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

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

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

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

Structure and entrainment in the plane of symmetry of a turbulent spot

Laser-Doppler velocity measurements in water are reported for the flow in the plane of symmetry of a turbulent spot. The unsteady mean flow, defined as an ensemble average, is fitted to a conical growth law by using data at three streamwise stations to determine the virtual origin in x and t. The two-dimensional unsteady stream function is expressed as ψ=U^2_∞tg(ξ,η) in conical similarity co-ordinates ζ = x/U_∞t and η = y/U_∞t. In these co-ordinates, the equations for the unsteady particle displacements reduce to an autonomous system. This system is integrated graphically to obtain particle trajectories in invariant form. Strong entrainment is found to occur along the outer part of the rear interface and also in front of the spot near the wall. The outer part of the forward interface is passive. In terms of particle trajectories in conical co-ordinates, the main vortex in the spot appears as a stable focus with celerity 0·77U_∞. A second stable focus with celerity 0·64U_∞ also appears near the wall at the rear of the spot. Some results obtained by flow visualization with a dense, nearly opaque suspension of aluminium flakes are also reported. Photographs of the sublayer flow viewed through a glass wall show the expected longitudinal streaks. These are tentatively interpreted as longitudinal vortices caused by an instability of Taylor-Görtler type in the sublayer

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

Stochastic geometric properties of scalar interfaces in turbulent jets

Experiments were conducted in which the behavior of scalar interfaces in turbulent jets was examined, using laser-induced fluorescence (LIF) techniques. The experiments were carried out in a high Schmidt number fluid (water), on the jet centerline, over a jet Reynolds number range of 1000<=Re<=24 000. Both two-dimensional scalar data, c(r,t) at fixed x/d, and one-dimensional scalar data, c(t) at fixed x/d and r/x, were analyzed using standard one- and two-dimensional fractal box-counting algorithms. Careful treatment was given to the handling of noise. Both long and short records as well as off-centerline measurements were also investigated. The important effect of threshold upon the results is discussed. No evidence was found of a constant (power-law) fractal dimension over the range of Reynolds numbers studied. On the other hand, the results are consistent with the computed behavior of a simple stochastic model of interface geometry

Scale distributions and fractal dimensions in turbulence

A new geometric framework connecting scale distributions to coverage statistics is employed to analyze level sets arising in turbulence as well as in other phenomena. A 1D formalism is described and applied to Poisson, lognormal, and power-law statistics. A d-dimensional generalization is also presented. Level sets of 2D spatial measurements of jet-fluid concentration in turbulent jets are analyzed to compute scale distributions and fractal dimensions. Lognormal statistics are used to model the level sets at inner scales. The results are in accord with data from other turbulent flows