Lecture 3

Question 1

Are solutions of the Mach-Area-Relation unique?

Answer 1

No, there are different for subsonic and supersonic flow.

Subsonic flow: If A increase M decrease, and the other way.

Supersonic flow: Exactly the opposite; A and M goes in the same direction.

All of these is just to maintain the mass flow density constant through the nozzle, as we have seen it should be.

Question 2

Why is there a kink in the state distribution for a certain back pressure?

Answer 2

Because we reach critical conditions. This mean, M=1 in the throat, not being possible Mach to be higher and therefore the pressure to be lower. At least with this theory.

Question 3

Why is total temperature constant across a steady normal shock?

Answer 3

Because of Total Entalpy H conservation

Question 4

How do static and total quantities vary across a normal shock?

Answer 4

We can see them in page 15 (learn them by heart). But basically:

Static quantities: All of them increase except velocity and Mach.

Total quantities: Pressure and density are smaller, and the rest constant.

The critical quantities are reduced, except T and c; they are the same.

Question 5

Sketch the pressure distribution for subsonic and ideally adapted supersonic flow

Answer 5

It just that it decreases exponentially until reaching 0 when M&raquo_space; 1.

Page 16

Question 6

Explain the idea of normal shock solutions in a subsonic nozzle

Answer 6

Explain them with what I’ve done in paper.

Question 7

Why do all transonic nozzle flows feature the same mass flow (for given p0, T0)

Answer 7

Once M=1 at the critical cross section, it’s impossible to increase the mass flow through a nozzle by just reducing the back pressure.

If you would like to increase the mass flow for a chock-nozzle (it means, it reaches M=1 at the throat), you would need to increase the Area at the throat, or the total pressure.

Question 8

Why is our theory not sufficient for explanation of all possible back pressures?

Answer 8

Some of these require more complicated objects, which are not representable by quasi 1D explanations. We would need 2D objects inside the nozzle, or multi dimensional expansions after the nozzle.

Question 9

Explain the relations between de Area and Mach, for subsonic and supersonic flows

Answer 9

Slide 7

But basically, in subsonic flows it’s the logical way for m_dor = const. For supersonic exactly the opposite (Area and Mach go together)

Question 10

What’s the Prandtl’s shock relation?

Answer 10

M* * M*_hat = 1

M: Critical Mach number before the shock
M_hat: Critical Mach number after the shock