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December 18, 2014, 18:28 
Turbulence Intensity & Velocity

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Mohammad
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Hello Guys
I have a question,if in a constant volume we increase the turbulence intensity what happened to velocity? is it increase rather than the first state or decrease? in other words is we have two same volume and one of them have more turbulnce intensity which one of them have higher volumeaveraged velocity? :confused thank you 

December 19, 2014, 05:21 

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Filippo Maria Denaro
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December 20, 2014, 16:07 

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December 20, 2014, 16:21 

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Dear Filippo Can You Explain More About The Eddy Magnitude And Total Kinetic Energy Or Turbulent Intensity In This Case (Turbulent Flow In A Volume Like IC Engine)? 

December 20, 2014, 16:25 

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Filippo Maria Denaro
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No, pressure obeys to an elliptic equation but velocity is governed by a parabolic equation


December 20, 2014, 16:32 

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Page 38. Anyway, I'm butting in, but I just believe its dangerous to say the velocity field is localized. :s 

December 20, 2014, 17:05 

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December 20, 2014, 17:10 

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I'm not debating that p is nonlocal. I'm just pointing out that you stated: "Velocity is a "local" field" when the book clearly says: "it makes little sense to think of velocity fields being localised in space" 

December 20, 2014, 18:01 

#9  
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Filippo Maria Denaro
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The velocity is governed by continuity (hyperbolic) and momentum (parabolic) equations, I just see this mathematical properties. Working with some statistical approach you can define some nonlocal properties from the velocity. 

December 20, 2014, 21:08 

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December 21, 2014, 04:53 

#11 
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Filippo Maria Denaro
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just to focus on the concept, if you consider a statistical formulation such as RANS, the the velocity is statistically steady and is governed by an elliptic equation. I now can say that the average velocity is nonlocal ...


December 22, 2014, 11:23 

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Having read source on this which I believe explains the process well (page 508 on the top left):
http://www.me.metu.edu.tr/courses/me...by_Hoffman.pdf The following is rather crude and should not be used as proper definitions. Consider a point P containing a solution value at time t=0. I've used page 514 to understand the time restraints. The domain of dependence at point p means that the solution at point P depends on all the values in that domain of dependence. In a parabolic equation, the domain of dependence is all the points in the fluid at t=0 and t<0. In an elliptic equation, the domain of dependence is all the points in the fluid at t<0, t=0 and t>0 (any time). The range of influence at point p determines the range to which an arbitrary point f (with f containing a solution) is influenced by point P (which also contains a solution). For a parabolic equation, this is for t=0 and t>0. For an elliptic equation, this is for any values for t (any time). So its quite clear, as you stated, elliptic fields aren't non local. If my interpretation of the source is correct, Davidson was right because he stated that t>0, the field is nonlocal, and for unsteady incompressible flows (which I believe from browsing the web are parabolic, not 100% sure), this would mean that the velocity introduced at t=0 would have a range of influence that extended to all parts of the domain at t>0, which fits exactly to what this source discusses about parabolic equations and in my mind, make the velocity field nonlocal. I think your understanding of being local stems from the fact that the range of influence and domain of dependence are not the same in a parabolic equation whereas for an elliptic equation, they are. Either way, I still believe that calling a velocity field nonlocal is decidedly misleading, but your welcome to interpret the information at hand in your own way and being fluid dynamics (and of course turbulence when it arises),there are a lot of different views on the physics. 

December 22, 2014, 13:38 

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Filippo Maria Denaro
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well, the framework is almost that, just a little more complex ...
I add that the elliptic equation state an equilibrium solution, therefore time is not relevant. For parabolic and hyperbolic equations, the domain of dependence (and influence) must be seen in the timespace domain. Thus, P is a point at (x,y,z,t). Now, note that the timedependent momentum equation is parabolic, but for vanishing viscosity it can be seen as a perturbed hyperbolic equation. Actually, the continuity equation is always hyperbolic, viscous or not is the flow.... 

December 23, 2014, 07:55 

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With regards to the original question asked,
Turbulence Intensity is the ratio of velocity fluctuations in a turbulent velocity field to the mean fluid velocity. So does a higher value of turbulence intensity really implies a higher kinetic energy (or velocity)? 

December 23, 2014, 12:06 

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Filippo Maria Denaro
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So depending on the case you study, more suitable definition should be used. Of course, in general the relation I =V'/V cannot says if V' increases or V decreases.... 

December 23, 2014, 13:35 

#16 
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The answer to the first question is that the turbulence intensity is measured with respect to an average value. Thus, you cannot just talk about this without stating what is your average operator. If you define the average as, say, a spatial average over that same volume, it's quite obvious that (division by zero apart) the volume average velocity is an independent parameter which is not specified by the statement 'Increase in turbulence intensity'. In practice, for almost all the definitions of turbulence intensity it happens that it is defined with respect to a mean velocity. So, actually, you can only say what the rms velocity fluctuations do with respect to the mean velocity and not what the mean velocity itself does. This is Pi theorem.
For what concerns the local/nonlocal aspect... physics is quite clear, there is no such thing as an incompressible fluid, but only mathematical approximations to that so, strictly speaking, there is nothing in fluids which is non local. From the Mathematical point of view, the low Mach limit of the equations is such that the lowest order pressure solution satisfies an elliptic equation. While it is somehow correct to say, as done by Davidson, that the velocity is indeed also nonlocal, this should be done carefully, especially for what concerns the discussion on vortices and so on. The fact is that only a part of the velocity field is actually influenced non locally by the pressure field. This part can be distinguished, by the HelmholtzHodge decomposition, as the one expressable as the gradient of a scalar field. The other part of the velocity field, the one building up the vorticity, does not feel anything about the pressure. In more general terms, for a given direction, only 2 out of 5 NavierStokes characteristics travel at sound speed. 

December 23, 2014, 17:36 

#17  
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Mohammad
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Thank You Dear Paolo 

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