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

AIM : To write a code that can solve an otto cycle and make plots for it

EXPLANATION :

PROCESS :

0 - 1 CONSTANT PRESSURE INTAKE

1 - 2 ISENTROPIC COMPRSSION

2 - 3 CONSTANT VOLUME HEAT ADDITION

3 - 4 ISENTROPIC EXPANSION

4 - 1 CONSTANT VOLUME HEAT REJECTION

1 - 0 MASS OF AIR RELEASED

• With the input of volume 1 (v1) and temperature1 (t1) then pressure 1(p1) is calculated.
• If the compression ratio is known then volume 2 (v2) is calculated.
• And then need to know about the engine parameters instead of starting from v1 can start from engine parameters.

ENGINE GEOMETRIC PARAMETERS

1. Bore.
2. Stroke.
3. Connecting rod length.
4. CR(copression ratio).

Calculating the sewpt volume & clearance volume

swept volume = (pi/4)*bore^2*stroke.

clearance volume = (swept volume/CR-1).

volume v1 = swept volume + clearance volume.

volume v2 = clearance volume.

• Swept volume is nothing but the volume of the cylinder through which a piston or plunger moves as it makes a stroke.
• clearance volume is the ratio of this volume to the swept volume determines the compression ratio of the engine.

state variable at state point 1 is computed.

now state variable at state point 2 has to be determined by the

p2v2^gamma = p1v1^gamma which refers the isentropic compression.

so p2 = p1*(v1/v2)^gamma. v1/v2 is nothing but the compression ratio(CR).

To compute the temperature2 (t2) at state point 2 using ideal gas law.

since pv/t is constant. so p1v1/t1 = p2v2/t2.

therefore t2 = p2v2t1/p1v1.

let's determined the state variable at state point 3.

state point 3 represents end point of constant volume compression process.

v3 = v2

At the end of the compression process the temperature hs be assumed in order to determined p3.

p3v3/t3 = p2v2/t2.

therefore p3 = p2t3/t2.

Determined the state variable at state point 3.

volume at state 4 = volume ate state 1.

To compute the pressure p4.

p3v3^gamma = 04v4^gamma.

therefore p4 = p3(v3/v4)^gamma.

Function to be compute volume and pressure that has to be change the adiabatic process in the above function.

Volume trace function that input the function of bore,stroke,con-rod,start-crank angle,end-crank angle using the formula of

v/vc = 1+0.5(cr-1)[R+1-cosdtheta - (R^2-sin^2theta)^0.5].

This forumla is divied into three term

term1 = 0.5*(cr-1).
term2 = r+1-cosd(theta).
term3 = (r^2-sind(theta).^2).^0.5.

NOTE : THE NAME OF THE FUNCTION & NAME OF THE SAVE FILE SHOULD BE SAME.

Compression:

constant c = p1v1^gamma
V compression = engine kinematics(bore,stroke,con_rod,cr,180,0)
P compression = (constant c./V compression.^gamma)

Expansion:

constant c = p3v3^gamma
V expansion = engine kinematics(bore,stroke,con_rod,cr,0,180)
P expansion = (constant c./V expansion.^gamma)

thermal efficiency = 1-(1/(cr^gamma-1))

CODE : 1

function [V] = engine_kinematics(bore,stroke,con_rod,cr,start_crank,end_crank)


a=stroke/2;
r=con_rod/a;

v_swept = (pi/4)*bore^2*stroke;
v_clearance = (v_swept/(cr-1));


theta = linspace(start_crank,end_crank,180);
term1 = 0.5*(cr-1);
term2 = r+1-cosd(theta);
term3 = (r^2-sind(theta).^2).^0.5;

V = (1+term1*(term2-term3))*v_clearance;


end

CODE : 2

close all
clear all
clc

%input
gamma = 1.4
t3 = 2300

%state variables
p1 = 101325
t1 = 500


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

%calculating 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 variable at state point 2
%p2v2^gamma = p1v1^gamma | p2 = p1*(v1/2)^gamma = p1*cr^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,180,0)
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,0,180)
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 efficiency
thermal_efficiency = 1-(1/(cr^gamma-1))
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')
xlabel('volume')
ylabel('pressure')
title('Correct plot')

figure (2)
plot([v1 v2 v3 v4],[p1 p2 p3 p4],'color','b')
xlabel('volume')
ylabel('pressure')
title('Incorrect plot')

THERMAL EFFICIENCY:

Thermal efficiency is calculated by

thermal efficiency = 1-(1/(cr^gamma-1)).

ERROR :

V_compression .capital 'V' is to be use. corrected in the above code 2.