Airfoil drag prediction in incompressible and inviscid flow

[lordvon]

What is the most elegant way of predicting drag on an airfoil in inviscid and incompressible flow? Or is this still an open problem?

It seems like the consensus for airfoils in incompressible and inviscid flow is that they cannot produce drag; or at least, we are not able to predict it elegantly. I think some people even believe that you simply cannot have drag in inviscid flow. Thin Airfoil Theory and Vortex Panel Methods predict zero drag. Wake momentum thickness approach (e.g. XFOIL) estimates drag by using (I think) control volumes and the airfoil wake flow field, but it does not seem like an elegant approach, and is much more complicated than computing lift.

I devised a physics model that predicts drag in an elegant way, as easy as lift, and matches almost exactly with NACA airfoil experimental data (before stall, of course). I am having a hard time believing no one else thought of this, so I am suspicious that something is wrong with my method or I missed it in literature.

 

[boneh3ad]

Inviscid flow? What drag? Inviscid flows are subject to D'Alembert's paradox, which predicts zero drag. This isn't an issue of inelegant modeling, but an issue of simply not capturing the relevant physics leading to drag when inviscid flow is assumed. In inviscid models that do predict drag, there has to have been some kind of modeling done internally that simulates the effects of viscosity on some level in order to predict drag.

Now, all of that said, drag is still incredibly difficult to predict. Even full CFD simulations have a difficult time getting accurate results, in large part because of the inherent dependence on the differences between laminar and turbulent boundary layers and the fact that predicting that transition is effectively impossible with current understanding, and simulating the full range of scales in a fully-turbulent boundary layer is computationally expensive.

 

[lordvon]

Thanks for your reply!

I am actually not sure D'Alembert's paradox should really be a "paradox" for a non-lifting body. As idealized as inviscid and incompressible flow is, why should we be surprised that there is no drag on a non-lifting body? We know plainly that including unsteadiness and viscosity can result in drag. As an analogy, is it paradoxical that gravity alone cannot predict a terminal velocity? It is plain to see that fluid resistance causes terminal velocity.

However, I do believe that for a lifting body, drag should be produced, and there is indeed additional physics missing from Thin Airfoil Theory and Vortex Panel Methods. What you say is extremely interesting, because a lot of people believe it -- that there can be no drag without viscosity. However, conservation of momentum must hold for fluid flow -- viscous or not. I believe there is much confusion about what drag is at a fundamental level.

My intuition was that we shouldn't need Navier-Stokes CFD (or empirical wake momentum thickness methods) to see any drag at all. Sure, drag (and lift) can be sensitive to turbulence and such, but drag is more fundamental than that level of physics, just like lift. It should be calculable in our inviscid and incompressible flow models.

This absence of an elegant explanation for drag (especially since lift is relatively easily calculated) has actually bothered me for a long time, and I finally came up with an elegant model that almost exactly matches NACA airfoil data up until stall. I just wanted to confirm that no such explanation already exists.