Week 4.1 - Genetic Algorithm

%Calculating Thermal Efficiency
   thermal_efficiency = 1-1./cr^(gamma-1);
   
   %Print the thermal efficiency 
   fprintf(['The thermal efficiency of the cycle is  : ' num2str(thermal_efficiency)]);
   fprintf('n');
   

ans:>> thermalefficiency
The thermal efficiency of the cycle is  : 0.62989n>> 

clear all
close all
clc

%input
gamma=1.4
t3 = 2300

%state variable
p1 = 101325
t1 = 500

%engine geometric 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 variable 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= p2v2*t1/(p1v1)
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;

%state variable at state point 3
v3=v2
%p3v3/t3=p2v2/t2  | p3= p2v3/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;

%state variable at state point 4
v4=v1

%p3v3^gamma = p4v4^gamma  | p4 = p3(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma;

figure(1)
hold on
plot(v1,p1,'*',"Color","r")
plot (V_compression,P_compression)
plot(v2,p2,'*','Color','r')
plot([v2,v3],[p2,p3],'Color','b')
plot(v3,p3,'*','Color','r')
plot(V_expansion,P_expansion)
plot(v4,p4,'*','Color','r')
plot([v4,v1],[p4,p1],'Color','b')
xlabel('Volume')
ylabel('Pressure')
title(' Otto cycle PVdiagram')




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,100);

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