Transcript Le colmatage

Pressure drop of pulp flow in pipes
Similarity and master curve
S. Skali Lami
Lorraine University
LEMTA - Nancy (FR)
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
1
Introduction
•
•
•
•
•
•
•
Pulp Flow
Experimental set-up - electrochemical method
Experimental results
Theoretical approach
Results - Master curve - Criteria of flocculation
Prediction for different diameters and concentrations
Conclusions and perspectives
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
2
DH/L for (L=100m, f=80mm)
Pulp flow in pipes
10
1
0.1
0.05
0.5
V (m/s) 5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
3
DH/L for (L=100m, f=80mm)
Pulp flow in pipes
10
1
0.1
0.05
0.5
V (m/s)
5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
4
DH/L for (L=100m, f=80mm)
Pulp flow in pipes
10
1
0.1
0.05
0.5
5
V (m/s)
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
5
Pulp flow in pipes
DH/L for (L=100m, f=80mm)
10
1
0.1
0.05
0.5
5
V (m/s)
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
6
Pulp flow in pipes
F80mm
F44mm
DH/L for (L=100m, f=44mm)
F44
10
F80
F44
1
3%
1,20%
0,70%
Water
F80
0.1
0.05
0.5
V (m/s)
5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
7
Experimental set-up
electrochemical method
Min
Max
C (g/l)
1
20
V(f80) (m/s)
10-2
3.8
V(f44) (m/s)
2 10-2
8.6
Q (l/mn)
2
1200
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
8
Experimental set-up
electrochemical method
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
9
Experimental set-up
electrochemical method
Flow
Min
Max
C (g/l)
1
20
V(f80) (m/s)
10-2
3.8
V(f44) (m/s)
2 10-2
8.6
Q (l/mn)
2
1200
U
y
Micro-electrode
wall
I
 dU 
 w   
 dy  y 0
 w   w   w'
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
10
Pulp flow in pipe - Wall behavior
Flow
U
y
Micro-electrode
wall
P1
Pressure sensors
 dU 

   w
 dy  y 0
DP P1  P2 4 w


L
L
D
P2
1.5
DP
V
DP D
w 
 water  w
4 L
w
1
0.5
0
0
50
100
150
200
250
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
300
350
11
400
Results
10
10
10
10
10
2
p (N/m2)
F80
e au
-- Water
C o (g/l)
en g/l
Co
0,848
1,437
2,955
4,895
5,586
7,287
10,69
11,87
13,45
17,06
20
1
0
-1
-2
Turbulent
Laminaire
Laminar
10
-3
10 -1
10
0
10
1
10
2
V(cm/s)
10
3
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
12
Results
U
V
Plug flow
Wall
f 80
1
Wall
f 80
1
0,5
0
Drag reduction
U
V
0
V= 3,8 cm/s
Water
C = 0,4%
20
 w  water  w  water
V
d
0,5
r (mm)40
0
0
V= 160 cm/s
Water
C = 0,4%
20
r (mm) 40
d : liquid film
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC
SIG43 "Fibre suspension flows". Trondheim – October 2012
13
Results
5000
100
DR
(%)
80
4000
60
f
Increasing Drag
40
20
3000
C en (g/l)
0
0,848
-20
2000
-40
Drag
Reduction
-60
0
1000
2,99
5,59
100
200
300
10,68
400
13,45
20
0
-500
0
100
200
300
V(cm/s)
400
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
14
Results
50
RMS of Shear
Wall (%)
40
Water curve
100
30
80
f
20
Consistency
en (g/l)
10
60
0,848
0
0
40
20
40
60
80
1,437
100
2,995
Water curve
4,895
20
5,586
7,287
0
0
100
200
300
V (cm/s)
400
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
15
Results
f
C = 10,7 g/l
RMS of Shear
Wall (%)
10
2
 W (N/m2)
f
C=10,7g/l
10
40
10
1
0
Water
RMS Water
30
10
-1
10
0
10
1
10
2
V(cm/s)
20
Wall
Roughness
Turbulence
Network
10
0
100
200
300
V (cm/s)
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre
suspension flows". Trondheim – October 2012
400
16
Theoretical approach
1.5
Pseudo-turbulence in liquid film
DH/L for (L=100m, f=80mm)
Plug Flow
1
10
0.5
0
d
e
1
0
50
100
150
200
250
300
Wall
350
400
ddd
Liquid film
Network
0.1
0.05
0.5
V
Network
V (m/s) 5
pseudo-turbulence in liquid film → e
a
V+dV
Elastic deformation of network → G
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
17
Theoretical approach
 ij   ijv   ijt
e
 ijt    ui' u 'j
 du 

dy
 
du V
and

dy d
Wall
w
d
Liquid film
2
 w    ui' u 'j    2 
  ke
 
2 V
e
w   k R
d
2
Network
V
2
w
 R
2
Liquid film
d
2 2
d  w2
N  E  w   2
R G
R G
 
 w5   k 2 e R G 4V 2
ddd
Wall
N
Network
2
 
1
5
a
V+dV
2
2



V
 w  G ke R 
V 5

 G 
2
5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
18
Theoretical approach
 pulp
 
 G ke
 water
1
5
 V 
1
2

C

V
fpulp
R  G 
2


2
5
1
 C fwater  V 2
2
2
C fpulp
C fwater
ke 

R

2
5
 Re 
 32 
0.079  27 
 Sk 

27
20
 GD
With Sk 

10
1
0.1
0.05
0.5
V (m/s) 5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43
"Fibre suspension flows". Trondheim – October 2012
19
Theoretical approach
3
10
Cfpulp
Cfwater
2
10
1
10
f
C(g/l)
f
C(g/l)
20
20
17
17
13
13
11
11
1
Re32/27
Sk
-1
10
-2
-1
10
10
3
10
2
10
Cfpulp
Cfwater
1
1
2
10
10
f
C(g/l)
f
C(g/l)
7,29
7,29
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC5,59
SIG43 "Fibre
5,59
suspension flows". Trondheim – October 2012 4,89
4,89
20
Theoretical approach
1
Re32/27
Sk
-1
10
-2
-1
10
10
3
10
2
2
10
Cfpulp
Cfwater
10
10
1
1
1
10
f
C(g/l)
f
C(g/l)
7,29
5,59
4,89
7,29
5,59
4,89
2,95
2,95
1,44
1,44
1
-1
10
10-2
-1
10
1
10 1
2
Re32/27
Sk
10
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre
suspension flows". Trondheim – October 2012
10 3
21
Master curve
1000
C fpulp
Experimental data (1200)
C fwater
Master Curve
100
10
Max of drag
reduction
Dispersed
regime
1
End of plug regime
0.1
0.1
11.5
10 15
 Re 
 32 
80100  27 
 Sk 
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre
suspension flows". Trondheim – October 2012
22
Master curve and Similary
32/27
0,1 0,15 0,2 0,3 0,4 0,5 0,6 0,7 C15g/l
0,8 0,9 1
Re/Skf80mm
Cfpulp/Cfwater 428 260 176 101 67 51 39 32 27 23 20
3
4
5
6
7
8
9 10
Re/Sk32/27 1,2 1,5 2
Cfpulp/Cfwater 15 10 5,30 2,49 1,61 1,17 0,98 0,89 0,83 0,80 0,75
Re/Sk32/27 12 15 20 30 40 50 60 70 80 90 100
Cfpulp/Cfwater 0,68 0,64 0,65 0,67 0,72 0,75 0,81 0,89 0,95 0,99 1
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43
"Fibre suspension flows". Trondheim – October 2012
23
Principal conclusions
• Pulp Flow – investigations near the wall needed
• Theoretical approach for plug flow -> mater curve
applicable for all regimes
• Master curve -> Criteria of flocculation and drag
reduction
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43
"Fibre suspension flows". Trondheim – October 2012
24
Perspectives
Theoretical approach for plug flow : 1 Elasticity of the network
 

 dij

f



 ij = - -------p dV + µ  Ui,j + Uj,i +  ij
 V

 

V-V0


1

n  



f
,
1


 ij = ------  
ikxjnk dA + ikxjnk dA 


V 1
 A -A1
A

 0

1
f

 ij   ijf 1 1   ijf 2

COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
25
Relevant parameters
Network roughness
Network
Liquid film
Wall
V
Wall
Network
V
Numerical simulation
2.5
2
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
COST FP1005 ''Fibre Suspension Flow Modelling''- ERCOFTAC SIG43 "Fibre suspension flows".
Trondheim – October 2012
26