OTTO CYCLE

AIM: To write the code that solve otto cycle and plot PV daigram.

THEORY: 

    OTTO CYCLE:    

                     The otto cycle is a cycle of engine operation which requires four strokes of the piston:for induction, compression, ignition, and exhaust. The fuel and air mixture is compressed before combustion is started by an electrical spark or other means.

PV daigram:

Process 1 to 2=isentropic compression.

    Here enters the cycle at point 1  when compression starts and it ends at point 2. The air is compressed in an isentropic process through a volume ratio callled compression ratio.

Process 2 to 3=Constant colume heat addition.

    Here heat addition starts at point 2 and ends at point 3. A quantity of heat is added at constant volume and thr working fluid temperature rises.

Process 3 to 4= Isentropic expansion

 Here the isentropic expansion starts at point 3 and it ends at point 4 to the original vloume

Process 4 to 1 = Constant volume heat rejection

 Here completes the cycle by a constant volume process in which heat is rejected .

 THERMAL EFFICIENCY:

              Te efficiency of a heat engine measured by the ratio of the work done by otto cycle to the heat supply to it.

        `ηth=W/(Qth)`

EQUATIONS USED:

`V/(vc)=1+.5*(cr-1)(R+1-cos(theta)-(R^2-sin(theta)^2)^.5)`

 where V=volume trace 

          vc=clearance volume

          cr= compression ratio

         R=connecting rod length

PROGRAM:
           

STEP 1

clear all 
close all
clc
%inputs
gamma=1.4
t3=2000

% state variables
p1=101325
t1=500

% engine geometric parameters
bore=.1;
stroke=.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 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)
% state variables at state point 3
v3=v2
%p3v3/t3=p2v2/t2    |    p3=p2*t3/t2
 p3=p2*t3/t2
 % state variables at point sate point 4
 v4=v1
 %p3v3^gammma=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')

SREP 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=.5*(cr-1);
term2=R+1-cosd(theta);
term3=(R^2-sind(theta).^2).^.5;
V=(1+term1*(term2-term3)).*v_c;
end

STEP 3: inserting step 2 function in step 1

clear all 
close all
clc
%inputs
gamma=1.4
t3=2000

% state variables
p1=101325
t1=500

% engine geometric parameters
bore=.1;
stroke=.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 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,180,0)
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,180,0)
P_expansion=constant_c./V_expansion.^gamma;

 % state variables at point sate point 4
 v4=v1
 % p3v3^gammma=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(v3,p3,'*','color','r')
plot(V_expansion,P_expansion)
plot(v4,p4,'*','color','r')
plot([v2 v2],[p2 p3])
plot([v1 v1],[p4 p1])

RESULT:      PV daigram for the otto cycle is plotted.