Air standard Cycle
OBJECTIVE:
To solve an otto cycle and make plots for the,
1)A PV diagram and
2) Output of the thermal efficiency of the engine.
THEORY:
DEFINITION:
The Otto Cycle, describes how heat engines turn gasoline into motion. It is an air-standard cycle which approximates the processes in disel and petrol engines. It is based on constant volume heat addition(combustion) and heat rejection process, and isentropic compression and expansion.
PROCESS TAKE PLACE IN OTTO CYCLE:
- Process 1–2 Isentropic compression stroke
- Process 2–3 ignition phase
- Process 3–4 Isentropic expansion stroke
- Process 4–1 idealized heat rejection
Process 1–2 Isentropic compression stroke :
In this process, the piston moves from bottom dead centre (BDC) to top dead centre (TDC) as the working gas with initial state 1 is compressed isentropically to state point 2, through compression. It is an isentropic process assumes that in this there is no mechanical energy is lost due to friction and no heat is transferred to or from the gas, hence it is an reversible process. In compression the volume decreases and pressure increases. In this process the volume decreases from v1 to v2 and the pressure increases from p1 to p2
Process 2–3 ignition phase:
It is an isochoric heat addition process. In this piston the piston remains at rest at TDC. During this period he air/fuel mixture remains in a small volume at the top of the compression stroke then heat is added to the working fluid by the combustion of the injected fuel. During this whole process the volume remains constant v2=v3 and pressure increases from p2 to p3.
Process 3–4 Isentropic expansion stroke :
The increased high pressure exerts a force on the piston and pushes it from the top dead centre (TDC) to the bottom dead centre (BDC). Hence the pressure decreases from p3 to p4 and volume increases from v3 to v4.
Process 4–1 idealized heat rejection:
In this process the piston remins res at BDC. Hence the volume remains constant v4=v1 and pressure decreases from p4 to p1
FORMULAS:
- Swept Volume = (pi/4)*bore^2*stroke
- Clearence Volume = Swept Volume/(cr-1)
- v1(volume1) = Swept Volume+Clearence Volume
- v2(volume2) = Clearence Volume
- v = (1+0.5*(cr-1)*(r+1-cosd(theta)-(r^2-sind(theta)^2)^0.5))*v_c
- a =stroke/2
- r =con_rod/a
- State variable at state point 2
1) p2=p1*cr^gamma
2) t2=p2*v2*t1/(p1*v1)
- State variable at state point 3
1)v3=v2
2)p3=p2*t3/t2
- State variable at state point 4
1)v3=v2
2)p3=p2*t3/t2
INPUTS:
- gamma=1.4
State variable parameters
- p1=10132
- t1=500
- t3=2300
Engine generated parameters
- bore=0.1
- stroke=0.1
- con_rod=0.15
- cr=12
DIFFERENCE BETWEEN OTTO CYCLE AND DISEL CYCLE:
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OTTO CYCLE |
DISEL CYCLE |
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PROGRAM:
clear all
close all
clc
%input
gamma=1.4;
%state variables
p1=101325;
t1=500;
t3=2300;
%engine generated parameter
bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;
%formula to calculate swept volume and clearence volume
v_swept=(pi/4)*bore^2*stroke;
v_clearence=v_swept/(cr-1);
v1=v_swept+v_clearence
v2=v_clearence
%state variable at state point2
%p2*v2^gamma = p1*v1^gamma
%p2=p1(v1/v2)^gamma=p1*cr^gamma
p2=p1*cr^gamma
t2=p2*v2*t1/(p1*v1)
constant_c=p1*v1^gamma;
v_compression=enginekinematics(bore, stroke, con_rod, cr,180,0)
p_compression=constant_c./v_compression.^gamma
%state variable at state point 3
v3=v2
p3=p2*t3/t2
constant_c=p3*v3^gamma;
v_expansion=enginekinematics(bore, stroke, con_rod, cr,0,180)
p_expansion=constant_c./v_expansion.^gamma
%state variable at state point 4
v4=v1
p4=p3*(v3/v4)^gamma
t4=(p4*v4*t3)/(p3*v3)
thermal_efficency=(1-(t4-t1)/(t3-t2))*100
figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(v_compression, p_compression,'linewidth',2)
plot(v2,p2,'*','color','r')
plot(v3,p3,'*','color','r')
plot(v_expansion, p_expansion,'linewidth',2)
plot(v4,p4,'*','color','r')
line([v2,v3],[p2,p3],'linewidth',2,'color','m')
line([v4,v1],[p4,p1],'linewidth',2,'color','m')
xlabel('volume')
ylabel('pressure')
title('pv diagram')
figure(2)
plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1],'color','b','linewidth',2)
xlabel('volume')
ylabel('pressure')
PROGRAM FOR ENGINE KINEMATICS:
In this we use function command called enginekinematics which has some input value stored in function[v]
function[v] = enginekinematics(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
OUTPUT:
1) PV diagram
2) Thermal efficiency of the engine:
ERROR:
In engine kinematics code i have forget to add bracket in the formula so that my whole pv diagram and output is changed.
and my output of the program is
RESULT:
Thus we have obtained code that can solve an otto cycle and make plots for the pv diagram and have found the output for the thermal efficiency of the engine.
https://drive.google.com/open?id=1HhQklzSFm3x1SP7SnmjCXtAuGvJ8jXoI
https://drive.google.com/open?id=1pefsfqKhgiiAM_UaeLGH5sv_R6fUDS5s
https://drive.google.com/open?id=10haj-xQWoIDgv2ZFOpFIPTPnZa2Dp_GF