wbeaty wrote: jmorgan3 wrote:
wbeaty wrote:And then it gets WORSE: It's impossible to understand airplanes by only employing 2D flow diagrams. These diagrams depict an odd sort of "flatland flight" where no work is performed on the air, and an airfoil could ideally coast along forever.
While it's true that most 2D flow diagrams you see are inviscid simulations, they still give a good conceptual picture of how lift is produced.
Nope, instead they explain the flight of infinitely-wide wings. They're a very useful shortcut in calculation, but they offer no explanation.
The flight of an infinitely-wide wing is almost the same as a finite one. If you're just trying to see the principle, you're good. I know of one glider that was laid out using 3D methods. All the others usually don't do that because apart from the outer 5% of the wing and a small part at the wing root, air behaves precisely as in a 2D simulation, on a highly stretched glider wing.
wbeaty wrote: To explore the hidden flaw in infinite-wingspan diagrams, just ask yourself where the other end of the 3rd-law force is located. There's an upward force on the airfoil, but where is the equal downward force? Answer: it's expressed as a pressure pattern on distant solid surfaces.
If you go just a little closer to the airfoil: it's expressed on air mass being moved downwards by the airfoil. Look at potential theory. You are pushing air around and that results in lift.
In a CFD computation, you're usually using a "far field" boundary condition, which stets a constant velocity and inflow direction, but will accept any variables where the flow exits the simulated far field. Now you have to ways of determining the lift from the results: You either integrate the pressure distribution over the surface of the airfoild or you integrate the impulse (that's velocity times density) over the surface of the far field boundary (or any other closed path around the airfoil. If your simulation is good, they will always arrive at the same result. There is of course always some numerical error, because you computer uses a finite volume discretisation and numbers are of finite accuracy and so on, but if the grid is fine enough, you're good!
Why don't we need a ground? Why would we? An aircraft doesn't need one, either. It could fly on a planet with no ground (a gas planet) just the same. The thing you're exerting the opposite of the lift force on is the fluid around you. What that does with this force does not need to bother you. Lifting vortices will decay via friction, the downard movement is eventually stopped by the ground (or not, if there isn't one), but that's really a detail that can't keep lift from being generated and therefore is not important when it comes to explaining it.
wbeaty wrote:Whenever infinite wingspan is used, the distant Earth's surface (or the distant walls of the wind tunnel) could either be close by the airfoil, or light years distant, and the instant down-force remains the same.
That is physically correct! As long as the ground isn't really close, it has no effect. You're pushing air downwards. What it then goes on to do with the impulse you've supplied it with is no your business, unless the ground is so close that the reaction of the air hitting the ground (local pressure increase will still affect your airfoil. That's called "ground effect", and it creates additional lift. But let's not get distracted. I'm afraid I already am
wbeaty wrote: The down-force on the wind tunnel is independent of the tunnel's width. In other words, withdrawing the floor and ceiling to arbitrarily large distance is ineffective. You can't get rid of the floor and ceiling or the down force, all you can do is refuse to include them in the diagram. But that sets up a misleading situation which violates Newton's 3rd.
Oh no sir, you don't violate laws of physics. You can't.
The potential flow equations, the Euler and the Navier-Stokes equations are all built around energy and momentum conservations. If I make a computations using any of these models, and the result converges, than that means that the solution is in agreement with all of the equations and thus with all the laws of physics that went into them.
Also, you speak of "diagrams". If I'm drawing a diagram by hand, of course the result will be inaccurate because I can't draw very well. The thing is just, no engineer draws a diagram by hand and than changes it until he likes it better and calls the result an airfoil design (ok, some might do that, but their geniuses). You get a geometry, you build a grid, you specify boundary conditions (speed, angle of attack and so on), you wait for a solution. That solution includes values for lift, drag pitching moment and what will you. It's amazing how precise those results can be if you paid attention to what you're doing, and there's no floor or ceiling included.
wbeaty wrote: I suppose you could try withdrawing them to infinity rather than to billions of miles, but it would create an un-physical situation: an infinite wingspan at infinite distance from a surface. Does the force on the distant surface suddenly go to zero when that distance hits infinity, yet the force remains constant for arbitrarily large values? Think hard, don't just choose an answer.
Ahhh.... I think I understand your problem. A bit.
No, the force that the air you pushed around exerts on the ground does not "suddenly" go to zero. It gradually goes to zero.
In a two-dimensional potential flow (that's a simplified model with no friction and no solid body rotation) every disturbance decays like the inverse of the distance from its origin. If you do have friction (or in 3D, where it's the squared inverse), it goes even faster. Now if your ground is really far away, the pressure difference noticed there will be asymptotically approaching zero with increasing flight altitude.
This means of course that the force will only be distributed over a larger area of the ground. Which will be very far away from the airfoil. So the reaction that the air will have to the presence of the ground is extremely small already. The effect on the flow around the airfoil will be even smaller by the same factor, thus can be comfortably ignored.
Imagine a supersonic airplane (or a supersonic airfoil in 2D -- big difference in your eyes, but it's really the same principle). Anything the airfoil does to pressure travels at the speed of sound, so the ground below the airfoil isn't even "aware" of what's passing over its head, until it's gone and the sonic boom hits it. The ground will reflect the shock wave, in essence putting the air that the airfoil deflected back into a "normal" state, but that reflected shock will be far behind the airfoil, and since it's faster than the speed of sound, the reaction of the ground can never ever reach the airfoil. If someone makes a computation of a supersonic case, the volume taken into account behind the model can be very small since nothing that happens there can affect the flow anyway, so why bother?
You are still right in that the kinetic energy that I put into the air will not magically dissappear. But the thing is that this doesn't have any influence on whether the airfoil creates lift. It's probably harder to imagine because there's no fixed point to "hold on to", but who needs firm ground when you can fly?
wbeaty wrote:As I understand it, the solution is simple: *always* include the starting vortex, and make sure the distance between the airfoil's bound vortex and the starting vortex is << than the distance between the airfoil and the Earth's surface. In that case the force on the Earth does go to zero as you pull the Earth away to arbitrarily large distance.
OK, we're in the mathamatician zone here. Anyone not wanting to get thoroughly confused (if you aren't already...), don't read this:
You need to formally include the starting vortex in a potential flow analysis, because the potential flow equations demand that a vortex cannot end inside the flow field.
The same reasoning explains the wing-tip vortices, which also strictly speaking cannot end within the flow field.
These are also of big importance when analyzing a configuration and trying to separate friction, wave and lift-dependent drag and so on. You can make a Navier-Stokes computation, get all the forces by surface integration, and then find out the single components of drag and lift by analyzing the vortices, supposed your grid is fine enough and the method good enough to represent them well.
However, in real life, where there is friction, these vortices and especially the starting vortex are being dissipated by means of friction. You cannot measure the stating vortex of an aircraft that took off somewhere three hours ago. If it's so weak you cannot measure it, and it's thousands of kilometers behind the aircraft, it stands to reason to assume that it doesn't actually still influence the aircraft, although mathematically it must still exist!
Even in potantial flow analyses, usually the wingtip vortices are assumed to be "infinite". There's an analytical solution for a semi-infinite votex (starting at the wing tip and going to infinity behind it).
The more elaborate methods use a "vortex sheet", because actually you are creating vortices wherever the wing lift is changing, because the lifting vortex that represents your airfoil is changing its strength. But still, these are modelled as semi-infinite vortices. And they can, too. Because the starting vortex that would tie up their ends, is so far away that although it mus exist, it is completely irrelevant to the actual flow around the model.
Another view: You are using your airfoil to push down air, which creates vortices (because face it: what goes down must come up in a continuous fluid), so the air gains kinetic energy while the airfoil passes through. This kinetic energy (equal to inviscid drag of the airfoil times distance traveled) is contained in the vortices. Once you leave a piece of vortex behind you, it does tell a story of what you did to it, and it does still influence the flow field you're in for a little while, but once you've left it behind for good, it cannot hurt you any more, except if you come back. It might to something to someone else coming its way, but apart from that, all it does is to contain the kinetic energy you left behind, and eventually fade to nothing. Sad fate, and I appreciate if people care for that. They're cruel things, airplanes, aren't they?
Ok, this post is so long I got logged out while writing it. So I'll just stop here. If you don't understand something or feel the need to disagree, PM me.
And congratulations to anyone who made it this far
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