Mixer Sizing Methods Four different sizing criteria Velocity

Mixer Sizing Methods Four different sizing criteria - Velocity - Shear Stress - Yield Stress - Mixing Time 8. 1

Velocity Mixing Duties – Circulation • u specified • heat or mass transfer specified • . . . – Homogeneous suspension • u depends on usettl and tank geometry • Standard u values in biological treatment systems 8. 2

Velocity Required thrust = (Size of Mixer) = Freq ~ u 2 k & • Losses (k) - Racetrack – Bends – Friction wall & bottom – Aeration – Obstacles 8. 3 • Losses (k) - Other tanks – Tank factor (geometry) – Propeller factor – Aeration – Obstacles

Shear Stress Mixing Duties – Off bottom suspension & Resuspension of sediment • Shear Stress calculated • Shear Stress measured • By experience – Erosion and transport of sediments 8. 4

Shear Stress Required thrust = (Size of Mixer) = • ts = Requires Shear stress to resuspend – measured – calculated – Experience 8. 5 F ~ ts

Yield Stress For mixing to be possible, the fluid must move at all. If it has a finite Yield Stress, this must be overcome. Hence this is an additional mixing criterion, often decisive. Applications – Thickened sludge – Paper pulp – Drilling mud – Slurries. . . 8. 6

Yield Stress Required thrust = (Size of Mixer) = • where ty is – Calculated or measured for municipal sludge, drilling mud & paper pulp – Specified by client – Measured by e. g. ITT Flygt Application Lab / known otherwise 8. 7 F ~ ty

Mixing Time Mixing Duties – Required blending time Q specified or given by • Throughflow; fluid leaving tank is mixed to a certain homogeneity xb. • Batch; customer requires a certain maximum time Q and a certain minimum homogeneity xb. 8. 8

Mixing Time Required thrust = (Size of Mixer) = • F ~ 1 / Q 2 Specified mixing time Inflow = Q – Given by customer – Given by process Volume = V – Retention time = V/Q 8. 9

Quantified mixing demands 8. 10 • Velocity F ~ u 2 • Shear stress F ~ ts • Yield stress F ~ ty • Time F ~ 1 / Q 2

Extra study 8. 11

Extra study Channels - Required thrust “The velocity Solver” The required thrust is 2 r u Freq = Ab k 2 r is the liquid density (1000 kg/m 3 for water) k = kf + kb + kaer + ko are loss factors due to friction, bends, aerators, other obstacles. Ab is the bulk flow area (projected area of cross section of main flow) 8. 12

A racetrack example r u 2 F = k · --· A b 2 • Wall friction • Bends • Aerators • Obstacles 8. 13

Bulk flow area Ab Height Width 8. 14

Wall friction Surface roughness Length of flow loop 8. 15

Friction loss factor kf = Ltot / (M Rh) Ltot total mean length of channel Rh = Ab / Pw hydraulic radius M » 80 (Inverse) Manning number M is larger for very small channels or very smooth surfaces, and conversely smaller in the opposite cases. Ab 8. 16 Wet perimeter Pw = 2 H + W

Bend loss factors kb 8. 17 1. 5 0. 6 0. 3 -- 1. 5 2. 5 1. 0 0. 8 0. 5 1. 1 1. 4

Bend losses kb = 1, 5 8. 18

Aerator losses • Diffusers act as flow obstacles • Bubble columns increase the hydraulic losses by – causing counterflow to the bulk flow – causing velocity distributions that increase losses on the bottom and on the diffusers 8. 19

Aeration loss factor kaer Bottom diffuser geometry Bottom diffuser density in grid (m-2) hdiff A^ diff 1 m shape ? 1 m 8. 20

Aeration loss factor kaer • • # grids Bottom coverage (%) Air flow Qair (Nm 3/h) Bulk flow velocity u ® kaer 8. 21

Obstacle loss factor ko The loss force from an obstacle is r u 2 F o = 2 A o c D, Projected area Ao And, to use Ab in the Freq - formula, ko = c D A o / A b. c. D is typically between 1. 0 and 2. 0. For the pipe, say Ao = 6. 0 ´ 0. 5 m 2, c. D = 1. 0 ko = c. D Ao / Ab = 0. 125 8. 22

A racetrack example 6 m 1 grid Sanitaire diff, 20% covered area 6 m 50 m H=4 m r u 2 F = k · --- · Abulk 2 0. 302 F = (0. 87 + 2 · 1. 5 + 0. 55 + 0. 125) · 1000 · --- · (6 · 4) = 4774 N 2 friction bends aerators obstacle 2 units 4430 8. 23

Other tank shapes The same principles as in channels. . 2 r u Freq = Ab k 2 8. 24