Granular flow through an orifice: solving the free fall arch paradox

Several theoretical predictions of the mass flow rate of granular flows through outlets are based on the existence of a free fall arch region covering the silo outlet. Early in the nineteenth century, it was suggested that the particles crossing this region lose their kinetic energy and start to fall freely under their own weight. However, there is not conclusive evidence of this hypothetical region. We examined experimentally and numerically the micro-mechanical details of the particle flow through an orifice placed at the bottom of a silo. Remarkably, the contact stress monotonously decreases when the particles approach to the exit and it only vanishes just at the outlet. The behavior of this magnitude was practically independent of the size of orifice indicating that particle deformation, is insensible to the size of the aperture. Contrary, the behavior of the kinetic stress puts on evidence that the outlet size controls the propagation of the velocity fluctuations inside the silo. Examining this magnitude, we conclusively argue that indeed there is a well-defined transition region where the particle flow changes its nature. Above this region, the particle motion is completely correlated with the macroscopic flow. Our outcomes clarifies why the free fall arch picture has served as an approximation to describe the flow rate in the discharge of silos

Non-spherical granular flows down inclined chutes

In this work, we numerically examine the steady-state granular flow of 3D non-spherical particles down an inclined plane. We use a hybrid CPU/GPU implementation of the discrete element method of nonspherical elongated particles. Thus, a systematic study of the system response is performed varying the particle aspect ratio and the plane inclination. Similarly to the case of spheres, we observe three well-defined regimes: arresting flows, steady uniform flows and accelerating flows. Both steady and dynamic macroscopic fields are derived from microscopic data, by time-averaging and spatial smoothing (coarse-graining), including density, velocity, as well as the kinetic and contact stress tensors. The internal morphology of the flow was quantified exploring the solid fraction profiles and the particle orientation distribution. Furthermore, the system¿s characteristic time and length scales are investigated in detail. Our aim is to achieve a continuum mechanical description of granular flows composed of non-spherical particles based on the micromechanical details. Thus, to evaluate the influence of particle shape on the constitutive response in granular of those systems. However, to meet the proceeding¿s page restrictions here we will only discuss the dependence of some terms of the continuum averaged equations on the coarse-graining scale, specifically the case of the kinetic part of the stress tensor

Velocity and density scaling at the outlet of a silo and its role in the expression of the mass flow rate

The role of density and velocity profiles in the flow of particles through apertures has been recently put on evidence in a two-dimensional experiment (Phys. Rev. Lett. 108, 248001). For the whole range of apertures studied, both velocity and density profiles are selfsimilar and the obtained scaling functions allow to derive the relevant scales of the problem. Indeed, by means of the functionality obtained for these profiles, an exact expression for the mass flow rate was proposed. Such expression showed a perfect agreement with the experiential data. In this work, we generalize this study to the three dimensional case. We perform numerical simulations of a 3D silo in which the velocity and volume fraction profiles are determined. Both profiles shows that the scaling obtained for 2D can be generalized to the 3D case. Finally, the scaling of the mass flow rate with the outlet radius is discussed

Disentangling the free-fall arch paradox in silo discharge

Several theoretical predictions of the mass flow rate of granular media discharged from a silo are based on the spontaneous development of a free-fall arch region, the existence of which is still controversial. In this Letter, we study experimentally and numerically the particle flow through an orifice placed at the bottom of 2D and 3D silos. The implementation of a coarse-grained technique allows a thorough description of all the kinetic and micromechanical properties of the particle flow in the outlet proximities. Though the free-fall arch does not exist as traditionally understood—a region above which particles have negligible velocity and below which particles fall solely under gravity action—we discover that the kinetic pressure displays a well-defined transition in a position that scales with the outlet size. This universal scaling explains why the free-fall arch picture has served as an approximation to describe the flow rate in the discharge of silos

Granular flow through an orifice: solving the free fall arch paradox

Several theoretical predictions of the mass flow rate of granular flows through outlets are based on the existence of a free fall arch region covering the silo outlet. Early in the nineteenth century, it was suggested that the particles crossing this region lose their kinetic energy and start to fall freely under their own weight. However, there is not conclusive evidence of this hypothetical region. We examined experimentally and numerically the micro-mechanical details of the particle flow through an orifice placed at the bottom of a silo. Remarkably, the contact stress monotonously decreases when the particles approach to the exit and it only vanishes just at the outlet. The behavior of this magnitude was practically independent of the size of orifice indicating that particle deformation, is insensible to the size of the aperture. Contrary, the behavior of the kinetic stress puts on evidence that the outlet size controls the propagation of the velocity fluctuations inside the silo. Examining this magnitude, we conclusively argue that indeed there is a well-defined transition region where the particle flow changes its nature. Above this region, the particle motion is completely correlated with the macroscopic flow. Our outcomes clarifies why the free fall arch picture has served as an approximation to describe the flow rate in the discharge of silos

Homogeneous cooling state of frictionless rod particles

In this work, we report some theoretical results on granular gases consisting of frictionless 3D rods with low energy dissipation. We performed simulations on the temporal evolution of soft spherocylinders, using a molecular dynamics algorithm implemented on GPU architecture. A homogeneous cooling state for rods, where the time dependence of the system’s intensive variables occurs only through a global granular temperature, has been identified. We have found a homogeneous cooling process, which is in excellent agreement with Haff’s law, when using an adequate rescaling time τ(ξ)τ(ξ), the value of which depends on the particle elongation ξξ and the restitution coefficient. It was further found that scaled particle velocity distributions remain approximately Gaussian regardless of the particle shape. Similarly to a system of ellipsoids, energy equipartition between rotational and translational degrees of freedom was better satisfied as one gets closer to the elastic limit. Taking advantage of scaling properties, we have numerically determined the general functionality of the magnitude Dc(ξ)Dc(ξ), which describes the efficiency of the energy interchange between rotational and translational degrees of freedom, as well as its dependence on particle shape. We have detected a range of particle elongations (1.5<ξ<4.01.5<ξ<4.0), where the average energy transfer between the rotational and translational degrees of freedom results greater for spherocylinders than for homogeneous ellipsoids with the same aspect ratio

Análisis numérico experimental de flujos granulares controlados

El objetivo de esta tesis doctoral se basa en describir numéricamente el comportamiento de sistemas granulares compuestos por partículas de diferente geometría, desde el caso esférico hasta otras formas m´as complejas. Se ha llevado a cabo la implementación de un algoritmo híbrido CPU-GPU del método de elementos discretos para el caso de medios granulares. Se han tenido en cuenta todos los grados de libertad presentes en el problema, incluyendo la implementación de un formalismo de quaterniones que permite modelar de forma eficiente las rotaciones en 3D. La interacción entre partículas se ha definido a partir de fuerzas de contacto constituidas por un término elástico y otro disipativo. La forma geométrica de las partículas juega un papel fundamental en la definición de la fuerza interacción entre dos granos. La implementación CPU-GPU incluye el modelado de partículas esféricas y no esféricas, tales como granos alargados o elipsoidales. Entre otras aplicaciones, este algoritmo ha permitido examinar flujos granulares de partículas esféricas, y se ha podido establecer la existencia de un estado de enfriamiento homogéneo para gases granulares constituidos por partículas no esféricas sin fricción. Por otro lado, observando muestras granulares fluyendo, se ha podido examinar tanto experimental como numéricamente las propiedades micro-mecánicas de ese flujo de partículas a través del orificio situado en la base de un silo. Este estudio ha permitido clarificar por qué, pese a las inconsistencias que supone, el tradicional concepto de arco de caída libre permite describir la forma funcional de la velocidad media de las partículas en las proximidades del orificio de salida

Análisis numérico experimental de flujos granulares controlados

El objetivo de esta tesis doctoral se basa en describir numéricamente el comportamiento de sistemas granulares compuestos por partículas de diferente geometría, desde el caso esférico hasta otras formas m´as complejas. Se ha llevado a cabo la implementación de un algoritmo híbrido CPU-GPU del método de elementos discretos para el caso de medios granulares. Se han tenido en cuenta todos los grados de libertad presentes en el problema, incluyendo la implementación de un formalismo de quaterniones que permite modelar de forma eficiente las rotaciones en 3D. La interacción entre partículas se ha definido a partir de fuerzas de contacto constituidas por un término elástico y otro disipativo. La forma geométrica de las partículas juega un papel fundamental en la definición de la fuerza interacción entre dos granos. La implementación CPU-GPU incluye el modelado de partículas esféricas y no esféricas, tales como granos alargados o elipsoidales. Entre otras aplicaciones, este algoritmo ha permitido examinar flujos granulares de partículas esféricas, y se ha podido establecer la existencia de un estado de enfriamiento homogéneo para gases granulares constituidos por partículas no esféricas sin fricción. Por otro lado, observando muestras granulares fluyendo, se ha podido examinar tanto experimental como numéricamente las propiedades micro-mecánicas de ese flujo de partículas a través del orificio situado en la base de un silo. Este estudio ha permitido clarificar por qué, pese a las inconsistencias que supone, el tradicional concepto de arco de caída libre permite describir la forma funcional de la velocidad media de las partículas en las proximidades del orificio de salida

Non-spherical granular flows down inclined chutes

In this work, we numerically examine the steady-state granular flow of 3D non-spherical particles down an inclined plane. We use a hybrid CPU/GPU implementation of the discrete element method of nonspherical elongated particles. Thus, a systematic study of the system response is performed varying the particle aspect ratio and the plane inclination. Similarly to the case of spheres, we observe three well-defined regimes: arresting flows, steady uniform flows and accelerating flows. Both steady and dynamic macroscopic fields are derived from microscopic data, by time-averaging and spatial smoothing (coarse-graining), including density, velocity, as well as the kinetic and contact stress tensors. The internal morphology of the flow was quantified exploring the solid fraction profiles and the particle orientation distribution. Furthermore, the system¿s characteristic time and length scales are investigated in detail. Our aim is to achieve a continuum mechanical description of granular flows composed of non-spherical particles based on the micromechanical details. Thus, to evaluate the influence of particle shape on the constitutive response in granular of those systems. However, to meet the proceeding¿s page restrictions here we will only discuss the dependence of some terms of the continuum averaged equations on the coarse-graining scale, specifically the case of the kinetic part of the stress tensor

Velocity and density scaling at the outlet of a silo and its role in the expression of the mass flow rate

The role of density and velocity profiles in the flow of particles through apertures has been recently put on evidence in a two-dimensional experiment (Phys. Rev. Lett. 108, 248001). For the whole range of apertures studied, both velocity and density profiles are selfsimilar and the obtained scaling functions allow to derive the relevant scales of the problem. Indeed, by means of the functionality obtained for these profiles, an exact expression for the mass flow rate was proposed. Such expression showed a perfect agreement with the experiential data. In this work, we generalize this study to the three dimensional case. We perform numerical simulations of a 3D silo in which the velocity and volume fraction profiles are determined. Both profiles shows that the scaling obtained for 2D can be generalized to the 3D case. Finally, the scaling of the mass flow rate with the outlet radius is discussed