Optimum wall impedance for spinning modes - A correlation with mode cut-off ratio

A correlating equation relating the optimum acoustic impedance for the wall lining of a circular duct to the acoustic mode cutoff ratio is presented and compared to exact calculations. The optimum impedance was correlated with cutoff ratio because the cutoff ratio appears to be the fundamental parameter governing the propagation of sound in the duct. Modes with similar cutoff ratios respond in a similar way to the acoustic liner. The correlating equation is useful for the design of suppressors for aircraft engine inlets having a steady mean flow with a boundary layer and spinning mode noise source excitation. The correlation is a semiempirical expression developed from an empirical modification of an equation originally derived from sound propagation theory in a thin boundary layer. Exact calculations of the optimum wall impedance were made over a wide range of frequency parameters, boundary-layer thicknesses and flow Mach numbers to develop and verify the correlation. This correlating equation represents a part of a simplified liner design method, based upon modal cutoff ratio, for multimodal noise propagation. c D F f G M0 m