Module 5 - Supersonic Flow

Question 1

Describe an example of reversible adiabatic process in terms of airflow? What is the term used to describe this process?

Answer 1

Isentropic

• A con-div nozzle where p1 is higher than p2
• Airflow will flow through the nozzle and becomes supersonic, and will flow the opposite direction under the same pressure conditions to become subsonic
• The air properties will return to their original values
• No energy is being transferred

Question 2

Describe an example of an irreversible adiabatic process in terms of airflow?

Answer 2

• Airflow through a normal shockwave
• As air passes through the shockwave it becomes subsonic
• Its pressure increase from p1 to p2 and the shockwave receives energy when it is formed
• The airflow cannot be made to flow back across the shockwave and gain energy back from the shockwave and become supersonic again

Question 3

Why is airflow across a normal shockwave irreversible and airflow through a con-div nozzle reversible?

Answer 3

The entropy (thermodynamic property) of air is not constant across a shockwave as some of the energy is used to form a shockwave.
Once the entry of a system has changed (even with no heat transfer) it is irreversible.

A con-div nozzle does not change the entropy of the air and so it is a reversible adiabatic process

Question 4

What is the relationship between the airspeed before a shockwave to the airspeed after the shockwave

Answer 4

• Flow after a NORMAL shockwave must always be subsonic

- The higher the airspeed before the shockwave, the lower the airspeed after the shockwave

Question 5

What is a typical situation where an oblique shockwave will form? Very basically, how is it formed?

Answer 5

When supersonic airflow flows over a concave corner, or on the leading edge of a supersonic aircraft

-Formed when compressive pressure waves accumulate from a compressive disturbance

Question 6

What happens to the properties of air as it passes through an oblique shockwave?

Answer 6

Pressure Temp and Density increase
Velocity decreases (not necessarily to subsonic)

Question 7

In what directions can airflow velocity be analysed as it crosses an oblique shockwave?

Answer 7

V(τ) = Tangental to shockwave
V(n) = Normal (perpendicular) direction to shockwave

Question 8

What is the difference between β and θ?

Answer 8

β: is the shock angle between the incoming RAF and the shockwave
θ: is the deflection angle between the incoming RAF and the deflected surface

Question 9

What is the relationship between the tangental velocity before the oblique shockwave and the tangental velocity after the shockwave? Why?

Answer 9

There is no change: V(1τ) = V(2τ)

This is because air does not cross there shockwave and there is an assumption that there is no air particle slip

Question 10

What is the relationship between the perpendicular velocity before the oblique shockwave and the perpendicular velocity after the shockwave? Why?

Answer 10

It will decrease across the shockwave:  V(1n) > V(2n)
The M(2n) will become subsonic but the overall M(2) may not be subsonic

Question 11

If you wish to analyse the relationship between air properties before and after an oblique shockwave, what mach number ratio will be applicable?

Answer 11

Ratio of V(1n) to V(2n) - ratio of velocity in perpendicular direction before and after

Question 12

What is the relationship between the incoming mach number, the deflection angle and the shock angle?

Answer 12

• Very complicated

- Expressed diagrammatically on the θ-β-M diagram

Question 13

For all oblique shockwaves with a shock angle (β) greater than that at the maximum deflection angle for the given M, what does this mean for the shockwave?

Answer 13

It is a strong shock where M2 < 1

The airflow behind the shockwave is subsonic

Question 14

For all oblique shockwaves with a shock angle (β) less than that at the maximum deflection angle for the given M, what does this mean for the shockwave?

Answer 14

It is a weak shock where M2 > 1

The airflow behind the shockwave is still supersonic

Question 15

What is the difference between the two lines on the θ-β-M diagram?

Answer 15

• Critical Mach line (blue) is the point for all mach speeds where M2 = 1
• Maximum deflection line (red) is the line which joins the turning points of all lines; the point where the maximum deflection angle occurs

Question 16

What happens if the maximum deflection angle is exceeded?

Answer 16

The oblique shockwave will not be attached to the surface

Question 17

In general, where will a strong shock form compared to a weak shock? Give examples

Answer 17

Strong: In internal flow such as inside a turbine or exit of a jet engine
Weak: In external flow such as airflow over a fuselage or aerofoil

Question 18

What causes an expansion wave?

Answer 18

• When compressible airflow travels into an increasing volume, or it encounters a pressure decreasing disturbance
• If the airflow is supersonic, a convex deflection will cause expansion waves

Question 19

In supersonic airflow, why is an expansion fan created?

Answer 19

• Because the expansion wave cannot propagate with the airflow
• An infinite series of expansion waves will form instead

Question 20

What happens to the properties of air when they are deflected through an expansion fan?

Answer 20

• Pressure Temperature and Density all decrease

- Velocity increases

Question 21

How is the angle of the expansion region determined?

Answer 21

The mach angles of the first and last mach wave are calculated using the incoming and outgoing mach number respectively.
These angles are ‘measured’ from the direction of the airflow

Question 22

What type of adiabatic process is airflow across an expansion wave?

Answer 22

Isentropic - a reversible adiabatic process

Question 23

What is the relationship between the deflection angle (expansion) and the outgoing airspeed and pressure when the incoming airflow is supersonic?

Answer 23

The larger the deflection angle, the lower the outgoing pressure and the higher the outgoing airspeed

Question 24

What is the name of the equation that determines the relationship between deflection angle and incoming vs. outgoing mach number? What is the equation?

Answer 24

Prandtl-Meyer Function

θ = ν(M2) - ν(M1)

Question 25

What is ν(M)?

Answer 25

It is an expansion angle

Question 26

What determines the limit of expansion region? What happens to airspeed?

Answer 26

The theoretical pressure can reduce to 0, and the expansion region will be at its limit

M = ∞

Question 27

What happens if the deflection angle exceeds the maximum theoretical deflection angle; θ > θ(max)? Theoretical vs actual?

Answer 27

• A slipstream between the θ(max) and the stagnation region will form.
• The stagnation region has theoretical p=0, and v=0
• In real airflow sudden change cannot be sustained due to viscosity
• Vortices would be formed, forming a street, and cause local oscillation in the airflow