What is lift "force"? NASA is wrong!
There is a classic figure shown in "theory of flight" (for pilots) and "aerodynamics" and "flight mechanics" subjects (for aeronautical engineering students) that shows a free body diagram with four "forces" acting on an airplane: weight (W), thrust (T), lift (L), and drag (D). Even the NASA Glenn Research Center website shows it:
NASA begins by answering the question, "What is lift?": "Lift is the force that directly opposes the weight of an airplane and holds the airplane in the air...Lift is a mechanical aerodynamic force produced by the motion of the airplane through the air". But are lift and drag really forces? Or are they just the perpendicular and parallel projections of a resulting force vector? I am pretty sure that all aerodynamicists at NASA know the correct answer. Presenting it in this way is indeed easier to explain to kids and aeronautics novices, however, such expressions ("lift force" and "drag force") are also commonly used in published articles in reputable scientific journals, not only in the text of the article, but even in the titles of the papers. A random search in Google Scholar shows some recent journal article titles (truncated):
- "Lift force in odd..." (2023)
- "Steady lift-force generation on a circular cylinder..." (2021)
- "...and impulse-based lift force analysis of oscillating airfoils" (2019)
- "Improved analysis of the lift force on a free-flying..." (2018)
NASA continues: "Lift is generated by every part of the airplane, but most of the lift on a normal airliner is generated by the wings.": This is true and quite obvious, since a body in a correct position to the wind, regardless of its shape, produces an aerodynamic force, i.e. lift and drag [2].
The next question that NASA asks is: "How is lift generated?": "Lift occurs when a moving flow of gas is turned by a solid object. The flow is turned in one direction, and the lift is generated in the opposite direction, according to Newton’s Third Law of action and reaction". Here it is clear that NASA has chosen, at least in the first instance, the Newtonian approach to explain how lift is generated. This continues: "For an aircraft wing, both the upper and lower surfaces contribute to the flow turning. Neglecting the upper surface’s part in turning the flow leads to an incorrect theory of lift". But, what happens when there is a massive air separation behind the wing? or even worse, how can this approach be explained in a stalled (quadrangular) flat plate (e.g., AoA=50 deg.), where the lift is still generated. In this case, is the massively separated flow also considered to be turning along the plate? Perhaps this question is a matter of perspective or interpretation... For now, I prefer to leave this question open.
The next section is called "No fluid, no lift": "Lift is a mechanical force. It is generated by the interaction and contact of a solid body with a fluid (liquid or gas)". At first glance, this seems to confirm NASA's position on the generation of lift in an inviscid fluid (flow) past an object: it cannot be generated. But, I do not want to be too rigid on this aspect, as I understand that this information is not given in the context of a scientific publication. Moreover, if this were the case, then the Circulation Theory of Lift (by M. Kutta and N. Zhukovsky) would have been wrong...or perhaps such a theory does not model a "true" (with a free-slip interface; without contact) inviscid fluid but a viscous one (no-slip interface)...
This continues: "The Space Shuttle does not stay in space because of lift from its wings but because of orbital mechanics related to its speed. Space is nearly a vacuum. Without air, there is no lift generated by the wings". I agree. Since a vacuum and an inviscid fluid are not the same (in an inviscid flow molecules are present, while in a vacuum they are absent), why should we think that the same result (no force, hence no lift-no drag) should be obtained for both cases? Perhaps, the fluid matter present does not change anything (i.e., collisions with surface)? Think again: Can a force be generated in an inviscid fluid? [3]. Now it is time to throw some rhetorical questions (my favorite part). If the Navier-Stokes equations (NSE) have already solved the fundamentals of fluid dynamics (i.e., the mechanism for lift generation and the effect of viscosity on it), as some minds claim (I guess that they mean by tricky simulations since even the incompressible NSE have not yet been solved analytically for all cases). By the way, why is not possible to solve an "inviscid direct numerical simulation" (DNS) by simply setting the viscosity to an extremely low value? I guess some kind of instability problems appear...So, have we understood what an inviscid fluid really means and implies? [4]
The last section is called: "No motion, no lift": "Lift is generated by the difference in velocity between the solid object and the fluid. There must be motion between the object and the fluid: no motion, no lift". I agree. The velocity field is the cause of the aerodynamic force [1] (in this particular approach, the pressure field is decoupled from the flow solution); the pressure field is a consequence of the velocity field since the first depends on the second (see, for example, the dynamic pressure in Bernoulli's equation), not the other way around. In fact, when integrating the pressure distribution to obtain the lift on an airfoil (Bernoulli's approach), one should implicitly integrate the velocity, since the pressure depends on it. This is probably why NASA has finally accepted both Newton's and Bernoulli's approaches as valid to avoid further suspicion: Bernoulli and Newton | Glenn Research Center | NASA
[1] No more fallacies. Why do airplanes fly? (librepenzzzador.blogspot.com)
[2] Can a brick 'fly' (glide)? (public: aerodynamicists) (librepenzzzador.blogspot.com)
[3] Could there be lift without viscosity? (librepenzzzador.blogspot.com)
[4] A fundamental question of fluid dynamics (librepenzzzador.blogspot.com)
[5] What is the 'hybrid vortex tube-vorton' method? (librepenzzzador.blogspot.com)
Here I am again. I just wanted to comment on a couple of points.
ReplyDelete- Strictly speaking, lift and drag are not the "vertical" and "horizontal" component. Also , all simplified explanations talk about lift only, because that is the most interesting effect.
- Just because a fluid is inviscid, it doesn't mean it does not interact with a solid. There is also pressure. In fact, forces in stationary fluids are very much a thing, and viscosity, velocity and vorticity have nothing to do there.
- Again on pressure: only because we can decouple the equations, it does't mean that velocity does not depend on pressure, even in the incompressible case. Also what does the dynamic pressure formula have to do with pressure being function of velocity? Most of the times, in fact, you actually use dynamic pressure to measure the velocity. Does that mean that velocity is a function of pressure?
- Navier-Stokes equations do describe astoundingly well all flows of fluids, under the hypothesis of their derivation. The fact that we can't describe lift only by looking at NS formulae is a testament to the complexity of fluid dynamics.
- You can't pass from viscid to inviscid by a vanishing viscosity argument: it is a singular perturbation problem, as well explained in literature; the equations are of a different order.
- Circulation and vorticity are useful, but ultimately, they are the velocity itself, they can't be the "cause" of velocity.
Yes, you are right. I just changed to "perpendicular" and "parallel" components in order to generalize the concept. I assume that you are agree that lift (and drag) are not forces per se.
DeleteI agree with the first part. I strongly disagree with the second; vorticity is present even in stationary fluids (e.g., wing tips; vorticity exists even when the flow is not turbulent).
In dynamical systems, decoupling one variable means that its influence on the remaining variables is zero. As you know, there are basically two ways to obtain the dynamic pressure: by measuring both the total and static pressure (e.g., pitot tube) and then obtaining the flow velocity, or by measuring the free-stream velocity directly (e.g., anemometer). From this perspective it is difficult to determine the cause and effect. However, IMO, the equation for dynamic pressure is clear: pressure depends on velocity.
Fluid dynamics (incompressible case) is quite similar to the dynamics of deformable solids; a fluid element can be represented by a simple tube that deforms under the action of the others. The complexity of NSE (in the Eulerian form) is due to its discretization (meshes) and all the tricks and assumptions to try to "close" them.
As far as I know, most natural phenomena are described by a continuous and gradual process. Just such an "exception" is that it does not allow to understand what an inviscid flow is (even from a PFT perspective) and its consequences in fluid dynamics.
This subject sounds like: which comes first, the chicken or the egg?
I understand your point when you say that vorticity (and circulation) is (a function of) velocity (w_ = nabla x u_). However, the term "induced" in "induced velocity" means "caused by", or in other words, the velocity caused by the vorticity. Note that in the text I am referring to the lift generation mechanism (total velocity acting on surface points; KJ theorem) caused by such a vorticity field (which inherently already includes the free-stream velocity, besides body and wake interactions). I mean, in the text I refer to lift generation, but not vorticity generation; vorticity generation is clear (at least to me) that it is due to velocity (even in an inviscid flow).
Thanks for your interest.
Thanks for answering my remarks.
Delete- I don't see the point of denying the label of "force" to lift and drag. I do agree that they are only components of the resultant fluid force, but that doesn't make them less "real", at worst it makes them dependent on the reference system. The resultant force is also just that, a summation of all the stresses acting on the surface of the body. If you want to be pedantic, "force" should only be one of the four fundamental forces. But I'm sure in structural mechanics you too distinguish between the normal and shear forces, for example, even though they are only components.
- I did not mean "stationary" as in "steady", but as in "static", e.g. water just sitting in a bucket. It was just to show that a fluid can exert a force even without viscosity playing a part.
- We can discuss the technicalities of the role of pressure in the incompressible NS equations, but my point is that the mathematical formulation does not necessarily reflect a physical cause-effect relation. There are many decompositions of the NSE, which one would be the "true" one? Similarly, if I said "IMO, the equation for dynamic pressure is clear: velocity depends on pressure", why should my interpretation be wrong?
Also there is no "dynamic pressure equation", dynamic pressure (which is not even a pressure in the true sense of the word) is only a definition. The equation you have is Bernoulli's theorem, which places no preference on velocity nor pressure.
- Fluid dynamics (even the compressible case) is of course quite similar to the dynamics of deformable solids. They are both branches of continuum mechanics, the only difference being the material (fluid vs solid). The complexity of NSE is in their non-linearity and unstable/chaotic behaviour (viz. turbulence), which has nothing to do with meshes or tricks. The fact that they are still an open problem doesn't mean they are false. The fact that they have been good for two centuries does not mean that they are true either, but they are a very very good model, which is the same as being "true". I think it's pretty bold of you to dismiss them with a "as some people claim", but if that's the case, I count myself among those people.
- "Natura non facit saltus". Of course continuum mechanics is the science of continua. But the difference between inviscid fluid and viscous fluid is essential: you can't model both with the same equations, because the equations are of a different order; for once, you would need different boundary conditions. Inviscid fluids are not an exception of viscous fluids, they are different fluids, just as Newtonian and non-Newtonian fluids are different.
- That's exactly the point: the chicken or the egg? "Induced velocity" is a misnomer, as recognized by some authors (see "Understanding Aerodynamics" by McLean on this). Saying that vorticity is generated by velocity is like saying that velocity is generated by displacement (with the difference that you can have velocity without vorticity, but not displacement without velocity): what help can it give us?
Hi back CT,
DeleteI really appreciate your time and contribution to this discussion. I will respond briefly for now, and hopefully expand on it in future posts.
- Ideally, things should be named as precisely as possible to avoid further confusion. I mean, forces are forces, and components are components or projections of a force.
- Then you are talking about fluid mechanics (without net forces), but not about fluid dynamics...
- By convention, dependent terms (pressure) are on the left side and independent terms (density and velocity) are on the right side of the equation or definition. IMO, this determines a cause-effect relationship. Iterative solvers in Eulerian NSE dilute such a relationship (velocity-->pressure-->velocity), similar to the chicken-and-egg paradox.
- The problem with incompressible NSE lies in its discretization: dynamical problems must ideally be solved by dynamical approaches. I know this sounds rigid, but it is also logical.
- In the continuum, the same equations should work the same when approaching their limits. At the limit, another equation is probably needed, but continuity will remain (above all under a continuum media assumption).
- Yes, I know that the term "induced" comes from electromagnetics, where potential theory also applies, but such a factor by itself does not mean that this term cannot be used in other fields. After all, a leaf of a tree moves because the velocity that induces (or causes) a tornado or hurricane is further away, far from its "structure". By the way, this is another aspect that cannot be denied: vortices cause velocities far away because of the existence of continuum media (flow density). This is a good topic for the next blog post.
Regards!
Hi Carlos, thank you for your response, I enjoy discussing this type of issues. By the way, nice restyling of the blog.
Delete-Is the confusion you mention about forces and components only related to the "lift without drag/drag without lift" distinction? I don't think saying "the lift component of the aerodynamic force" would make any difference wrt simply saying "the lift force". By saying "lift force" we are not negating drag existance no more than we are neglecting the weight of the body. It's merely a different focus. By talking of aerodynamic force alone, it would be arguably harder to understand, for example, that some thrust is required to counteract drag. And this has nothing to do with viscous or inviscid flow. There is a reason why abbreviated talk like this is used, and almost never anything is gained from being more pedantic. It's a bit how some people say gravity is not a force, because it represents spacetime curvature etc. etc.; is it formally more precise? maybe. Is it a useful distinction? I doubt it.
-You might call it fluid statics, but I would find it rather weird if we needed two different approaches (in terms of the treatment of forces, pressure, etc.) for a still fluid and one in motion. As things stand, the equations normally used work equally well in both cases.
-Firstly, yes, it is a convention, hence it has no meaning. Take F=ma, what should that mean? Secondly, again, the dynamic pressure "equation" you mention is only a definition (of dynamic pressure), and dynamic pressure is not a "pressure" (ie a stress component, or, even further, a thermodynamic variable).
-Discretisation of NSE is an issue related to a specific way of solving the equations, not to the equation themselves. It is unlikely that "easier" equations will be found, that describe phenomena equally well. It is more likely that more elegant ways to solve NSE will be found.
-"Continuum" refers to the body and the configuration it occupies. Inviscid and viscous are properties of different materials the body are constituted of. There is no continuous transition from inviscid and viscous, no more than there is from compressible to incompressible.
-The problem with the term "induced velocity" is not as much that it suggests action at a distance, rather, that it suggests that vorticity predates and produces velocity. I will gladly have a look at the newest blog post.
Hi CT,
DeleteYes, the blog looks better now :D
-On lift and drag: No, it has nothing to do with forms, but with substance. A theory of lift cannot be based on explaining how a component of a force is produced; it should explain what the resulting force is. Kutta and Zhukovskiy did this for lift, and Prandtl for drag, but there is nothing yet that explains both in a single theory.
By the way, thanks for the suggestions in the latest blog post.
A general description of aerodynamic forces is available, see e.g. https://doi.org/10.2514/3.50966. Even more generally, in fluid dynamics equations can be written for the motion and the related stresses, which determine the forces on bodies. The fact that they usually don't have a closed-form solution, much less a simple one, doesn't mean that they are not valid. The theories you mentioned are absolutely valid too, but of course they should be taken in the context they were derived from.
Delete