7.7 Exercises
281
• Consider that, at the design operating point, the inlet flow of the rotor is aligned
with the blade direction after the flow has entered. Determine the design rotor
flow rate under this condition.
• Take into account that the deceleration in a rotor channel cannot be stronger than
0.70. Interpret that this applies to the inlet flow after rotor entrance ( )
w
b
1 and the
outlet flow before rotor exit, so before slip ( )
w
b
2 . Observe that the deceleration
limit is reached. Take as flow model a core flow with uniform flow velocity ( )
w
b
2
at the pressure side of a rotor channel and a zero flow velocity zone at the suction
side (jet and stagnant wake model). Assume that Pfleiderer’s work reduction factor formulae (Chap. 3: 3.23–3.25) apply to the core flow. Determine rotor work
with this assumption.
• Consider the dump diffusion at the entrance of the volute as between the core
flow in the rotor channels and a uniform flow immediately downstream of the rotor outlet, filling the full width of the volute. Due to the partial filling of the rotor
channels, the dump diffusion loss is considerably larger than with full throughflow.
• Calculate the leakage flow between the volute and the rotor inlet assuming that
the total pressure at the volute side of the gap is the static pressure at the volute
entrance after dump diffusion (station 2’) and that the pressure at the rotor side
of the gap is the inlet pressure of the rotor (station 1). Ignore contraction in the
leakage flow. Assume that the gap width is 2 mm.
• Calculate the incidence loss at the entrance of the volute assuming that angular
momentum is conserved between the volute inlet, after tangential deflection due
to incidence (station 2’), and the volute outlet (station 3). The velocity distribution at the volute outlet follows from the net flow rate.
• Determine the total pressure rise of the fan taking into account the dump diffusion loss and the incidence loss at volute entrance. Neglect the other losses.
This leads to some overestimation of the total pressure rise. Take as density
ρ = 1.20 kg/m
3
.
A:
3
3
3
0
0.853 / ,
0.816,
3290.1 / ,
180.27 / , ( / )
2086.5 / ,
3
0.0763 / ,
0.911,
0.777 / ,
726
4.75 / ,
,
0.944.
rotor
Pfleiderer
dump
irr
gap
leak
v
incid
net
irr
i
Q
m s
W
J kg
q
J kg p
J kg Q
m s
Q
m s q
J kg p
Pa
e
r
h
h
=
=
∆ =
=
∆
=
=
=
=
=
∆ =
=
The calculated flow rate is somewhat lower than the target value. The calculated
pressure rise is larger than the target value, but the inlet loss in the rotor eye and
friction losses are not taken into account. The internal efficiency should decrease
until 0.887 for obtaining the target value of the total pressure rise.
7.7.7. Calculate flow rate and total pressure rise in the design point of the fan rendered in Figs. 7.21 and 7.22 from the measured values at 2750 rpm (Chap. 5). Scale
the laboratory test results from 2750 rpm to 2900 rpm with kinematic similitude,
assuming that efficiency is unchanged.
A: The scaled measured values of flow rate and total pressure rise at the best efficiency operating point are 0.725 m
3
/s and 3590 Pa. The best efficiency flow rate is
281
• Consider that, at the design operating point, the inlet flow of the rotor is aligned
with the blade direction after the flow has entered. Determine the design rotor
flow rate under this condition.
• Take into account that the deceleration in a rotor channel cannot be stronger than
0.70. Interpret that this applies to the inlet flow after rotor entrance ( )
w
b
1 and the
outlet flow before rotor exit, so before slip ( )
w
b
2 . Observe that the deceleration
limit is reached. Take as flow model a core flow with uniform flow velocity ( )
w
b
2
at the pressure side of a rotor channel and a zero flow velocity zone at the suction
side (jet and stagnant wake model). Assume that Pfleiderer’s work reduction factor formulae (Chap. 3: 3.23–3.25) apply to the core flow. Determine rotor work
with this assumption.
• Consider the dump diffusion at the entrance of the volute as between the core
flow in the rotor channels and a uniform flow immediately downstream of the rotor outlet, filling the full width of the volute. Due to the partial filling of the rotor
channels, the dump diffusion loss is considerably larger than with full throughflow.
• Calculate the leakage flow between the volute and the rotor inlet assuming that
the total pressure at the volute side of the gap is the static pressure at the volute
entrance after dump diffusion (station 2’) and that the pressure at the rotor side
of the gap is the inlet pressure of the rotor (station 1). Ignore contraction in the
leakage flow. Assume that the gap width is 2 mm.
• Calculate the incidence loss at the entrance of the volute assuming that angular
momentum is conserved between the volute inlet, after tangential deflection due
to incidence (station 2’), and the volute outlet (station 3). The velocity distribution at the volute outlet follows from the net flow rate.
• Determine the total pressure rise of the fan taking into account the dump diffusion loss and the incidence loss at volute entrance. Neglect the other losses.
This leads to some overestimation of the total pressure rise. Take as density
ρ = 1.20 kg/m
3
.
A:
3
3
3
0
0.853 / ,
0.816,
3290.1 / ,
180.27 / , ( / )
2086.5 / ,
3
0.0763 / ,
0.911,
0.777 / ,
726
4.75 / ,
,
0.944.
rotor
Pfleiderer
dump
irr
gap
leak
v
incid
net
irr
i
Q
m s
W
J kg
q
J kg p
J kg Q
m s
Q
m s q
J kg p
Pa
e
r
h
h
=
=
∆ =
=
∆
=
=
=
=
=
∆ =
=
The calculated flow rate is somewhat lower than the target value. The calculated
pressure rise is larger than the target value, but the inlet loss in the rotor eye and
friction losses are not taken into account. The internal efficiency should decrease
until 0.887 for obtaining the target value of the total pressure rise.
7.7.7. Calculate flow rate and total pressure rise in the design point of the fan rendered in Figs. 7.21 and 7.22 from the measured values at 2750 rpm (Chap. 5). Scale
the laboratory test results from 2750 rpm to 2900 rpm with kinematic similitude,
assuming that efficiency is unchanged.
A: The scaled measured values of flow rate and total pressure rise at the best efficiency operating point are 0.725 m
3
/s and 3590 Pa. The best efficiency flow rate is