Flow effects on the acoustic end correction of a sudden in-duct area expansion

For scattering of plane waves at a sudden area expansion in a duct, the presence of flow may significantly alter the reactive properties. This paper studies the influence of a mean flow field and unstable separated flow on the reactive properties of the expansion, formulated as an end correction. Theoretical and experimental results show that the expansion end correction is significantly affected by the flow and hydrodynamic waves excited at the edge of the expansion. The effects are different in three regions where the Strouhal number is small, of order 1, and large. The influence is most significant at Strouhal numbers of the order 1, with specific limiting values for large and small Strouhal numbers, respectively. In the analytic model, an important feature is the shear layer at the edge modeled as a vortex sheet with the unsteady Kutta condition applied at the edge. The influence of Mach number, Helmholtz number, and area expansion ratio is studied, and a quasistationary, small Strouhal number, approximation yields an expression for the end correction. Further, the influence of edge condition is explored, emphasizing the importance of interaction between sound and unsteady vorticity shedding at the edge of the area expansion.