Compressible Inviscid Flow 8 - Normal Shock Waves and Pitot Tubes

Question 1

Examples of when normal shock can occur

Answer 1

In front of a blunt body
In a converging-diverging nozzle
On transonic aircraft wings

Question 2

How are supersonic flow and shock waves shown by Schlieren imaging?

Answer 2

Criss-cross lines in image caused by roughness and effects on walls
Shock wave forms at front of supersonic flow and past this the flow is subsonic

Question 3

Shock in external flow (e.g. around a cube)

Answer 3

Shock forms ahead of body in a supersonic air stream
Flow behind the front, near normal shock, is subsonic
As flow expands passing the corner of the body, it speeds up to supersonic again and an oblique shock forms on the side of the body

Question 4

Which conservation laws can be used across a shock?

Answer 4

1D conservation laws are still valid (i.e. continuity, momentum and adiabatic energy equations)

Question 5

Properties upstream and downstream of shocks

Answer 5

Downstream properties are functions of M1 only (shows influence of Mach number in compressible flow)
Temperature, density, pressure and entropy increase
Velocity and Mach number decrease
M2 is always subsonic for normal shocks
Total pressure decreases
Total temperature remains the same across normal shock (adiabatic)

Question 6

Normal shock properties

Answer 6

Upstream flow is supersonic, downstream flow is subsonic
Entropy increases across a shock, total pressure and total density decrease and total temperature remains the same
Rarefaction (expansion) shocks are not possible due to second law of thermodynamics, as this would lead to entropy reduction

Question 7

How is velocity measured in compressible flow on an aircraft?

Answer 7

Pitot tubes measure air speed