Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

life” and also the “percentage creep”, which is the elongation strain at the allowable
stress and temperature of the blade. To enable operation at high temperatures and
for long life of the blades, the creep strength criterion is the one usually applied by
designers.
An estimate of the average rotor blade temperature Tb can be made using the
approximation
i.e. 85% temperature recovery of the inlet relative kinetic energy.
(4.31)
EXAMPLE 4.4. Combustion gases enter the first stage of a gas turbine at a stagnation
temperature and pressure of 1200K and 4.0 bar. The rotor blade tip diameter is 0.75m,
the blade height is 0.12m and the shaft speed is 10,500 rev/min. At the mean radius
the stage operates with a reaction of 50%, a flow coefficient of 0.7 and a stage loading
coefficient of 2.5.
Determine
(i) the relative and absolute flow angles for the stage;
(ii) the velocity at nozzle exit;
(iii) the static temperature and pressure at nozzle exit assuming a nozzle efficiency of
0.96 and the mass flow;
(iv) the rotor blade root stress assuming the blade is tapered with a stress taper factor
K of 2/3 and the blade material density is 8000kg/m 2 ;
(v) the approximate mean blade temperature;
(vi) taking only the centrifugal stress into account suggest a suitable alloy from the
information provided which could be used to withstand 1000hr of operation.
Solution. (i) The stage loading is
From eqn. (4.20) the reaction is
Adding and subtracting these two expressions, we get
Substituting values of y, f and R into the preceding equations, we obtain
and for similar triangles (i.e. 50% reaction)
Axial-flow Turbines: Two-dimensional Theory 119
(ii) At the mean radius, r m = (0.75 - 0.12)/2 = 0.315m, the blade speed is Um =
Wrm = (10500/30) ¥ p ¥ 0.315 = 1099.6 ¥ 0.315 = 346.36m/s. The axial velocity
cx = fUm = 0.5 ¥ 346.36 = 242.45m/s and the velocity of the gas at nozzle exit is c2 =
cx/cos a2 = 242.45/cos 68.2 = 652.86m/s.