Flow Separation of Airfoil in terms of Reynolds Number

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boneh3ad

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Aero51 said:
Sorry for the late response, it was a busy weekend. Anyway, when I was speaking about the Reynolds number ranges I was coming from a historical perspective. Many papers cite those ranges typical to the aircraft mentioned above.
Those papers were likely not written by people familiar with the subject or were written for a very specific geometry, as there has never been an effective way to predict the onset of turbulence. There are various empirical methods that apply only to specific geometries in specific flow regimes and conditions i.e. it will be different if it is traveling Mach 0.3 than Mach 0.8, which will be different than at Mach 2, which will be different than at Mach 5 and results in flight will be different than in a wind tunnel.

Aero51 said:
I cant say I know much about Görtler vortices or a lot of details about turbulence/turbulence modeling as I have not taken any classes on the material yet. However, in lieu of these facts I will proceed to read some more papers on the subject.
I can tell you I know almost precisely zero about turbulence modeling. Personally, I am not a fan of it, though it certainly has its uses. I do, however, enjoy quite a bit the stability and transition problem (which is more relevant to the Reynolds number range discussion at present). For that, by far the most comprehensive paper is by L. M. Mack (1984) covering the linear stability theory of boundary layers. That ignores crossflow and centrifugal (Görtler) instabilities though. For those, the most comprehensive view of the work that has been done would likely be two Annual Review papers by Saric (2003 and 1994 respectively). They aren't easy reads unless you are already somewhat familiar with viscous flows, but they are effectively the books of the Bible on the subject.

If you truly are interested in the subject though, then here are the three sources I mentioned.
http://www.dtic.mil/cgi-bin/GetTRDoc?Location=U2&doc=GetTRDoc.pdf&AD=ADA147243 (Mack 1984, ch. 3 is on linear stability theory, long read)
http://www.annualreviews.org/doi/abs/10.1146/annurev.fluid.35.101101.161045 (Saric 2003)
http://www.annualreviews.org/doi/abs/10.1146/annurev.fl.26.010194.002115 (Saric 1994)
 
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Thanks ill look into those. One thing im really interested in is a statistical mechanical description of fluid flow and turbulence.
 

boneh3ad

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Ha. Can't help you there. I am not personally a fan of the statistical approach to fluid mechanics (turbulence modeling, etc.). Count me among the camp that believes that if we had powerful and accurate enough computers, it would be a form of spatio-temporal chaos: crazy but still deterministic.

It's certainly a useful field, but not my thing.
 
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Given the speeds and Reynolds numbers involved, that teardrop shape is certainly not separated at all and I would actually contend that even the sphere likely is not separated, as it appears that the experiment satisfies the requirements for Stokes flow. It has no wake and therefore effectively has only viscous drag. As a result, you have one shape with small surface area and one with large surface area, both dominated by viscous drag. Of course the one with large surface area (the teardrop) will move more slowly. In the air, the Reynolds number is going to be much, much larger and while the teardrop will still be dominated by viscous drag, the sphere will be dominated by pressure drag. In these situations, pressure drag is dominant and so the sphere had higher drag in the air flow.

At the kind of low Reynolds numbers ([itex]\mathrm{Re} \ll 1[/itex]) seen in the glycerine experiment, there certainly is an effect due to Reynolds number. You have to remember what the Reynolds number represents. Recall the definition
[tex]\mathrm{Re} = \frac{\rho U_{\infty} D}{\mu}[/tex]
The number represents a ratio of the inertial forces due to the fluid motion to the viscous forces. For the extremely low Reynolds number, the viscous forces are dominant. For most practical flows such as on cars, planes, etc., the Reynolds number typically falls more within the range [itex]10^3 \leq \mathrm{Re} \leq 10^7[/itex]. Anywhere in that range, the inertial forces are many orders of magnitude more important than viscous forces.

The behavior when [itex]\mathrm{Re} \ll 1[/itex] and [itex]10^3 \leq \mathrm{Re} \leq 10^7[/itex] are fundamentally different in essentially all regards. However, within one range or the other, the fluid behaves fundamentally the same regardless of where you fall in that range.
Hi

My apologies for the late response.

So essentially flow separation location would be the same in whatever range is considered (i.e. for Re between 10 and 100 it wouldn't change, but would be different than Re 10^3 to 10^7)? So for the same "level of turbulence", I can have Re at whatever I want without affecting the separation location?

[tex]\mathrm{Tu} = \frac{u^{\prime}}{U}[/tex]
where
[tex]u^{\prime} = \sqrt{\frac{1}{3}\left(u_x^{\prime 2}+u_y^{\prime 2}+u_z^{\prime 2}\right)}[/tex]
I'm wondering if separation location is strongly dependent on this turbulence intensity, as it was mentioned in a earlier post that it is the physical effect of turbulence that makes it seem that separation location is dependent on Re? What other flow characteristics would separation location also depend on (i.e. if the geometry were to be unchanged)?

Lastly, I'm wondering how come Cf and Cp varies with Re if the size of the wake is unchanged?

Thanks very much
 
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Hi

My apologies for the late response.

So essentially flow separation location would be the same in whatever range is considered (i.e. for Re between 10 and 100 it wouldn't change, but would be different than Re 10^3 to 10^7)? So for the same "level of turbulence", I can have Re at whatever I want without affecting the separation location?
Not necessarily. The separation point depends on the state of the boundary layer which depends on the Reynolds number. Increasing the Reynolds number from 10^3 to 10^7 will almost certainly change where the flow separates on an airfoil, because the state of the boundary layer will change. The transition point may move or the laminar separation bubble will no longer form and the flow will separate at the trailing edge instead. Keep in mind you can change the Reynolds number and the separation point may not change, it all depends on how the change in Reynolds number influences the boundary layer. And over a range as large as that it will likely change quite a bit. And of course to make things more complicated all of this depends on geometry and surface quality and various other factors. The same increase in Reynolds may dramatically effect the performance of one airfoil but not change it at all for another.

Boneh3ad mentioned that the flows in this range are fundamentally the same which is true. They are both dominated by inertial forces but that does not mean the details of the flow are the same.
 
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Not necessarily. The separation point depends on the state of the boundary layer which depends on the Reynolds number. Increasing the Reynolds number from 10^3 to 10^7 will almost certainly change where the flow separates on an airfoil, because the state of the boundary layer will change. The transition point may move or the laminar separation bubble will no longer form and the flow will separate at the trailing edge instead. Keep in mind you can change the Reynolds number and the separation point may not change, it all depends on how the change in Reynolds number influences the boundary layer. And over a range as large as that it will likely change quite a bit. And of course to make things more complicated all of this depends on geometry and surface quality and various other factors. The same increase in Reynolds may dramatically effect the performance of one airfoil but not change it at all for another.

Boneh3ad mentioned that the flows in this range are fundamentally the same which is true. They are both dominated by inertial forces but that does not mean the details of the flow are the same.
Hi thanks very much for the response

Am I correct in saying that one can see separation point changing with Re in real life but such an effect is not due to the change in Re but other changes that are typically associated with flows as Re increases (assuming flow is in the laminar region), thus there is actually no theoretical relationship but only a correlative effect? Also, in the instance you described, is there a "typical" direction in which flow separation point moves?

Thanks very much
 

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