6. Special slurry flow conditions

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6. Special slurry flow conditions

  1. 1. oe4625 Dredge Pumps and Slurry Transport Vaclav Matousek October 13, 2004 1 Dredge Pumps and Slurry Transport Vermelding onderdeel organisatie
  2. 2. 6. SPECIAL SLURRY FLOW CONDITIONS INCLINED FLOWS UNSTEADY SOLIDS FLOWS October 13, 2004 2 Dredge Pumps and Slurry Transport
  3. 3. INCLINED FLOWS PRINCIPLES AND MODELINGOctober 13, 2004 3Dredge Pumps and Slurry Transport
  4. 4. Inclined Flows P1 −ω dx dh ρ g dh f -dP = P1 - P2 total pressure differential P2 manometer hose filled with fluid (water) -dP + dh ρ g f manometric pressure differentialOctober 13, 2004 4Dredge Pumps and Slurry Transport
  5. 5. Inclined Flows P1 −ω dx dhA. Physical background:The total pressure gradient: ρ g dh f (P1-P2)/dx = -dP/dx over a pipe -dP = P1 - P2 total pressure differential section of the length dx is composed P2 manometer hose filled with fluid (water) of -dP + dh ρ g f manometric pressure differentialthe 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 h andthe 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. October 13, 2004 5 Dredge Pumps and Slurry Transport
  6. 6. Inclined Flows: Worster-Denny ModelB. 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 solids effect in inclined pipe I m ,θ − I f = = cos θ < 1 solids effect in horizon pipe Im − I f October 13, 2004 6 Dredge Pumps and Slurry Transport
  7. 7. Inclined Flows: Woster-Denny Model vertical flow w d flo ne incli horizontal flowOctober 13, 2004 7Dredge Pumps and Slurry Transport
  8. 8. Inclined Flows: Woster-Denny Model inΘ )s -1 Im=If+Cvd(Ss-1) (S s + C vd o sΘ )c -I f + (I m =I f Im Im=If+(Im-If)October 13, 2004 8Dredge Pumps and Slurry Transport
  9. 9. Inclined Flows: Worster-Denny ModelC. 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. solids effect in inclined pipe Im,θ − I f = = cosθ <1 solids effect in horizon pipe Im − I f October 13, 2004 9 Dredge Pumps and Slurry Transport
  10. 10. Inclined Flows: Lab Tests October 13, 2004 10 Dredge Pumps and Slurry Transport
  11. 11. Inclined Flows: Two-Layer ModelA. Physical background:• For layered inclined flows the two-layer model is much better predictive tool than the empirical Worster-Denny model. October 13, 2004 11 Dredge Pumps and Slurry Transport
  12. 12. Inclined Flows: Coarse slurry d=1.8 mm Incl Angle: 0 deg October 13, 2004 12 Dredge Pumps and Slurry Transport
  13. 13. Inclined Flows: Coarse slurry d=1.8 mm Incl Angle: 16 deg October 13, 2004 13 Dredge Pumps and Slurry Transport
  14. 14. Inclined Flows: Coarse slurry d=1.8 mm Incl Angle: 25 deg October 13, 2004 14 Dredge Pumps and Slurry Transport
  15. 15. Inclined Flows: Coarse slurry d=1.8 mm Incl Angle: 35 deg October 13, 2004 15 Dredge Pumps and Slurry Transport
  16. 16. Inclined Flows: Coarse slurry d=1.8 mm Ascending pipe October 13, 2004 16 Dredge Pumps and Slurry Transport
  17. 17. Inclined Flows: Coarse slurry d=1.8 mm Descending pipe October 13, 2004 17 Dredge Pumps and Slurry Transport
  18. 18. Inclined Flows: Wilson-Tse Model Effect of inclination on the deposition limit velocity. The empirical model based on visual observations in a small pipe. Vsm,0 =Vsm + ∆D 2gD(Ss −1) Vsm is the velocity from the demi-McDonald’s diagram for horizontal flow.October 13, 2004 18Dredge Pumps and Slurry Transport

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