106
3 Fans
Equation (3.6) represents a straight line in the
0,
(
, )
1
t
p
Q
r D ∞
-diagram (Fig. 3.8).
With forward curved blades, the theoretical total pressure rise increases with the
flow rate. The total pressure rise stays constant with radial end blades and it is a
decreasing function of the flow rate with backward curved blades. The theoretical
power P t∞ follows from
(3.7)
The relation is linear for radial end blades, quadratic and steeper than linear for
forward curved blades, and quadratic and flatter than linear for backward curved
blades (Fig. 3.8). The real characteristics of radial fans are discussed in Sects. 3.4
and 3.6.
3.3 Radial Fan Analysis for Lossless Two-Dimensional
Flow with Finite Number of Rotor Blades
3.3.1 Relative Vortex in Blade Channels
We still consider the flow as occurring in a plane perpendicular to the shaft. The
flow within a blade channel of a rotor with a finite number of blades may be considered as the superposition of two flows. The first flow is the translation flow applied until now. This flow follows the blade direction and has a uniform velocity
at a given radius. The second flow is a circulation flow in the relative frame, as
sketched in Fig. 3.9, showing the superposition of both flows as well. On a blade,
a side forms with a higher velocity and a lower pressure ( suction side) and another
2
2
0,
2
2
2
2 2
.
t
t
Q
P
p Q
u Q
u
tg
d b
D
r
r
b
p
∞
∞
=
=
+
Fig. 3.8 Total pressure rise and absorbed power as a function of the flow rate with forward curved
(β 2 > 0), radial end (β 2 = 0) and backward curved (β 2 < 0) blades
3 Fans
Equation (3.6) represents a straight line in the
0,
(
, )
1
t
p
Q
r D ∞
-diagram (Fig. 3.8).
With forward curved blades, the theoretical total pressure rise increases with the
flow rate. The total pressure rise stays constant with radial end blades and it is a
decreasing function of the flow rate with backward curved blades. The theoretical
power P t∞ follows from
(3.7)
The relation is linear for radial end blades, quadratic and steeper than linear for
forward curved blades, and quadratic and flatter than linear for backward curved
blades (Fig. 3.8). The real characteristics of radial fans are discussed in Sects. 3.4
and 3.6.
3.3 Radial Fan Analysis for Lossless Two-Dimensional
Flow with Finite Number of Rotor Blades
3.3.1 Relative Vortex in Blade Channels
We still consider the flow as occurring in a plane perpendicular to the shaft. The
flow within a blade channel of a rotor with a finite number of blades may be considered as the superposition of two flows. The first flow is the translation flow applied until now. This flow follows the blade direction and has a uniform velocity
at a given radius. The second flow is a circulation flow in the relative frame, as
sketched in Fig. 3.9, showing the superposition of both flows as well. On a blade,
a side forms with a higher velocity and a lower pressure ( suction side) and another
2
2
0,
2
2
2
2 2
.
t
t
Q
P
p Q
u Q
u
tg
d b
D
r
r
b
p
∞
∞
=
=
+
Fig. 3.8 Total pressure rise and absorbed power as a function of the flow rate with forward curved
(β 2 > 0), radial end (β 2 = 0) and backward curved (β 2 < 0) blades