Otto cycle - Air standard Cycle

AIM:

To Write code on solve an otto cycle and make plots for it.

1. create a PV diagram
2. Find the thermal efficiency of the engine.

OTTO CYCLE:

basicaly the otto cycle are four strokes. Otto cycle is based on IC engine are petrol engine.there is contain six stroke but 2 strokes are mechanical rotation .So the is 4 main strokes. Otto cycle is based on IC engine are petrol engine.also thre is called as a spark - ignition engine .

1 TO 2 : is a isentropic compresssion process. [p.v^gamma = constant]

2 TO 3 : is a constant volume Heat- addition process.[p/t = constant]

3 TO 4 : is a isentropic expanssion process. [p.v^gamma=constant]

4 TO 1 : is a constant volume Heat-Rejection process. .[p/t = constant]

i workout the program to find the p-v diagram on a otto cycyle. And also calculate the thermal efficiency.

`p2v2^gamma=p1v1^gamma`

`p2=p1*(cr)^gamma`

`t2=t1*(cr)^(gamma-1)`

p= pressure (pa) ; v=volume (m^3); cr= compression ratio; t=temperature (k) ; R = ratio of the length of connecting rod to the crank pin radius;

a= crank pin radius; gamma = specific Heat ratio

clear all 
close all
clc
bore = 0.1; % bore (m) ia inner diameter of the cylinder
stroke =0.1; % stroke (m) is piston move BDC to TDC
cr=12;   % cr = v1/v2
con_rod =0.15;  % length of a conecting rod(m)

v_s =pi/4*bore^2*stroke; % Swept volume is the piston move TDC toBDC(displacment volume)
v_c = v_s/(cr-1);  % v_c is a clerance volume there equal to v2

%inputs
gamma = 1.4; %specific Heat ratio

% STATE VARIABLE 1
v1 = v_s +v_c; % total volume of the piston
p1 = 101325;   % Stanterd air pressure At state point 1 (IS GIVEN INPUT)
t1 = 500;      % Temperature At the state point 1 (is given input)
v2 = v_c;      % v2 is Equal to clerance volume


% STATE VARIABLES AT POINT 2
% p2v2^gamma =p1v1^gamma
% p2 = p1*(v1/v2)^gamma = p1*cr^gamma

p2 =p1*cr^gamma; % Pressure At State point 2

% t2=t1*cr^(gamma-1)

t2 = p2*v2*t1/(p1*v1);   % Temperature At the state point 2



% STATE VARIABLE AT THE POINT 3
v3=v2; % there is CONSTANT VOLUME HEAT ADD PROCESS
t3 = 2300;
p3 = p2*t3/t2;




% STATE VARIABLE AT POINT 4
v4 = v1; % thete is a CONSTANT VOLUME HEAT REJECTION PROCESS  % t4=t3*cr^(1-gamma)
p4 = p3*(v3/v4)^gamma;           
t4 = t3*cr^(1-gamma);



% PLOTING OF GRAPH

figure(1)

hold on 



plot(v1,p1,'*','Color','r') % There is state variable at point 1
plot(v2,p2,'*','Color','r') % There is state variable at point 2
plot(v3,p3,'*','Color','r') % There is state variable at point 3
plot(v4,p4,'*','Color','r') % There is state variable at point 4



plot([v2,v3],[p2,p3]) % there is a curve of constant volume heat-addition 
plot([v4,v1],[p4,p1]) % there is a curve of constant volume heat-Rejection​

OUTPUT :

And connect the point's on

plot([v2,v3],[p2,p3])

plot([v4,v1],[p4,p1])

plot([v1,v2],[p1,p2])

plot([v3,v4],[p3,p4])

plot([v1,v2],[p1,p2])

plot([v3,v4],[p3,p4])

plot this line of this two in deferend way [there is engine kinematics] .So i write the Engine Kinematics progaram.

`(v/v_c) = 1+(1/2)(cr-1)(R+1-cos(theta)-sqrt(R-sin(theta)^2))`

ENGINE KINEMATICS PROGRAM :

function [V] = engine_kinematics_1(bore, stroke, con_rod, cr, start_crank, end_crank)
 
a=stroke/2 ; % crank pin radius
 
R=con_rod/a ; % ratio of the length of connecting rod to the crank pin radius
 
v_s = pi/4*bore^2*stroke; % Calculaction of the SWEPT VOLUME
 
v_c = v_s/(cr-1); % Calculaction of the CLERANCE VOLUME
 
theta = linspace(0,180,180); % calculating the THETA VALUE
term1 =0.5*(cr-1); % Defind trem 1 of the characteridtic eqaction
 
term2 = R +1 -cosd(theta); % Defind trem 2 of the characteridtic eqaction
term3 = (R^2 -sind(theta).^2).^0.5; % Defind trem 3 of the characteridtic eqaction
V = (1+term1*(term2-term3)).*v_c ; % calculaction of volume
end​

MAIN PROGRAM :

clear all 
close all
clc
bore = 0.1; % bore (m) ia inner diameter of the cylinder
stroke =0.1; % stroke (m) is piston move BDC to TDC
cr=12;   % cr = v1/v2
con_rod =0.15;  % length of a conecting rod(m)

R = con_rod/(bore/2); % R is a dimanction ratio of the crank pin
v_s =pi/4*bore^2*stroke; % Swept volume is the piston move TDC toBDC(displacment volume)
v_c = v_s/(cr-1);  % v_c is a clerance volume there equal to v2

%inputs
gamma = 1.4;

% STATE VARIABLE 1
v1 = v_s +v_c; % total volume of the piston
p1 = 101325;   % Stanterd air pressure At state point 1 (IS GIVEN INPUT)
t1 = 500;      % Temperature At the state point 1 (is given input)
v2 = v_c;      % v2 is Equal to clerance volume


% STATE VARIABLES AT POINT 2
% p2v2^gamma =p1v1^gamma
% p2 = p1*(v1/v2)^gamma = p1*cr^gamma

p2 =p1*cr^gamma; % Pressure At State point 2

% t2=t1*cr^(gamma-1)

t2 = p2*v2*t1/(p1*v1);   % Temperature At the state point 2


constant_c = p1*v1^gamma; % calculating instantaneous pressure
v_compression = engine_kinematics_1(bore,stroke,con_rod,cr,180,0); % function of engine kinematics
p_compression = constant_c./v_compression.^gamma;  % pressure value obtained


% STATE VARIABLE AT THE POINT 3
v3=v2; % there is CONSTANT VOLUME HEAT ADD PROCESS
t3 = 2300;
p3 = p2*t3/t2;


constant_c = p3*v3^gamma; % calculating instantaneous pressure
v_expansion = engine_kinematics_1(bore,stroke,con_rod,cr,0,180); % function of engine kinematics
p_expansion = constant_c./v_expansion.^gamma; % pressure value obtained

% STATE VARIABLE AT POINT 4
v4 = v1; % thete is a CONSTANT VOLUME HEAT REJECTION PROCESS  % t4=t3*cr^(1-gamma)
p4 = p3*(v3/v4)^gamma;           
t4 = t3*cr^(1-gamma);



% PLOTING OF GRAPH

hold on 


plot(v1,p1,'*','Color','r') % There is state variable at point 1
plot(v2,p2,'*','Color','b') % There is state variable at point 2
plot(v3,p3,'*','Color','g') % There is state variable at point 3
plot(v4,p4,'*','Color','y') % There is state variable at point 4


plot([v2,v3],[p2,p3]) % curve of constant volume Heat-Addition
plot([v4,v1],[p4,p1]) % curve of constant volume Heat-Rejection

plot(v_compression,p_compression) % curve of Isentropic compression
plot(v_expansion,p_expansion)   % curve of Isentropic expanssion
xlabel('volume(kg/m3)') % xlabel call volume
ylabel('pressuer(pa)') % ylabel call pressure
legend("initial state","isentropic compression","before heat addition","constant volume heat addition","before expanssion","isentropic expanssion","before Eehaust","constant volume hrat rejection") % for labeling curve
title("OTTO CYCLE")

grid on

                                                                                                                                             
% Thermal effiencr (or) ENGINE EFFIENCY
efficiency = ((1-(1/(cr)^(gamma-1)))*100);

RESULT:

CONCLUSION :

• THE Matlab Program is Successful COMPLIED
• THE P-V Diagram For the Otto cycle was successfully plotted
• THE THERMAL EFFICIENCY IS 62.9893 %
• THE Efficiency is Depends on Compression Ratio. So the Compression Ratio is incress.it's Also incressyhe Efficiency .