Why do air foils produce lift?

[boneh3ad]

Assuming th flow is steady then there is going to be no drag (see D'Alembert's Paradox). If there is an unsteady component then drag is nonzero.

 

[rcgldr]

Assuming th flow is steady then there is going to be no drag (see D'Alembert's Paradox). If there is an unsteady component then drag is nonzero.

The paradox could be indicating an issue with the assumptions made about the flow. I'm not sure why a possible outcome of a an object flowing through a super fluid couldn't be a head and/or tail of super fluid that simply flows along with the object, rather than flowing around the object as it flows through the surrounding super-fluid. With zero viscosity, it's not clear what the path of least resistance would be for the fluid that the moving object collides with.

 

[boneh3ad]

With zero viscosity the system is entirely conservative and in a steady flow, the air parcels would end up exactly where they started before the object passed through. The only assumptions made in deriving D'Alembert's paradox are inviscid, incompressible and steady flow. All of these are met in the above example involving a perfect superfluid. It was called a paradox because, at the time of its discovery, potential flow was the state of the art in fluid mechanics analysis and the results were not in line with reality.

A superfluid is one with, among other things, zero viscosity. Without viscosity there is no way for a passing object to drag fluid along with it. Instead it just neatly pushes the fluid out of the way and, given the potential nature of the system, the fluid then neatly falls back into place where it started.

Flows in fluids with zero viscosity are very well-studied phenomena. Many, many books have been written on the subject and the mathematics are straightforward. Most if not all of the books discuss this very phenomenon.

 

[rcgldr]

A superfluid is one with, among other things, zero viscosity. Without viscosity there is no way for a passing object to drag fluid along with it. Instead it just neatly pushes the fluid out of the way and, given the potential nature of the system, the fluid then neatly falls back into place where it started.

Take the case of a flat plate moving through a super fluid. Why would there be any more of a tendency for the fluid to flow around the plate, as opposed to some portion of the fluid simply moving along with the plate?

 

[boneh3ad]

On the contrary, why woul it move with the plate. Even with viscosity it wouldn't. Shoot a hose at an inclined plate and water won't tend to build up, it will just be deflected.

 

[rcgldr]

Take the case of a flat plate moving through a super fluid. Why would there be any more of a tendency for the fluid to flow around the plate, as opposed to some portion of the fluid simply moving along with the plate?

On the contrary, why would it move with the plate?

Since there's no viscosity, there's no "friction" or interaction with the surrounding fluid to prevent some volume of fluid from simply traveling along with the plate, potentially creating relatively large "stagnation" zones in front of and behind the plate.

Say there's a frictionless hollow cylinder with a cross sectional flat plate in the middle of the cylinder, and that the cylinder is moving within a super fluid. I'm assuming that within the cylinder, there's a 1/2 cylinder of fluid fore and aft of the plate. Now stop frictionless cylinder, but allow the place to continue onwards at the same initial velocity. The only effects on the fluid before and after the plate is related to momentum, not viscosity. Over time would these "stagnations" zones eventually vanish?

 

[Aero51]

The shape of the airfoil changes the molecular velocity distribution such that a mean pressure gradient is produced generating lift

 

[A.T.]

Over time would these "stagnations" zones eventually vanish?

No, there are stagnation zones in potential flow. But you have stagnation in front and behind the object, so no pressure difference between front and back and no net force:

http://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder

 

[boneh3ad]

I am having trouble picturing what you describe but regardless, what you describe is an unsteady flow and thus not applicable here.

There would not be any sort of buildup of "stagnation zone". There would still be one upstream and one downstream stagnation point (or possibly line in 3 dimensions) and everywhere else the fluid would just slide conservatively over the surface without sticking.