Page 309 - Fluid Mechanics and Thermodynamics of Turbomachinery

290 Fluid Mechanics, Thermodynamics of Turbomachinery
(3) Substituting into eqn. (9.1), the power specific speed is,
6 1/2
4.0 ð 10 5/4
 sp D 39.27 ð /.9.81 ð 200/
10 3
D 0.190 rad.

Reaction turbines
The primary features of the reaction turbine are:

(1) only part of the overall pressure drop has occurred up to turbine entry, the
remaining pressure drop takes place in the turbine itself;
(2) the flow completely fills all of the passages in the runner, unlike the Pelton
turbine where, for each jet, only one or two of the buckets at a time are in
contact with the water;
(3) pivotable guide vanes are used to control and direct the flow;
(4) a draft tube is normally added on to the turbine exit; it is considered as an
integral part of the turbine.

The pressure of the water gradually decreases as it flows through the runner and
it is the reaction from this pressure change which earns this type of turbine its
appellation.

The Francis turbine

The majority of Francis turbines are arranged so that the axis is vertical (some
smaller machines can have horizontal axes). Figure 9.11 illustrates a section through
a vertical shaft Francis turbine with a runner diameter of 5 m, a head of 110 m and
a power rating of nearly 200 MW. Water enters via a spiral casing called a volute or
scroll which surrounds the runner. The area of cross-section of the volute decreases
along the flow path in such a way that the flow velocity remains constant. From
the volute the flow enters a ring of stationary guide vanes which direct it onto the
runner at the most appropriate angle.
In flowing through the runner the angular momentum of the water is reduced
and work is supplied to the turbine shaft. At the design condition the absolute flow
leaves the runner axially (although a small amount of swirl may be countenanced)
into the draft tube and, finally, the flow enters the tail race. It is essential that the
exit of the draft tube is submerged below the level of the water in the tail race in
order that the turbine remains full of water. The draft tube also acts as a diffuser;
by careful design it can ensure maximum recovery of energy through the turbine
by significantly reducing the exit kinetic energy.
Figure. 9.12 shows a section through part of a Francis turbine together with the
velocity triangles at inlet to and exit from the runner at mid-blade height. At inlet
to the guide vanes the flow is in the radial/tangential plane, the absolute velocity is
c 1 and the absolute flow angle is ˛ 1 . Thus,
1
˛ 1 D tan .c 1 /c r1 /. (9.13)