Vorticity structure and evolution in a transverse jet with new algorithms for scalable particle simulation

Abstract

Transverse jets arise in many applications, including propulsion, effluent dispersion, oil field flows, V/STOL aerodynamics, and drug delivery. Furthermore, they exemplify flows dominated by coherent structures that cascade into smaller scales, a source of many current challenges in fluid dynamics. This study seeks a fundamental, mechanistic understanding of the relationship between the dispersion of jet fluid and the underlying vortical structures of the transverse jet-and of how to develop actuation that optimally manipulates their dynamics to affect mixing. We develop a massively parallel 3-D vortex simulation of a high-momentum transverse jet at large Reynolds number, featuring a discrete filament representation of the vorticity field with local mesh refinement to capture stretching and folding and hair-pin removal to regularize the formation of small scales. A novel formulation of the vorticity flux boundary conditions rigorously accounts for the interaction of channel vorticity with the jet boundary layer. This formulation yields analytical expressions for vortex lines in near field of the jet and suggests effective modes of unsteady actuation at the nozzle. The present computational approach requires hierarchical N-body methods for velocity evaluation at each timestep, as direct summation is prohibitively expensive. We introduce new clustering algorithms for parallel domain decomposition of N-body interactions and demonstrate the optimality of the resulting cluster geometries. We also develop compatible techniques for dynamic load balancing, including adaptive scaling of cluster metrics and adaptive redistribution of their centroids. These tools extend to parallel hierarchical simulation of N-body problems in gravitational astrophysics,

(cont.) molecular dynamics, and other fields. Simulations reveal the mechanisms by which vortical structures evolve; previous computational and experimental investigations of these processes have been incomplete at best, limited to low Reynolds numbers, transient early-stage dynamics, or Eulerian diagnostics of essentially Lagrangian phenomena. Transformation of the cylindrical shear layer emanating from the nozzle, initially dominated by azimuthal vorticity, begins with axial elongation of its lee side to form sections of counter-rotating vorticity aligned with the jet trajectory. Periodic rollup of the shear layer accompanies this deformation, creating arcs carrying azimuthal vorticity of alternating signs, curved toward the windward side of the jet. Following the pronounced bending of the trajectory into the crossflow, we observe a catastrophic breakdown of these sparse periodic structures into a dense distribution of smaller scales, with an attendant complexity of tangled vortex filaments. Nonetheless, spatial filtering of this region reveals the persistence of counter-rotating streamwise vorticity. We further characterize the flow by calculating maximum direct Lyapunov exponents of particle trajectories, identifying repelling material surfaces that organize finite-time mixing.