Characterization and low-order representation of the vortex meandering motion in upswept afterbody wakes

Abstract

Vortex meandering is often characterized by seemingly stochastic motions of the vortex core. An elucidation of the underlying mechanisms of core movement aids not only in characterizing the meandering phenomenon but also forms a starting point to guide flow control techniques. This paper investigates the complex motion of longitudinal vortices behind an abstracted cargo aircraft fuselage. In contrast to wingtip vortices that arise in relative isolation, in this case the large aft region upsweep generates a meandering counter-rotating vortex pair that retains its coherence for long distances downstream. High-resolution spatio-temporal datasets obtained from large-eddy simulation of a cylindrical fuselage with longitudinally aligned axis and a sharp-edged base are used for this purpose. The circulation of each vortex in the pair initially increases immediately after formation and asymptotes to a near constant value downstream. Although the time-mean form of the vortices becomes nearly axisymmetric, the transient disorganized motions include time-local regions of opposite vorticity. The complicated meandering motion is decomposed using proper-orthogonal decomposition (POD) modes as primary building blocks. The first two modes constitute a mutually orthogonal $\left|m\right|=1$ elliptic pair, accounting for about 35% of the total energy; individually these modes account for the displacement of vortex cores along straight lines whose slopes coincide with their respective dipole axes. The wake outside of the immediate vicinity of the base displays low-rank behavior, in that the number of modes required to reproduce the flow to a given degree of accuracy diminishes rapidly. Beyond two fuselage (cylinder) diameters downstream, the two leading POD modes can reconstruct the dominant meandering motion and spatial structure in the LES data with less than 15% error using a suitable loss measure.