Page 79 - Fluid Mechanics and Thermodynamics of Turbomachinery

60 Fluid Mechanics, Thermodynamics of Turbomachinery

FIG. 3.4. Lift and drag forces exerted by a cascade blade (of unit span) upon the fluid.

FIG. 3.5. Axial and tangential forces exerted by unit span of a blade upon the fluid.

Experimental data are often presented in terms of lift and drag when the data may
be of greater use in the form of tangential force and total pressure loss. The lift and
drag forces can be resolved in terms of the axial and tangential forces. Referring to
Figure 3.5,

L D X sin ˛ m C Y cos ˛ m , .3.12/

D D Y sin ˛ m X cos ˛ m . .3.13/
From eqn. (3.5)

X/ D sp 0 cos ˛ m . (3.14)
D D cos ˛ m .Y tan ˛ m
Rearranging eqn. (3.14) for X and substituting into eqn. (3.12) gives,

L D .Y tan ˛ m sp 0 / sin ˛ m C Y cos ˛ m

D Y sec ˛ m sp 0 sin ˛ m
2
D sc .tan ˛ 1 tan ˛ 2 / sec ˛ m sp 0 sin ˛ m , .3.15/
x
after using eqn. (3.9).
Lift and drag coefficients may be introduced as

L
C L D , .3.16a/
1 c l
2
2 m
D
C D D . .3.16b/
1 c l
2
2 m