485
13.3 Radial Flow Variation
• rotor blade twist is acceptable: ≈ 31.5°;
• flow turning at the rotor hub is acceptable: 42° at Mach number 0.80;
• deceleration at the stator hub is less strong: velocity ratio ≈ 0.62.
Unfavourable findings are that the deceleration at the rotor hub becomes strong and
that the Mach number at the rotor inlet at the tip becomes high. Further raising the
degree of reaction on the average radius causes further decrease of the deceleration
ratio at the rotor hub and further increase of the inlet Mach number at the rotor tip,
as demonstrated by the results in Table 13.3 for ψ = 0.4, ϕ = 0.5 and R = 0.8 on the
mean radius.
Free vortex blades do not result in an entirely advantageous variation of the
flow parameters, unless work is decreased ( ψ under 0.40 on the mean radius) or
the choice for a repeating stage is abandoned. The best flow for the radius ratio
1.20/0.75 is obtained with R = 0.70 on the mean radius (Table 13.2). The corresponding velocity triangles are shown in Fig. 13.9. Remark that the flow at inlet
and outlet of the stage deviates from the meridional plane ( α 1 ≈ 15° at the hub). This
deviation from the meridional plane mainly has as benefit that the Mach number of
the relative flow at the rotor inlet lowers somewhat with respect to the value without pre-swirl. Further improvement at the rotor tip is possible by forcing the vortex
distribution somewhat, as discussed in the next section.
13.3.4 Forcing of the Vortex Distribution
A more favourable variation of flow parameters may be achieved by forcing the
swirl distribution somewhat away from the free vortex. The following relations
apply:
v
v
v
v
W
u
u
u m
u
um
1
2
2
=
−
=
−
∆
∆ ,
v
v
v
v
W
u
u
u m
u
um
2
2
2
=
+
=
+
∆
∆ .
Table 13.3 Flow parameter variation with free vortex blades; R = 0.80 on the mean radius
u
v a
v u1
v u2
v 1 /v 2
w u1
w u2
w 2 /w 1
0.75
0.5
0
0.533
0.684
− 0.75
− 0.217
0.605
1
0.5
0
0.4
0.781
− 1
− 0.6
0.698
1.20
0.5
0
0.333
0.832
− 1.20
− 0.867
0.770
R
α 1
α m
Δα
v 2
β m
Δβ
w 1
0.65
0
23.42
46.83
0.73
− 39.89
32.85
0.90
0.80
0
19.33
38.66
0.64
− 56.81
13.24
1.12
0.86
0
16.84
33.67
0.60
− 63.71
7.35
1.30
13.3 Radial Flow Variation
• rotor blade twist is acceptable: ≈ 31.5°;
• flow turning at the rotor hub is acceptable: 42° at Mach number 0.80;
• deceleration at the stator hub is less strong: velocity ratio ≈ 0.62.
Unfavourable findings are that the deceleration at the rotor hub becomes strong and
that the Mach number at the rotor inlet at the tip becomes high. Further raising the
degree of reaction on the average radius causes further decrease of the deceleration
ratio at the rotor hub and further increase of the inlet Mach number at the rotor tip,
as demonstrated by the results in Table 13.3 for ψ = 0.4, ϕ = 0.5 and R = 0.8 on the
mean radius.
Free vortex blades do not result in an entirely advantageous variation of the
flow parameters, unless work is decreased ( ψ under 0.40 on the mean radius) or
the choice for a repeating stage is abandoned. The best flow for the radius ratio
1.20/0.75 is obtained with R = 0.70 on the mean radius (Table 13.2). The corresponding velocity triangles are shown in Fig. 13.9. Remark that the flow at inlet
and outlet of the stage deviates from the meridional plane ( α 1 ≈ 15° at the hub). This
deviation from the meridional plane mainly has as benefit that the Mach number of
the relative flow at the rotor inlet lowers somewhat with respect to the value without pre-swirl. Further improvement at the rotor tip is possible by forcing the vortex
distribution somewhat, as discussed in the next section.
13.3.4 Forcing of the Vortex Distribution
A more favourable variation of flow parameters may be achieved by forcing the
swirl distribution somewhat away from the free vortex. The following relations
apply:
v
v
v
v
W
u
u
u m
u
um
1
2
2
=
−
=
−
∆
∆ ,
v
v
v
v
W
u
u
u m
u
um
2
2
2
=
+
=
+
∆
∆ .
Table 13.3 Flow parameter variation with free vortex blades; R = 0.80 on the mean radius
u
v a
v u1
v u2
v 1 /v 2
w u1
w u2
w 2 /w 1
0.75
0.5
0
0.533
0.684
− 0.75
− 0.217
0.605
1
0.5
0
0.4
0.781
− 1
− 0.6
0.698
1.20
0.5
0
0.333
0.832
− 1.20
− 0.867
0.770
R
α 1
α m
Δα
v 2
β m
Δβ
w 1
0.65
0
23.42
46.83
0.73
− 39.89
32.85
0.90
0.80
0
19.33
38.66
0.64
− 56.81
13.24
1.12
0.86
0
16.84
33.67
0.60
− 63.71
7.35
1.30