Project

Air standard Cycle: solve an Otto cycle and make plots for it

SShakti Nath Ojha21 May 2020

AIM:

solve an otto cycle and make plots for it.

OBJECTIVE:

create a PV diagram
output the thermal efficiency of the engine.

INTRODUCTION:

Otto cycle: automobiles The Otto cycle is the name for the cycle used in spark-ignition IC Engine such as gasoline/petrol. Its theoretical efficiency depends on the compression ratio cr of the engine and the specific heat ratio γ of the gas in the combustion chamber.
Thus, the efficiency increases with the compression ratio. However, the compression ratio of Otto cycle engines is limited by the need to prevent the uncontrolled combustion known as knocking. Modern engines have compression ratios in the range 8 to 11, resulting in ideal cycle efficiencies of 56% to 61%.

PROCESSES:

Intake Stroke(0-1)
Compression Stroke(1-2)
Ignition Phase(2-3)
Expansion Stroke(3-4)
Heat Rejection(4-1)
Exhaust Stroke(1-0)

MATLAB CODE:

clear all   
close all
clc
 
%State all inputs variables
p1=101325
t1=500
t3=2300

%ENGINE  GEOMETRIC  PARAMETERS
bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;
gamma=1.4;

%Calculating the swept volume and the clearance volume
%formula of swept volume calculation
v_swept=(pi/4)*bore^2*stroke; 

%Formula of clearance volume calculation
v_clearance=v_swept/(cr-1); 

%State point 1 
v1=v_swept + v_clearance
v2=v_clearance


% state variable at state point 2
p2=p1*cr^gamma;
t2=p2*v2*t1/(p1*v1);
constant_c = p1*v1^gamma;
v_compression = engine_Kinematic(bore,stroke,con_rod,cr,180,0)
p_compression =constant_c./v_compression.^gamma
 

%state variables at state point 3
v3=v2
p3=p2*t3/t2
constant_c = p3*v3^gamma;

v_expansion = engine_Kinematic(bore,stroke,con_rod,cr,0,180)
p_expansion = constant_c./v_expansion.^gamma


%state variable at state point 4
v4=v1
p4=p3*(v3/v4)^gamma
t4 = p4*v4*t3/(p3*v3);


%Calculating thermal Efficiency 
thermal_term1 = t4-t1;
thermal_term2 = t3-t2;
Eff_Thermal = (1-(thermal_term1/thermal_term2))*100


%Plotting PV diagram actual curve
figure(1)
hold on
plot(v1,p1,'*','color','r')
plot(v_compression, p_compression)
plot(v2,p2,'*','color','g')
plot(v3,p3,'*','color','r')
plot(v_expansion, p_expansion)
plot(v4,p4,'*','color','r')
line([v2,v3],[p2,p3])
line([v4,v1],[p4,p1])
xlabel('volume')
ylabel('pressure')



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

MATLAB CODE FOR FUNCTION:

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

v_s = pi/4*bore^2*stroke
v_c = v_s/(cr-1)

theta = linspace(start_crank,end_crank,100)
a = stroke/2
R = con_rod/a


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

ERRORS AND REMEDIES:

the function was saved in a different directory:
resolved by saving them in the same folders.

RESULTS:

Output PV Diagram :

REFERENCE:

Air standard Cycle: solve an Otto cycle and make plots for it

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Ship work like thisin your own course.

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Ship work like this
in your own course.