THE BOUNDARY CONDITION AT AN IMPEDANCE WALL IN A NON-UNIFORM DUCT WITH POTENTIAL MEAN FLOW

The boundary condition at an impedance wall in a duct with a steady mean flow requiring the specification of the normal component of acoustic particle velocity is examined. It is found that when implemented in the weak formulation of the finite element method it can be considerably simplified. The boundary condition would appear to require data which includes the tangential derivative of the tangential mean flow velocity, the normal derivative of the normal component of mean flow velocity, and the derivatives of the mean flow density and the boundary admittance along the boundary. It is shown that with suitable rearrangement the normal and tangential velocity derivatives can be eliminated, as can the derivatives of the mean flow density and admittance. The boundary condition becomes only slightly more complicated than the corresponding boundary condition when mean flow is absent, and is no more difficult to implement, requiring only local values of tangential mean flow velocity, density, and admittance which are already required as data for the weak formulation of the field equation.