Oscillations, Waves, and Interactions - GWDG

78 D. Ronneberger et al.
|t + acoustic transmission coefficient
|
10
1
0.1
0.01
U/c = 0
U/c = 0.2
U/c = 0.15
U/c = 0.1
U/c = 0.25
U/c = 0.3
0.001
0.6 0.8 1
frequency [kHz]
1.2 1.4
Figure 4. Acoustic transmission coefficient of the unmodified resonator section as functions
of the freqency for various flow velocities. The incident sound wave travels in the direction
of flow. Resonance frequency: 840 Hz.
median of the distribution of the power spectral density (psd) is taken as 0 dB. The
enhancement of the psd at low frequencies is not caused by the resonator section but
is due to the internal noise of the flow facility.
The most prominent peak in Fig. 2(a) is marked by A 1 . The amplitude of this
peak becomes very large at high flow velocities so that higher harmonics (A 2 and A 3 )
appear in the spectra. At these high flow velocities the pressure fluctuations are also
radiated to the opposite direction of flow ( 1 A and 2 A in Fig. 2(c)). The peak B 1 in
Fig. 2(b) slightly above the frequency of the second radial resonance of the cavities
(3.3 kHz) is possibly based on the same mechanism as the peak A 1 , while the peak D
in Fig. 2(c) has been identified by Brandes [29,30] to be the result of another type of
instability that will be reconsidered in Sect. 4.1.5.
The amplitude and the mid-frequency of the A 1 -peak are plotted as functions of
the flow velocity in Fig. 3 for different geometric parameters of the resonator section.
While the dimensions of the cavity remain unmodified, the number of cavities is
varied, and besides the circular duct cross-section also various annular cross-sections
have been investigated characterized by the width of the annular gap between a central
cylindrical body and the pipe wall. The peak frequencies continuously increase
when the flow velocity is increased except for an interval between 1200 Hz and 1260 Hz
which is always skipped. The jump of the frequency occurs at U jump/c ≈ 0.35 for the
the sound speed if definite values are given, however the term ‘Mach number’ is avoided;
in fact we have not succeeded in finding an adequate and practical reference speed which
remains constant during a typical experiment and does not depend, e. g., on the frequency
or the acoustical admittance of the lining.