Point vortex modelling of the wake dynamics behind asymmetric vortex generator arrays

Abstract

In this work, we present a simple inviscid point vortex model to study the dynamics of asymmetric vortex rows, as might appear behind misaligned vortex generator vanes. Starting from the existing solution of the in_nite vortex cascade, a numerical model of four base-vortices is chosen to represent two primary counter-rotating vortex pairs and their mirror plane images, introducing the vortex strength ratio as a free parameter. The resulting system of equations is also de_ned in terms of the vortex row separation and the qualitative features of the ensuing motion are mapped. A translating and orbiting regime are identi_ed for di_erent cascade separations. The latter occurs for all unequal strength vortex pairs. Thus, the motion is further classi_ed by studying the cyclic behaviour of the orbiting regime and it is shown that for small mismatches in vortex strength, the orbiting length and time scales are su_ciently large as to appear, in the near wake, as translational (non-orbiting). However, for larger mismatches in vortex strength, the orbiting motion approaches the order of the starting height of the vortex. Comparisons between experimental data and the potential ow model show qualitative agreement whilst viscous e_ects account for the major discrepancies. Despite this, the model captures the orbital mode observed in the measurements and provides an impetus for considering the impact of these complex interactions on vortex generator designs.