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Josh April 29, 2010 19:02

Momentum and displacement thickness: du/dy calculation
Hi all -

I am calculating the momentum and displacement thicknesses along an airfoil polyline I created. I require the displacement thickness to calculate the momentum thickness. I am using the integral von Karman momentum equation, found here on page 2 (I will be solving for theta, the momentum thickness):

I know how to export the wall shear, density, and velocity data along the polyline to an Excel file. However, I am unsure of how to properly integrate the displacement thickness at each point along the curve. I could create lines at various points along the curve, integrate along those lines to calculate the displacement thicknesses, and then use the integral von Karman momentum equation to find the momentum thicknesses corresponding to those points. However, that would be very time consuming, and would only give me select points rather than a smooth curve.

Alternatively, if there is an easier method of finding the momentum thickness in CFX, I'd love to hear it.

Any help is appreciated.

ghorrocks April 30, 2010 06:36

This type of analysis is not easily done in CFD-Post. I think your best bet is to do as you describe, but you should be able to script it so that will involve some setup time but once done it should be easy to process data sets.

Josh April 30, 2010 12:48

As usual, thanks so much for the reply, Glenn.

One problem I am having with creating the lines (to integrate the displacement thickness on) is that I'd like them to be orthogonal to the surface at each point. Since I don't have an equation for the airfoil curvature, I am unsure of how to go about this.

Any ideas, or should I just guess-and-check?

ghorrocks May 2, 2010 07:17

You might be able to get the surface normal from the normal variable which I think is defined on wall boundaries. Have you tried that?

Josh May 4, 2010 12:08

I haven't tried that recently, Glenn, but I recall using it at another time with little success. I may try it again.

However, after contacting the authors of the paper, we have discovered that they assumed a constant pressure within the boundary layer, meaning that the momentum thickness calculation is only based on the wall shear, velocity, and density. So much for integrating the displacement thickness.

Thanks for your help, Glenn. I really ought to put you as an author on our research paper.

Raj007 June 30, 2010 13:22

How to calcualate Momentum thicknees in CFX-post
Dear Joshua, if you are able to find the momentum thickness in CFX-post then please let me know the processor. waiting for your reply. Thanks

Josh June 30, 2010 13:51

Hi Raj -

Unfortunately, I never successfully found a way to calculate momentum/displacement thickness without it being a huge headache. The above methods are the only ideas we've had.

Good luck.

Josh June 30, 2010 19:20

For the record, here is what I sent to Raj:

I'm not sure what the form factor is. Could you tell me what equation you're using for total pressure loss coefficient is?

As for the momentum thickness...

In Post, I created a polyline to wrap around the airfoil. Then, I exported the wall shear data from this polyline to a .csv (comma separated values) file. The file comes out in this format:

X Y Z Wall Shear
. . . .
. . . .
. . . .

I converted the coordinates (x, y, z) into a curve length, s. I found the difference between each curve value, delta_s. I multiplied each shear value by each delta_s value and summed up the totals to give me the accumulated drag force at each point. I defined momentum thickness using the Blasius similarity solution:

mom. thickness = D(x) / (density * b * U^2)

where D(x) is the drag force in the x direction, b is the span, and U is the freestream velocity. b = 1 for me since my simulations were 2D. Now, I had a format like this:

s Wall Shear delta_s (Wall Shear * delta_s) D(x) mom. thick.
. . . . . .
. . . . . .
. . . . . .

Here's a sample calculation:

s Wall Shear delta_s (Wall Shear * delta_s) D(x)
s1 w1 d1=s2-s1 wd1=w1*d1 D1=wd1
s2 w2 d2=s3-s2 wd2=w2*d2 D2=wd1+wd2.
s3 w3 d3=s4-s3 wd3=w3*d3 D3=wd1+wd2+wd3

momentum thickness
m1=D1/(density * U^2)
m2=D2/(density * U^2)

Using this method, I predicted very poor values of momentum thickness, so I suspect I did something incorrectly.

Good luck!

Josh June 30, 2010 19:23

Guess the html format treats multiple spaces as one unit, so the formatting is poor. Sorry about that.

iffy April 10, 2011 15:09

Does anybody knows how to create lines normal to the airfoil surface in CFX-Post? I have to compute displacement and momentum thickness for an airfoil for which I need lines normal to the airfoil surface?
If anyone here can help?



Josh April 11, 2011 02:11

Hi iffy -

Unfortunately, it's not easy. For my airfoil, the NACA 0012, I did the following:

Obtain the equation describing your airfoil. If the airfoil does not have one specific equation describing it, subdivide the airfoil into sections of similar slope and create individual equations for each section. y1 = (m)(x1) + b1

Use the equation of the airfoil curve to find the negative, inverse slope (-m^-1) at every point of interest (I had 10 evenly spaced points from x/c = 0 to 1).

Determine how long you want each line to be (I used a length of L = 2 m).

Find the angle between your new, normal lines and the horizontal.

Use L, the angles, and this equation (y2 = (-m^-1)(x2) + b2) to find your new points.

Create your lines.

Hope this helps.

iffy April 11, 2011 03:01

Hi Josh,
Thank you for your reply. I am also simulating naca 0012 airfoil. I will try the method which you speicified.


kiddmax October 8, 2013 05:38

Hello, guys.

Did you find good methods to calculate the displacement thickness? How is the method working as Josh mentioned? is it working well?

Best regards,

syavash October 27, 2013 15:38


I think there might be a way! In Fluent, we create a line normal to the airfoil surface. Then we export the velocity magnitude along that line to a file. Now we should export cell wall distance to another file. By having cell wall distance, we can calculate each cell "dy" via writing a simple script. Now we are able to compute thickness and momentum thickness by integrating the following equations:


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