Vortex-dipole impingement with convex and concave boundaries

Abstract

The vortex-dipole interactions with convex and concave boundaries in a two-dimensional domain are analyzed using the Bhatnagar–Gross–Krook (BGK) collision-based lattice Boltzmann method (LBM). The formation and detachment of the boundary layers at the flat wall creates new dipoles of non-identical vortices, following cyclic trajectories and exhibiting logarithmic variations in the production of maximum vorticity with Reynolds number (Re). The vortex-dipole interactions with concave boundaries produce a series of secondary dipoles, whose relative strength linearly decreases for the given Re in subsequent vortex-releasing events. Oblique interactions with cavity corners cause secondary dipoles to undergo head-on collisions at the domain center, influencing partner exchange and orthogonal propagation. Conversely, convex boundaries split the primary vortex-dipole upon impingement, intensifying the vorticity production and strain effects. Whereas, the larger ingestion of vorticity at the convex corners of the “T-shaped” cavity forms new dipoles, which deflect, rebound, and follow a parabolic trajectory for the vortex exchange. Normalized enstrophy, Ω(t), and palinstrophy, P(t), show distinct peaks during dipole interactions with boundary walls, influencing enhanced kinetic energy, E(t), decay. Moreover, the evolution of E(t) and Ω(t) satisfies the relation valid for no-slip boundaries. The collision behavior, vorticity production, and vortex rebound are functions of Re. The convex boundaries modify the scaling results of maximum Ω(t) and P(t) to higher exponent values than the dipole interactions with flat and concave boundaries.