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November 18, 2005, 11:46 
Timestep and RANS assumption

#1 
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Hello!
While browsing an old thread on this forum, I found an interesting post (http://www.cfdonline.com/Forum/flue...cgi?read=22310) in which the following is stated: "Care must, however, be taken to ensure that the time step used, is not so small that the Reynoldsaveraging assumptions are violated, i.e. averaging time <= dt. " This really confuses me... From what I know, RANS means that the instantaneous variables are averaged over a time period which is large compared to the turbulent time scales (but small compared to the time scale of the mean components). I guess you could define the turbulent timescale as k/e, right? From what I understand this would severly limit how low timesteps you can use in a transient simulation with a turbulence model based on RANS (for example std ke)..? So, is this limitation true? Have I misunderstood something? What would the consequences be if this is violated? I mean, a rule of thumb is to always use a shorter time step than the fastest physical process in the system that is simulated, and really there must be many processes in which there are things happening on timescales smaller than the turbulent timescale (for example chemical reactions)? If anyone can shed any light on this I would be very interested! Thanks, Henrik 

November 18, 2005, 15:48 
Re: Timestep and RANS assumption

#2 
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Hi Henrik
I believe what you are reffering to is the Continuum Hypothesis which allows the use of field representations for velocity, pressure etc. Using this hypothesis it is assumed that that all macroscopic length and time scales are considerably larger than the largest molecular length and time scales. The continuum hypothesis will eventually break down as the length and time scales of a particular problem become smaller and smaller. When the imposed scales are small enough the molecular structure will eventually become evident and the macroscopic theory is expected to break down. At these small time and length scales the NavierStokes equations break down and are no longer valid. Hope this helps answer your question! 

November 19, 2005, 18:10 
Re: Timestep and RANS assumption

#3 
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Hi!
Thank you for your answer, which certainly answered some part of my question. There is yet another thing that puzzles me, though. When we do averaging to construct the RANSequations, we filter out turbulent structures so that we only capture the mean flow, right? What does this mean when doing a transient simulation with timesteps smaller than the turbulent timescale? If we are simulating on a timescale smaller than the timescale used for RANSaveraging (which could still be a lot larger than the timescale for a very fast chemical reaction, though), does this mean that we are jeopardizing the accuracy? Because that seemed to be the point in the original post I was referring to, and as far as I can see that would severly limit the applicability for RANSbased turbulence models for transient simulations? What I thought was that the timescale for RANSaveraging only sets the limit between what is directly simulated (larger timescales) and what is modelled (smaller timescales), which to me would seem to mean that the RANS timescale would not limit the choice of timestep at all..? /Henrik 

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