Low-wavenumber wall pressure fluctuations in turbulent flows within concentric annular ducts

Compressible direct numerical simulations of turbulent channel flows in concentric annular ducts of height 2δ are performed to study the low-wavenumber wall pressure fluctuations (WPF) over cylindrical walls at a bulk Mach number M_b = 0.4. The radius of the inner cylinder R is varied between 0.2δ, δ, 2δ and ∞, while the bulk Reynolds number remains fixed at 3000. As R decreases, the one-point power spectral density of the WPF decreases at intermediate but increases at high frequencies. When R decreases, the 1D (streamwise) wavenumber-frequency spectrum of the WPF decreases at high wavenumbers. At low wavenumbers, however, as R reduces to 0.2δ the 1D wavenumber-frequency spectrum exhibits multiple spectral peaks whose strengths increase with frequency. These spectral peaks represent acoustic ducts modes that closely match theoretical predictions. The magnitude of the all-important low-wavenumber components of the 0th-order (azimuthal) 2D wavenumber-frequency spectrum increases at R reduces; this increase is increasingly pronounced at higher frequencies. Analytical modelling shows that this increase appears to arise from the geometric propagation connected with the Green's function, and they are generated mainly by radial and azimuthal disturbances. Disturbances closer to the wall are increasingly important in WPF generation as R reduces, which highlights a potential in WPF control using wall treatment on thin cylinders.