WORKING OF AN OTTO CYCLE ENGINE BY USING MATLAB

AIM: To study the working of an OTTO cycle by using matlab and determine the engine parameters.

KEYWORDS: Otto cycle, Thermal efficiency, Isentropic, Isochoric.

SOFTWARE: Matlab

OBJECTIVE:

1. To study the working method of an Otto cycle.

2. To determine the thermal efficiency of an engine.

INTRODUCTION:

Otto cycle engine ia also called as petrol engine. The petrol engine invented by Nikolaus Otto in the year 1862. An otto cycle is an idealized thermodynamic cycle which invloves transfer of heat and work into the system while varying temperature (K), pressure (kPa) and other state variable within the system. An otto cycle basically describes the mass of fluid as it is subjected to changes of Pressure, Temperature, Volume, addition of heat and removal of heat. As the changes occurs is called as system. Otto cycle is a 4 stroke engine cycle, the working of an otto cycle as shown in Figure 1.

PROCESS:

In an otto cycle, workdone carried out by 4 process Intake, Compression, Combustion and Expansion respectively. In Intake process the mass of Air Fuel mixture takesplace (A/F), when the piston positioned bottom dead centre (BDC) the volume of the cylinder is more and the temperature remains constant throughout the process. In compression process the piston moves from bottom dead centre (BDC) to top dead centre (TDC) in which compresses the A/F mixture at a high pressure and increses the temperature thus the volume decreases. In combustion process the compressed A/F mixture ignites by means of sparkplug. The combusted gases carried out the workdone in the system at a high temperature and pressure, the volume remain constant throughout the process. In expansion process the piston moves from TDC to BDC in which the burnt gases used for work and the temperature & pressure of the cylinder reduces and volume increases. The remaining burnt gases used for next cycle thus the process repeats.

Isentropic: The process is both adiabatic and reversible, in which the work transfer of the system are frictionless and there is no heat transfer.

Isochoric: The process carried out constant volume. (V1=V4, V2=V3)

Adiabatic: The process occurs without transfer of heat or mass of substances between thermodynamic system and surroundings.

Entropy: To measure the disorder or randomness in the system.

FORMULA:

1. PVγ=Constant (ideal gas constant)

2. Vs=π/4⋅d2⋅L

3. Vc=Vs/(Cr−1)

4. V=(1+0.5(Cr−1)[R+1−cosθ−(R2−sin2θ)0.5])⋅Vc

5.P/T=Constant (Isochoric process)

6. η=[1-(T1/T2)]*100

where,

P = pressure (Pa)

V = volume (m3">m3)

T = temperature(K)

Cr = compression ratio

Vs = Swept volume

Vc = Clearance volume

a = Crankpin radius (m)

η = thermal efficiency (%)

MATLAB PROGRAM:

%AIR STANDARD CYCLE (OTTO cycle)

#main_program

clear all
close all;clc

%Inputs
gamma = 1.4;
t3 = 2300;

%State variables
p1 = 101325;
t1 = 500;
%Engine geometric parameters
bore = 0.1;
stroke = 0.1;
con_rod = 0.15;
Cr = 12;

% Calculating 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
%p2 = p1*Cr^gamma
p2 = p1*Cr^gamma;

%p1v1/t1 = p2v2/t2
t2 = (p2*V2*t1)/(p1*V1);

%PV^gamma = Constant
constant_c = p1*V1^gamma;
V_comp = eng_parameters(0.1,0.1,0.15,12,180,0);
P_comp = constant_c./V_comp.^gamma;

%State Variables at state point 3
V3 = V2;

%p3v3/t3 = p2v2/t2
p3 = p2*(t3/t2);

%PV^gamma = Constant
constant_c = p3*V3^gamma;
V_exp = eng_parameters(0.1,0.1,0.15,12,0,180);
P_exp = constant_c./V_exp.^gamma;

%State Variables at state point 4
V4 = V1;

%p3v3^gamma = p4v4^gamma
p4 = p3*(V3/V4)^gamma;
t4 = p4*t1/p1;
%t4 = (p4*V4*t3)/(p3*V3);

%Thermal efficiency
%Thermal_efficiency = 1-(t1/t2);
%Thermal_efficiency = 1-((t4 - t1)/(t3-t2))
Thermal_efficiency = 1-(1/Cr^(gamma-1));
figure(1)
hold on
plot(V1,p1,'*','color','r')
plot(V_comp,P_comp)
plot(V2,p2,'*','color','r')
plot([V2 V3],[p2 p3])
plot(V3,p3,'*','color','r')
plot(V_exp,P_exp)
plot(V4,p4,'*','color','r')
plot([V4 V1],[p4 p1])
xlabel('Volume')
ylabel('Pressure')
title('PV diagram of an OTTO cycle')

#function_program

function [V] = eng_parameters(bore,stroke,con_rod,Cr,start_crank,end_crank)

%crankpin radius
a = stroke/2;
R = con_rod/a;
V_Swept = (pi/4)*bore^2*stroke;
V_clearance = V_Swept/(Cr-1);
theta = linspace(start_crank,end_crank,100); %one cycle
%(V/Vc) = (1+0.5(cr-1)[R+1-cosd(theta)-(R^2-sind(theta)^2)^0.5])
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:

1. η=[1-(T1/T2)]*100

η =[1-(500/1351)]*100

η =62.99%

CONCLUSION:

1. In the above graph, it is clearly explained that the ideal process of an otto cycle.

2. Process (1-2) is Isentropic compression.

3. Process (2-3) is constant volume heat addition (V2=V3).

4. Process (3-4) is Isentropic expansion.

5. process (4-1) is constant volume heat rejection (V4=V1).

6. Calculated the thermal efficiency of an otto cycle.