Data on turbulent mixing and other turbulent-flow phenomena suggest that a (mixing) transition, originally documented to occur in shear layers, also occurs in jets, as well as in other flows and may be regarded as a universal phenomenon of turbulence. The resulting fully-developed turbulent flow requires an outer-scale Reynolds number of Re = U[delta]/v [greater, similar] 1–2 × 104, or a Taylor Reynolds number of ReT = u[prime prime or minute] [lambda]T/v [greater, similar] 100–140, to be sustained. A proposal based on the relative magnitude of dimensional spatial scales is offered to explain this behaviour.

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The mixing transition in turbulent flows

https://www.dimotakis.caltech.edu/pdf/Dimotakis_JFM2000.pdf

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.

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Transition stages of Rayleigh{Taylor instability between miscible fluids

Reynolds number effects within the development region of a turbulent round free jet

The stirring and mixing properties of one-phase coaxial jets, with large outer (annular) to inner velocity ratio ru = u2/u1 are investigated. Mixing is contemplated according to its geometrical, statistical and spectral facets with particular attention paid to determining the relevant timescales of the evolution of, for example, the interface area generation between the streams, the emergence of its scale-dependent (fractal) properties and of the mixture composition after the mixing transition. The two key quantities are the vorticity thickness of the outer, fast stream velocity profile which determines the primary shear instability wavelength and the initial size of the lamellar structures peeled-off from the slow jet, and the elongation rate γ = (u2 − u1)/e constructed with the velocity difference between the streams and the gap thickness e of the annular jet. The kinetics of evolution of the interface corrugations, and the rate at which the mixture evolves from the initial segregation towards uniformity is prescribed by γ−1. The mixing time ts, that is the time needed to bring the initial scalar lamellae down to a transverse size where molecular diffusion becomes effective, and the corresponding dissipation scale s(ts) areformula herewhere Re and Sc denote the gap Reynolds number and the Schmidt number, respectively. The persistence of the large-scale straining motion is also apparent from the spectra of the scalar fluctuations which exhibit a k−1 shape on the inertial range of scales.

Mixing in coaxial jets

We report on the results from a set of incompressible, shear-layer flow experiments, at high Reynolds number (Re_δ ≡ ρΔUδ_T(x)/μ ≃ 2×10^5), in which the inflow conditions of shear-layer formation were varied (δ_T is the temperature-rise thickness for chemically-reacting shear layers). Both inert and chemically-reacting flows were investigated, the latter employing the (H_2+NO)/F_2 chemical system in the kinetically-fast regime to measure molecular mixing. Inflow conditions were varied by perturbing each, or both, boundary layers on the splitter plate separating the two freestream flows, upstream of shear-layer formation. The results of the chemically-reacting ‘flip experiments’ reveal that seemingly small changes in inflow conditions can have a significant influence not only on the large-scale structure and shear-layer growth rate, as had been documented previously, but also on molecular mixing and chemical-product formation, far downstream of the inflow region.

/pdf/turbulent-shear-layer-mixing-at-high-reynolds-numbers-15qz2cekf6.pdf

Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions

Fundamental aspects of mixing between two gaseous streams in a complex geometry are studied and discussed. In the present paper, a supersonic top-stream is expanded over a 30° ramp, through which a secondary lower-stream is injected. The mass flux through the secondary stream is purposely insufficient to provide the entrainment requirements of the resulting shear layer, causing it to attach to the lower guidewall. Part of the shear layer fluid is directed upstream forming a recirculation zone, with enhanced mixing characteristics. The pressure coefficient of the device is quantified as a function of velocity ratio. The effect of heat release on the pressure coefficient is also reported. Molecular mixing was measured employing “flip” experiments based on the hypergolic hydrogen-fluorine chemical reaction. The amount of mixing for the expansion-ramp geometry is found to be higher than in classical free shear layers. However, as in free shear layers, the level of mixing decreases with increasing top-stream velocity. Results for a similar configuration with subsonic/transonic flow in the top stream are reported in Part I of this two-part series.

Michael D. Slessor

Papers

Turbulent shear-layer mixing at high Reynolds numbers: effects of inflow conditions

Molecular Mixing and Flowfield Measurements in a Recirculating Shear Flow. Part II: Supersonic Flow