Otto Cycle with PV Diagram

% To solve otto cycle and plot the graph volume vs pressure  

clear all 
close all
clc
 
% Inputes parameter 
 gamma = 1.4
 t3 = 2300
 p1 = 101325
 t1 = 500
 
 % Engine parameter 
 bore = 0.1 
 stroke =0.1
 con_rod =0.15
 cr = 12
 
 
 
 v_swept  = pi/4*bore^2*stroke
 v_clear = v_swept/(cr-1)
 
 % the state variable at state point 1 
 v1 = v_swept + v_clear 
 v2 = v_clear 
 
 c_constant = p1*v1^gamma
 v_compression = engine_kinematics(bore,stroke,con_rod,cr,0,180)
 p_compression = c_constant./v_compression.^gamma

 % The state variable at state point2
 % p1v1^gamma = p2v2^gamma| p2 = p1 (v1/v2)^gamma  
 
 p2 = p1*cr^gamma 
 
 %p2v2/t2 = p1v1/t1 | t2 = p2v2t1/p1v1
 
 t2 = p2*v2*t1/(p1*v1)
 
 
 %state variable at state point 3 
 v3 = v2 
 
 %p2v2^gamma = p3v3^gamma 
 
 p3 = p2*t3/t2
 
 %calculate the pressure at the expanstion 
 c_constant = p3*v3^gamma
 v_expanstion = engine_kinematics(bore,stroke,con_rod,cr,0,180)
 p_expanstion = c_constant./v_expanstion.^gamma

 % The state variable at state point2
 % p1v1^gamma = p2v2^gamma| p2 = p1 (v1/v2)^gamma  
 
 p2 = p1*cr^gamma 
 
 %p2v2/t2 = p1v1/t1 | t2 = p2v2t1/p1v1
 
 t2 = p2*v2*t1/(p1*v1)
 
 
 %state variable at state point 3 
 v3 = v2 
 
 %p2v2^gamma = p3v3^gamma 
 
 p3 = p2*t3/t2
 
 % state variable at point 4 
 
 v4 = v1
 
 %p3v3^gamma = p4v4^gamma | p4 = p3*(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma
 % To plot pv graph using the above data 
  
 figure (1)
 hold on 
  
 plot (v1,p1,'*','color','b')  
 plot(v_compression,p_compression,'linewidth',1,'color','r')
 
 plot (v2,p2,'*','color','b')   
 plot([v2 v3],[p2 p3],'linewidth',1,'color','r')
  
 plot (v3,p3,'*','color','b')  
 plot(v_expanstion,p_expanstion,'linewidth',1,'color','r')
  
 plot (v4,p4,'*','color','b')  
 plot([v4 v1],[p4 p1],'linewidth',1,'color','r')
  
  xlabel('volume')
  ylabel('ptressure')

To solve the otto cycle and the plot the graph PV(pressure volume)

Step wise solution of otto cycle

1. Give the inputs parameter that is the [pi,p1,t1,t3]
2. Give the engine piston specification [bore, stroke, connecting rod, compression ratio, crank angle ]
3. Calculate the pressure, volume, temperature, at the four state point in which that we have to give the all value of the PVT
4. Then the we have to plot the graph of PV diagram [ but this graph does not show the proper format of graph in which that compression and expansion are does not straight ]
5. For the more accuracy of graph we have the use the function
6. Calculate the volume at the compression for using formula [V = 1+0.5(cr-1)[R+1-cos(theta)-(R^2-(sin(theta)^2))^0.5] this volume is more accurate
7. After that that volume can used for the to calculate pressure at the compression after that we got the value of P_ compression and v_ compression
8. Then plot the graph P _compression and v_ compression this graph is more accurate and smooth this is show the proper why of graph
9. Same use the expansion process in that we give the graph of compression and expansion we got the two line of cycle
10. Then using plot command to joint the 2-3 and 4-1 point [here is volume is constant that why line is straight in the graph ]
11. We got the proper graph of otto cycle

Errors when the run the programing

• Missing the alphabet d in sin it will write in [sind] format

• when you call the function then write the calling value in proper format