### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 2pPAb9. Propagation of sound in a lined circular duct with sheared mean
flow.

**Jinlong Wu
**

**
Mark F. Hamilton
**

**
**
*Dept. of Mech. Eng., Univ. of Texas at Austin, Austin, TX 78712-1063
*

*
*
This presentation describes an analytical investigation of the propagation
of sound in a lined circular duct with sheared mean ambient flow. The main
assumptions are that the ambient flow is turbulent and unaffected by the sound,
the Mach number for the flow is small compared to unity, the thickness of the
viscous boundary layer is small in comparison with the radius of the duct, and
the acoustical lining is locally reactive. The mean flow profile away from the
wall is assumed to be uniform, but the profile within the boundary layer can
take one of several analytic forms. Outside the boundary layer, the acoustic
mode structure is described by Bessell functions. The solution within the
boundary layer is expressed in terms of Kummer functions, and the dispersion
relation is obtained by matching the inner and outer solutions, taking the wall
impedance into account. The dispersion relation is solved numerically for the
attenuation and phase speed of the sound as a function of mode number, complex
wall impedance, boundary layer thickness, and flow profile within the boundary
layer. Both upstream and downstream propagation are considered. Comparisons are
made with published numerical results.