Compressible airflow

Question 1

What is ‘critical point’?

Answer 1

The intercept at which the speed of airflow (v) is equal to the speed of sound (a), where the Mach number = 1.

Question 2

What is the temperature at the critical point called?

Answer 2

Critical temperature (Tc).

Question 3

What is the speed coefficient (M*) the ratio of? What does it represent?

Answer 3

• The ratio of the speed of the air to the critical speed of sound. M* = v/ac
• M* can be used as a representation of M to indicate if the airflow is subsonic or supersonic.

Question 4

Does the critical speed of sound change with speed along the flow stream?

Answer 4

No.

Question 5

When M* = 1, what does it indicate? Note, also answer it properly from the book (e.g. using equations)

Answer 5

When the speed coefficient (M*=1), it indicates that the flow is sonic, M = 1, the flow is sonic.

Question 6

When M* < 1 what does it indicate? Note, also answer it properly from the book (e.g. using equations)

Answer 6

When the speed coefficient M*<1, it indicates the flow is subsonic, the airflow definitely is subsonic because M

Question 7

When M* > 1 what does it indicate? Note, also answer it properly from the book (e.g. using equations)

Answer 7

When the speed coefficient indicates flow is supersonic M>1, the airflow definitely is supersonic because M>M>1.

Question 8

Examining a subsonic airflow (using equations), what happens to speed and pressure when area decreases? What is the airflow state in? (refer to nozzles etc).

Answer 8

• dA/A = (M^2 - 1)*dv/v, where M < 1 and (M^2 - 1) < 0, and (1 M^2) > 0, and dA/A = (1-M^2 / γM^2) * dp/p
• Using the equations above, it shows that if the change of area of flow is negative (decreasing area).
• Change in speed will be positive (increasing speed).
• Change in pressure will be negative (decreasing pressure).
• The airflow is in a converging nozzle.

Question 9

What happens to dA/A when M = 1?

Answer 9

dA = 0, A reaches its minimum, so the speed of sound if the maximum speed the convergent nozzle can achieve.

Question 10

Examining a subsonic airflow (using equations), what happens to speed and pressure when area increases? What is the airflow state in? (refer to nozzles etc).

Answer 10

• Using dA/A = (M^2 - 1)*dv/v and dA/A = (1-M^2 / γM^2) * dp/p.
• When dA/A > 0, i.e. change of area is positive, the change in speed will be negative (decreasing speed).
• Change in pressure will be positive (increasing pressure).
• The airflow is in a “diffusor”.

Question 11

Examining a supersonic airflow (using equations), what happens to speed and pressure when area increases? What is the airflow state in? (refer to nozzles etc).

Answer 11

• Using dA/A = (M^2 - 1)*dv/v and dA/A = (1-M^2 / γM^2) * dp/p. Where M > 1, (M^2 - 1) > 0 and (1 - M^2) < 0.
• Using the above equations, if the change in area of flow path is positive (dA > 0) (increasing area):
• The change in speed will be positive (increasing speed).
• The change in pressure will be negative (decreasing pressure).
• The airflow is in a diverging nozzle.

Question 12

Examining a supersonic airflow (using equations), what happens to speed and pressure when area decreases? What is the airflow state in? (refer to nozzles etc).

Answer 12

• Using dA/A = (M^2 - 1)*dv/v and dA/A = (1-M^2 / γM^2) * dp/p. Where M > 1, (M^2 - 1) > 0 and (1 - M^2) < 0.
• Using the above equations, if the change in area of flow path is negative (dA < 0) (decreasing area):
• The change in speed will be negative (decreasing speed).
• The change in pressure will be positive (increasing pressure).
• Air flow is in a ‘diffusor’.

Question 13

From the inlet to the throat, what happens to area, airspeed and pressure in a C-d tunnel? SUBSONIC

Answer 13

• dA < 0, i.e. area is decreasing.
• dV > 0, i.e. airspeed is increasing.
• dP < 0, i.e. air pressure is decreasing.

Question 14

At the throat, what happens to area and airspeed in a C-d tunnel? SUBSONIC

Answer 14

• dA = 0 i.e. area is at its minimum.
• dA/A = (M^2 - 1) * dv/v = 0, i.e. M^2 - 1 = 0. So M = 1 at the throat.
• Area reaches an extreme value: local minimum and v reaches speed of sound. This is the speed limit for a convergent nozzle.

Question 15

From the throat to the outlet of the nozzle, what happens to area, airspeed and pressure in a C-d tunnel? SUBSONIC

Answer 15

• M > 1 and M^2 - 1 > 0.
• dA > 0, i.e. area is increasing, thus:
• dV < 0, i.e. air pressure is decreasing at the same time.
• Airflow is supersonic at the exit of the nozzle, i.e. M > 1.

Question 16

From the inlet to the throat, what happens to area, airspeed and pressure in a C-d tunnel? SUPERSONIC

Answer 16

• dA < 0, i.e. area is decreasing.
• dV < 0, i.e. airspeed is decreasing.
• dP > 0, i.e. pressure is increasing.

Question 17

At the throat, what happens to area and airspeed in a C-d tunnel? SUPERSONIC

Answer 17

• dA = 0 i.e. area is at its minimum.
• dA/A = (M^2 - 1) * dv/v = 0, i.e. M^2 - 1 = 0. So M = 1 at the throat.
• Area reaches an extreme value: local minimum and v reaches speed of sound. This is the speed limit for a convergent nozzle.

Question 18

From the throat to the outlet of the nozzle, what happens to area, airspeed and pressure in a C-d tunnel? SUPERSONIC

Answer 18

• dA > 0, i.e. area is increasing.
• dV < 0, i.e. airspeed is decreasing.
• dP > 0, i.e. air pressure is increasing.
• At the outlet, airflow becomes subsonic, i.e. M < 1.

Question 19

Explain in detail how a shockwave forms? (5)

Answer 19

• When airflow is supersonic, air particles travel faster than the speed of sound.
• If there’s a compression pressure disturbance in the supersonic airflow, the disturbance propagates at the speed of sound.
• The source of the disturbance (air particles) move faster than the disturbance, or the pressure change itself.
• Because ‘change’ cannot catch up to the air particles within the vicinity of the sources, the air property is not uniform, not continuous throughout the flow field because the pressure disturbances or changes are all propagating at the speed of sounds.
• The disturbance from the moving source accumulate to form a wave front, known as a shockwave.
• Air properties change suddenly across a shockwave.

Question 20

How thick is a shockwave?

Answer 20

Very thin, about 1mm.

Question 21

Using the equation: 1 = M1* M2*, what is the airflow like after a normal shockwave? What happens if M1 is far greater than M2?

Answer 21

• Airflow after normal shockwave is always subsonic.
• The higher M1 is, the lower M2 will be, meaning that the higher the airspeed before a normal shockwave, the lower airspeed after the shockwave will be.

Question 22

What happens to stagnation pressure, temperature before and after a shockwave?

Answer 22

• Stagnation pressure is not the same.

- Stagnation temperature is the same.

Question 23

Are the properties of air before and after a normal shockwave a reversible adiabatic process?

Answer 23

No, it is a irreversible adiabatic process.