238
6 Steam Turbines
6.10.3. Superheated steam can accurately be represented as an ideal gas with a
specific heat ratio g around 1.30. Wet steam deviates quite strongly from an ideal
gas. Nevertheless, the most essential ideal gas relations can be used. These are, for
an expansion process in a nozzle (Fig. 4.5), the polytropic relation between density
and pressure
1/
00
00
/
( /
)
n
p p
r r =
and the relation between enthalpy and pressure
n 1
00
n
00
00
00
p
p
h
h
[ 1 (
) ].
1
p
g
g
r
−
− =
−
−
These relations can be fitted very accurately to
an isentropic expansion in the wet steam region. Verify first for the density-pressure
relation. Take as an example an isentropic expansion starting from saturated vapour
at 6 bar until 0.5 bar. Calculate density for the pressure levels 3.5, 2, 1 and 0.5 bar.
Use steam tables from a book on thermodynamics or from a website. A basic Mollier-diagram for water-steam can be found on: http://www.engineeringtoolbox.com/
mollier-diagram-water-d_308.html. Steam properties may be calculated with:
http://www.spiraxsarco.com/resources/steam-tables.asp. The starting point of the
expansion defines the entropy. Values of specific volume (inverse of the density),
entropy and enthalpy are obtained by linear interpolation as a function of the dryness factor (also called steam quality: ratio of the mass fraction of vapour to the
mass of the mixture of saturated liquid and saturated vapour). (A: the specific heat
ratio g is 1.1334 for a fitting to the 5 data couples). Verify then that the enthalpypressure relation is very accurately satisfied with the obtained value of the specific
heat ratio. Observe that the ideal gas law p
RT
r
=
is not well satisfied (R is not a
constant), but remark that the ideal gas law can easily be avoided in the calculation of the expansion of a nozzle. Consider subsequently the polytropic efficiency
h ∞ = 0.90 for characterisation of irreversibility. Verify that couples of density and
enthalpy calculated on the polytropic expansion correspond very well with real
steam data for the pressure levels used before.
6.10.4. Figures 6.26 and 6.27 represent the HP-IP rotor and an LP rotor of
the Arabelle impulse type steam turbine of Alstom. The machine is built with
two LP parts for electric power 900 MW–1400 MW and with 3 LP parts for
1300 MW–1700 MW. The machines are not strictly unique and are adapted somewhat to the particular application. We consider here Flamanville 3 (France) with
1750 MW electric power, which is the largest turbine up to now. The steam conditions are: inlet at 75 bar, 290 °C (saturated) with expansion to 11 bar in the HP
part; moisture separation and reheat on 11 bar to 275 °C (superheated); condenser
pressure is 46 mbar. Mass flow at turbine inlet is 2500 kg/s (lower flow rate in IP
and LP parts) and rotational speed is 1500 rpm. For the last stage, the tip diameter
and hub diameter are 6.00 and 2.50 m (blade length is 1750 mm). The hub diameter
of the first stage in the HP part is 1.75 m (the hub diameter varies slightly in the
HP-IP part). The corresponding blade speeds are 471.24, 196.35 and 137.45 m/s.
The blade speed in the HP part is very low, causing a low stage work. The reason
is that the shafts of the HP-IP part and the 3 LP parts are coupled inline to drive a
single generator (so called tandem-compound machine). A more comfortable blade
speed at the hub of the HP-IP part would be the double speed, being about 275 m/s,
6 Steam Turbines
6.10.3. Superheated steam can accurately be represented as an ideal gas with a
specific heat ratio g around 1.30. Wet steam deviates quite strongly from an ideal
gas. Nevertheless, the most essential ideal gas relations can be used. These are, for
an expansion process in a nozzle (Fig. 4.5), the polytropic relation between density
and pressure
1/
00
00
/
( /
)
n
p p
r r =
and the relation between enthalpy and pressure
n 1
00
n
00
00
00
p
p
h
h
[ 1 (
) ].
1
p
g
g
r
−
− =
−
−
These relations can be fitted very accurately to
an isentropic expansion in the wet steam region. Verify first for the density-pressure
relation. Take as an example an isentropic expansion starting from saturated vapour
at 6 bar until 0.5 bar. Calculate density for the pressure levels 3.5, 2, 1 and 0.5 bar.
Use steam tables from a book on thermodynamics or from a website. A basic Mollier-diagram for water-steam can be found on: http://www.engineeringtoolbox.com/
mollier-diagram-water-d_308.html. Steam properties may be calculated with:
http://www.spiraxsarco.com/resources/steam-tables.asp. The starting point of the
expansion defines the entropy. Values of specific volume (inverse of the density),
entropy and enthalpy are obtained by linear interpolation as a function of the dryness factor (also called steam quality: ratio of the mass fraction of vapour to the
mass of the mixture of saturated liquid and saturated vapour). (A: the specific heat
ratio g is 1.1334 for a fitting to the 5 data couples). Verify then that the enthalpypressure relation is very accurately satisfied with the obtained value of the specific
heat ratio. Observe that the ideal gas law p
RT
r
=
is not well satisfied (R is not a
constant), but remark that the ideal gas law can easily be avoided in the calculation of the expansion of a nozzle. Consider subsequently the polytropic efficiency
h ∞ = 0.90 for characterisation of irreversibility. Verify that couples of density and
enthalpy calculated on the polytropic expansion correspond very well with real
steam data for the pressure levels used before.
6.10.4. Figures 6.26 and 6.27 represent the HP-IP rotor and an LP rotor of
the Arabelle impulse type steam turbine of Alstom. The machine is built with
two LP parts for electric power 900 MW–1400 MW and with 3 LP parts for
1300 MW–1700 MW. The machines are not strictly unique and are adapted somewhat to the particular application. We consider here Flamanville 3 (France) with
1750 MW electric power, which is the largest turbine up to now. The steam conditions are: inlet at 75 bar, 290 °C (saturated) with expansion to 11 bar in the HP
part; moisture separation and reheat on 11 bar to 275 °C (superheated); condenser
pressure is 46 mbar. Mass flow at turbine inlet is 2500 kg/s (lower flow rate in IP
and LP parts) and rotational speed is 1500 rpm. For the last stage, the tip diameter
and hub diameter are 6.00 and 2.50 m (blade length is 1750 mm). The hub diameter
of the first stage in the HP part is 1.75 m (the hub diameter varies slightly in the
HP-IP part). The corresponding blade speeds are 471.24, 196.35 and 137.45 m/s.
The blade speed in the HP part is very low, causing a low stage work. The reason
is that the shafts of the HP-IP part and the 3 LP parts are coupled inline to drive a
single generator (so called tandem-compound machine). A more comfortable blade
speed at the hub of the HP-IP part would be the double speed, being about 275 m/s,