Question

The net power of a combined gas-steam power plant is 450 MW. The pressure ratio of the gas turbine cycle is 14, the air enters the compressor at a temperature of 300 K and the turbine at a temperature of 1400 K. Combustion end gases coming out of the gas turbine produce steam at a waste heat boiler at 8 MPa pressure and 400 degrees Celsius temperature and exit the boiler at 460 K temperature. The steam cycle has an open feed water heater operating at 0.6 MPa pressure, the condenser pressure is 20kPa. Recognizing that all compression and expansion are isentropic;

a)

The ratio of mass flow of air to mass flow of steam,

b)

In the combustion chamber, the air is given to the air in unit time,

c)

calculate the thermal efficiency of the combined cycle.

Answer 1

Compression ratio pr=14

Pressure at exchanger inlet P1 = 20KPa

Pressure at pump exit P2 = 8MPa

Pressure at steam turbine inlet P3=8 MPa

Temperature at steam turbine inlet T3=400 degC

Temp at compressor inlet T5=300 K

Temp at Combustion chamber inlet T6= ?

Temperature at gas turbine inlet T7=1400 K

Temperature at heat exchanger inlet T8=?

Temperature at heat exchanger exit T9=460 K

Since we have considered all expansion and compression isentropic. The work can be calculated as ideal reversible system

The outlet temp of Compressor

Work done by Compressor

The outlet temp of the turbine

Work produced from turbine

Heat input in the gas cycle in combustion chamber

Net work from gas cycle

For steam cycle

Steam property at P=8MPa and T=400 deg C can be obtained from steam table. We will use values as follow:

h3 = 3139.3kJ/kg and s3=6.366 kJ/kgK

Steam properties at 20kPa

s_f4=0.8320kJ/kgK

s_fg4 = 7.70752 kJ/kgK

h_f4 = 251.42kJ/kg

h_fg4 = 2357.50 kJ/kg

The quantity of steam at exit of steam turbine

s₃=s_f4+x(s_fg4)

x = (6.366-0.8320)/7.0752 = 0.78

Enthalpy at steam turbine exit

h₄= h_f4+x(h_fg4) = 251.42+0.78*2357.50 = 2090.30 kJ/kg

At the condenser outlet, steam is considered to be saturated liquid at 20kPa

h₁= 251.42 kJ/kg

Work done by pump to pump liquid into boiler to 8MPa

Enthalpy at pump exit

h₂ = 8.11+251.42 = 259.5kJ/kg

Applying energy balance on the waste heat recovery system

..............A

Work produced from steam turbine

Net work generated in steam cycle

Total work in cycle = 450MW

---------B

Total Heat input in the gas cycle in combustion chamber

Thermal efficiency

---------------C