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3. Flow of soil-water mixture

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  • 1. oe4625 Dredge Pumps and Slurry Transport Vaclav Matousek October 13, 2004 1 Dredge Pumps and Slurry Transport Vermelding onderdeel organisatie
  • 2. 3. FLOW OF SOIL-WATER MIXTURE FLOW REGIMES FLOW PATTERNS FLOW QUANTITIES/PARAMETERSOctober 13, 2004 2Dredge Pumps and Slurry Transport
  • 3. FLOW REGIMES LAMINAR TURBULENTOctober 13, 2004 3Dredge Pumps and Slurry Transport
  • 4. Regimes: Flow confined by boundaries Example of general flowOctober 13, 2004 4Dredge Pumps and Slurry Transport
  • 5. Laminar and turbulent flowsLaminar flow Structure of Comparison laminar turbulence and turbulent flows Initiation of turbulenceOctober 13, 2004 5Dredge Pumps and Slurry Transport
  • 6. FLOW REGIMES Re > 10000 u [m/s] u’ u u t [s] u [m/s] Re < 2300 t [s]October 13, 2004 6Dredge Pumps and Slurry Transport
  • 7. Laminar Flow in Pipe• - composed of thin layers (lamina) that move over each other at different velocities forming a typical parabolic velocity profile in a pipeline cross section• - no exchange of mass and momentum between neighboring layers• - a stability of a laminar flow is given by Reynolds number of the flow and its value 2300 is experimentally determined as a threshold for the maintaining of a laminar flow regime in a conduit. October 13, 2004 7 Dredge Pumps and Slurry Transport
  • 8. Laminar versus Turbulent Flow in PipeThe dimensionless group Re, Reynolds number, is a ratio of the inertial forces and the viscous forces in the pipeline flow Vf Dρ f inertial . force Re = = µf viscous. forceRemark: The Reynolds number determines a threshold between the laminar and the turbulent flows in a pipe.The flow is LAMINAR if Re < 2300. October 13, 2004 8 Dredge Pumps and Slurry Transport
  • 9. Turbulent Flow in Pipe• - a result of disturbances occurring at the interface between neighboring layers• - turbulent eddies are developed as a result of the disturbances; they are responsible for an intensive random transfer of mass and momentum in all directions within a liquid stream; this is sensed as a continuous fluctuation of velocity of fluid particles in time and space within a stream• - the flow eddies due to turbulence produce energy dissipation additional to that due to friction in a laminar flow. Turbulent flows dissipate more mechanical energy than laminar flows. October 13, 2004 9 Dredge Pumps and Slurry Transport
  • 10. Internal Structure of Pipe FlowOctober 13, 2004 10Dredge Pumps and Slurry Transport
  • 11. FLOW PATTERNS FULLY SUSPENDED PARTIALLY STRATIFIED FULLY STRATIFIEDOctober 13, 2004 11Dredge Pumps and Slurry Transport
  • 12. Fully stratified flows Example of fully stratified flowOctober 13, 2004 12Dredge Pumps and Slurry Transport
  • 13. Flow Patterns: Indicators• - a tendency of a solid particle to settle in a flowing carrying liquid (given by the particle settling velocity )• - a tendency of a flowing carrier to suspend solid particles (given by intensity of turbulence, i.e. basically by mean velocity of a stream in a pipe).October 13, 2004 13Dredge Pumps and Slurry Transport
  • 14. Extreme Flow Patterns Fully-stratified flow: intensity of turbulence of a carrierflow is not sufficient to suspend any solid particle in apipeline; all solid particles occupy a granular bed that iseither stationary or slides over the bottom of a pipeline Fully-suspended flow: all solid particles are suspendedwithin a stream of a carrying liquid; no granular bed occursin a pipeline; if particles distributed uniformly across thepipeline cross section than pseudo-homogeneous flow.October 13, 2004 14Dredge Pumps and Slurry Transport
  • 15. Transitional Flow Pattern Partially-stratified flow: mixture flow exhibits aconsiderable concentration gradient across a pipeline crosssection indicating an accumulation of a portion of solids nearthe bottom of a pipeline and a non-uniform distribution ofthe rest of solids across the rest of a pipeline cross-sectionalarea; this pattern is also known as a heterogeneous flow.October 13, 2004 15Dredge Pumps and Slurry Transport
  • 16. vm c vi cvd F profile profile profile P L I. Pseudo-homogeneous flow A O T W T II. Heterogeneous flow w ithout a granular bed at the bottom of a pipe E R III. Heterogeneous flow with a low developed bed N S IV. Heterogeneous flow with an en bloc sliding bed V. Stratified flow with a stationary bedOctober 13, 2004 16Dredge Pumps and Slurry Transport
  • 17. Drop of velocity from 2.6 m/s to 1.0m/s in the horizontal 150-mm pipe:October 13, 2004 Medium sand 0.2-0.5 mm 17Dredge Pumps and Slurry Transport
  • 18. Extremely low velocity (0.2-0.3 m/s)in the horizontal 150-mm pipe:October 13, 2004 Medium sand 0.2-0.5 mm 18Dredge Pumps and Slurry Transport
  • 19. FLOW PARAMETERS FLOW VELOCITY PRODUCTION OF SOLIDS PRESSURE DROP SPECIFIC ENERGY CONSUMPTIONOctober 13, 2004 19Dredge Pumps and Slurry Transport
  • 20. Flow ParametersPipeline-flow parameters should be controlled during adredging operation in order to optimize the safety and theeconomy of the transportation system. The parameters are: the mean velocity of mixture and its threshold value(s) the production of solids the frictional pressure loss the specific energy consumption. October 13, 2004 20 Dredge Pumps and Slurry Transport
  • 21. Flow Parameters: Mean Velocity Mean velocity in a pipeline of a circular pipe of an inner diameter D is written as flow rate 4Q V= = cross sec tional area π D 2The determination of an appropriate value of the mean mixture velocity is crucial to safe and low-cost pipeline operation.The mean slurry velocity at the limit of stationary deposition is called the deposition-limit velocity or the critical velocity. This is the threshold velocity at which solid particles occupying a bed at the bottom of a pipeline stop their sliding and start to form a stationary bed at the bottom of a pipeline. October 13, 2004 21 Dredge Pumps and Slurry Transport
  • 22. Flow Parameters: Production of Solids The production of solids (production of solid particles) is an important parameter from the economic point of view. It gives the amount of dry solids delivered at the pipeline outlet over a certain time period.This is defined as the (volumetric) flow rate of solids (flow rate of solid particles) at the outlet of a slurry pipeline π  m3  Qs = 2 D V m C vd 3600  hour  4  During a dredging operation the parameters Vm and Cvd are usually measured in a pipeline of known D so that the production of solids given by a solids flow rate can be determined. October 13, 2004 22 Dredge Pumps and Slurry Transport
  • 23. Flow Parameters: Production of SolidsFor the payment of a dredging work, the production based on in-situ volume of transported soil (production of solid particles + porous liquid) is decisive. Cvd The delivered concentration of the in-situ soil Cvdsi = 1− n so that the production of in-situ soil can be calculated as π Qs  m3  Qsi = D VmCvdsi 3600 = 2  hour  4 1− n  Since the porosity is lower than one (typically n = 0.4 for a loose-poured sand), the production of in-situ soil (Qsi) is higher than the production of the solid particles (Qs). October 13, 2004 23 Dredge Pumps and Slurry Transport
  • 24. Flow Parameters: Pressure DropFlow resistance is given by the amount of P1 P2mechanical energy dissipated in a slurry flowwhen flowing through a pipeline. The energydissipation in a steady slurry flow is t0characterized by the pressure difference V Dalong a horizontal pipeline section of constantdiameter. The resistance is evaluated as t0the pressure drop ∆P = P1-P2 (differential L pressure over a pipeline section) [Pa],the pressure gradient (pressure drop over P − P2 1 a pipeline section divided by the length L of a pipeline section) [Pa/m] Lthe hydraulic gradient due to friction, also P1 − P2 termed the frictional head loss (Im) [-] ρ f gL October 13, 2004 24 Dredge Pumps and Slurry Transport
  • 25. Flow Parameters: Hydraulic GradientThe hydraulic gradient due to friction, also termed the P1 − P2 frictional head loss (Im) [-], is the head (that is lost owing ρ f gL to friction) divided by the length of a pipeline section, L.The head [m] is a measure of the P1 P2mechanical energy of a flowing liquid per unitmass. It is expressed as the height of the t0fluid column exerting the pressure that isequivalent to the pressure differential P1 – P2. V D P − P2 1 t0 ρf g L October 13, 2004 25 Dredge Pumps and Slurry Transport
  • 26. Flow Parameters: Hydraulic GradientThe relation between the mechanical dissipation due to mixture flow and the mean mixture velocity in the pipeline section is expressed by a pipeline-resistance curve (I – V curve) giving a relation between the head losses and the mean mixture velocity in a pipe. October 13, 2004 26 Dredge Pumps and Slurry Transport
  • 27. Flow Parameters: Hydraulic GradientThe relation between the mechanical dissipation due to mixture flow and the mean mixture velocity in the pipeline section is expressed by a pipeline-resistance curve (I – V curve) giving a relation between the head losses and the mean mixture velocity in a pipe. October 13, 2004 27 Dredge Pumps and Slurry Transport
  • 28. Flow Parameters: Hydraulic Gradient . 12 =0 30The relation between the Head los t due to friction [m.w.c.] vd 2 ,C 0.1 .3 e tu r mechanical dissipation due to 0 25 7m v = m mi x C w, mixture flow and the mean 0 fl o us flo v = 20 C o w, Wa og ene mixture velocity in the t er 15 m Ho pipeline section is expressed 10 by a 5 (a 0.18 mm mixture) Develo ped bed Lo w bed No bed pipeline-resistance curve 0 0 1 2 3 (I – V curve) Mixture veloc ity [m/s] giving a relation between the 6 head losses and the mean 4 Minimum velocity 2 mixture velocity in a pipe. for mixture 0.18 mm 0 0 1 2 3 3 Mixture flow rate [m /s] October 13, 2004 28 Dredge Pumps and Slurry Transport
  • 29. Flow Parameters: Hydraulic GradientThe relation between the mechanical dissipation due to mixture flow and the mean mixture velocity in the pipeline section is expressed by a pipeline-resistance curve (I – V curve) giving a relation between the head losses and the mean mixture velocity in a pipe. October 13, 2004 29 Dredge Pumps and Slurry Transport
  • 30. Flow Parameters: SECThe efficiency of a slurry pipeline is evaluated by means of a parameter called specific energy consumption (SEC).The SEC is an appropriate optimization parameter because it contains both a measure of energy dissipation and a measure of solids load in a pipeline flow.The SEC determines the energy required to move a given quantity of solids over a given distance in a pipeline. October 13, 2004 30 Dredge Pumps and Slurry Transport
  • 31. Flow Parameters: SECThe specific energy consumption SEC is defined as a ratio between- the power consumption per metre of pipe, ImρfgQm, and- the (dry) solids throughput in a pipe, ρfCvdQm. I m ρ f gQm Im g  J  SEC = = kgm ρ s Cvd Qm Ss Cvd  .  Im  kWh  SEC = 2.7  tonne.km  SsCvd   October 13, 2004 31 Dredge Pumps and Slurry Transport
  • 32. Flow Parameters: SECThe optimization of transport can be done using the SEC – Production diagram (SEC – Qs curve). October 13, 2004 32 Dredge Pumps and Slurry Transport

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