Oscillations, Waves, and Interactions - GWDG

Sound absorption, sound amplification, and flow control in ducts 103
the free cross-section of the flow duct by a cylindrical coaxial body such that only
an annular gap remains open to the flow. A sound-induced increase of the pressure
gradient of up to 5% of the dynamic pressure per gap width has been observed, however
the relative increase of the pressure drop remains rather independent of the gap
width.
Many of the observed phenomena can be explained, at least on a qualitative level,
if the convective instability of the flow is taken for granted. The enhancement of
the Reynolds shear stress caused by the spatial growth of the instability wave plays
an essential role in the interaction between the mean and the oscillating part of the
flow. Thus both, the mean velocity profile as well as the intensity and the structure
of the turbulence experience a strong alteration along the way through the lined
duct section, and the spatial development of the flow on its part strongly affects the
growth of the instability wave. The exact nature of the instability however remains
unclear. So far, the search for an adequate description of the dynamics of the flow has
been restricted to approaches that are based on homogeneous mean flow conditions
or at the most on a slowly developing mean flow, and on a mode decomposition of
the oscillating field. The interaction between the instability wave and the turbulence
has been introduced by means of an eddy-viscosity and has been found to have a
dominant influence on the dynamics of the flow. All these attempts have ended up in
unrealistic dispersion relations and particularly in the detection of absolute instability
which however has not been observed in the experiments. Therefore, though not all
the implications of the eddy-viscosity have been studied up to now, we conjecture
that the spatial development of both, the mean flow and the instability wave have to
be considered in a joint analysis.
A few of the observations have not yet been explained even on the qualitative level
mentioned above. Among these are the reduction (in contrast to an increase) of the
pressure drop by superimposed sound as well as the frequency gap that exists between
1200 Hz and 1260 Hz for the m = 0 mode but is particularly favourable for the m = 1
mode; by the way a similar gap has been observed for the C-mode (m = 1) between
300 Hz and 380 Hz (see Fig. 10). Presumably these observations are caused by some
interaction between different instability waves, whether turbulent or coherent, and
can be explained only by deeper insight into the dynamics of the considered flow.
Acknowledgements. The authors are indebted to Sabine Förster, Jörg Rebel, Michael
Krause, Lars Enghardt, Andreas Pöthke, Michael Brandes, Björn Lange, and Jakob Großer
who, by their diploma- and doctoral theses have essentially contributed to the material which
has been presented here. Part of this research has been funded by the Deutsche Forschungsgemeinschaft
(German Research Foundation) whose support is gratefully acknowledged.
References
[1] M. Lighthill, ‘On Sound Generated Aerodynamically. I. General Theory’, Proc. Roy.
Soc. Lond. Ser. A 211, 564 (1952).
[2] E. Meyer, F. Mechel, and G. Kurtze, ‘Experiments on the Influence of Flow on Sound
Attenuation in Absorbing Ducts’, J. Acoust. Soc. Am. 30, 165 (1958).
[3] F. Mechel, ‘Schalldämpfung und Schallverstärkung in Luftströmungen durch absorbierend
ausgekleidete Kanäle’, Acustica 10, 133 (1960).