Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

104 Fluid Mechanics, Thermodynamics of Turbomachinery
FIG. 4.7. Velocity diagram and Mollier diagram for a 50% reaction turbine stage.
tion is clear from eqn. (4.18); the reaction is negative for the impulse turbine stage
when account is taken of the irreversibility.
50% reaction stage
The combined velocity diagram for this case is symmetrical as can be seen from
Figure 4.7, since b3 = a2. Because of the symmetry it is at once obvious that b2 = a3,
also. Now with R = 1 – 2 , eqn. (4.18) implies that the enthalpy drop in the nozzle row
equals the enthalpy drop in the rotor, or
(4.23)
Figure 4.7 has been drawn with the same values of cx, U and DW, as in Figure 4.5 (zero
reaction case), to emphasise the difference in flow geometry between the 50% reaction
and zero reaction stages.
Diffusion within blade rows
Any diffusion of the flow through turbine blade rows is particularly undesirable and
must, at the design stage, be avoided at all costs. This is because the adverse pressure
gradient (arising from the flow diffusion) coupled with large amounts of fluid deflection
(usual in turbine blade rows), makes boundary-layer separation more than merely
possible, with the result that large scale losses arise. A compressor blade row, on the
other hand, is designed to cause the fluid pressure to rise in the direction of flow, i.e.
an adverse pressure gradient. The magnitude of this gradient is strictly controlled in a
compressor, mainly by having a fairly limited amount of fluid deflection in each blade
row.
The comparison of the profile losses given in Figure 3.14 is illustrative of the undesirable
result of negative “reaction” in a turbine blade row. The use of the term reaction
here needs qualifying as it was only defined with respect to a complete stage. From
eqn. (4.22a) the ratio R/f can be expressed for a single row of blades if the flow angles
are known. The original data provided with Figure 3.14 gives the blade inlet angles for
impulse and reaction blades as 45.5 and 18.9deg respectively. Thus, the flow angles
can be found from Figure 3.14 for the range of incidence given, and R/f can be calculated.
For the reaction blades R/f decreases as incidence increases going from 0.36
to 0.25 as i changes from 0 to 10deg. The impulse blades, which it will be observed