MATLAB PROGRAMMING A CODE THAT CAN SOLVE AN OTTO CYCLE AND MAKE PLOTS FOR IT.

1.AIM:

• Writing a code that can solve an otto cycle and make plots for it.

2.GOVERNING EQUATIONS :

• In this equation, the ratio V₁/V₂is known as the compression ratio, CR. When we rewrite the expression for thermal efficiency using the compression ratio, we conclude the air-standard Otto cycle thermal efficiency is a function of compression ratio and κ = c_p/c_v.

3.OBJECTIVES OF THE PROJECT :

• The code should create a PV diagram.
• The output the thermal efficiency of the engine should be mentioned.

4.CONTENT OF THE PROJECT :

• MATLAB CODE

  clear all
  close all
  clc
  %programme for otto cycle
  %inputs
  gamma = 1.4
  t3 = 2300
  %state 1 variables
  p1=1.01325
  t1=600
  %engine geometric parameters
  bore = 0.1;
  stroke = 0.1;
  con_rod = 0.15
  cr = 8
  %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 2 variables
  %p2v2^gamma=p1v1^gamma
  p2 = (p1*v1/v2)^gamma
  constant_c = p1*v1^gamma;
  v_compression = piston_kinematics(bore,stroke,con_rod,cr,180,0)
  p_compression = constant_c./v_compression.^gamma;
  % p1v1/t1=p2v2/t2
  t2 = p2*v2*t1/(p1*v1)
  %state 3 variables
  v3=v2
  %p3v3/t3=p2v2/t2
  p3 = p2*t3/t2
  constant_c = p3*v3^gamma;
  v_expansion = piston_kinematics(bore,stroke,con_rod,cr,0,100) 
  p_expansion = constant_c./v_expansion.^gamma
  %state 4 variables
  v4=v1
  %p3v3^gamma=p4v4^gamma
  p4 = p3*v3^gamma/v4^gamma
  %thermal efficiency
  efficiency = 1-1/cr^(gamma-1)
  
  hold on
  plot(v1,p1,'^','Color','g')
  plot(v_compression,p_compression,'Color','r')
  plot(v2,p2,'*','Color','g')
  plot([v2 v3],[p2 p3],'Color','r')
  plot(v3,p3,'*','Color','g')
  plot(v_expansion,p_expansion,'Color','r')
  plot(v4,p4,'*','Color','g')
  plot([v4 v1],[p4 p1],'Color','r')
  plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1],'color','g')
  xlabel('volume (in m^3)')
  ylabel('pressure (in Pa)')
  
  grid on
  
  
  ​

and the function used in this script.

MATLAB CODE

function [v] = piston_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)
%otto cycle piston kinematics

 
a = stroke/2
r= con_rod/a
v_s = (pi/4)*bore*2*stroke
v_c = v_s/(cr-1)
theta = linspace(0,180,100)
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

Description :

Execute the program to create a PV diagram for otto cycle and to determine pressure and volume at the respective steps.

In the 1st step is to assume engine geometric parameters relevance to practical parameters of engine working on an otto cycle.

The engine parameters are as the follows:

1. Bore = 0.1 m

2. Stroke = 0.1 m

3. Connecting rod length = 0.15 m

4. Compression Ratio = 8

5. Pressure at step 1(p1) = 1.01325 Pa

6.Temperature at step 1(t1) = 600 K

7.Temperature at step 3(t3) = 2300 K

Calculating the volume at step 1 (i.e. v1), to calculate the swept volume and clearance volume using the formula,

v_swept = (pi/4)*bore*2*stroke

v_clearance = v_swept/(cr-1)

Then v1 = v_swept+v_clearance

and v2 = v_clearance

with the v1,t1,p1and cr (compression ratio),the volume,pressure and temperature at other steps can be obtained using following equations

PV^gamma = constant

PV = mRT.

the error found running the program displayed on the screen are :

The below PV diagram is generated :

5.CONCLUSION OF THE PROJECT :

1. The Thermal effieciency is calculated to be be 0.5647 or 56.47%.

2.The PV diagram shows the changes in isentropic processes are curve.