A MATLAB code for Air Standard Cycle(otto cycle)

A MATLAB code for Air Standard Cycle(otto cycle):-

The otto cycle approximates the processes in petrol or diesel engines. At constant volume Heat is transferred to the working fluid. It Consists of four internally reversible processes

1. Isentropic compression.
2. Constant volume heat addition.
3. Isentropic expansion.
4. Constant volume heat rejection.

Main Code:-

• Initially provide the all required values (bore,stroke,connecting rod, and compression ratio etc.).
• The values of swept volume and clearance volume is calculated with the following formula-

`v_s= pi/4*bore^2*stroke` and

`v_c= v_s/(cr-1)`

For the isentropic compression we knows

`p2*v2^gamma= p1*v1^gamma`

`p2= p1*((v1 )/( v2))^gamma`

so `p2 = p1 * cr^gamma`

For an ideal gas `(p1*v1) /( t1)= (p2*v2) / (t2)`

so `t2 = (p2 * v2 * t1) / (p1 * v1)`

• As the values of theta and other varivables varies in a function of

`p * v^ gamma = constant`

• due to adiabatic process, a function 'engine_keinematics' is created to generate a non-linear p-v curve and also get the value of V_compression and to calculate P_compression we use the above equation.
• At state point-3 the volume is constant `(v3=v2)`

`(p3 v3) / (t3) = (p2v2) / (t3)`

so `p3 = (p2*t3) / (t2)`

• During the expansion process the curve will follow the expression(`v4=v1`)

`p3*v3^gamma = p4*v4^gamma`

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

• Simlilarly, by using the function 'engine_keinematics' we can get the value of V_expansion and P_expansion.
• Finally use the plot() command and plot all the curves .

Main Code:

% creating a PV diagram otto cycle


  clear all 
  close all
  clc
  
% given values
  bore= 1;
  stroke= 1;
  connecting_rod= 1.5; 
  gamma=1.5;
% compression ratio 
  cr = 5;
% swept volume
  v_swept= pi/4*bore^2*stroke;
% clearance volume
  v_clearance= v_swept/(cr-1);
% at state point 1
  p1 = 1000;
  t1 = 500;
  v1 = v_clearance + v_swept;
  v2 = v_clearance;
  
% Compression
  
  p2 = p1*cr^gamma;
  t2 = p2*v2*t1/p1*v1;
   V_compression = engine_keinematics(bore, stroke, connecting_rod, cr, 180 , 0);
   constant_c = p1* v1 ^gamma;
   P_compression = constant_c./V_compression.^gamma;
   
   
% at state point 2-3 
  v3=v2;
  t3 = 2000;
  p3= p2*t3/t2;
  
% Expansion  
   constant_c = p3* v3 ^gamma;
   V_expansion = engine_keinematics(bore, stroke, connecting_rod, cr, 0 ,180);
   P_expansion = constant_c./V_expansion.^gamma;
   
  v4 = v1;
  p4 = p3*(v3/v4)^gamma;
  t4 = p4*v4*t3/p3*v3;
  
  
  hold on
   plot(v1,p1, '*' , 'color', 'g' )
  plot( V_compression ,P_compression)
   plot(v2,p2, '*' , 'color', 'g' )
   plot(v3,p3, '*' , 'color', 'g' )
  plot( V_expansion   ,P_expansion ) 
   plot(v4,p4, '*' , 'color', 'g' )
   plot([v2 v3],[p2 p3], 'color', 'b')
   plot([v4 v1],[p4 p1], 'color', 'b')
   xlabel('VOLUME')
   ylabel('PRESSURE')
   
   
% Thermal Efficency
 Th_eff = (1-(1/cr^(gamma-1)))* 100;
 

Function Calling Code:

% calling a function
function [V] = engine_keinematics(bore, stroke, connecting_rod, cr, start_cranc, end_cranc)

   a = stroke/2;
   r = connecting_rod/a;
   v_swept= pi/4*bore^2*stroke;
   v_clearance= v_swept/(cr-1);
   
   theta= linspace(start_cranc,end_cranc,180);
   
   term1 = 0.5*(cr-1);
   term2 = r + 1 - cosd(theta);
   term3 = (r^2 - sind(theta)).^0.5;
  
   V = (1 + term1*(term2 - term3)).* v_clearance ;
    
 end
   

Results-

Thermal efficiency = 55.27864

Error :-

Wrong clossing of brackets in the following expression

"V = (1 + term1*(term2 - term3)).* v_clearance"