Project

AIR_STANDARD_OTTO_CYCLE

SSrinivas Bhairi6 Jun 2022

DETAIL REPORT ON AIR_STANDARD_OTTO_CYCLE

Otto_cycle : An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a spark ignition piston engine which is the thermodynamic cycle .

Process of otto cycle : 1 . ISENTROPIC COMPRESSION .

2 . CONSTANT VOLUME HEAT ADDITIION .

3 . ISENTROPIC EXPANSION .

4 . CONSTANT VOLUME HEAT REJECTION .

AIM :

Creating the code to plot the pressue-volume diagram of otto cycle .
Calculating the thermal efficiency of the air standard otto cycle .

GOVERNING EQUATIONS :

Ideal gas equation :

2. Isentropic Equation :

P = constant / V^κ

3. The above equations were used at different state of points i.e ISENTROPIC CONDITION & CONSTANT VOLUME PROCESS .

OBJECTIVE OF THE PROJECT :

Creating the code to plot the pressue-volume diagram of otto cycle & Calculating the thermal efficiency of the air standard otto cycle .

BODY OF THE CONTENT :

* FIRST PROGRAMME

close all 

clear all 

clc 

%input 

gamma = 1.4 ; 

%state_vriables 

p1 = 101325; 

t1 = 500;  

t3 = 2500; 

%engine_geometric parameters 

bore = 0.1; 

stroke = 0.1; 

cr = 12; 

con_rod = 0.15; 

%swept vol, clearance vol 

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

v_clearance = v_swept/(cr-1); 

v1 = v_swept + v_clearance; 

v2 = v_clearance; 

%condition_at_state_point_2 

%p2v2^gamma = p1v1^gamma 

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

p2 = p1*cr^gamma; 

%p1v1/t1 = p2v2/t2 

t2 = p2*v2*t1 / (p1*v1); 

%condition_at_state_point_3_using_ideal_gas_equation 

v3 = v2; 

%pv=t; p2v2/t2 = p3v3/t3 

p3 = p2*t3/t2 

%condition at state point 4 

v4 = v1; 

%p3v3^gamma = p4v4^gamma 

p4 = p3*(v3/v4)^gamma 

figure(1) 

hold on 

plot(v1,p1,'*','color','g') 

plot(v2,p2,'*','color','g') 

plot(v3,p3,'*','color','g') 

plot(v4,p4,'*','color','g') 


OUTPUT :
https://drive.google.com/file/d/1DUp5hn1uzV7EDa9u2QwdvAwWaWh45tJg/view?usp=sharing

* SECOND PROGRAMME

function [V] = engine_kinematics(bore,stroke,cr,con_rod,Start_crank,end_crank) 

%bore = 0.1; 

%stroke = 0.1; 

%cr = 12; 

%con_rod = 0.15; 

a = stroke/2; 

R = con_rod/a;    %ratio of con rod to the crank pin radius 

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

v_clearance = v_swept/(cr-1); 

theta = linspace(Start_crank,end_crank,720); 

term_1 = 0.5*(cr-1); 

term_2 = R+1-cosd(theta); 

term_3 = (R^2-sind(theta).^2).^0.5; 

V = (1+term_1*(term_2-term_3))*v_clearance; 

end 


OUTPUT:
https://drive.google.com/file/d/1DrT1GtR5lSsz_BbR7w8j8MFd9xsfTi3E/view?usp=sharing

* THIRD PROGRAMME :

%Engine_kinematics_final_code 

close all 

clear all 

clc 

%input 

gamma = 1.4 ; 

%state_vriables 

p1 = 101325; 

t1 = 500;  

t3 = 2500; 

%engine_geometric parameters 

bore = 0.1; 

stroke = 0.1; 

cr = 12; 

con_rod = 0.15; 

%swept vol, clearance vol 

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

v_clearance = v_swept/(cr-1); 

v1 = v_swept + v_clearance; 

v2 = v_clearance; 

%condition_at_state_point_2 

%p2v2^gamma = p1v1^gamma 

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

p2 = p1*cr^gamma; 

constant_c = p1*v1^gamma 

v_compression = engine_kinematics(bore,stroke,cr,con_rod,180,0) 

p_compression = constant_c./(v_compression.^gamma) 

%p1v1/t1 = p2v2/t 

t2 = p2*v2*t1 / (p1*v1); 

%condition_at_state_point_3_using_ideal_gas_equation 

v3 = v2; 

%pv=t; p2v2/t2 = p3v3/t3 

p3 = p2*t3/t2  

constant_c = p3*v3^gamma 

v_expansion = engine_kinematics(bore,stroke,cr,con_rod,0,180) 

p_expansion = constant_c./(v_expansion.^gamma) 

%condition at state point 4 

v4 = v1; 

%p3v3^gamma = p4v4^gamma 

p4 = p3*(v3/v4)^gamma 

figure(1) 

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') 

OUTPUT :
https://drive.google.com/file/d/1fgF1xpPujSyVLIw-dOJpf2RNVhXyRaaD/view?usp=sharing

EXPLANATION OF ABOVE MENTIONED PROGRAMMES :

COMMENTS :

1. The first code describes about the plotting of the volume-pressure diagram :
  
   Body of the programme describes the inputs of the engine geometry factors which were 
   used to define engine volume kinematics.
   
   Defining the global equations i.e the isentropic equations and constant volume 
   expressions.
   
   So,the state of variables which atre pressure , temperature and volume were defined.
   Finally , by using the state variables the plot is defined and drive link is attached 
   at the end of the code.

   Finally , we can define only the points of the various states in the plot but it is 
   not efficient .
   

2. The Second code programme describes which is more efficient than the first one.
  

    where the one more equation comes into picture which is defined from the engine 
    kinematics to solve the volume .

    So , we define the volume by using the angles which were required in the combustion 
    process in the engine i.e TDC to BDC (0 to 180)...

    Here , using the linkspace command we can get count of the varies values of angles.
   
    But , we will be using the function command instead of pasting the second code in 
    the first one .

    where the function inputs will be defined and we ca called in the main code i.e first
    code.

    but by using the second body of code , we can get a output and drive link is 
    provided .

3. The third code programme describes which is the efficient one which can describes the 
    complete PV diagram of the air standard cycle .


   in this code we will be caaling the function inputs in to this code and make the code 
   easy to derive the plot ,

   At , the compression and expansion the function has been called so that by using those 
   values the plot can be defined at the compression and expansion .

  NOTE : THE FUCTION INPUT FILE SHOULD EXIST IN THE SAME FOLDER TO CALL THE FUNCTION INTO  
  THE ANOTHER CODE .
  THE FUNCTION NAME WHICH IS CONSIDERED IN THE CODE , MUST BE THE FILE NAME .