Slow sound in lined flow ducts.

The acoustic propagation in lined flow duct with purely reactive impedance at the wall is considered. This reacting liner has the capability to reduce the speed of sound, and thus to enhance the interaction between the acoustic propagation and the low Mach number flow ( M≃0.3). At the lower frequencies, there are typically four acoustic or hydrodynamic propagating modes, with three of them propagating in the direction of the flow. Above a critical frequency, there are only two propagating modes that all propagate in the direction of the flow. From the exact two-dimensional formulation an approximate one-dimensional model is developed to study the scattering of acoustic waves in a straight duct with varying wall impedance. This simple system, with a uniform flow and with non-uniform liner impedance at the wall, permits to study the scattering between regions with different wave characteristics. Several situations are characterized to show the importance of negative energy waves, strong interactions between acoustic and hydrodynamic modes, or asymmetric scattering.

[1]  M. K. Myers,et al.  On the acoustic boundary condition in the presence of flow , 1980 .

[2]  W. Unruh.  Experimental black hole evaporation , 1981 .

[3]  D. G. Crighton,et al.  Fluid loading with mean flow. I. Response of an elastic plate localized excitation , 1991, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[4]  Nigel Peake,et al.  On the behaviour of a fluid-loaded cylindrical shell with mean flow , 1997, Journal of Fluid Mechanics.

[5]  Willi Möhring,et al.  Energy conservation, time-reversal invariance and reciprocity in ducts with flow , 2001, Journal of Fluid Mechanics.

[6]  Vincent Pagneux,et al.  Scattering matrix properties with evanescent modes for waveguides in fluids and solids , 2004 .

[7]  Ej Brambley,et al.  Fundamental problems with the model of uniform flow over acoustic linings , 2009 .

[8]  R. Parentani,et al.  Black hole lasers in Bose–Einstein condensates , 2010, 1005.4024.

[9]  Ej Brambley,et al.  Well-Posed Boundary Condition for Acoustic Liners in Straight Ducts with Flow , 2011 .

[10]  Sergey I. Bozhevolnyi,et al.  Acoustic transparency and slow sound using detuned acoustic resonators , 2011 .

[11]  M. Visser,et al.  Analogue Gravity , 2005, Living reviews in relativity.

[12]  Sevag H. Arzoumanian.  Stability of fluid-loaded structures , 2011 .

[13]  Yves Aurégan,et al.  Failure of the Ingard-Myers boundary condition for a lined duct: an experimental investigation. , 2011, The Journal of the Acoustical Society of America.

[14]  G. Lawrence,et al.  Measurement of stimulated Hawking emission in an analogue system. , 2010, Physical review letters.

[15]  Mustafa YILMAZ,et al.  Slow sound propagation in a sonic crystal linear waveguide , 2012 .

[16]  Lei Xiong,et al.  Acoustical behaviour of purely reacting liners , 2013 .

[17]  G. Theocharis,et al.  Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures , 2013, 1312.2851.

[18]  V. Pagneux,et al.  Slow sound in a duct, effective transonic flows, and analog black holes , 2015, 1503.02634.