Analysis of the co-rotating vortex pair as a test case for computational aeroacoustics

The co-rotating vortex pair arrangement is a frequently applied test case in computational aeroacoustics. Its flow quantities and far-field radiated sound pressure can be computed analytically, assuming delta-distribution potential vortices. When this configuration is used for verification in a numerical computation, the singular vortex cores cannot be modeled directly; they have to be desingularized, which affects the associated flow and acoustical fields. Closed-form expressions for the aeroacoustic source terms are derived for the Scully vortex model and used for detailed numerical computations of the radiated sound pressure. The effects of desingularization and finite source region size are analyzed in the frequency domain for Lighthill's equation and the perturbed convective wave equation by means of an efficient numerical approach that computes the convolution of the aeroacoustic source terms and the 2D free-field Green's function. It is shown that the deviations of the far-field radiated sound pressure from the idealized analytical solution depend on the Mach number, vortex core radius, and truncation limit of the source region. A significant increase in the effective size of the source region due to the desingularization is demonstrated. Minimal error bounds compared to the analytic far-field pressure solution are established. The presented converged numerical results serve as reference solutions for validating implementations of hybrid computational aeroacoustic workflows.