Large Eddy Simulation of Variable Density Turbulent Axisymmetric Jets

Three cases of variable-density turbulent round jets discharging from a straight circular pipe into a weakly confined low-speed co-flowing air stream are studied with the aid of large eddy simulation. The density ratios considered are 0.14 [He/air], 1.0 [air/air] and 1.5 [CO2/air], with Reynolds numbers of 7000, 21000 and 32000, respectively. Detailed comparisons of the statistics show good agreement with the corresponding experiments. They confirm that a lower-density jet develops more rapidly than a denser jet with the same exit momentum flux. The coherent structures of the three jets are investigated by visualization of the iso-surface of pressure fluctuations and vorticity. In the developing stage of the Kelvin-Helmholtz instability, large finger-shape regions of vorticity are observed for the helium jet close to the nozzle lip. This feature is not found in the air and the CO2 jet. The occurrence of strong streamwise vorticities across the shear layer in the helium jet is demonstrated by a characteristic variable related to the orientation of the vorticity. INTRODUCTION Turbulent flows with variable density, which may be due to temperature variations stemming from reactions or variations in the composition by fluids of different density, exist widely in nature as well as in technical devices. The ability to predict the turbulent mixing in flows with variable density is vital for the modelling of the dynamics of such flows and a prerequisite for predicting turbulent combustion situations. Unlike the extensively studied turbulent flows with constant density, turbulent flows with variable density are less well understood. Relatively few experimental studies were reported on variable-density turbulent flow situations and especially for flows with large density differences. An experiment with helium/air mixture discharging into a confined swirling flow was carried out by Ahmed et al. (1985). Panchapakesan and Lumley (1993) conducted an experiment with helium injected into open quiescent air from a round nozzle. Later, Djeridane et al. (1996) and Amielh et al. (1996) performed experimental studies of variable-density turbulent jets, including helium, air and CO2 jets exiting into a low-speed air co-flow. Numerical investigations of this type of flow are also relatively scarce. Jester-Zürker et al. (2005) performed a numerical study of turbulent non-reactive combustor flow under constant and variable-density conditions using a Reynolds-stress turbulence model. They obtained good agreement between simulation and experiment for the constant-density flow, whereas the results for the variabledensity flow were less satisfactory. Some large-eddy simulation (LES) of variable density round jets were also performed recently (Zhou et al., 2001, Tyliszczak and Boguslawski, 2006). To the authors’ knowledge, however, detailed comparisons of LES results and experimental data for round jets, covering density ratios both lower and larger than unity, are not available in the literature. The aim of the present work is to perform a detailed comparison of LES results and experimental data for three round jets with density ratios 0.14, 1, and 1.52 respectively, to gain a deeper understanding of the effect of density differences on the jet development. NUMERICAL METHOD In this study, the so-called low-Mach number version of the compressible Navier-Stokes equations is employed. With this approach, the pressure P is decomposed into a spatially constant component P, interpreted as the thermodynamic pressure, and a variable component P, interpreted as the dynamic pressure. P is connected to temperature and density, while P is related to the velocity field only and does not influence the density. Due to this decomposition, sonic waves are eliminated from the flow, so that the time step is not restricted by the speed of sound. Applying large eddy filtering to the low-Mach number equations, the corresponding filtered LES equations are obtained. The unclosed terms in these equations have to be determined by a subgrid scale (SGS) model. The variabledensity dynamic Smagorinsky model by Moin et al. (1991) is used to determine the SGS eddy viscosity, μT, in the momentum equations. The SGS scalar flux is modeled by the gradient diffusion model: