Project 2 - Rankine cycle Simulator

AIM : To Create a Rankine Cycle Simulator using MATLAB.

OBJECTIVE :

• To calculate the state points of the Rankine Cycle based on given inputs.
• To plot the corresponding T-s and h-s plots for the given set of inputs.
• To Calculate the Thermal Efficiency of the Rankien Cycle and Steam Rate.

THEORY : RANKINE CYCLE

Simple Rankien cycle Consists of the following reversible processes.

1.Isentropic Expansion`(1rarr2)` of steam in turbine.

2.Isobaric Cooling `(2rarr3)` of steam in condenser.

3.Isentropic Pumping `(3rarr4)` of saturated liquid (water) to boiler.

4.Isobaric Heating `(4rarr1)` in boiler.

fig: Simple Rankien Cycle and T-S ,H-S and P-V Diagram is as shown in above fig.

1.Cycle Efficiency :Applying the steady flow energy equation to each of the processes on the basis of unit mass of working substance and neglecting changes in kinetic energy and potential energy , the heat supplied and heat rejected is given as,

`Q_s=h_1-h_4`

`Q_R=h_2-h_3`

work done by the system on the turbine , and the work done by the pump on the steam respectively,are

`W_t=h_2-h_1`

`W_p=h_4-h_3`

Therefore, the efficiency of rankien cycle is

`eta_(Rankien)=(W_(Net))/(Q_s)`

`=(Wt-Wp)/Q_s`

`=((h_1-h_2)-(h_4-h_3))/((h_1-h_4))`

`=1-(h_2-h_3)/(h_1-h_4)`

2.Pump Work :Considering the water as incompressive fluid, the work done by the pump on water during isentropic process (`3rarr4,d_s=0`)can be found using,

`T_(ds)=dh-vdp`

`dh=vdp`

since the change in specific volume is negligible,

`Deltah=vDeltap`

Hence,

`W_p=h_4-h_3=v_3(p_1-p_2)`

3.Steam Rate :Thecapacity of steam power plant is generally expressed in terms of steam rate(kg/h-kW),which is defined as the rate of steam flow required to produce unit shaft output power.

Steam rate =`3600/(W_t-W_p)`kg/h.

MATLAB CODE :

clear
close all
clc
% Rankien cycle simulator
fprintf('Rankien Cycle Simulator\n')

% displaying the Rankien cycle processes
fprintf('1-2 is Isentropic Expansion in the Turbine\n')
fprintf('2-3 is Constant Pressure Heat Rejection by the Condensor\n')
fprintf('3-4 is Isentropic Compression in the Pump\n')
fprintf('4-1 is Constant Pressure Heat Addition by the Boiler\n')

% defining the given inputs P1,T1,P2
p1=input('Enter the pressure at the Turbine Inlet (in Bar):');
t1=input('Enter the Temperature at the Turbine Inlet (in Degree Celcius):');
p2=input('Enter the pressure at Condenser (in Bar):');

% extracting the Enthalpy & Entropy from the XSteam Table
h1=XSteam('h_pT',p1,t1); % entalhpy for pressure & temperature for super heated steam
s1=XSteam('s_pT',p1,t1); % entropy for pressure & temperature for super heated steam

% for process 1-2 reverible adiabatic process
%entropy is constant
s2=s1;
sf2=XSteam('sL_P',p2);
sg2=XSteam('sV_P',p2);
hf2=XSteam('hL_P',p2);
hg2=XSteam('hV_P',p2);
hfg2=hg2-hf2;
sfg2=sg2-sf2;
x2=((s2-sf2)/(sfg2)); % X2 is the Dryness Fraction
h2=hf2+(x2.*(hfg2));

% at state point 3
% pressure is constant
p3=p2;
h3=XSteam('hL_P',p3);
s3=XSteam('sL_P',p3);
v3=XSteam('vL_P',p3);

% Entropy is constant 
s4=s3;
p4=p1;

% Pump work Wp=h4-h3=v3(p1-p2)
Wp=v3*(p1-p2)*100;
h4=Wp+h3;

% work done by the steam on the turbine
WT=h1-h2;

% net work done (expansion work-pump work)
Wnet=(WT-Wp);

% heat supplied 
Q1=h1-h4;

% Efficiency of Rankien cycle
efficiency=(Wnet/Q1)*100;

%Steam rate in Kg/h
steam_rate=(3600/(WT-Wp));

% At state point 3 finding temperature to plot the points
t3=XSteam('Tsat_P',p3);
t2=t3;
Cp4=XSteam('Cp_ps',p4,s4);
Cv4=XSteam('Cv_ps',p4,s4);
k=Cp4/Cv4;
t4=t3/((p3/p4)^((k-1)/k));

%calculating temperature ,enthalpy,entropy at liquid and vapor 
t6=XSteam('Tsat_p',p1);
s5=XSteam('sL_p',p1);
s6=XSteam('sV_p',p1);
h5=XSteam('hL_p',p1);
h6=XSteam('hV_p',p1);
t5=t6;

%plotting
T=linspace(1,400,1000);
for i=1:length(T)
    sf(i)=XSteam('sL_T',T(i));
    sg(i)=XSteam('sV_T',T(i));
    hf(i)=XSteam('hL_T',T(i));
    hg(i)=XSteam('hV_T',T(i));
end
% plotting T-s diagram
figure(1)
hold on
plot(sf,T,'color','r','linewidth',2)
plot(sg,T,'color','r','linewidth',2)
plot([s1 s2],[t1 t2],'color','b','linewidth',1.5)
plot([s2 s3],[t2 t3],'color','b','linewidth',1.5)
plot([s3 s4],[t3 t4],'color','b','linewidth',1.5)
plot([s4 s5],[t4 t5],'color','b','linewidth',1.5)
plot([s5 s6],[t5 t6],'color','b','linewidth',1.5)
sc1=linspace(s6,s1,1000);
for l=1:length(sc1)
    Tc1(l)=XSteam('T_ps',p1,sc1(l));
end
plot(sc1,Tc1,'color','b','linewidth',1.5)
text(s1-0.1,t1+12,'1','fontsize',10)
text(s2,t2-5,'2','fontsize',10)
text(s3,t3,'3','horizontalalignment','right','verticalalignment','top','fontsize',10)
text(s4,t4,'4','horizontalalignment','right','verticalalignment','bottom','fontsize',10)
xlabel('Enthalpy [kJ/kg]','fontsize',14)
ylabel('Temperature [Degree celcius]','fontsize',14)
title('T-S Diagram For Rankien Cycle','fontsize',12)

% plotting the H-S  diagram
figure(2)
hold on
plot(sf,hf,'color','r','linewidth',2)
plot(sg,hg,'color','r','linewidth',2)
plot([s1 s2],[h1 h2],'color','b','linewidth',1.5)
plot([s2 s3],[h2 h3],'color','b','linewidth',1.5)
plot([s3 s4],[h3 h4],'color','b','linewidth',1.5)
plot([s4 s5],[h4 h5],'color','b','linewidth',1.5)
plot([s5 s6],[h5 h6],'color','b','linewidth',1.5)
sc2=linspace(s6,s1,1000);
for k=1:length(sc2)
    hc1(k)=XSteam('h_ps',p1,sc2(k));
end
plot(sc2,hc1,'color','b','linewidth',1.5)
text(s1,h1+50,'1','fontsize',10)
text(s2,h2-50,'2','fontsize',10)
text(s3,h3,'3','horizontalalignment','right','verticalalignment','top','fontsize',10)
text(s4,h4,'4','horizontalalignment','right','verticalalignment','bottom','fontsize',10)
xlabel('Entropy [kJ/kgK]','fontsize',14)
ylabel('Enthalpy [kJ/kg]','fontsize',14)
title('H-S Diagram For Rankien Cycle','fontsize',12)

% displaying the Result in command window
fprintf('RESULTS\n')
fprintf('At State Point 1:\nP1 is : %5.3f Bar\nT1 is : %5.3f Degree Celcius\nH1 is : %5.3f kJ/kg\nS1 is : %5.3f kJ/kgK\n',p1,t1,h1,s1)
fprintf('At State Point 2:\nP2 is : %5.3f Bar\nT2 is : %5.3f Degree Celcius\nH2 is : %5.3f kJ/kg\nS2 is : %5.3f kJ/kgK\n',p2,t2,h2,s2)
fprintf('X2 is : %5.3f\n',x2)
fprintf('At State Point 3:\nP3 is : %5.3f Bar\nT3 is : %5.3f Degree Celcius\nH3 is : %5.3f kJ/kg\nS3 is : %5.3f kJ/kgK\n',p3,t3,h3,s3)
fprintf('At State Point 4:\nP4 is : %5.3f Bar\nT4 is : %5.3f Degree Celcius\nH4 is : %5.3f kJ/kg\nS4 is : %5.3f kJ/kgK\n\n',p4,t4,h4,s4)
fprintf('Work Done By Turbine (Wt) is : %5.3f kJ/kg\n',WT)
fprintf('Work Done By Pump (Wp) is : %5.3f kJ/kg\n',Wp)
fprintf('Net Work Done By (Wnet) is : %5.3f kJ/kg\n',Wnet)
fprintf('Thermal Efficiency is : %5.3f percent\n',efficiency)
fprintf('Steam Rate is : %5.3f kg/h\n',steam_rate)

CODE EXPLANATION :

STEP 1:

• Start the MATLAB program with clear removes all variables from the current workspace, releasing them from system memory.close all closes the one or more figure window.clc clears the command window.
• fprintf Write data to text file to print the Rankien Cycle Simulator in the output window.
• Displaying the Rankien cycle processes using the fprintf command to display all the following process as mention in the above theory.
• Defining the given inputs P1,T1,P2

T1=Turbine Inlet temperature = 400° C

P1=Turbine Inlet Pressure = 30 bars

P2=Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure.

STEP 2 :

Extracting the Entropy and Enthalpy from the XSteam table for pressure & temperature for super heated steam