writing a program on Otto cycle using MATLAB Programming

Aim :Writing a program on OTTO cycle

1.create a plot on PV diagram

2. Thermal Efficiency of the otto cycle

Introduction :

Process:

0-1 is suction process

1-2 is Isentropic compression

2-3 is constant volume heat Addition

3-4 is Isentropic expansion

4-1 is Constant volume heat rejection

1-0 is exhaust process

Thermal Efficeiency:

Software Used : MATLAB Programming

% for create a PV diagram on otto cycle we need Pressure and volume at respected stages

% Assuming Engine Geometric Parameters:

1.bore = 0.1m;

2.stroke = 0.1m;

3.Correcting rod length = 0.15m;

4.Compression ratio = cr = 14;

5.Pressure at stage 1= p1 =1.01235pa

6.Temparature at stage 1= T1 = 500K

7.Peak Temperature at stage2 = T3 = 2300K

8. Gamma= 1.4;

Relations:

PV^gamma = c

PV = MRT

Program:

% otto cycle Progamming

clear all
close all
clc

% inputs
gamma = 1.4;

% Assuming P1, T1 values

p1 = 1.01325
t1 = 500

% Assuming Engine Geometric Parameters

bore = 0.1;
stroke = 0.1;
con_rod = 0.15;
cr =14;

% 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

% Process 1-2 Isentropic compression
% p2*v2^gamma = p1*v1^gamma
% p2 = p1*(v1/v2)^gamma

p2 = (p1*v1/v2)^gamma

% P1V1/T1 = P2V2/T2
% T2 = (P2*V2/(P1V1))*T1

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

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

% 2-3 Constant volume Heat addition
% Assuming t3 is peak temperature = 2300K

t3 = 2300;
v3 = v2
p3 = p2*t3/t2

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

% 4-1 constant volume heat rejection

v4 = v1

% P3*V3^gamma = P4*V4^gamma
p4 = p3*v3^gamma/v4^gamma

% Thermal effecincy
efficiency = 1-1/cr^(gamma-1)

figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(v_compression,p_compression,'color','b')
plot(v2,p2,'*','color','r')
plot([v2,v3],[p2 p3],'color','b')
plot(v3,p3,'*','color','r')
plot(v_expansion,p_expansion,'color','b')
plot(v4,p4,'*','color','r')
plot([v4 v1],[p4 p1],'color','b')
xlabel('volume')
ylabel('pressure')

grid on

Function Script:

% Otto-Cycle Kinematics of piston

function [v] = piston_kinematics(bore, stroke, con_rod, cr, start_crank, end_crank)

crank_pin_radius = stroke/2;
r = con_rod/crank_pin_radius;

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

end

Output:

Thermal efficiency =

0.6520

PV diagram:

Conclusion:

The termal effeciency of a otto cycle is 65.20% as per the given inputs