Gravity-driven Granular Flows Research Articles

Modeling heat and mass transfer in granular flows between vertical parallel plates

Gravity-driven granular flows between vertical parallel plates at elevated temperatures are integral in the development of the next generation of particle-based heat exchangers for concentrated solar power. Efficient modeling methodologies that accurately captures the heat transfer mechanisms of temperature-dependent granular flows are essential to effectively design and evaluate these heat exchangers. Transient, pseudo-one-dimensional heat and mass transfer models were developed for inlet flow temperatures between 473 and 1073 K. The mass transfer models for the granular flows were resolved using discrete element method simulation, providing detailed temporal and spatial distributions of flow parameters in good agreement with experimental measurements. The heat transfer model employed a one-dimensional, two-phase, continuum approach, and a system of non-linear differential equations was solved via finite difference method. The particle-to-wall contact heat transfer was determined with an effective thermal conductance model. Radiative heat transfer between particles and walls was also considered. The predicted particle and wall temperatures for two different channel widths of 6.4 and 2 mm were well-correlated to previously obtained experimental measurements with Pearson’s correlation coefficients greater than 0.91. A significant disparity in particle temperature of up to 72 K was observed when radiative heat transfer was omitted, and a maximum temperature difference of 11 K was observed when temperature-dependent granular flow properties were not considered. The model revealed that radiative heat transfer potentially contributed to > 30 % of heat losses in wider channels at high inlet temperatures, and conduction was the dominated heat transfer mechanisms in narrower channels (∼70 %) due to increased particle-to-wall contact. This accurate model, leveraging discrete element method in a streamlined approach, advances the understanding and modeling of heat transfer in granular flows at elevated temperatures, enabling more efficient and reliable solar thermal energy storage and transport.

A novel mathematical approach for gravity-driven granular flows in block caving

This study presents a novel mathematical model aimed at elucidating the distinctive behavior observed in the flow of flat-bottom silos. A scheme analogous to the spot model proposed by Bazant is adopted, in which groups of particles move in relation to a static medium. However, we assume that the movement of the particles is driven by the local change in the tensional state instead of the increment of interstitial space through the diffusion of spots. We propose that the tensional state and gravity might induce a driving force with a larger magnitude than the friction exerted at the boundary of the group of mobilized particles. Thus, the dynamics of the flow is controlled by the driving and frictional force. Finally, we have introduced a dimensionless number (Y) corresponding to the ratio of driving to frictional force to characterize the movement of particles. By assuming that frictional force at the interface has a viscous component proportional to the relative speed of the mobilized particles, we have writen an equation analogous to Darcy's law for the flow of a Bingham fluid in a porous medium. The finite element method is utilized to solve the model, and the numerical findings demonstrate a strong correspondence with experimental results achieved in flat-bottom silos featuring one or two openings. Comparatively, the results of the kinematic model are surpassed, with a notable enhancement in the depiction of the velocity field.

Experimental and numerical analyses of gravity-driven granular flows between vertical parallel plates for solar thermal energy storage and transport

Gravity-driven granular flows between vertical parallel plates were considered at elevated temperatures to examine flow behavior and inform solar thermal energy storage and transport infrastructure design and performance. A series of experiments was performed at inlet temperatures of 23, 200, 400, 600, and 800 °C in a high-temperature granular flow experimental rig and spatial and temporal velocity and surface temperature fields were measured. Granular flows were observed to change as a function of temperature. The interaction between the particles and the wall significantly increased with decreases in channel widths. Particle velocities at the outlet of the channel were compared with results from numerical model using the discrete element method. Temperature-dependent flow properties directly related to the assembly were measured and used for granular flow simulation. Flow behavior within the channel was investigated from the simulated results by obtaining particle volume fractions and particle velocities. Wall temperature and outlet granular flow temperature were monitored during the flow experiment and temporal heat loss in the flow was calculated. The granular flow behavior and heat transfer analysis from both the experiment work and simulation provide important mass transfer information for heat transfer modeling at elevated temperature.

Gravity-driven granular flows in pipes: teaching experimental skills in the context of granular flows

Granular flows appear frequently in the natural world and in civil engineering applications. These flows can exhibit features which are surprising and counter-intuitive and are often used to test the limits of the classical continuum approximation for modelling of fluid flows. An important sub-class of the granular flows are the gravity-driven granular flows, which include the granular column collapse and the flow of granular material down through a vertical pipe. In this article, quantitative analysis is performed of the flow using video analysis software. The utility and relevance of the experiment for development of experimental skills in physics students and modelling of unexpected phenomena is discussed.

Effects of obstacle's curvature on shock dynamics of gravity-driven granular flows impacting a circular cylinder

Granular flows, such as rock avalanches and debris flows, are gravity-driven and often hit engineering structures that are placed in their paths, generating dynamic impact pressures and potentially causing hazard to infrastructures. To improve the design of protective structures and the hazard assessment, it is important to understand the physical mechanism of such granular flows impacting on obstacles with variable sizes and shapes. In this study, the dynamics of granular shock waves generated by experimental flows impacting on a circular cylinder varying in diameter and on a closed barrier were investigated by conducting systematic laboratory experiments. Pressure sensors were mounted at the bottom of the experimental chute and the upstream cylinder surface to measure the dynamic impact pressures in the granular shock area. Accelerometers that were installed at the underside of the chute bed were used to record the seismic signals of granular flows during the entire impacting process. The velocity and depth of a granular flow impacting (or just before impacting) on a cylinder were estimated using an image processing method. The results showed that the dimensionless standoff distance DDstandoff of the granular shock wave decreases nonlinearly with increasing Froude number ranging from 5.8 to 12.3. The values of DDstandoff tend to change less for the larger investigated Froude numbers, approaching a limit of about 0.19. The dimensionless runup and the pinch-off distance correlated linearly with increasing Froude number and can be affected by the radius of curvature (RC) of the obstacle at the stagnation point. The impact pressures grow linearly as Froude number increases, and the RC with a smaller value usually excites a larger impact pressure. Additionally, the effect of RC on the dimensionless pressures was observed to be weakened by an increase in Froude number. The mean frequency of the seismic signals produced by the impacts of a granular flow also indicates a dependency on RC. The findings of this study contribute to the understanding of the dynamic signal response generated by a granular flow, which may result in improving the design of the protective structures.

Enhanced weakly-compressible MPS method for immersed granular flows

We develop and validate a three-dimensional particle method based on an Enhanced Weakly-Compressible MPS approach for modeling immersed dense granular flows. For this purpose, we adopt a generalized rheological model, using a regularized visco-inertial rheology, for all regimes of multiphase granular flow. Moreover, we propose a new consistent formulation to estimate the effective pressure of the solid skeleton based on the continuity equation of the pore-water. To improve the accuracy of the multiphase particle methods, especially near boundaries and interfaces, we introduce a modified high-order diffusive term by employing the convergent form of the Laplacian operator. The effectiveness of the new diffusive term is particularly demonstrated by modeling the hydrostatic pressure of two fluid phases. Further, coupling the generalized rheology model with the flow equations, we investigate the gravity-driven granular flows in the immersed granular collapse and slide in three dimensions. As a part of this study, we represent the experiment on the immersed granular collapse to validate the model. The evolution and runout length of the granular bulk are compared with those from experiments confirming good compatibility. Overall, the qualitative and quantitative results justify the proposed developments shown to be essential for predicting different states of the immersed granular flows.

Remote acoustic measurement of the velocity within water-immersed gravity-driven granular flows

Measuring bedload transport at high spatial and temporal resolution in energetic aqueous environments is challenging. Acoustic remote-sensing technologies are attractive because the measurement can be made without disturbing the mobile bed or the near-bed flow. Of particular interest is the development of broadband MHz-frequency acoustic systems capable of simultaneous measurements of backscatter amplitude and phase at mm-scale range resolution and 100 Hz sampling frequencies. Using such an instrument, we study granular flow in a water-submerged rectangular chute. By releasing sediments in the upstream portion of the chute, a O(1)cm-thick layer of avalanching sediment is produced. Trials were carried out for both erodible and fixed roughness beds. Natural sand and glass beads with median grain sizes ranging from 0.22 to 0.4 mm were used. The thickness of, and velocity profile within, the moving layer were measured using a wide bandwidth coherent Doppler profiler operating at 1.2 MHz. The velocity profiles are compared to estimates made with video imagery through the chute sidewall. The velocities at the sediment-water interface are compared to estimates made with a commercially available Doppler profiler (Vectrino) operating at 10 MHz and with imagery from a submerged video camera.

On the validity of the two-fluid-KTGF approach for dense gravity-driven granular flows as implemented in ANSYS Fluent R17.2

As a subproblem of solid transport in wellbores, we have investigated the cliff collapse problem by means of the Two-Fluid-Model (TFM), where the rheological description of the second phase (sand) is governed by the Kinetic Theory of Granular Flows (KTGF) and additional closures from soil mechanics for dense (frictional) regions of the solid phase. Using ANSYS Fluent R17.2, we have studied the influence of the aspect ratio and scale of the initial cliff, the scale of the particle size, four different interstitial fluids (air, water, and two viscous but shear-thinning solutions), and the role of the initial condition (IC) of the solid volume fraction. The latter was evaluated by two different strategies: (1) Let solids settle to establish a compacted granular bed in dynamic equilibrium prior to allow the cliff to collapse and (2) simply patch the solid volume fraction into the computational domain at t = 0.While most of the simulations produced a final deposit featuring a slope, validation with experimentally obtained scaling laws from the literature was not comprehensively successful. The primary reason identified is that, at steady-state, for which a sloped deposit must exist, a thin layer at the top of the sediment bed remains flowing, yielding a scale-dependent disintegration of the cliff over longer periods of time which ultimately results in a flat bed. We suspect this phenomenon, hereafter termed top bed velocity defect, to be a consequence of the numerical solutions strategy of Fluent which may result in some momentum solid flux imbalance at top-bed regions where the gradient of the solids kinetic/collisional pressure is high.Comprehensive model tuning is required to yield a better physical representation of the IC. In addition, alternative closures for both solid frictional pressure and solid viscosity may be helpful to better replicate the experimental data. On the other hand, experimental spread and missing experimental data for the shear-thinning fluids requires more comprehensive experimental data for validation purposes.If the model in its current form is used for transport modeling of cuttings in wellbore flows, the velocity defect will lead to an unknown overestimation of the mass flux of solids. When it comes to the modeling of dune migration, the top bed velocity defect will likely cause disintegration of the dune over longer periods of time.

Rapid granular flows on a vibrated rough chute: Behaviour patterns and interaction effects of particles

The objective of this study is to examine the segregation and interdiffusion-induced migration effects in the course of interaction of particles differing in size, density and roughness while undergoing rapid gravity-driven granular flows on a vibrated rough chute. An experimental and analytical method is proposed in order to obtain the profiles of velocity, fraction of the void volume and test particle distribution along the bed depth. It was found out that interdiffusion migration is the main physical mechanism of nonuniform particle interaction determining separation effect in rapid gravity-driven granular flows of granular materials on a rough chute vibrating at low frequencies. Segregation dominates when high frequencies of vibrating chute take place.

Rapid dry granular flows down an incline: a constitutive theory with an independent kinematic internal length

Rapid, isothermal, gravity-driven dry granular flows with incompressible solid grains down an incline are investigated by the thermodynamically consistent constitutive model. To this end, the revised Goodman–Cowin theory is applied for the time evolution of the volume fraction, in which a kinematic internal length is introduced. The Muller–Liu entropy principle is carried out to derive the equilibrium constitutive models, with their dynamic responses postulated in the context of a quasi-static theory. Numerical simulations show that both the volume fraction and velocity increase from the minimum values on the plane toward the maximum values on the free surface with an “exponential-like” tendency, while the internal length increases in a logarithmic manner. With the equilibrated stress system in the revised Goodman–Cowin theory, the kinematic internal length is recognized as a characteristic length of the long-term enduring frictional contact and sliding between the grains (a characteristic length of the inelastic network among the grains).

2D dry granular free-surface flow over complex topography with obstacles. Part I: experimental study using a consumer-grade RGB-D sensor

Avalanches, debris flows and other types of gravity-driven granular flows are a common hazard in mountainous regions. These regions often have human settlements in the lower parts of valleys, with human structures dangerously exposed to the destructive effects of these geophysical flows. Therefore a scientific effort has been made to understand, model and simulate geophysical granular flows. In order for computer models and simulations to be of predictive value they need to be validated under controlled, yet nature-like conditions. This work presents an experimental study of granular flow over a simplified mountain slope and valley topography. The experimental facility has a rough bed with very high slope at the upstream end and adverse slope on the downstream end, following a parabolic profile. Obstacles are present in the lower regions. Transient measurements of the moving granular surfaces were taken with a consumer-grade RGB-D sensor, providing transient 2D elevation fields around the obstacles. Three experimental configurations were tested, with semispheres of different diameters and a square dike obstacle. The experimental results are very consistent and repeatable. The quantitative, transient and two-dimensional data for all three experiments constitute excellent benchmarking tests for computational models, such as the one presented in a companion paper.

Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning

AbstractIt is well-known that in a dense, gravity-driven flow, large particles typically rise to the top relative to smaller equal-density particles. In dense flows, this has historically been attributed to gravity alone. However, recently kinetic stress gradients have been shown to segregate large particles to regions with higher granular temperature, in contrast to sparse energetic granular mixtures where the large particles segregate to regions with lower granular temperature. We present a segregation theory for dense gravity-driven granular flows that explicitly accounts for the effects of both gravity and kinetic stress gradients involving a separate partitioning of contact and kinetic stresses among the mixture constituents. We use discrete-element-method (DEM) simulations of different-sized particles in a rotated drum to validate the model and determine diffusion, drag, and stress partition coefficients. The model and simulations together indicate, surprisingly, that gravity-driven kinetic sieving is not active in these flows. Rather, a gradient in kinetic stress is the key segregation driving mechanism, while gravity plays primarily an implicit role through the kinetic stress gradients. Finally, we demonstrate that this framework captures the experimentally observed segregation reversal of larger particles downward in particle mixtures where the larger particles are sufficiently denser than their smaller counterparts.

DEM simulation of oblique shocks in gravity-driven granular flows with wedge obstacles

Deflecting wedge obstacles are often built to divert hazardous flows away from residential areas that are in the way of harm. When a rapid avalanche flow is deflected by an obstacle, this usually causes abrupt changes in the flow thickness and velocity and exhibits characteristics like oblique shock waves in the aerodynamic system or oblique hydraulic jumps in the open channel flows. In this study, the Discrete Element Method (DEM) is employed to simulate the motion of granular materials impinging on a wedge obstacle in an adjustable inclination chute. We use chutes with four different inclined angles combined with wedge obstacles having different angles to investigate the overall flow behavior. Both the flow velocity and the flow depth are obtained by averaging the numerical simulation data, and then the granular temperature and the shock angle are calculated. The results of the DEM simulation are compared with that of the classical oblique shock theory. We find that there is good agreement between the classical oblique granular shock theoretical calculations and the DEM simulation results. Moreover, the microdynamic variables related to flow structure such as the packing density and the coordination number are also discussed in the present study.

The importance of digital elevation model resolution on granular flow simulations: a test case for Colima volcano using TITAN2D computational routine

The mobility of gravity-driven granular flows such as debris flows or pyroclastic density currents are extremely sensitive to topographic changes, such as break in slopes, obstacles, or ravine deviations. In hazard assessment, computer codes can reproduce past events and evaluate hazard zonation based on inundation limits of simulated flows over a natural terrain. Digital Elevation Model (DEM) is a common input for the simulation algorithm and its accuracy to reproduce past flows is crucial. In this work, we use TITAN2D code to reproduce past block-and-ash flows at Colima volcano (Mexico) over DEMs with different cell size (5, 10, 30, 50, and 90 m) in order to illustrate the influences of the resolution on the numeric simulations. Our results show that topographic resolution significantly affects the flow path and runout. Also, we found that simulations of past flows with the same input parameters (such as the basal friction angle) over topography with different resolutions resulted in different flow paths, areas, and thickness of the simulated flows. In particular, the simulations performed with the 5- and 10-m DEMs produced similar results. Also, we obtained consistent simulation results for the 30- and 50-m DEMs. However, for the coarser 90-m DEM results are largely different and inaccurate. We recommend generating a benchmark table in order to acquire characteristic values for the basal friction angle of studied events. In case of rugged topographies, a DEM with high resolution should be used for more confident results.

Dynamical fluctuations in dense granular flows

We have made measurements of force and velocity fluctuations in a variety of dense, gravity-driven granular flows under flow conditions close to the threshold of jamming. The measurements reveal a microscopic state that evolves rapidly from entirely collisional to largely frictional, as the system is taken close to jamming. On coarse-grained time scales, some descriptors of the dynamics-such as the probability distribution of force fluctuations, or the mean friction angle-do not reflect this profound change in the micromechanics of the flow. Other quantities, such as the frequency spectrum of force fluctuations, change significantly, developing low-frequency structure in the fluctuations as jamming is approached. We also show evidence of spatial structure, with force fluctuations being organized into local collision chains. These local structures propagate rapidly in the flow, with consequences far away from their origin, leading to long-range correlations in velocity fluctuations.

Gravity-driven dry granular slow flows down an inclined moving plane: a comparative study between two concepts of the evolution of porosity

Two concepts in modeling the effects of the evolution of porosity in dry granular flows are investigated to illuminate their performance and limitations. To this end, the thermodynamic analysis, based on the Muller-Liu entropy principle, and the quasi-linear theory, are employed to deduce the ultimate constitutive models and the restrictions on their thermodynamic consistencies. The models are employed to study an isothermal dry granular slow flow down an inclined moving plane, of which the results are compared with the experimental outcomes. Results show that, while the two models deliver appropriate equilibrium expressions of the Cauchy stress tensor for compressible grains, the model in which the evolution of porosity is treated kinematically yields a spherical stress tensor for incompressible grains. Only the model with a dynamic evolution of porosity can give rise to a non-spherical stress tensor at equilibrium. Moreover, whilst the former model can better capture the characteristics of flows with slow to moderate speeds, the latter model is more able to describe the features of very rapid flows like avalanches. The present study illustrates the essential difference between the two concepts in modeling the effects of the evolution of porosity, and can be extended for further studies on other microstructural effects in granular flows.

Relationship between interparticle contact lifetimes and rheology in gravity-driven granular flows

The validity of the Bagnold constitutive relation in gravity-driven granular flow down an inclined plane is studied by discrete element (DEM) simulations. In the limit of infinitely hard particles, the Bagnold relation is known to hold exactly. We determine deviations from this relation as a function of all parameters governing interparticle interactions. These include elastic compliance, inelastic dissipation, friction coefficient, and interparticle cohesion. We find significant deviations from Bagnold rheology in some regions of this parameter space and propose a generalized Bagnold relation to account for this effect. Moreover, we note a significant correlation between the breakdown of Bagnold rheology in the bulk and the appearance of a long-time tail in the two-particle contact time distributions.

Breaking size segregation waves and particle recirculation in granular avalanches

Particle-size segregation is a common feature of dense gravity-driven granular free-surface flows, where sliding and frictional grain–grain interactions dominate. Provided that the diameter ratio of the particles is not too large, the grains segregate by a process called kinetic sieving, which, on average, causes the large particles to rise to the surface and the small grains to sink to the base of the avalanche. When the flowing layer is brought to rest this stratification is often preserved in the deposit and is known by geologists as inverse grading. Idealized experiments with bi-disperse mixtures of differently sized grains have shown that inverse grading can be extremely sharp on rough beds at low inclination angles, and may be modelled as a concentration jump or shock. Several authors have developed hyperbolic conservation laws for segregation that naturally lead to a perfectly inversely graded state, with a pure phase of coarse particles separated from a pure phase of fines below, by a sharp concentration jump. A generic feature of these models is that monotonically decreasing sections of this concentration shock steepen and eventually break when the layer is sheared. In this paper, we investigate the structure of the subsequent breaking, which is important for large-particle recirculation at the bouldery margins of debris flows and for fingering instabilities of dry granular flows. We develop an exact quasi-steady travelling wave solution for the structure of the breaking/recirculation zone, which consists of two shocks and two expansion fans that are arranged in a ‘lens’-like structure. A high-resolution shock-capturing numerical scheme is used to investigate the temporal evolution of a linearly decreasing shock towards a steady-state lens, as well as the interaction of two recirculation zones that travel at different speeds and eventually coalesce to form a single zone. Movies are available with the online version of the paper.

Weak, strong and detached oblique shocks in gravity-driven granular free-surface flows

Hazardous natural flows such as snow-slab avalanches, debris flows, pyroclastic flows and lahars are part of a much wider class of dense gravity-driven granular free-surface flows that frequently occur in industrial processes as well as in foodstuffs in our kitchens! This paper investigates the formation of oblique granular shocks, when the oncoming flow is deflected by a wall or obstacle in such a way as to cause a rapid change in the flow height and velocity. The theory for non-accelerative slopes is qualitatively similar to that of gasdynamics. For a given deflection angle there are three possibilities: a weak shock may form close to the wall; a strong shock may extend across the chute; or the shock may detach from the tip. Weak shocks have been observed in both dense granular free-surface flows and granular gases. This paper shows how strong shocks can be triggered in chute experiments by careful control of the downstream boundary conditions. The resulting downstream flow height is much thicker than that of weak shocks and there is a marked decrease in the downstream velocity. Strong shocks therefore dissipate much more energy than weak shocks. An exact solution for the angle at which the flow detaches from the wedge is derived and this is shown to be in excellent agreement with experiment. It therefore provides a very useful criterion for determining whether the flow will detach. In experimental, industrial and geophysical flows the avalanche is usually accelerated, or decelerated, by the net effect of the gravitational acceleration and basal sliding friction as the slope inclination angle changes. The presence of these source terms necessarily leads to gradual changes in the flow height and velocity away from the shocks, and this in turn modifies the local Froude number of the flow. A shock-capturing non-oscillating central method is used to compute numerical solutions to the full problem. This shows that the experiments can be matched very closely when the source terms are included and explains the deviations away from the classical oblique-shock theory. We show that weak shocks bend towards the wedge on accelerative slopes and away from it on decelerative slopes. In both cases the presence of the source terms leads to a gradual increase in the downstream flow thickness along the wedge, which suggests that defensive dams should increase in height further down the slope, contrary to current design criteria but in accordance with field observations of snow-avalanche deposits from a defensive dam in Northwestern Iceland. Movies are available with the online version of the paper.

Cellular automata model of gravity-driven granular flows

A cellular automata model is used to simulate a variety of granular chute flows. The model is tested against several case studies: flow down a chute, flow past an obstacle, chute flow in which complex, counter-rotating vortices result in streamwise surface stripes and flow near a boundary. The model successfully reproduces experimental observations in all of these cases. These results lead us to propose that simple, rule-based, models such as this can improve our detailed understanding of dynamics and flow within an opaque granular bed.