Project #2:- solve an otto cycle and make plots for it.

Write code that can solve an otto cycle and make plots for it.

Here are the requirements

• Your code should create a PV diagram
• You should output the thermal efficiency of the engine.

Basic of ideal otto cycle:-

Otto cycle is used for SI engine. Its consist of four strokes and four processes. These four processes of an engine will be responsible for the four strokes. strokes are responsible for developing the power of power of engine that results in vehicle movement. The ideal otto cycle mainly consists for processes

1. Iscentropic/Adiabatic compression(1-2)
2. Contant volume heat addition(2-3)
3. Iscentropic//Adiabatic expansion(3-4)
4. Contant volume heat rejection(4-1)

fig1:- PV diagram of otto cycle

• Compression Ratio:- Its ratio of volume of piston at BDC to volume of piston at TDC

compression ration(cr)=volume of piston at BDC/volume of piston at TDC

also

compression ration=swept volume+clearance volumn/clearnace volume

cr=s_v+c_v/c_v

also,

v1=piston at BDC=s_v+c_v

v2=piston at TDC=c_v

so, Compression ratio=v1/v2

• Expansion Ratio:- its ratio of volume before expansion to volumn after expansion.

expansion ratio(er)=v3/v4

• Swept volume(v_s):- Its volume of cylinder when piston is at BDC or volume of cylinder before compresion.
• Clearance volume(v_c):- Its volume of cylinder when piston is at TDC or volume after compression.

Program 1:- Otto cycle using MATLAB(Only state points)

clear all

close all

clc

%PV Diagram for air standard otto cycle

%state variables

p1=101325 % 1atm pressure

t1=400% kelvin

t3=2500

gamma=1.4

%engine geometric parameters

%engine bore(d)

bore=0.1;

%compression ratio

cr=12;

% stroke length

stroke=0.1;

%connecting rod length

con_length=0.17;

%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 point2

% according to ideal gas law

% p1v1^gamma=p2v2^gamma

% p2=p1v1/v2^gamma

% where v1/v2=cr

% p2=p1*cr^gamma

p2=p1*cr^gamma;

%also, p1v1/t1=p2v2/t2

t2=p2*v2*t1/(p1*v1);

% state variables at point 3

% as it is contant volume heat additon process

v3=v2

% p3v3/t3=p2v2/t2

% p3= p2v2t3/v3t2

%p3= P2*t3/t2 where v2=v3

p3= p2*t3/t2;

% state variables at point 4

v4=v1

% as it is contant volume heat rejection process

% p3v3^gamma=p4v4^gamma

% p4=p3v3/v4 ^gamma

% p4=p3*(v3/v4)*gamma

p4=p3*(v3/v4)^gamma;

%plotting

figure

hold on

plot(v1,p1,'*','color','r')

plot(v2,p2,'*','color','r')

plot(v3,p3,'*','color','r')

plot(v4,p4,'*','color','r')

xlabel('volume(m3)');

ylabel('pressure(kg/m3)');

now,in above program

clear all- used to clear all text from commond window

close all- used to close files open in window

clc- used to clear command window

Input parameters are taken as per given in program.

finally plot function is used to plot pv digram. after running all program we are getting state points at four different conditions.

Problem facing during this program-

while writing code for p4, i had written p4=p3*(v3/v4)*gamma; . Due to this mistake gamma getting multiflied with other values. i had use * instead of using ^.

fig2:PV diagram of otto cycle

Now, we have all state points of otto cycle. we have to join this but if we use plot function directly then its show straight line as a output. However in actual, there is no striaght line in iscentropic process. so, according coming output its error. Lets try to use plot function to join all state points in program 1 to check.

clear all

close all

clc

%PV Diagram for air standard otto cycle

%state variables

p1=101325 % 1atm pressure

t1=400% kelvin

t3=2500

gamma=1.4

%engine geometric parameters

%engine bore(d)

bore=0.1;

%compression ratio

cr=12;

% stroke length

stroke=0.1;

%connecting rod length

con_length=0.17;

%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 point2

% according to ideal gas law

% p1v1^gamma=p2v2^gamma

% p2=p1v1/v2^gamma

% where v1/v2=cr

% p2=p1*cr^gamma

p2=p1*cr^gamma;

%also, p1v1/t1=p2v2/t2

t2=p2*v2*t1/(p1*v1);

% state variables at point 3

% as it is contant volume heat additon process

v3=v2

% p3v3/t3=p2v2/t2

% p3= p2v2t3/v3t2

%p3= P2*t3/t2 where v2=v3

p3= p2*t3/t2;

% state variables at point 4

v4=v1

% as it is contant volume heat rejection process

% p3v3^gamma=p4v4^gamma

% p4=p3v3/v4 ^gamma

% p4=p3*(v3/v4)*gamma

p4=p3*(v3/v4)^gamma;

%plotting

figure

hold on

plot(v1,p1,'*','color','r')

plot(v2,p2,'*','color','r')

plot(v3,p3,'*','color','r')

plot(v4,p4,'*','color','r')

plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1])

xlabel('volume(m3)');

ylabel('pressure(kg/m3)');

after using this program we can get output as,

fig3: Error Due to use of plot command directly

Now, To correct this error we have to use thermodynamic relation during compression and expansion process.Also we have to determine how volumn is changes according to crank angle

Program 2- Code to create funtion

During this calling or saving the code of function we have to take care of that function name and file name is same.

Problem-

My function is not running due to different file and function name during this coding. j have made it same to correct this error.

Now we have to calculate volume during compression and expansion process.

so for compression process,

To find volume,

v_compression=engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)

Now during compression piston is travelling from BDC to TDC.so,

v_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0)

To find pressure,

p1*v1^gamma=c_contant

p_compression=c_contant/v_compression.^gamma

For expansion process,

To find volumn,

v_expansion=engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)

Now during expansion piston is travelling from TDC to BDC.so,

v_expansion=engine_kinematics(bore,stroke,con_rod,cr,0,180)

To find pressure,

p3*v3^gamma=c_contant

p_expansion=c_contant/v_expansion.^gamma

Thermal efficiecy can be calculated

percentage_efficency=(1-(cr^(gamma-1))^-1)*100

Final Matlab Program:-

clear all

close all

clc

%PV Diagram for air standard otto cycle

%state variables

p1=101325 % 1atm pressure

t1=500 % kelvin

t3=2300

gamma=1.4

%engine geometric parameters

%engine bore(d)

bore=0.1;

%compression ratio

cr=12;

% stroke length

stroke=0.1;

%connecting rod length

con_rod=0.15;

%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 point2

% according to ideal gas law

% p1v1^gamma=p2v2^gamma

% p2=p1v1/v2^gamma

% where v1/v2=cr

% p2=p1*cr^gamma

p2=p1*cr^gamma;

%also, p1v1/t1=p2v2/t2

t2=p2*v2*t1/(p1*v1);

%to find pressure and volumn during compression

c_contant=p1*v1^gamma

V_compression=engine_kinematics(bore,stroke,con_rod,cr,180,0);

P_compression=c_contant./V_compression.^gamma;

% state variables at point 3

% as it is contant volume heat additon process

v3=v2

% p3v3/t3=p2v2/t2

% p3= p2v2t3/v3t2

%p3= P2*t3/t2 where v2=v3

p3= p2*t3/t2;

%To find pressure during expansion,

c_contant=p3*v3^gamma

V_expansion=engine_kinematics(bore,stroke,con_rod,cr,180,360);

P_expansion=c_contant./V_expansion.^gamma;

% state variables at point 4

v4=v1

% as it is contant volume heat rejection process

% p3v3^gamma=p4v4^gamma

% p4=p3v3/v4 ^gamma

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

p4=p3*(v3/v4)^gamma;

%thermal efficiency

percentage_efficency=(1-(cr^(gamma-1))^-1)*100

%plotting

figure(1)

hold on

plot(V_expansion,P_expansion,'linewidth',2,'Color','b')

plot(V_compression,P_compression,'linewidth',2,'Color','b')

plot(v1,p1,'*','color','r')

plot(v2,p2,'*','color','r')

plot([v2 v3],[p2 p3],'linewidth',2,'Color','g')

plot(v3,p3,'*','color','r')

plot(v4,p4,'*','color','r')

plot([v4 v1],[p4 p1],'linewidth',2,'Color','g')

xlabel('volume(m3)');

ylabel('pressure(kg/m3)');

Problem while doing this program

I have mistakely mark ' term3=[R*2-sind(theta).^2].^0.5;' in function coding.Due to this error i am getting wrong graph.

Output Graph:

Fig3:- pv diagram of air standard cycle

All variables value(output)

Thermal efficiency:-