# How should the pressure coefficient distribution from a wind tunnel experiment be interpreted?

I'm doing a wind tunnel experiment and I'm trying to plot the pressure coefficient distribution for the upper and the lower surfaces of an airfoil based on experimental data. The airfoil chord is 150 mm.

I have the pressure static ports located at:

Upper static port #: 1    3    5     7     9     11    13    15     17     19
X-coord [mm]:        0.76 3.81 11.43 19.05 38.00 62.00 80.77 101.35 121.92 137.16

Lower static port #: 2    4    6     8     10    12    14    16    18     20
X-coord [mm]:        1.52 7.62 15.24 22.86 41.15 59.44 77.73 96.02 114.30 129.54


And the pressure readings for each static port are the following:

Static port #:     1      2      3      4      5      6      7      8      9     10    11     12     13    14     15     16    17   18     19     20
Pressure [kPa]:   -0.034 -0.113 -0.087 -0.172 -0.136 -0.168 -0.148 -0.17 -0.15 -0.156 -0.133 -0.15 -0.124 -0.139 -0.12 -0.13 -0.13 -0.13 -0.117 -0.12


I also have Pitot velocity reading: $U_\infty=12.26$ m/s, density: $\rho=1.225$ kg/$m^3$ and $p_\infty=101.3$ kPa.

I know that to compute the pressure coefficient for each static port, I have to use: $$c_p(x,z(x)) = \dfrac{p(x,z(x))-p_\infty}{1/2\cdot \rho_\infty \cdot U_\infty^2 }$$

I coded a MATLAB script that allows me to compute this equation for the upper part of the airfoil using the odd static ports readings, and for the lower part of the airfoil by using the even static ports readings of pressure.

But I'm having two problems that are a bit strange,

1. Pressure coefficient must be dimensionless. I have the pressure values in "kPa" and the problem is that if I convert them into "Pa" by multiplying a 1000 factor. The pressure coefficients values will not be around 1, which is what I'm used to seeing in the Cp-chord graphs. How can I fix this? I'm not sure it's correct to use a dividing 1000 factor to compensate this effect.

2. When I plot the the result I obtain the following result, which is not very similar to the typical Cp-chord plots I have seen in experiments. Am I doing something wrong? Or is it a problem of the experiment in which I obtained bad data? Could you help me solve my doubts by giving me a little help based on your experience? I'm not asking to get the problem solved, I just want to know how to do it properly.

First, your pressure values cannot be the measured pressure, because they are negative. This indicates that they are pressure differences.

Next, their magnitude is too low to be in Kilopascal. Could it be that you list already the pressure coefficient?

Third, when plotting the pressure coefficient, it is customary to invert the Y axis, so the most negative value is on top. This just makes the plot look more familiar.

If I do this with the tabulated values, this is what I get: Plot of tabulated values (own work). I extended the Y axis down to +1 on purpose, because this is the stagnation pressure coefficient in in compressible flow. Your data looks like that of a very thin symmetrical airfoil at an angle of attack near 0°.

Now look at this computed plot of pressure coefficients of symmetrical airfoils at zero angle of attack (source): Inviscid pressure distribution of symmetrical NACA airfoils. The black line looks like your data. Unfortunately you never mentioned which airfoil the measurement is from, but to me it looks awfully like a NACA 0006 (or even something thinner).

• Thank you very much! The airfoil is a NACA0012 and the AoA was 0 degrees, as you guessed. And the values I have are literally "readings of static pressure from the ports". So, these are pressure differences? I think I know where was my mistake. Your answer was extremely helpful and elaborated. – user3780731 Nov 29 '15 at 0:33
• @user3780731: The NACA 0012 is the Drosophila of aerodynamics, but due to thickness reaches a minimum $c_P$ of -0.4 at 0°, whereas your data does not even reach -0.2. So these might not be pressure coefficients, after all. – Peter Kämpf Nov 29 '15 at 6:04
• Thank you, very much. Your answer was really helpful. One question, should I assume the Kutta condition in the trailing edge of the airfoil and assume there's a stagnation point at the trailing edge, when plotting upper vs. lower pressure coefficient distribution? (Later I have to compute lift by integrating from leading edge to trailing edge) – user3780731 Dec 8 '15 at 15:53
• @user3780731: Only in inviscid flow - the air needs energy to achieve stagnation pressure, and after being slowed down in the boundary layer, this energy is gone. You will have some recompression, but not nearly as much that you could really speak of a stagnation point. Kutta condition: If no separation occurs, then yes. With separation, the rear airfoil shape matters less; what really counts is the combination of airfoil and momentum thickness – Peter Kämpf Dec 8 '15 at 16:08
• @user3780731 You are very welcome! Just keep asking. – Peter Kämpf Dec 8 '15 at 19:10