Biomedical Engineering Reference
In-Depth Information
TABL E 5.2. Scale-Down Implications of Different Scaling Criteria Based on Agitation Speed at Constant P/V
Scale-Down Relationship
Assuming Equal P/V and
Aspect Ratios (N
/
D
2/3
)
Basis for Scaling
Criteria
Scaling
Relationship
Consideration
Equation
Po
g
N
3
D
i
=
V
/ N
3
D
i
Power/volume (P/V)
at constant V
s
Constant k
L
a
Constant
1
=
3
i
Tip speed
Similar “shear
stress”
p
N
D
i
/
N
D
i
/ D
(lower)
5.9T
2/3
(P/V)
1/3
(D
i
/T)
1/3
for H
¼
T
/ N
3
D
i
, T
2/3
,
(D
i
/T)
1/3
for H
¼
T
/
(H/D
i
)
2.5
for H
>
T
/
T
2/3
(lower)
Mixing time (
q
m
)
Similar characteristic
mixing time
4
=
3
i
ND
i
r
=
m
/ ND
i
Reynolds number (Re)
Similar turbulent
flow patterns
/ D
(lower) not relevant
when remaining in
turbulent flow regime
Source: Based on [16].
V
s
, superficial gas velocity; V, volume; Po
g
, impeller power number under sparging conditions; N, agitation rate (rev s
1
); D
i
, impeller diameter; T, tank diameter; H, liquid
height;
r
, liquid density;
h
, viscosity (Pa
s); P, power (watts).
