Air Standard Cycle simulation using Matlab

Air Stadard Cycle Simulation using Matlab

Aim: To Simulate an Air standard cycle using Matlab.

Objective: The objective of this project is to get the thermal efficiency of a engine and to create a PV diagram for a Otto cycle.

Description:

Otto cycle:

FIG1: Process in Otto cycle

An otto cycle is an idealized thermodynamic cycle that describes ths functioning of a typical spark ignition piston engine. It is the thermodynamic cycle most commonly found in Automobile engines. The otto cycle is the 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.

FIG2: Pressure-Volume diagram

The process of the above PV diagram are as follows:

process 1-2 : Isentropic compression

process 2-3 : Common volume heat addition

process 3-4 : Isentropic expansion

process 4-1 : Common volume heat rejection

Isentropic process: In thermodynamics an isentropic process is an idealized thermodynamic process that is both adiabatic and reversible.

Thermal efficieny for Otto cycle: In general the thermal efficieny η_th, of any heat engine is defined as the ratio of the work this does, W, to the heat input at the high temperature, Q_H. In this equation, the ratio V₁/V₂ is known as the compression ratio,CR.

Formula:

thermal efficieny = (1-1/cr^(gamma-1))*100

where,cr- compression ratio

Program:

(i)program for creating a function:

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

(ii)program to create a Pv diagram and to find the thermal efficieny:

clear all 
close all
clc

%input

gamma=1.4
t3=2300
%state_varibales

p1=101325
t1=500

%engine geometric parameters

bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;

%calculation of 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 variable at state point 2
%p2v2^gamma=p1v1^gamma
%p2=p1(v1/v2)^gamma
p2=p1*cr^gamma;

%p1v1/t1=p2v2/t2 | t2=p2*v2*t1/(p1*v1)
t2=p2*v2*t1/(p1*v1)

constant_c=p1*v1^gamma;
V_compression=engine_kinematics(bore,stroke,con_rod,cr,360,0);
P_compression= constant_c./V_compression.^gamma; 

%state variables at state point 3
v3=v2

%p3v3/t3=p2v2/t2 | p3=p2*t3/t2 
p3=p2*t3/t2

constant_c=p3*v3^gamma;
V_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,360); 
P_expansion= constant_c./V_expansion.^gamma;

%state variables at state point 4
v4=v1

%p3v3^gamma=p4v4^gamma | p4=p3(v3/v4)^gamma
p4=p3*(v3/v4)^gamma

%thermal efficieny
thermal_efficieny= (1-1/cr^(gamma-1))*100

figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(V_compression,P_compression)
plot(v2,p2,'*','color','r')
plot(v3,p3,'*','color','r')
plot(V_expansion,P_expansion)
plot(v4,p4,'*','color','r')
plot([v2 v2],[p2 p3])
plot([v1 v1],[p1 p4])
xlabel('volume')
ylabel('pressure')
grid on

Output:

The PV diagram has been created :

Thermal efficiency of a engine if found:

Result:

(i)The PV plot has been created using Matlab.

(ii)The thermal efficieny of the engine , η= 63%