3.4 Internal Losses with Radial Fans
133
When applying Pfleiderer’s slip representation, the reasoning is similar, but with a
different value of Q s
* .
Figure 3.22 (same figure as Fig. 1.18) draws the characteristic Δp 0 as a function
of the flow rate, theoretically taking slip into account (both Stodola’s and Pfleiderer’s reasoning lead to a linear characteristic) and obtained by subtracting friction
losses (a common term for all losses proportional to the flow rate squared) and
incidence losses. The representation is simplified by assuming that the volute is
matched to the rotor, so that a unique design flow rate Q * exists (
)
*
*
*
Q Q
Q
r
s
= =
.
With this simplification, the resulting characteristic becomes a parabola, assuming
constant friction loss coefficients. At zero flow rate, ∆p
u
0
2
2
2
≈ ρ / with backward
curved blades. At zero net flow rate, the absolute velocity at the rotor outlet equals
on average about u 2 , since the rotor flow rate is low as there is only internal leakage flow. The rotor work is approximately u 2
2
. There is nearly standstill within
the volute, with incidence loss amounting to about ρu 2
2
2
/ . At zero net flow rate
with forward curved blades,
0
p
∆ is much higher, due to the energy transfer by the
recirculation flow within the rotor (Fig. 3.19).
0
p
∆ for zero flow rate is typically
about the same as the design value. The resulting characteristic then typically has a
maximum and a minimum (see section 3.6).
The internal efficiency is
(3.41)
The internal efficiency attains its maximum at a flow rate that is lower than the
design flow rate, due to part of the losses being proportional to the square of the
flow rate (friction losses and diffusion losses). This phenomenon persists, even if
the machine has a unique design flow rate (operating point without incidence losses
in rotor and stator). Normally there is mismatch between the rotor and the stator and
0
i
0,t
p .
p
D
h
D
=
Fig. 3.22 Characteristic of a radial fan with backward curved blades
133
When applying Pfleiderer’s slip representation, the reasoning is similar, but with a
different value of Q s
* .
Figure 3.22 (same figure as Fig. 1.18) draws the characteristic Δp 0 as a function
of the flow rate, theoretically taking slip into account (both Stodola’s and Pfleiderer’s reasoning lead to a linear characteristic) and obtained by subtracting friction
losses (a common term for all losses proportional to the flow rate squared) and
incidence losses. The representation is simplified by assuming that the volute is
matched to the rotor, so that a unique design flow rate Q * exists (
)
*
*
*
Q Q
Q
r
s
= =
.
With this simplification, the resulting characteristic becomes a parabola, assuming
constant friction loss coefficients. At zero flow rate, ∆p
u
0
2
2
2
≈ ρ / with backward
curved blades. At zero net flow rate, the absolute velocity at the rotor outlet equals
on average about u 2 , since the rotor flow rate is low as there is only internal leakage flow. The rotor work is approximately u 2
2
. There is nearly standstill within
the volute, with incidence loss amounting to about ρu 2
2
2
/ . At zero net flow rate
with forward curved blades,
0
p
∆ is much higher, due to the energy transfer by the
recirculation flow within the rotor (Fig. 3.19).
0
p
∆ for zero flow rate is typically
about the same as the design value. The resulting characteristic then typically has a
maximum and a minimum (see section 3.6).
The internal efficiency is
(3.41)
The internal efficiency attains its maximum at a flow rate that is lower than the
design flow rate, due to part of the losses being proportional to the square of the
flow rate (friction losses and diffusion losses). This phenomenon persists, even if
the machine has a unique design flow rate (operating point without incidence losses
in rotor and stator). Normally there is mismatch between the rotor and the stator and
0
i
0,t
p .
p
D
h
D
=
Fig. 3.22 Characteristic of a radial fan with backward curved blades