XFoil Reynolds Number Calculations

[Thusithatck]

Can someone explain to me how XFoil calculates the Reynolds Number for computational analysis. I have the XFoil manual which explains the method used in calculating the Reynolds Number. But what I don't understand is that it says that the "Reynolds Number is defined with the freestream velocity and viscosity, and an implied unit chord.

My experimental data are,

Re,_chord = 380,000
V = 16.67 m/s
T = 293 K
P = 101325 Pa
Viscosity = 1.813 e-5 kg/ms
Density = 1.205 kg/m3

above values are extracted from an experiment, where I'm intending to use XFoil for the validation of experimental data. According to the Reynolds Number equation mentioned below where,

Re = (V x density x chord) / viscosity

if the implied chord is taken as a unit, then the Reynolds number I should enter in XFoil should be 1107872 (not 380,000), approximately. Having said that, when it say freestream velocity and viscosity, does it mean I should use the velocity as 16.67 m/s (which is the correct speed of the wind tunnel during the experiment) and the sea level viscosity which is 1.78 e-5 (not 1.813 e-5, which is the correct density at the wind tunnel during the experiment).

Since the force coefficients (C_L, C_D, C_M) are calculated (in XFoil) by normalizing the forces with ONLY the freestream dynamic pressure, which is given in below equation,

q = 0.5 x density x V²

C_L = L / q
C_D = D / q
C_m = M / q

where the only input parameter options available in XFoil are Reynolds Number and the Mach Number. Hence I believe that velocity in the dynamic pressure equation above is calculated from the Reynold number equation and the other parameters such as viscosity and density are taken as sea level conditions (not the experimental values). Therefore the Reynolds number has to be adjusted by using sea level values. Is this is correct ??

 

[boneh3ad]

Free stream velocity and viscosity are the wind tunnel conditions in the free stream, not average sea level values.

When XFoil assumes a unit chord length, that means it is essentially outputting the unit Reynolds number. Just multiply it by your actual chord length to compare with your wind tunnel results.

 

[Thusithatck]

Just to confirm, my wind tunnel experimental Reynolds number is 380,000. So when I specify the Reynolds number in XFoil using the "Re" command, do I need to enter it as 1107872 (Reynolds number based on a UNIT chord) which will be 380,000 when multiplied by 0.343m (actual chord length).

Or...

multiply 380,000 (Reynolds number during the experiment) by 0.343m, which would give 130,340 as the Reynolds number.

The input (airfoil section used for the analysis) airfoil co-ordinate file has an unit chord (x/c = 1), not 0.343m as well.

 

[boneh3ad]

I have confused myself here actually. Reynolds number is not something that should be played with. Just leave the Reynolds number the same in both cases so that it properly scales. Sorry about that. I have been thinking bass ackwards today.

You are essentially simulating the wing in XFoil at 1m chord length and comparing to a scaled-down test in the tunnel. The correct way to do that is by matching Reynolds number.

 

[pmacias]

I can confirm that your understanding of XFoil's Reynolds Number calculations is correct. The Reynolds Number is a dimensionless quantity that represents the ratio of inertial forces to viscous forces in a flow, and it is defined by the freestream velocity, viscosity, and an implied unit chord. This unit chord is a reference length used to normalize the Reynolds Number, and it is typically chosen to be the chord length of the airfoil being analyzed.

In your case, since you are using XFoil to validate experimental data, it is important to use the correct values for the freestream velocity, viscosity, and density. As you mentioned, the velocity should be the actual speed of the wind tunnel during the experiment, while the viscosity and density should be taken at sea level conditions. This is because XFoil assumes standard sea level conditions for its calculations, and using the experimental values may result in incorrect calculations.

To adjust your Reynolds Number to account for the sea level conditions, you can use the following equation:

Re_sea level = Re_experimental x (viscosity_sea level / viscosity_experimental) x (density_experimental / density_sea level)

In your case, this would give a Reynolds Number of approximately 1,107,872, which is the value you should enter into XFoil for accurate calculations.

It is also important to note that the Reynolds Number is used in the calculation of the freestream dynamic pressure, which is then used to normalize the force coefficients (CL, CD, CM). Therefore, using the correct Reynolds Number is crucial for accurate results.

I hope this explanation helps clarify the Reynolds Number calculations in XFoil and how to adjust it for experimental data validation.