VORTEX 01: Analytic solution of the flow, aeroacoustic source and acoustic field from a co-rotating vortex pair

This aeroacoustic reference example (often referred in literature as "Co-rotating vortex pair") provides the analytic solution of the flow, aeroacoustic source and acoustic field. Details on the example and derivation can be found in the article "Analysis of the co-rotating vortex pair as a test case for computational aeroacoustics" on which the analytic functions are based on can be found here: 10.1016/j.jsv.2024.118496. The following Matlab functions can be used for computing the aero-acoustic radiation of a co-rotating vortex pair:

Main script:

compute_pfar - Computes the radiated acoustic field. Use the "method" variable to change the aeroacoustic model

Computing the source terms:

vpair_pic - Incompressible pressure field p_ic and Dp_ic / Dt at a given time instance

vpair_u -   Velocity field u, and its first and second spatial derivatives at a given time instance

plot_source_terms - Create a plot of the source terms of both Lighthill and PCWE

plot_quadrupole_field - Plots the analytical quadrupole field solution

Utility functions used by the main script:

gaussquad - Gauss-Legendre quadrature in 1D (original version from Mathworks FTP)

subdiv_graded - Graded subdivision of one or more sections in 1D

vpair_quadrature - Quadrature base points and weights for numerical convolution

Resource:

colormap.png - Blue -> Gray -> Red color scale

All functions and scripts, except gaussquad.m were created by the authors:

P. Rucz, M. Á. Ulveczki, J. Heinz, S. Schoder