Page 110 - Fluid Mechanics and Thermodynamics of Turbomachinery
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Two-dimensional Cascades 91
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2
pressure loss coefficient ω D p 0 /. c 1 / D 0.015. At positive incidence over a limited
2
range (0 6 i 6 6 ° ) the variation of both υ and ω for this particular cascade can be represented
with sufficient accuracy by linear approximations, viz.
dυ dω
D 0.06, D 0.001
di di
where i is in degrees.
For a flow incidence of 5.0 deg determine
(i) the flow angles at inlet and outlet;
(ii) the diffuser efficiency of the cascade;
(iii) the static pressure rise of air with a velocity 50 m/s normal to the plane of the cascade.
3
Assume density of air is 1.2 kg/m .
5. (a) A cascade of compressor blades is to be designed to give an outlet air angle ˛ 2
of 30 deg for an inlet air angle ˛ 1 of 50 deg measured from the normal to the plane of the
cascade. The blades are to have a parabolic arc camber line with a/l D 0.4 (i.e. the fractional
distance along the chord to the point of maximum camber). Determine the space/chord
ratio and blade outlet angle if the cascade is to operate at zero incidence and nominal
conditions. You may assume the linear approximation for nominal deflection of Howell’s
cascade correlation:
Ł
Ł
D .16 0.2˛ /.3 s/l/ deg
2
as well as the formula for nominal deviation:
" #
2 Ł r
2a ˛ 2 s
Ł
υ D 0.23 C deg.
l 500 l
(b) The space/chord ratio is now changed to 0.8, but the blade angles remain as they are
in part (a) above. Determine the lift coefficient when the incidence of the flow is 2.0 deg.
Ł
Ł
Ł
Assume that there is a linear relationship between / and .i i // over a limited region,
Ł
Ł
Ł
Ł
Ł
viz. at .i i // D 0.2, / D 1.15 and at i D i , / D 1. In this region take C D D 0.02.
1
2
6. (a) Show that the pressure rise coefficient C p D p/. c / of a compressor cascade
2 1
is related to the diffuser efficiency D and the total pressure loss coefficient by the
following expressions:
2
2
2
2
C p D D .1 sec ˛ 2 / sec ˛ 1 / D 1 .sec ˛ 2 C // sec ˛ 1
1
2
where d D p/f .c 2 c /g
2 1 2
2
1
D p 0 /. c /
2 x
˛ 1 ,˛ 2 D flow angles at cascade inlet and outlet.
(b) Determine a suitable maximum inlet flow angle of a compressor cascade having a
space/chord ratio 0.8 and ˛ 2 D 30 deg when the diffusion factor D is to be limited to 0.6.
The definition of diffusion factor which should be used is the early Lieblein formula (1956),
cos ˛ 1 s cos ˛ 1
D D 1 C .tan ˛ 1 tan ˛ 2 /.
cos ˛ 2 l 2
(c) The stagnation pressure loss derived from flow measurements on the above cascade is
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149 Pa when the inlet velocity c 1 is 100 m/s at an air density of 1.2 kg/m . Determine the
values of
