Turbulent mixing

The ability of turbulent flows to effectively mix entrained fluids to a molecular scale is a vital part of the dynamics of such flows, with wide-ranging consequences in nature and engineering. It is a considerable experimental, theoretical, modeling, and computational challenge to capture and represent turbulent mixing which, for high Reynolds number (Re) flows, occurs across a spectrum of scales of considerable span. This consideration alone places high-Re mixing phenomena beyond the reach of direct simulation, especially in high Schmidt number fluids, such as water, in which species diffusion scales are one and a half orders of magnitude smaller than the smallest flow scales. The discussion below attempts to provide an overview of turbulent mixing; the attendant experimental, theoretical, and computational challenges; and suggests possible future directions for progress in this important field

Turbulent Mixing in Transverse Jets

Turbulent mixing is studied in liquid-phase transverse jets. Jet-fluid concentration fields were measured using laser-induced fluorescence and digital-imaging techniques, for jets in the Reynolds number range 1000 <= Re <= 20,000, at a jet-to-freestream velocity ratio of 10. Analysis of the measured scalar fields indicates that turbulent mixing is Reynolds-number dependent, as manifest in the evolving probability density functions of jet-fluid concentration. Enhanced homogenization is found with increasing Reynolds number. Turbulent mixing is also seen to be flow dependent, based on differences between jets discharging into a crossflow and jets into a quiescent reservoir. A novel technique for whole-field measurement of scalar increments was used to study the distribution of difference (scalar increments) of the scalar field. These scalar increments are found to tend toward exponential-tailed distributions with decreasing separation distance. Finally, the scalar field is found to be anisotropic, particularly at small length scales. This is seen in power spectra, directional scalar microscales, and directional PDFs of scalar increments. The local anisotropy of the scalar field is explained in terms of the global dynamics and large-scale strain field of the transverse jet

Reynolds number dependence of scalar fluctuations in a high Schmidt number turbulent jet

The scalar rms fluctuations in a turbulent jet were investigated experimentally, using high-resolution, laser-induced fluorescence techniques. The experiments were conducted in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 30003000 or 6500

Shape Complexity in Turbulence

The shape complexity of irregular surfaces is quantified by a dimensionless area-volume measure. A joint distribution of shape complexity and size is found for level-set islands and lakes in two-dimensional slices of the scalar field of liquid-phase turbulent jets, with complexity values increasing with size. A well-defined power law, over 3 decades in size (6 decades in area), is found for the shape complexity distribution. Such properties are important in various phenomena that rely on large area-volume ratios of surfaces or interfaces, such as turbulent mixing and combustion

Transition stages of Rayleigh–Taylor instability between miscible fluids

Direct numerical simulations (DNS) are presented of three-dimensional, Rayleigh–Taylor instability (RTI) between two incompressible, miscible fluids, with a 3:1 density ratio. Periodic boundary conditions are imposed in the horizontal directions of a rectangular domain, with no-slip top and bottom walls. Solutions are obtained for the Navier–Stokes equations, augmented by a species transport-diffusion equation, with various initial perturbations. The DNS achieved outer-scale Reynolds numbers, based on mixing-zone height and its rate of growth, in excess of 3000. Initial growth is diffusive and independent of the initial perturbations. The onset of nonlinear growth is not predicted by available linear-stability theory. Following the diffusive-growth stage, growth rates are found to depend on the initial perturbations, up to the end of the simulations. Mixing is found to be even more sensitive to initial conditions than growth rates. Taylor microscales and Reynolds numbers are anisotropic throughout the simulations. Improved collapse of many statistics is achieved if the height of the mixing zone, rather than time, is used as the scaling or progress variable. Mixing has dynamical consequences for this flow, since it is driven by the action of the imposed acceleration field on local density differences

Similarity of the concentration field of gas-phase turbulent jets

This work is an experimental investigation of the turbulent concentration field formed when the nozzle gas from a round, momentum-driven, free turbulent jet mixes with gas entrained from a quiescent reservoir. The measurements, which were made with a non-intrusive laser-Rayleigh scattering diagnostic at Reynolds numbers of 5000, 16000, and 40000, cover the axial range from 20 to 90 jet exit diameters and resolve the full range of temporal and spatial concentration scales. Reynolds-number-independent and Reynolds-number-dependent similarities are investigated. The mean and r.m.s. values of the concentration are found to be consistent with jet similarity laws. Concentration fluctuation power spectra are found to be self-similar along rays emanating from the virtual origin of the jet. The probability density function for the concentration is also found to be self-similar along rays. Near the centreline of the jet, the scaled probability density function of jet fluid concentration is found to be nearly independent of the Reynolds number

Reynolds-number effects and anisotropy in transverse-jet mixing

Experiments are described which measured concentration fields in liquid-phase strong transverse jets over the Reynolds-number range 1.0×10^3 ≤ Rej ≤ 20×10^3. Laser-induced-fluorescence measurements were made of the jet-fluid-concentration fields at a jet-to-freestream velocity ratio of Vr =10. The concentration-field data for far-field (x/dj =50) slices of the jet show that turbulent mixing in the transverse jet is Reynolds number dependent over the range investigated, with a scalar-field PDF that evolves with Reynolds number. A growing peak in the PDF, indicating enhanced spatial homogenization of the jet-fluid concentration field, is found with increasing Reynolds number. Comparisons between transverse jets and jets discharging into quiescent reservoirs show that the transverse jet is an efficient mixer in that it entrains more fluid than the ordinary jet, yet is able to effectively mix and homogenize the additional entrained fluid. Analysis of the structure of the scalar field using distributions of scalar increments shows evidence for well-mixed plateaux separated by sharp cliffs in the jet-fluid concentration field, as previously shown in other flows. Furthermore, the scalar field is found to be anisotropic, even at small length scales. Evidence for local anisotropy is seen in the scalar power spectra, scalar microscales, and PDFs of scalar increments in different directions. The scalar-field anisotropy is shown to be correlated to the vortex-induced large-scale strain field of the transverse jet. These experiments add to the existing evidence that the large and small scales of high-Schmidt-number turbulent mixing flows can be linked, with attendant consequences for the universality of small scales of the scalar field for Reynolds numbers up to at least Re=20×10^4

Cover illustration: Non-premixed hydrocarbon flame

This year’s cover illustration, reproduced here as figure 1, depicts an image formed by a short-time (1/1000 s) exposure of a non-premixed hydrocarbon flame. The flow is driven by the buoyancy forces generated by the density difference from the combustion heat release and resulting temperature rise. The Reynolds number for this buoyancy-induced, turbulent flow is relatively low, estimated at a few thousand

The lift of a cylinder executing rotary motions in a uniform flow

The mean lift coefficient of a circular cylinder executing rotary motions in a uniform flow is investigated. These motions include steady rotation, and rotary oscillations with a net rotation rate. Results for the steadily rotating cylinder show that for a given rotation rate, larger cylinder aspect ratios yield higher lift coefficients. It was also found that the addition of forced rotary oscillations to the steady rotation of the cylinder increases the lift coefficient in the cases where the wake would normally be separated in the steadily rotating case, but decreases it otherwise. In addition, a method for estimating the mean lift of a rotating cylinder is presented. Estimates based on this method compare favourably with similar data published for steadily rotating cylinders