Sound generated in laminar flow past a two-dimensional rectangular cylinder

The far-field sound generated from low Mach number flow past a two-dimensional rectangular cylinder is studied by using a two-step aeroacoustic prediction method. In the first step, the incompressible Navier–Stokes equations are solved numerically. This allows the time-dependent acoustic source to be determined from Powell's vortex sound theory. Using this information, in the second step, the inhomogeneous wave equation is solved numerically to predict the time-evolving acoustic field. This study considers the effects of the Reynolds and Mach number on the sound generation and propagation characteristics. Results show that acoustic wave generation can be associated with the shedding of vortices at both the leading and trailing edges of the cylinder. In particular, an attempt is made to quantify the individual contributions, showing that the trailing-edge region is a considerably stronger source. Similar to the case for a circular cylinder, the predicted sound field has a dipolar far-field directivity with the lift dipole dominating. However, the drag dipole becomes relatively more important as the Reynolds number is increased. Overall, the relative amplitude of the far-field acoustic signal increases substantially with Reynolds number. In addition, as the Reynolds number is increased, the far-field pressure signal contains significant harmonic content, unlike the situation at the lowest Reynolds number investigated. A harmonic decomposition in terms of polar angle allows the multipole content of the signal to be quantified. Results showed that the acoustic field is dominated by the lift forcing which is predominantly dipolar, at least up to a Mach number (MaMa) of 0.2. While this is also true for the drag forcing for low Mach numbers, we found that for Ma>0.1Ma>0.1, the quadrupole term is of a magnitude comparable to the drag dipole. By taking into account the Doppler effect through a spatial transformation of the predicted acoustic solution, the dipolar field becomes skewed towards the upstream direction as the Mach number is increased. Various difficulties associated with direct acoustic computations, such as convergence problems associated with initial transients and grid stretching, and the introduction of errors from under-resolving the acoustic source, and treatment of the slowly decaying wake, are discussed. The methods used to overcome these problems are reported.