Project

Write a code to solve that can solve an otto cycle and makes plots for it.

SSandeep Kolaparthi2 Apr 2022

Aim : Write a code to solve that can solve an otto cycle and makes plots for it.

1. create PV diagram 2. Output the thermal efficiency of the engine.

Theory :

Otto cycle The otto cycle is named after Nikolaus Otto (1832-1891, german) who is credited as the first creator of a petroleum fuel based internal combustion engine operating under a four stroke cycle. Ottos engine work during the eve of the industrial revolutiom was a critical development leading to the dawn of the automotive industry in the late 19th century.

On this cycle petrol, gas and many types of oil engines work. It is the standard of comparison for ineternal combustion engines.

The below diagrams shows the theoretical p-v diagram and T-s diagrams of this cycle respectively.

The point 1 represents that cylinder is full of air with volume V1 pressure p1 and absolute temperature T1.
Line 1-2 represents the adiabatic compression of air due to which p1, V1 and T1 change to p2, V2 and T2 respectively.
Line 2-3 shows the supply of heat to the air at constant volume so that p2 and T2 change to p3 and T3 ( V3=V2).
Line 3-4 represents the adiabatic expansion the air. During expansion p3, V3 and T3 change to final value of p4. V4 or V1 and T4 respectively.
Line 4-1 shows the rejection of heat by air at constant volume till original state(point 1) reaches.

Formulas used:

1. change in volume inside the cylinder

`V_s/V_c = 1 + 1/2 (r_c-1)[R+1-costheta-(R^2-sin^2theta)^0.5]`

Where,

V_s = swept volume

V_c = clearance volume

cr = compression ratio

R = radius of pistion

2. Thermal efiiciency =

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

Where

nth = Thermal efficiency

cr = compression ratio

Objectives :

1. plot p-v diagram

2. Thermal efficeiency of the engine.

Procedure / Explanation of the code :

Step -1 we need to assign the values for cyclinder parameters

bore = 0.1

stroke = 0.1

con_rod = 0.15

cr = 12

Step-2 provide the values at state 2,

gamma = 1.4

t3 = 2300

p1 = 101325

t1 = 500

Step -3 write the eaquations for 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

Now we got V1 & V2 values

Step 4 V1,V2, p1, t1, t3, gamma values are known and to obtain p2 value

Write adiabatic process 1-2 : p1V1^gamma = p2V2^gamma

p2 = p1*(v1/v2)^gamma

p2 = p1*cr^gamma

Step 4 Now V1,V2,V3, p1, p2, t1, t3, gamma values are known (Since V2=V3)

To provide state variable at state point 3 and to obtain p3 value,

At constant volume proces 2-3,

%p3v3/t3 = p2v2/t2 | p3 = p2*t3/t2

p3 = p2*t3/t2;

Now V1,V2,V3, p1, p2, p3, t1, t3, gamma values are known

Step 5 write the function for the engine kinematics to obtain v_expansion and p_expansion.

Step 6 Now state the variables at state pont 4, To obtain p4 value

Since, v4 = v1

%p3v3^gamma = p4v4^gamma | p4 = p3(v3/v4)^gamma

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

V1,V2,V3,V4, p1, p2, p3, p4, t1, t3, gamma values are known

create the plots for (V1,p1)(V2, p2)(V3,p3)(V4,p4) and execute the program.

Code for Otto cycle p-v Diagram :

Programming language - Matlab

clear all

close all

clc

% state variables

p1 = 101325

t1 = 500

% Inputs

gamma = 1.4

t3 = 2300

% 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 variables at state point 2

% p2v2^gamma = p1v1^gamma

% p2 = p1*(v1/v2)^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 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_kinematics(bore, stroke, con_rod, cr,0,180);

P_expansion = constant_c./V_expansion.^gamma;

% state variable at state point 4

v4 = v1

%p3v3^gamma = p4v4^gamma | p4 = p3(v3/v4)^gamma

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

figure(1)

 hold on
 plot(v1,p1,'*','color','r')
 plot(V_compression, P_compression)
 plot(V_expansion, P_expansion)
 plot(v2,p2,'*','color','r')
 plot(v3,p3,'*','color','r')
 plot(v4,p4,'*','color','r')

figure(2)

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

Code for the function : Engine kinematics

function V = engine_kinematics(bore, stroke, cond_rod, cr, start_crank, end_crank)

a = stroke/2;

R = cond_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

% Thermal Efficiency calculation :

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

Results and Outputs:

1. Obtained pressure points on graph

2. Graph for 180values by using linspace command

3. Graph for 720 values by using linspace command

4. garaph of figure 1 for (V_compression, p_compression)(v_expansion, p_expansion)

6 . Plotted the graph combining all variables p1,p2,p3,p4 and V1,V2,V3,V4

7 . Thermal efficiency of the otto cycle

Errors occured :

1. error occured due to parentheses forgot in an equation and it corrected after error messsage appeared in command window.

2. Error occured due to some input arguments missed in function of engine kinematics and it is corrected by giving proper input arguments.

References :

1. PV & TS Diagram : https://www.sciencedirect.com/topics/chemical-engineering/otto-cycle

2. Work done equation : https://sist.sathyabama.ac.in/sist_coursematerial/uploads/SMEA1404.pdf

Write a code to solve that can solve an otto cycle and makes plots for it.

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in your own course.

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Ship work like thisin your own course.

Talk to a career counsellor

Ship work like this
in your own course.