Otto Cycle

This is a program to simulate the Otto cycle, by taking the inputs Pressure and volume at state 1. the temperature at state 3 is also provided.

A graph for volume versus the pressure is to be obtained for the Otto cycle using a MATLAB program.

clear all
close all
clc

%Inputs
gamma=1.4;
p1=101325;
t1=500;
t3=2300;

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

%calculating the swept volume and the clearance volume
v_swept=(pi/4)*bore^2*stroke;
v_clearance=v_swept/(cr-1);

v1=v_swept+v_clearance
v2=v_clearance

%State variables at state point 2
%p2v2^gamma=p1v1^gamma
%p2=p1*(v1/v2)*gamma=p1*cr^gamma

p2=p1*cr^gamma;

%p1v1/t1=p2v2/t2 | t2=p2*v2*t1/(p1*v1)
t2=p2*v2*t1/(p1*v1)

constant_c=p1*v1^gamma;
v_com= e_k(bore, stroke, con_rod, cr, 180, 0);
p_com=constant_c./v_com.^gamma;

%State variable for state point 3
v3=v2
%p3v3/t3=p2v2/t2 | p3=p2*t3/t2
p3 = p2*t3/t2

constant_c=p3*v3^gamma;
v_exp= e_k(bore, stroke, con_rod, cr, 0, 180);
p_exp=constant_c./v_exp.^gamma;

%State variable at State point 4
v4=v1
%p3v3^gamma=p4v4^gamma | p4=p3*(v3/v4)^gamma
p4=p3*(v3/v4)^gamma

thermal_efficiency =1- (1/(cr^(gamma-1)))

figure(1)
hold on
plot([v2,v3],[p2,p3])
plot(v_com, p_com)
plot(v_exp, p_exp)
plot([v4, v1],[p4, p1])
xlabel('Volume')
ylabel('Pressure')

function [V] = e_k(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);
 
%v/vc= 1 + (0.5)* (cr-1) [R+1-cosd(theta)- (R^2 - (sind(theta))^2)^(1/2)

theta=linspace(start_crank, end_crank, 180)

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