Non dimensional BL thickness

fred_jones · December 5, 2017, 14:22

Hi Folks,

I am doing some simple CFD work on paper and am trying to non dimensionalise the maximum boundary layer thickness of a turbulent flow travelling over a airfoil (simplified as a flat plate). I've given it a go but I'm not sure if I'm doing it right.

I think that to non dimensionlise the BL I can simply do:

Normal BL [m] * frictional velocity [m/s] / kinematic viscosity [m^2/s]

I would then set the free stream velocity and the fluid density to equal 1 and then calculate the non-dimensional BL thickness using the equation above and I think I'd get the same dimensionless BL thickness as if I used actual flow values (for example the defaults in Fluent of rho = 1.2047 and dynamic viscosity = 1.789e-5)

Am I going about this right?

Thanks,

Fred

FMDenaro · December 5, 2017, 14:57

for a turbulent BL you can estimate the non-dimensional thickness as

delta(x)/x = C Re_x^(-1/5)

fred_jones · December 5, 2017, 15:56

Thanks for your reply!

Thank you for that equation. Out of interest, does the way I've done it worked? (and also making U_freestream and rho = 1)

Ravindra Shende · December 6, 2017, 01:50

In addition to changing the free stream U and rho, you will also have to change the dynamic viscosity.
The dynamic viscosity should be such that the Reynolds number is the same in dimensional as well as non-dimensional cases.

December 5, 2017, 14:22	Non dimensional BL thickness	#1
fred_jones New Member Join Date: Dec 2017 Posts: 2 Rep Power: 0	Hi Folks, I am doing some simple CFD work on paper and am trying to non dimensionalise the maximum boundary layer thickness of a turbulent flow travelling over a airfoil (simplified as a flat plate). I've given it a go but I'm not sure if I'm doing it right. I think that to non dimensionlise the BL I can simply do: Normal BL [m] * frictional velocity [m/s] / kinematic viscosity [m^2/s] I would then set the free stream velocity and the fluid density to equal 1 and then calculate the non-dimensional BL thickness using the equation above and I think I'd get the same dimensionless BL thickness as if I used actual flow values (for example the defaults in Fluent of rho = 1.2047 and dynamic viscosity = 1.789e-5) Am I going about this right? Thanks, Fred

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December 5, 2017, 14:57		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,764 Rep Power: 71	for a turbulent BL you can estimate the non-dimensional thickness as delta(x)/x = C Re_x^(-1/5)

December 5, 2017, 15:56		#3
fred_jones New Member Join Date: Dec 2017 Posts: 2 Rep Power: 0	Thanks for your reply! Thank you for that equation. Out of interest, does the way I've done it worked? (and also making U_freestream and rho = 1)

December 6, 2017, 01:50		#4
Ravindra Shende Member Ravindra Shende Join Date: Feb 2011 Location: Pune, India Posts: 45 Rep Power: 15	In addition to changing the free stream U and rho, you will also have to change the dynamic viscosity. The dynamic viscosity should be such that the Reynolds number is the same in dimensional as well as non-dimensional cases.