close all
clear all
clc
%inputs
gamma=1.4
t3=2300
% state variables(state point 1, presuure(p1)and temperature(t1))
p1=103125
t1=500
% Engine geometric parameters(bore,stroke,connecting rod length,compression ratio)
bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;
% Isentropic compression
%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
%cr=(v1/v2)
%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_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0);
P_compression = constant_c./V_compression.^gamma;
% constant volume heat addition
%state variables at state point 3
v3=v2
%p3v3/t3=p2v2/t2 | p3=p2*t3/t2
p3=p2*t3/t2
constant_c=p3*v3^gamma;
V_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180);
P_expansion = constant_c./V_expansion.^gamma;
%isentropic expansion
%state variables at state point 4
v4=v1
% p3v3^gamma=p4v4^gamma | p4=p3*(v3/v4)^gamma
p4=p3*(v2/v1)^gamma
% To find efficiency
E=1-(t1/t2)
% plotting given data
figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(V_compression,P_compression)
plot(v2,p2,'*','color','r')
plot(v3,p3,'*','color','r')
plot(V_expansion,P_expansion)
plot(v4,p4,'*','color','r')
plot([v2 v3],[p2 p3])
plot([v4 v1],[p4 p1])
xlabel('pressure')
ylabel('volume')
title('PV diagram otto cycle')
function [V]=otto_cycle_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);
thetha=linspace(start_crank,end_crank,100);
% formula
%(v/v_c)=1+0.5*(cr-1)[R+1-cos(thetha)-(R^2-sin^2(thetha))^0.5]
term1=0.5*(cr-1);
term2=R+1-cosd(thetha);
term3=(R^2-sind(thetha).^2).^0.5;
V=(1+term1*(term2-term3)).*v_c;
end