8 . 1

Mixer Sizing Methods

Four different sizing criteria - Velocity

- Shear Stress

- Yield Stress

- Mixing Time

8 . 2

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 . 3

Velocity

• Losses (k) - Racetrack

– Bends

– Friction wall & bottom

– Aeration

– Obstacles

• Losses (k) - Other tanks

– Tank factor (geometry)

– Propeller factor

– Aeration

– Obstacles

Freq ~ u2 k Required thrust = (Size of Mixer) =

&

8 . 4

Shear Stress

Mixing Duties

– Off bottom suspension & Resuspension of

sediment

• Shear Stress calculated

• Shear Stress measured

• By experience

– Erosion and transport of sediments

8 . 5

Shear Stress

Required thrust = (Size of Mixer) =

• ts = Requires Shear stress to resuspend

– measured

– calculated

– Experience

F ~ ts

8 . 6

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 . 7

Yield Stress

• 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

Required thrust = (Size of Mixer) = F ~ ty

8 . 8

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 . 9

Mixing Time

Required thrust = (Size of Mixer) = F ~ 1 / Q2

• Q2 Specified mixing

time

– Given by customer

– Given by process

– Retention time

Inflow = Q

Volume = V

Retention time = V/Q

8 . 10

Quantified mixing demands

• Velocity F ~ u2

• Shear stress F ~ ts

• Yield stress F ~ ty

• Time F ~ 1 / Q2

8 . 11

Extra study

8 . 12

Channels - Required thrust “The velocity Solver”

The required thrust is

Freq = Ab k

r is the liquid density (1000 kg/m3 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)

r u2

2

Extra study

8 . 13

A racetrack example

• Wall friction

• Bends

• Aerators

• Obstacles

F = k · --- · Ab

r u2

2

8 . 14

Bulk flow area

Width

Height

Ab

8 . 15

Wall friction

Surface roughness

Length of flow loop

8 . 16

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 Wet perimeter

Pw = 2 H + W

8 . 17

Bend loss factors kb

1.5 0.6 0.3 -- 1.5

2.5 1.0 0.8

0.5 1.1 1.4

8 . 18

Bend losses

kb = 1,5

8 . 19

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 . 20

Aeration loss factor kaer

Bottom diffuser geometry

Bottom diffuser density in grid (m-2)

hdiff

A^ diff shape ? 1 m

1 m

8 . 21

Aeration loss factor kaer

• # grids

• Bottom coverage (%)

• Air flow Qair (Nm3/h)

• Bulk flow velocity u

kaer

8 . 22

Obstacle loss factor ko

The loss force from an obstacle is

Fo = Ao cD,

And, to use Ab in

the Freq - formula,

ko = cD Ao / Ab.

cD is typically between 1.0 and 2.0.

For the pipe, say Ao = 6.0 0.5 m2, cD = 1.0

ko = cD Ao / Ab = 0.125

r u2

2 Projected

area Ao

8 . 23

A racetrack example

50m

6m

6m

H=4m

1 grid Sanitaire diff,

20% covered area

r u2

2

2 units 4430

friction bends aerators obstacle

F = k · --- · Abulk

F = (0.87 + 2 · 1.5 + 0.55 + 0.125) · 1000 · --- · (6 · 4) = 4774 N 0.302

2

8 . 24

Other tank shapes The same principles as in channels....

Freq = Ab k r u2

2