ENGINE KINEMATICS AND EFFICIENCY OF OTTO CYCLE USING MATLAB

Air Standard Otto Cycle -:

Otto cycle is also called the constant volume cycle as the heat addition and heat rejection is done at a constant volume. Otto cycle is used in petrol and many other gas engines. It consists of two reversible constant volume processes and two adiabatic processes.

Efficiency of Otto cycle is given as,

η = 1 - 1/r^(γ-1).

In order to plot the P-V diagram we need to find the parametres like Temperature, Pressure, Volume associated at the points in the processes. For showing the correct plot we need kinematics of engine concept.

And by using the formula,

(v/v_c )= 1+0.5(r-1)[R+1-cos(theta)-(R^2 - sin^2(theta))^0.5]

we will be able to show the P-V diagram at different crank angle positons.

CALLING A FUNCTION:-

The codes written below will help us to call a function i.e. These functions is needed to create a proper P-V diagram.

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,180)

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

CODES FOR THERMAL EFFICIENCY AND P-V DIAGRAM:-

clear all
close all
clc

% inputs
gamma = 1.4;
t3 = 2300;%temprature at state point 3 in kelvin

% State Variables
p1 = 101325;%pressure at state point 1 in bar
t1 = 500;%temperrature at state point 1 in kelvin

% Engine geometric parameters
bore = 0.1;%diameter of the cylinder
stroke = 0.1;%stroke length 
con_rod = 0.15;%connecting rod length
cr = 12; %compression ratio

%Calculation for swept volume and clearance volume
v_s = (pi/4)*bore^2*stroke; %Swept volume
v_c = v_s/(cr-1);

v1 = v_s+v_c;
v2 = v_c;

%State variables at point 2
% p2v2^gamma =p1v1^gamma|p2 = pi*(vi/v2)^gamma|where v1/v2 = cr(compression ratio)
p2 = p1*(cr)^gamma;
%p1v1/t1 =p2v2/t2|t2 = p2*v2*t/p1*v1
t2 = (p2*v2*t1)/(p1*v1);

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


%State variables at point 3
v3 = v2;
%p3v3/t3 = p2v2/t2|p3 = p2*v2*t3/t2*v3|p3 = p2*t3/t2
p3 = p2*t3/t2;

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




%State variables at state point at point 4
v4 = v1;
%p3v3^gamma = p4v4^gamma|p4 = p3*(v3/v4)^gamma
p4 = p3*(v3/v4)^gamma;

figure(1)
hold on
plot(v_compression,p_compression,'linewidth',2,'color','r');
line([v2 v3],[p2 p3],'linewidth',2,'color','y');
plot(v_expansion,p_expansion,'linewidth',2,'color','g');
line([v1 v4],[p1 p4],'linewidth',2,'color','b');
xlabel('VOLUME');
ylabel('PRESSURE');
title('P-V DIAGRAM OF AIR STANDARD OTTO CYCLE')
legend('Compression','Heat addition','Expansion','Heat rejection');
grid on;


%EFFICIENCY OF OTTO CYCLE
eta = 1 - 1/cr^(gamma-1);
disp(eta);

THERMAL EFFICIENCY-