Code for solving an Air standard Cycle and calculating the thermal Efficiency using MATLAB

% engine Kinematics function code

function [V]= engine_kinematics1(bore,stroke,con_rod,cr,start_crank,end_crank)

a =stroke/2;
R = con_rod/a;

%swept and clearance volume calculations

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

theta= linspace(start_crank,end_crank,100);

%combustion volume calculations in parts

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

• The function is established and the values are defined for the various components like stroke, con rod length, etc.
• an array is created for theta using the linspace command.
• the various formulas are defined in 3 terms and in the end, all of them are combined together to make the function(V) work.

Code for PV diagram and Thermal Efficiency

clear all
close all
clc

%inputs
gamma=1.4;
t3=2300;

%state variables
p1=101325
t1=500

%engine parameters

bore=0.1;
stroke=0.1;
con_rod=0.15;
cr=12;

% calculating swept and clearance volumes
v_swept=(pi/4)*bore^2*stroke
v_clearance= v_swept/(cr-1);

v1=v_swept+v_clearance;
v2= v_clearance

%state variables at state2 
%p2*v2^gamma=p1v1^gamma
%p2= p1*(v1/v2)^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_kinematics1(bore,stroke,con_rod,cr,180,0);
P_compression=constant_c./V_compression.^gamma;

 %state at point 3
 v3=v2;
 %(p3v3)/t3==(p2v2)/t2 |p3==p2*(t3/t2);
 p3=p2*(t3/t2);


constant_c=p3*v3^gamma;
 V_expansion= engine_kinematics1(bore,stroke,con_rod,cr,0,180);
P_expansion=constant_c./V_expansion.^gamma;

 %variable at point 4
 v4=v1;

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

 %thermal efficiancy
 thermal_efficiency=(1-(1/cr^(gamma-1)))*100

 figure(1)
 hold on
 
plot(V_compression,P_compression,'linewidth',1.25)
plot([v2,v3],[p2,p3],'linewidth',1.25)
plot(V_expansion,P_expansion,'linewidth',1.25)
plot([v4,v1],[p4,p1],'LineWidth',1.25)

xlabel('VOLUME')
ylabel('PRESSURE')
legend('isentropic compression','constant volume heat addition','isentropic expansion','constant volume heat rejection')

Code explanation

• The code is started using the basic commands like close all, clear all, and clc
• the input variables are added i.e. gamma.
• the state variables and the engine parameters are entered which include the stroke, bore, etc.
• The swept and clearance volumes are calculated.
• pressure and volume are calculated at point 2.
• calculating the V_compression by calling up the function and also P_compression.
• calculating the pressure and volume at points 3. and 4.
• then calculating the thermal efficiency using the formula (1-(1/cr^(gamma-1)))*100
• Then using the plot command to plot the PV diagram
• using the label command to label the x and y axis accordingly
• A legend command was also used to explain the different processes going on in the plot

Errors faced while programming

Basic typo errors were solved by checking and observing the code.

RESULTS:

Outputs

Thermal efficiency

Workspace

PV diagram