7 Dynamic Similitude
276
7.6 Turbomachine Design Example: Centrifugal Fan
This book aims at fundamental understanding of turbomachines. Design of turbomachines requires, in principle, more in-depth study, but design of a rather simple
machine, such as a radial fan, is achievable with the material provided herein. As
an example, we choose the fan of the laboratory test in Chap. 5. Design data for the
fan are Q = 0.8 m
3
/s and ∆p 0 = 3500 Pa. We immediately mention that attaining a
total pressure rise of 3500 Pa is rather challenging. From the fan chapter we learned
that a head coefficient of a radial fan with backward curved blades can attain about
ψ = 0.5. With ρ ≈ 1.20 kg/m
3
air density it follows:
So, the required peripheral speed is rather high.
The design starts from the Cordier diagram as given in Fig. 7.7. In specialised
literature, such a diagram is complemented with geometric data as diameter ratio ( d 1 /d 2 ) and width to diameter ratio ( d 2 /d 2 ) as functions of specific speed [6,
9]. These supplementary data are not strictly necessary however. The couple on
the Cordier line, leading to the maximum possible speed of about 2900 rpm is
s
s
0.70,D 3.80.
W =
=
This results in d 2 = 0.46 m, n = 2966 rpm, which we may reduce somewhat to d 2 = 0.45 m, n = 2900 rpm, so u 2 = 68.33 m/s. The required ψ then
becomes 0.625.
With (3.37), for maximum deceleration in the rotor eye b d
1
1
0 40
/
.
=
(
) :
We take d 1 = 0.20 m. Then: v
Q
m s
1
2 3 1 3
1 2
20 97
=
=
Ω
/
/
.
/ . With d 0 = 0.18 m:
0
2
0
4Q
v
31.43 m / s.
d
p
=
=
The value of v 0 is acceptable, because a typical duct
velocity may be up to 20 m/s, but with direct aspiration from the atmosphere, the
inflow velocity may be as high as 30 m/s. The through-flow velocity of the rotor
cannot be much lower than 20.97 m/s, because then v v
1
0
/
,
= 0.667 which is quite
low. So, in principle, we accept the value of v 1 .
With 1 0.90
t ≈
it follows that b 1 = 75 mm. But with b 1 /d 1 = 0.40 we obtain
b 1 = 80 mm. We choose b 1 = 80 mm. This lowers somewhat v 1 to v 1
b
= 19 65 m s
.
/ .
The velocity ratio v v
625
1
0
0
b
/
.
=
is still realisable (0.60 is the limit value).
ψ
ρ
=
=
→ ≈
∆ p
u
u
m s
0
2
2
2
0 5
75
.
/ .
1/ 3
1 o
Q
( d )
2( )
0.195 m.
W
=
=
b
rotor
1 1 1 1
Q
d b v Q / 0.9.
p
t
=
≈
/
/
/
/
2
2
1
1
rot
1 1
1
1
1
u 30.37 m s;v Q ( d b ) 17.68m s; w
u v
35.14 m s.
p
=
=
=
=
+ =
276
7.6 Turbomachine Design Example: Centrifugal Fan
This book aims at fundamental understanding of turbomachines. Design of turbomachines requires, in principle, more in-depth study, but design of a rather simple
machine, such as a radial fan, is achievable with the material provided herein. As
an example, we choose the fan of the laboratory test in Chap. 5. Design data for the
fan are Q = 0.8 m
3
/s and ∆p 0 = 3500 Pa. We immediately mention that attaining a
total pressure rise of 3500 Pa is rather challenging. From the fan chapter we learned
that a head coefficient of a radial fan with backward curved blades can attain about
ψ = 0.5. With ρ ≈ 1.20 kg/m
3
air density it follows:
So, the required peripheral speed is rather high.
The design starts from the Cordier diagram as given in Fig. 7.7. In specialised
literature, such a diagram is complemented with geometric data as diameter ratio ( d 1 /d 2 ) and width to diameter ratio ( d 2 /d 2 ) as functions of specific speed [6,
9]. These supplementary data are not strictly necessary however. The couple on
the Cordier line, leading to the maximum possible speed of about 2900 rpm is
s
s
0.70,D 3.80.
W =
=
This results in d 2 = 0.46 m, n = 2966 rpm, which we may reduce somewhat to d 2 = 0.45 m, n = 2900 rpm, so u 2 = 68.33 m/s. The required ψ then
becomes 0.625.
With (3.37), for maximum deceleration in the rotor eye b d
1
1
0 40
/
.
=
(
) :
We take d 1 = 0.20 m. Then: v
Q
m s
1
2 3 1 3
1 2
20 97
=
=
Ω
/
/
.
/ . With d 0 = 0.18 m:
0
2
0
4Q
v
31.43 m / s.
d
p
=
=
The value of v 0 is acceptable, because a typical duct
velocity may be up to 20 m/s, but with direct aspiration from the atmosphere, the
inflow velocity may be as high as 30 m/s. The through-flow velocity of the rotor
cannot be much lower than 20.97 m/s, because then v v
1
0
/
,
= 0.667 which is quite
low. So, in principle, we accept the value of v 1 .
With 1 0.90
t ≈
it follows that b 1 = 75 mm. But with b 1 /d 1 = 0.40 we obtain
b 1 = 80 mm. We choose b 1 = 80 mm. This lowers somewhat v 1 to v 1
b
= 19 65 m s
.
/ .
The velocity ratio v v
625
1
0
0
b
/
.
=
is still realisable (0.60 is the limit value).
ψ
ρ
=
=
→ ≈
∆ p
u
u
m s
0
2
2
2
0 5
75
.
/ .
1/ 3
1 o
Q
( d )
2( )
0.195 m.
W
=
=
b
rotor
1 1 1 1
Q
d b v Q / 0.9.
p
t
=
≈
/
/
/
/
2
2
1
1
rot
1 1
1
1
1
u 30.37 m s;v Q ( d b ) 17.68m s; w
u v
35.14 m s.
p
=
=
=
=
+ =