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Bin and Hopper Design

Bin and Hopper Design. Karl Jacob The Dow Chemical Company Solids Processing Lab jacobkv@dow.com. The Four Big Questions. What is the appropriate flow mode? What is the hopper angle? How large is the outlet for reliable flow?

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Bin and Hopper Design

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  1. Bin and Hopper Design Karl Jacob The Dow Chemical Company Solids Processing Lab jacobkv@dow.com KVJ

  2. The Four Big Questions • What is the appropriate flow mode? • What is the hopper angle? • How large is the outlet for reliable flow? • What type of discharger is required and what is the discharge rate? KVJ

  3. Hopper Flow Modes • Mass Flow - all the material in the hopper is in motion, but not necessarily at the same velocity • Funnel Flow - centrally moving core, dead or non-moving annular region • Expanded Flow - mass flow cone with funnel flow above it KVJ

  4. Mass Flow D Does not imply plug flow with equal velocity Typically need 0.75 D to 1D to enforce mass flow Material in motion along the walls KVJ

  5. Funnel Flow Active Flow Channel “Dead” or non-flowing region KVJ

  6. Expanded Flow Funnel Flow upper section Mass Flow bottom section KVJ

  7. Problems with Hoppers • Ratholing/Piping KVJ

  8. Void Ratholing/Piping Stable Annular Region KVJ

  9. Problems with Hoppers • Ratholing/Piping • Funnel Flow KVJ

  10. Funnel Flow -Segregation -Inadequate Emptying -Structural Issues Coarse Coarse Fine KVJ

  11. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming KVJ

  12. Arching/Doming Cohesive Arch preventing material from exiting hopper KVJ

  13. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming • Insufficient Flow KVJ

  14. Insufficient Flow - Outlet size too small - Material not sufficiently permeable to permit dilation in conical section -> “plop-plop” flow Material under compression in the cylinder section Material needs to dilate here KVJ

  15. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming • Insufficient Flow • Flushing KVJ

  16. Flushing • Uncontrolled flow from a hopper due to powder being in an aerated state - occurs only in fine powders (rough rule of thumb - Geldart group A and smaller) - causes --> improper use of aeration devices, collapse of a rathole KVJ

  17. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming • Insufficient Flow • Flushing • Inadequate Emptying KVJ

  18. Inadequate emptying Usually occurs in funnel flow silos where the cone angle is insufficient to allow self draining of the bulk solid. Remaining bulk solid KVJ

  19. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming • Insufficient Flow • Flushing • Inadequate Emptying • Mechanical Arching KVJ

  20. Mechanical Arching • Akin to a “traffic jam” at the outlet of bin - too many large particle competing for the small outlet • 6 x dp,large is the minimum outlet size to prevent mechanical arching, 8-12 x is preferred KVJ

  21. Problems with Hoppers • Ratholing/Piping • Funnel Flow • Arching/Doming • Insufficient Flow • Flushing • Inadequate Emptying • Mechanical Arching • Time Consolidation - Caking KVJ

  22. Time Consolidation - Caking • Many powders will tend to cake as a function of time, humidity, pressure, temperature • Particularly a problem for funnel flow silos which are infrequently emptied completely KVJ

  23. Segregation • Mechanisms - Momentum or velocity - Fluidization - Trajectory - Air current - Fines KVJ

  24. What the chances for mass flow? Cone Angle Cumulative % of from horizontal hoppers with mass flow 45 0 60 25 70 50 75 70 *data from Ter Borg at Bayer KVJ

  25. Mass Flow (+/-) + flow is more consistent + reduces effects of radial segregation + stress field is more predictable + full bin capacity is utilized + first in/first out - wall wear is higher (esp. for abrasives) - higher stresses on walls - more height is required KVJ

  26. Funnel flow (+/-) + less height required - ratholing - a problem for segregating solids - first in/last out - time consolidation effects can be severe - silo collapse - flooding - reduction of effective storage capacity KVJ

  27. How is a hopper designed? • Measure - powder cohesion/interparticle friction - wall friction - compressibility/permeability • Calculate - outlet size - hopper angle for mass flow - discharge rates KVJ

  28. What about angle of repose? Pile of bulk solids    KVJ

  29. Angle of Repose • Angle of repose is not an adequate indicator of bin design parameters “… In fact, it (the angle of repose) is only useful in the determination of the contour of a pile, and its popularity among engineers and investigators is due not to its usefulness but to the ease with which it is measured.” - Andrew W. Jenike • Do not use angle of repose to design the angle on a hopper! KVJ

  30. Bulk Solids Testing • Wall Friction Testing • Powder Shear Testing - measures both powder internal friction and cohesion • Compressibility • Permeability KVJ

  31. Solids Bridges -Mineral bridges -Chemical reaction -Partial melting -Binder hardening -Crystallization -Sublimation Interlocking forces Attraction Forces -van der Waal’s -Electrostatics -Magnetic Interfacial forces -Liquid bridges -Capillary forces Sources of Cohesion (Binding Mechanisms) KVJ

  32. Testing Considerations • Must consider the following variables - time - temperature - humidity - other process conditions KVJ

  33. N F Wall Friction Testing Wall friction test is simply Physics 101 - difference for bulk solids is that the friction coefficient, , is not constant. P 101 F = N KVJ

  34. W x A Bracket Cover Ring S x A Bulk Solid Wall Test Sample Wall Friction Testing Jenike Shear Tester KVJ

  35. Wall Friction Testing Results Wall Yield Locus (WYL), variable wall friction Wall shear stress,  Wall Yield Locus, constant wall friction ’ Normal stress,  Powder Technologists usually express  as the “angle of wall friction”, ’ ’ = arctan  KVJ

  36. Jenike Shear Tester W x A Bracket Cover Ring S x A Bulk Solid Bulk Solid Shear plane KVJ

  37. Other Shear Testers • Peschl shear tester • Biaxial shear tester • Uniaxial compaction cell • Annular (ring) shear testers KVJ

  38. Ring Shear Testers Arm connected to load cells, S x A Bulk solid Bottom cell rotates slowly W x A KVJ

  39. Shear test data analysis  C fc 1  KVJ

  40. Stresses in Hoppers/Silos • Cylindrical section - Janssen equation • Conical section - radial stress field • Stresses = Pressures KVJ

  41. Stresses in a cylinder Consider the equilibrium of forces on a differential element, dh, in a straight-sided silo Pv A = vertical pressure acting from above  A g dh = weight of material in element (Pv + dPv) A = support of material from below   D dh = support from solid friction on the wall Pv A h   D dh dh (Pv + dPv) A  A g dh D (Pv + dPv) A +   D dh = Pv A +  A g dh KVJ

  42. Stresses in a cylinder (cont’d) Two key substitutions  =  Pw (friction equation) Janssen’s key assumption: Pw = K Pv This is not strictly true but is good enough from an engineering view. Substituting and rearranging, A dPv =  A g dh -  K Pv  D dh Substituting A = (/4) D2 and integrating between h=0, Pv = 0 and h=H and Pv = Pv Pv = ( g D/ 4  K) (1 - exp(-4H K/D)) This is the Janssen equation. KVJ

  43. Stresses in a cylinder (cont’d) hydrostatic Bulk solids Notice that the asymptotic pressure depends only on D, not on H, hence this is why silos are tall and skinny, rather than short and squat. KVJ

  44. Stresses - Converging Section Over 40 years ago, the pioneer in bulk solids flow, Andrew W. Jenike, postulated that the magnitude of the stress in the converging section of a hopper was proportional to the distance of the element from the hopper apex.  =  ( r, ) This is the radial stress field assumption.  r KVJ

  45. Silo Stresses - Overall hydrostatic Bulk solid Notice that there is essentially no stress at the outlet. This is good for discharge devices! KVJ

  46. Janssen Equation - Example A large welded steel silo 12 ft in diameter and 60 feet high is to be built. The silo has a central discharge on a flat bottom. Estimate the pressure of the wall at the bottom of the silo if the silo is filled with a) plastic pellets, and b) water. The plastic pellets have the following characteristics:  = 35 lb/cu ft ’ = 20º The Janssen equation is Pv = ( g D/ 4  K) (1 - exp(-4H K/D)) In this case: D = 12 ft  = tan ’ = tan 20º = 0.364 H = 60 ft g = 32.2 ft/sec2  = 35 lb/cu ft KVJ

  47. Janssen Equation - Example K, the Janssen coefficient, is assumed to be 0.4. It can vary according to the material but it is not often measured. Substituting we get Pv = 21,958 lbm/ft - sec2. If we divide by gc, we get Pv = 681.9 lbf/ft2 or 681.9 psf Remember that Pw = KPv,, so Pw = 272.8 psf. For water, P =  g H and this results in P = 3744 psf, a factor of 14 greater! KVJ

  48. Types of Bins Conical Pyramidal Watch for in-flowing valleys in these bins! KVJ

  49. Types of Bins Chisel Wedge/Plane Flow L B L>3B KVJ

  50. 1 c A thought experiment KVJ

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