Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

58 Fluid Mechanics, Thermodynamics of Turbomachinery
x/l. Some examples of these tables are quoted by Horlock (1958, 1966). Summarising,
the useful parameters for describing a cascade blade are camber line shape, b/l, a/l, type
of thickness distribution and maximum thickness to chord ratio, tmax/l.
Two important geometric variables, which define the cascade shown in Fig. 3.2, are
the space–chord ratio, s/l, and the stagger angle, x, the angle between the chord line
and the reference direction which is a line perpendicular to the cascade front.
Throughout the remainder of this book unless stated to the contrary, all fluid and blade
angles are referred to this reference direction so as to avoid the needless complication
arising from other directional references. However, custom dies hard; in steam turbine
practice, blade and flow angles are conventionally measured from the tangential direction
(i.e. parallel to the cascade front). Despite this, it is better to avoid ambiguity of
meaning by adopting the single reference direction already given.
The blades angles at entry to and at exit from the cascade are denoted by a¢1 and a¢2
respectively. A most useful blade parameter is the camber angle q which is the change
in angle of the camber line between the leading and trailing edges and equals a¢1–a¢2
in the notation of Figure 3.2. For circular arc camber lines the stagger angle is
x = 1 – 2 (a¢1 + a¢2).
Analysis of cascade forces
The fluid approaches the cascade from far upstream with velocity c1 at an angle a1
and leaves far downstream of the cascade with velocity c 2 at an angle a 2. In the
b
t
a
a¢ 2
x
c 2
d
y
q
a¢ 2
a 2
FIG. 3.2. Compressor cascade and blade notation.
x
s
a¢
1
a¢ 1
a 1
c 1 = inlet flow velocity vector
c 2 = outlet flow velocity vector
(averaged across the pitch)
i
c 1