PV diagram and thermal efficiency of otto cycle

clear all

close all

clc

%Inputs of the required values

p1 = 101325;

t1 = 500;

gamma = 1.4;

t3 = 2300;

%Engine geometric parameters

bore = 0.1;

stroke = 0.1;

con_rod =0.15;

cr = 12;

%Calculating swept volume, clearance volume and total cylinder volume

v_swept = (pi/4)*bore^2*stroke;

v_clearance = v_swept/(cr-1);

v1 = v_swept + v_clearance;

v2 = v_clearance;

%Piston Kinematics

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

v_s = (pi/4)*bore^2*stroke;

v_c = v_s/(cr-1);

y = stroke/2;

R = con_rod/y;

theta = linspace(start_crank,end_crank,100);

x1 = 0.5*(cr-1);

x2 = R + 1 - cosd(theta);

x3 = (R^2 - sind(theta).^2).^0.5;

V = (1 + x1*(x2 - x3)).*v_c;

end

%Calculations at state point 1

constant_c = p1*v1^gamma;

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

p_compression = constant_c./v_compression.^gamma;

%Calculation of pressure and temperature at state point 2

p2 = p1*cr^gamma;

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

%Values of parameters at state point 3

v3 = v2;

p3 = p2*t3/t2;

%Calculation of volume and pressure during expansion stroke

constant_c1 = p_expansion*v_expansion^gamma;

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

p_expansion = constant_c./v_expansion.^gamma;

%Determining values at state point 4

v4 = v1;

p4 = p3*(v3/v4)^gamma;

t4 = p4*v4*t3/(p3*v3);

%Thermal Efficiency of the otto cycle

x = (t4-t1)/(t3-t2);

TE = 1-x;

%plotting

hold on

plot(v1,p1,\'*\',\'color\',\'r\')

plot(v_compression,p_compression,\'color\',\'r\')

plot(v2,p2,\'*\',\'color\',\'r\')

plot(v3,p3,\'*\',\'color\',\'r\')

plot([v2 v3],[p2 p3],\'color\',\'b\')

plot(v_expansion,p_expansion,\'color\',\'b\')

plot(v4,p4,\'*\',\'color\',\'r\')

plot([v4 v1],[p4 p1],\'color\',\'b\')

grid on