Bumpy Base Research Articles

Granular Segregation in Gravity-Driven, Dense, Steady, Fluid–Particle Flows over Erodible Beds and Rigid, Bumpy Bases

Kinetic theory is used to propose and solve boundary value problems for fully developed, steady, dense gravity-driven flows of mixtures composed of identical inelastic spheres and water over both inclined erodible beds and rigid, bumpy bases confined by vertical sidewalls. We solve the boundary value problems assuming values of the mass density and of the size of the spheres typical of natural materials and show the numerical solutions for the profiles of the mean velocities of the particles and fluid, the intensity of the particle velocity fluctuations, and the granular concentration. In addition, we indicate how the features of the grain velocity fluctuations profile would influence segregation in three situations when the particle phase consists of two sizes of spheres: (1) the spheres are of the same material, and only gradients of temperature influence their segregation; (2) the mass densities of the material of the spheres are such that only gravity influences segregation; and (3) the mass densities are such that the coefficients of the temperature gradients and gravity segregation mechanisms are equal. For spheres of the same material, over a rigid bumpy base, the concentration of larger spheres increases from zero at the bed to the maximum value at the top of the flow; while over an erodible bed, this concentration has its maximum value at both the bed and the top of the flow.

Analytical solutions for dense, inclined, granular flow over a rigid, bumpy base

We first phrase a boundary-value problem for a dense, steady, fully-developed, gravitational flow of identical inelastic spheres over in inclined bumpy base in the absence of sidewalls. We then obtain approximate analytical solutions for the profiles of the solid volume fraction, the strength of the velocity fluctuations, and the mean velocity of the flow. We compare these with those obtained in numerical solutions of the exact equations.

PCA-Based on Feature Extraction and Compressed Sensing for Dimensionality Reduction

Compressive sensing reduces the number of samples required to achieve acceptable reconstruction for medical diagnostics, therefore this research will implement dimensional reduction algorithms through compressed sensing for electrocardiogram signals (EKG). dimensional reduction is performed based on the fact that ECG signals can be reconstructed with linear combination coefficients with a bumpy base of small measurements with high accuracy. This study will use PCA for feature extraction on ECG signals. The data used are the ECG patient records on the website page www.physionet.org as many as 1200 with each attribute as many as 256 attributes. The total data dimension used is 1200x256, which means the data has 1200 rows and has as many as 256 columns. To show the accuracy of the dimensional reduction result, so it is performed classification on data using KNN and Naive Bayes. The classification results show that KKN can classify well with 84,02% accuracy rate and the Naive Bayes accuracy is 65,78%. for 100 dimensions The conclusion is those dimensional reductions for ECG data that have large dimensions, it still able to provide valid information like it uses the original data. Principle Component Analysis is a good method for reducing data dimensions by selecting certain features, so the dimensions of the data become smaller but still able to provide good accuracy to the reader.

Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology.

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with planar slide walls and a bumpy base, using discrete element method simulations. For low particle-sidewall friction coefficients, the flowing particles are disordered, however, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cross section of the channel, with the highest ordering near the sidewalls. The flow transition significantly affects the local rheology-the effective friction coefficient is lower, and the packing fraction is higher, in the ordered state compared to the disordered state. A simple model, incorporating the extent of local ordering, is shown to describe the rheology of the system.

Effect of geometric base roughness on size segregation

The geometric roughness at boundaries has a profound impact on the dynamics of granular flows. For a bumpy base made of fixed particles, two major factors have been separately studied in the literature, namely, the size and spatial distribution of base particles. A recent work (Jing et al. 2016) has proposed a roughness indicator Ra , which combines both factors for any arbitrary bumpy base comprising equally-sized spheres. It is shown in mono-disperse flows that as Ra increases, a transition occurs from slip (Ra > 0.62) conditions. This work focuses on such a phase transition in bi-disperse flows, in which Ra can be a function of time. As size segregation takes place, large particles migrate away from the bottom, leading to a variation of size ratio between flow- and base-particles. As a result, base roughness Ra evolves with the progress of segregation. Consistent with the slip/non-slip transition in mono-disperse flows, basal sliding arises at low values of Ra and the development of segregation might be affected; when Ra increases to a certain level (Ra > 0.62), non-slip condition is respected. This work extends the validity of Ra to bi-disperse flows, which can be used to understand the geometric boundary effect during segregation.

Characterization of base roughness for granular chute flows

Base roughness plays an important role in the dynamics of granular flows but is still poorly understood due to the difficulty of its quantification. For a bumpy base made of spheres, at least two factors should be considered in order to characterize its geometric roughness, namely, the size ratio of flow to base particles and the packing arrangement of base particles. In this paper, we propose an alternative definition of base roughness, R_{a}, as a function of both the size ratio and the distribution of base particles. This definition is generalized for random and regular packings of multilayered spheres. The range of possible values of R_{a} is presented, and optimal arrangements for maximizing base roughness are studied. Our definition is applied to granular chute flows in both two- and three-dimensional configurations, and is shown to successfully predict whether slip occurs at the base. A transition is observed from slip to nonslip conditions as R_{a} increases. Critical values of R_{a} are identified for the construction of a nonslip base at various angles of inclination.

Transport Properties and Segregation Phenomena in Vibrating Granular Beds

Granular materials are common in daily life and in many industrial processes. Both fundamental research and industrial application studies are crucial for understanding the transport properties and segregation mechanisms of vibrating granular beds. One major related research topic is granular materials subjected to external vibration; such granular materials exhibit complex movement and Brazil nut segregation. Understanding the transport properties and the rising of an intruder immersed in granular materials is a challenge in granular flow research. This paper presents a review of transport properties and segregation phenomena in a vibrating granular bed, and discusses the relationship between transport properties and granular segregation. Furthermore, how the vibration conditions, liquid bridge force, bed height, surface roughness of granular materials, and a bumpy base of granular beds affect the transport properties, convection, and granular segregation are reported. The results indicate that the transport properties and segregation behavior are significantly influenced by the addition of small amounts of liquids and by the surface roughness and a bumpy base. Diffusive and convective motions are weakened as the base roughness increases, leading to a weaker Brazil nut effect.

Multisized immersed granular materials and bumpy base on the Brazil nut effect in a three-dimensional vertically vibrating granular bed

In this study, the Brazil nut segregation problem was experimentally investigated in a 3D vertically vibrating granular bed. A high-speed camera was used to record the rise time of larger particles (i.e., intruders). The results showed that the rise time decreased with an increase in the size ratio of monosized immersed granular materials. The percolation effect is the dominant mechanism that influences the Brazil nut segregation behavior of monosized immersed granular materials. The percolation effect is stronger when the size ratio is higher, leading to a stronger Brazil nut effect. In addition, the results indicated that the rise times of the intruder are shorter with multisized immersed granular materials than those with monosized immersed granular materials. The rise velocity does not increase monotonically with an increase in the filling bed height. In addition, the base roughness significantly influences granular segregation. The Brazil nut effect is mitigated, resulting in longer rise times with the bumpy base.

Investigation of the effect of a bumpy base on granular segregation and transport properties under vertical vibration

This study experimentally investigates the effect of a bumpy base on the Brazil-nut phenomenon in a vertically vibrated granular bed. The rise dynamics of an intruder is determined by the particle tracking method. The results indicate that the rise time increases with an increase in the base roughness, and the variation of the rise time with different base factors is more pronounced with smaller vibration acceleration and higher vibration frequency. A theoretical model is employed to measure the penetration length of the intruder and the drag force between the intruder and the immersed beads. The penetration length is reduced and the drag force is enhanced with surface roughness of the base. Additionally, the transport properties of the vibrated glass beads are also measured and discussed. With greater base roughness, the strength of the diffusive and convective motion is reduced leading to a weaker Brazil-nut effect.

Shallow granular flows down flat frictional channels: Steady flows and longitudinal vortices

Granular flows down inclined channels with smooth boundaries are common in nature and industry. Nevertheless, flat boundaries have been much less investigated than bumpy ones, which are used by most experimental and numerical studies to avoid sliding effects. Using numerical simulations of each grain and of the side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base can be seen as flows over an effective bumpy base made of the basal rolling layer, giving Bagnold-type profiles in the overburden. We have tested a simple viscoplastic rheological model [Nature (London) 441, 727 (2006)] in average form. The transition between the unidirectional and the convective flows is then clearly apparent as a discontinuity in the constitutive relation.

High-speed granular chute flows

AbstractThis paper reports experimental findings on the flow of sand down a steep chute. Nearly all granular flow models have a maximum value for the friction and therefore predict that flows on steep slopes will accelerate at a constant rate until the interaction with the ambient fluid becomes important. This prediction has not been tested by previous work, which has focused on relatively low slope angles where steady, fully developed flows occur after short distances. We test this by investigating flows over a much greater range of slope angles (30–50${}^{\ensuremath{\circ} } $) and flow depths (4–130 particle diameters). We examine flows with two basal conditions, one flat and frictional, the other bumpy. The latter imposes a no-slip condition for slow, deep flows, but permits some degree of slip for high flow velocities. The data suggests that friction can be much larger than theories such as the $\ensuremath{\mu} (I)$ rheology proposed by Jop, Forterre & Pouliquen (Nature, vol. 441, 2006) suggest and that there may be constant velocity states above the angle of vanishing ${h}_{\mathit{stop}} $. Although these flows do not vary in time, all but the flows on the bumpy base at low inclinations accelerate down the slope. A recirculation mechanism sustains flows with a maximum mass flux of $20~\mathrm{kg} ~{\mathrm{s} }^{\ensuremath{-} 1} $, allowing observations to be made at multiple points for each flow for an indefinite period. Flows with Froude number in the range 0.1–25 and bulk inertial number 0.1–2.7 were observed in the dense regime, with surface velocities in the range 0.2–5.6 $\mathrm{m} ~{\mathrm{s} }^{\ensuremath{-} 1} $. Previous studies have focused on $I\lessapprox 0. 5$. We show that a numerical implementation of the $\ensuremath{\mu} (I)$ rheology does not fully capture the accelerating dynamics or the transverse velocity profile on the bumpy base. We also observe the transverse separation of the flow into a dense core flanked by dilute regions and the formation of longitudinal vortices.

Kinetic theory applied to inclined flows

We apply the continuum equations of a kinetic theory to predict the features of uniform, steady, inclined flows of identical, frictional, inelastic spheres over a rigid, bumpy base between vertical, frictional side walls. Numerical solutions of these equations over a range of mass flow rates exhibit features seen in physical experiments and numerical solutions in the absence of side walls. For the densest flows, we employ a phenomenological extension of kinetic theory that involves a length scale associated with particle correlations. When a dense flow is thick enough, an algebraic balance between the production and dissipation of fluctuation energy reproduces the relation between mass flow rate and mass hold-up obtained when solving the boundary-value problem of the extended theory.

Density segregation in vibrated granular beds with bumpy surfaces

AbstractSegregation of granular materials by virtue of density or size is a commonly encountered phenomenon in nature. Despite its widespread interest among many researchers in recent years, a complete and unified understanding of granular segregation remains elusive to date. Using molecular dynamics simulations, we report a novel technique of inducing density segregation in a binary mixture of granular materials subjected to vibrations by the use of a bumpy vibrating base. Density segregation in the vertical directions may be induced by oscillating the bumpy base composed of discrete solid particles vertically or horizontally. In both cases, lighter particles tended to rise to the top of the granular bed and form a layer above the heavier particles. We suggest that differences in granular temperature profiles arising from the two different modes of vibrations may play an important role in determining the extent of density segregation occurring in binary granular mixtures. © 2010 American Institute of Chemical Engineers AIChE J, 2010

Dense inclined flows of inelastic spheres: tests of an extension of kinetic theory

Using the results of recent numerical simulations, we extend an existing kinetic theory for dense flows of identical, nearly elastic, frictionless spheres to identical, very dissipative, frictional spheres. The existing theory incorporates an additional length scale in the expression for the collisional rate of dissipation; this length scale is identified with the size of a cluster of correlated particles. Parameters of the theory for very dissipative, frictional spheres are set using the results of physical experiments on inclined flows of spheres over a rigid, bumpy base in the absence of sidewalls. The resulting theory is then tested against the results of physical experiments on flows of the same material over the surface of an erodible heap when frictional sidewalls are present.

Vibrated granular bed on a bumpy surface

We investigate effects of physical characteristics of the vibrating base in a vibrated granular bed system on the bulk granular behavior of the bed using molecular dynamics simulations. With a vibrating base that exhibits low coefficient of restitution for particle-base collisions, a monolayer of granular materials was observed to form dynamically on the surface of the base. Such a system was shown to be both qualitatively and quantitatively equivalent to one with a bumpy base composed of discrete solid particles undergoing the same type of imposed oscillatory motion. The "bumpiness" of such a base, as defined by the size of particles constituting the vibrating base, was also found to have insignificant effects on the behavior of the bulk granular materials. The observations made in this study may point toward a possible methodology to model vibrating granular bed systems with inelastic bases using continuum theories.

Density inversion in rapid granular flows: the supported regime

This paper presents numerical findings on rapid 2D and 3D granular flows on a bumpy base. In the supported regime studied here, a strongly sheared, dilute and agitated layer spontaneously appears at the base of the flow and supports a compact packing of grains moving as a whole. In this regime, the flow behaves like a sliding block on the bumpy base. In particular, for flows on a horizontal base, the average velocity decreases linearly in time and the average kinetic energy decreases linearly with the travelled distance, those features being characteristic of solid-like friction. This allows us to define and measure an effective friction coefficient, which is independent of the mass and velocity of the flow. This coefficient only loosely depends on the value of the micromechanical friction coefficient whereas the infuence of the bumpiness of the base is strong. We give evidence that this dilute and agitated layer does not result in significantly less friction. Finally, we show that a steady regime of supported flows can exist on inclines whose angle is carefully chosen.

Boundary effects and self-organization in dense granular flows

Boundary effects in gravity-driven, dense granular flows down inclined planes are studied using large-scale molecular dynamics simulations. We find that the flow behavior and structure of the flowing pile changes dramatically as we vary the roughness of the supporting base. For a rough, bumpy base, there are three principal flow regimes that depend on the inclination angle θ: at small angles θ<θr, where θr is the angle of repose, the system does not flow; for large angles θ>θmax, where θmax is the maximum angle for which stable, steady state flow exists, the flow is unstable; and for θr<θ<θmax, the energy input from gravity is balanced by that dissipated through friction and the system reaches a stable, steady state flow. In the stable regime, we find no slip boundary conditions with a bulk density that is independent of the height above the base. For a chute base that is ordered, the steady state regime splits into a further three distinct flow regimes: at lower angles, the flowing system self-organizes into a state of low-dissipation flow consisting of in-plane ordering in the bulk; at higher angles, a high-dissipation regime similar to that for a rough base but with considerable slip at the bottom is observed; and between these two sub-regions we observe a transitional flow regime characterized by large oscillations in the bulk averaged kinetic energy due to the spontaneous ordering and disordering of the system as a function of time.

A ploughing model for the origin of weak tills beneath ice streams: a qualitative treatment

Glaciological studies of West Antarctic ice streams have shown that weak sub-ice-stream tills provide the basal lubrication that makes fast ice streaming possible under low driving stresses. Given the significant current interest in time-dependent ice stream behavior, there is a clear need for a conceptual model of weak sub-ice-stream tills that treats in a simple, but physically correct, way the coupling between evolution of till properties and ice stream dynamics. As a possible alternative to the previous, viscous-bed model, we propose a ploughing model that is consistent with the experimentally determined Coulomb-plastic rheology of sub-ice-stream till. In the ploughing model, the till is a several-meters-thick layer of sedimentary material that is disturbed and transported by ploughing that occurs during sliding of a bumpy ice base. The thickness of the till layer is determined in the ploughing model by the amplitude of the largest roughness elements (“ice keels”). There is no direct proof for the existence of ice bumps and ice keels beneath the modern West Antarctic ice streams but bedforms (e.g. megalineations and bundle structures) left behind by Pleistocene ice streams strongly support our assumption that an ice stream base is irregular. Generation of new till material occurs when ice keels protrude through the existing till layer and erode the top of the sub-till preglacial sediments. Based on a single tethered stake measurement of Engelhardt and Kamb (J. Glaciol. 44 (1998) 223) made at the UpB camp, Ice Stream B, West Antarctica (Fig. 1), we estimate that the till flux due to sliding with ploughing is there <88 m 3 yr −1 per meter width. To balance the estimated till flux in the UpB area, substrata erosion by ice keels would have to take place at a high, but not unreasonable, non-dimensional rate of <1.7×10 −4 (assuming 1% contact area). In the case of the West Antarctic ice streams, erosion of sub-till materials by ice keels may be particularly fast and unimpeded because these ice streams are overriding unlithified preglacial (Tertiary) sediments. The most significant implication of the proposed ploughing model is that it permits treating basal resistance to ice motion as being velocity independent (plastic till rheology) while allowing subglacial transport of till as in the viscous-bed model. Models of ice streams with a plastic bed exhibit a greater potential for unstable behavior than models of ice streams with viscous beds.

Simulations and physical measurements of glass spheres flowing down a bumpy incline

An inclined chute facility and its associated diagnostics has been developed and utilized to study the flow of granular materials. A variety of flow regimes and flow phenomena were observed. Fully developed flows were observed over a bumpy base for a range of slopes. Under some conditions, these flows were dominated by friction and under other conditions, collisions played a dominant role. A variety of unsteady flows were also observed. These include decelerating flows, accelerating flows, and wavy (periodic) flows. The characteristics of the base strongly influenced the flow regime and flow dynamics. Discrete particle simulation model parameters were determined from individual particle tests and particle impact experiments. Simulations of nominally steady flows at two fixed angles showed relatively good agreement with experimental values for particle velocities near the side-walls and on the top surface. The mass flow rate and the flow depth were also consistent with the experiments; however, both experiments and simulations exhibited significant fluctuations about the nominal mean values. The simulations were utilized to interpret flow parameters interior to the flow (i.e., in regions that cannot easily be measured non-intrusively). Far from the side-walls, the granular temperature was found to have a maximum near the bumpy base and to decrease toward the top surface — consistent with granular kinetic theory predictions for flows on bumpy inclines, without side-walls. Near the side-walls the behavior was substantially different with granular temperature decreasing from the top to a minimum at the lower `corners' of the chute. This behavior is consistent with experimental measurements of fluctuation velocities near the side-walls. The simulations confirm that the previous discrepancy in the variation of the granular temperature with depth between kinetic theory and near-side-wall measurements was a result of the side-walls, which cause strong three-dimensional structure in the flow.