Air Standard Cycle simulation using MatLab

Simulation of Air Standard Cycle using Matlab

Objective:-

Calculation of thermal efficiency and simulating process of Air Standard Cycle

Theory for Air Standard Cycle

Air Standard cycle processes:-

Process 1-2: Isentropic Compression

Process 2-3: Constant Volume Heat Addition

Process 3-4: Isentropic Expansion

Process 4-1: Constant Volume Heat Rejection.

Ideal gas equation

• `(PV) / T = constant`

Isentropic process means Adiabatic and reversible Process

• `PV^γ = constant`
• Heat Capacity ratio for air in adiabatic process is `γ = 1.4`

Engine Geometric Parameters

Note:- All dimensions are in metres

• bore = 0.063;
• stroke = 0.056;
• connecting rod = 0.104;
• compression ratio(cr)= 9.5;
• crank pin radius (a) = stroke/2;
• R = con_rod/a;
• `Swept Volume = (pi/4)*(bore^2)*stroke`
• `Clearance volume = Swept volume/(cr-1)`

The equation for calculating volume during compression and expansion processes

`V = 1 + (1/2)(cr-1)[R + 1-cos(theta)-(R^2-sin(theta))^(1/2)]*Vc`

MATLAB PROGRAM

MATLAB FUNCTION CODE VOLUME DURING COMPRESSION AND EXPANSION

function[v] = piston_kinematics(bore, stroke, con_rod, cr, crank_s_angle, crank_e_angle)

a = stroke./2;
R = con_rod./a; 
v_swept = (pi/4).*bore.^2.*stroke;
v_clearance = v_swept./(cr-1);



theta = linspace(crank_s_angle,crank_e_angle,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_clearance;


end

MATLAB CODE FOR AIR STANDARD CYCLE.

clear all
close all
clc

%% inputs 

gamma = 1.4;
 
% engine geometric parameters(dimensions in m)

bore = 0.063;
stroke = 0.056;
con_rod = 0.104;
cr = 9.5;

% pressure and temperature at state 1 

p1 = 101325;          % pressur in 'pa'
t1 = 300;             % temperature in 'k'

% heat added to system per kg mass in joules

q_in = 1850*1000;      % in J

% specific heat at constant volume for air 

c_v = 718;             % J/kg.K

%% Calculation of variables at differents state of the cycle

% volume calculation 
v_swept = (pi/4).*bore.^2.*stroke;    % volume in m^3
v_clearance = v_swept./(cr-1);        % volume in m^3

% volume at state 1
v1 = v_swept + v_clearance;           % total volume in m^3

% pressure, temperature & volume calculation at state 2

% volume at state 2
v2 = v_clearance;                     % volume in m^3

% pressure at state 2
p2 = p1.*(v1/v2).^gamma;             % pressure in pa

% temperature at state 2
t2 = (p2*v2*t1) / (p1*v1) ;          % temperature in k


constant_c2 = p1*v1.^gamma;
v_comp = piston_kinematics(bore,stroke,con_rod,cr,180,0);
p_comp = (constant_c2./v_comp.^gamma);

% pressure, temperature & volume calculation at state 3

% volume at state 3
v3 = v2;

% temperature at state 3
t3= (q_in/c_v)+t2 ;                  % temperature in k

% pressure at state 3
p3 = p2.*(v2/v3).*(t3/t2);           % pressure in pa

constant_c3 = p3*v3.^gamma;
v_expan = piston_kinematics(bore,stroke,con_rod,cr,180,360);
p_expan = (constant_c3./v_comp.^gamma);


% pressure, temperature & volume calculation at state 4

% volume at state 4
v4 = v1;                     % volume in m^3

% pressure at state 4
p4 = p3.*(v3/v4).^gamma;          % pressure in pa

% temperature at state 2
t4 = (p4*v4*t3) / (p3*v3);        % temperature in k


%% results and plots 

% plot for otto cycle
figure(1)
hold on

plot(v1,p1,'*','color','r');
plot(v_comp,p_comp,'r')
plot(v2,p2,'*','color','r');
plot([v2 v3],[p2,p3],'g-');
plot(v3,p3,'*','color','r');
plot(v_expan,p_expan,'b')
plot(v4,p4,'*','color','r');
plot([v4 v1],[p4,p1],'k-');
xlabel('Volume')
ylabel('Pressure')
title('P-V diagram for Otto Cycle')
axis([0 2.5e-4 0 13e6])

% plot for Volume during compression
figure(2)
plot(v_comp)
ylabel('volume')
title('Volume during compression process')


% thermal efficiency 

Thermal_eff = (1 - (t1/t2))*100

Results:-

1.P-V diagram for Air standard cycle

2. Plot for volume during compression

3. Thermal efficiency for this Engine

Thermal_efficicnecy = 59.3640 %