Page 320 - Fluid Mechanics and Thermodynamics of Turbomachinery

Hydraulic Turbines 301
2
Solution. From the group D gH/.ND/ we get:
N p D N m .D m /D p /.H p /H m / 0.5 D .360/5/.60/1.8/ 0.5 D 415.7 rev/min.

3
From the group D Q/.ND / we get:
3
3
3
Q p D Q m .N p /N m /.D p /D m / D 0.215 ð .360/415.7/ ð 5 D 23.27 m /s.
5
3
Lastly, from the group O P D P/. N D / we get:
5
5
3
3
P p D P m .N p /N m / .D p /D m / D 3 ð .415.7/ ð 5 D 14 430 kW D 14.43 MW.
This result has still to be corrected to allow for scale effects. First we must calculate
the efficiency of the model turbine. The efficiency is found from
3
3
m D P/. QgH/ D 3 ð 10 /.10 ð 0.215 ð 9.81 ð 1.8/ D 0.79.
Using Moody’s formula the efficiency of the prototype is determined:
.1 p / D .1 m / ð 0.2 0.25 D 0.21 ð 0.6687

hence
p D 0.8596.

The corresponding power is found by an adjustment of the original power obtained
under dynamically similar conditions, i.e.
Corrected P p D 14.43 ð 0.8596/0.79 D 15.7MW.

Cavitation

A description of the phenomenon of cavitation, mainly with regard to pumps, was
given in Chapter 1. In hydraulic turbines, where reliability, long life and efficiency
are all so very important, the effects of cavitation must be considered. Two types
of cavitation may be in evidence,
(a) on the suction surfaces of the runner blades at outlet which can cause severe
blade erosion; and
(b) a twisting “rope-type” cavity that appears in the draft tube at off-design operating
conditions.
Cavitation in hydraulic turbines can occur on the suction surfaces of the runner
blades where the dynamic action of the blades acting on the fluid creates low
pressure zones in a region where the static pressure is already low. Cavitation will
commence when the local static pressure is less than the vapour pressure of the
water, i.e. where the head is low, the velocity is high and the elevation, z,ofthe
turbine is set too high above the tailrace. For a turbine with a horizontal shaft the
lowest pressure will be located in the upper part of the runner, which could be of
major significance in large machines. Fortunately, the runners of large machines are,