CREATION OF OTTO CYCLE P-V DIAGRAM AND CALCULATION OF THERMAL EFFICIENCY USING MATLAB

AIM

To create an output of p-v diagram of otto cycle and calculation of thermal efficiency

INTRODUCTION

otto cycle built by otto and also known as constant volume cycle as heat is added and rejected in constant volume.

this cycle mostly used for petrol engines where ignition takes place. this cycle involves totally six processes here we going to explain about only four main processes for more about the other two process refer this link https://en.wikipedia.org/wiki/Otto_cycle#Process_1%E2%80%932_compression_stroke_(B_on_diagrams)

1. isentropic compression

2. constant volume heat addition

3. isentropic expansion

4. constant volume heat rejection

simply

1. compression

2. ignition

3.expansion

4. exhaust

before this four process starts the suction stroke will take place to intake some air fuel mixture to the engine

DESCRIPTION

process(1-2) - isentropic compression

This is also known as adiabatic compression. adiabatic or isentropic process means there will be no heat transfer incurred in the process. compression means reduction of volume of cylinder by pressing it using external force.

in this process Piston moves from crank end (BDC, bottom dead centre and maximum volume) to cylinder head end (TDC, top dead centre and minimum volume) as the working gas with initial state 1 is compressed isentropically to state point 2, through compression ratio (V₁/V₂). Mechanically this is the isentropic compression of the air/fuel mixture in the cylinder, also known as the compression stroke. This isentropic process assumes that no mechanical energy is lost due to friction and no heat is transferred to or from the gas, hence the process is reversible. The compression process requires that mechanical work be added to the working gas. Generally the compression ratio is around 9–10:1 (V₁:V₂) for a typical engine

process(2-3) - constant volume heat addition

In this process heat is added to the system where volume kept as constant that is there will be no volume change in which v2 will be equal to v3

During this process the The piston is momentarily at rest at TDC. During this instant, which is known as the ignition phase, the air/fuel mixture remains in a small volume at the top of the compression stroke. Heat is added to the working fluid by the combustion of the injected fuel, with the volume essentially being held constant. The pressure rises and the ratio {\displaystyle (P_{3}/P_{2})} is called the "explosion ratio"

process(3-4) - isentropic expansion

This is also known as adiabatic expansion. expansion means increasing of volume of cylinder by power stroke produced by ignition process

The increased high pressure exerts a force on the piston and pushes it towards the BDC. Expansion of working fluid takes place isentropically and work is done by the system on the piston. The volume ratio {\displaystyle V_{4}/V_{3}} is called the "isentropic expansion ratio". (For the Otto cycle is the same as the compression ratio {\displaystyle V_{1}/V_{2}}). Mechanically this is the expansion of the hot gaseous mixture in the cylinder known as expansion (power) stroke.

process(4-1) - constant volume heat rejection

In this process heat is removed from the system where volume kept as constant that is there will be no volume change in which v1 will be equal to v4

During this process The piston is momentarily at rest at BDC. The working gas pressure drops instantaneously from point 4 to point 1 during a constant volume process as heat is removed to an idealized external sink that is brought into contact with the cylinder head. In modern internal combustion engines, the heat-sink may be surrounding air (for low powered engines), or a circulating fluid, such as coolant. The gas has returned to state 1.

now to generate the programme in we need to find the pressure and temp values at respective stages

ASSUMPTIONS

gamma = 1.4
t3 = 2300
p1 = 1.01325
t1 = 500
engine geometric parameters
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 7

MATLAB PROGRAM

clear all
close all 
clc
% programme for otto cycle 
% inputs
gamma = 1.4
t3 = 2300
% state 1 variables
p1 = 1.01325
t1 = 500
% engine geometric parameters 
bore = 0.1
stroke = 0.1
con_rod = 0.15
cr = 7
%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 2 variables 
% p2v2^gamma = p1v1^gamma
% p2 = p1*(v1/v2)^gamma
p2 = p1*cr^gamma
constant_c = p1*v1^gamma;
v_compression = engine_kinematics(bore,stroke,con_rod,cr,180,0);
p_compression=constant_c./v_compression.^gamma;
% p1v1/t1 = p2v2/t2
t2 = p2*v2*t1/(p1*v1)
% state 3 variables
v3 = v2
% p3v3^gamma = p2v2^gamma
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 4 variables 
v4 = v1
% p3v3^gamma = p4v4^gamma
p4 = p3*(v3/v4)^gamma
% thermal efficiency
sn
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 v1],[p4 p1])
plot(v4,p4,'*','color','r')
xlabel('volume (in m^3)')
ylabel('pressure (in pa)') 
grid on

FUNCTION DEFINITION PROGRAM

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,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

THE OUTPUT (P-V) DIAGRAM

EFFICIENCY CALCULATION

thermal efficiency = 1-1/cr^(gamma-1)

the thermal efficiency calculated to be 0.5408 *100 = 54.08%

CONCLUSION

The otto cycle processes has been analysed and thermal effiency has been calculated by using MATLAB programme successfully and the output of p-v diagram also been generated