OTTO Cycle

Otto Cycle

An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in automobile engines.

Processes

• Process 0–1 a mass of air is drawn into piston/cylinder arrangement at constant pressure.
• Process 1–2 is an adiabatic (isentropic) compression of the charge as the piston moves from bottom dead centre (BDC) to top dead centre (TDC).
• Process 2–3 is a constant-volume heat transfer to the working gas from an external source while the piston is at top dead centre. This process is intended to represent the ignition of the fuel-air mixture and the subsequent rapid burning.
• Process 3–4 is an adiabatic (isentropic) expansion (power stroke).
• Process 4–1 completes the cycle by a constant-volume process in which heat is rejected from the air while the piston is at bottom dead centre.

Engine Parameters and Kinematics

• Bore Diameter (`b`) =0.3m
• Stroke length (`s`) = 0.25m
• Connecting Rod length (`cr`)= 0.2m
• Clearance Volume (`r_c`) = 5

Swept Volume (`v_s`) = `pi/4*b^2*s` `m^3`

Clearance Voume (`v_c`) = `v_s/(r_c-1)` `m^3`

`V=(1+ 0.5*(r_c-1)*(R +1- cos(theta)-(R^2 - sin^2(theta))^(1/2)))*v_c`

State Points

At Point 0:

`P0= 101325` Pa

`v0= v_c`

At Point 1:

`P1 = 101325` Pa

`T1=500` K

`v1= v_c+ v_s`

At Point 2:

`P2= P1*r_c^gamma`............(`gamma = 1.4`)

`T2= P2*v2*(T1)/(P1*v1)`

At Point 3:

`v3=v2`

`P3= P2*(T3)/(T2)`

At Point 4:

`P4= P3*((v3)/(v4))^gamma`

`v4=v1

CODE

• Engine Kinematics

function [V]= engine_kinematics(b,s,cr,r_c,start_crank,end_crank)
    
    
    a= s/2;
    R= cr/a;
    
     v_s= pi/4*b^2*s;
    v_c= v_s/(r_c-1);
    theta= linspace(start_crank,end_crank,150);
    
    term1 = 0.5*(r_c-1);
    term2 = R +1- cosd(theta);
    term3 = (R^2 - sind(theta).^2).^0.5;
    
    
    V=(1+ term1*(term2-term3)).*v_c;
   


end

• Otto Cycle

clear all
clc
close all

 %Inputs
 gamma= 1.4;
 T3=3000;
 
 %Static Variables
  P1= 101325;
  P0=P1;
   T1= 500;
 
 %Engine Geometric Parameters
 b= 0.3;
 s= .25;
 cr= .2;
 r_c= 5;
 
 %Calculating swept volume and clearnace volume
 v_s= pi/4*b^2*s;
 v_c= v_s/(r_c-1);
 
 v1= v_c+ v_s;
 v2= v_c;
 v0= v2; 
 % At Point 2
 P2= P1*r_c^gamma;
 T2= P2*v2*T1/(P1*v1);

c= P1*v1^gamma;

 V_compression= engine_kinematics(b,s,cr,r_c,180,0);
 P_compression= c./V_compression.^gamma;
 
 % At point 3
 v3=v2;
 P3= P2*T3/T2;
 
 %At point 4
 
v4=v1;
P4= P3*(v3/v4)^gamma;

c= P3*v3^gamma;
V_expansion= engine_kinematics(b,s,cr,r_c,0,180);
 P_expansion= c./V_expansion.^gamma;

 figure(1)
 title('P-V plot')

 hold on
 plot (v0,P0,'marker','.','markersize',8,'color','k')
 plot (v1,P1,'marker','.','markersize',8,'color','k')
 plot (v2,P2,'marker','.','markersize',8,'color','k')
 plot (v3,P3,'marker','.','markersize',8,'color','k')
 plot (v4,P4,'marker','.','markersize',8,'color','k')
 plot (V_compression,P_compression,'color','b')
 plot (V_expansion,P_expansion,'color','b')
 plot ([v0 v1],[ P0 P1],'color', 'g')
 plot ([ v2 v3], [P2 P3 ], 'color','r')
 plot ([v4 v1], [P4 P1], 'color' , 'r')
 
 text(v0,P0,'0', "HorizontalAlignment","right","VerticalAlignment","middle","FontSize",10)
 text(v1,P1,'1', "HorizontalAlignment","left","VerticalAlignment","middle","FontSize",10)
 text(v2,P2,'2',"HorizontalAlignment","right","VerticalAlignment","middle","FontSize",10)
 text(v3,P3,'3',"HorizontalAlignment","right","VerticalAlignment","middle","FontSize",10)
 text(v4,P4,'4',"HorizontalAlignment","left","VerticalAlignment","middle","FontSize",10)
 

 hold off
 xlabel('VOLUME')
 ylabel('PRESSURE')
  
 
 efficiency = 1-(1/(r_c^(gamma-1)))

PLOT

OUTPUT