116
2 Experiments in Pebble Flows
arching particles show a higher correlation with the mean velocity of total particles. It could be predicted that not only the blocking arches but also bulk arches
should be responsible for the velocity fluctuations. In other words, the bulk arching
dynamics dominate the velocity fluctuations in the particle packing.
Based on the experimental measurements and analyses of velocity characteristics
in the dense flow of a silo bed from both macroscopic and microscopic perspectives, two parameters, i.e., the correlation time τ c and a new intermittency index C 2
are proposed, and how they affect the whole flow on the streamlines are analyzed.
Besides, the relationship between autocorrelation and intermittency is analyzed to
characterize the three flow patterns. The brief conclusion and summary are given as
follows:
• The granular motion correlations in the slow and dense flow of a silo bed present
well-defined periodic and oscillatory tails. The autocorrelation time τ c decreases
with the reduction of height, following a power-law regression (τ c ∼ H
α ) with
height. The radial distribution of autocorrelation time indicates a higher correlation
at larger radial coordinates.
• A new intermittency index C 2 is proposed based on the multifractal analysis with
the WTMM method to measure the intermittency of particle bulk (cluster) motion
events. From the central to the near-wall region, distinct cluster motion events
become more visible and their intervals become longer.
• The relationship among the autocorrelation, intermittency, and shear function is
discussed and three flow patterns are characterized. The central region (P1) is
characterized by lower intermittencies and shear rates; the near-wall region (P3)
displays higher intermittency and lower shear rate; in addition, in the P2 region,
autocorrelation and intermittency are positively correlated.
References
1. Yang, X.T., W.P. Hu, S.Y. Jiang, K.K.L. Wong, and J.Y. Tu. 2012. Mechanism analysis of
quasi-static dense pebble flow in pebble bed reactor using phenomenological approach. Nuclear
Engineering and Design 250: 247–259.
2. Medina, A., J.A. Córdova, E. Luna, and C. Treviño. 1998. Velocity field measurements in
granular gravity flow in a near 2d silo. Physics Letters A 250 (1): 111–116.
3. Jaehyuk Choi, Arshad Kudrolli, Rosales Rodolfo R, and Bazant Martin Z. Diffusion and mixing
in gravity-driven dense granular flows. Physical Review Letters, 92(17):174301, 2004.
4. Jia, Xinlong, Xingtuan Yang, Yu. Nan Gui, Jiyuan Tu Li, and Shengyao Jiang. 2015. Experimental and numerical study of stagnant zones in pebble bed. Science & Technology of Nuclear
Installations 2014 (8–10): 1–10.
5. Rycroft, C.H., G.S. Grest, J.W. Landry, and M.Z. Bazant. 2006. Analysis of granular flow in
a pebble-bed nuclear reactor. Physical Review E Statistical Nonlinear & Soft Matter Physics
74: 021306.
6. Kadak A.C. and Bazant M.Z. Pebble flow experiments for pebble-bed reactors. In Proceedings
of the Second International Topical Meeting on High Temperature Reactor Technology, Beijing,
China, 2004.
2 Experiments in Pebble Flows
arching particles show a higher correlation with the mean velocity of total particles. It could be predicted that not only the blocking arches but also bulk arches
should be responsible for the velocity fluctuations. In other words, the bulk arching
dynamics dominate the velocity fluctuations in the particle packing.
Based on the experimental measurements and analyses of velocity characteristics
in the dense flow of a silo bed from both macroscopic and microscopic perspectives, two parameters, i.e., the correlation time τ c and a new intermittency index C 2
are proposed, and how they affect the whole flow on the streamlines are analyzed.
Besides, the relationship between autocorrelation and intermittency is analyzed to
characterize the three flow patterns. The brief conclusion and summary are given as
follows:
• The granular motion correlations in the slow and dense flow of a silo bed present
well-defined periodic and oscillatory tails. The autocorrelation time τ c decreases
with the reduction of height, following a power-law regression (τ c ∼ H
α ) with
height. The radial distribution of autocorrelation time indicates a higher correlation
at larger radial coordinates.
• A new intermittency index C 2 is proposed based on the multifractal analysis with
the WTMM method to measure the intermittency of particle bulk (cluster) motion
events. From the central to the near-wall region, distinct cluster motion events
become more visible and their intervals become longer.
• The relationship among the autocorrelation, intermittency, and shear function is
discussed and three flow patterns are characterized. The central region (P1) is
characterized by lower intermittencies and shear rates; the near-wall region (P3)
displays higher intermittency and lower shear rate; in addition, in the P2 region,
autocorrelation and intermittency are positively correlated.
References
1. Yang, X.T., W.P. Hu, S.Y. Jiang, K.K.L. Wong, and J.Y. Tu. 2012. Mechanism analysis of
quasi-static dense pebble flow in pebble bed reactor using phenomenological approach. Nuclear
Engineering and Design 250: 247–259.
2. Medina, A., J.A. Córdova, E. Luna, and C. Treviño. 1998. Velocity field measurements in
granular gravity flow in a near 2d silo. Physics Letters A 250 (1): 111–116.
3. Jaehyuk Choi, Arshad Kudrolli, Rosales Rodolfo R, and Bazant Martin Z. Diffusion and mixing
in gravity-driven dense granular flows. Physical Review Letters, 92(17):174301, 2004.
4. Jia, Xinlong, Xingtuan Yang, Yu. Nan Gui, Jiyuan Tu Li, and Shengyao Jiang. 2015. Experimental and numerical study of stagnant zones in pebble bed. Science & Technology of Nuclear
Installations 2014 (8–10): 1–10.
5. Rycroft, C.H., G.S. Grest, J.W. Landry, and M.Z. Bazant. 2006. Analysis of granular flow in
a pebble-bed nuclear reactor. Physical Review E Statistical Nonlinear & Soft Matter Physics
74: 021306.
6. Kadak A.C. and Bazant M.Z. Pebble flow experiments for pebble-bed reactors. In Proceedings
of the Second International Topical Meeting on High Temperature Reactor Technology, Beijing,
China, 2004.