plotting PV diagram for air standard otto cycle and calculate thermal efficiency

This projects demonsrates plotting of PV diagram for air standard otto cycle and calculating thermal efficiency of engine.

MATLAB code-

part-1

%programme for otto cycle
clear all
close all
clc

%inputs
gamma= 1.4
t3 = 2300

%state varables
p1= 101325
t1= 500

%Engine geometric parameters
bore =0.1;
stroke=0.1;
con_rod=0.15;
cr =12;

%calculating swept volume and 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 
%p1v1^gamma=p2v2^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_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
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 4
v4=v1
p4 = p3*(v3/v4)^gamma

%thermal efficiency
thermal_efficiency =1-(1/(cr^(gamma-1)))

figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(V_compression,P_compression)
plot(v2,p2,'*','color','r')
plot(V_expansion,P_expansion)
plot(v3,p3,'*','color','r')
plot(v4,p4,'*','color','r')
line([v2 v3],[p2 p3])
line([v4 v1],[p4,p1])

part-2

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

Explanation of code -

firstly we clear all existing variable,clear the command window.

we take usual for phases of air standard otto cycle as -

1)isentropic compression

2)constant volume heat addition

3)isentropic expansion

4)constant volume heat rejection

we define engine parameter values, and assume heat addition,rejection temperatures for simplicity of calculations.

then we calculated clearance volume and swept volume. and corresponding v1,v2

after that by using compression relationship we computed p2, and using ideal gas equation t2.since volume is constant during addition and rejection we get v3,v4 and p3,p4 also.

now we can plot all four points on pv diagram.

to join these point we have create function to compute compression and expansion plot with help of engine kinematics.

so we defined a function in seperate file. and called it inmain function for expansion and compression by putting appropriate values.

and finally plot the pv diagram.

thermal efficiency is calculated and found to be 0.6299.

RESULTS-

pv plot-

thermal efficiency- 62.99%