MATLAb Programme to solve an otto cycle.

AIM:- To Write a Code that can solve an Otto Cycle and make Plots for it.

Theory:-

Otto Cycle : The Otto cycle is a set of processes used by spark ignition internal combustion engines (2-stroke or 4-stroke cycles). These engines

1. ingest a mixture of fuel and air,
2. b) compress it,
3. c) cause it to react, thus effectively adding heat through converting chemical energy into thermal energy,
4. d) expand the combustion products, and then
5. e) eject the combustion products and replace them with a new charge of fuel and air.
6. The different processes are shown in Figure.

The Otto cycle 1 → 2 → 3 → 4 consists of following four processes:-

Process 1 → 2: Reversible adiabatic compression of air;

Process 2 → 3: Heat addition at constant volume;

Process 3 → 4: Reversible adiabatic expansion of air;

Process 4 → 1: Heat rejection at constant volume.

Since processes 1 → 2 and 3 → 4 are adiabatic processes, the heat transfer during the cycle takes place only during processes 2 → 3 and 4 → 1, respectively

Objective:-

1. Thermal efficiency of the engine.
2. Plot PV Diagram

Procedure:

Step 1- Firstly we need to assign the values for Engine Parameters

Engine Geometric Parameters;

bore = 0.1

stroke = 0.1

con_rod = 015

cr = 12

Step 2- Now, At state-1 we will provide the values-

gamma = 1.4

t3 = 2300

p1 = 101325

t1 = 500

Step 3- Typed coding to Calculate the pressure, volume, temperature & at all the States(2,3,4) by using the Thermodynamics Equations in the code.
Also I write the code to get the Thermal Efficiency as output.

Step4- Here, this is most important step, where I am coding and generating a function for calculating the ratio of swept volume by clearance volume,
which means how the volume is changing inside the cylinder at every process.
I did this to get the exact work done by the engine, and to represent it on the graph.
To code this function I use the formula (V/Vc) by dividing it in small terms so that to make it easy in code.
Then put the all the terms according to the formula.

Step5- After the function is created I call the function inside the code to get the points for all the process and join them according to the process.

Step6- Finally I plot all the point of Pressure And Volume on PV- Diagram and join them according to the process taking place inside the cylinder.
also I plot the output of Thermal Efficiency on the PV -Diagram.

Formulas:

1. Change in Volume inside the Combustion Chamber=

Where;-

V = Swept Volume

Vc = Clearance Volume

rc = Compression Ratio

R = Radius of Piston

2. Thermal Efficiency =

nth = 1 - 1/(cr^gamma-1)

Where;-

nth = Thermal Efficiency

cr = Compression ratio

MATLAB PROGRAMME:-

• Matlab code to get the Graphical representation of PV-Diagram Of Otto Cycle
  And Thermal Efficiency as the Outputs

clear all
close all
clc

%Inputs
gamma = 1.4;
t3 = 2300;

%Engine Geometric Parameters
bore = 0.1;
stroke = 0.1;
con_rod = 015;
cr = 12;

%State Variables At Point 1
p1 = 101325;
t1 = 500;

 %Calculate The Swept Volume And The 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 State point 2
 %p2v2^gamma = p1v1^gamma 
 %To calculate p2 = p1(v1/v2)*gamma = p1*cr^gamma
 p2 = p1*cr^gamma;
 
 %p1v1/t1 = p2v2/t2 | t2 = p2v2*t2/(p1*v1)
 t2 = p2*v2*t1/(p1*v1);
 
 constant_c = p1*v1^gamma;
 V_compression = engine_kinem(bore,stroke,con_rod,cr,180,0);
 
 P_compression = constant_c./V_compression.^gamma;
 
 %State variable 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_kinem(bore,stroke,con_rod,cr,0,180);
 
 P_expansion = constant_c./V_expansion.^gamma;
 
 %state variable aty state point 4
 v4 = v1;
 
 %p3v3^gamma = p4v4^gamma | p4 = p3*(v3/v4)^gamma
 p4 = p3*(v3/v4)^gamma;
 
 
 
 %output- Thermal Efficiency - Graphical representation
 %Thermal Efficiency = nth = 1 - 1/(cr^gamma-1)
 nth = 1 - 1/(cr^gamma-1)
 
 figure(1)
 hold on
 plot(v1,p1,'*','color','b')
 plot(v2,p2,'*','color','b')
 plot(v3,p3,'*','color','b')
 plot(v4,p4,'*','color','b')
 grid on
 
 plot(V_compression,P_compression,'color','m')
 plot([v2 v3],[p2 p3],'color','m')
 plot(V_expansion,P_expansion,'color','m')
 plot([v4 v1],[p4 p1],'color','m')
 title('Otto Cycle','fontsize',30)
 
 
 text(v1,p1,'state-1')
 text(v2,p2,'state-2')
 text(v3,p3,'state-3')
 text(v4,p4,'state-4')
 
%  text(5*10^(-4),4*10^6,['Thermal Efficiency(nth) = 1 - 1/(cr^g^a^m^m^a-1)','fontsize',15])
 text(5*10^(-4),4*10^6,[ sprintf('Thermal Efficiency=%d',nth)])


 xlabel('Volume')
 ylabel('Pressure')
 

• Matlab Coding to create the Function named engine_kinem as follows:-

function[V] = engine_kinem(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

Result:- Otto cycle Graph & Thermal Efficiency Obtained as Follows:-

Otto Cycle is Thermodynamics Process occurs in any Internal Combustion Engine. By Coding MATLAB Programme we can Visualize our Data.

Errors:- The errors, i faced while coding the Programms are mostly due to the mistyped the alphabet, ehich i overcome by checking my programme again.
I am overcoming thses by the programme slowly and checking it 2times beofor executing