# Delaying boundary layer transition and flow separation

1. ### Separ8shun

5
Hi all,

I am looking to learn more about boundary layer control devices that can delay boundary layer transition (Laminar to Turbulent) and also BL devices that can delay flow separation.

I have already found loads of info on Vortex Generators but i am having trouble finding info on things like BL Suction and Blowing, Surface Roughness, why cooling the wing surface would encourage laminar flow, wing fences, saw tooth leading edges etc.

I am hoping to understand their effects on the pressure and velocity of the freestream in a descriptive sense.

Any information, knowledge or links to descriptions of these control devices would be greatly appreciated.

Thank you.

1,716
That's quite a large topic. I guess before starting, what is your level of familiarity with fluid mechanics/aerodynamics to begin with? That would help with tailoring an answer.

3. ### Separ8shun

5
I did a degree in uni on aero eng and got myself a 2.2 BEng. unfortunately i havent actually had to use the degree a lot so most of it is gone :S and now i am trying to do an Masters of Science degree part time.

If you can let me know what you know i'll tell you if i get it.

e.g. why is a dogtooth/saw tooth leading edge needed? what does it need to do to rectify the problem? how does it work in terms of the pressure and velocity of airflow.

For my essay I need a few hundred words out of each BLCD i mentioned so going right down into the depths isnt really needed. Thats why i preferred links, i dont want anyone to be doing it for me. I have had a terrible time trying to find information online that describes what the BLCD does to delay either separation or transition rather than just stating that it does.

Thanks

1,716
I've never heard of a sawtooth leading edge to be honest, and boundary layer stability, transition and control is an area I actively research.

At any rate, I can't grab links for you at the moment because I'm out of town, but look up a paper by Joslin titled "Aircraft Laminar Flow Control" out of Annual Review of Fluid Mechanics. It is a excellent primer on LFC technology. It just covers experiments that have been done. For the physics begin it you can look through the references in that paper or I can probably run down a little but of it on here after The weekend if you still have questions. From here the best I can do is point you to sources.

5. ### Separ8shun

5
a paper by Joslin titled "Aircraft Laminar Flow Control" out of Annual Review of Fluid Mechanics

I think i have seen this paper and if i remember it right it contained quite a lot of calculations that were over my head.

Papers like that seemed to be a little calc-heavy with less time taken to explain what the results of the calcuation meant i.e. we have this value and therefore this means that this method has done this and produced this.

It may be that i was reading it too quickly trying to find what i was after. I will try again.

I would be grateful for those links next week though ;) thank you for the help.

1,716
Alright, so flow separation is easier to explain, so I will start there. Imagine the boundary layer (search Blasius boundary layer if you have a hard time remembering what it looks like). If you put this flat plate in an adverse pressure gradient ($\frac{\partial p}{\partial x}>0$) then, as you travel further down the plate, you end up seeing the boundary layer get "pushed back" on itself. Eventually, the derivative of the boundary layer profile at the wall ($\frac{\partial u}{\partial y}$) goes to zero and passes back to negative values (in other words, the wall shear stress vanishes). At this point, we say the boundary layer is separated. Because of the fact that airfoils necessarily have a section with an adverse pressure gradient, they are prone to separation which, if allowed to grow, can lead to stall. The problem is compounded by the presence of large roughness or steps on the surface as well.

There a few popular ways to control separation. You implement surface suction, which draws higher momentum fluid from the boundary layer edge down closer to the surface, effectively "filling out" the boundary layer profile to look more like that of a turbulent boundary layer. You can implement a blowing system that blows higher momentum fluid into the boundary at and parallel to the surface. This high momentum air injection serves the same purpose of filling out the profile. The other way you can control it is designing the airfoil such that the pressure minimum (where the favorable pressure gradient ends and the adverse gradient begins) is as far aft as possible.

That is the very basics of the flow control methods for preventing or delaying transition. Is that the sort of level you are comfortable with? I can talk about transition next but it is significantly more complicated so it would be good to know what level to explain it at ahead of time.

7. ### Separ8shun

5
I understood the flow separation description completely (apart from 'pushed back'. i assume you mean that the pressure increases with distance along the chord resulting in a net force acting upstream? if you dont mean that then i am in BIIIIIIGG trouble!)

I understand enough (I think) about what transition and flow separation themselves are. It is the detail of the methods used to delay them that i am shaky on.

The examples you mentioned are good. I knew about them before but if you could describe (or link to) how they create that favourable pressure gradient or re-energise the flow that would be outstanding.

Could you elaborate on how rough surfaces create transition. It seems fairly obvious but i have not seen any scientific wording and all i have is 'rough surfaces disrupt the smooth layers of laminar flow by inconsistent shear stress due to random surface geometry' which sounds like crap but is all i can come up with off the top of my head. It is something to replace that statement that i am hoping to find.

The other method i am interested in is the designing the aerofoil to have a favourable pressure gradient (I think this is called a supercritical flow and involves moving the point of max thickness aft as far as possible and flattening the upper surface of the wing though i am not certain). Could you explain/link to how this works in terms of pressures, shear stresses and velocities?

I'm not sure if this is too deep into the subject to be easily explained, but if it is then please just say.

1,716
Yes. This image on Wikipedia illustrates what an adverse pressure gradient does to a boundary layer the farther downstream you go.

Since you have an aerospace engineering degree, I presume you know a bit about airfoils. As air moves over the top, it accelerates. This is indicative of a favorable pressure gradient. However, once it reaches the pressure minimum and the airfoil begins tapering back towards the trailing edge, the flow slows down indicating an adverse pressure gradient. When there is a favorable pressure gradient, there is nothing to cause that little "hitch" in the boundary layer profile and it looks like a typical (or slightly fuller) Blasius boundary layer (below). Injecting momentum in the form of wall parallel jets counteracts the effects of an adverse pressure gradient by helping push that little hitch back out. Suction works similarly by helping pull the high-momentum fluid down and filling out the profile that way.

Every boundary layer is essentially just a complicated dynamical system. As such, the Navier-Stokes equations can by broken down through a stability analysis into the Orr-Sommerfeld equation. This essentially constitutes an eigenvalue problem, meaning a number of different modes can satisfy the equation and grow at a variety of different rates. Like any other dynamical system, it is sensitive to perturbations of certain frequencies and types and not very sensitive to perturbations of certain other frequencies and types.

It is also important to note that boundary layers with inflection points in them (i.e. $\frac{\partial^2 u}{\partial y^2} = 0$ somewhere in the profile) are incredibly unstable. This is called the Rayleigh criterion. I won't go into its derivation unless you want to see it, but it probably would warrant its own post.

There are a variety of different instabilitiy mechanisms, but there are three that dominate nearly every type of subsonic wing (with slight additional complications when moving into the supersonic regime). The first are Tollmien-Schlichting waves. These dominate the transition process of most two-dimensional boundary-layers such as over a flat plate or on a 2-D wing. They are essentially sound waves that get trapped in the boundary layer.

Next, on any surface with concave curvature (such as wind tunnel nozzles or near the trailing edge of some airfoils, you see the Görtler vortices develop. These are counter-rotating vortices that align themselves with the streamlines and convect downstream, modifying the mean-flow such that secondary, inflectional instabilities develop and lead to transition. This can also happen on a convex surface that is rotating through a fluid.

The third type of instability is what is called attachment line contamination. A boundary layer develops over the fuselage of planes, and this is pretty much always turbulent no matter what. On a swept wing, this turbulent boundary layer can continue on down the attachment line of the swept wing and cause the entire boundary layer over the wing to be turbulent as a result. This is fairly easy to fix using a Gaster bump, which essentially just involves creating a point on the wing near the root that serves as a stagnation point and causes the turbulent fuselage boundary layer to continue down the wing near the root and allows a fresh, laminar boundary layer to form at that stagnation point and travel down the wing.

The final major instability is the crossflow instability, which develops on swept wings. On a swept wing, the pressure gradient over the wing combined with sweep leads to a phenomenon where the inviscid streamlines do not line up perfectly with the streamlines at the wall. This means the boundary layer is three-dimensional and has an inflection point in it, which is unstable. The result is streamwise (w.r.t. the inviscid streamlines), co-rotating vortices that eventually cause breakdown much like Görtler vortices, through mean flow distortion and secondary instability breakdown.

These are all primary instability modes. The overall transition process can be described graphically with the following "roadmap" originally created by Morkovin:

Surface roughness comes into play in the "receptivity" phase of the process. You start out with disturbance in the free stream. These come in the form of acoustic disturbances (sound waves), vortical disturbances (turbulence) and entropy disturbances (temperature fluctuations). Different instability modes are sensitive to different types of disturbances, in particular the acoustic and vortical disturbances. For a given free stream, the disturbances maybe be of any variety of sizes and magnitudes. When it comes to flight or a well-designed wind tunnel, these disturbances are very small and generally on a fairly large scale.

Going back to what I said earlier, boundary layers are only sensitive to perturbations of specific scales and frequencies as determined by linear stability theory. Other disturbances die out (except in the case of transient growth, which is a whole other animal). Environmental disturbances are rarely of a scale that readily excites a boundary layer, so something has to provide a means for their scales to be changed to those to which the boundary layer is receptive. Surface roughness is this mechanism. Free-stream disturbances interact with surface roughness. They are diffracted and enter into the boundary layer as the tiny initial conditions in the stability problem. From there they grow according to the characteristics of the boundary layer.

In general, T-S waves are sensitive to acoustic disturbances and 2-D steps and can be stabilized with a favorable pressure gradient (the basis for the concept of Natural Laminar Flow [NLF] airfoils, which are similar to what you described here). Crossflow is sensitive to 3-D roughness and vortical disturbances and is destabilized by a favorable pressure gradient (making it arguably the most difficult to control). The methods for controlling these primary modes are collectively known as Laminar Flow Contro (LFC)l, and to get a good read on all of the strategies that have been employed, I would have to again point you to that Joslin paper, which is reasonably light on the technical side and is instead more like 29 pages of fairly general overview (with figures!).

Surface suction has shown to be effective at controlling all of these mechanisms, but hasn't been implemented commercially because the added maintenance cost of the suction system is too high to be worth the fuel savings. The focus lately has been on designing using many of the NLF concepts to prevent growth of T-S waves and attachment line contamination, which is very unstable to crossflow, so all further attention can be directed there. There are a couple potential options being researched for controlling crossflow specifically, but again, for the sake of brevity, I won't go into that in this post.

Supercritical airfoils are a different topic and involve transonic flight and controlling the Mach number that is achieved over the wing to minimize the effects of shocks or prevent said effects entirely. This is similar to but not identical to NLF. I am not 100% familiar with designing a supercritical airfoil, so if that is really your goal, then I can't really elaborate. NLF is much as you have described but also involves considerations on the radius of the leading edge to help control the attachment line boundary layer. Also of note is that the combination of NLF with surface suction is a technique known as Hybrid LFC.

Hopefully that was helpful. It may be a bit disjoint, as I wrote this largely during breaks from writing a different paper, so I may sound a bit crazy, haha.

9. ### voltron

6

I'm very new to fluid mechanics, but I'm interested in the step between the closed NS equations and the point at where it becomes a problem with multiple possible solution modes. Is this what turbulence does? And does this mean that DNS is not applicable to turbulent flows? And all the additional parameters/equations in CFD are attempting to converge the flow solution to the 'most likely' mode?

I will be quite surprised if any of that makes sense :p

1,716
I am not 100% sure what you mean by the "closed NS equations" but as far as turbulence goes, as far as we understand it currently, the end result of turbulence is the same regardless of the mode that eventually transition.

DNS is absolutely valid in a turbulent flow. There is strong evidence that turbulence is entirely deterministic and may be an extraordinarily complicated form of spatio-temporal chaos (a field that is still in its infancy). No one yet knows with any certainty, but there are a growing number of scientists that feel this way. This implies that every bit of information that you need to simulate turbulence is wrapped up in the Navier-Stokes equations. In fact, while not proven, it is generally accepted that much like with chaos, the breakdown of a laminar boundary layer happens when the disturbances get large and start becoming nonlinear, at which point the aforementioned Orr-Sommerfeld equation is no longer valid. This leads to continued growth in all three dimensions, eventually breaking down into turbulence as the disturbances start generating vorticity, etc. Like I said though, a lot of this has not yet been proven, but this is the prevailing theory.

The problem that DNS has is that to fully capture turbulence, you have to make your grid so fine that you capture the Kolmogorov scale features (which are extraordinarily tiny) and that requires an incredibly fine mesh. At the same time, there are large features that you have to capture, and everything is three-dimensional. In other words, in order to simulate any sort of useful air or water vehicle, you need an enormous number of grid points in a 3-D mesh. It simply pushes the limits of modern supercomputing. Eventually, supercomputers will become powerful enough to, in theory, solve these sorts of flows.

All the additional parameters/equations you refer to are a field called turbulence modeling. The idea is simply to admit that we can't solve turbulence directly, so instead we will introduce other parameters such that we can approximate the turbulent solution and draw limited conclusions from it such as drag or heat transfer. However, no model is even close to perfect, and while you may end up with the correct drag with one model, most other parameters will be off. Each model is only accurate for certain quantities. That is about as far as I go with turbulence modeling. I personally am not very interested in it so I have tended to stay clear, as I am more interested in the true flow physics rather than finding models to simplify the physics. Still, it is a huge and important field within fluid mechanics. You will just have to find someone else if you want to know more (or buy/rent/check out Turbulent Flows by Pope).

I hope all that made sense. Personally, I am not a turbulence guy so someone can jump in here and correct me if I am wrong on anything, but I think I stayed basic enough to avoid looking like too big of a fool. :tongue:

11. ### voltron

6
Thanks, all very interesting. And I agree, I wouldn't fancy working in a field that will some day be made completely redundant :tongue:

12. ### Separ8shun

5
THanks for the posts guys. I think i understand transition slightly better now.

I have a few small questions that have come up in the last few days (mostly i have become confused reading through different papers)

1) I have noted that the chord position at which we get critical Reynolds number (Xcr) can be found using the Reynolds number equation (assuming we know the critical reynolds number itself which as i understand it does not change for a wing (unless you change angle of attack)) - can i ask, is reducing the velocity a reasonable method of delaying transition? I only ask as it seems a little too simple for this subject.

2) Does a reduction in wing chord affect transition or separation?

3) What is the effect of cooling the aerofoil surface on transition/separation? (I think i asked this before but i went back through and couldnt find any comment on it - apologies in advance if i have just missed it)

4) Confirm whether suction can be used to delay both transition and separation? If so does it depend on placement of the porous surface/slot?

5) Define the attachment line with respect to attachment line contamination? I have not seen anything explaining where the attachment line is (tempted to think it might basically be a line of stagnation points along the span but not willing to assume it)

6) Confirm that vortex generators, wing fences and vortilons create a vortex in the same way a wingtip vortex is created (high pressure on 'lower' surface wraps round to low pressure upper surface?) what about dogtooths?

7) Confirm that minimum pressure on upper surface is at point of maximum thickness? (i am basing that statement on 4 year old knowledge - dont have any of my books with me unfortunately)

Sorry about all the questions guys. If you know the answer to one or more then feel free to just answer that one. I suspect most of these questions are just nerves-created doubt!

Thanks!

1,716
Sure you could reduce the velocity (and thus the Reynolds number) and transition would move back. The question is, is that a viable solution for a given application? Most planes aren't going to want to go slower either because they are trying to get somewhere in a short time or they need to maintain lift or any number of reasons. Reduction of speed will lower the Reynolds number but at a cost that likely isn't advantageous.

In absolute units, not directly. For example, if you had an airfoil that was 2 meters in chord and it naturally transitioned 0.5 meters from the leading edge, then chopped off the read half of the wing, it would still transition 0.5 meters from the leading edge (ignoring any effects from the now missing aft chunk of the wing, of course). However, if you are just taking a 2-meter airfoil and shrinking it to 1 meter, then you have changed the pressure distribution so you would affect transition. The transition location would still be fairly close to 0.5 m in all likelihood though rather than scaling with the wing, after all, the Reynolds number didn't change.

I couldn't really tell you what cooling would do to separation. I would expect not much for a subsonic boundary layer and maybe it would affect a compressible boundary layer. I do know that it has little effect on subsonic transition but a very real effect on supersonic transition. For example, cooling the wall below the adiabatic wall temperature will stabilize the T-S instability by destabilize the second mode acoustic instability. This means that below about Mach 4, wall cooling is stabilizing while above Mach 4 it is destabilizing.

It can delay both. For transition, suction needs to be near the leading edge to be most effective. For separation, it needs to be farther downstream closer to the separation point to be most effective.

Your assumption is correct. On a 3-D (swept) wing, you don't have a true stagnation point, but a line along the span from which all streamlines emanate. This is the attachment line.

Vortex generators have a number of applications and create vorticity in a number of ways depending on design. A simple bump can act as a VG on the one hand while on the other hand, so can a small airfoil. The method and end result of VGs depends on the application. Vortilons, to my knowledge, are essentially a type of VG.

Wing fences generally are used to control spanwise flow and the associated stall. Their function doesn't really depend on creation of vorticity (as far as I know) but rather the fences tend to stretch over the whole chord and simply prevent spanwise flow from one portion of the wing from affecting another.

Other than knowing what a dogtooth leading edge is and what it does, I am not incredibly familiar with how it actually physically creates the vorticity. I am not near any of my normal sources to look it up at the moment either. If I had to make an educated guess, I would say it is because the dogtooth forces the air at that point over the wing instead of along the front, causing a vortex to form along the chord at that point and acting as sort of a virtual wing fence. Still, that is just an educated guess. Maybe someone else can be more specific.

In general, for zero angle of attack, this is the case. It will shift slightly with angle of attack, but on a modern airfoil design, it often doesn't shift a ton.

14. ### voltron

6
Hi boneh3ad, I've got a few more questions if you'd be kind enough to help me out, related to drag.

I understand skin friction drag reasonably well, but I'm having a bit of trouble understanding pressure drag in its entirety. So for an inviscid irrotational flow, there will be no pressure drag regardless of body shape, as the integral of the pressure distribution on the surface cancels out. Now when the flow is viscous, there's the no slip condition, which creates a boundary layer (and skin friction drag), but the boundary layer itself also creates no pressure drag. As the boundary layer encounters adverse gradients, it gets 'pushed back'. The point where the velocity profile has an inflection at the object surface is where the boundary layer separates. Further along(?) the reverse flow caused by the adverse gradient will cause the flow to separate and form eddies/vortices. This separation causes the pressure to decrease within the wake and hence the pressure distribution integrated over the surface will be non-zero, resulting in pressure drag. That's as I currently understand it... There's a few things I'm not too sure about.

The first is probably a stupid question, but what actually causes the adverse gradients? Is it as simple as the flow 'slowing down' after it passes a certain point in the objects geometry?

I'm also a bit hazy on the distinction between BL separation and flow separation, and what that means for the flow. It kind of makes sense intuitively to imagine flow separation as the velocity profile 'breaking' at the point it goes from +ve to -ve flow direction, then this broken off bit spinning away as an eddy. What does it mean if a flow is "fully" separated? And I don't really understand what BL separation is, only that it occurs when the point of inflection is at the surface... Does another BL form at this point?

Also can I just clarify: The pressure is decreased in the wake of the object, which is the reason bluff bodies have higher drag (bluff bodies have larger wakes and more surface area normal to the flow)

Lastly and probably most importantly, how does a separated flow actually decrease the pressure in the wake?

Thanks very much!

1,716
The inflection point criterion (Rayleigh's criterion) refers to boundary layer stability, not separation. An inflection point means the boundary layer is very unstable even without the influence of viscosity (aside from creating the boundary layer of course).

Separation occurs when the wall shear stress passes zero ($\frac{\partial u}{\partial y} = 0$). When combined with no slip condition, that means that at the wall, the profile is locally normal to the wall. As it continues under the influence of the pressure gradient, the flow will even reverse.

Like I said in an earlier post, the pressure gradient is a result of the geometry of the object. Of you look at the $C_p$ distribution over an airfoil, for example, you will notice it does not stay the same. This is indicative of a pressure gradient.

Boundary-layer separation and flow separation are the same thing. A fully separated flow is just one that is completely separated over the region of interest, be it an airfoil surface, an interrogation window or anything else.

When the boundary layer separates, it is essentially no longer under the influence of the adverse pressure gradient that separated it and instead "rides up over" the separation bubble that occurs. Basically, the flow never recovers the additional rise in pressure between the separation point and the downstream stagnation point on the body and is therefore lower than the pressure at the forward stagnation point. That is the easiest way I can think of to describe it.

http://galileo.phys.virginia.edu/classes/311/notes/fluids2/node11.html

Another way to think of it is that if you have a large wake, your object is basically dragging more fluid along with it. It takes a force to accelerate this fluid, and the equal and opposite force required by Newton's third law is the drag force.