Page 300 - Fluid Mechanics and Thermodynamics of Turbomachinery

Hydraulic Turbines 281
here) are plotted in Figure 9.2 on a ln Q vs ln H diagram, and reflect the present state
of the art of hydraulic turbomachinery design. Also in Figure 9.2 lines of constant
power output are conveniently shown and have been calculated as the product gQH,
where the efficiency is accorded the value of 0.8 throughout the chart.
Capacity of large Francis turbines

The size and capacity of some of the recently built Francis turbines is a source of
wonder, they seem so enormous! The size and weight of the runners cause special
problems getting them to the site, especially when rivers have to be crossed and the
bridges are inadequate.
The largest installation now in North America is at La Grande on James Bay
in eastern Canada where 22 units each rated at 333 MW have a total capacity of
7326 MW. For the record, the Itaipu hydroelectric plant on the Paran´ a river (between
Brazil and Paraguay), dedicated in 1982, has the greatest capacity of 12 870 MW in
full operation (with a planned value of 21 500 MW) using 18 Francis turbines each
sized at over 700 MW.
The efficiency of large Francis turbines has gradually risen over the years and
now is about 95 per cent. An historical review of this progress has been given
by Danel (1959). There seems to be little prospect of much further improvement
in efficiency as skin friction, tip leakage and exit kinetic energy from the diffuser
now apparently account for the remaining losses. Raabe (1985) has given much
attention to the statistics of the world’s biggest turbines. It would appear at the
present time that the largest hydroturbines in the world are the three vertical shaft
Francis turbines installed at Grand Coulee III on the Columbia River, Washington,
USA. Each of these leviathans has been uprated to 800 MW, with the delivery
(or effective) head, H D 87 m, N D 85.7 rev/min, the runner having a diameter of
D D 9.26 m and weighing 450 ton. Using this data in eqn. (9.1) it is easy to calculate
that the power specific speed is 1.74 rad.

The Pelton turbine
This is the only hydraulic turbine of the impulse type now in common use. It
is an efficient machine and it is particularly suited to high head applications. The
rotor consists of a circular disc with a number of blades (usually called “buckets”)
spaced around the periphery. One or more nozzles are mounted in such a way that
each nozzle directs its jet along a tangent to the circle through the centres of the
buckets. There is a “splitter” or ridge which splits the oncoming jet into two equal
streams so that, after flowing round the inner surface of the bucket, the two streams
depart from the bucket in a direction nearly opposite to that of the incoming jet.
Figure. 9.3 shows the runner of a Pelton turbine and Figure 9.4 shows a six-
jet vertical axis Pelton turbine. Considering one jet impinging on a bucket, the
appropriate velocity diagram is shown in Figure 9.5. The jet velocity at entry is c 1
U. At exit
and the blade speed is U so that the relative velocity at entry is w 1 D c 1
from the bucket one half of the jet stream flows as shown in the velocity diagram,
leaving with a relative velocity w 2 and at an angle ˇ 2 to the original direction of
flow. From the velocity diagram the much smaller absolute exit velocity c 2 can be
determined.