Otto Cycle

A pressure–volume diagram (or PV diagram) is used to describe corresponding changes in volume and pressure in a system. A PV diagram plots the change in pressure P with respect to volume V for some processes. Typically in thermodynamics, the set of processes forms a cycle, so that upon completion of the cycle there has been no net change in state of the system; i.e. the device returns to the starting pressure and volume.

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.

The Otto cycle is a description of what happens to a mass of gas as it is subjected to changes of pressure, temperature, volume, addition of heat, and removal of heat. The mass of gas that is subjected to those changes is called the system. The system, in this case, is defined to be the fluid (gas) within the cylinder. By describing the changes that take place within the system, it will also describe in inverse, the system\'s effect on the environment. In the case of the Otto cycle, the effect will be to produce enough net work from the system so as to propel an automobile and its occupants in the environment.

The Otto cycle is constructed from:

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

Left and right sides of the loop: a pair of parallel isochoric processes (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. Hence the cylinder, and piston are assumed impermeable to heat during that time. Work is performed on the system during the lower isentropic compression process. Heat flows into the Otto cycle through the left pressurizing process and some of it flows back out through the right depressurizing process. The summation of the work added to the system plus the heat added minus the heat removed yields the net mechanical work generated by the system.

A mathematical model of otto cycle is created to evaluate the combustion process in an IC Engine. The MATLAB code for a otto cycle in an automobile is given as 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*stroke;
v_c= v_s/(cr-1);

theta= linspace(start_crank,end_crank,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

clear all
close all
clc

%State variables
p1= 101325;  %N/m^2
t1= 500;  %Kelvin
t3= 2300;

%engine generating parameters
gamma= 1.4;
bore= 0.1;
stroke= 0.1;
con_rod= 0.15;
cr= 12;

%calculating the swept volume and clearance volume
v_swept= (pi/4)*stroke*bore;
v_clearance= v_swept/(cr-1);

v1= v_swept+ v_clearance;
v2= v_clearance;

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

constant_c= p1*v1^gamma;
V_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0);
p_compression= constant_c./V_compression.^gamma;

v3=v2;
p3= p2*(t3/t2);

V_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180);
constant_c= p3*v3^gamma;
p_expansion= constant_c./V_expansion.^gamma;

v4= v1;
p4= p3*((v3/v4)^gamma);

figure(1)
hold on
plot(v1,p1,\'*\',\'color\',\'r\')
plot(V_compression,p_compression)
plot(v2,p2,\'*\',\'color\',\'r\')
plot([v2 v3],[p2 p3])
plot(v3,p3,\'*\',\'color\',\'r\')
plot(V_expansion,p_expansion)
plot(v4,p4,\'*\',\'color\',\'r\')
plot([v4 v1],[p4 p1])

%thermal efficiency
n= 1-(cr^(1-gamma))
fprintf(\'The thermal efficiency of the air standard cycle is given by:%d\\n\',n)

REMARK : where are results ?

Also please follow the format as we use to write a report and make sure you use 
INSERT OPTION to insert a code and don\'t just copy and paste the code.

According to the model, the thermal efficiency of the Otto cycle is 63%. The otto cycle can be visualized in the figure given below: