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Research Papers

Wave Propagation in Rapid Granular Flows

[+] Author and Article Information
Hojin Ahn

Mem. ASME
Faculty of Engineering & Architecture,
Yeditepe University,
Kayışdağı/Istanbul, Turkey
e-mail: erdeman@yeditepe.edu.tr

Manuscript received May 5, 2012; final manuscript received December 7, 2012; accepted manuscript posted January 31, 2013; published online July 12, 2013. Assoc. Editor: Vikram Deshpande.

J. Appl. Mech 80(5), 051008 (Jul 12, 2013) (7 pages) Paper No: JAM-12-1183; doi: 10.1115/1.4023538 History: Received May 05, 2012; Revised December 07, 2012; Accepted January 31, 2013

One-dimensional wave propagation in granular flow has been investigated using a three-dimensional discrete element model (DEM). Cohesionless, dry, smooth, elastic, hard spheres are randomly distributed in a cylinder-piston system with initial granular temperature and solid fraction. Upon a sudden motion of the piston, subsequent wave propagation in granular materials between two ends of the cylinder is numerically simulated. The simulation results of wave speed normalized by the square root of granular temperature are found to be well correlated as a function of solid fraction. Comparison with several analytical works in the literature shows that the simulated wave speed is in good agreement with the wave speed calculated at the isentropic condition but is higher than that at the constant granular temperature condition. Finally the simulation result is employed to describe shock waves observed in the literature. It has been found that, when particles rapidly flow through an orifice, a shock is formed very near the location of the maximum granular temperature. It has also been observed that a shock can be formed even when the flow does not appear to be choked due to its low density upstream of the orifice.

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References

Figures

Grahic Jump Location
Fig. 1

Measurements of granular temperature and solid fraction at the midpoint between two ends of the cylinder as a function of time. Case of zw = 3 mm and tw = 3 ms.

Grahic Jump Location
Fig. 2

Time moving averages of granular temperature at the midpoint between two ends of the cylinder and of normal stress at the stationary end of the cylinder. Time moving average taken over the interval of 10 ms. Case of the same simulation of Fig. 1.

Grahic Jump Location
Fig. 3

Wave speed versus granular temperature for solid fractions: v = 0.2, ▴; v = 0.3, ▪; v = 0.4, •; v = 0.5, ▾

Grahic Jump Location
Fig. 4

Dimensionless wave speed, c/T0.5, as a function of solid fraction. •, the simulation results; —, the curve fitting of the simulation results by c/T0.5=3/(1-v/vM)1.5 with vM = 0.64.

Grahic Jump Location
Fig. 5

Dimensionless wave speed, c/T0.5, as a function of solid fraction. Comparison of the present simulation with Savage [7], and Ocone and Astarita [10], the model at constant granular temperature condition, and the simple model (Eq. (9)) with vM = 0.64.

Grahic Jump Location
Fig. 6

Ratio of (f/v)2 to df/dv in Eqs. (2) and (3) as a function of solid fraction

Grahic Jump Location
Fig. 7

Case of 2000 particles in the system with an orifice 10 mm in radius from Ahn [15]. The location of z/d = 3.3 is also shown with a dashed line. The wave speed (solid line) is plotted together with the mean particle velocity (dashed line).

Grahic Jump Location
Fig. 8

Case of 1600 particles in the system with an orifice 10 mm in radius from Ahn [15]. The location of z/d = 3.3 is also shown with a dashed line. The wave speed (solid line) is plotted together with the mean particle velocity (dashed line).

Grahic Jump Location
Fig. 9

Case of 500 particles in the system with an orifice 10 mm in radius from Ahn [15]. The location of z/d = 3.3 is also shown with a dashed line. The wave speed (solid line) is plotted together with the mean particle velocity (dashed line).

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