Plotting actual PV diagram for air standard otto cycle and determine efficiency

Aim:Plotting actual PV diagram for otto cycle and determine efficiency

Objective:

1.genrate code for plotting PV diagram?

2.find efficiency

Theory:

Otto cycle:Otto cycle is a thermodinamic cycle which represents various thermodynamic process for petrol or spark engines

in petrol engine thre are four?strokes 1. suction stroke?2.compression stroke 3. expanssin?stroke 4. exhaust stroke?

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???????????????????????????????????????????fig1

When these strokes happen there are some themodynamic process occure ,refer fig2

1.Compression-Isentropic compression (1-2)

2-Heat addition (spark ignition of fuel)-Constant volume heat addition(2-3)

3.Expanssion-Isentropic expanssion(3-4)

4-Heat rejection(heat rejected to surrounding)-Constant volume heat rejection (4-1)

Constant volume process: A thermodynamic pprocess during which volume of closed system remains constant

Isentropic process: An revercible adiabatic process called has isentropic process where heat loss from system?to surrounding is zero

so for otto cycle we dont consider any heat loss during compression or expanssion .

?

PV diagram : Here we plot Pressure(P) on Y axis at?volume (V) on X axis for carnk angle (theta)

?

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fig. 2

Stroke - distance traveled by piston from top dead center to bottom dead center?

Swept Volume: Volume of cylender for length os stroke (v1)

clearance volume :Volume remain in cylinder when pistoon reaches tod dead center?

compression ratio : it is ratio of coomplete cylinder volume and clearance volume (vs+vc/vc)

?Code:

note :Here we are going to create function to determine p and v values during compression and expanssion stroke at every angle .

Complete Code

%otto cycle calculations
clear alll
close all
clc

                    %variables
p1=101.325;
t1=300     % in kelvin
gama=1.4

                    %engine geometric parameters
bore=0.1;
stroke=0.1;
con_rod=0.15
cr=12

                    %calculate swept volume and clearence v
v_swept=(pi/4)*bore^2*stroke
v_clear=v_swept/(cr-1)

                    %calc at pt 2
v1=v_swept+v_clear;
v2=v_clear;
                    %for pressure in isentropic process pv^gama=c
%p1v1^gama=c=p2v2^gama
p2=(v1/v2)^gama*p1;
t2=t1*(cr^0.4);
[v_comprression]=engine_kinematics(v_clear,stroke,con_rod,cr,bore,180,0)
C=p1*v1^gama
[p_compression]=C./([v_comprression].^gama)

                   

                    %calc at pt 3

v3=v2               %v2=v3 (isochoric process)
t3=1800
p3=(p2/t2)*t3

                   
                    %calc at pt 4
v4=v1
p4=((v3/v4)^gama)*(p3)
t4=t1*(v4/v3)^(gama-1)
C=p3*v3^gama
[v_expanssion]=engine_kinematics(v_clear,stroke,con_rod,cr,bore,0,180)
[p_expanssion]=C./((v_expanssion).^gama)

figure(1)
hold on
plot([v1 v2 v3 v4 v1 ],[p1 p2 p3 p4 p1],'*')
plot(v_comprression,p_compression)
plot(v_expanssion,p_expanssion)
line([v2 v3],[p2 p3])
line([v1 v4],[p1 p4])
xlabel('volume')
ylabel('pressure')
legend('points','compression','expanssion','heat_addition','heat_rejection')
title('Otto cycle actual plot')
saveas(figure(1),'Otto cycle plot 2','jpeg')
figure(2)
hold on
plot([v1 v2 v3 v4 v1 ],[p1 p2 p3 p4 p1],'*')
line([v2 v3],[p2 p3])
line([v1 v4],[p1 p4])
line([v2 v1],[p2 p1])
line([v3 v4],[p3 p4])
xlabel('volume')
ylabel('pressure')
legend('points','compression','expanssion','heat_addition','heat_rejection')
title('Otto cycle act plot')
saveas(figure(2),'Otto cycle plot 1','jpeg')


%calculate eficiency for otto cycle
%eta=(1-(1/(rc^gamma))
x=cr.^0.4; 
eta=(1-(1/x))*100
disp('efficiency is')
disp(eta)
        

Formule:

We can simply determine p and v values at TDC and BDC with this formulas?

PV^gama=C- aplicable for both isentropic process

pv/t =c - aplicable to constant volume process?

by using above 2 eqn we can find values of P and V at start and end of process?(we will get Figure (2))

But here we cant se the actual behaviour of compression and expanssion curve so we use Engine kinematics to determine volume at perticular angle of crank?

formula is:

??note-while writing program we devide it in three terms to avoid mistakes

Function Code:

%we have formula to calculate cylnder volume at each stage so..
function[V]=engine_kinematics(v_clear,stroke,con_rod,cr,bore,start_crank,end_crank)
theta=linspace(start_crank,end_crank,180)
v_swept=(pi/4)*bore^2*stroke
v_clear=v_swept/(cr-1)
a=stroke/2
R=con_rod/a
% deivide the formula in 3 terms 
term1=0.5*(cr-1)
term2=R+1-cosd(theta);
term3=(R^2-sind(theta).^2).^0.5
V=(1+term1*(term2-term3))*v_clear
%we have formula to calculate cylnder volume at each stage so..
end        

Final plot :(figure(1))

Efficiency:62.98%

Conclusion :

1.From abouve fugure(2) we can determiine the actual nature of compression and expanssion curve for otto cycle

2.efficiency of otto cycle is 62.98 percent?