Time-domain calculation of sound propagation in lined ducts with sheared flows

A recent application of the time-domain equivalent of the classical acoustic impedance condition, i.e., the particle displacement continuity equation, to numerical simulations of a flow-impedance tube in the time domain yielded reasonably good results with uniform mean flows. The present paper extends this application to include sheared mean-flow effects on sound propagation over acoustically treated walls. To assess the prediction improvements with sheared flows, especially at relatively high Mach numbers, numerical simulations of the NASA Langley Research Center flow-impedance tube are carried out at actual conditions. Calculations are realized for mean-flow peak velocities as high as Mach 0.5 at various frequencies. Results are compared with those obtained with uniform mean flows and experimental data. It is shown that solutions that were not attainable previously with uniform flows at high Mach numbers can now be obtained with the help of the no-slip conditions of sheared background flows at the wall.