Plotting pressure coefficient over a flat plate against its length

We conducted an experiment to measure the surface pressure distribution around a flat plate (dimensions below). The plate has 104 equally distributed tappings (i.e. points where pressure is measured) as shown below.

Where the arrows indicate order of measurement.

I would like to plot the pressure coefficient (https://en.wikipedia.org/wiki/Pressure_coefficient) against length(L) to width(W) ratio L/W

The following data is the pressure recorded clockwise (as suggested by the diagram) at the corresponding tap. Saved in a file called "combined_pressures.txt".

The first four rows are pressure data over the upper part of the plate, while the other four rows contain pressure data over the lower part of the plate.

First row from tap 0 to upper tap 12, second row from upper tap 13 to upper tap 25, third row from upper tap 26 to upper tap 38, fourth row from upper tap 39 to upper tap 51, fifth row from tap 52 to lower tap 40, sixth row from lower tap 39 to lower tap 27, seventh row from lower tap 26 to lower tap 14, eighth row from lower tap 13 to lower tap 1.

100.016	-15.341	-24.538	-29.053	-31.768	-32.851	-33.200	-33.873	-33.885	-33.219	-32.734	-33.104	-32.086
98.884	-16.562	-25.100	-29.238	-31.768	-32.662	-32.833	-33.473	-33.504	-32.833	-32.317	-32.712	-31.540
-30.698	-29.985	-27.909	-26.277	-24.625	-22.845	-20.910	-20.444	-19.227	-17.962	-17.722	-18.021	-17.137
-16.762	-17.085	-16.109	-16.469	-17.106	-17.181	-16.875	-17.638	-17.704	-17.575	-17.722	-19.000	-18.960
-19.587	-20.746	-20.792	-22.206	-24.061	-26.243	-28.981	-35.477	-32.742	-31.288	-31.274	-32.124	-31.540
-31.829	-32.426	-31.656	-31.828	315.657	-32.851	-36.318	-30.867	-27.032	-24.142	-22.726	-22.330	-20.601
-19.587	-19.525	-17.982	-17.950	-17.670	-17.370	-16.508	-16.836	-16.562	-16.223	-16.263	-17.237	-16.772
-16.950	-17.433	-16.671	-17.025	-17.482	-18.125	-18.159	-19.643	-20.559	-22.017	-24.185	-28.402	-30.628

I used the following code

% Define plate dimensions
plate_length = 0.225; % m
plate_width = 0.025; % m

% Load pressure data from the text file
pressure_data = load('combined_pressures.txt'); 

% Split the data into upper and lower parts
num_points = size(pressure_data, 2); % Number of pressure data points

% Define freestream conditions 
P_infinity = 101984*(1/101325); % bars
rho = 1.225; % kg/m^3 (air density)
V = 14; % m/s (freestream velocity)

% Define the chord length
chord_length = plate_length + plate_width;

% Calculate the length-width ratio for each data point
length_width_ratio = chord_length * (1:num_points) / num_points;

% Calculate pressure coefficients for upper and lower parts
Cp_upper = (pressure_data(1, :) - P_infinity) / (0.5 * rho * V^2);
Cp_lower = (pressure_data(5, :) - P_infinity) / (0.5 * rho * V^2);

% Create a plot
figure;
plot(length_width_ratio, Cp_upper, 'r', 'DisplayName', 'Cp top');
hold on;
plot(length_width_ratio, Cp_lower, 'b', 'DisplayName', 'Cp bottom');
xlabel('Length-Width Ratio');
ylabel('Pressure Coefficient (Cp)');
legend('Location', 'Best');
title('Pressure Coefficient vs. Length-Width Ratio');
grid on;

Which yields

This is not what I expected. I expected a plot similar to the following

I am wondering whether I made a mistake with the code or it's due to faulty experimental data.

Sidenote: how can be the shape plotted as they did with the airfoil above?

Thanks.

Answer 1

[Torsten]

Your plot is correct, your measurement values are ... strange.

Usually, one has functional equations or at least points that represent the profile of a foil. This can be used like a normal function to plot the contours of the airfoil in your graph above.