Question

2. Consider a combined gas steam power cycle. The gas cycle is a simple Brayton cycle that has a pressure ratio of 7. Air enters at 9.8 kg / s at the compressor at 15 ° C and 100 kPa, and at the gas turbine at 950 ° C. The steam cycle is a Rankine cycle with overheating between the pressure limits of 6 MPa and 10 kPa. The water vapor is heated in the heat exchanger at a rate of 1.15 kg / s by the exhaust gases leaving the gas turbine, and the exhaust gases leave the heat exchanger at 200 ° C. Steam enters the high pressure turbine at 6 MPa and exits at 1.0 MPa, then reheats to 400 ° C in the heat exchanger before it expands under low pressure pressure. Assuming an isentropic efficiency of 80 percent for all pumps, turbines, and the compressor. Use a software and determine the input heat, the output heat, the thermal efficiency of each cycle and the combined cycle, and the power generated in the combined cycle.

Combustio chamber Gas Compressor exchanger 1-0 Code Pump

Answer 1

SOLVED BY USING MATLAB:

SCRIPT:

clc;

%considering constant specific heat of air in KJ/kg K as

c_a = 1.005;

gamma = 1.4; %specific heat ratio

eff = 0.8; %isentropic efficiency for compressor, turbine and pump

%Data for the gas turbine cycle

m_a = 9.8; %mass flow rate of air in kg/s

r_p = 7; %pressure ratio

P7 = 100 ; P9 = P7 * r_p; %pressure in kPa

T7 = 15 + 273 ; T9 = 950 +273; T11 = 200+273; %Temperaure in Kelvin

T8_s = T7 * (r_p^((gamma-1)/gamma));%Temperature after isentropic compression

T8_a = (1/eff)*(T8_s - T7) + T7;%actual temperature after compression

T10_s = T9 / (r_p^((gamma-1)/gamma));%Temperature after isentropic expansion

T10_a = T9 - eff*(T9 - T10_s);%actual temperature after expansion

%Data for the steam turbine

m_s = 1.15; %mass flow rate of steam in kg/s

P3=60;P4=10;P5=10;P6=0.1;P1=0.1;P2=60; %Pressure at all the states in rankine cycle in bar

T5=400; %temperature of steam at low pressure turbine entry

%specific enthalpy and specific entropy at low pressure steam turbine

%inlet

h5 = XSteam('h_pT',P5,T5);

s5 = XSteam('s_pT',P5,T5);

s6_s = s5;%entropy at the low pressure tubine exit when expanded isentrpically

h6_s = XSteam('h_ps',P6,s6_s);%enthalpy at the low pressure turbine exit when expanded isentrpically

h6_a = h5 - eff*(h5 - h6_s);%actual enthalpy at the low pressure turbine exit

%specific volume at state 1

v1=XSteam('vL_p',P1);

%pump work in kJ/kg is given by

Work_pump=(v1*(P2-P1)*100)/eff;

h1=XSteam('hL_p',P1);%specific enthalpy at pump inlet

%enthalpy at pump exit

h2=h1+Work_pump;

%applying energy balance at heat exchanger, we get the specific enthalpy at

%high pressure turbine inlet

h3 = (m_a/m_s)*(T10_a - T11) + h2;

s3= XSteam('s_ph',P3,h3);

%at hight pressure turbine exit

s4_s = s3;

h4_s=XSteam('h_ps',P4,s4_s);

h4_a= h3 - eff*(h3 - h4_s);%actual enthalpy at the high pressure turbine exit

%solution

%heat input in the combustion chamber of gas turbine

fprintf("1-Heat input = %d KW \n",m_a*c_a*(T9 - T8_a));

%heat output in the condensor of stem turbine

fprintf("2-Heat output = %d KW \n",m_s*(h6_a-h1));

%thermal efficiency of the gas turbine cycle

fprintf("3-Thermal efficiency of the gas turbine cycle = %d %% \n",(T9-T10_a-T8_a+T7)*100/(T9-T8_a));

%thermal efficiency of the rankine cycle

fprintf("4-Thermal efficiency of the rankine cycle = %d %% \n",(h3-h4_a+h5-h6_a-Work_pump)*100/(h3-h2));

%net power generated in the gas turbine cycle

P_gasturbine = m_a*(T9-T10_a-T8_a+T7);

%net power generated by the steam turbine cycle

P_steamturbine = m_s*(h3-h4_a+h5-h6_a-Work_pump);

%efficiency of the combined cycle

fprintf("5-Combined cycle efficiency = %d %% \n",(P_gasturbine+P_steamturbine)*100/(m_a*c_a*(T9 - T8_a)));

%power generated in the combined cycle

fprintf("6-Power generated in the combine cycle = %d KW\n", P_gasturbine+P_steamturbine);

COMMAND WINDOW:

1-Heat input = 6.572139e+03 KW
2-Heat output = 2.707239e+03 KW
3-Thermal efficiency of the gas turbine cycle = 2.241374e+01 %
4-Thermal efficiency of the rankine cycle = 3.571628e+01 %
5-Combined cycle efficiency = 4.002255e+01 %
6-Power generated in the combine cycle = 2.630337e+03 KW

1 - 2 3 4 5 - 6 7 8 9 10 11 12 13 - 14 - clc; %considering constant specific heat of air in KJ/kg K as c_a = 1.005; gamma = 1.4; %specific heat ratio eff = 0.8; %isentropic efficiency for compressor, turbine and pump %Data for the gas turbine cycle m_a = 9.8; %mass flow rate of air in kg/s r_p = 7; %pressure ratio P7 = 100; P9 = P7 * r_P; %pressure in kPa 17 = 15 + 273 ; 19 = 950 +273; T11 = 200+273; %Temperaure in Kelvin T8_5 = 17 * (r_p^((gamma-1)/gamma));%Temperature after isentropic compression T8_a = (1/eff)*(T8_5 - 17) + 17;%actual temperature after compression T10_5 = T9 / (r_p^((gamma-1)/gamma)); %Temperature after isentropic expansion T10_a = T9 - eff*(T9 - T10_5);%actual temperature after expansion %Data for the steam turbine m_5 = 1.15; %mass flow rate of steam in kg/s P3=60;P4=10;P5=10;P6=0.1;P1=0.1;P2=60; %Pressure at all the states in rankine cycle in bar T5=400; %temperature of steam at low pressure turbine entry %specific enthalpy and specific entropy at low pressure steam turbine %inlet h5 = XSteam('h_pt',P5, T5); s5 - XSteam('s_pt',P5, T5); S6_5 55;%entropy at the low pressure tubine exit when expanded isentrpically h6_5 XSteam("h_ps',P6,56_s); %enthalpy at the low pressure turbine exit when expanded isentrpically h6_a = h 5 eff*(h5 - 66_5); actual enthalpy at the low pressure turbine exit 15 16 - 17 18 19 20 21 22 23 24 25

26 27 - 28 29 - 30 - 31 32 33 34 35 - 36 37 38 39 - %specific volume at state 1 v1=XSteam('vL_P',P1); %pump work in kJ/kg is given by Work_pump-(v1* (P2-P1)*100)/eff; h1=XSteam("hL_P',P1);%specific enthalpy at pump inlet %enthalpy at pump exit h2-h1+Work_pump; %applying energy balance at heat exchanger, we get the specific enthalpy at %high pressure turbine inlet h3 = (m_a/m_5)*(T10_a - T11) + h2; s3= XSteam's_ph',P3, h3); %at hight pressure turbine exit 54_5 = 53; h4_s=XSteam('h_ps',P4,54_s); h4_a= h3 - eff*(h3 - h4_s); %actual enthalpy at the high pressure turbine exit %solution Wheat input in the combustion chamber of gas turbine fprintf("1-Heat input = %d Kw \n",m_a*c_a*(T9 - T8_a)); %heat output in the condensor of stem turbine fprintf("2-Heat output %d Kw \n", m_s* (h6_a-h1)); %thermal efficiency of the gas turbine cycle fprintf("3-Thermal efficiency of the gas turbine cycle = %d %% \n",(T9-T10_a-T8_a+T7)*100/(T9-T8_a)); %thermal efficiency of the rankine cycle fprintf("4-Thermal efficiency of the rankine cycle = %d %% \n", (h3-h4_a+h5-h6_a-Work_pump) *100/(h3-h2)); net power generated in the gas turbine cycle 40 - 41 42 43 - 44 45 - 46 47 1 48 49 50

51 - 52 53 - 54 P_gasturbine m_a* (T9-T10_a-T8_a+T7); %net power generated by the steam turbine cycle P_steamturbine = m_s* (h3-h4_a+h5-h6_a-Work_pump); %efficiency of the combined cycle fprintf("5-Combined cycle efficiency = %d %% \n", (P_gasturbine+P_steamturbine) *100/(m_a*c_a*(T9 - T8_a))); %power generated in the combined cycle fprintf("6-Power generated in the combine cycle = %d KW\n", P_gasturbine+P_steamturbine); 55 56 57 - 58 COMMAND WINDOW 1-Heat input 6.572139e+03 kW 2-Heat output = 2.707239e+03 KW 3- Thermal efficiency of the gas turbine cycle = 2.241374e+01 % 4-Thermal efficiency of the rankine cycle 3.571628e+01 % 5-Combined cycle efficiency = 4.602255e+01 % 6-Power generated in the combine cycle 2.630337e+03 KW > >