A direct numerical simulation study of higher order statistics in a turbulent round jet

Abstract

Up until recently direct numerical simulation (DNS) studies involving round turbulent jets have focused on first and second order statistics and vortical behavior near the source of the jet. The third order statistics necessary to compute the turbulent kinetic energy and Reynolds stress transport equations have been examined using LES studies. However, further examination with DNS is important as, on the subgrid scale, LES uses models for Reynolds stress. In this study a DNS of a turbulent free jet with a Reynolds number equal to ReJ = 2000 is computed using a second order accurate, time splitting finite volume scheme. First, second, and third order statistics are compared with previous experimental and numerical studies. All terms of the turbulent kinetic energy balance are calculated directly. The results are compared to experimental studies such as those of Hussein et al. [“Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet,” J. Fluid Mech. 258, 31–75 (1994)], Panchapakesan and Lumley [“Turbulence measurements in axisymmetric jets of air and helium. Part 1. Air jet,” J. Fluid Mech. 246, 197–233 (1993)], and others. The assumptions made by the various experimental studies in order to solve the dissipation and pressure diffusion terms are discussed and examined using the data from the current study. The Reynolds stress transport equations are also calculated and discussed. Vortical structures are visualized by the λci method and discussed along with entrainment of ambient fluid into the jet. The one dimensional energy spectra in the azimuthal direction are calculated directly and are also discussed.