Dense Flow Regime Research Articles

Modeling free-surface flows of granular column collapses using a mesh-free method

The dry granular mass in the dense flow regime can be considered as continuum and incompressible and is modeled in this study by using a mesh-free method, moving particle semi-implicit method (MPS). A local rheology model is employed to calculate the effective viscosity and shear stress in granular flows in the numerical method. Flows of cylindrical column collapse on planes and rectangular dam-break in channels containing glass beads and sands were respectively simulated in two-dimensional. From modeling a series of granular flows, the rheology model in MPS reproduced the flow characteristics of granular materials including flowing surface and the distinct static internal part where low velocity exists. The simulations prove that the initial column ratio played an important role in the spreading of granular mass. The surface profiles and wave front movements were compared with experimental data from literatures. After a transient period in the initial flow, the wave front of the granular flow approximately travels in a constant speed which was similar to that observed in the experiments. The final wave front in the simulations also showed good agreement with the relationship obtained from experiments.

Discrete modeling of penetration tests in constant velocity and impact conditions

The paper presents investigations on the penetration tests in granular material. A discrete numerical study is proposed for the modeling of penetration tests in constant velocity conditions and also in impact conditions. The model reproduces qualitatively the mechanical response of samples of granular material, compared to classical experimental results. Penetration tests are conducted at constant velocity and from impact, with similar penetration rates ranging from 25mms−1 to 5000mms−1. In constant velocity condition, the value of tip force remains steady as long as the penetration velocity induces a quasi-static regime in the granular material. However, the tip force increases rapidly in the dense flow regime corresponding to higher penetration rate. Impact tip force increases with the impact velocity. Finally, the tip forces obtained from impact penetration tests are smaller compared to the one obtained in constant velocity conditions in both quasi-static and dense flow regimes.

A two‐scale model for sheared fault gouge: Competition between macroscopic disorder and local viscoplasticity

AbstractWe develop a model for sheared gouge layers that accounts for the local increase in temperature at the grain contacts during sliding. We use the shear transformation zone theory, a statistical thermodynamic theory, to describe irreversible macroscopic plastic deformations due to local rearrangements of the gouge particles. We track the temperature evolution at the grain contacts using a one‐dimensional heat diffusion equation. At low temperatures, the strength of the asperities is limited by the flow strength, as predicted by dislocation creep models. At high temperatures, some of the constituents of the grains may melt leading to the degradation of the asperity strength. Our model predicts a logarithmic rate dependence of the steady state shear stress in the quasistatic regime. In the dense flow regime the frictional strength decreases rapidly with increasing slip rate due to thermal softening at the granular interfaces. The transient response following a step in strain rate includes a direct effect and a following evolution effect, both of which depend on the magnitude and direction of the velocity step. In addition to frictional heat, the energy budget includes an additional energy sink representing the fraction of external work consumed in increasing local disorder. The model links low‐speed and high‐speed frictional response of gouge layers and provides an essential ingredient for multiscale modeling of earthquake ruptures with enhanced coseismic weakening.

Crossover from quasi-static to dense flow regime in compressed frictional granular media

Being ubiquitous in a large variety of geomaterials, granular assemblies play a crucial role in the mechanical stability of engineering and geophysical structures. For these applications, an accurate knowledge of the processes at the origin of shear localization, i.e. faulting, in frictional granular assemblies submitted to compressive loading is needed. Here we tackle this problem by performing discrete-element numerical simulations. A thorough analysis of the evolution of multi-scale mechanical properties as approaching sample macroscopic instability is performed. Spatial correlations operating within the shear stress and strain fields are analyzed by means of a coarse-graining analysis. The divergence of correlation lengths is reported on both shear stress and strain fields as approaching the transition to sample instability. We thus show that the crossover from a quasi-static regime where the sample deforms infinitely slowly to a dense flow regime, where inertial forces play a significant role, can be interpreted as a critical phase transition. At this transition, no shear band of characteristic thickness can be defined.

Investigation on Hydrodynamics of Triple-Bed Combined Circulating Fluidized Bed Using Electrostatic Sensor and Electrical Capacitance Tomography

To investigate the hydrodynamics, a cold model of triple-bed combined circulating fluidized bed (TBCFB) has been built with an electrostatic sensor and a twin-plane electrical capacitance tomography (ECT) sensor. Experimental results show that with the increase in the superficial air velocity, the flow regime in the riser would transit from a dense plug flow to a core-annular flow, and finally to a dilute suspension flow. In the dense plug flow regime, the passage of the solids plugs in the riser can be monitored and the velocity measured using the twin-plane ECT sensor. In the core-annular flow regime, when the solids holdup is moderate, the measured solids velocities by the electrostatic sensor and the ECT sensor are comparable and complementary. With a dilute suspension flow in the riser, a homogeneous flow is observed with a nearly flat velocity profile of solid particles. On the contrary, in the downer the flow becomes inhomogeneous, and the solids velocities in the center of the downer are higher th...

Dense particle cloud dispersion by a shock wave

The study of particle cloud dispersion by a shock wave is important to many applications, including multiphase explosives that comprise a condensed explosive surrounded with packed micrometric reactive metal particles. Detonation of the explosive generates a shock wave which accelerates and compacts the particles. The particles are further accelerated from the reflected rarefaction as the shock wave arrives at the free-surface of the particles, leading to their rapid dispersal into the air. Generally speaking, the shock wave initially propagates through a granular particle bed and much later in time the particle cloud is dispersed and the flow becomes a dilute gas-solid flow. Between these two regimes the flow is characterized by a dense gas-solid flow [1]. Reactive multiphase flow models have been used to simulate the acceleration and dispersion of the particle cloud [2]. The fidelity of the simulations is severely limited by the physical drag models that need to take into account the interactions in the dense gas-solid flow [1]. In order to develop an accurate particle drag model that describes particle acceleration in the dense flow regime, representative experimental data need to be generated.While dispersal experiments have been carried out using a spherical multiphase explosive charge [3], controlled shock wave experiments are necessary to gain understanding of the fundamental physics of the dense supersonic gas-solid flow interactions and quantitative data concerning the particle cloud dispersion. Shock tube experiments have been carried out but typically the particle suspension method influences the shock flow [2] and the particle size is not typical of multiphase explosives. This paper reports on shock tube experiments looking at the acceleration and dispersion of 100 micron-sized aluminum oxide particles. The shock wave propagating into the packed particles provides a low-pressure analogy to multiphase explosive dispersal.

Numerical study of gas–solid flow in a coal beneficiation fluidized bed using kinetic theory of granular flow

Modeling the dynamic behavior of gas -solid flow in a pilot scale coal beneficiation fluidized bed (CBFB) model was performed in this work, a transient two-dimensional simulation was done based on the Eulerian model together with the kinetic theory of granular flows. Three steps were conducted to testify the choices of sub-models in CBFB modeling, including gas -solid exchange drag models, gas phase turbulence models, granular temperature models and wall boundary condition models for solid phase. Instantaneous and time-averaged results of particle volume fraction, bubble number and size, particle velocity distributions and vortices, as well as bed density distributions were obtained. The impacts of the sub-models on the flow characteristics in the dense CBFB were illustrated in detail and suitable models with better predictions of CBFB flow pattern were then demonstrated. The Syamlal -O'Brien drag model predicted better results in bed characteristics. The dispersed k-ε turbulence model should be used to describe the gas turbulence in the dense CBFB flow regime. The partial slip wall condition for particles had a slight influence in the small model. The partial differential equation granular temperature model could predict the inter-phase surfaces more clearly and the flow pattern more accurately.

Discrete simulation of dense flows of polyhedral grains down a rough inclined plane

The influence of grain angularity on the properties of dense flows down a rough inclined plane are investigated. Three-dimensional numerical simulations using the nonsmooth contact dynamics method are carried out with both spherical (rounded) and polyhedral (angular) grain assemblies. Both sphere and polyhedra assemblies abide by the flow start and stop laws, although much higher tilt angle values are required to trigger polyhedral grain flow. In the dense permanent flow regime, both systems show similarities in the bulk of the material (away from the top free surface and the substrate), such as uniform values of the solid fraction, inertial number and coordination number, or linear dependency of the solid fraction and effective friction coefficient with the inertial number. However, discrepancies are also observed between spherical and polyhedral particle flows. A dead (or nearly arrested) zone appears in polyhedral grain flows close to the rough bottom surface, reflected by locally concave velocity profiles, locally larger coordination number and solid fraction values, smaller inertial number values. This dead zone disappears for smooth bottom surfaces. In addition, unlike sphere assemblies, polyhedral grain assemblies exhibit significant normal stress differences, which increase close to the substrate.

High Speed Visualization of Pneumatic Conveying of Materials in Bypass System

Dense phase pneumatic conveying is preferable over dilute phase conveying in many industries as lower transport velocities are beneficial due to reduced attrition of the particles and reduced wear. However, dense phase conveying is critically dependent on the physical properties of the materials to be conveyed. For many materials which are either erosive or fragile, they do not exhibit the physical properties required to be conveyed reliably in a low velocity, dense phase flow regime. This can be serious problem in the food, chemical and pharmaceutical industries. One satisfactory approach which has been widely applied is the use of bypass systems. Bypass pneumatic conveying systems provide the capacity of transporting some materials that are not naturally suitable for dense phase flow. Bypass pneumatic conveying systems also provide a passive capability to reduce minimum particulate transport velocities. In this study, pneumatic conveying experiments were carried out in a 79 mm diameter main pipe with a 27 mm inner diameter bypass pipe with orifice plate flute arrangement. Alumina, fly ash and sand were conveyed in the tests. High speed camera visualization was employed to study the flow regimes of bypass pneumatic transport systems and investigate the mechanism of material blockage inhibition provided by these systems. For alumina and fly ash, it was found that particulate material blockages were inhibited in bypass systems due to the air penetration into the particulate volume as a result of orifice plate airflow resistance. For the bypass pneumatic conveying of sand, the splitting of a long plug into two smaller plugs was observed. One of the primary concerns of bypass system is the wear of the bypass line. Material such as alumina is inherently abrasive by nature. For internal bypass systems, there is limited ability to monitor the state of the inner bypass tube while in operation. The particle velocity in the pipeline has been measured from the high speed video of the flow. The experimental result also showed that the conveying velocity of bypass system is much lower when compared conventional single bore pipelines. Based on the models developed for the assessment of service life of pneumatic conveying pipelines, the thickness loss of the bypass pipe has been estimated. It has been estimated that for a 3mm bypass tube wall thickness, a wear hole is created in approximately 2.5 years for a particle velocity of 3 m/s and 4 months for a particle velocity of 10 m/s.

Rheology of binary granular mixtures in the dense flow regime

We study the rheology of granular mixtures in a steady, fully developed, gravity-driven flow on an inclined plane, by means of discrete element method (DEM) simulations. Results are presented for a single component system and binary mixtures with particles of different size and density. Inclination angles, composition, size ratios and density ratios are varied to obtain different segregated configurations at equilibrium. Steady state profiles of the mean velocity, volume fractions, shear stress, shear rate, inertial number and apparent viscosity across the depth of the flowing layer are reported for the different cases. The viscosity varies with height and is found to depend on the local bulk density and composition, which, in turn, depend on the size ratio, the mass ratio and the degree of segregation. For a single component system, a viscoplastic rheological model [P. Jop et al., Nature 441, 727 (2006)] describes the data quite well. We propose a modification of the model for the case of mixtures. The mixture model predicts the viscosity for both well-mixed and segregated granular mixtures differing in size, density or both, using the same model parameters as obtained for the single component system. The predictions of a model for the volume fraction of the mixtures also agree well with simulation results.

Influence of stirrer type on mixture homogeneity in continuous powder mixing: A model case and a pharmaceutical case

Continuous powder mixers offer a viable alternative to batch processes, but have received very little attention in scientific literature and in the industrial world. Mixer design is still very empirical and is not based on assessed methodologies. In this paper, we report experiments that aimed to compare two very different types of stirrers for a pilot-scale continuous powder mixer, and for two types of mixtures: a model mixture and a real pharmaceutical mixture. The first stirrer A is of the frame type with inclined paddles and internal transporting screw, the other stirrer B is of the shaft type with paddles mounted on it. Results are first presented from the viewpoint of bulk powder flow by hold-up determination and correlation with operating conditions. General relationships are derived which show that the mobile B leads to higher hold-ups, which may be an important drawback. The study of mixture homogeneity globally confirms these findings, especially in a dense phase flow regime. In the fluidised regime, where the stirrer B can be used, attention is drawn to the negative effect of excessive rotational speeds on the quality of the mixtures.

Friction law in dense granular flows

The understanding of the dense granular flow regime (intermediate between quasi-static and collisional regimes) has recently progressed significantly. We shall review the results concerning the friction law, which we have obtained with the help of discrete numerical simulations of flow of assemblies of disks in various geometries (homogeneous plane shear, annular shear and inclined plane). In the case of cohesionless quasi-mono-dispersed and rigid grains, the analysis of the dependencies of the effective friction coefficient, ratio of shear to normal stress, on the shear state (defined by the shear rate and pressure) and on the mechanical characteristics of the material has made possible the formulation of a local constitutive law. This has shown the crucial role of a dimensionless parameter, called inertial number, which rules the friction law in the dense regime. This law remains true in the case of bi-dispersed flows, as early as the average diameter of the grains in taken into account. It is also true in the case of cohesive grains, once a second dimensionless number, characterizing the intensity of cohesion, is introduced.

Flows of Dense Granular Media

We review flows of dense cohesionless granular materials, with a special focus on the question of constitutive equations. We first discuss the existence of a dense flow regime characterized by enduring contacts. We then emphasize that dimensional analysis strongly constrains the relation between stresses and shear rates, and show that results from experiments and simulations in different configurations support a description in terms of a frictional visco-plastic constitutive law. We then discuss the successes and limitations of this empirical rheology in light of recent alternative theoretical approaches. Finally, we briefly present depth-averaged methods developed for free surface granular flows.

A model for gas–solid flow in a horizontal duct with a smooth merge of rapid–intermediate–dense flows

Granular flow in the rapid flow regime is dominated by particle–particle collisions and the constitutive relations for the solid stress are obtained from the classic kinetic theory of granular flow. In the dense flow regime, on the other hand, particles interact via enduring contacts and the solid stress can be deduced from soil mechanics theories. In this paper, constitutive equations, recently proposed by Tardos et al. [2003. Slow and intermediate flow of frictional bulk powder in the Couette geometry. Powder Technology 131, 23–39.] has been incorporated in the simulation of gas–solid flow in a horizontal duct. These equations smoothly merge the rapid granular flow solution with the so-called “intermediate” regime (where both kinetic/collisional and frictional contributions might play a role) and reduce to Coulomb yield condition for slow frictional flow (shear rate → 0). The results of this new modelling approach have shown good qualitative agreement with the reported experimental observation on wide range of gas–solid flow conditions. In this study, we also present the definition of boundaries between rapid–intermediate–dense flow regimes based on the dimensionless shear rate ( λ ), and a modified Reynolds number ( Re). We have shown that the intermediate flow regime can be classified at approximately 0.1 < λ < 1.0 and 100 < Re < 3000 .

Flow Regime Study of a Light Material in an Industrial Scale Cold Flow Circulating Fluidized Bed

A series of experiments was conducted in the 0.3meter diameter circulating fluidized bed test facility at the National Energy Technology Laboratory (NETL) of the U. S. Department of Energy. The particle used in this study was a coarse, light material, cork, which has a particle density of 189kg∕m3 and a mean diameter of 812μm. Fluidizing this material in ambient air approximates the same gas-solids density ratio as coal and coal char in a pressurized gasifier. The purpose of this study is twofold. First, this study is to provide a better understanding on the fundamentals of flow regimes and their transitions. The second purpose of this study is to generate reliable data to validate the mathematical models, which are currently under development at NETL. Utilization of such coarse, light material can greatly facilitate the computation of these mathematical models. Furthermore, the ratio of density of cork to air under ambient conditions is similar to the density ratio of coal to gas at the gasification and pressurized fluidized bed combustion environment. This paper presents and discusses the data, which covered operating flow regime from dilute phase, fast fluidization, and to dense phase transport by varying the solid flux, Gs at a constant gas velocity, Ug. Data are presented by mapping the flow regime for coarse cork particles in a ΔP∕ΔL‐Gs‐Ug plot. The coarse cork particles exhibited different behavior than the published literature measurements on heavier materials such as alumina, sand, FCC, silica gel, etc. A stable operation can be obtained at a fixed riser gas velocity higher than the transport velocity, e.g., at Ug=3.2m∕s, even though the riser is operated within the fast fluidization flow regime. Depending upon the solids influx, the riser can also be operated at dilute phase or dense phase flow regimes. Experimental data were compared to empirical correlations in published literature for flow regime boundaries as well as solids fractions in the upper dilute and the lower dense regions for fast fluidization flow regime. Comparisons of measured data with these empirical correlations show rather poor agreements. These discrepancies, however, are not surprising since the correlations for these transitions were derived from experimental data of comparative heavier materials such as sands, FCC, iron ore, alumina, etc.

Submarine granular flows down inclined planes

Submarine flows of granular material down a rough inclined plane are experimentally investigated. We focus on the dense flow regime when the whole sediment layer is flowing down the slope and when no deposition nor entrainment occurs. In this regime, steady uniform flows are observed for which we systematically measure the depth-averaged velocity, the thickness, and the excess pore pressure for different inclinations and different flow rates. The experimental measurements are analyzed within a theoretical approach inspired by recent results obtained for dry granular flows. The basic assumption of the model is that the constitutive law obtained in the dry case still holds for submarine flow, if one substitutes the inertial time scale coming into play in the rheology by a viscous time scale. The agreement between the measurements and the theory supports this assumption.

Rheophysics of dense granular materials: Discrete simulation of plane shear flows

We study the plane shear flow of a dense assembly of dissipative disks using discrete simulation and prescribing the pressure and the shear rate. Those shear states are steady and uniform, and become intermittent in the quasistatic regime. In the limit of rigid grains, the shear state is determined by a single dimensionless number, called the inertial number I , which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasistatic critical state of soil mechanics, while large values of I correspond to the fully collisional regime of kinetic theory. When I increases in the intermediate dense flow regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. The mechanical characteristics of the grains (restitution, friction, and elasticity) have a small influence in the dense flow regime. Finally, we show that the evolution of the relative velocity fluctuations and of the contact force anisotropy as a function of I provides a simple explanation of the friction law.

Improving the power consumption in pneumatic conveying systems by a daptive control of the flow regime

The pneumatic conveying of solids in a gas stream is a recurrent process in petrochemical industries. However, due to practical limitations the majority of existing systems have capacities ranging from 1 to 400 tones per hour over distances less than 1000 m, mainly because of a high power consumption per transported unit mass. More specifically, to avoid the formation of dense structures such as dunes and plugs, which, depending on the characteristics of the material and on the availability of a pressure head from the carrier phase may cause a violent pressure surge or a possible line blockage, the system is preferably operated at homogeneous dispersed flow. To sustain such a flow regime high velocities are needed and, accounting for the resulting higher pressure drops, higher power consumption is demanded. An optimized pneumatic conveying system can be conceived with the help of adaptive control techniques. In the context described above, lower transport velocities are allowed if the formation of aggregates that precedes the transition to dense phase flow regimes are automatically detected and destroyed, thus, artificially stabilizing the light phase homogeneous flow regime. This work assesses the reduction in the necessary power that the application of such adaptive control technique could produce. Experimental results are presented for a 45 mm i.d. pneumatic conveying system used to transport Setaria Italica seeds. The instrumentation used to identify the flow regime is constituted of several pressure sensors installed along the transport line. The proposed control strategy is based on processing these signals through a neural network model to assess the flow condition and to mimic an optimized gain scheduled PID algorithm. Preliminary results show that reductions in power consumption can reach 50% when compared with classical non controlled transport.

Theoretical analysis of the flow regimes and their characteristics in vertically flowing gas–solids suspensions

This paper analyses the detailed flow structure characteristics of a vertical, fully developed gas–solids suspension. It is based on an asymptotic approach to general multiphase flow equations, in the range of low or moderate solids concentrations. Three distinct flow structures are identified, defining the Similar Profiles, Transition and Dense Phase Flow Regimes, as well as the local mechanism generating the transitions. The predicted properties of the trends of variation of local flow variables, with overall solids loading are, then, compared with existing experimental data. The observed wide agreement encourages the use of the theory for the interpretation and the prediction of the behavior of existing industrial units.

Two-dimensional granular Poiseuille flow on an incline: multiple dynamical regimes.

We investigate experimentally the flow of a monolayer of spherical beads through a channel on a smooth incline that is bounded by rough sidewalls. Using high-speed video imaging and particle tracking, we measure the positions and velocities of all particles in the field of view. We find that the flows are accelerating and dilute if the channel exit is open. On the other hand, if the exit is constricted, flows can reach a state in which the local time-averaged velocity is invariant along the stream. In the latter case, we find a continuous transition from an oscillatory two-phase flow (2PF) regime with wide density variations to a uniform dense flow regime, depending on the channel width and the mean flow speed. These two regimes exhibit distinct density variation, time regularity, and transverse profiles. The rough sidewalls are found to be necessary for the 2PF regime. In the dense regions of both flows, particles exhibit temporary arches, long-range correlated velocities, inhomogenuous propagation of disturbances, and hexagonal lattice structures. On the other hand, the dilute regions of the two-phase flow are nearly collisionless. Existing models can neither fully describe the dynamics of both the dense and the dilute regions nor explain the spontaneous switching between them.