Page 315 - Fluid Mechanics and Thermodynamics of Turbomachinery

296 Fluid Mechanics, Thermodynamics of Turbomachinery
NB. The head H 3 is relative to the tailrace.
2
.3.5 2 10.5 /
∴ H 3 D C 1 2 D6.0m,
2 ð 9.81
i.e. the pressure at runner outlet is below atmospheric pressure, a matter of some
importance when we come to consider the subject of cavitation later in this chapter.
From eqn. (9.18),
2
2
c /.2g/ D 150 6 38.73 /.2 ð 9.81/ D 67.22 m.
H 2 D H E H N
2
From eqn. (9.18),
c
W D g.H E H N H R z / 1 2 gH 3
2 3
2 2 2
D 9.81 ð .150 6 10 2/ 10.5 /2 C 9.81 ð 6 D 1298.7m /s
∴ c 2 D W/U 2 D 1298.7/35 D 37.1 m/s
37.1
˛ 2 D tan 1 c 2 D tan 1 D 74.2 deg
c r2 10.5
37.1 35
ˇ 2 D tan 1 c 2 D tan 1 D 11.31 deg .
c r2 10.5
The hydraulic efficiency is

W
H D D 1298.7/.9.81 ð 150/ D 0.8826.
gH E
From the definition of the power specific speed, eqn. (9.1),
 SP .gH E / 5/4 0.8 ð 9114
 D p D p D 45.24 rad/s.
QW 20 ð 1298.7

Thus, the rotational speed is N D 432 rev/min and the runner diameter is
D 2 D 2U 2 / D 70/45.24 D 1.547 m.

The Kaplan turbine

This type of turbine evolved from the need to generate power from much lower
pressure heads than are normally employed with the Francis turbine. To satisfy
large power demands very large volume flow rates need to be accommodated in the
Kaplan turbine, i.e. the product QH E is large. The overall flow configuration is from
radial to axial. Figure 9.16 is a part sectional view of a Kaplan turbine in which the
flow enters from a volute into the inlet guide vanes which impart a degree of swirl
to the flow determined by the needs of the runner. The flow leaving the guide vanes
is forced by the shape of the passage into an axial direction and the swirl becomes
essentially a free vortex, i.e.

rc D a constant.