Air standard cycle using matlab

Objective: plotting the otto cycle using matlab code.

Theory :

otto cycle is air standard cycle and it is also it describe the functioning of spark ignition engines . it has 4 processes basically 2 of them are adiabatic and 2 of them are constant volume process . In S .I engine expansion stroke and exhaust stroke are replaced by constant volume heat addition and constant volume heat rejection . In otto cycle working substance is air .

Matlab code :

close all 
clear all
clc

%input 

p1 = 1.01*10^5
t1 = 400
t3 = 1900

gamma = 1.4
% volume input 
bore = 0.1
stroke = .1
con_rod = 0.15
cr = 9
% volume caluclation 
v_swept = pi/4*bore^2*stroke
v_clearence = (v_swept)/(cr-1)

% volume caluclation and pressure calculation At each point 
v1 = v_swept +v_clearence
v2 = v_clearence
p2 = (p1*v1^gamma)/v2^gamma
t2 = (p2*v2*t1)/(p1*v1)
p3 = p2*t3/t2
p4 = (p3*v2^gamma)/v1^gamma
t4 = p4*t1/p1
v3 = v2
v4 =v1
%relation of how volume changes from t.d.c to b.d.c in engine based on that
%compression vol. and expansion vol.
const = p1*v1^gamma
v_c = engine_kinematics(bore,stroke,con_rod,cr,180,0)
p_c = const./v_c.^gamma
const = p3*v3^gamma
v_e = engine_kinematics(bore,stroke,con_rod,cr,0,180)
p_e = const./v_e.^gamma

%plotting the result 
figure(1)
hold on
plot(v1,p1,'.','color','b')
plot(v_c,p_c,'color','r','linewidth',3)
plot(v2,p2,'.','color','b')
plot(v3,p3,'.','color','b')
plot(v_e,p_e,'color','r','linewidth',3)
plot([v2,v3],[p2,p3],'color','b','linewidth',3)
plot(v4,p4,'.','color','b')
plot([v4,v1],[p4,p1],'color','b','linewidth',3)

so above is the code for the otto cycle plotting now in this we have input as intial pressure (p1) and intial temprature (t1),and maximun temprature (t3) is given as input now as in i.c. engine we also given various parameters like

bore,stroke,length of connecting rod so from that we can find swept voume ,

v_s wept = swept volume

now also we have compression ratio so we can find v1 and v2 from that now

v1 = swept volume + clearence volume

v2 = clearance volume

so that now we have all the values so we can now calculate the rest of points by use of process equations like given below

p 1 ⋅ v 1 ^γ = p 2 ⋅ v 2 ^γ we can find p2 from (here gamma value also has been given to us )

now we have found p2 so to find t2 we use the foloowing equation

(t2/t1) = (p2/p1)^(gamma-1/gamma)

we can find t2 ,simmilarly we can find p4 and t4 also the same way so now that we have all the points we can start plotting the result

but if we directly plot the reslut the volume change will be linear so we have to use piston kinematics to show how voilume changes from top dead center to bottom dead center this is very much important to get the exact plot for an otto cycle so we create a function by the same name engine kinematics to give volume change .

Function for piston kinematics :

function[v] = engine_kinematics(bore,stroke,con_rod,cr,start,End)
% crating function from piston kinematics 

% inputs

a = stroke/2
R = con_rod/a

v_swept = pi/4*bore^2*stroke;
v_clearence = v_swept/(cr-1);
theta = linspace(start,End,180);

% formula from piston kinematics divideing the formula in two terms 
term1 = 0.5*(cr-1);
term2 = R+1-cosd(theta);
term3 = (R^2 - sind(theta).^2).^0.5;
v = (1+term1.*(term2-term3)).*v_clearence
end

so here is the code to create function for piston kinamatics to show how volume changes now the formula for change in volume is given by below ,

v/(vc)=(1+0.5⋅(cr−1)⋅[(R+1⋅cos^2(θ)−(R^2−sin^2(θ))^0.5]

so from this we can get the otto cycle plot as given below .

RESULT