Air Standard Otto Cycle_1

OTTO CYCLE

AIM :

* To write a code for the PV Diagram of Otto cycle and derive the thermal efficiency of the otto cycle.

OBJECTIVE :

* Write a program to plot the curves of PV-diagram of the Otto Cycle .

* Find the Thermal Efficiency of the Otto Cycle.

INTRODUCTION OF OTTO CYCLE :

PV DIAGRAM OF OTTO CYCLE

• 1-2 : Isentropic compression
• 2-3 : constant volume heat addition
• 3-4 : Isentropic Expansion
• 4-1 : Constant volume heat rejection

PARAMETERS :

Engine Geometric Prameters :

• Bore = 0.2
• stroke= 0.2
• Connecting Rod Length = 0.25
• Compression Ratio (cr) = 13
• Swept Volume = (/4)*Bore^2*Stroke
• Clearance Volume = Swept Volume/(cr-1)

GIVEN PARAMETERS :

P1 = 101335 Pa

T1 = 600k

Gamma = 1.4

Wher,

P = Pressure

T = Temperture

STATE POINT : 1

V1 = Swept Volum+Clearance Volume

V2 = Clearance Volume

Wher,

V = Volume

STATE POINT : 2

P2V2 =P1V1^gamma

P2 = P1(V1/V2)^gamma

T2 = P2V2/T2V3

STATE POINT : 3

V3 = V2

P3 =P2V2T3/T2V3

STATE POINT : 4

V4 = V1

P4 = P3(V3/V4)^gamma

THERMAL EFFICIENCY OF OTTO CYCLE :

Thermal Efficiency (eff) = 1-(1/cr^(gamma-1))

% = Thermal Efficiency *100

VOLUME TRACE :

V/VC = 1+((1/2)(cr-1)[R+1- cosdθ - (R^2 - sindθ ^2)^(1/2)

Wher,

a = Stroke/2

R Connecting Rod length/a

PROGRAM COAD :

CASE : 1

clear all
close all
clc

% Inputs
gamma = 1.4
t3 = 2300

% Stste variables
p1 = 101335
t1 = 600

% Engine geometric parameters
bore = 0.2;
stroke = 0.2;
con_rod = 0.25;
cr = 13

% Calculating the swept volume and the clearance volume
v_swept = (pi/4)*bore^2*stroke;
v_claerance = v_swept/(cr-1);

v1 = v_swept + v_claerance
v2 = v_claerance

% State variables at state point 2
% p2v2^gamma = p1v1^gamma

% p2 = p1*(v1/v2)^gamma =v_claerance
p2 = p1*cr^gamma;

%p1v1/t1 = p2v2/t2 | t2 = p2*v2*t1/(p1*v1)
t2 = p2*v2*t1/(p1*v1);

% State variables at state point 3
v3 = v2

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

% State variables 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','g')

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

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

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

figure(2)
plot([v1 v2 v3 v4 v1],[p1 p2 p3 p4 p1],'color','b')

xlabel('volume')
ylabel('pressure')

grid on
title("OTTO CYCLE")

CASE OUTPUT :1

CASE : 2

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

CASE OUTPUT : 2

FINAL PROGRAM CODE :

% Otto Cycle

clear all
close all
clc

% Inputs
gamma = 1.4
t3 = 2300

% Stste variables
p1 = 101335
t1 = 600

% Engine geometric parameters
bore = 0.2;
stroke = 0.2;
con_rod = 0.25;
cr = 13

% Calculating the swept volume and the clearance volume
v_swept = (pi/4)*bore^2*stroke;
v_claerance = v_swept/(cr-1);

v1 = v_swept + v_claerance
v2 = v_claerance

% State variables at state point 2
% p2v2^gamma = p1v1^gamma
% p2 = p1*(v1/v2)^gamma =v_claerance
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
eff = (1-1/cr^(gamma-1))*100

% Plotting

figure(1)
hold on
plot(v1,p1,'*','color','g')
plot(V_compression,P_compression)

plot(v2,p2,'*','color','r')
plot([v2 v3],[p2 p3],'color','b')

plot(v3,p3,'*','color','m')
plot(V_expansion,P_expansion)

plot(v4,p4,'*','color','c')
plot([v4 v1],[p4 p1],'color','y')

xlabel('volume')
ylabel('pressure')

grid on

legend("Initial State","Isentropic Compression","Before Heat Addition","Isochoric Heat Addition","Before Expansion","Isentropic Expansion","Before Exhuaust","Isochoric Heat rejection")

title("OTTO CYCLE")

FINAL OUTPUT :

THERMAL EFFICIENCY OF OTTO CYCLE :

Thermal Efficiency (eff ) = 64.1555%

EXPLAINATION OF PROGREM CODE :

• First set given value of the offer; Gamma,T3,P1,T1,Engine geomatry,Bore,Stroke,Cond_rod,cr.
• After calculat the V_swept and V_clearanace using Engine geomatryv1 = v_swept + v_claerance
  v2 = v_claerance
• p2v2^gamma = p1v1^gamma, p2 = p1*(v1/v2)^gamma =v_claerance,p2 = p1*cr^gamma.
• p1v1/t1 = p2v2/t2 | t2 = p2*v2*t1/(p1*v1)
  t2 = p2*v2*t1/(p1*v1).
• Function comment is used,
• Calculate compression ,constant_c = p1*v1^gamma;
  V_compression = engine_kinematics(bore, stroke, con_rod, cr,stroke_start,stroke_end)
  P_compression = constant_c./V_compression.^gamma;
• Calculate v3 = v2
• Calculate p3v3/t3 = p2v2/t2 | p3 = p2*t3/t2
  p3 = p2*t3/t2
• Calculate Expansion ,constant_c = p3*v3^gamma;
  V_expansion = engine_kinematics(bore, stroke, con_rod, cr,stroke_start,stroke_end)
  P_expansion = constant_c./V_expansion.^gamma;

• Calculate ,v4 = v1.

• Calculate, p3v3^gamma = p4v4^gamma | p4 = p3*(v3/v4)^gamma
  p4 = p3*(v3/v4)^gamma.

• Calculate ,Thermal Efficiency
  eff = (1-1/cr^(gamma-1))*100

• And Plotting the code at last Title to Run the program.

Wher,

P = Pressure

V = Volume

T = Temperture

V_swept = Swept volume

V_clearanace = Clearance volume

cr = Compression Ratio

ERRORS :

• No Errors

CONCLUSION :

Therefore,the otto cycle plot is submitted and thermal efficiency is calculated.