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TECHNICAL PAPERS

Computer Simulation of Rapid Granular Flow Through an Orifice

[+] Author and Article Information
Hojin Ahn

Department of Mechanical Engineering,  Yeditepe University, 34755 Kayışdağı/Istanbul, Turkey

J. Appl. Mech 74(1), 111-118 (Jan 18, 2006) (8 pages) doi:10.1115/1.2187529 History: Received October 13, 2005; Revised January 18, 2006

Rapid granular flow through an orifice (nozzle-shaped flow restrictor) located at the bottom of a vertical tube has been studied using three-dimensional direct computer simulation with the purpose of investigating (1) characteristics of rapid granular flows through the flow restrictor, (2) the choking condition of rapid flow at the orifice and thus conditions at which the maximum discharge rate takes place for the given orifice, and (3) a functional relationship between the discharge rate and flow quantities such as granular temperature and solid fraction. In the present simulation, where the frictional hard-sphere collision operator was employed, it was possible to obtain both rapid and slow (choked) flows through the orifice by controlling the number of particles in the system. The results show that the profile of granular temperature in the vicinity of the orifice plays an important role in determining the choking condition at the orifice. Flow appears to be choked when an adverse granular conduction occurs locally at the orifice in the direction opposite to the mean flow. On the other hand, flow is not choked when the fluctuation energy is conducted in the mean flow direction near the orifice. When flow is not choked, the discharge rate through the orifice increases with increasing solid fraction or normal stress. Once the flow becomes choked, however, the discharge rate decreases as the solid fraction or normal stress increases. Also for inelastic, rough particles, the discharge rate is found to be proportional to the granular temperature to the power of 1.5 and inversely proportional to the gravitational acceleration and the tube length.

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Copyright © 2007 by American Society of Mechanical Engineers
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Figures

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Figure 1

Schematic of gravitational flow through the flow restrictor

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Figure 2

Case of 2000 particles in the system with an orifice 10mm in radius. The location of zo∕d=3.3 is also shown with a dashed line.

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Figure 3

Case of 1600 particles in the system with an orifice 10mm in radius. The location of zo∕d=3.3 is also shown with a dashed line.

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Figure 4

Case of 500 particles in the system with an orifice 10mm in radius. The location of zo∕d=3.3 is also shown with a dashed line.

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Figure 5

Discharge rate from the orifice against the mean solid fraction upstream of the orifice for various orifice sizes

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Figure 6

Discharge rate from the orifice against the normal stress exerted on the orifice for various orifice sizes

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Figure 7

Profiles of granular temperature as a function of the distance from the exit for cases with different numbers of particles in the system with an orifice 10mm in radius. The location of zo∕d=3.3 is also shown with a dashed line.

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Figure 8

Non-dimensionalized normal stress versus solid fraction for the case of ep=0.95. Data from the current simulation results are compared with the result of Lun (14).

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Figure 9

The non-dimensionalized discharge rate against solid fraction for various orifice sizes

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Figure 10

Non-dimensionalized discharge rate as a function of solid fraction with various values for the gravitational acceleration and tube lengths

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