mixer sizing methods
Post on 09-Jan-2022
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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 . 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 . 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 . 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
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