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 sylvain October 27, 2005 17:36

inviscid flow and turbulnces

Guys I posted this message on the FLuent forum but I thought it might have its place on the main forum as well.

I might be wrong, but I thought turbulence is due to little fluctuations growing exponentially (if Reynolds number is large enough) due to nature of Navier Stokes equation. So the origin of turbulence lays in the flow and the fluctuations of BC and not in the fluid properties (even if reynolds is linked to the fluid property). For me, if we take an inviscid fluid, viscosity is close to 0 and the Reynolds number is very large (tends toward infinity). Hence the Reynolds number is big enough to enable the tiny fluctuations to grow exponentially and cause vorticity and come up with a turbulent flow. So my question is why Fluent overlooks the fact that inviscid flow should be turbulent? My assumption is that the inertial forces are so large (due to high velocity) that any eddies are negligible compared to what the bulk flow is. But I am really not sure of it. Can someone confirm or bring up another idea or tell me that I am saying crap and I should better open a fluid mechanic book before bothering you guys (even though I promise I did open a fluid mechanic book)

Thank you

 Mani October 27, 2005 18:12

Re: inviscid flow and turbulnces

I agree with your assessment on turbulence, as long you talk about flows at high Reynolds number. You need to be aware, though, that high-Re flows are not "inviscid flows". Although most of the flow field may be inviscid, a very important part of the flow (the boundary layer) is not. The behavior and equations for inviscid vs. high-Re flows are substantially different. True inviscid flow is governed by the Euler equations and cannot not satisfy the no-slip condition, as satisfied by the viscous Navier-Stokes equations (even at very large Re). In truly inviscid flow you don't have the generation of vorticity near the surface that you observe in viscous high-Re flows. The reason why I am pointing this out: You have to be clear on what you would like to discuss -- inviscid flow, or high-Reynolds-number flow. There is no truly inviscid flow in reality, and that's why I understand that you are thinking of high Reynolds numbers instead, but what is Fluent's idea of "inviscid" flow?

Now, in order to see how the modelling of turbulence would be useful in either inviscid flow or flow of high Re, you should probably think more about possible applications. For attached flow over slender bodies (e.g. airfoils), turbulence may be important for drag prediction, but you need to consider viscous flow if you want to go there. For separated flows, turbulence is also very important, but again these flows cannot be accurately described by the inviscid equations -- with or without turbulence. Maybe turbulent mixing is a process where viscosity could be neglected, but I am not sure... What other applications did you have in mind?

 Sylvain October 27, 2005 18:48

Re: inviscid flow and turbulnces

Thank you very much.

I have no application in mind. I guess I was just wondering what Fluent was having in mind when invoking the inviscid viscous model. So I understand with your answer that when the Reynolds number is very large (which can be assumed as inviscid) we can invoke the inviscid model, that this model does not take into account turbulent effect, and that it is only an approximation, and if we want to determine the drag (for instance) it is required to solve for the boundary layer (and in this case of course a turbulent model is to be chosen). But still to me it seems like solving a problem by evoking an inviscid flow (out of the boundary layer) should give bad results. It should be as bad as considering the flow laminar. However, in the literrature it seems very well accepted to invoke inviscid flow out of the oundary layer.

 Mani October 28, 2005 13:38

Re: inviscid flow and turbulnces

"evoking an inviscid flow (out of the boundary layer) should give bad results"

Not always. It depends on what you call "result". If you're interested in the lift of an airfoil with fully attached flow (on a cruising airplane), you will get a very good approximation by an inviscid model (saving a lot of time compared to a viscous analysis). If you talk about drag, or lift with separation, it's a different story. Sometimes inviscid flow phenomena are dominant over viscous phenomena, for example when the drag of a space shuttle is dominated by losses through shock waves, rather than viscous drag. Sometimes viscous phenomena cannot be neglected.

That's why I suggested to think about applications. Each application has its own requirements, and it's impossible to generalize over all fluid dynamics problems. Inviscid analysis does have its merits in such cases where the effect of viscosity (and turbulence) is not very significant as compared to inviscid effects. Although you can take a brute force position and say that the full Navier-Stokes equations should always be better, so why do we need anything else... the answer, of course, is all about finding the maximum computational efficiency to achieve the necessary accuracy.

 sylvain October 30, 2005 14:55

Re: inviscid flow and turbulnces

Thank you Mani