Explanation for moving fluids having lower pressure

[Aero51]

Once again, I ask you: were the lift coefficients using the reference area of the clean wing? If so, those numbers do sound completely achievable. In many cases, the reference area is kept fixed for a given aircraft (to reduce the number of variables), and then the Cl is calculated based on the clean wing reference area, even in the presence of high-lift devices (even though high-lift devices frequently increase the wing's area, sometimes dramatically, as is the case with the Boeing 727 seen here or the Boeing 747 seen here). This method is completely mathematically valid, and even allows for slightly more intuitive treatment of the aircraft's behavior, but it also makes your derivation wrong (since the actual area the pressure is acting over is different than the reference area used for deriving the coefficient of lift).

They were calculated using the clean wing configuration as a reference area. You raise a good point noting that the wing area will change and thereby reduce the lift coefficient. In that case the velocities above and below the wing may not change so drastically and do seem plausible.

As for safety requirements for emergency landings? Those don't necessarily require a high Cl - they require the right combination of Cl, wing area, and acceptable landing speed. Modern airliners are actually going towards simpler high lift devices, along with lower Clmax values because modern airfoils perform much better at high speed, allowing for a larger wing area, higher aspect ratio, and less sweep for a given cruise speed. This increase in wing area and aspect ratio allows for lower landing and takeoff speeds without needing dramatic high lift devices, which allows for a simpler mechanical design as well.

In the paper I mentioned above there is an illustration showing how much wing area would be required if an aircraft did not employ high lift devices. It seems counter intuitive that aerospace companies would want larger wings because this will result in an increase of material cost, drag and weight. If the wing area is reduced, on the other hand, all a company has to lose is fuel volume. Also, I believe it is safe to assume that safety requirements will call for a higher CL. For example, in a case when a full loaded airliner has to make an emergency landing the aircraft must reduce its speed significantly - the increase in wing area due to the flaps being deflected is not sufficient to account for the new speed. I would also argue that increasing the aspect ratio will increase the likelyhood of stall and weight. As you said, it comes down to design optimization

 

[boneh3ad]

I also believe my statement about slight separation on most airfoils is a fair generalization (even if it is negligible for practical calculations) because total pressure is never fully recovered on a wing.

Total pressure if never recovered in any situation with a boundary layer or any other viscous phenomena so your point is moot. This has nothing necessarily to do with separation (though it can) since it happens even on an unseparated airfoil due to viscous dissipation.

A true stagnation point does not exist at the trailing edge. The argument you made about lift being dictated by the boundary layer, pressure distribution and angle of attack is somewhat trivial because those facts are true for anything that generates lift - even a brick.

It isn't trivial at all. You can't make such generalizations because the separation phenomenon is much more involved than the shape simply being an airfoil, which is effectively what you have suggested though not expressly stated. In fact, I routinely work with airfoils that do not experience separation until fairly large angles of attack. That alone disproves your assertion that any airfoil has some degree of separation. It doesn't.

The Kutta condition does not apply to real flows - it can neither be satisfied nor unsatisfied. In theory introducing viscosity into the model will accurately predict the flow pattern.

I already agreed with cjl by stating that the Kutta condition is a mathematical boundary condition based on observation.

However, you also said this:

The Kutta condition, to be exact, is a mathematical boundary condition based on empirical observation for nonviscus flows.

That is false. You can't even have empirical observations of an inviscid flow because such a flow does not exist in any situation that would lead to the development of the Kutta condition. The only truly and globally inviscid flow is a uniform free stream. The Kutta condition is, mathematically, a boundary condition used to rectify inviscid computations with the viscous reality. Of course, the Kutta condition itself applies to viscous flow because originally it was just the statement that "A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge." It is satisfied by default in a viscous flow and need not be independently enforced, but that does not mean that it does not apply to viscous flows, after all, without viscosity there would be no Kutta condition.

Also, your point about the velocity at the peak of the cylinder being twice the freestream flow is invalid because the discussion pertains to differences between the upper and lower surfaces of a wing. The difference in velocities for the case you described is 0 and no lift is generated. I used the freestream flow as the flow speed on the lower surface purely for simplicity.

If you didn't mean the free stream, then don't say the free stream. Regardless, the principle remains the same. Bernoulli does not physically explain lift, but that doesn't mean that you can't have the flow moving twice as fast over the upper surface of the wing than it is over the bottom surface. In fact, in just about 5 min of playing around with a simple Euler solver that NASA has available online can show situations where the flow moves 4 times as fast over the top compared to over the bottom. Camber the airfoil a bit and you can see the effect if you tell it to plot velocity.

 

[Aero51]

Sorry for the belated response. I recently moved about 400 miles from my old home and it took me about week to get things settled. Anyway, on to "business".

Total pressure if never recovered in any situation with a boundary layer or any other viscous phenomena so your point is moot. This has nothing necessarily to do with separation (though it can) since it happens even on an unseparated airfoil due to viscous dissipation.

You make a good point, total pressure is not recovered in stokes flow, but there is no separation. I believe in the context of your typical airfoil flow regime (RE>=10^6) there is always a little bit of separation at the trailing edge. I found a video on youtube showing this effect, though I can't find it now.

That is false. You can't even have empirical observations of an inviscid flow because such a flow does not exist in any situation that would lead to the development of the Kutta condition. The only truly and globally inviscid flow is a uniform free stream. The Kutta condition is, mathematically, a boundary condition used to rectify inviscid computations with the viscous reality. Of course, the Kutta condition itself applies to viscous flow because originally it was just the statement that "A body with a sharp trailing edge which is moving through a fluid will create about itself a circulation of sufficient strength to hold the rear stagnation point at the trailing edge." It is satisfied by default in a viscous flow and need not be independently enforced, but that does not mean that it does not apply to viscous flows, after all, without viscosity there would be no Kutta condition.

Quite frankly I think this argument is becoming too philosophical and less scientific.

 

[Aero51]

Plus, I tried the Euler Solver. I got flow speeds about 4.5 x as fast between the top and the bottom surfaces. These points were inside the boundary layer though (the program uses Zhukovski transformations), so the difference between the top/bottom is probably slightly less. I also noticed that the flow below the surface was also less than the freestream velocity, invalidating one of the assumptions I made in the equation I wrote earlier.