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Incompressible Flow > Chapter 5 > Flashcards

Chapter 5 Flashcards

1
Q

Dimensionally speaking, what is the difference between an airfoil and a finite wing.

A

An airfoil has 2D geometry while a finite wing has 3D geometry.

Ref: Anderson Pg. 427

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2
Q

How do tip vortices affect streamlines above and below the wing?

A

The streamlines on the top are pushed toward the root while the streamlines on the bottom are pulled toward the tips.

Ref: Anderson Pg. 428

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3
Q

What is the equation for the effective angle of attack?

A

alpha_eff = alpha - alpha_induced

Ref: Anderson Pg. 429

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4
Q

Does d’Alembert’s paradox occur for a finite wing? Why or why not?

A

No, the reason is that drag (induced) is predicted by inviscid incompressible theory.

Ref: Anderson Pg. 430

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5
Q

Can induced drag be considered a type of pressure drag?

A

Yes

Ref: Anderson Pg. 430

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6
Q

The total drag is a combination of what?

A

Induced drag, skin friction drag, and pressure drag (due to flow separation).

Ref: Anderson Pg. 431

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7
Q

What components of the total drag are due to viscous effects? What is the common name of the sum of these two drag components?

A

Skin friction drag and pressure drag.
Profile Drag

Ref: Anderson Pg 431

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8
Q

True or False

If the circulation is taken about any path enclosing a vortex filament, a constant value of circulation is attained.

A

True

Ref: Anderson Pg. 432

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9
Q

What are the three Helmholtz vortex theorems?

A
  1. The strength of a vortex filament is constant along its length.
  2. A vortex filament cannot end in a fluid; it must extend to the boundaries of the fluid (which can be +/- infinity) or form a closed path.
  3. A fluid that is initially rotational remains rotational and vv unless non-conservative forces act.

Ref: Anderson Pg 435

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10
Q

Define washout with respect to geometric twist.

A

The tip is at a lower geometric angle of attack than the root.

Ref: Anderson Pg. 435

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11
Q

Define washin with respect to geometric twist.

A

The tip is at a higher geometric angle of attack than the root.

Ref: Anderson Pg. 435

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12
Q

True or False

For a finite wing, the lift distribution will b zero at the tips.

A

True

Ref: Anderson Pg. 435

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13
Q

What is the difference between a bound vortex and a free vortex?

A

A bound vortex is fixed to a geometric body while a free vortex moves with the same fluid elements throughout a flow.

Ref: Anderson Pg. 436

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14
Q

Give the equation for lift from the Kutta-Joukowski (KJ) theorem.

A

L’=rho_infifnityV_infinityGamma

Ref: Anderson Pg. 440

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15
Q

True or False

A vortex filament can end in a fluid.

A

False

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16
Q

Describe the “lifting line.”

A

A line upon which a large number of horseshoe vortices, each with a different length of the bound vortex, but with all the bound vortices are coincident.

17
Q

For an infinite number of horseshoe vortices along a lifting line, what is the total strength of the sheet integrated across the span?

A

Zero.

Ref: Anderson Pg. 438

18
Q

What is the effective angle of attack?

A

The angle of attack actually seen by the local airfoil section.

19
Q

Is the effective angle of attack a variable? Why?

A

Yes. Since downwash varies across the span, the effective angle of attack varies with span unless the wing is elliptic.

20
Q

When will the angle of attack at zero lift be a variable?

A

When there is aerodynamic twist.

Ref: Anderson Pg. 440

21
Q

When will the angle of attack at zero lift be constant?

A

When there is no aerodynamics twist in the wing.

Ref: Anderson Pg. 440

22
Q

For an elliptic wing what two properties are constant with respect to the chord?

A

Downwash and induced angle of attack.

Ref: Anderson Pg. 443

23
Q

The induced drag coefficient for an elliptic wing is directly proportional to what other important parameter? Inversely proportional to what other parameter?

A

Directly: C_L^2
Inversely: A_R (aspect ratio)

Ref: Anderson Pg. 444

24
Q

The power required from an aircraft engine to overcome the induced drag is ______.

A

The same power required to generate the lift of the aircraft.

Ref: Anderson Pg. 445

25
Q

To reduce induced drag, what should be done to the aspect ratio?

A

Make it as high as possible (see eq 5.43 in the book)

Ref: Anderson Pg. 445

26
Q

In order for a lift distribution to be elliptical, what must the platform of the wing look like?

A

An ellipse.

Ref: Anderson Pg. 446

27
Q

What is the difference between geometric twist and aerodynamic twist?

A

Geometric twist changes the geometric angle of attack through a geometric in-wash or out-wash. Aerodynamic twist occurs then the angle of attack at zero lift changes as a function of span (due to chamber change).

Ref: Anderson Pg. 446

28
Q

Important!

How does the lift slope of a finite wing compare to an airfoil?

A

The airfoil’s lift slope is higher than the finite wing. The difference is due to induced drag.

Ref: Anderson Pg. 454

29
Q

For an elliptic wing with no geometric twist what factors are constant?

A
  1. Induced angle of attack
  2. effective angle of attack
  3. c_l
  4. C_L

Ref: Anderson Pg. 454

30
Q

For an elliptic wing with no geometric twist, is the local lift coefficient (c_l) equal, greater, or less than the total lift coefficient (C_L)?

A

Equal.

Ref: Anderson Pg. 454

31
Q

At zero lift what values do the induced angle of attack and induced drag ratio take on?

A

Zero.

Ref: Anderson Pg. 454

32
Q

In what scenario will the angle of attack at zero lift be the same for both an airfoil and a finite wing?

A

When C_L=0 and the geometric angle of attack (alpha) is equal to the effective angle of attack (alpha_eff).

Ref: Anderson Pg. 454

33
Q

As the aspect ratio approaches infinity, what happens to the lift slopes for the airfoil and finite wing?

A

They start to become equal.

Ref: Anderson Pg. 456

34
Q

What actually induces downwash at the lifting line? The lifting line itself or the trailing vortex sheet?

A

The trailing vortex sheet.

Ref: Anderson Pg. 457

35
Q

Can a discontinuous change in tangential velocity theoretically cross a vortex sheet? In real life, do such discontinuities exist?

A

Yes
No

Ref: Anderson Pg. 457

36
Q

What lift distribution yields a minimum induced drag?

A

Elliptic

Ref: Anderson Pg. 449

37
Q

Define the taper ratio:

A

TR = ct/cr

Ref: Anderson Pg 450

38
Q

A plot of the lift coefficient vs the drag coefficient is called the_____.

A

Drag Polar.

Ref: Anderson Pg 452

Incompressible Flow (6 decks)

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