A characteristic non-reflective boundary for low Mach number flow-induced noise.

Characteristic boundary conditions are widely used to simulate compressible flow-induced noise. This study extends the application to incompressible flow-induced noise by introducing a low Mach number characteristic boundary condition (LMCBC) to eliminate sound wave reflections at boundaries. This boundary condition is derived from the second type of acoustic perturbation equations (APE-2) and implemented within the open-source software OpenFOAM (OpenCFD Ltd, Bracknell, Berkshire, UK). The flow field is computed using the incompressible Navier-Stokes equations, and APE-2 predicts the acoustic field. The accuracy and robustness of the coupled solver and the new boundary condition are validated through multiple benchmark problems. Plane-wave test cases are then used to compare the non-reflection performance of LMCBC, perfectly matched layers (PML), and damping layers under varying incidence angles and Mach numbers. To further improve performance, LMCBC is combined with PML to form PLMCBC, and a zonal low Mach number characteristic boundary condition (ZLMCBC) is proposed by gradually attenuating characteristic waves within a buffer zone. Both extended schemes exhibit enhanced non-reflective performance for low Mach number flows (Ma= 0-0.3), with ZLMCBC achieving the lowest reflection levels and the reduced sensitivity to wavelength variations within the tested range.