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The seventh lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics. …

The seventh lecture in the module Particle Technology, delivered to second year students who have already studied basic fluid mechanics.

Centrifugal Separation covers both sedimenting and filtering centrifuges as well as hydrocyclones. Adaptation of the gravity settling and conventional filtration models, to account for the conceptual centrifugal acceleration, is included. Examples of industrial equipment for centrifugal separation are included.

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  • 1. Centrifugal Separation
    Chapter 8 in Fundamentals
    Watch this lecture at http://www.vimeo.com/10203052
    Visit http://www.midlandit.co.uk/particletechnology.htm for further resources.
    Course details:
    Particle Technology,
    module code: CGB019 and CGB919,
    2nd year of study.
    Professor Richard Holdich
    R.G.Holdich@Lboro.ac.uk
  • 2. Centrifugal separation
    • Sedimenting centrifuges
    • 3. Particle motion in a centrifugal field
    • 4. Sigma theory
    • 5. Hydrocyclones
    • 6. Grade efficiency & cut size
    • 7. Filtering centrifuges
    • 8. Adaptation of filtration equations
    • 9. Washing (ratio) & Drying
  • Scroll Discharge Decanter
    Archimedian screw to convey solids out of the centrifuge
    Imperforate bowl, i.e. sedimenting not filtering
    Image courtesy of Thomas Broadbent & Sons Limited
    Image courtesy of Siebtechnik GmbH
  • 10. Scroll Discharge Decanter
    Screw rotates at only slight differential speed to the centrifuge - solids leave at one end, centrate at the other.
    Image courtesy of Siebtechnik GmbH
  • 11. Tubular bowl centrifuge
    This one is vertical axis - simple design with no internals for clarification or liquid/liquid separation - a more complicated design is the chamber bowl.
    Image removed for copyright reasons. For an example product please see http://www.sharpenntechnologies.com/pcat-gifs/products-large2/high-speed-centrifuge1111-2.jpg.
  • 12. Disc stack centrifuge
    Like a lamella clarifier: internal surfaces to encourage settling - usually used in oil/water separation and cream
  • 13. Sedimenting Centrifuges –
    Let’s confine our analysis to a simple geometry - ignoring the complicated internal structures required to remove deposited solids and oil concentrates.
    Liquid flow out
    Inner radius
    Air core
    Outer radius
  • 14. Gravity settling
    Field force (weight) is:
    • Drag force is:
    • 15. Giving:
  • Centrifugal settling
    Field force (weight) is:
    • Drag force is:
    • 16. Giving:
  • Centrifugal settling
    i.e. U = f(r)
    r
    • i.e. U = dr/dt
  • Sedimenting Centrifuges
  • 17. Centrifugal settling
    • limits: r=r1 at t=0 to r=r2 at t=t
    • 18. Giving:
    i.e. the radial residence time in the machine
  • 19. Horizontal/axial residence time
    where
  • 20. Sedimenting Centrifuges
  • 21. Critical trajectory model
    • Residence time axially and radially is the same.
  • Critical trajectory model
    • Multiply through by ‘g’:
  • Critical trajectory model
    • Multiply through by ‘g’:
    • 22. Square bracketed term is the terminal settling velocity of a particle of size x.
  • Critical trajectory model- Eq 8.10 & 5.28!
    • Rearrange:
    m2
    • c.f. a gravity settling basin
  • Machine parameters
    m2
    • The theoretical settling basin equivalent PLAN area given the dimensions of the machine in question and its operating conditions.
  • Process parameters
    m2
    • The measured value given the process flow rate and operating performance for the 100% cut-off.
  • Sigma values
    • Sigma machine
    m2
    • Sigma process
    m2
    • The two sigma values are equal for 100% efficient machines - normally 40 to 60% may be achieved.
  • Uses of sigma values
    To compare between different machines of same geometry
    Attempts to compare between different types of machines
    Estimate of machine size required to replace gravity settling clarifier
    You need a density difference!
  • 23. Flue gas desulphurisation
    Feed:CaSO4 - 35water - 65 100%
    Cake:CaSO4 - 70water - 30 100%
    Centrate:CaSO4 - 2.7water - 97.3 100%
    All concentrations as mass percent
  • 24. Hydrocyclone
    Single unit and array:
    Defined by diameterof cylindrical section
    Image showing "Krebs gMAX® Hydrocyclones" courtesy of FLSmidth Krebs Inc.
  • 25. Means of separation
    Centrifugal:
    800 g in 300 mm hydrocyclone
    50000 g in 10 mm hydrocyclone
    Type of separator:
    a classifier (i.e. splits into sizes)
    a thickener (i.e. concentrates suspensions)
  • 26. Operating data
    Diameters: 0.01 to 1 metre
    Solid (cut) sizes: 2 to 250 microns
    Flow rates (single unit): 0.1 - 5000 m3 h-1
    Pressure drop: 6 to 0.4 bar
    U/F solid content: up to 50% v/v (claimed)
  • 27. Principal features
    Note: primary & secondary vortex, air core, U/F, O/F, tangential feed
  • 28. Tangential velocity
  • 29. Radial velocity
  • 30. Axial velocity
  • 31. Grade efficiency – Cut Point
    • Feed distribution is split into two fractions:
    Overflow
    Underflow
  • 32. Grade efficiency
    • Fraction by mass of each grade entering the U/F of the hydrocyclone.
    • 33. Recovery is the overall fraction entering the U/F - usually by volume.
  • Grade efficiency
    • Equation:
  • Grade efficiency
    • What is the grade efficiency of the following?
    Overflow50 kg/h
    Underflow50 kg/h
  • 34. Grade efficiency
    • Equation:
    100%
    Rf
    0%
  • 35. Grade efficiency
    • i.e. we need to correct for effect due to flow split in order to reliably record the ability of the device to act as a classifier.
    • 36. The reduced grade efficiency.
  • Grade efficiency
    <100%
    • Reduced grade efficiency:
    • 37. Normalised reduced grade efficiency:
    100%
  • 38. Equilibrium Orbit Theory
    A particle orbiting on the LZVV has no net tendency to move into the primary vortex (then O/F) or secondary vortex (then U/F).
    It must be equal to the cut size x50%.
  • 39. Equilibrium Orbit Theory
    Force balance:
    centrifugal
    • Tangential velocity:
    • 40. Liquid drag:
    FD
    FC
  • 41. Hydrocyclones - types and configurations
    Oil/water separation - often offshore
  • 42. Filtering Centrifuges
    A perforated bowl - similar to a spin dryer
    See box on page 83 for descriptions
  • 43. Filtering Centrifuge – Section 8.3
    Pusher
    generally coarse solids > 50 microns
    (semi)-continuous solids output
    careful balance of slurry in
    Image courtesy of Siebtechnik GmbH
  • 44. Filtering Centrifuge
    Peeler
    generally solids > 5 microns
    usually intermittent solids output - slow to 50 rpm
    Image removed for copyright reasons.
    Please search online for an image of a peeler centrifuge.
  • 45. Filtering Centrifuge
    Inverting Bag
    generally solids > 5 microns
    intermittent solids output
    Image removed for copyright reasons.
    Please search online for an image of an inverting bag centrifuge.
  • 46. Filtering centrifuge - full cycle
    Function Time(s) Time(%) Accelerate from 50 to 500 rpm 40 5
    Load/Filter at 500 rpm 277 32
    Accelerate to 1050 rpm 90 10
    Spin dry at 1050 rpm 119 14
    Wash at 1050 rpm 10 1
    Spin dry at 1050 rpm 236 27
    Slow down to 50 rpm 90 10
    Unload at 50 rpm 15 2
    Total cycle time 877 100
    Basket load per cycle of solids 140 kg
    Productivity 575 kg/hour
  • 47. Centrifuge - simple analysis – Fig 8.9
    Ptotal
    = Pcake
    + Pmedium
    Definitions:
  • 48. Centrifuge - simple analysis
    - same as for conventional filtration
    However, the radius at which the cake forms is continually moving inwards and the geometry is not planar.
    where:
  • 49. Centrifuge - simple analysis
    Centrifugal head - the driving pressure:
    where omega is in seconds-1 = (2 pi/60)RPM
    Density is that of the slurry or liquid depending upon the operation: filtering or washing
  • 50. Centrifuge - washing
    but rc remains constant during the washing stage. The time to wash with Vw m3 of solvent is:
  • 51. Centrifuge - washing
    Typical washing performance:
    1
    Solute concn.
    Initial concn.
    0.5
    Flooded cake
    Dewatered cake
    0
    1
    2
    3
    Wash volumes
  • 52. Centrifuge - drainage
    1
    Relative saturation
    0.5
    S* = S
    Irreducible saturation
    Sinitial
    0
    0.2
    0.4
    0.6
    Time or dimensionless drainage time
  • 53. This resource was created by Loughborough University and released as an open educational resource through the Open Engineering Resources project of the HE Academy Engineering Subject Centre. The Open Engineering Resources project was funded by HEFCE and part of the JISC/HE Academy UKOER programme.
    Slide 3 (Left). Image of a decanter centrifuge provided courtesy of Thomas Broadbent and Sons Ltd. See http://www.broadbent.co.uk/en/about for details.
    Slides 3 (right), 4, and 42. Images courtesy of Siebtechnik GmbH. See http://www.tema.co.uk/images/products/7_1.jpg for details.
    Slide 24. Image of"Krebs gMAX® Hydrocyclones" photo courtesy of FLSmidth Krebs Inc. See http://www.flsmidthminerals.com/Products/Classification/Hydrocyclones/Hydrocyclones.htm for details.
    © 2009 Loughborough University
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