Effect of the acoustic boundary layer on the wave propagation in ducts

An analysis is presented for the wave propagation in two‐dimensional and circular lined ducts taking into account the effects of viscosity in both the mean and the acoustic problems. The method of composite expansions is used to express each acoustic flow quantity as the sum of an inviscid part and a boundary layer part insignificant outside a thin layer next to the wall. The problem is reduced to solving a second‐order ordinary differential equation for the pressure perturbation as in the inviscid acoustic case but with a modified specific wall admittance. An analytic expression is presented for the variation of the modified admittance with the wall and flow parameters, such as the acoustic boundary layer thickness, the mean velocity and temperature gradients at the wall, the frequency of oscillation, and the wavelength.