Lecture 8 - Momentum injection and wake control

Question 1

What is the kelvin theorem?

Answer 1

The circulation around a closed curve consisting of the same fluid elements remains constant as the fluid elements move through the flow.

Question 2

When does the kelvin theorem not hold?

Answer 2

In cases with viscous stresses,
non-conservative body forces (for example a Coriolis force)
or non-barotropic pressure-density relations

Question 3

Describe the explanation for the drag crisis.

Answer 3

1. At high speed, the boundary layer become turbulent. For a smooth sphere, this happens
   at a Reynolds number of about 250 000.
2. The turbulence mixes fast-moving air outside the boundary layer into the slow air of the
   boundary layer, thereby speeding it up.
3. The air in the boundary layer can therefore resist the high-pressure air from behind the
   ball for longer, and boundary-layer separation occurs farther downwind.
4. The low-pressure trailing wake is therefore narrower, reducing drag

Question 4

How do birds do adaptive shape change and dynamic lift creation

Answer 4

variable sweepback of the wings
variable angle of attack across the span
controlled variable camber
changeable curvature of the wing in the chordwise direction
variable wing tip control with feathers deflected downward

Question 5

mechanisms of biological drag reduction?

Answer 5

Streamlining
Flow splitters
Surface micro-structure
Effects on viscosity
(surface heating)
Momentum injection
Adaptive shape change