Page 172 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Compressors and Fans 153
Ł
The nominal deflection ε D 0.8 max and, from Figure 3.12, ε max D 37.5 ° . Thus,
Ł
ε D 30 ° and the nominal incidence is
Ł
Ł
i D ˇ C ε Ł ˇ 0 1
2
°
D 10.2 C 30 44.5 D4.3 .
Ł
Ł
(ii) At the operating point i D 0.4ε C i D 7.7 ° . Thus, the actual inlet flow
angle is
0
°
ˇ 1 D ˇ C i D 52.2 .
1
From Figure 3.12 at i D 7.7 ° , the deflection ε D 37.5 ° and the flow outlet angle is
°
ˇ 2 D ˇ 1 ε D 14.7 .
(iii) From Figure 5.2, U D c x1 .tan ˛ 1 C tan ˇ 1 / D c x2 .tan ˛ 2 C tan ˇ 2 /. For c x D
constant across the stage and R D 0.5
°
ˇ 1 D ˛ 2 D 52.2 and ˇ 2 D ˛ 1 D 14.7 °
and the flow coefficient is
c x 1
D D D 0.644.
U tan ˛ 1 C tan ˇ 1
2
The stage loading factor, D h 0 /U D .tan ˛ 2 tan ˛ 1 / using eqn. (5.29).
Thus, with D 0.86,
D 0.568.
(iv) The lift coefficient can be obtained using eqn. (3.18)
tan ˇ 2 /
C L D 2.s/l/ cos ˇ m .tan ˇ 1
ignoring the small effect of the drag coefficient. Now tan ˇ m D .tan ˇ 1 C tan ˇ 2 //2.
Hence ˇ m D 37.8 ° and so
C L D 2 ð 0.9 ð 0.7902 ð 1.027 D 1.46.

(v) Combining eqns. (3.7) and (3.17) the drag coefficient is
!
3
s p 0 cos ˇ m
C D D .
2
l 1 w 2 cos ˇ 1
2 1
Again using Figure 3.12 at i D 7.7 ° , the profile total pressure loss coefficient
1
2
p 0 /. w / D 0.032, hence the profile drag coefficient for the blades of either
2 1
row is
3
2
D 0.9 ð 0.032 ð 0.7902 /0.6129 D 0.038.
C D p
Taking account of the annulus wall drag coefficient C Da and the secondary loss
drag coefficient C Ds
C Da D 0.02.s/l/.l/H/ D 0.02 ð 0.9 ð 0.5 D 0.009
2
2
C Ds D 0.018C D 0.018 ð 1.46 D 0.038.
L