Lecture 8

Question 1

What does “homentropic” mean and is it identical to “isentropic”?

Answer 1

No

Homentropic: Entropy is constant within the whole field
Isentropic: Entropy is constant within streamlines

Question 2

What’s a really important condition for having an homentropic and isoenergetic flow?
What does these terms mean?

Answer 2

Homentropic: s is constant in the whole domain.
Isoenergetic: Enthalpy is constant in the whole domain.

Condition: M>1

Question 3

For small disturbances, how is the module of the velocity related to the horizontal velocity?

Answer 3

Same

Question 4

Equation for the pressure coeficient around the reference state?
With and without simplification

Answer 4

cp = (p-p_inf)/(0.5pho_infu_inf^2) = -2*(delta_u/u_inf)

Question 5

What does „isoenergetic“ mean?

Answer 5

The total enthalpy is constant within the whole field

Question 6

How is the Mach angle defined?

Answer 6

sin(alpha) = 1/M

alpha: Mach angle

Question 7

Give the formulas for linearized characteristic quantities and curves?

Answer 7

In the papers

Question 8

Can we apply this theory to subsonic flow regions?

Answer 8

No

A lot of equations and quantities are only applicable when M is 1 or higher

Question 9

How do compressions and expansions turn the flow?
Give the equations of u and cp as a function of theta

Answer 9

Expansions: Increase the relative angle
Compressions: Decrease the relative angle

Equations in the papers

Question 10

When obtaining the eigenvalues of the matrix C for the 2D Euler Equations, what do represent them?
Which are the 2 important values/angles that we can obtain from them?

Answer 10

They represent the characteristic velocities of the system.

tan(theta) = v/u: Local flow angle
sin(alpha) = 1/M: Mach angle