102
3 Fans
flow direction is not perpendicular to the inlet circle and has some pre-swirl velocity v 1u . With most machines, no pre-swirl occurs, however. Analogous to the rotor,
we assume an incidence-free inlet of the volute and no friction within the volute.
Quantities related to the above defined flow get as subscripts t (theoretical flow =
no losses) and ∞ (infinite number of blades). The assumptions regarding losses and
flow direction coinciding with blade orientation will gradually be abandoned in
further analysis steps.
3.2.2 Degree of Reaction
The degree of reaction with adiabatic flow is the ratio of the static enthalpy increase
to the total enthalpy increase in the rotor. The total enthalpy increase in the rotor
equals the total enthalpy increase in the machine. The static enthalpy increase is
The reversible part of this enthalpy increase is 1
ρ
dp
∫
.
This follows from the entropy definition:
One can thus suppose that, for a small pressure increase with a compressible fluid,
the isentropic enthalpy increase corresponding to the pressure increase is well approximated by
with ρ being the average density. A strict justification for this approximation is
presented in Chap. 13. Obviously, the relation is exact for constant density. Thus the
degree of reaction may be approximated with
(3.1)
which is the ratio of the static pressure rise in the rotor to the total pressure rise in
the machine.
The degree of reaction according to (Eq. 3.1) is applied in practice to fans. There
is a small difference with the general definition. This is obvious, as both values
h h
p
p e e
2
1
2
2
1
1
2
1
− =
− + −
ρ
ρ
.
(1 / )
or
(1 / ) .
s
Tds dh
dp
dh
dp
r
r
= −
=
2
1
2
1 s
p
p
(h h )
,
r
−
−
≈
0
,
rot
p
p
R
p
D
D
=