Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

have a dramatic increase in blade profile loss, has R/f decreasing from zero to -0.25
in the same range of incidence.
It was shown above that negative values of reaction indicated diffusion of the rotor
relative velocity (i.e. for R < 0, w3 < w2). A similar condition which holds for diffusion
of the nozzle absolute velocity is that, if R > 1, c2 < c1.
Substituting tan b3 = tan a 3 + U/c x into eqn. (4.22b) gives
(4.22c)
Thus, when a3 = a2, the reaction is unity (also c2 = c3). The velocity diagram for R = 1
is shown in Figure 4.8 with the same values of cx, U and DW used for R = 0 and R = 1 – 2 .
It will be apparent that if R exceeds unity, then c2 < c1 (i.e. nozzle flow diffusion).
EXAMPLE 4.2. A single-stage gas turbine operates at its design condition with an
axial absolute flow at entry and exit from the stage. The absolute flow angle at nozzle
exit is 70deg. At stage entry the total pressure and temperature are 311kPa and 850°C
respectively. The exhaust static pressure is 100kPa, the total-to-static efficiency is 0.87
and the mean blade speed is 500m/s.
Assuming constant axial velocity through the stage, determine
(i) the specific work done;
(ii) the Mach number leaving the nozzle;
(iii) the axial velocity;
(iv) the total-to-total efficiency;
(v) the stage reaction.
Take Cp = 1.148kJ/(kg°C) and g = 1.33 for the gas.
Solution. (i) From eqn. (4.10), total-to-static efficiency is
Thus, the specific work is
Axial-flow Turbines: Two-dimensional Theory 105
FIG. 4.8. Velocity diagram for 100% reaction turbine stage.