Question

Section B – combined cycles
Overview: a combined gas – steam power cycle in Sweden provides electricity and hot
water for heating duties for a small city. The gas turbine drives an electricity generator
with an efficiency of 97%. A sub-critical coal fired boiler is used as a heat recovery steam
generator, as well as providing additional steam from coal during the winter months. The
steam turbine drives an electricity generator with an efficiency of 95%. The plant is
located at sea level.
Detailed information:
a. The gas turbine has a pressure ratio of 8.0, compressor isentropic efficiency 88%,
turbine isentropic efficiency 89%, gas temperature at compressor inlet 15 °C, gas
temperature at turbine inlet 1070 °C. The air flow into the compressor is a constant
70 kg/s.
b. The boiler / heat exchanger drives a simple Rankine cycle with a heat exchanger
pressure of 6.2 MPa absolute and a turbine outlet pressure of 10 kPa absolute. The
steam is heated to 400 °C. The final gas exhaust temperature from the boiler/heat
recovery steam generator is 150 °C. The feedwater temperature is 98 °C. The
feedwater pump isentropic efficiency is 86% and the turbine isentropic efficiency is
83%. Assume there are no pressure losses in the piping. Assume the heat transfer
efficiency of the boiler/heat exchanger does not change in both modes of operation.
The boiler performance details are given in Table 1.
Table 1. Boiler performance details
Performance Parameter Value
Boiler efficiency (%) 70
Gross calorific value of coal (kJ/kg) 25500
Coal use in a week (tonnes) 1600
Tasks
1. Draw a schematic of the actual gas turbine cycle and temperature/specific entropy
diagram. Determine the actual cycle efficiency, back work ratio and the power [in
MW] produced by the gas turbine. Use air standard assumptions. Interpolate the
values in the tables when required. Carry out the calculations by using the tables for
ideal gas properties of air, such as Pr.
2. Work out the mass flow rate of steam produced by the gas turbine exhaust (use the
turbine gas exhaust temperature determined using the relative pressure equation
method), and the mass flow of steam produced by coal combustion.
3. Draw a schematic of the actual steam turbine cycle and temperature/specific entropy
diagram. Then show the interaction between the Brayton and Rankine cycles.
4. Work out the net work, the cycle efficiency and the total power produced by the
steam.
5. Determine the electrical power produced by the electricity generator driven by the
gas turbine, by the electricity generator driven by the steam turbine, and the total
electrical power.

Answer 1

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