3.2 Idealised Mean Line Analysis of a Radial Fan
103
of the degree of reaction coincide for lossless flow of constant density fluid. The
degree of reaction according to the general definition is strictly termed kinematic
degree of reaction as this degree of reaction may be related to velocity components,
as will be derived hereafter. There is no specific term in the fan literature for the degree of reaction according to definition (Eq. 3.1). We will use the term pressure degree of reaction. By the simple term degree of reaction, we will mean the kinematic
degree of reaction. A definition of the degree of reaction, slightly deviating from
the general definition is sometimes applied to other machines as well, for instance,
with steam turbines (Chap. 6). Deviating definitions are always used for practical
purposes. Pressure differences required to determinate the degree of reaction according to (Eq. 3.1) may be measured easily. Reliable measurement of the enthalpy
differences for the general definition is impossible, as temperature differences with
fans are very small. For instance, a total pressure increase of 3600 Pa corresponds
to an adiabatic temperature difference of just 3 K with a density 1.20 kg/m
3
and a
specific heat 1000 J/kgK. This difference cannot be measured reliably because of
the effect of heat transfer.
3.2.3 Relation Between Rotor Blade Shape and Performance
Parameters
The kinematic degree of reaction is given by
(3.2)
In the absence of pre-swirl,
Then, (Eq. 3.2) becomes
In order to obtain a simple expression for the degree of reaction, we assume that
the radial component of the velocity is equal at the rotor inlet and outlet. This is approximately met in real rotors and is achieved by decreasing the axial rotor width
with increasing diameter.
With
it follows that, with ζ = v u
u
2
2
/
,
R
h h
h
h
u u w w
u v
u v
t
u
u
∞ =
−
−
=
− +
−
−
2
1
02
01
2
2
1
2
1
2
2
2
2 2
1 1
2(
)
.
2
2
2
1
1
1
1
0 and
.
u
v
w
u v
=
= +
R
u v w
u v
t
u
∞ =
+ −
2
2
1
2
2
2
2 2
2
.
2
2
2
1
2
2
2
2
2
and
(
) ,
r
r
u
v v
w v
u v
=
−
=
−
103
of the degree of reaction coincide for lossless flow of constant density fluid. The
degree of reaction according to the general definition is strictly termed kinematic
degree of reaction as this degree of reaction may be related to velocity components,
as will be derived hereafter. There is no specific term in the fan literature for the degree of reaction according to definition (Eq. 3.1). We will use the term pressure degree of reaction. By the simple term degree of reaction, we will mean the kinematic
degree of reaction. A definition of the degree of reaction, slightly deviating from
the general definition is sometimes applied to other machines as well, for instance,
with steam turbines (Chap. 6). Deviating definitions are always used for practical
purposes. Pressure differences required to determinate the degree of reaction according to (Eq. 3.1) may be measured easily. Reliable measurement of the enthalpy
differences for the general definition is impossible, as temperature differences with
fans are very small. For instance, a total pressure increase of 3600 Pa corresponds
to an adiabatic temperature difference of just 3 K with a density 1.20 kg/m
3
and a
specific heat 1000 J/kgK. This difference cannot be measured reliably because of
the effect of heat transfer.
3.2.3 Relation Between Rotor Blade Shape and Performance
Parameters
The kinematic degree of reaction is given by
(3.2)
In the absence of pre-swirl,
Then, (Eq. 3.2) becomes
In order to obtain a simple expression for the degree of reaction, we assume that
the radial component of the velocity is equal at the rotor inlet and outlet. This is approximately met in real rotors and is achieved by decreasing the axial rotor width
with increasing diameter.
With
it follows that, with ζ = v u
u
2
2
/
,
R
h h
h
h
u u w w
u v
u v
t
u
u
∞ =
−
−
=
− +
−
−
2
1
02
01
2
2
1
2
1
2
2
2
2 2
1 1
2(
)
.
2
2
2
1
1
1
1
0 and
.
u
v
w
u v
=
= +
R
u v w
u v
t
u
∞ =
+ −
2
2
1
2
2
2
2 2
2
.
2
2
2
1
2
2
2
2
2
and
(
) ,
r
r
u
v v
w v
u v
=
−
=
−