Oscillations, Waves, and Interactions - GWDG

Sound absorption, sound amplification, and flow control in ducts 79
R / / L L ⋅ ⋅ ∆p ∆p / / pp ac ac dyn dyn
0.07 0.07
0.06 0.06
0.05 0.05
0.04 0.04
0.03 0.03
0.02
0.01
0
−0.01
U/c = 0.1
0.15
0.2
0.25
0.3
0.8 0.9 1 1.1
frequency [kHz]
1.2 1.3 1.4
Figure 5. Sound-induced static pressure drop ∆pac along the unmodified resonator section
as a function of the frequency with various flow velocities. The average pressure gradient
∆pac/L within the resonator section is normalized with the dynamic pressure per radius
p dyn/R.
unmodified resonator section depicted in Fig. 1, and a hysteresis is associated with
the jump of the frequency (black curve in Fig. 3). The maximum peak amplitudes are
reached slightly below U jump which strongly depends on the geometric parameters of
the resonator section.
Besides the pressure spectra the sound transmission through the lined duct section
has been investigated. A multi-microphone method with two independent sound
fields has been used [31] for this purpose. Figure 4 shows the transmission coefficient
for the sound propagating in the mean flow direction. At frequencies close to the resonance
frequency and with U = 0 the sound transmission is very effectively blocked,
and this blockage becomes even more effective by mean flow in the opposite direction
of the sound propagation (not shown in Fig. 4). However, with mean flow in the
direction of sound propagation, the transmission coefficient considerably increases
and becomes even much greater than unity, at high flow velocities. Considering the
dependency on the freqency and on the flow velocity, obvious agreement is found
between the sound amplification and the spectral peak (A 1 ) downstream of the resonator
section. Therefore we conclude that the A 1 -peak is caused by the amplification
of the axisymmetric component of the turbulent pressure fluctuations that enter the
lined duct section.
In conjunction with the sound amplification Krause [25] and Brandes [26,29] have
observed an increase of the static pressure drop along the lined duct section, i. e.
an increase of the mean wall shear stress in the resonator section. The dependency
of the sound-induced pressure drop on the frequency is plotted in Fig. 5 for various