Otto cycle

%otto cycle

close all;
clear all;
clc ;

%inputs
gamma=1.4;

%state variables
p1=101325; %pressure in bar

%temperature in kelvin
t1=500;
t3=2300;

%engine geometric parameters
bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;

%calculation of swept cvolume and clearance volume

v_swept =(pi/4)*bore^2*stroke;
v_clearance = (v_swept/(cr-1));

v1=v_swept+v_clearance;
v2=v_clearance;

%determine constant for 1st process

constant_c=p1*v1^gamma;

V_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0);

P_compression=constant_c./V_compression.^gamma;

%state variables for state 2

%p1*v1^gamma=p2*v2^gamma
%p2=p1*((v1/v2)^gamma)

p2=p1*(cr^gamma);

%t2=((p2*v2)/(p1*v1))*t1

t2=((p2*v2)/(p1*v1))*t1;

%state variables for point 3
v3=v2;
p3=t3*p2/t2;

%determine constant for 3rd process

constant_c=p3*v3^gamma;
V_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180);

P_expansion=constant_c./V_expansion.^gamma;

%state variables for point 4
v4=v1;
p4=p3*(v3/v4)^gamma;

%PLOTTING
hold on
figure(1)
plot(v1,p1,\'o\',\'color\',\'r\');
plot(V_compression,P_compression,\'linewidth\',2,\'color\',\'r\')
plot(v2,p2,\'o\',\'color\',\'r\');
plot([v2,v3],[p2,p3],\'linewidth\',2,\'color\',\'r\')
plot(v3,p3,\'o\',\'color\',\'r\');
plot(V_expansion,P_expansion,\'linewidth\',2,\'color\',\'r\')
plot(v4,p4,\'o\',\'color\',\'r\');
plot([v4,v1],[p4,p1],\'linewidth\',2,\'color\',\'b\')
xlabel(\'volume\');
ylabel(\'pressure\');
grid on
title(\'pv diagram of otto cycle\');

%calculating thermal efficiency of 4 stroke otto cycle
n_efficiency=1-(1/(((cr)^gamma)-1))

%Function call program

function [V]=engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)

a=stroke/2;
R=con_rod/a;

v_s=(pi/4)*bore^2*stroke;
v_c=v_s/(cr-1);
theta=linspace(start_crank,end_crank,1000);

%v/vc=1+.5*{cr-1}*[R+1-cos(theta)-(R^2-sin(theta^2)^0.5)]

term1=0.5*(cr-1);
term2= R+1-cosd(theta);
term3=[R^2-(sind(theta).^2)].^0.5;

V=(1+term1*(term2-term3))*v_c

end