Reverse Ordering in Dynamical Reverse Ordering in Dynamical Two- - PowerPoint PPT Presentation

2012 APCYS Reverse Ordering in Dynamical Reverse Ordering in Dynamical Two- -Dimensional Hopper Flow Dimensional Hopper Flow Two Hao-Wen Dong and Chen-Chieh Ping

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Entry Order Entry Order Later Earlier Exit Order Exit Order  =30 o Earlier Later  =60 o Earlier Later Reverse Ordering Reverse Ordering

Tracker Program Original Video Program Output

2000 I i Entry order 1500 1000 500 1

2000 O i Exit order 1500 1000 500 1

2000 2000 2000 2000 O i Entry order I i Exit order 1500 1500 1500 1500 1000 1000 1000 1000 500 500 500 500 1 0 0 1 2000 Entry order – – Exit order Exit order I i - O i Entry order 1000 0 -1000 -2000

   2000  i I O i i i ID Entry Order Exit Order 1000 0 -1000 Red: Advance Blue: Retard -2000

N  1   2 Degree of Degree of   i reverse ordering f N reverse ordering  i 1 More Reverse Less Reverse 0 1  

Hopper angle / Reclining angle and  0.8 0.6  0.4 0.2 Hopper angle  Reclining angle  0.0 0 20 40 60 80 Angles (deg.)

Blue: Central Flow Central Flow Yellow: Side-wall Flow 。 t s = 5.62 -) t c = 2.01 Side-wall Flow  t = 3.61

t s = 5.62 -) -) t c = 2.01  t = 3.61  t = 3.61

 = 60 o  = 30 o □ □ t s = 3.80 t c = 3.62 t s = 5.62 t c = 2.01  t = 3.61 (sec.)  t = 0.18 (sec.)  = 0.53  = 0.12 Not in real time.

Relation between  and the time difference 0.8 0.6  0.4  =  t 1/2 +  0.2  =0.26  =0.0090 0.0 0 1 2 3 4 Time difference  t

Relation between  and avalanches 0.8 0.6  0.4  =  n +   =0.0023 0.2  =0.14 0.0 0 30 60 90 120 150 180 Number of grains undergoing surface avalanches n

2000 N  1   2   i f N  i 1 1000 0 -1000 -2000

Blue: Central Flow Central Flow Yellow: Side-wall Flow Side-wall Flow

References [1] T. Nguyen, C. Brennen, R. Sabersky (1980). Funnel Flow in Hoppers. Journal of Applied Mechanics, 102 (4). pp. 729-735. [2] M. Hou, W. Chen, T. Zhang, K. Lu, C. K. Chan (2003). Global nature of dilute-to-dense transition of granular flows in a 2D channel. Phys. Rev. Lett., 91. pp. 204301.

2000 2000 O i Entry order I i Exit order 1500 1500 1000 1000 500 500 0 0 2000 Entry order – – Exit order Exit order I i - O i Entry order 1000 0 -1000 -2000