piston kinematics of an Otto cycle shown in P-V diagram and its Thermal Efficiency

P-V diagram of an otto cycle

%MatLab code for the piston kinematics of an otto cycle and also showing the different processes occuring inside of engine via P-V diagram and hence calculating the thermal efficiency of the otto cycle.

%input

p1=101325;

t1=500;

t3=2300;

gamma=1.4;

bore=0.1;

stroke= 0.1;

con_rod=0.15;

cr=12;

a = stroke/2;

R = con_rod/a;

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

v_c=v_s/(cr-1);

v1=v_s+v_c;

v2=v_c;

%p1*v1^gamma = p2*v2^gamma, v1/v2 = cr;

p2 = p1*cr^gamma;

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

theta1 = linspace(0, 180, 100);

term1 = 0.5*(cr-1);

term2 = R+1-cosd(theta1);

term3 = (R^2 - sind(theta1).^2).^0.5;

v_compression = (1+term1.*(term2 - term3)).*v_c;

constant_c = p1*v1^gamma;

p_compression = constant_c./(v_compression).^gamma;

v3 = v2;

p3 = p2*t3/t2;

theta2 = linspace(180, 0, 100);

term4 = 0.5*(cr-1);

term5 = R+1-cosd(theta2);

term6 = (R^2 - sind(theta2).^2).^0.5;

v_expansion = (1+term4.*(term5 - term6)).*v_c;

constant_c = p3*v3^gamma;

p_expansion = constant_c./(v_expansion).^gamma;

v4 = v1;

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

figure(1)

hold on

plot(v1,p1,'r*');

plot(v_compression,p_compression,'k');

plot(v2,p2,'b*');

plot([v2 v3],[p2 p3],'k');

plot(v3,p3,'g*');

plot(v_expansion,p_expansion,'k');

plot(v4,p4,'y*');

plot([v4 v1],[p4 p1],'k');

grid on

xlabel('volume');

ylabel('presure');

%thermal efficiency

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