Page 73 - Fluid Mechanics and Thermodynamics of Turbomachinery

54 Fluid Mechanics, Thermodynamics of Turbomachinery
An axial flow turbine has a small stage efficiency of 86%, an overall pressure ratio of 4.5
to 1 and a mean value of
equal to 1.333. Calculate the overall turbine efficiency.
2. Air is expanded in a multi-stage axial flow turbine, the pressure drop across each stage
being very small. Assuming that air behaves as a perfect gas with ratio of specific heats
,
derive pressure-temperature relationships for the following processes:
(i) reversible adiabatic expansion;
(ii) irreversible adiabatic expansion, with small stage efficiency p ;
(iii) reversible expansion in which the heat loss in each stage is a constant fraction k of the
enthalpy drop in that stage;
(iv) reversible expansion in which the heat loss is proportional to the absolute temperature T.
Sketch the first three processes on a T, s diagram.
If the entry temperature is 1100 K, and the pressure ratio across the turbine is 6 to 1, calculate
the exhaust temperatures in each of these three cases. Assume that
is 1.333, that p D 0.85,
and that k D 0.1.
3. A multi-stage high-pressure steam turbine is supplied with steam at a stagnation pressure
of 7 MPa. and a stagnation temperature of 500 ° C. The corresponding specific enthalpy is
3410 kJ/kg. The steam exhausts from the turbine at a stagnation pressure of 0.7 MPa, the
steam having been in a superheated condition throughout the expansion. It can be assumed
that the steam behaves like a perfect gas over the range of the expansion and that
D 1.3.
Given that the turbine flow process has a small-stage efficiency of 0.82, determine.
(i) the temperature and specific volume at the end of the expansion;
(ii) the reheat factor.
The specific volume of superheated steam is represented by pv D 0.231.h 1943/, where
3
p is in kPa, v is in m /kg and h is in kJ/kg.
4. A 20 MW back-pressure turbine receives steam at 4 MPa and 300 ° C, exhausting from
the last stage at 0.35 MPa. The stage efficiency is 0.85, reheat factor 1.04 and external losses
2% of the actual sentropic enthalpy drop. Determine the rate of steam flow.
At the exit from the first stage nozzles the steam velocity is 244 m/s, specific volume
3
68.6 dm /kg, mean diameter 762 mm and steam exit angle 76 deg measured from the axial
direction. Determine the nozzle exit height of this stage.
5. Steam is supplied to the first stage of a five stage pressure-compounded steam turbine
at a stagnation pressure of 1.5 MPa and a stagnation temperature of 350 ° C. The steam leaves
the last stage at a stagnation pressure of 7.0 kPa with a corresponding dryness fraction of
0.95. By using a Mollier chart for steam and assuming that the stagnation state point locus
is a straight line joining the initial and final states, determine
(i) the stagnation conditions between each stage assuming that each stage does the same
amount of work;
(ii) the total-to-total efficiency of each stage;
(iii) the overall total-to-total efficiency and total-to-static efficiency assuming the steam enters
the condenser with a velocity of 200 m/s;
(iv) the reheat factor based upon stagnation conditions.