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October 13, 2004
Vermelding onderdeel organisatie
1
oe4625 Dredge Pumps and Slurry Transport
Vaclav Matousek
Dredge Pumps and Slurry Transport
October 13, 2004 2
6. SPECIAL SLURRY FLOW CONDITIONS
INCLINED FLOWS
UNSTEADY SOLIDS FLOWS
Dredge Pumps and Slurry Transport
October 13, 2004 3
INCLINED FLOWS
PRINCIPLES AND MODELING
Dredge Pumps and Slurry Transport
October 13, 2004 4
Inclined Flows
dx
-dP + dhρf
g
P1
P2
ρf
g dh
-dP = P1- P2
− ω
dh
total pressure differential
manometric pressure differential
hose filled with fluid (water)manometer
Dredge Pumps and Slurry Transport
October 13, 2004 5
dx
-dP + dhρf
g
P1
P2
ρf
g dh
-dP = P1- P2
− ω
dh
total pressure differential
manometric pressure differential
hose filled with fluid (water)manometer
A. Physical background:The total pressure gradient:
(P1-P2)/dx = -dP/dx over a pipe section of the length dx is composed of
Inclined Flows
the static pressure gradient: d(gh)/dx, giving the potentially reversible effect of elevation change on the total pressure gradient in a slurry flow of the density gaining the height hand
the pressure gradient due to friction: -dP/dx - d(gh)/dx that is the irrecoverable energy loss due to friction in inclined slurry flow over the pipe length dx.
Dredge Pumps and Slurry Transport
October 13, 2004 6
Inclined Flows: Worster-Denny Model
B. Construction of the model for Im:• An inclined flow is a transitional flow between a horizontal flow and a
vertical flow. • The hydrostatic effect: all particles in a pipe contribute to the static
slurry column; the manometric static head considered in the model = slurry column (in the pipe) – water column (in hoses of different. pressure transmitter).
• The frictional effect: the pressure drop due to friction is lower in inclined pipe than in horizontal pipe. The solids effect for inclined flow
, cos 1m f
m f
I Isolids effect in inclined pipesolids effect in horizon pipe I I
θ θ−
= = <−
Dredge Pumps and Slurry Transport
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Inclined Flows: Woster-Denny Model
horizontal flow
vert
ical
fl o
w
inclined flo
w
Dredge Pumps and Slurry Transport
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Inclined Flows: Woster-Denny Model
Im=If+(Im-If)
I m=
I f+
Cvd
( Ss-
1)
I m=I f+
(I m-I f)c
os Θ+C vd
(S s-1)si
n Θ
Dredge Pumps and Slurry Transport
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Inclined Flows: Worster-Denny Model
C. Discussion on the Worster-Denny model:• The model predicts the same frictional pressure losses in the ascending
and descending pipes of the same inclination angle [cos(0)=cos(-0)]. This means that the model expects the same solids distribution in both pipes. The assumption is correct only for non-stratified flows.
, cos 1m f
m f
I Isolids effect in inclined pipesolids effect in horizon pipe I I
θ θ−
= = <−
Dredge Pumps and Slurry Transport
October 13, 2004 10
Inclined Flows: Lab Tests
Dredge Pumps and Slurry Transport
October 13, 2004 11
Inclined Flows: Two-Layer Model
A. Physical background:• For layered inclined flows the two-layer model is much better predictive
tool than the empirical Worster-Denny model.
Dredge Pumps and Slurry Transport
October 13, 2004 12
Inclined Flows: Coarse slurry d=1.8 mm
Incl Angle: 0 deg
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October 13, 2004 13
Inclined Flows: Coarse slurry d=1.8 mm
Incl Angle: 16 deg
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October 13, 2004 14
Inclined Flows: Coarse slurry d=1.8 mm
Incl Angle: 25 deg
Dredge Pumps and Slurry Transport
October 13, 2004 15
Inclined Flows: Coarse slurry d=1.8 mm
Incl Angle: 35 deg
Dredge Pumps and Slurry Transport
October 13, 2004 16
Inclined Flows: Coarse slurry d=1.8 mm
Ascending pipe
Dredge Pumps and Slurry Transport
October 13, 2004 17
Inclined Flows: Coarse slurry d=1.8 mm
Descending pipe
Dredge Pumps and Slurry Transport
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Inclined Flows: Wilson-Tse Model
,0 2 ( 1)sm sm D sV V gD S∆= + −
Effect of inclination on the deposition
limit velocity. The empirical model based
on visual observations in a small pipe.
Vsm is the velocity from the demi-McDonald’s
diagram for horizontal flow.
Dredge Pumps and Slurry Transport