Swept wings, Mcr and Span-wise flow

[PA32]

I've been reading a bit about transonic flow and wondering if I could get a bit more info here. Exactly how do swept wings delay the on-set of Critical Mach? Is "span-wise" flow "bad", and if so, why, and how are the bad effects mitigated on current generation jet aircraft? Thanks!

 

[boneh3ad]

With a swept wing, you have the same free-stream velocity encountering the wing at an angle. That means only one component of the velocity (the chordwise component) is accelerated, and that component is initially slower than on a corresponding straight wing due to the angle. That would mean that the wing can encounter a higher free stream velocity (and therefore Mach number) before it is accelerated to sonic speed at some point on the wing.

Spanwise flow is both good and bad. As previously stated, it can help raise the critical Mach number, but it can also lead to boundary-layer breakdown and transition to turbulence. On a swept wing (or anybody with a pressure gradient that isn't aligned with the free stream) you end up with a the spanwise acceleration of the boundary layer. The resulting 3-D boundary layer develops inflection points which lead to very strong instabilities and becomes the dominant mode of laminar-turbulent transition on most swept-wing aircraft. Right now, this effect can't be mitigated, and aircraft designers just have to live with it and the associated drag penalties in order to reap the benefits of the swept wing. Controlling transition on any wing is one of the holy grails of aerodynamics.

 

[PA32]

Thank you Boneh3ad. Could you elaborate a bit on the following: What is (are) inflection points? Are wing fences and winglets meant to mitigate the "bad" effects of span-wise flow? Or do they do something else?

I am a pilot who is very interested in aerodynamics, but my math abilities do not go beyond algebra. Can you recommend any textbooks or web references that go into greater depth on aerodynamics, but do not require math beyond algebra?

 

[boneh3ad]

When I talk about an inflection point, I mean if you plotted the boundary layer profile it would have an inflection point in the plot. An inflection point is a point where the curvature changes sign.

Wing fences are used to try and cut down on spanwise flow for the purpose of decreasing the stall speed. I don't think any modern aircraft really use them, however.

Winglets are used to decrease drag and increase lift on the wing created by the wingtip vortices by moving them from the edge of the wing to the tip of the winglet. This gets the vortices out of the way of the flow over the wing, allowing the flow near the wing tip to continue unimpeded over the surface and generate lift as it is supposed to.

I am a pilot who is very interested in aerodynamics, but my math abilities do not go beyond algebra. Can you recommend any textbooks or web references that go into greater depth on aerodynamics, but do not require math beyond algebra?

Not that I know of. Aerodynamics really requires a basic understanding of differential calculus even at the lower levels. Without that, you would likely be able to look at some of the empirical relations and simplified formulas and get a superficial idea of some of the relationships in aerodynamics, but you would be missing the physics behind it.

At any rate, a good starting point would be "Fundamentals of Aerodynamics" by Anderson. It does require calculus but many universities do use it for their introductory aerodynamics course. Maybe someone else knows of a more basic text, but I don't.

https://www.amazon.com/dp/0073398101/?tag=pfamazon01-20

 

[PA32]

Thanks!

 

[enigma]

"Introduction to Flight" by the same author is the lower level textbook. Used that one for the sophomore level course (taught by the author) and the aerodynamics textbook for Junior year.

I'd hyperlink it for you, but I'm on my phone.

 

[RandomGuy88]

In addition to the things mentioned above, spanwise flow results in a thicker boundary layer near the tip of the wing. The opposite is true near the root, where the spanwise flow essentially acts as boundary layer suction creating a thinner boundary layer near the root. The net result is that swept wings are very susceptible to tip stall which is highly undesirable from a stability standpoint. This is why many swept wings have have large amounts of twist (the tip is at a lower geometric angle of attack) because it is important for the root to stall first.

The resulting 3-D boundary layer develops inflection points which lead to very strong instabilities and becomes the dominant mode of laminar-turbulent transition on most swept-wing aircraft. Right now, this effect can't be mitigated, and aircraft designers just have to live with it and the associated drag penalties in order to reap the benefits of the swept wing. Controlling transition on any wing is one of the holy grails of aerodynamics.

Actually there are ways to control/delay the transition due to cross-flow instabilities on a swept wing. And ironically it is done by distributing roughness along the leading-edge of the wing. The idea is that instabilities are triggered in the wake of the roughness elements and the height of the roughness elements is chosen so that the instabilities that are triggered will decay without leading to transition. The key is that these instabilities (from the roughness) rob energy from the cross-flow instabilities preventing them from growing so that transition can actually be delayed past where it would occur on a smooth surface.

 

[boneh3ad]

Actually there are ways to control/delay the transition due to cross-flow instabilities on a swept wing. And ironically it is done by distributing roughness along the leading-edge of the wing. The idea is that instabilities are triggered in the wake of the roughness elements and the height of the roughness elements is chosen so that the instabilities that are triggered will decay without leading to transition. The key is that these instabilities (from the roughness) rob energy from the cross-flow instabilities preventing them from growing so that transition can actually be delayed past where it would occur on a smooth surface.

I am highly aware of this fact. Search a little more on this topic and figure out who came up with this idea, more commonly known as spanwise-periodic discrete roughness elements, or DREs. You will find it happens to be a guy by the name of William Saric, who just happens to be my graduate advisor.

The problem is, they have demonstrated this technique in low-disturbance wind tunnels very successfully with a permanent applique set of DREs, but has been much less successful in flight where the free stream turbulence is much lower. Even the low-disturbance wind tunnel in which many of these experiments were carried out still had a free stream turbulence level around Tu ~ 0.02%, which is incredibly low for a tunnel but still higher than flight. Additionally, the successful tests have been done an Reynolds numbers that are quite a bit lower than a commercial airliner.

The final hurdle is the fact that you don't always want to have the DREs permanently located in a single location. They work best (and almost exclusively) if you place them at the first neutral point. Too far from there and they no longer affect the transition. In other words, they only work for a single angle of attack. The trick is finding a way to make them adjustable so that you can move their chord position and change their spacing so that you can create different effects in different flight regimes. Sometimes you don't want them at all such as during climb or when close to stall.

In other words, DREs are still quite a way from being a practical transition control mechanism. We are working on a few things right now to solve some of these issues but have had mixed results so far, even in the wind tunnel.

 

[RandomGuy88]

I am highly aware of this fact. Search a little more on this topic and figure out who came up with this idea, more commonly known as spanwise-periodic discrete roughness elements, or DREs. You will find it happens to be a guy by the name of William Saric, who just happens to be my graduate advisor.

Very cool. Is this what your research is on? Its not related to my research, I just saw a paper about it once and thought it seemed interesting.

In other words, they only work for a single angle of attack.

Unfortunately this is common problem with a lot of passive flow control techniques.

 

[boneh3ad]

Part of my research is a new idea for how to implement DREs so they are adjustable. Part of my research is moving that same idea into the hypersonic regime, and part of it is using similar techniques just to look at second-mode growth in a hypersonic boundary layer. It seems kind of scattered about, but it sort of makes sense (as much as anything along the path to a PhD I suppose). To be honest, I am more excited by the more fundamental aspects rather than just trying to make DREs work, but the DREs are a lot more applicable to air travel if we can get it working.