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October 23, 2001, 07:11 
Reynolds stress transformation

#1 
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Hi all,
Is the answer on my question from several days ago too simple or does no one know how to do it??? Therefore, again my problem: I have performed a simulation using a Reynolds stress model in cartesian coordinates. I know how to convert my x,y and z velocities to an x, r and phivelocity (Bird, Stewart and Lightfoot). But how should I transform my Reynolds stresses to cylindrical coordinates????????? Does anyone know? Any help or reference is appreciated. P.Fonteijn 

October 23, 2001, 10:46 
Re: Reynolds stress transformation

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I believe there is an Imperial College report by Wolfgang Rodi around 1972 that gives the Reynolds stress equations in cylindricalpolar coordinates. I think they also appear in the Imperial College Phd Theses of Bassam Younis (early 1980s), Alan Morse (late 1970s) and possibly, Rodi (1972). They also appear in several UMIST theses (Brian Launder's research group)in the 1980s. If these references are too vague to follow up, let me know and I will try and dig out the exact references.


October 24, 2001, 10:52 
Re: Reynolds stress transformation

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Hi,
I am working on swirling flow computation. It is not easy to find Reynolds stress equation in cylindrical coordinates in the literature. When you find something, they are either incomplete or with typing errors. I put the transformed NavierStokes, kepsilon and RSM equations in our ftp server (ftp://ftp.ecnantes.fr/incoming/axis.ps). The Daly & Harlow model is used for the turbulent diffusion in the RSM model. Bye the way, concerning swirling flow computation with Reynolds stress model, with RANS computation, I am unable to confirme the result published in Phys, Fluids Vol.29 (1), pp 3848 by Gibson & Younis for the free swirling jet (Morse test case). Result obtained with the SSG model is similar to the GibsonYounis model and is not as good as presented in the paper by Younis, Gatski and Speziale (J. of Fluids Eng., Vol 118, 1996, pp 800809). Any similar experiences or comments on turbulence modelling for swirling flow? 

October 24, 2001, 16:39 
Re: Reynolds stress transformation

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Actually, I am not looking for Reynolds stress equation in the cylindrical coordinates as I don't want to perform simulations in cylindrical coordinates. I have already performed a cartesian solution providing u,v, wvelocities and:
u'u', v'v', w'w', u'v', u'w' and v'w' I know how to transfrom the u,v and wvelocities to Vtangential (Vt) Vradial (Vr) and Vaxial (Va=u). How do I obtain: Vt'Vt', Vr'Vr', Va'Vt', Va'Vr' and Vr'Vt? To make a connection to your work, I have compared keand a RSM in a swirling flow. Average velocities and periodic fluctuations were about the same. Main difference were the random fluctuations mentioned above which one could expect before hand (turbulent kinetic energy). The difference could be made visible using scalar mixing simulations. I will dig up the references from you and Malin. But, still every suggestion is highly appreciated. Thank you all, P.Fonteijn 

October 25, 2001, 04:10 
Re: Reynolds stress transformation

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You can transforme the Reynolds stress in the same way. Since the instantaneous and the mean velocity follow the same transformation, you can obtain the similar relation for the fluctuation by substracting these two expressions, that is:
Vr'=V'cos(theta)+W'sin(theta) Vt'=V'sin(theta)+W'cos(theta) Multiply the two expressions and apply the mean operator to obtain: Vr'Vt'=V'V'cos(theta)sin(theta)+V'W'(cos(theta)**2sine(theta)**2)+W'W'sin(theta)cos(theta) Other stress components can be deduced in similar way. 

October 26, 2001, 16:38 
Re: Reynolds stress transformation

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I think this is only possible when the Reynolds Stresses are vectors. I am not an expert but I thought they were scalars (I will check my literature). Could you comment on that?
Thanks, P.Fonteijn 

October 26, 2001, 17:23 
Re: Reynolds stress transformation

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Reynolds stress are entries of "stress tensor". I suggest you check out some engineering statics/dynamics or continuum mechanincs textbooks. Some of the books can show you how to convert stress/strain from one coordinate system to the other. You can follow the same "procedures" to convert Reynolds stresses.


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