# Will air accelerate over a wing and generate lift, if the air has zero viscosity? [duplicate]

Will air accelerate over a wing, if the air has zero viscosity? Will the wing produce any lift under these conditions?

• Will wing produce any lift? You haven't provided much detail to what you've arrived at, but it seems like you're asking the relation between lift and viscosity (which is responsible for boundary layers), therefore: Does this answer your question? What is the relation between the boundary layer and lift of an aerofoil?
– ymb1
Sep 7 '21 at 21:23
• This is a great question. When there is lift, there is drag. Can there be lift without drag? Air with zero viscosity would have no friction, and thus there would be no air resistance and no drag. I don't think you would be able to fly. I'm gonna ask my aerodynamics and physics teacher to give him a real mind-bender. Sep 8 '21 at 13:06
• @mins Huh, that's neat, i'm gonna be reading up some more on this! Thank you, very interesting! Sep 8 '21 at 14:59
• @mins that page seems to assume the flow field will still look the same without viscosity, but it will not. Sep 8 '21 at 20:57
• This question was closed as being already asked and and answered elsewhere. Really the other question is not about viscosity and the selected answer doesn't even mention it. Of course the boundary layer is linked to viscosity, but the question asks for a better level of explanation. Voting to reopen. (As a side comment, duplicates are not to be evaluated by their answers but by the question itself. It not because some answers in the other page mentions viscosity that the question itself is the same.)
– mins
Sep 9 '21 at 17:08

TLDR: No viscosity -> no friction, no friction -> no boundary layer, and no boundary layer -> no pressure difference, no pressure difference -> no lift.

Let's start here though, an excerpt from some NASA educational material.

Aerodynamic forces depend in a complex way on the viscosity of the gas. As an object moves through a gas, the gas molecules stick to the surface. This creates a layer of air near the surface, called a boundary layer, which, in effect, changes the shape of the object. The flow of gas reacts to the edge of the boundary layer as if it was the physical surface of the object. (grc.nasa.gov)

The viscosity - its friction, stickiness, and compressibility, is what gives us the boundary layer on our airfoil.

ok

If we dive deep into the lift and drag, we will at some point meet viscosity with the Reynolds number.

Reynolds number is defined as

$$\text{Re} = \frac{r \times V \times L}{\mu}$$

Where $$\mu$$ is the viscosity of our gas.

First of all, with a viscosity of 0, our equation would fail us already since you can't divide with 0. We'll just go ahead and say our viscosity is really small then.

Dividing anything with a really small number, will give us a really big number as a result.

I found this to describe what happens aerodynamically with really high Reynolds numbers:

Image from (eng.cam.ac.uk)

If we take a look at 8.5, we see that our boundary layer becomes turbulent before the equator, and we don't see flow separation until we reach the back side of the ball.

This is with a Reynolds number at 200000 (so there's still some viscosity)

This looks great for our theory of lift without viscous air! higher Reynolds number = less drag!

While this is true, it doesn't necessarily mean our lift is getting any better because of this reduced drag.

The problem we run into, is pressure. We need pressure to build lift. If there is no friction, our air molecules won't stay around long enough for us to build pressure.

With no viscosity, we have no friction, and with no friction, we have no boundary layer, and no pressure buildup.

What generates lift (according to Bernoulli) is the difference in pressure over the wing, compared to under the wing. With no friction, we won't be able to achieve this.

There is no lift without viscosity

Extra

Just after finishing this answer, i found this paper (researchgate.net) Titled: the Explicit Role of Viscosity in Generating Lift. In their conclusion they state:

The formal expression for the fluid-mechanical force (or aerodynamic force) of a body in an incompressible viscous flow is given, which explicitly elucidates the critical role of the fluid viscosity in generating the force (the lift particularly)

and

the vortex lift is evaluated as the consequence of the viscous boundary layer

• So in potential flow, which assumes an inviscid fluid, lift is impossible? That is not in agreement with a lot of well established software. Sep 8 '21 at 20:13
• @PeterKämpf I am gonna refer you to the top answer in this physics stack by tpg2114, its introduction and conclusion. physics.stackexchange.com/questions/46131/… And to quote Vladimir F from the comments: The overall answer is, no, it does not. Or it does not have to. Unless you introduce the circulation by some additional means and then it can have any lift depending on the amount of circulation introduced. "no viscosity" is an artificial thing, but so is irotational potential flow. Sep 8 '21 at 21:15
• @PeterKämpf, doesn't all that software enforce the trailing stagnation point to the trailing edge (which is the one thing that wouldn't be defined without viscosity)? Sep 8 '21 at 21:24
• The argument that you cannot generate a pressure difference without a boundary layer doesn't make much sense. Unfortunately as with most theoretical aerodynamics, there is not a simple cause & effect relationship - flow stays attached because there is circulation induced by the shape of the airfoil and a pressure field that causes the flow to bend around the airfoil. None of this can be seperated from the other, these are all just human invented ways of explaining something very complex. Sep 9 '21 at 3:43
• @JanHudec That is exactly right. The Kutta condition needs to be enforced to get the correct lift. However, of all rear stagnation point positions there is only a single one which does not involve lift. All others produce some lift, albeit one that does not fit to viscous reality. Sep 9 '21 at 8:07

TL;DR: Inviscid flow is not physical, however theoretical inviscid flow can still flow around a streamlined body (such as a wing) and it will produce lift.

There is no such thing as zero viscosity, so all we can use to answer your question is theory.

In the theory, there is "inviscid flow", and it's an extremely useful tool we very commonly use to explore preliminary designs, especially high Reynolds number flows where the viscous effects are far outweighed by the inertial effects. Essentially inviscid flow isn't some special case, it is just flow with an infinite Reynolds number. If you increase Reynolds number further and further, the flowfield changes less and less. It is not crazy to think that this converges are Re approaches infinity.

Before CFD and all the complicated ways of modelling fluids existed, physicists used Potential flow to model theoretical flow. Potential flow follows all the same behaviour as real flow, except it does not account for viscosity. It's impressive how many geometries were modelled by combining sources, sinks, vortices, and doublets. One of the simplest and most famous examples is the Zhukovski/Joukowsky (depending on your textbook!) airfoil, which is a simple doubled (source + sink) with a vortex. The vortex induces circulation in the fluid and gives the airfoil it's cambered shape. Because the vortex induces circulation in the fluid, it generates lift (Kutta-Joukowski Theorem).

The common misconception is there has to be some viscosity to "hold" the fluid together or "stick" it to the surface. In fact, the opposite is true: the fluid cannot detach from the surface because there is nothing to fill in the void. This can easily be seen when using an inviscid flow solver such as JavaFoil - try increasing the angle of attack more and more, and the flow never separates.

Even very sharp corners will keep attached (unless the Kutta condition is explicitly applied). The force required to turn the flow around a sharp corner is "reacted" by the force felt by the surface that is turning the flow, the flow direction bends towards the surface, and the surface feels an upwards pressure - essentially Newton's Third Law. This pressure reduces further away from the wall, and so does the amount of turning on the flow. This should hopefully explain how flow can remain attached to a surface as it bends away from the flow.

When modelling inviscid flow, you must be careful not to take the results as physical. Seperation will never be predicted, even with add-on Boundary Layer models.

Hopefully this makes enough sense, but please feel free to ask for clarification on anything.

• Thanks @mins. What do you think needs elaboration? Yes there will be flow across the wing, and that will produce a pressure difference (plus acceleration/deceleration) and therefore a lifting force. I'm happy to provide further details where you think. Sep 9 '21 at 21:23
• Stuart, actually when I read again your answer I find it talks about everything needed, for some reason I misread it the first time and focused on the KJ solver part, but I see you talk about viscosity not required to maintain the flow against the airfoil, which is I think the main point of controversy, and you also emphasized that it's a misconception. The only thing to add, would be a superfluid airfoil experiment, but I guess that will be difficult! So +1, and more if I could, and I apologize for the first comment. I hope the question will be re-opened.
– mins
Sep 9 '21 at 22:39
• Finally I found something related to lift in superfluid which contradicts the original thesis of non-lifting superfluid helium.
– mins
Sep 9 '21 at 22:52
• @mins glad you found it useful - I'm always happy to try and communicate clearer. That paper you found is fascinating. Very interesting that they use the Zhukovski airfoil so as to get a direct comparison with the closed form potential flow solution. Thank you for sharing it! Sep 9 '21 at 23:39
• Awesome paper! Question though, doesn't the kutta joukowski theorem only concern 2D potential flow? There's a great leap between 2D flow and 3D flow. I feel like the answer to this question is very double sided. Sep 10 '21 at 7:08