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Phil October 1, 2006 16:23

Reynolds stresses without velocity correlations?
 
Hi all, I have a quick question about calculating the Reynolds stresses in a URANS code without using the velocity correlations directly!

Notation I'll be using:

ui Instantaneous velocity component

Mean(ui) Time arithmetic average of velocity component

u'i Flucuating component of velocity component

The Reynolds stresses are defined as:

Mean(u'iu'i) = Mean(uiui) - Mean(ui)Mean(ui)

In the closed code I am using I have easy access to the following variables:

Mean(ui)

RMS(ui)

Stddev(ui)

I dont have direct access to the velocity correlations e.g. Mean(uiui).

I can calculate the *normal* Reynolds stresses using the available variables with the following formula:

Mean(u'iu'i) = RMS(ui)RMS(ui) - Mean(ui)Mean(ui)

However, this last formula is not valid for the Reynolds *shear* stresses. For example:

Mean(u'v') = RMS(u)RMS(v) - Mean(u)Mean(v)

, is not valid and does not produce the correct values for Mean(u'v').

Does anyone know if it is even possible to calculate the Reynolds shear stresses if you only have access to Mean(ui), RMS(ui), Stddev(ui) ??

If all else fails I could create a user routine to calculate the shear velocity correlations from first principles but I'd rather use the available pre-prepared variables if that is feasible.


Pennysworth October 2, 2006 04:29

Re: Reynolds stresses without velocity correlation
 
I think if you are doing URANS then the Reynolds stresses come directly from whatever turbulence model it is you are using. It is part of the system of equations you are solveing for (i.e. it is already calculated/modleled).

> u'i Flucuating component of velocity component

I would think that this is the resolved part of the velocity fluctuation. The unresolved part is what comes from your model. Anyway, I think the following notes might be helpful:

http://www.tfd.chalmers.se/doct/comp...iles/urans.pdf

At leaset you can trust them more than me ;-)


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