Project 2 - Rankine cycle Simulator

AIM:

Create a rankine cycle simulator plot T-S and H-S diahgram.

THEROY:

The Rankine cycle closely describes the process by which steam engines commonly found in thermal POWER GENERATION PLANT harness the thermal energy of a fuel or other heat source to generate electricity. Possible heat sources include combustion of fossil fuels such as coal, natural gas, or oil, renewable fuels like biomass or ethanol, nuclear fusion, and concentrated solar power. Common heat sinks include ambient air above or around a facility and bodies of water such as rivers, ponds, and oceans.

The ability of a Rankine engine to harness energy depends on the relative temperature difference between the heat source and heat sink. The greater the differential, the more mechanical power can be efficiently extracted out of heat energy, as per carnot theroem.

The efficiency of the Rankine cycle is limited by the high heat of vaporization of the working fluid. Unless the pressure and temperature reach super critical levels in the boiler the temperature range, that the cycle can operate over, is quite small: Steam turbine entry temperatures are typically around 565 °C and condenser temperatures are around 30 °C. This gives a theoretical maximum carnot efficiency for the turbine alone of about 63.8% compared with an actual overall thermal efficiency of less than 50% for typical power stations. 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 gas cycle power stations.

Rankine engines generally operate in a closed loop where the working fluid is reused. 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 "Q_out" flowing out of the lower side of the cycle shown in the T–s diagram below. cooling tower operate as large heat exchangers by absorbing the latent heat of vaporization of the working fluid and simultaneously evaporating cooling water to the atmosphere.

The four processes in the Rankine cycle:

There are four processes in the Rankine cycle. The states are identified by numbers (in brown) in the T–s diagram.

• Process 1–2: The working fluid is pumped from low to high pressure. As the fluid is a liquid at this stage, the pump requires little input energy.

In other words, Process 1-2 is [Isentropic compression]

• Process 2–3: The high-pressure liquid enters a boiler, where it is heated at constant pressure by an external heat source to become a dry saturated vapour. The input energy required can be easily calculated graphically, using an enthalpy–entropy chart (h–s chart, or Mollier diagram), or numerically, using steam tables or software.

In other words, Process 2-3 is [Constant pressure heat addition in boiler]

• Process 3–4: The dry saturated vapour expands through a turbine, generating power. This decreases the temperature and pressure of the vapour, and some condensation may occur. The output in this process can be easily calculated using the chart or tables noted above.

In other words, Process 3-4 is [Isentropic expansion]

• Process 4–1: The wet vapour then enters a condenser, where it is condensed at a constant pressure to become a saturated liquid.

Equations[edit]

In general, the efficiency of a simple rankine cycle can be written as

Each of the next four equations^[1] is derived from the energy and mass balance for a control volume. defines the thermodynamic efficiency of the cycle as the ratio of net power output to heat input. As the work required by the pump is often around 1% of the turbine work output, it can be simplified.

When dealing with the efficiencies of the turbines and pumps, an adjustment to the work terms must be made:

h1=enthalpy at turbine inlet

h2=enthalpy at turbineoutlet

h3=enthalpy at pump inlet

h4=enthalpy at pump outlet

wt=work done by turbine

wp=worktaken by pump

(pi,ti,hi,si)=pressure,temperature,enthalpy,entropy at i_th state respectively.

clear all
close all
clc
disp('Rankine cycle simulator')
fprintf('n 1-2 is the isentropic expansion proceess')
fprintf('n 2-3 is the constant pressure heat rejection proceess')
fprintf('n 3-4 is the isentropic compression process')
fprintf('n 4-1 is the constant pressure heat addition process')

%variables for stage 1
p1=30;
t1=400;
h1=XSteam('h_pt',30,400);
s1=XSteam('s_ph',30,h1);
fprintf('nn results')
fprintf('nn At state point 1')
fprintf('n P1 is:%f bar',p1)
fprintf('n T1 is:%f deg celcius',t1)
fprintf('n H1 is:%f kj/kg',h1)
fprintf('n S1 is:%f kj/kgk',s1)


%variables for stage 2
p2=0.05;
s2=s1;
t2=XSteam('T_ps',0.05,6.1858);
sf2=XSteam('sL_p',p2);
sg2=XSteam('sV_p',p2);
hf2=XSteam('hL_p',p2);
hg2=XSteam('hV_p',p2);
x=((s2-sf2)/(sg2-sf2));
h2=hf2+(x*(hg2-hf2));
v2=XSteam('v_ph',p2,h2);
fprintf('nn At state point 2')
fprintf('n P2 is:%f bar',p2)
fprintf('n T2 is:%f deg celcius',t2)
fprintf('n H2 is:%f kj/kg',h2)
fprintf('n S2 is:%f kj/kgk',s2)


%variables for stage 3
t3=t2;
p3=p2;
s3=XSteam('sL_p',p3);
h3=XSteam('hL_T',32.875);
v3=XSteam('v_ph',p3,h3);
fprintf('nn at state point 3')
fprintf('n P3 is:%f bar',p3)
fprintf('n T3 is:%f deg celcius',t3)
fprintf('n H3 is:%f kj/kg',h3)
fprintf('n S3 is:%f kj/kgk',s3)


%variables for stage 4
s4=s3;
v4=v3;
p4=p1;
h4=XSteam('h_ps',p4,s4);
t4=XSteam('T_hs',h4,s4);
fprintf('nn at state point 4')
fprintf('n P4 is:%f bar',p4)
fprintf('n T4 is:%f deg celcius',t4)
fprintf('n H4 is:%f kj/kg',h4)
fprintf('n S4 is:%f kj/kgk',s4)

%variables for stage 5
p5=p4;
t5=XSteam('Tsat_p',p5);
h5=XSteam('hL_T',t5);
s5=XSteam('sL_p',p5);
fprintf('nn at state point 5')
fprintf('n P5 is:%f bar',p5)
fprintf('n T5 is:%f deg celcius',t5)
fprintf('n H5 is:%f kj/kg',h5)
fprintf('n S5 is:%f kj/kgk',s5)

%variables for stage 6
t6=t5;
p6=XSteam('psat_T',t6);
s6=XSteam('SL_T',t6);
h6=XSteam('hV_T',t6);
fprintf('nn at state point 6')
fprintf('n P6 is:%f bar',p6)
fprintf('n T6 is:%f deg celcius',t6)
fprintf('n H6 is:%f kj/kg',h6)
fprintf('n S6 is:%f kj/kgk',s6)


%LOOP TO FIND VARIABLES ON SATURATION LINES
t=linspace(0,400,1000);
for i=1:length(t)
    s_line1(i)=XSteam('sL_T',t(i));
end

for j=i:length(t)
    s_line2(j)=XSteam('sV_T',t(j));
end

for i=1:length(t)
    h_line1(i)=XSteam('hL_T',t(i));
end

for j=i:length(t)
    h_line2(j)=XSteam('hV_T',t(j));
end

%net work output calculation 
w_turbine=h1-h2;
w_pump=h4-h3;
work=w_turbine-w_pump;
q_in=h1-h4;
q_out=h2-h3;

%thermal efficiency
n=work/q_in;

%back work ratio
BWR=w_pump/w_turbine;

%specific steam consumption
ssc=3600/work;

%plotting t-s graph
figure(1)
hold on
plot([s_line1 s_line2],[t t])
plot([s1 s2 s3 s4 s5 s6 s1],[t1 t2 t3 t4 t5 t6 t1])
text(s1,t1,'1')
text(s2,t2,'2')
text(s3,t3,'3')
text(s4,t4,'4')
text(s5,t5,'5')
text(s6,t6,'6')
title("Rankine cycle T-S diagram")
xlabel('entropy(kj/kgk)')
ylabel('temperature(k)')
axis([0,8,0,450])


%plotting h-s graph
figure(2)
hold on
plot([s_line1 s_line2],[h_line1 h_line2])
plot([s1 s2 s3 s4 s5 s6 s1],[h1 h2 h3 h4 h5 h6 h1])
text(s1,h1,'1')
text(s2,h2,'2')
text(s3,h3,'3')
text(s4,h4,'4')
text(s5,h5,'5')
text(s6,h6,'6')
title("Rankine cycle H-S diagram")
xlabel('entropy(kj/kgk)')
ylabel('enthalpy(kj/kg)')
axis([0,8,0,3500])

CODE EXPLANATION:

1.First of all display -rankine cycle simulator,using disp command.

2.now write all the rankine cycle process using fprintf command.

3.assign the value of given parameters.turbine inlet pressure(p1)=30,turbine inlet temperature(t1)=400 degree celcius.turbine outlet pressure (p2)=0.5bar.

4.put XSteam.m file in same directory ans call XSteam function with suitable arguments tofind the values of eenthalpy,entropy for state 1.

5.use fprintf command to print the values of variation we found.repeat the procedure for all ofthe other states.

6.now apply the loop to find the values of enthalpy at saturatedtemperature and store them with the variables.

7.find the net work output and back work ratio with suitable formula.

8.plot the t-s and h-s diagram using all of the values found in different states and give proper x and y labeland state number by the text command.

9.plot the saturated line using the values we have found by for loop.