Incompressible Flow over Airfoils Questions and Answers

Answer: A

Correct answer: The same lift coefficient at the same angle of attack

This is what dynamic similarity means. Geometrically similar shapes at the same Reynolds number, angle of attack and Mach number have identical non-dimensional flow fields and therefore identical coefficients. The forces themselves will differ, because they scale with dynamic pressure and area - which is exactly why wind tunnel testing on a small model is useful at all.

Answer: B

For a two-dimensional section there are no tip vortices and no shocks at low speed, so the only contributions are friction and the pressure drag arising from boundary layer displacement. Induced and wave drag belong to finite wings and high speed respectively.

Answer: C

Correct answer: Induced drag

Induced drag is the price of generating lift on a finite wing, and it arises from the trailing vortices shed at the tips. A two-dimensional section has no tips and no trailing vortex system, so it has no induced drag. Its drag is entirely profile drag: skin friction plus the pressure drag arising from the boundary layer and any separation.

Answer: D

Correct answer: Increases skin friction but delays separation

A turbulent boundary layer mixes high-momentum fluid down toward the wall, which raises the wall shear stress and hence the friction drag, but also gives the layer more momentum to carry it against an adverse pressure gradient. The trade is often worth making, and it is exactly why golf balls are dimpled and why vortex generators are fitted.

Answer: A

Correct answer: Separates and then reattaches further downstream

A laminar boundary layer can separate under an adverse gradient, become turbulent in the free shear layer above the surface, and then reattach because the now turbulent layer carries more momentum. The enclosed region is the separation bubble. Short bubbles are largely benign, but a bubble that bursts and fails to reattach produces an abrupt leading edge stall.

Answer: B

Correct answer: A reduced maximum lift coefficient and a higher stall speed

Ice roughens and reshapes the leading edge, thickening the boundary layer and provoking early separation. Maximum lift falls, sometimes by thirty per cent or more, and the stall occurs at a lower angle of attack, so the stalling speed rises - often without the usual buffet warning. The aerodynamic penalty far outweighs the added weight.

Answer: C

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason gives the mechanism. At higher Reynolds number the boundary layer is thinner relative to the chord and more likely to be turbulent, so it carries more momentum near the wall and resists the adverse gradient better. A low Reynolds number model therefore separates earlier and shows a lower maximum lift than the full-size wing will achieve.

Answer: D

Correct answer: Both A and R are true, and R is the correct explanation of A

Both are true and the reason is the explanation - this is d’Alembert’s paradox. With no viscosity there is no boundary layer, so the flow follows the surface all the way round and the pressure recovered over the rear exactly balances that acting on the front, leaving zero net force along the flow. Real drag exists only because viscosity spoils that recovery.

Answer: A

Correct answer: 1 and 2 only

Statements 1 and 2 are the two components of profile drag: direct skin friction, and the pressure drag that arises because the boundary layer displaces the outer flow and prevents full pressure recovery. Statement 3 is wrong - profile drag is a minimum near the zero-lift angle but never vanishes, since the air is still flowing over the surface.

Answer: B

Correct answer: 100

\[ \frac{l}{d} = \frac{c_l}{c_d} = \frac{0.8}{0.008} = 100. \] Section lift-to-drag ratios of this order are ordinary, because a two-dimensional section has no induced drag. A complete aircraft does far worse - fifteen to twenty for a transport - and almost all of the difference is induced drag and the drag of everything that is not the wing.