150
3 Fans
approximately constant on similarity parabolas. Repeat the reasoning for axial fans
and mixed-flow fans (velocity triangles on Figs. 3.28 and 3.33). Observe that the
conclusion is the same.
3.8.11 Two-Stage Axial Fan
Consider a two-stage axial fan according to Fig. 3.3, but consider that the machine
is a stator-rotor combination followed by a rotor-stator, with the intermediate vane
ring made of struts not causing flow deflection. The velocity triangles are as in
Fig. 3.28 (but in reversed order). Two-stage axial fans are used for rather high flow
rates (above 500 m
3
/s), combined with a rather high pressure rise (above 4000 Pa).
Such combinations cannot be realised with centrifugal fans or single-stage axial
fans. Consider flow rate Q = 660 m
3
/s and rise of total pressure Δp 0 = 6500 Pa, for
rotor dimensions d hub = 2.10 m and d tip = 4.20 m at 590 rpm. Take as air density
1.25 kg/m
3
and assume equal work done by both rotors. Estimate the internal efficiency η i = 0.885 and ignore leakage flow ( η v = 1) and mechanical loss ( η m = 1).
1. Determine the velocity triangles on the quadratic mean radius r m = 1.660 m
2
2
2
2 m t
h
r
r r
= +
.
2. Determine the degree of reaction and the work coefficient on the mean radius.
3. Assume that the fan is realised with free vortex flow. Estimate the necessary
solidity at the hub of the rotor for a Zweifel coefficient of unity. Verify the deceleration ratio w 2 /w 1 .
4. Determine the number of blades for an axial chord equal to 20 % of the blade
height.
A: I: w 2u = −102.58 m/s; R = 1.14; ( σ a ) hub = 0.70; ( w 2 /w 1 ) hub = 0.714; Z = 22; II:
w 2u = −73.93 m/s; R = 0.86, ( σ a ) hub = 1.30; ( w 2 /w 1 ) hub = 0.732; Z = 41.
Variants of the two-stage fan are manufactured. The more common design is
with 2 equal stages, either stator-rotor or rotor-stator. These configurations are also
possible with the sketch of Fig. 3.3. Remark that the combination stator-rotor is the
most favourable with respect to necessary solidity. A special configuration is rotorstator-rotor, also realisable with Fig. 3.3. This machine can be seen as a contraction
of a rotor-stator and a stator-rotor according to Fig. 3.28 with the 2 stator vane rows
merged. The machine is kinematically equivalent with the fan calculated, but with
the order of the stages reversed. Another variant is a two-stage fan with contrarotating rotors. This variant is kinematically equivalent to the previous build. There
are no stator vanes, but the machine requires two shafts rotating in opposite senses.
The contra-rotating version is sometimes used with smaller fans where the rotors
are mounted directly on the shafts of the driving motors. It is normally not used for
larger fans with external motors.
3 Fans
approximately constant on similarity parabolas. Repeat the reasoning for axial fans
and mixed-flow fans (velocity triangles on Figs. 3.28 and 3.33). Observe that the
conclusion is the same.
3.8.11 Two-Stage Axial Fan
Consider a two-stage axial fan according to Fig. 3.3, but consider that the machine
is a stator-rotor combination followed by a rotor-stator, with the intermediate vane
ring made of struts not causing flow deflection. The velocity triangles are as in
Fig. 3.28 (but in reversed order). Two-stage axial fans are used for rather high flow
rates (above 500 m
3
/s), combined with a rather high pressure rise (above 4000 Pa).
Such combinations cannot be realised with centrifugal fans or single-stage axial
fans. Consider flow rate Q = 660 m
3
/s and rise of total pressure Δp 0 = 6500 Pa, for
rotor dimensions d hub = 2.10 m and d tip = 4.20 m at 590 rpm. Take as air density
1.25 kg/m
3
and assume equal work done by both rotors. Estimate the internal efficiency η i = 0.885 and ignore leakage flow ( η v = 1) and mechanical loss ( η m = 1).
1. Determine the velocity triangles on the quadratic mean radius r m = 1.660 m
2
2
2
2 m t
h
r
r r
= +
.
2. Determine the degree of reaction and the work coefficient on the mean radius.
3. Assume that the fan is realised with free vortex flow. Estimate the necessary
solidity at the hub of the rotor for a Zweifel coefficient of unity. Verify the deceleration ratio w 2 /w 1 .
4. Determine the number of blades for an axial chord equal to 20 % of the blade
height.
A: I: w 2u = −102.58 m/s; R = 1.14; ( σ a ) hub = 0.70; ( w 2 /w 1 ) hub = 0.714; Z = 22; II:
w 2u = −73.93 m/s; R = 0.86, ( σ a ) hub = 1.30; ( w 2 /w 1 ) hub = 0.732; Z = 41.
Variants of the two-stage fan are manufactured. The more common design is
with 2 equal stages, either stator-rotor or rotor-stator. These configurations are also
possible with the sketch of Fig. 3.3. Remark that the combination stator-rotor is the
most favourable with respect to necessary solidity. A special configuration is rotorstator-rotor, also realisable with Fig. 3.3. This machine can be seen as a contraction
of a rotor-stator and a stator-rotor according to Fig. 3.28 with the 2 stator vane rows
merged. The machine is kinematically equivalent with the fan calculated, but with
the order of the stages reversed. Another variant is a two-stage fan with contrarotating rotors. This variant is kinematically equivalent to the previous build. There
are no stator vanes, but the machine requires two shafts rotating in opposite senses.
The contra-rotating version is sometimes used with smaller fans where the rotors
are mounted directly on the shafts of the driving motors. It is normally not used for
larger fans with external motors.