# How to calculate Reynolds Stress using LES data?

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 February 22, 2001, 19:04 How to calculate Reynolds Stress using LES data? #1 Jongdae Kim Guest   Posts: n/a I have u,v,w velocities on staggered grid. The velocities are from Large Eddy Simulation. I'd like to compare LES results with experimental data (from LDV). Please let me know how to calculate Reynolds stress with LES data. ************************************************** ****** LES data : space averaged values Reynolds Stress (from Experimental data) : time averaged values

 March 1, 2001, 09:18 Re: How to calculate Reynolds Stress using LES dat #2 Lionel Larcheveque Guest   Posts: n/a LES is by nature an unsteady computation. So to calculate components of the Reynolds stress tensor, you need to time average u, v, w, u^2, v^2, w^2, uv, uw, vw as soon as the flow seems establish and for a time period long enough. Then use the formula : =-, and so on, ..., where <> denotes time averaging, with ' defined by u'=u- (Reynolds decomposition, assuming ergodicity, i.e. time average and average on multiple identical experiences are equivalent). I suppose that space averaged values you mentioned correspond to homogeneous direction(s) of the flow. You can use averaged values along this (these) direction(s) at each time step to perform time averaging, in order to accelerate the convergence of statistical values and greatly reduce data size.

 March 1, 2001, 09:24 Re: How to calculate Reynolds Stress using LES dat #3 Lionel Larcheveque Guest   Posts: n/a It seems that there is a little HTML problem in the formula I've just posted (use of <>). The correct one is : [u'v']=[uv]-[u][v], where [] denotes time averaginf, with ' defined by u'=u-[u]...

 March 1, 2001, 09:43 Re: How to calculate Reynolds Stress using LES dat #4 andy Guest   Posts: n/a But what about the SGS contribution? (particularly the normal components).

 March 1, 2001, 18:44 Re: How to calculate Reynolds Stress using LES dat #5 Jongdae Kim Guest   Posts: n/a Notations : { * } space (or volume) averaging [ * ] time averaging Procedure of calculation of Reynolds stresses [1] DNS & Experiments (1) measure u (= [u]+u') for longtime (2) u'=u-[u] (3) u'v' = u' * v' (4) [u'v'] : time averaging of (3) or [uv]-[u][v] : this is not space averaged [2] RANS equations with Finite volume method : tau = [u' * v'] : calculated from model = {[uv]}-{[u][v]} [3] LES : implicit box-filter Governing equation : space averaged-NS Numerical scheme : Finite volume method Output of numerical scheme : space averaged velocity R12={uv}-{u}{v} [R12]=[{uv}]-[{u}{v}] Questions : 1. [{*}] = {[*]} .ie. tau=[R12] ? 2. How to compare Reynolds stress of LES output with DNS(Experiment) output ? hityangsir likes this.