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March 7, 2005, 03:43 
reynolds stress

#1 
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Hi everybody,
I've some experience on laminar flow, however,I'm new to turbulent flows. I've some books on this subject, all start with Reynolds averaging. Then they come to reynolds stress and TKE, etc.. It's OK, in those books the terms representing reynolds stress, or equations for TKE transport are all given. But I could not find the physical meaning turbulent quantities, and their significance. Can you suggest any resource in which the physics is explained clearly. second trouble: I've a transient 2D DNS code for axisymmetric geometry. I solve the incompressible NS equations and get instantaneous velocity, pressure and temperature values. the questions are now; do I have to solve extra equation for TKE?, do I have to set up my governing eqns including reynolds stress terms?, or may I obtain the turbulent quantities by postprocessing the instantaneous values that I already have. I'm sorry if I mess up the subjects, which might be very clear for most of you. thanks in advance tufito 

March 9, 2005, 20:19 
Re: reynolds stress

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1) For theory read "A first course in turbulence" by H. Tennekes and J. L. Lumley. The main idea is this: In RANS you obtain the Reynolds stress terms that have to be closed. For this, an eddy viscosity model has been proposed which is based on a length and time scale. All the related models (eg. kepsilon) are a means to predict these length and time scales. For details on modeling, refer "Turbulence modeling for CFD" by David C. Wilcox
2) To get the turbulent quantities eg. Reynolds stresses you can use the DNS results. In fact with your results you can verify these RANS models, and predict the coefficients that go into RANS models (for eg. using DNS results you can calculate C_mu, a constant that is used in Kepsilon model). Then you can use these coefficients and perform RANS simulations for your problem at higher Reynolds numbers for which the models are known to work well. Good luck. 

March 10, 2005, 05:54 
Re: reynolds stress

#3 
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Thank you so much agg, for your advice. I've already ordered the book you suggested; "A first course in turbulence". One more question, that is still fuzzy for me. Think that I compute u, v, T, and p values at every 10^6 sec. Would it be reasonable if I find some average from those results and then if I take the fluctuations (using average and instantaneous values). If this is ok, I may calculate turbulent quatities. Am I right?


March 10, 2005, 16:40 
Re: reynolds stress

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You should calculate averages carefully. This will involve some trial and error. Do not save every 10^6 sec. Maybe save every 10 time steps. After collecting about 2000 to 3000 realizations, average it. Try to do it in the code rather than postprocess inorder to save storage space. Then run simulation again, maybe save every 5 time steps and do the same procedure. This is just one example. You must also try with more than 2000 to 3000 iterations to check that statistics are independent of runs.
For Reynolds stresses, you will also need to store squares of the means and then later on you can calculate the variance for eg. <u'^2> = <uu>  <u>^2, <u'v'> = <uv><u><v> and so on and kinetic energy similarly. I suggest you make a list of all statistics that you intend to compute and then code it in your program. Good Luck. 

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