Fluid Mechanics and Thermodynamics of Turbomachinery, 5e

312 Fluid Mechanics, Thermodynamics of Turbomachinery
2
3
1
The relations for the flow angles are
r 1
Exit
flow
(9.22a)
(9.22b)
Example 9.4. A small-scale Kaplan turbine has a power output of 8MW, an available
head at turbine entry of 13.4m and a rotational speed of 200rev/min. The inlet
guide vanes have a length of 1.6m and the diameter at the trailing edge surface is
3.1m. The runner diameter is 2.9m and the hub–tip ratio is 0.4.
Assuming the hydraulic efficiency is 92% and the runner design is “free-vortex”,
determine
(i) the radial and tangential components of velocity at exit from the guide vanes;
(ii) the component of axial velocity at the runner;
(iii) the absolute and relative flow angles upstream and downstream of the runner at
the hub, mid-radius and tip.
Solution. As P = hHrgQHE, then the volume flow rate is
As the specific work done is DW = U 2cq2 and hH =DW/(gHE), then at the tip
b 2
W 2
U
c 3 = c x
c 2
a 2
Blade motion
FIG. 9.17. Section of a Kaplan turbine and velocity diagrams at inlet to and exit from
the runner.
b 3
U
W 3