Air Standard Cycle(OTTO CYCLE)

• 0-1 - Mass of air is drawn into the cylinder
• 1-2 - Isentropic compression - This process involves an adiabatic(isentropic) compression of the charge as the piston moves from BDC to TDC.
• 2-3 - Constant volume heat addition - This process involves the ignition of the charge(fuel-air mixture) and subsequent rapid burning.
• 3-4 - Isentropic expansion - This process involves the power stroke in which the piston moves from TDC to BDC.
• 4-1 - Constant volume heat rejection - This process involves heat rejection while the piston is at BDC.
• 1-0 - The burnt charge is sent out through the exhaust port in a constant pressure process.

FORMULAS

1. Volume Trace

2.Thermal Efficiency

Inputs

Engine Geometric parameters such as bore, stroke length, connecting rod length, compression ratio.

Main Program

clear all
close all
clc

%inputs 
gamma = 1.4;
%engine geometry parameters
bore = 0.1;
stroke_length = 0.1;
cond_length = .15;
cr = 14;
%swept volume 
Vs = pi/4*(bore)^2 * stroke_length;
%clearance volume cr = Vtotal/ Vclearance; 
Vc = Vs/(cr-1);
V1 = Vs+Vc;
V2 = Vc;

% state variables at state point 1 
T1 = 500;
P1 = 101325;
constant_c = P1*V1^gamma;
V_compression = engine_kinematics1(bore, stroke_length,cond_length,180,0);
P_compression = constant_c./V_compression.^gamma;
%P_compression*V_compresion.^gamma = constant
% state variables at state point 2
%P1*V1^gamma = P2*V2^gamma; P2 = P1*cr^gamma
P2 = P1*(cr)^gamma;
%P*V/T = const;
T2 = P2*V2*T1/(P1*V1);

%state variables at state point 3
%P3V3/T3 = P2V2/T2; V2 = V3
T3 = 2300;
P3 = (P2*T3)/T2;
V3 = V2;

constant_e = P3*V3^gamma;
V_expansion = engine_kinematics1(bore, stroke_length,cond_length,0,180);
P_expansion = constant_e./V_expansion.^gamma;
%P_expansion*V_expansion.^gamma = constant

%state variables at state point 4
V4 = V1;
%P4*V4^gamma = P3*V3^gamma
P4 = P3*(V3/V4)^gamma;
T4 = P4*V4*T3/(P3*V3);
%Thermal Efficiency
thermal_term1 = T4-T1;
thermal_term2 = T3-T2;
Eff_Thermal = (1-(thermal_term1/thermal_term2))*100



figure
hold on
plot(V1,P1,'*','color', 'r')
plot(V_compression,P_compression)
plot(V2,P2,'*','color', 'b')
plot(V3,P3,'*','color', 'r')
plot(V_expansion,P_expansion)
plot(V4,P4,'*','color', 'b')
line([V2,V3],[P2,P3])
line([V4,V1],[P4,P1])
xlabel('volume')
ylabel('pressure')

STEPS INVOLVED

1. Input all the engine geometry parameters.

2. Define volumetric parameters.

3. Define swept volume and clearance volume.

4. Using PV^gamma and PV/T = constant find out Pressure, Volume and Temperature at all the state points 1,2,3 and 4.

5. Write a Function Program as below and use it to plot the volume trace for the 1-2 and 3-4 processes.

6. Plot the PV diagram using plot command.

6. Define the Thermal Efficiency formula.

Function Program

function [V] = engine_kinematics1(bore, stroke_length, cond_length,start_crank,end_crank)
cr = 14;
a = stroke_length/2;
R = cond_length/a;
Vs = pi/4*(bore)^2 * stroke_length;
Vc = Vs/(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)).*Vc;

end

Errors

1.

This error was due to an already existing linspace program file in C drive.

The error resolved after deleting the file.

2.

Through this error, I realised that we cannot execute or run the function program file but we can open the input function in the command window.

3.

The element-wise operator '.' was missing and thus this error.

OUTPUT

1.PV PLOT

2.Thermal Efficiency

REFERENCES

1. https://en.wikipedia.org/wiki/Otto_cycle

2.https://www.khanacademy.org/science/physics/thermodynamics/laws-of-thermodynamics/a/what-are-pv-diagrams