Page 155 - Fluid Mechanics and Thermodynamics of Turbomachinery

136 Fluid Mechanics, Thermodynamics of Turbomachinery
Static pressure at stage exit, p 3 D 200 kPa
Estimated total-to-static efficiency, ts D 0.85.
Assuming that the axial velocity is unchanged across the stage, determine:
(1) the specific work done by the gas;
(2) the blade speed;
(3) the static temperature at stage exit.
3
(c) The blade material has a density of 7850 kg/m and the maximum allowable stress
in the rotor blade is 120 MPa. Taking into account only the centrifugal stress, assuming
untapered blades and constant axial velocity at all radii, determine for a mean flow rate of
15 kg/s:
(1) the rotor speed (rev/min);
(2) the mean diameter;
(3) the hub/tip radius ratio.
For the gas assume that C P D 1050 J/(kg K) and R D 287 J/(kg K).
11. The design of a single-stage axial-flow turbine is to be based on constant axial velocity
with axial discharge from the rotor blades directly to the atmosphere.
The following design values have been specified:
Mass flow rate 16.0 kg/s
Initial stagnation temperature, T 01 1100 K
Initial stagnation pressure, p 01 230 kN/m 2
Density of blading material, m 7850 kg/m 3
8
Maximum allowable centrifugal stress at blade root, 1.7 ð 10 N/m 2
p 2 / 0.06
Nozzle profile loss coefficient, Y P D .p 01 p 02 //.p 02
Taper factor for blade stressing, K 0.75
In addition the following may be assumed:
Atmospheric pressure, p 3 102 kPa
Ratio of specific heats,
1.333
Specific heat at constant pressure, C P 1150 J/(kg K)
In the design calculations values of the parameters at the mean radius are as follows:

Stage loading coefficient, D W/U 2 1.2
Flow coefficient, D c x /U 0.35
Isentropic velocity ratio, U/c 0 0.61
p
where c 0 D [2.h 01 h 3SS /]
Determine:
(1) the velocity triangles at the mean radius;
(2) the required annulus area (based on the density at the mean radius);
(3) the maximum allowable rotational speed;
(4) the blade tip speed and the hub/tip radius ratio.