523
14.4 Rotor Shape
For D loc < 0.5 this criterion also results in (14.8). This value of D loc is the critical
value for separation in axial cascades. Deceleration in the boundary layer at the
suction side is more disadvantageous with a centrifugal rotor, due to the turbulence
segregation effect by the Coriolis force (Chap. 3, Sect. 3.3.4). The Coriolis force
drives high-energy cores within the turbulent motion away from the suction side to
the pressure side. This effect weakens the suction side boundary layer. Therefore,
the critical value of D loc is rather 0.45. So, in practice, separation at the suction side
occurs rather than flow reversal at the pressure side. Therefore, we further apply
criterion (14.9) as
(14.10)
The effect of streamline curvature in the vicinity of the rotor outlet is quite modest
with centrifugal compressors. In practice, only rotors with radial end blades ( β 2
= −15º, after slip), with slight backward sweep ( β 2 = −20° to −30°) and with moderate backward sweep ( β 2 = −45°) are applied. The curvature factor f R in (14.10)
may therefore, by way of simplification, be taken as 0.80, so that approximately
holds
(14.11)
This simplification spares us then deriving an expression for the curvature effect, as
in Chap. 3. Note that the reasoning in Chap. 3 is not applicable to centrifugal compressors for high work due to the presence of the inducer. The effect of the curvature
is rather a local rotor outlet phenomenon with a centrifugal compressor, but the reasoning in Chap. 3 deducts the curvature effect from the overall rotor through-flow.
This is only justified for centrifugal fans since these have small or modest solidity.
For the same reason, the Wiesner formula for slip is better justified for centrifugal
compressors than the Pfleiderer formula.
With the velocity triangles of Fig. 14.3, we may estimate the ratio 2 2
w u
to about 0.35. With b ≈ − °
2
15 , it follows from (14.11) that min
Z
17
≈ . For
b
b
≈ − °
≈ − °
b
2
2 2
2
45 (
40 ), w u may be up to 0.45, which results in min
Z
10
≈ .
Values used in practice are often 20 and 14 or 16.
14.4.2 Inducer
Rotors with radial end blades or with slightly backward swept blades are intended
to realise the maximum attainable work. Therefore, such applications aim at maximum attainable peripheral speed (Figs. 14.2 and 14.7). This requires adaptation of
the rotor inlet. Bending stress generated by the centrifugal force at the inlet side of
the impeller must be avoided. This may be achieved by adding an axial part, termed
p
b
<
2 2 R
2
2 cos u f
0.80w .
Z
p
b
<
2 2
2
2 cos u
w .
Z
14.4 Rotor Shape
For D loc < 0.5 this criterion also results in (14.8). This value of D loc is the critical
value for separation in axial cascades. Deceleration in the boundary layer at the
suction side is more disadvantageous with a centrifugal rotor, due to the turbulence
segregation effect by the Coriolis force (Chap. 3, Sect. 3.3.4). The Coriolis force
drives high-energy cores within the turbulent motion away from the suction side to
the pressure side. This effect weakens the suction side boundary layer. Therefore,
the critical value of D loc is rather 0.45. So, in practice, separation at the suction side
occurs rather than flow reversal at the pressure side. Therefore, we further apply
criterion (14.9) as
(14.10)
The effect of streamline curvature in the vicinity of the rotor outlet is quite modest
with centrifugal compressors. In practice, only rotors with radial end blades ( β 2
= −15º, after slip), with slight backward sweep ( β 2 = −20° to −30°) and with moderate backward sweep ( β 2 = −45°) are applied. The curvature factor f R in (14.10)
may therefore, by way of simplification, be taken as 0.80, so that approximately
holds
(14.11)
This simplification spares us then deriving an expression for the curvature effect, as
in Chap. 3. Note that the reasoning in Chap. 3 is not applicable to centrifugal compressors for high work due to the presence of the inducer. The effect of the curvature
is rather a local rotor outlet phenomenon with a centrifugal compressor, but the reasoning in Chap. 3 deducts the curvature effect from the overall rotor through-flow.
This is only justified for centrifugal fans since these have small or modest solidity.
For the same reason, the Wiesner formula for slip is better justified for centrifugal
compressors than the Pfleiderer formula.
With the velocity triangles of Fig. 14.3, we may estimate the ratio 2 2
w u
to about 0.35. With b ≈ − °
2
15 , it follows from (14.11) that min
Z
17
≈ . For
b
b
≈ − °
≈ − °
b
2
2 2
2
45 (
40 ), w u may be up to 0.45, which results in min
Z
10
≈ .
Values used in practice are often 20 and 14 or 16.
14.4.2 Inducer
Rotors with radial end blades or with slightly backward swept blades are intended
to realise the maximum attainable work. Therefore, such applications aim at maximum attainable peripheral speed (Figs. 14.2 and 14.7). This requires adaptation of
the rotor inlet. Bending stress generated by the centrifugal force at the inlet side of
the impeller must be avoided. This may be achieved by adding an axial part, termed
p
b
<
2 2 R
2
2 cos u f
0.80w .
Z
p
b
<
2 2
2
2 cos u
w .
Z