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Granular flow in a wedge-shaped hopper with smooth walls and radial gravity: Theory and simulations

Afroz F. Momin and Devang V. Khakhar*

  • *Contact author: khakhar@iitb.ac.in
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Phys. Rev. Fluids 10, 034303 – Published 31 March, 2025

DOI: https://doi.org/10.1103/PhysRevFluids.10.034303

Abstract

Hoppers with inclined walls are commonly used in industrial applications to facilitate the gravity-driven discharge of materials through a bottom outlet. The simplest form of this flow configuration, a wedge-shaped, quasi-two-dimensional hopper with frictionless walls and a gravitational force radially directed toward the apex of the wedge, is considered. A closed form solution of the flow was given in the classical work of Savage [Br. J. Appl. Phys. 16, 1885 (1965)]. Discrete element method (DEM) simulations are performed to analyze the stress and velocity fields for granular flow in a close replica of the system considered in the theory. Results are presented for varying hopper parameters (orifice size and wedge angle) and particle properties (particle diameter, friction coefficient, and stiffness). A detailed comparison of the computational results with the predictions of the Savage model indicates that the model predicts the stress accurately, except near the exit, but predicts velocities significantly higher than the computational values. The deviation is due to the assumption that the stress at the exit is zero, which is contrary to the significant exit stress obtained from computations. The flow is purely extensional and is found to follow the μ−I rheology, which includes frictional and collisional stresses. A flow model based on the μ−I rheology is presented, and model predictions of the stress and solid fraction profiles closely match the computational results. Correlations for the velocity and the mass flow rate, in terms of the system parameters, are obtained from the simulation data.

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Phys. Rev. Fluids 10, 034303– Published 31 March, 2025
  • Received 12 June 2024
  • Accepted 5 March 2025
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