Plot engine cycle with all the curves from given data

I have calculated values of p [Pa] and V [m^3] for all for points of the cycle, as well as polytropic exponents for compression and expansion.

I need to plot a diagram, I manage to plot single points, but I need also all the curves, which I fail to do.

% Given data

V1 = 0.007; % m^3

V2 = 9.66e-5; % m^3

V3 = V2;

V4 = V1;

p1 = 101325; % Pa

p2 = 1.82e6; % Pa

p3 = 4.58e6; % Pa

p4 = 309210; % Pa

nk = 1.35; % Polytropic exponent for compression 1-2

ne = 1.26; % Polytropic exponent for expansion 3-4

[Dyuman Joshi]

Are you sure the data is correct?

Given two points for the same polytropic process, they should follow the relation P*V^k = constant. That is not the case here though -

V1 = 0.007; % m^3
V2 = 9.66e-5; % m^3
V3 = V2;
V4 = V1;
p1 = 101325; % Pa
p2 = 1.82e6; % Pa
p3 = 4.58e6; % Pa
p4 = 309210; % Pa
nk = 1.35; % Polytropic exponent for compression 1-2
ne = 1.26; % Polytropic exponent for expansion 3-4

[p1*V1^nk p2*V2^nk]

ans = 1×2

124.9105 6.9150

[p3*V3^ne p4*V4^ne]

ans = 1×2

39.9886 595.7678

scatter([V1 V2 V3 V4],[p1 p2 p3 p4],'filled')
xlabel('Volume')
ylabel('Pressure')

Answer 1

[SOUMNATH PAUL]

Hi,

I understand that you need help in plotting an engine cycle, although the data you provided is not consistent with the equation P*V^k = constant, you can follow the below mentioned code for a reference on how to proceed further:

% Given data
V1 = 0.007; % m^3
V2 = 9.66e-5; % m^3
V3 = V2; % m^3
V4 = V1; % m^3
p1 = 101325; % Pa
p2 = 1.82e6; % Pa
p3 = 4.58e6; % Pa
p4 = 309210; % Pa
nk = 1.35; % Polytropic exponent for compression 1-2
ne = 1.26; % Polytropic exponent for expansion 3-4

% Calculate constants for polytropic processes
Ck = p1 * V1^nk; % Constant for compression
Ce = p3 * V3^ne; % Constant for expansion

% Generate volumes for the compression and expansion curves
V_compression = linspace(V1, V2, 100);
V_expansion = linspace(V3, V4, 100);

% Calculate the pressures for the compression and expansion curves
p_compression = Ck ./ V_compression.^nk;
p_expansion = Ce ./ V_expansion.^ne;

% Plot the engine cycle
figure;
hold on;

% Plot the compression and expansion curves
plot(V_compression, p_compression, 'b', 'LineWidth', 2); % Compression curve
plot(V_expansion, p_expansion, 'r', 'LineWidth', 2); % Expansion curve

% Plot the constant volume process (2-3 and 4-1)
plot([V2, V3], [p2, p3], 'g', 'LineWidth', 2); % Constant volume heat addition
plot([V4, V1], [p4, p1], 'g', 'LineWidth', 2); % Constant volume heat rejection

% Plot the points
plot(V1, p1, 'ko', 'MarkerFaceColor', 'k');
plot(V2, p2, 'ko', 'MarkerFaceColor', 'k');
plot(V3, p3, 'ko', 'MarkerFaceColor', 'k');
plot(V4, p4, 'ko', 'MarkerFaceColor', 'k');

% Label the points
text(V1, p1, '1', 'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'right');
text(V2, p2, '2', 'VerticalAlignment', 'top', 'HorizontalAlignment', 'left');
text(V3, p3, '3', 'VerticalAlignment', 'top', 'HorizontalAlignment', 'left');
text(V4, p4, '4', 'VerticalAlignment', 'bottom', 'HorizontalAlignment', 'right');

% Set the graph labels and title
xlabel('Volume (m^3)');
ylabel('Pressure (Pa)');
title('p-V Diagram of the Engine Cycle');

% Set the axis limits
xlim([min([V1, V2, V3, V4]) * 0.9, max([V1, V2, V3, V4]) * 1.1]);
ylim([min([p1, p2, p3, p4]) * 0.9, max([p1, p2, p3, p4]) * 1.1]);

% Add a grid for better readability
grid on;

hold off;

Hope it helps!

Regards,

Soumnath.

[Dyuman Joshi]

The curves plotted are incorrect, as can be seen from the figure.