fluctuations, recorded at a sampling frequency of 1 kHz. Subsequently, the power spectral densities and the power content of different frequency intervals are analysed. Meaningful correlations are observed between these power components and other relevant measurements, such as the mass flow rates and the flow depths. These preliminary results may be useful for a better understanding of the momentum exchange mechanisms in granular flows and the related fluctuation energy fluxes.

Laboratory measurements of impact forces of supercritical granular flow against mast-like obstacles

Digital image analysis (DIA) groups the post-processing methods that study the kinematics recorded by a digital camera. The DIA may be compromised by the flow constraints that could lead to an arbitrary definition of the region of interest and arbitrary selection of the representative sequence of frames. This paper presents a space–time technique that is able to synthesise a sequence of frames, abstract the flow features and identify the representative domain in space and time. The space–time technique is implemented in the study of free-surface dry sand flows down an inclined plane in a geotechnical centrifuge. The effect of orientation of the inclined plane in a centrifugal acceleration field is investigated. This implementation enables a standardised study of granular flows, delimiting the particle image velocimetry analysis to a representative domain in the flow sequence. The resultant space–time representation successfully identifies the effective flow width, and allows the representation of transient flow processes such as the flow-front evolution and the initiation of deposition on the inclined plane. Furthermore, it is found that the orientation of the sand flows in the centrifugal acceleration field may contribute to the occurrence of material deposition at slope angles higher than the material friction angle.

This study investigated the display station physical adjustments preferred by a sample of visual display terminal (VDT) operators preselected to span the 5th, 50th, and 95th percentiles in physical stature with respect to United States or Japanese anthropometric surveys. Thirty-seven operators were taken individually through a step-by-step sequence to determine their preferred adjustments of seat height, keyboard height and slope angle, and CRT height and tilt angle. Each operator then performed a brief transcription task. Measurements corresponding to the final preferred height and angle adjustments do not agree with some currently evolving German ergonomic display station requirements. In addition, intermeasure correlations strongly suggest that “flat” (low slope angle) keyboards are inappropriate for operators who select low seat heights and are short in stature.