Question

A gas turbine plant consists of a compressor with a pressure ratio of 10, a combustion chamber, and a turbine mounted on the same shaft as the compressor; the net electrical power of the unit is 20 MW. The inlet air conditions are 1.013 bar and 15 ?C and the maximum cycle temperature is 1100 K. The exhaust gases from the turbine are passed through a heat exchanger to heat water for space heating before passing to the chimney; by this means water at 60 ?C flowing at a rate of 2×106 kg/h is heated to 80 ?C. Using the further data below and neglecting the mass flow rate of fuel, calculate; (i) the temperature of the gases leaving the turbine;

(ii) the mass flow rate of air entering the unit;

(iii) the temperature of the gases entering the chimney;

(iv) the overall efficiency of the system defined as the useful energy output divided by the energy input from the fuel. Combined mechanical and electrical efficiency of gas turbine unit, 90 %; combustion efficiency, 99 %; isentropic efficiency of air compressor, 80 %; isentropic efficiency of gas turbine, 83 %; pressure drop in combustion chamber, 0.20 bar; pressure drop of gases in heat exchanger, 0.15 bar; pressure drop in chimney, 0.05 bar; specific heat capacity and ? of combustion gases, 1.15 kJ/kg K and 4/3; mean specific heat capacity of water, 4.191 kJ/kg K.

ANSWER (453.8 ?C; 240 kg/s; 285 ?C; 50 %)

Answer 1

Given

For Gas Turbine T1,P1 be the inlet temperature and pressure of air in the compressor

T2,P2 be the exit temperature and pressure of gas after compression for combustion

T3,P3 be the temperature and pressure of gas into the Tubine after combustion

T4,P4 be the exit temperature and pressure of gas of Turbine

(i) Inlet air temperature T1 = 15⁰C = (15+273) = 288 K

Maximum temperature of gas is after combustion so T3= 1100K

Pressure ratio R =(P2/P1) = (P3/P4)=10

Given  gamma = 4/3 = 1.33

To find out the exit temperature of gas,

Using pressure and temperation relation T3/T4 = (P3/P4)^(-1/)

=(10)^{(1.33-1/1.33)} = 1.770

thus 1100/T4= 1.770

T4 =621.25K

the Isentropic efficiency of the turbine is given as 0.83

_{isentropic Turbine}= (Actual workdone / Isentropic Workdone)

= (T3-T4^")/ (T3- T4)

0.83 = (1100-T4^")/(1100-621.25)

Thus, the exit temperature of the gas T4^" = 702.6 K =(702.6- 273)

=429.6⁰C