SLIDE 1
2012 APCYS
Reverse Ordering in Dynamical Reverse Ordering in Dynamical Two Two-
- Dimensional Hopper Flow
Dimensional Hopper Flow
Hao-Wen Dong and Chen-Chieh Ping
Reverse Ordering in Dynamical Reverse Ordering in Dynamical Two- - - PowerPoint PPT Presentation
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 Entry Order Entry Order Later Earlier Exit Order Exit Order
SLIDE 2
SLIDE 3
SLIDE 4
Entry Order Entry Order Exit Order Exit Order
Reverse Ordering Reverse Ordering
Earlier Later Earlier Later Earlier Later =30o =60o
SLIDE 5
Original Video Program Output
Tracker Program
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2000 1500 1000 500 1
Entry order
Ii
SLIDE 7
SLIDE 8
SLIDE 9
SLIDE 10
2000 1500 1000 500 1
Exit order
Oi
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2000 1500 1000 500 2000 1500 1000 500 1 2000 1000
- 1000
- 2000
2000 1500 1000 500 2000 1500 1000 500 1
Entry order Exit order Entry order Entry order – – Exit order Exit order Ii Oi Ii - Oi
SLIDE 12
i i i
I O
Entry Order Exit Order ID
Red: Advance Blue: Retard
i
2000 1000
- 1000
- 2000
SLIDE 13
2 1
1
N i i
f N
Degree of Degree of reverse ordering reverse ordering
1
More Reverse Less Reverse
SLIDE 14
Hopper angle / Reclining angle and
Angles (deg.)
20 40 60 80 0.0 0.2 0.4 0.6 0.8
Hopper angle Reclining angle
SLIDE 15
SLIDE 16
SLIDE 17
Central Flow Side-wall Flow Blue: Central Flow Yellow: Side-wall Flow
tc = 2.01 ts = 5.62 t = 3.61
- )
。
SLIDE 18
tc = 2.01 ts = 5.62 t = 3.61
- )
t = 3.61
- )
SLIDE 19
= 30o = 60o
t = 3.61 (sec.) t = 0.18 (sec.)
Not in real time.
ts = 5.62 tc = 2.01 ts = 3.80 tc = 3.62 = 0.53 = 0.12
□ □
SLIDE 20
Relation between and the time difference
1 2 3 4 0.0 0.2 0.4 0.6 0.8
Time difference t
=t1/2+
=0.26 =0.0090
SLIDE 21
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SLIDE 24
Relation between and avalanches
30 60 90 120 150 180 0.0 0.2 0.4 0.6 0.8
Number of grains undergoing surface avalanches n =0.0023 =0.14
=n+
SLIDE 25
2 1
1
N i i
f N
2000 1000
- 1000
- 2000
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Central Flow Side-wall Flow Blue: Central Flow Yellow: Side-wall Flow
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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
- f granular flows in a 2D channel. Phys. Rev. Lett.,
- 91. pp. 204301.
SLIDE 29
2000 1500 1000 500 2000 1000
- 1000
- 2000
2000 1500 1000 500
Entry order Exit order Entry order Entry order – – Exit order Exit order Ii Oi Ii - Oi