Flow Separation of Airfoil in terms of Reynolds Number

Aero51

The different sized wakes in different fluids may be attributed to differences in viscosity, though I cannot be certain unless you provide the name/link to the paper. In general, a higher viscosity in the flow will correspond to higher diffusion rates and a quicker dissipation of the wake. Again, this goes back to the debate on how turbulence levels affect the flow/separation. If there is a specific concept or question that you have regarding the papers you have read feel free to ask.

boneh3ad

Might I just point out that different viscosity means a different Reynolds number if all else is held constant?

As long as the Reynolds numbers are the same, the fluid shouldn't matter for the size of the wake so long as it is incompressible regardless of the viscosity. If the viscosity is higher for one, just increase the speed or size of the model a little bit.

Aero51

Actually you made me realize that if the viscosities are the same and the reynolds numbers are constant then differences in mach number may affect the wake. However neither of us have the paper to make a firm statement.

Red_CCF

Hi

I was actually not referring to a paper, but this video:

http://vimeo.com/7507698

An experiment was done for two objects (one streamlined, one spherical) traveling in air(around 15:00) and glycerin (around 19:00). The streamlined object traveled slower than the spherical in glycerin for the same drag force applied (also I could not see the wake for either object) which wasn't the case when air was used. Speed was decreased and viscosity increased in the glycerin, so the Re must be extremely low.

From pictures of separation in air for a sphere, I can see that there's usually quite a large wake. I'm not sure if separation was actually occurring at the same location but the glycerin simply dissipated the effects or something else altogether.

Thanks very much

boneh3ad

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.

Aero51

Last night I happened to be looking through my aircraft design book and came across an excerpt that is very pertinent to the discussion of this thread. The Book is "Aircraft Design: A Conceptual Approach 4th Edition" from page 306, the paragraphs (truncated) read:


And one more thing I wanted to ask/add with regards to the notion that a fluid behaves essentially the same when E3≤Re≤E7:

I was always under the impression that, for a generic wing, the flow is assumed to be fully (or close to fully) turbulent when the Reynolds number is Re≥E6. The flow shares a laminar and turbulent boundary layer when (~E5)≤Re≤E6 and when Re≤E4 this is in the aircraft and micro-air vehicle range which is considered a fully laminar flow regime.

boneh3ad

This is a very misleading statement. I understand what the author is trying to say, which is that a turbulent boundary layer diffuses momentum (and thus kinetic energy) much more efficiently than a laminar boundary layer so it tends to have higher momentum lower in the boundary layer, but saying it has more energy can lead to some pretty wild interpretations. That's just an interesting way to put it.

If it is in the range of 10⁴, then the flow is almost certainly laminar. There are probably some ways you could still trip that boundary layer (transient growth, for example), but at that low Reynolds number the eigenmodes that arise in the linear stability problem are pretty much all stable and you would need an extraordinarily long airfoil or surface to see transition from crossflow or Görtler vortices. However, fundamentally, the flows are the same. They still are dominated by inertial forces and are subject to instabilities, even if those instabilities are stable in parts of the regime.

Otherwise, there is no generic Reynolds number where the flow is assumed laminar or turbulent. The problem is extraordinarily more complicated than that. We don't even have a general model for the transition location on a zero-pressure-gradient flat plate at zero angle of attack as a function of Reynolds number, let alone an airfoil.

Aero51

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.

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.

boneh3ad

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.

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...f&AD=ADA147243 (Mack 1984, ch. 3 is on linear stability theory, long read)
http://www.annualreviews.org/doi/abs....101101.161045 (Saric 2003)
http://www.annualreviews.org/doi/abs....010194.002115 (Saric 1994)

Aero51

Thanks ill look into those. One thing im really interested in is a statistical mechanical description of fluid flow and turbulence.

boneh3ad

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.

Red_CCF

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?

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

RandomGuy88

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.

Red_CCF

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

Brettcm

Hey guys I have a questions on the Reynolds number and you seem to be pros on the subject could you help me out.

http://www.physicsforums.com/showthr...78#post4126078

Thanks!