Discharge of elongated grains in silos under rotational shear

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate Q by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate Q on orifice diameter D, the spheres and rods show two distinct trends. For rods, in the small-aperture limit Q seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall

Particle flow rate in silos under rotational shear

Very recently, To et al. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate Q as a function of the frequency of rotation f . Namely, we find that for small outlet diameters D the flow rate increased with f , while for larger D a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure (pk) and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that (pk) changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear

Discharge of elongated grains from silo with rotating bottom

We study the flow of elongated grains (wooden pegs of length L = 20 mm with circular cross section of diameter d(c) = 6 and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter D. In the small orifice range (D/d approximate to 15 degrees to the motion of the bottom

The role of the particle aspect ratio in the discharge of a narrow silo

The time evolution of silo discharge is investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, we confirm the widely known typical behavior with constant discharge rate (except for initial and final transients). For elongated particles with aspect ratios between 2 < L/d < 6.1, we find a peculiar flow rate increase for larger orifices before the end of the discharge process. While the flow field is practically homogeneous for spherical grains, it has strong gradients for elongated particles with a fast-flowing region in the middle of the silo surrounded by a stagnant zone. For large enough orifice sizes, the flow rate increase is connected with a suppression of the stagnant zone, resulting in an increase in both the packing fraction and flow velocity near the silo outlet within a certain parameter range

The role of the particle aspect ratio in the discharge of a narrow silo

The time evolution of silo discharge is investigated for different granular materials made of spherical or elongated grains in laboratory experiments and with discrete element model (DEM) calculations. For spherical grains, we confirm the widely known typical behavior with constant discharge rate (except for initial and final transients). For elongated particles with aspect ratios between 2 < L/d < 6.1, we find a peculiar flow rate increase for larger orifices before the end of the discharge process. While the flow field is practically homogeneous for spherical grains, it has strong gradients for elongated particles with a fast-flowing region in the middle of the silo surrounded by a stagnant zone. For large enough orifice sizes, the flow rate increase is connected with a suppression of the stagnant zone, resulting in an increase in both the packing fraction and flow velocity near the silo outlet within a certain parameter range

Particle flows in silos, significance of particle shape, stiffness and friction

Granular flows are frequently observed in nature and appear in many industrial processes as well. In this numerical work the focus is mainly directed at the understanding of how the change of different grain properties, such as shape, friction and stiffness, influences the flow out of a silo. However, the heating dynamics of a granular gas of rods is also analyzed. In all these scenarios, the simulations are paired with experiments to calibrate and validate the results. The numerical analysis indicated that the discharge of soft, low-friction grains from a container exhibits a height-dependent flow rate, which is not usual for granular media. The systematic study mapped the parameter space of particle friction and stiffness, exploring the system’s macroscopic response in detail. Moreover, the examination of the coarse-graining fields helped us to explain when and why the flow rate depends on the column height. The answers include the material response to pressure gradients, but also the way stress is transmitted in the system. The outcomes allowed us to propose simple theoretical arguments, connecting the macroscopic flow rate with the pressure gradient at the orifice. As a result, we have come up with a well-reasoned explanation for the height-dependent discharge flow rate, shown experimentally and numerically by soft low-frictional grains. Our numerical investigation of a 2D silo flow of mixtures of soft and hard grains reproduced the high impact that even 5% of hard frictional grains have on the flow of an ensemble of low-friction, soft particles. Numerical results signaled the importance of the friction between the two types of grains. When the frictional hard grains are added to the soft grains, the flow gets slower, clogging becomes more frequent, and the force measured on the bottom plate decreases. Moreover, we obtained that these effects are enhanced when the interspecies friction is increased. The introduction of a rotational shear through the rotation of the flat silo bottom leads to a surprising effect on the discharge of rods: the flow rate is reduced significantly, by up to 70%. Our simulations and the application of the coarse-graining methods reveal the underlying reasons for this observation. The exit velocity of particles is the main contributing factor to this drop, which is in correlation with the vertical orientation of the grains. Our numerical tool allowed the exploration of the dependence of flow rate on the orifice size . In the limit of large orifices, the classical power-law correlation ∼ 5/2 was reproduced. For small apertures, however, we obtained a power-law relation but with a notably larger exponent. Furthermore, the size of the so-called free fall arch region is also found to decrease due to the rotation. Finally, granular gas made up of rods and heated by the walls has been studied numerically. Our study provides additional insight into the process for instance by describing the system behavior in the non-symmetrically heated direction, which was not accessible experimentally. The velocity distributions of the particles are examined and found to be well-fitted by stretched exponential distributions, in agreement with previous experiments. Moreover, in the experimentally not accessible direction, we obtained asymmetrical distribution tails. Additionally, the collapsing of the velocity distributions lead us to conclude that the energy scales with the square of the characteristic velocity of the wall.Los flujos granulares se observan con frecuencia en procesos naturales e industriales. El enfoque de este trabajo se dirige a la comprensión de cómo el cambio de las diferentes propiedades de los granos (forma, fricción y rigidez) influye en el caudal de los silos. Complementariamente, se analiza la dinámica del calentamiento de un gas granular de partículas alargadas. En todos estos escenarios, las simulaciones se combinan con experimentos para calibrar y validar las herramientas numéricas empleadas. En primer lugar, el análisis numérico de la descarga de granos blandos-lisos de un contenedor indicó el desarrollo de un caudal másico dependiente de la altura, lo cual no es habitual en los medios granulares. Nuestro estudio sistemático examinó el espacio de parámetros de fricción y rigidez de las partículas, explorando detalladamente la respuesta macroscópica de este sistema. Complementariamente, el análisis de los campos medios nos ayudó a explicar cuándo y por qué el caudal depende de la altura de la columna. La explicación general incluye: la respuesta del material a los gradientes de presión en el orificio de salida, pero también la forma en que se transmiten los esfuerzos en el sistema. Los resultados nos permitieron proponer argumentos teóricos simples, conectando el caudal macroscópico con el gradiente de presión en el orificio. Como resultado, hemos encontrado una explicación bien razonada de los valores de caudal dependiente de la altura, lo cual ha sido encontrado, experimental y numéricamente, para granos blandos de baja fricción. En segundo lugar, realizamos una investigación numérica del flujo en un silo bidimensional, usando una de mezclas de granos blandos-lisos y duros-rugosos. Partiendo de un sistema homogéneo de granos blandos-lisos, nuestros resultados numéricos reproducen el alto impacto que produce la inclusión de solo un 5% de los granos duros, en el flujo del conjunto de partículas. Además, resaltaron la importancia de la fricción entre granos de diferente tipo, en le desarrollo de este proceso. Cuando los granos durosrugosos son agregados al sistema, el flujo se vuelve más lento, los atascos resultan más frecuentes y la fuerza medida sobre el fondo disminuye. Además, resulta que estos efectos se potencian cuando aumenta la fricción entre especies. También estudiamos, sistemáticamente, la introducción de esfuerzos cortantes, imponiendo la rotación del fondo de un silo plano. Estas condiciones de contorno producen un efecto sorprendente en la descarga de partículas alargadas: el caudal se reduce significativamente, hasta en un 70%. Nuestras simulaciones y la aplicación de los métodos de promediación espacio-temporales revelan las razones subyacentes de esta observación. La velocidad de salida de las partículas es el principal factor que contribuye a esta caída, lo cual correlaciona con la orientación vertical de los granos. Nuestra herramienta numérica permitió explorar la dependencia del caudal del tamaño del orificio . En el límite de los orificios grandes, se reprodujo la clásica correlación de ley de potencia ∼ 5/2. Sin embargo, para aberturas pequeñas obtuvimos una ley de potencia pero con un exponente notablemente mayor. Además, también se encontró que el tamaño de la región denominada ”arco de caída libre” disminuye debido a la rotación. Finalmente, se ha estudiado numéricamente un gas granular agitado formado por partículas alargadas. Este sistema fue estudiado experimentalmente con anterioridad, y nuestro estudio proporciona información adicional sobre el proceso. Por ejemplo, describiendo el comportamiento del sistema en la dirección de calentamiento asimétrico, al que no se accedió experimentalmente. Se estudiaron las distribuciones de velocidad de las partículas, encontrando que ajustan muy bien con distribuciones exponenciales con colas largas, lo cual está en acuerdo con experimentos previos. Además, en la dirección no accesible experimentalmente, obtuvimos colas asimétricas. El colapso de las distribuciones de velocidad nos lleva a concluir que la energía media del sistema escala con el cuadrado de la velocidad característica de la pared

Particle flows in silos, significance of particle shape, stiffness and friction

Granular flows are frequently observed in nature and appear in many industrial processes as well. In this numerical work the focus is mainly directed at the understanding of how the change of different grain properties, such as shape, friction and stiffness, influences the flow out of a silo. However, the heating dynamics of a granular gas of rods is also analyzed. In all these scenarios, the simulations are paired with experiments to calibrate and validate the results. The numerical analysis indicated that the discharge of soft, low-friction grains from a container exhibits a height-dependent flow rate, which is not usual for granular media. The systematic study mapped the parameter space of particle friction and stiffness, exploring the system’s macroscopic response in detail. Moreover, the examination of the coarse-graining fields helped us to explain when and why the flow rate depends on the column height. The answers include the material response to pressure gradients, but also the way stress is transmitted in the system. The outcomes allowed us to propose simple theoretical arguments, connecting the macroscopic flow rate with the pressure gradient at the orifice. As a result, we have come up with a well-reasoned explanation for the height-dependent discharge flow rate, shown experimentally and numerically by soft low-frictional grains. Our numerical investigation of a 2D silo flow of mixtures of soft and hard grains reproduced the high impact that even 5% of hard frictional grains have on the flow of an ensemble of low-friction, soft particles. Numerical results signaled the importance of the friction between the two types of grains. When the frictional hard grains are added to the soft grains, the flow gets slower, clogging becomes more frequent, and the force measured on the bottom plate decreases. Moreover, we obtained that these effects are enhanced when the interspecies friction is increased. The introduction of a rotational shear through the rotation of the flat silo bottom leads to a surprising effect on the discharge of rods: the flow rate is reduced significantly, by up to 70%. Our simulations and the application of the coarse-graining methods reveal the underlying reasons for this observation. The exit velocity of particles is the main contributing factor to this drop, which is in correlation with the vertical orientation of the grains. Our numerical tool allowed the exploration of the dependence of flow rate on the orifice size . In the limit of large orifices, the classical power-law correlation ∼ 5/2 was reproduced. For small apertures, however, we obtained a power-law relation but with a notably larger exponent. Furthermore, the size of the so-called free fall arch region is also found to decrease due to the rotation. Finally, granular gas made up of rods and heated by the walls has been studied numerically. Our study provides additional insight into the process for instance by describing the system behavior in the non-symmetrically heated direction, which was not accessible experimentally. The velocity distributions of the particles are examined and found to be well-fitted by stretched exponential distributions, in agreement with previous experiments. Moreover, in the experimentally not accessible direction, we obtained asymmetrical distribution tails. Additionally, the collapsing of the velocity distributions lead us to conclude that the energy scales with the square of the characteristic velocity of the wall.Los flujos granulares se observan con frecuencia en procesos naturales e industriales. El enfoque de este trabajo se dirige a la comprensión de cómo el cambio de las diferentes propiedades de los granos (forma, fricción y rigidez) influye en el caudal de los silos. Complementariamente, se analiza la dinámica del calentamiento de un gas granular de partículas alargadas. En todos estos escenarios, las simulaciones se combinan con experimentos para calibrar y validar las herramientas numéricas empleadas. En primer lugar, el análisis numérico de la descarga de granos blandos-lisos de un contenedor indicó el desarrollo de un caudal másico dependiente de la altura, lo cual no es habitual en los medios granulares. Nuestro estudio sistemático examinó el espacio de parámetros de fricción y rigidez de las partículas, explorando detalladamente la respuesta macroscópica de este sistema. Complementariamente, el análisis de los campos medios nos ayudó a explicar cuándo y por qué el caudal depende de la altura de la columna. La explicación general incluye: la respuesta del material a los gradientes de presión en el orificio de salida, pero también la forma en que se transmiten los esfuerzos en el sistema. Los resultados nos permitieron proponer argumentos teóricos simples, conectando el caudal macroscópico con el gradiente de presión en el orificio. Como resultado, hemos encontrado una explicación bien razonada de los valores de caudal dependiente de la altura, lo cual ha sido encontrado, experimental y numéricamente, para granos blandos de baja fricción. En segundo lugar, realizamos una investigación numérica del flujo en un silo bidimensional, usando una de mezclas de granos blandos-lisos y duros-rugosos. Partiendo de un sistema homogéneo de granos blandos-lisos, nuestros resultados numéricos reproducen el alto impacto que produce la inclusión de solo un 5% de los granos duros, en el flujo del conjunto de partículas. Además, resaltaron la importancia de la fricción entre granos de diferente tipo, en le desarrollo de este proceso. Cuando los granos durosrugosos son agregados al sistema, el flujo se vuelve más lento, los atascos resultan más frecuentes y la fuerza medida sobre el fondo disminuye. Además, resulta que estos efectos se potencian cuando aumenta la fricción entre especies. También estudiamos, sistemáticamente, la introducción de esfuerzos cortantes, imponiendo la rotación del fondo de un silo plano. Estas condiciones de contorno producen un efecto sorprendente en la descarga de partículas alargadas: el caudal se reduce significativamente, hasta en un 70%. Nuestras simulaciones y la aplicación de los métodos de promediación espacio-temporales revelan las razones subyacentes de esta observación. La velocidad de salida de las partículas es el principal factor que contribuye a esta caída, lo cual correlaciona con la orientación vertical de los granos. Nuestra herramienta numérica permitió explorar la dependencia del caudal del tamaño del orificio . En el límite de los orificios grandes, se reprodujo la clásica correlación de ley de potencia ∼ 5/2. Sin embargo, para aberturas pequeñas obtuvimos una ley de potencia pero con un exponente notablemente mayor. Además, también se encontró que el tamaño de la región denominada ”arco de caída libre” disminuye debido a la rotación. Finalmente, se ha estudiado numéricamente un gas granular agitado formado por partículas alargadas. Este sistema fue estudiado experimentalmente con anterioridad, y nuestro estudio proporciona información adicional sobre el proceso. Por ejemplo, describiendo el comportamiento del sistema en la dirección de calentamiento asimétrico, al que no se accedió experimentalmente. Se estudiaron las distribuciones de velocidad de las partículas, encontrando que ajustan muy bien con distribuciones exponenciales con colas largas, lo cual está en acuerdo con experimentos previos. Además, en la dirección no accesible experimentalmente, obtuvimos colas asimétricas. El colapso de las distribuciones de velocidad nos lleva a concluir que la energía media del sistema escala con el cuadrado de la velocidad característica de la pared

Discharge of elongated grains in silos under rotational shear

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate Q by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate Q on orifice diameter D, the spheres and rods show two distinct trends. For rods, in the small-aperture limit Q seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall

Particle flow rate in silos under rotational shear

Very recently, To et al. have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall [Phys. Rev. E 100, 012906 (2019)]. Here we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate Q as a function of the frequency of rotation f . Namely, we find that for small outlet diameters D the flow rate increased with f , while for larger D a nonmonotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors, macroscopic velocity and density fields, we obtain that the nonmonotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure (pk) and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that (pk) changes nonmonotonically, which might explain the nonmonotonic behavior of Q when varying the rotational shear

Discharge of elongated grains from silo with rotating bottom

We study the flow of elongated grains (wooden pegs of length L = 20 mm with circular cross section of diameter d(c) = 6 and 8 mm) from a silo with a rotating bottom and a circular orifice of diameter D. In the small orifice range (D/d approximate to 15 degrees to the motion of the bottom