Compressible Inviscid Flow 7 - Wave Propagation and Speed of Sound

Question 1

What is a sound wave?

Answer 1

A weak perturbation propagating in space (isentropic)

Question 2

Relationship between speed of sound and average molecular velocity

Answer 2

Proportional
Speed of sound is around 75% of the average molecular velocity
This is because the sound wave is propagated by molecular collisions
Compressibility becomes important when the flow velocity is comparable with the molecular velocity or speed of sound

Question 3

How is the speed of sound variable?

Answer 3

Changes with temperature
Therefore changes with altitude

Question 4

Define Mach number

Answer 4

Ratio of gas velocity to speed of sound
Most important non-dimensional parameter in compressible flows, making it possible to define subsonic, transonic, supersonic and hypersonic flows

Question 5

Incompressible flow - Mach number and examples

Answer 5

M<0.3
Automotive
Liquid flow
Racing car

Question 6

Subsonic flow - Mach number and examples

Answer 6

0.3<M<0.7
Light aircraft
Regional aircraft

Question 7

Transonic flow - Mach number and examples

Answer 7

0.7<M<1.2
Flow field includes subsonic and supersonic regions even if flight speed is subsonic
Large transport aircraft (Airbus/Boeing)
Military aircraft

Question 8

Supersonic flow - Mach number and examples

Answer 8

1.2<M<5
Concorde
Military aircraft
Missiles

Question 9

Hypersonic flow - Mach number and examples

Answer 9

M>5
Spacecraft
Rockets
Space shuttle

Question 10

Define total/stagnation conditions

Answer 10

If a fluid element is isentropically decelerated or stagnated to zero velocity, the resultant flow conditions at v=0 are the total conditions

Question 11

Difference between static and total conditions

Answer 11

Static conditions are the actual fluid properties
The corresponding total state is achieved by an imaginary process where the fluid is reduced to rest isentropically
Total properties are another way of writing static properties to include flow velocity
In high pressure tank in a supersonic wind tunnel, total and static properties are the same as v=0

Question 12

Total conditions for an adiabatic compressible process

Answer 12

Total enthalpy is constant
Therefore all other total constants are constant for a perfect gas

Question 13

Total conditions for non-isentropic flows

Answer 13

Total conditions are viewed as local flow properties (e.g. total pressure can vary from point to point)

Question 14

What is another way to view total pressure?

Answer 14

Capability of the flow to do useful work
Loss of total pressure is undesirable in engineering flow processes

Question 15

What are critical conditions?

Answer 15

Sonic properties (i.e. putting M=1, sonic flow, into the relations)

Question 16

Critical properties in isentropic flow

Answer 16

Constant

Question 17

Critical properties in adiabatic non-isentropic flow

Answer 17

Speed of sound and temperature are constant
Pressure and density may vary
This is because the first two relations only assume adiabatic condition

Question 18

Why is Bernoulli’s equation not applicable to compressible flows?

Answer 18

As Mach number increases, Bernoulli equation becomes less accurate as high order terms become larger
Bernoulli equation is the 1st order term of the Taylor expansion of the isentropic compressible flow relation at the low Mach number limit

Question 19

When is flow compressible?

Answer 19

Density ratio is 1 for incompressible flow
Density variation increases as Mach number increases
For M<0.3 the variation is <5%, close to incompressible flow

Question 20

Sound propagation in subsonic flow

Answer 20

Beeper (weak perturbation source) moves to left subsonically, M<1, v<a
Domain of disturbance moves with the wave front to infinite

Question 21

Wave propagation in supersonic flow

Answer 21

Beeper moves supersonically, M>1, v>a
Wave fronts form an envelope given by a straight line tangent to family of circles
This line/cone (3D) is the Mach wave front/Mach cone (3D), separating the domain of disturbance and domain and silence
This is why sonic boom sounds after supersonic aircraft passes overhead

Question 22

How are shock waves formed?

Answer 22

Strong perturbation waves are generated from all points on the aircraft surface
These waves pile up and coalesce, forming a standing wave (shock wave)

Question 23

Properties of shock waves

Answer 23

Extremely thin compression layer, typically of order 10^-4mm (0.1 micron)
Flow properties change drastically across the shock
Entropy increases across shock - physically irreversible process
Shock is adiabatic (no heat addition)
Total enthalpy and total temperature are unchanged across shocks

Question 24

When can a normal shock appear?

Answer 24

On aircraft wings at transonic speeds due to entropy increase

Question 25

Results of normal shocks

Answer 25

Reduced performance
Aerodynamic noise