Compressible Inviscid Flow 7 - Wave Propagation and Speed of Sound Flashcards
What is a sound wave?
A weak perturbation propagating in space (isentropic)
Relationship between speed of sound and average molecular velocity
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
How is the speed of sound variable?
Changes with temperature
Therefore changes with altitude
Define Mach number
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
Incompressible flow - Mach number and examples
M<0.3
Automotive
Liquid flow
Racing car
Subsonic flow - Mach number and examples
0.3<M<0.7
Light aircraft
Regional aircraft
Transonic flow - Mach number and examples
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
Supersonic flow - Mach number and examples
1.2<M<5
Concorde
Military aircraft
Missiles
Hypersonic flow - Mach number and examples
M>5
Spacecraft
Rockets
Space shuttle
Define total/stagnation conditions
If a fluid element is isentropically decelerated or stagnated to zero velocity, the resultant flow conditions at v=0 are the total conditions
Difference between static and total conditions
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
Total conditions for an adiabatic compressible process
Total enthalpy is constant
Therefore all other total constants are constant for a perfect gas
Total conditions for non-isentropic flows
Total conditions are viewed as local flow properties (e.g. total pressure can vary from point to point)
What is another way to view total pressure?
Capability of the flow to do useful work
Loss of total pressure is undesirable in engineering flow processes
What are critical conditions?
Sonic properties (i.e. putting M=1, sonic flow, into the relations)
Critical properties in isentropic flow
Constant
Critical properties in adiabatic non-isentropic flow
Speed of sound and temperature are constant
Pressure and density may vary
This is because the first two relations only assume adiabatic condition
Why is Bernoulli’s equation not applicable to compressible flows?
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
When is flow compressible?
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
Sound propagation in subsonic flow
Beeper (weak perturbation source) moves to left subsonically, M<1, v<a
Domain of disturbance moves with the wave front to infinite
Wave propagation in supersonic flow
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
How are shock waves formed?
Strong perturbation waves are generated from all points on the aircraft surface
These waves pile up and coalesce, forming a standing wave (shock wave)
Properties of shock waves
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
When can a normal shock appear?
On aircraft wings at transonic speeds due to entropy increase
Results of normal shocks
Reduced performance
Aerodynamic noise
