Project 2 - Rankine cycle Simulator

Aim: To simulate basic Rankine Cycle

Objective:

1. Creating a Rankine Cycle Simulator using OCTAVE/MATLAB. Calculating the state points of the Rankine Cycle based on user inputs.
2. Then plotting the corresponding T-S and H-S plots for the given set of inputs.

Rankine cycle:

The different processes here are:

Process 1-2: Isentropic Expansion in the turbine

Process 2-3: Isobaric Heat Rejection by the condenser

Process 3-4: Isentropic Compression in the pump

Process 4-1: Isobaric Heat Addition by the boiler

Here the given inputs values are:

Turbine inlet temperature = 400^oC

Turbine Inlet Pressure = 30 bars

Turbine Outlet Pressure = 0.05 bars = Condenser Inlet Pressure

MATLAB Program:

clear all

close all

clc

%Inputs

disp('Rankine Cycle Simulator')

disp('1-2 corresponds to isentropic expansion in turbine')

disp('2-3 corresponds to constant pressure heat rejection in condenser')

disp('3-4 orresponds to isentropic compression in pump')

disp('4-1 corresponds to constant pressure heat addition in boiler')

fprintf('n')

p1 = input('Enter the pressure at the inlet of turbine (bar):');

t1 = input('Enter the temp at the inlet of the turbine (degree C):');

p2 = input('Enter the pressure at the inlet of condensor (bar):');

%At state point 1

h1 = XSteam('h_pT', p1, t1);

s1 = XSteam('s_pT', p1, t1);

%At state point 1

%Since 1-2 is isentropic process

s2=s1;

sf2 = XSteam('sL_p', p2);

sg2 = XSteam('sV_p', p2);

sfg2 = (sg2 - sf2);

%Finding dryness fraction (s2 = sf2 + x2* sfg2)

x2 = (s2 - sf2)/sfg2;

x2<1;

disp('Steam is wet at the inlet of the condenser')

fprintf('n')

%Finding Enthalpy

hf2 = XSteam ('hL_p',p2);

hg2 = XSteam ('hV_p',p2);

hfg2 = hg2 - hf2;

h2 = hf2 + x2*hfg2;

t2 = XSteam('Tsat_p',p2);

%Workdone by Turbine

wt = h1 - h2;

%For state point 3

%Work done by pump

p3 = p2;

vf3 = XSteam('vL_p',p3);

v3 = vf3;

wp = v3*(p1 - p2)*100;

t3 = XSteam('Tsat_p',p2);

h3 = XSteam('hL_p', p2);

s3 = XSteam('sL_p',p2);

%At point 4

p4 = p1;

h4 = wp + h3;

t4 = XSteam('T_ph',p4, h4);

s4 = s3;

%Heat supplied to boiler

qs = h1 - h4;

%Heat Rejected by condenser

qr = h2 - h3;

%Work ratios and efficiency of turbine

w_net = wt - wp;

net_work_ratio = w_net/wt;

efficiency = w_net/qs;

%back work ratio

back_work_ratio = wp/wt;

%Specific Steam Consumption

SSC = 3600/w_net;

tf_sat = XSteam('Tsat_p',p1);

sf_sat = XSteam('sL_p',p1);

hf_sat = XSteam('hL_p',p1);

sg_sat = XSteam('sV_p',p1);

hg_sat = XSteam('hV_p',p1);

%Plotting saturation liquid and vapour lines

temp_range = linspace(1,373,1000);

for i = 1:length(temp_range)

S_L(i) = XSteam('sL_T',temp_range(i));

S_V(i) = XSteam('sV_T', temp_range(i));

end

%Plotting T-S diagram

figure(1)

hold on

plot(S_L,temp_range,'b')

plot(S_V,temp_range,'b')

plot([s1 s2], [t1 t2],'r')

plot([s2 s3], [t2 t3],'g')

plot([s3 s4], [t3 t4],'b')

%Plotting curved constant pressure line 3 to 4

t_cons_p = linspace(t4, XSteam('Tsat_p',p1),30);

for i = 1:length(t_cons_p)

S(i) = XSteam('s_pt',p1,t_cons_p(i));

end

plot(S,t_cons_p,'k')

t0_cons_p = linspace(XSteam('Tsat_p',p1),t1,300);

for i=1:length(t0_cons_p)

S0(i)=XSteam('s_pt',p1,t0_cons_p(i));

end

plot(S0,t0_cons_p,'k')

%Plotting the straight line of the phase change region

plot([sf_sat sg_sat], [tf_sat tf_sat], 'k')

title('T-S diagram')

xlabel('Entropy kJ/kgK')

ylabel('Temperature degree C')

axis([0 10 0 700])

legend('Saturation curve L', 'Saturation curve R', 'Turbine', 'Condenser', 'Pump', 'Boiler', 'location','northwest')

%Plotting H-S diagram

figure(2)

hold on

%Plotting saturation curves

temp_range1 = linspace(1, 373, 1000);

for i=1:length(temp_range1)

H_L1(i) = XSteam('hL_T', temp_range1(i));

H_V1(i) = XSteam('hV_T', temp_range1(i));

end

plot(S_L, H_L1,'b')

plot(S_V, H_V1,'b')

plot([s1 s2], [h1 h2],'r')

plot([s2 s3], [h2 h3],'g')

plot([s3 s4], [h3 h4],'r')

%For plotting the line between the pump and boiler

s_pump = linspace(s3, s1, 1000);

for i =1:length(s_pump)

h_pump(i)=XSteam('h_ps',p1,s_pump(i));

end

plot(s_pump, h_pump, 'k')

title('H-S Diagram')

xlabel('Entropy kJ/kgK')

ylabel('Enthalpy kJ/kgK')

legend('Saturation curve L','Saturation curve R','Turbine','Condenser','Pump','Boiler','location','northwest')

%Displaying the value of state point variables at each point

P_final = [p1 p2 p3 p4];

T_final = [t1 t2 t3 t4];

H_final = [h1 h2 h3 h4];

S_final = [s1 s2 s3 s4];

for i=1:4

fprintf('At state point %d n', i)

fprintf('Pressure p%d : %4.4f (bar) n',i,P_final(i))

fprintf('Temperature t%d : %4.4f (degree C) n',i,T_final(i))

fprintf('Enthalpy h%d : %4.4f (kJ/kgK) n',i,H_final(i))

fprintf('Entropy s%d : %4.4f (kJ/kg) n',i,S_final(i))

fprintf('n')

end

fprintf('The net work ratio is: %f n', net_work_ratio)

fprintf('The back work ratio is: %f n', back_work_ratio)

fprintf('The entered values are not valid as the steam is either Saturated or Super-saturated at the inlet of the condenser n')

fprintf('Enter the valid values by running the program again n')

return;

Explanation for the code:

1. The known inputs are collected initially using the input command (p1, t1 and p2)
2. Using the relations between the various properties of the ideal rankine cycle the values are calculated for all the state points
3. In order to obtain the values from the steam table, the function XSteam is added to the current working folder of MATLAB. Using the appropriate input parameters for the XSteam function, the required values can be obtained
4. Once the state point variables are calculated, the et work ratio and back work ratio can be calculated
5. Plot command is used to obtain T-S and H-S diagram
6. Finally, fprintf command is used to display all the values of the state point variables in the command window.

Outputs:

1. T-S diagram:
2. H-S diagram

Command Window Output:

At state point 1 nPressure p1 : 30.0000 (bar)

Temperature t1 : 400.0000 (degree C)

Enthalpy h1 : 3231.5710 (kJ/kgK)

Entropy s1 : 6.9233 (kJ/kg)

At state point 2 nPressure p2 : 0.0500 (bar) n

Temperature t2 : 32.8755 (degree C) n

Enthalpy h2 : 2110.7082 (kJ/kgK) n

Entropy s2 : 6.9233 (kJ/kg) nn

At state point 3 nPressure p3 : 0.0500 (bar) n

Temperature t3 : 32.8755 (degree C) n

Enthalpy h3 : 137.7651 (kJ/kgK) n

Entropy s3 : 0.4763 (kJ/kg) nn

At state point 4 nPressure p4 : 30.0000 (bar) n

Temperature t4 : 32.9639 (degree C) n

Enthalpy h4 : 140.7761 (kJ/kgK) n

Entropy s4 : 0.4763 (kJ/kg) nn

The net work ratio is: 0.997314 n

The back work ratio is: 0.002686

Workspace Output: