OTTO CYCLE-PISTON KINAMATICS

AIM:

To simulate piston kinematics in ottocycle in MATLAB and plot a graph and to find the thermal efficiency

THEORY:

Otto cycle:

Otto cycle is an idealised thermodynamic cycle that describs the functioning of a spak ignition piston engine.It is the thermodynamic cycle most commonly found in automobile engines.The otto cycle is the discription of what hapens when the mass of gas is subjected to the changes of pressure,temperature , volume,addition of heat and removel of heat.

IC engine:

IC engine is the heat engine in whichthe combustion of the fuel occures with the oxidiser in a combustion chamber that is an integral of part of hte working fluid.

MATHEMATICAL EQUATION

`v/v_c=1+(r_c-1)*[R+1-cos(theta)-(R^2-sin(theta)^2)^(1/2)]`

Where

v=volume

`v_c`=cleaeance volume

`r_c`=compression ratio

R=connecting rod/a

a=stroke/2

`theta`=angle of stroke

swept volume=`pi/4*`bore`^2*`stroke

clearance volume=swept volume`*(c_r-1)`

bore=0.2

stroke=0.2

connecting rod=0.3

`c_r`=15

thermal efficiency=(t4-t1)/(t3-t2)

t1,t2,t3,t4=temperature of diffrent points

PROGRAM OF OTTO CYCLE:

clear all
close all
clc

%inputs
gamma=1.4
t3=2300

%state variables
p1=100000
t1=500

%engine geometric parameters
bore=0.2
stroke=0.2
con_rod=3
cr=15

%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
%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,180,360)
p_compression=constant_c./v_compression.^gamma

%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


%state variables 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(v2,p2,'*','color','r')
plot(v3,p3,'*','color','r')
plot(v4,p4,'*','color','r')
plot([v1 v1],[p1 p4])
plot([v2 v2],[p2 p3])
plot(v_compression,p_compression)
plot(v_expansion,p_expansion)

FUNCTION

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

a=stroke/2;
R=con_rod/a;

v_swept=(pi/4)*bore^2*stroke;
v_clearance=v_swept/(cr-1);

theta=linspace(start_crank,end_crank,180);

term1=0.5*(cr-1);
term2=R+1-cosd(theta);
term3=(R^2-sind(theta).^2).^0.5;

v=(1+term1*(term2-term3)).*v_clearance;


end

OUTPUT:

THERMAL EFFICIENCY

RESULT

• Otto cycle is simulated and the diagram is plotted
• the thermal efficiency of otto cycle is 16%