Summary
Sound (or more appropriately noise) generated by airflow has been
familiar for a long time. The increased use of fluid machines and engines has led to
an increasing level of noise generation, and hence to an increasing interest in this
area of research.
Aeroacoustics deals with noise generated by aeronautic systems or their components.
Aerodynamic noise is one of the main concerns in the design process of any new jet
engine (or re-engineering of old ones).
Other fields of research are the following:
In hydrodynamics it is of particular interest the noise from bubble cavitation.
Fundamental studies in aerodynamic sound were started in the 1950s by Lighthill and
Ffowcs-Williams in the 1970s. General theories of sound are much older (Rayleigh,
1896).
As reported anecdotically by Ffowcs-Williams (1977) and Crighton (1993), it has been
calculated that the first generation of Boeing 707 at take-off produced as much sound
as the world population shouting in phase together!
A Boeing 767 of 30 years later (with four times as much thrust per engine) produced
as much sound as the city of New York shouting in phase. However, the energy radiated
by such sound in the first 45 seconds is just enough to cook one egg !
The only supersonic jet transport in service, the Concorde, exceeds by far
the noise regulations for transport aircraft (this is one of the reasons why the
Concorde is still banned from most of the world's aircraft). The noise generated at
take off is well above 100 dB (that is the level of a rock band noise).
Dynamic levels of sound range from about 0 dB (threshold of audibility) to
about 120 dB (threshold of pain). The range of frequencies perceived by the
human ear is only 20 Hz - 20000 Hz. However, the ear is much more
sensitive in the 2-4 KHz range.
Experimental studies in aero-acoustics are very expensive. They require anechoic
tunnels (insulated against external sources) and delicate instruments able to measure
the high-frequency pressure fluctuations. On turns this instrumentation has to be
coupled with flow visualization techniques in order to understand the relationship
between aerodynamics and acoustics.
As the computational resources increase and the numerical techniques are refined, it
has become more interesting, and certainly more efficient, to employ computer
simulations. Computational aero-acoustics is that branch of computational fluid
dynamics concerned with aerodynamic noise.
The Doppler effect is characterized by frequency changes due to a source of sound
approaching an observer at speed u. In this case a single frequency
Thus, a train approaching a station at a speed of 100 Km/h, and
emitting a single frequency sound of 8 KHz would be heard by the passengers on
the platform at 8.7 KHz.
Consider now a body of finite dimension, with characteristic length L in the
direction of motion.
A source of sound at rest travels the distance
Figure 1: Supersonic source radiation
Sounds emitted by s source travelling at supersonic speed u > c are
heard by the observer on the ground in reverse order: pap pep pip pop pup
will be heard pup pop pip pep pap. At sonic condition u=c all
the sounds are heard at the same time: this is the sonic boom.
A sonic boom is a loud noise caused by an aircraft travelling faster than the speed
of sound (M > 1). The sound propagates along the Mach cone, Fig. 1, which
represents a surface of discontinuity for most of the thermo-aerodynamic variables
(pressure, velocity, density, entropy).
The boom is due to a combination of volume and lift. While the boom due to volume
can be virtually eliminated (Busemann, 1935), the boom due to lift can only be
minimized.
Minimization is not straightforward, because it is constrained by structural,
aerodynamic and design parameters, and not least by the variation of the
thermo-dynamic properties of the atmosphere.
The minimum sonic boom generally does not correspond to the best aircraft. There is
among others: sonic boom minimization at given drag; minimization at given volume,
etc. (Seebass, 1998). Because the shock energy is nearly conserved as the shock
radiates, its strength decays only slightly with the distance from the aircraft.
The boom is characterized by a typical over-pressure signature on the ground and a
total impulse (time integral of the over-pressure).
The wave associated to the over-pressure is generally N-shaped, which is a result of
a sonic boom due to two shocks (front and rear). The N-wave is a function of the
aircraft geometry (length, volume, etc), flight altitude, speed, atmospheric
conditions.
Figure 2: Waves from Sonic Boom Optimization
Seebass-George (1961) defined a figure of merit, FM, to characterize the sonic boom
levels. This figure is proportional to the aircraft weight divided with the
three-halves of the aircraft length W/L^(3/2). The lower this value, the better the
aircraft.
Some values are given in the following table.
The B-2707 was a project aborted in 1972. Forecasts for a supersonic business jet
(Seebass, 1998) flying at M=1.6 would give a FM = 0.4, that is considered acceptable.
Aeroacoustics
Acoustic Energy
Some Noise Levels
Frequency Ranges
Doppler Effect
(having period
)
travels a distance cT (c = speed of sound), while the source travels a
distance uT. The apparent wavelength is changed to (c - u) T.
and the frequency is shifted to its Doppler-value.
in the unit of time. The volume involved by the sound is therefore proportional to
T³
The same source travelling at
subsonic speed u < c after the time T will be close to its
front end, Fig. 1. At sonic conditions the
source will be coincident with the front end of the wave. The volume involved is the
infinite space behind the source. At supersonic speed the source will always be
ahead of its sound. The waves radiate from the source along characteristic lines
making an angle
(Mach angle).
Sonic Boom
Over-Pressure at the Ground
Figure of Merit
Aircraft M FM Concorde 2.0 1.41 NASA-Boeing 2707 (1972) 2.4 1.9 Supersonic business jet (*) 1.6 0.4 Related Material
Selected References