104
3 Fans
(3.3)
A total pressure coefficient is defined by
(3.4)
A static pressure coefficient is similarly, with
rot,t
p ¥
D
the static pressure rise in the
rotor:
(3.5)
Equation (3.4) and Eq. (3.5) are only correct for lossless flow.
The dimensionless coefficients for the total pressure rise in the machine and for
the static pressure rise in the rotor are termed performance parameters. They are
related to the degree of reaction, which is determined by the rotor blade shape, as
derived hereafter.
Figure 3.6 shows the degree of reaction and the pressure coefficients as functions of v u
2u
2
/ . Some dimensionless outlet velocity triangles are represented. The
total pressure coefficient increases with increasing v u
u
2
2
/ . The degree of reaction
decreases. This implies an increase of the fraction of the rotor work used for kinetic
energy rise in the flow through the rotor. The efficiency of the entire machine thus
decreases when a significant part of the kinetic energy at the rotor outlet is to be
converted into pressure energy downstream of the rotor. The degree of reaction is 1
for ζ = 0. The total pressure rise is then zero and the rotor blades are strongly curved
backward. No work is done by the rotor. A machine without any rotor work is useless, of course. So, a practical minimal value is ζ ≈ 0.2. The degree of reaction is 0.5
for ζ = 1. Within the rotor, the increase of pressure energy then equals the increase
of kinetic energy. The outlet part of the rotor blades is in the radial direction. There
is no static pressure rise within the rotor for ζ = 2. Such a machine only generates
kinetic energy rise. It is a pure action machine with forward curved blades and a
high total pressure rise. In practice, a machine with a low degree of reaction is of
little use. Most applications require some static pressure rise, and it is advisable
for good efficiency to have some static pressure rise in the rotor. So, a practicable
maximum value is ζ ≈ 1.8.
The inlet rotor blade orientation is independent of its outlet shape. Figure 3.7
schematically shows the blade shapes with forward curved blades, radial end
blades and backward curved blades. The corresponding degrees of reaction being
respectively low, 0.5 and high. So it is clear that the degree of reaction determines
the rotor blade shape.
R
u
u v
u v
t
u
u
∞ =
−
−
= −
2
2
2
2
2
2 2
2
1 2
(
)
.
ζ
0,
2 2
2
0,
2
2
2
2
2
.
t
u
u
t
p
u v
v
u
u
u
D
y
z
r
∞
∞ =
=
=
=
,
,
0,
2
2
1
.
2
rot t
r t
t
t
p
R
u
D
z
y
y
z
r
∞
∞
∞
∞
=
=
=
−
3 Fans
(3.3)
A total pressure coefficient is defined by
(3.4)
A static pressure coefficient is similarly, with
rot,t
p ¥
D
the static pressure rise in the
rotor:
(3.5)
Equation (3.4) and Eq. (3.5) are only correct for lossless flow.
The dimensionless coefficients for the total pressure rise in the machine and for
the static pressure rise in the rotor are termed performance parameters. They are
related to the degree of reaction, which is determined by the rotor blade shape, as
derived hereafter.
Figure 3.6 shows the degree of reaction and the pressure coefficients as functions of v u
2u
2
/ . Some dimensionless outlet velocity triangles are represented. The
total pressure coefficient increases with increasing v u
u
2
2
/ . The degree of reaction
decreases. This implies an increase of the fraction of the rotor work used for kinetic
energy rise in the flow through the rotor. The efficiency of the entire machine thus
decreases when a significant part of the kinetic energy at the rotor outlet is to be
converted into pressure energy downstream of the rotor. The degree of reaction is 1
for ζ = 0. The total pressure rise is then zero and the rotor blades are strongly curved
backward. No work is done by the rotor. A machine without any rotor work is useless, of course. So, a practical minimal value is ζ ≈ 0.2. The degree of reaction is 0.5
for ζ = 1. Within the rotor, the increase of pressure energy then equals the increase
of kinetic energy. The outlet part of the rotor blades is in the radial direction. There
is no static pressure rise within the rotor for ζ = 2. Such a machine only generates
kinetic energy rise. It is a pure action machine with forward curved blades and a
high total pressure rise. In practice, a machine with a low degree of reaction is of
little use. Most applications require some static pressure rise, and it is advisable
for good efficiency to have some static pressure rise in the rotor. So, a practicable
maximum value is ζ ≈ 1.8.
The inlet rotor blade orientation is independent of its outlet shape. Figure 3.7
schematically shows the blade shapes with forward curved blades, radial end
blades and backward curved blades. The corresponding degrees of reaction being
respectively low, 0.5 and high. So it is clear that the degree of reaction determines
the rotor blade shape.
R
u
u v
u v
t
u
u
∞ =
−
−
= −
2
2
2
2
2
2 2
2
1 2
(
)
.
ζ
0,
2 2
2
0,
2
2
2
2
2
.
t
u
u
t
p
u v
v
u
u
u
D
y
z
r
∞
∞ =
=
=
=
,
,
0,
2
2
1
.
2
rot t
r t
t
t
p
R
u
D
z
y
y
z
r
∞
∞
∞
∞
=
=
=
−