6. Special slurry flow conditions

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


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INCLINED FLOWS

PRINCIPLES AND MODELING


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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


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.


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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−

= = <−


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Inclined Flows: Woster-Denny Model

horizontal flow

vert

ical

fl o

w

inclined flo

w


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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


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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−

= = <−


October 13, 2004 10

Inclined Flows: Lab Tests


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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.


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Inclined Flows: Coarse slurry d=1.8 mm

Incl Angle: 0 deg


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Incl Angle: 16 deg


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Incl Angle: 25 deg


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Incl Angle: 35 deg


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Ascending pipe


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Descending pipe


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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.


6. Special slurry flow conditions

Technology