Rankine cycle Simulator
AIM:- Create a Rankine Cycle Simulator using OCTAVE/MATLAB.
DESCRIPTION:- The Rankine cycle closely describes the process by which steam-operated heat engines commonly found in thermal power generation plants generate power.
Power depends on the temperature difference between a heat source and a cold source. The higher the difference, the more mechanical power can be efficiently extracted out of heat energy, as per Carnot's theorem.
The heat sources used in these power plants are usually nuclear fission or the combustion of fossil fuels such as coal, natural gas, and oil, or concentrated solar power. The higher the temperature, the better.
The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Also, unless the pressure and temperature reach super critical levels in the steam boiler, the temperature range the cycle can operate over is quite small: steam turbine entry temperatures are typically around 565 °C and steam condenser temperatures are around 30 °C.[citation needed] This gives a theoretical maximum Carnot efficiency for the steam turbine alone of about 63.8% compared with an actual overall thermal efficiency of up to 42% for a modern coal-fired power station. This low steam turbine entry temperature (compared to a gas turbine) is why the Rankine (steam) cycle is often used as a bottoming cycle to recover otherwise rejected heat in combined-cycle gas turbine power stations.
The cold source (the colder the better) used in these power plants are usually cooling towers and a large water body (river or sea). The efficiency of the Rankine cycle is limited on the cold side by the lower practical temperature of the working fluid.
The working fluid in a Rankine cycle follows a closed loop and is reused constantly. The water vapor with condensed droplets often seen billowing from power stations is created by the cooling systems (not directly from the closed-loop Rankine power cycle). This 'exhaust' heat is represented by the "Qout" flowing out of the lower side of the cycle shown in the T–s diagram below. Cooling towers operate as large heat exchangers by absorbing the latent heat of vaporization of the working fluid and simultaneously evaporating cooling water to the atmosphere.
While many substances could be used as the working fluid in the Rankine cycle, water is usually the fluid of choice due to its favorable properties, such as its non-toxic and unreactive chemistry, abundance, and low cost, as well as its thermodynamic properties. By condensing the working steam vapor to a liquid the pressure at the turbine outlet is lowered and the energy required by the feed pump consumes only 1% to 3% of the turbine output power and these factors contribute to a higher efficiency for the cycle. The benefit of this is offset by the low temperatures of steam admitted to the turbine(s). Gas turbines, for instance, have turbine entry temperatures approaching 1500 °C. However, the thermal efficiency of actual large steam power stations and large modern gas turbine stations are similar.
PROCESS:-
- Four processes of the Rankine cycle:
1 2: Isentropic Expansion
Turbine (1-2): Superheated steam enters into the Turbine and expands isentropically resulting in the production of work. The shaft of the turbine is connected to the generator. This results in the production of electricity i.e Mechanical energy gets converted into electric energy. Work produced by the turbine,
WT=m⋅(h1−h2)⋅K⋅W⋅T=m⋅(h1−h2)⋅KWT=m⋅(h1−h2)⋅K⋅W⋅T=m⋅(h1-h2)⋅K
2-3: Constant Pressure Heat Rejection
Condenser (2-3): The expanded vapour is then passed through a condenser, where it gets condensed and converts into liquid again. This liquid is again pumped to the boiler.
Qr=m⋅(h2−h3)⋅K⋅Q⋅r=m⋅(h2−h3)⋅KQr=m⋅(h2−h3)⋅K⋅Q⋅r=m⋅(h2-h3)⋅K
3-4: Isentropic Compression by the Pump
Pump (3-4): The water enters into the pump in a saturated state. Then the liquid is compressed isentropically until it meets the boiler pressure. Work done by the pump is,
WP=m⋅(h3−h4)⋅K⋅W⋅P=m⋅(h3−h4)⋅KWP=m⋅(h3−h4)⋅K⋅W⋅P=m⋅(h3-h4)⋅K
4-1: Constant Pressure Heat Addition
Boiler (4-1): The water enters into the boiler as compressed and leaves as superheated from the boiler. Thus the phase changes from liquid to vapour. The heat supplied by the boiler is
Qb=m⋅(h1−h4)⋅KQb=m⋅(h1−h4)⋅K
CODES:-
Xsteam code will be taken from challenge dicreption,
close all
clear all
clc
% Print Process Description
fprintf('1-2 Isobaric heat Transfer\n')
fprintf('2-3 Isentropic Expansion\n')
fprintf('3-4 Isobaric heat Rejection\n')
fprintf('4-1 Isentropic Compression\n')
%step 1:Enter Inputs
p1 = input('Enter the Pressure at the Turbine Inlet (in bar):');
T1 = input('Enter the Temperature at the Turbineinlet (in Degree Celcius):');
p2 = input('Enter the Pressure at the Condensor (in bar):');
%step 2: Calculate each state point values.
% state point 1
h1 = XSteam('h_pt',p1,T1);
s1 = XSteam('s_pt',p1,T1);
%step 3: state point 2
s2=s1;
sf2 = XSteam('sL_p',p2);
sg2 = XSteam('sV_p',p2);
hf2 = XSteam('hL_p',p2);
hg2 = XSteam('hV_p',p2); %x2 = (s2-sf2)/(sg2-sf2);
s2 = sg2;
h2 = hg2; %hf2 +(x2*(hg2-hf2));
T2=XSteam('T_hs',h2,s2);
%step 4: state point 3
T3=T2;
p3= p2;
s3=XSteam('sL_T',T3);
h3=XSteam('hL_T',T3);
v3 = XSteam('vL_p',p2);
%step 5: state point 4
p4 =p1;
s4= s3;
Cp4 = XSteam('Cp_ps',p4,s4);
Cv4 = XSteam('Cv_ps',p4,s4);
gamma = Cp4/Cv4;
r = (gamma - 1)/gamma;
T4 = T3 *(p4/p3)^r;
%step 6: Calculate other output values.
Wt = h1-h2; % Turbine Work
Wp = v3*(p1-p2)*100; % Pump Work
h4 = Wp + h3;
W_net = Wt-Wp; % Net Work unit in kj/kg
Qs = h1 - h4;%heat suppied
N_per = (W_net/Qs)*100;%Efficiency
steam_rate = 3600/(Wt - Wp);%Steam rate per second
%step 7: state point 5 and 6 which help in plotting
T5=XSteam('Tsat_p',p1);
T6=T5;
s5=XSteam('sL_p',p1);
s6=XSteam('sV_p',p1);
h5=XSteam('hL_p',p1);
h6=XSteam('hV_p',p1);
%step 8: print all state poont values to show.
fprintf('\n------------------RESULT------------------\n')
fprintf('At State point 1:\nP1 is : %4.2f Bar\nT1 is : %4.2f Degree Celcius\nH1 is : %4.2f kJ/kg\nS1 is : %4.2f kJ/kgk\n\n',p1,T1,h1,s1)
fprintf('At State point 2:\nP2 is : %4.2f Bar\nT2 is : %4.2f Degree Celcius\nH2 is : %4.2f kJ/kg\nS2 is : %4.2f kJ/kgk\n\n',p2,T2,h2,s2)
fprintf('At State point 3:\nP3 is : %4.2f Bar\nT3 is : %4.2f Degree Celcius\nH3 is : %4.2f kJ/kg\nS3 is : %4.2f kJ/kgk\n\n',p3,T3,h3,s3)
fprintf('At State point 4:\nP4 is : %4.2f Bar\nT4 is : %4.2f Degree Celcius\nH4 is : %4.2f kJ/kg\nS4 is : %4.2f kJ/kgk\n\n',p4,T4,h4,s4)
fprintf('Wt is :%4.2f kJ/kg\nWp is : %4.2f kJ/kg\nWnet is : %4.2f kJ/kg\nNtherm is : %4.2f percent\nS.S.C is : %4.2f kg/kWh',Wt,Wp,W_net,N_per,steam_rate)
%step 9:plot T-S Diagram
subplot(1,2,1)
T_rankine = linspace(T5,T1,5000);
for i = 1:length(T_rankine)
s_rankine(i) = XSteam('s_pT',p1,T_rankine(i));
end
plot([s1 s2 s3 s4 s5 s6 s_rankine],[T1 T2 T3 T4 T5 T6 T_rankine],'linewidth',1.5);
hold on
T_curve = linspace(1,400,500);
for i=1:length(T_curve)
s_l(i) = XSteam('sL_T',T_curve(i));
s_v(i) = XSteam('sV_T',T_curve(i));
h_l(i) = XSteam('hL_T',T_curve(i));
h_v(i) = XSteam('hV_T',T_curve(i));
end
plot(s_l,T_curve);
plot(s_v,T_curve);
text(s1,T1,'1','FontSize',15)
text(s2,T2,'2','FontSize',15)
text(s3,T3,'3','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','top')
text(s4,T4,'4','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','bottom')
text(s5,T5,'5','FontSize',15)
text(s6,T6,'6','FontSize',15)
xlabel('Entropy in kJ/KgK');
ylabel('Temperature in Degree Celcius');
%step 10:plot H-S diagram
subplot(1,2,2)
plot([s1 s2 s3 s4 s1],[h1 h2 h3 h4 h1],'linewidth',2)
hold on
plot(s_v,h_v,'color','r')
plot(s_l,h_l,'color','r')
text(s1,h1,'1','FontSize',15)
text(s2,h2,'2','FontSize',15)
text(s3,h3,'3','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','top')
text(s4,h4,'4','FontSize',15,'HorizontalAlignment','right','VerticalAlignment','bottom')
xlabel('Entropy in kJ/KgK')
ylabel('Enthalpy in kJ/kg')
output:-
CONCLUSION:-
1)Rankine cycle is a power generating cycle.
2)Superheating increase the thermal efficiency of cycle.
3)It is the most practical cycle.
References