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.

Budgets of turbulent kinetic energy, Reynolds stresses, variance of temperature fluctuations and turbulent heat fluxes in a round jet

“…In the present study, the pressure diffusion term Π k is estimated using Lumley's model, and dissipation is taken as the closing balance of the budget. The use of Lumley's model to evaluate Π k is also supported by Taub et al (2013) based on their DNS results. However, PL adopted a different strategy, making the assumption that the pressure diffusion term is negligible.…”

“…Bogey & Bailly (2009) found that the pressure diffusion term Π k could be neglected away from the jet centreline, but was of some importance close to the centreline. However, for a much lower Reynolds number (Re D = 2000), Taub et al (2013) presented a direct numerical simulation (DNS) study, showing that the pressure diffusion term was negligible on the jet centreline and reached a maximum value at a radial distance of ξ = r/R u = 0.3. Further away from the jet centreline, the LES and DNS just mentioned produced pressure diffusion terms of the same magnitude.…”

An examination of the high-order statistics of developing jets, lazy and forced plumes at various axial distances from their source

“…The simulation of the pure jet with Re I = 2000 is the same simulation that was discussed in detail in Taub et al [23]. In order to more clearly compare the various axisymmetric flows, some of the more significant results will be repeated here.…”

“…Taub et al [23] reported that for the jet simulation discussed here, the various terms of approximation (17) change with axial distance, but that the mean flow term, 2π ∞ 0 U z 2 rdr, accounts for more than 93% the time-averaged momentum flux throughout the domain and that the total flux is conserved as predicted by Hussein. [11] Due to the non-zero buoyancy term in the axial velocity momentum equation, the momentum flux will not be conserved in plumes.…”

Complete self-preservation on the axis of a turbulent round jet

“…They also showed that iso = 15ν(∂u/∂x) 2 , which according to SP can be as expressed by (3.5) which uses local isotropy, is practically equal to on the centreline. Further, the fact that the direct numerical simulation of Taub et al (2013) shows that the pressure term on the centreline is negligible, as predicted by Lumley's model, provides support for (2.1) on the centreline and gives confidence that iso . We thus use iso as the surrogate of .…”