Page 154 - Fluid Mechanics and Thermodynamics of Turbomachinery

Axial-flow Turbines: Two-dimensional Theory 135
and the following blade geometry was selected:

Nozzles Rotor

Inlet angle, deg 0 48
Outlet angle, deg 70.0 56.25
Space/chord ratio, s/l 0.42
Blade length/axial chord ratio, H/b 2.0 2.1
Max. thickness/axial chord 0.2 0.2

The deviation angle of the flow from the rotor row is known to be 3 deg on the evidence
of cascade tests at the design condition. In the absence of cascade data for the nozzle row,
the designer estimated the deviation angle from the approximation 0.19 s/l where is the
blade camber in degrees. Assuming the incidence onto the nozzles is zero, the incidence onto
the rotor 1.04 deg and the axial velocity across the stage is constant, determine:
(i) the axial velocity;
(ii) the stage reaction and loading factor;
(iii) the approximate total-to-total stage efficiency on the basic of Soderberg’s loss correla-
tion, assuming Reynolds number effects can be ignored;
(iv) by means of a large steam chart (Mollier diagram) the stagnation temperature and
pressure at stage exit.
9. (a) A single-stage axial flow turbine is to be designed for zero reaction without any
absolute swirl at rotor exit. At nozzle inlet the stagnation pressure and temperature of the
gas are 424 kPa and 1100 K. The static pressure at the mean radius between the nozzle row
and rotor entry is 217 kPa and the nozzle exit flow angle is 70 ° .
Sketch an appropriate Mollier diagram (or a T s diagram) for this stage allowing for the
effects of losses and sketch the corresponding velocity diagram. Hence, using Soderberg’s
correlation to calculate blade row losses, determine for the mean radius,
(1) the nozzle exit velocity,
(2) the blade speed,
(3) the total-to-static efficiency.
(b) Verify for this turbine stage that the total-to-total efficiency is given by
2
1 1
D
tt ts 2
where D c x /U. Hence, determine the value of the total-to-total efficiency.
Assume for the gas that C p D 1.15 kJ/(kg K) and
D 1.333.
10. (a) Prove that the centrifugal stress at the root of an untapered blade attached to the
drum of an axial flow turbomachine is given by
2
c D m N A n /1800,
where m D density of blade material, N D rotational speed of drum and A n D area of the
flow annulus.
(b) The preliminary design of an axial-flow gas turbine stage with stagnation conditions at
stage entry of p 01 D 400 kPa, T 01 D 850 K, is to be based upon the following data applicable
to the mean radius:
Flow angle at nozzle exit, ˛ 2 D 63.8 deg
Reaction, R D 0.5
Flow coefficient, c x /U m D 0.6