DEM Simulations of Spheres Flowing Through a Hopper: Validation of Beverloo Law
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| Format: | Preprint |
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2025
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| _version_ | 1866908690959826944 |
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| author | da Silva, Leticia M. V. Rocha, Erlifas Moreira Gargarella, Piter Moreira, Pedro Augusto F. P. |
| author_facet | da Silva, Leticia M. V. Rocha, Erlifas Moreira Gargarella, Piter Moreira, Pedro Augusto F. P. |
| contents | This work presents a detailed investigation of the discharge behavior of spherical granular materials through a conical--cylindrical hopper using \emph{Discrete Element Method (DEM)} simulations. The aim is to assess the applicability limits of the empirical \emph{Beverloo law}. The system was modeled with a monodisperse particles whose mechanical properties correspond to the $Al_{95}Fe_2Cr_2Ti_1$ alloy, and interparticle contacts were described using the Hertz--Mindlin (no slip) model. The simulations systematically explored the influence of particle diameter ($d$) and bed height ($h$) on the resulting mass flow rate ($Q$).
The results reveal the coexistence of transient and steady-state discharge regimes. Good agreement with the Beverloo scaling was observed for relatively small diameter ratios ($D/d = 10$) and sufficiently large bed heights, where the flow stabilizes rapidly. For larger $D/d$ ratios, the discharge rate decays exponentially, indicating a breakdown of the constant-hydrostatic-pressure assumption underlying the Beverloo model. A dimensionless criterion for the validity of the Beverloo law is proposed as $Π_h = h/D > 2$, or equivalently $N = h/d > 20$. The quantitative agreement between DEM simulations and experimental measurements for polydisperse particle size distributions further validates the computational model and demonstrates its predictive capability for granular discharge in confined geometries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_03698 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DEM Simulations of Spheres Flowing Through a Hopper: Validation of Beverloo Law da Silva, Leticia M. V. Rocha, Erlifas Moreira Gargarella, Piter Moreira, Pedro Augusto F. P. Materials Science This work presents a detailed investigation of the discharge behavior of spherical granular materials through a conical--cylindrical hopper using \emph{Discrete Element Method (DEM)} simulations. The aim is to assess the applicability limits of the empirical \emph{Beverloo law}. The system was modeled with a monodisperse particles whose mechanical properties correspond to the $Al_{95}Fe_2Cr_2Ti_1$ alloy, and interparticle contacts were described using the Hertz--Mindlin (no slip) model. The simulations systematically explored the influence of particle diameter ($d$) and bed height ($h$) on the resulting mass flow rate ($Q$). The results reveal the coexistence of transient and steady-state discharge regimes. Good agreement with the Beverloo scaling was observed for relatively small diameter ratios ($D/d = 10$) and sufficiently large bed heights, where the flow stabilizes rapidly. For larger $D/d$ ratios, the discharge rate decays exponentially, indicating a breakdown of the constant-hydrostatic-pressure assumption underlying the Beverloo model. A dimensionless criterion for the validity of the Beverloo law is proposed as $Π_h = h/D > 2$, or equivalently $N = h/d > 20$. The quantitative agreement between DEM simulations and experimental measurements for polydisperse particle size distributions further validates the computational model and demonstrates its predictive capability for granular discharge in confined geometries. |
| title | DEM Simulations of Spheres Flowing Through a Hopper: Validation of Beverloo Law |
| topic | Materials Science |
| url | https://arxiv.org/abs/2512.03698 |