An Otto cycle is an idealized thermodynamic cycle that describes the functioning of a typical spark ignition engine. It is the thermodynamic cycle most commonly found in automobile engines.

STROKES:-

Process 0–1 intake stroke

in this stroke the piston moves from tdc(top dead center) to bdc (bottom dead center), due to that the vaccume will genarate inside the cylinder same time inlet valve will open and the air will enter into the cylinder

Process 1–2 compression stroke

in this stroke the piston move from bdc to tdc in this time air-fuel mixture in the cylinder will compressed

Process 2–3 ignition phase

at a constat volume the ignition will take place from the spark plug

Process 3–4 expansion stroke

due to the spark the hot air-fuek mixture will get bun due to that the expansion take place in this stroke so this stroke is also called power stroke becase we will getting power from the stroke

Process 4–1 idealized heat rejection

after some time of expansion due to the piston movment the burned gas will get geat rejection , compared to the time of ignition

Process 1–0 exhaust stroke

in this stroke the piston will take displacement from bdc to tdc with the help of exhast valve the exhast gas will go out from the engine cylinder

the process will occure agine and agine

Pessure–volume diagram

The Otto cycle is constructed from:

Top and bottom of the loop: a pair of quasi-parallel and isentropic processes (frictionless, adiabatic reversible).

Left and right sides of the loop: a pair of parallel isocharic process(constant volume).

The isentropic process of compression or expansion implies that there will be no inefficiency (loss of mechanical energy), and there be no transfer of heat into or out of the system during that process. The cylinder and piston are assumed to be impermeable to heat during that time.

The idealized diagrams of a four-stroke Otto cycle both diagrams the intake (A) stroke is performed by an isobaric expansion, followed by an adiabatic compression (B) stroke. Through the combustion of fuel, heat is added in a constant volume (isocharic process) process, followed by an adiabatic expansion process power (C) stroke. The cycle is closed by the exhaust (D) stroke, characterized by isochoric cooling and isentropic compression processes.

Temperature-Entropy diagram

program :-

clear all
close all
clc

    
%input
gamma=1.4
t3=2300
%state variables
p1=101325
t1=500
 
%engine geometric parameters
bore=0.1;
stroke=0.1;
can_rod=0.15;
cr=12;

%calculating the 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 variables at state point 2
%p2v2^gamma=p1v1^gamma
%p2=p1*(v1/v2)^gamma=p1*cr^gamma
p2=p1*cr^gamma;

constant_c=p1*v1^gamma;

V_compresion=engine_kinematics(bore,stroke,can_rod,cr,180,360)

P_compresion=constant_c./V_compresion.^gamma;

%p1v1/t1=p2v2/t2 | t2=p2*v2*t1/(P1*V1)

t2=p2*v2*t1/(p1*v1)
%state variable at state point 3

v3=v2
%p3v3/t3=p2v2/t2 | p3=p2*t3/t2

p3=p2*t3/t2

constant_c=p3*v3^gamma;
V_expansion=engine_kinematics(bore,stroke,can_rod,cr,180,360)
P_expansion=constant_c./V_expansion.^gamma;

%state varioable at state point 4
v4=v1

%p3v3^gamma=p4v4^gamma  | p4=p3(v3/v4)^gamma
p4=p3*(v3/v4)^gamma

figure(1)

hold on

plot(v1,p1,'*','color','r');
plot(v2,p2,'*','color','r');
plot(V_compresion,P_compresion);
plot([v2 v3],[p2 p3]);
plot(v3,p3,'*','color','r');
plot(v4,p4,'*','color','r');
plot(V_expansion,P_expansion)
plot(v4,p4,'*','color','r');
plot([v4 v1],[p4 p1]);
figure(2)

plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1],'color','b');

explination :-

1.First we are taken the know or input values to find the unknow parameters (by using the air standerd derivation as support)

2.To get the compression as per the angels of requirment taken the support of matlab and genarated the function as per the requirements and name it as engine_kinematics.

The function engine_kinematics is below

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

a=stroke/2
R=con_rod/a

v_s=pi/4*bore^2*stroke;
v_c=v_s/(cr-1);

theta=linspace(start_crank,end_crank,720);

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

3.then to get the result engine_kinematics function interduced into the main program.

4.ploted the result as per requirement

RESULT:-1

Error occured at the time of programing:-

correction made to correct it:- dot product

Result:-2

Thermal efficiency () is a DIMENSIONLESS performance measure of a device that uses thermal energy, such as an internal combution engine

Formula:-

`n=1-1/(cr)^(gamma-1)

THERMAL EFFICIENCY=63.1