210
6 Steam Turbines
Work has, for constant ,
r
f a parabolic variation in u, and reaches a maximum for
The value of the maximum is
The maximum efficiency value is
This result is somewhat approximate because the rotor velocity coefficient varies
slightly with varying blade speed.
Applied to the nozzle for
,
1 75
d a
°
=
=
Soderberg’s formula results in ξ = 0.0763,
for aspect ratio = 4.
With
,
2
2
2
1s
1
1
s
v
v
v
2
2
2
x
=
−
it follows that
.
ss
s
1
0 929
1
h
x
=
=
+
and
. .
s
s
1
0 964
1
f
x
=
=
+
We define the velocity obtained by the enthalpy drop s
h
D converted loss-free in
kinetic energy, i.e. v
h
s
s
2
2
/
,
= ∆ as an energy reference velocity v s of the stage . This
velocity is called the spouting velocity. With an impulse turbine is v
v
s
s
1 = . We call
speed ratio the ratio of the blade speed to the spouting velocity:
The optimum speed ratio with an impulse turbine is
s
1
o
sin
0.465.
2
=
≈
f
a
l
With a 1 = 75° corresponds β 1 ≈ 62°. Rotor loss can be expressed, with
,
2
r 1
w
w
f
=
by
.
1u
s 1s
1
o
v
v sin
u u
2
2
f
a
= =
=
2
2
2
2
1s
r
o
r o
s
1
v
1
( W ) ( 1
)u
(
) sin
.
2
2
f
D
f
f
a
+
= +
=
2
2
o
r
i o
s
1
s
( W )
1
( )
(
) sin
.
h
2
D
f
h
f
a
D
+
=
=
/ .
s
u v
l =
2
2
2
2
1
2
2
2
r
2
r
w
w
w
w
1
(
1)
,
2
2
2
2
x
f
−
=
−
=