Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

102 Fluid Mechanics, Thermodynamics of Turbomachinery
The velocity triangles are symmetrical, so that a 2 = b 3. Also, R = N = a 2 = 68.2°,
This value appears to be the same as the peak value of the efficiency curve DW/U 2
= 1.0, in Figure 4.4.
Stage reaction
The classification of different types of axial turbine is more conveniently described
by the degree of reaction, or reaction ratio R, of each stage rather than by the ratio
cy2/U. As a means of description the term reaction has certain inherent advantages which
become apparent later. Several definitions of reaction are available; the classical definition
is given as the ratio of the static pressure drop in the rotor to the static pressure
drop in the stage. However, it is more useful to define the reaction ratio as the static
enthalpy drop in the rotor to the static enthalpy drop in the stage because it then
becomes, in effect, a statement of the stage flow geometry. Thus,
If the stage is normal (i.e. c1 = c3), then
Using eqn. (4.4), h2 - h 3 = 1 – 2 (w 3 2 + w2 2 ) and eqn. (4.18) gives
Assuming constant axial velocity through the stage
since, upon referring to Figure 4.1, it is seen that
Thus,
(4.17)
(4.18)
(4.19)
(4.20)
(4.21)
(4.22a)