A fixed microphone in an airstream measures the same acoustic pressure as a microphone at the same location moving with the airstream as long as the diaphragm is exposed to the mean static pressure of the flow. This is the case
apparent noise noise source
Fig. 1.21. Sound propagation paths and angles in a moving stream
of the FITE forebody. A diaphragm ported to the total pressure of the airstream measures unsteady pressures that depend on sound levels, Mach number, and acoustic incidence angles, which are undesirable complications (Morse and Ingard 1968).
A fixed microphone in an airstream produces no Doppler frequency shift when exposed to sound from fixed noise sources despite sound convection by wind. To a fixed observer, the change in wave propagation speed caused by wind is offset by a change in wavelength so that the measured frequency is what was emitted by the source.
From the statements above, it is clear that in-airstream microphones mea-sure true acoustic presmea-sures at the emitted source frequencies even though there is flow around the microphone. However, the convection of acoustic waves by the airstream does affect the sound radiation pattern and propaga-tion losses.
Consider a fixed noise source that is radiating sound measured at a fixed microphone in a steady wind with Mach number, M, as shown in Figure 1.21.
The angle,
e',
and path, R', represent the emission angle and propagation path that would occur with the source in still air. Anglee'
also represents the angle to the wave normal vector and apparent noise source as seen at the mi-crophone. Because of wind convection, the sound waves actually travel along path R at an anglee
as shown,e
is the propagation angle.4 The anglee
is1800 -
e',
the microphone incidence angle. From the geometry, the angles are related as follows (Allen and Soderman 1997):e'
= cos-1 [M sin2e
+ cose -Jl -
W sin2e]
(1.21)4 The emission angle e' should not be confused with the propagation angle e even though the sound propagates along path R and appears to have originated on the source at angle e. In reality, the sound was emitted at angle e' and swept downstream by the wind. This is clear from the analogous situation of an aircraft flying over an observer on the ground.
An observer at angle e relative to the aircraft will hear a sound that was emitted previ-ouslyat angle e'. The source emission angles in flight and in the wind tunnel are identi-cal. In both situations, e'defines the source emission direction and the wave front normal vector.
The distance, R', is the proper distance to use for computing sound pressure reduction from wave spreading and sound absorption because it represents the distance the sound waves travel relative to an observer moving with the wind.
R'=
-_-~--c-o-s-e-+--Vr~=72=c=os~2=e==_=~=7+==1 R (1.22)Estimation of sound absorption is important so acoustic data can be corrected to standard day atmosphere and compared with other data acquired under different conditions. The airflow's mean static temperature, static pressure and relative humidity are used for the computation of air absorption.
Because sound waves in an airstream lose energy from air absorption at the frequency seen by an observer moving with the wind, the energy loss occurs at a Doppler frequency shifted relative to a fixed microphone. The Doppler fre-quency,fd, is given by:
fd = -1 ---~-'--co-s-e-'
f
(1.23)where
f
is the source frequency measured at the microphone.Equation 1.23 is also valid for a moving source and fixed microphone. As discussed in the following section on scaling and extrapolation, the Doppler frequency is used for converting wind tunnel data to simulated aircraft flyover.
For open-jet wind tunnels, the above analysis is appropriate for sound prop-agation inside the jet. Once the sound waves pass through the shear layer, the new path, atmospheric conditions in the anechoic room, and measured fre-quency are used for computation of air absorption. As within the jet, the mea-sured frequency is the same as the source frequency - no Doppler shift occurs for a fixed source and microphone. Of course, shear layer effects are important as will be discussed below.
Even though there is no Doppler frequency shift, sound waves from a fixed noise source recorded at a fixed microphone in a wind tunnel undergo con-vective amplification just as in flight. Noise radiated upstream will be ampli-fied, and noise radiated downstream will be attenuated relative to the noise from the same source stationary in still air. It can be shown analytically that a simple monopole-type noise source in motion will radiate sound as (Morse and Ingard 1968):
p2 oc (1 - ~F cos e')-4
where p2 is the average sound pressure squared
~F is the flight Mach number of the source
e' is the source emission angle relative to the flight direction (1.24)
More complicated noise sources radiate sound with the same Doppler factor (1 - Mp cos 8') raised to a different exponent. Norum et al. (2000) found that jet broadband shock noise from an F15 aircraft in flight had convective ampli-fication like that of Equation 1.24, but with exponents ranging from - 2.4 to - 2.8. Because of the analogy between a source in motion and a fixed source in a moving medium, convective amplification occurs in wind tunnel simula-tions as has been observed many times (Soderman et al. 1991, Krothapalli et al. 1997). Therefore, no correction of wind tunnel data is needed to match con-vective amplification effects observed during aircraft flight. Flight parameters Mp and 8' are equivalent to M and 8' in Figure 1.21. When predicting flyover noise from static aircraft tests or computations, however, convective amplifi-cation must be estimated.