ISSN:
1089-7666
Source:
AIP Digital Archive
Topics:
Physics
Notes:
For industrial and environmental purposes there is a need for broad concepts and general models to describe many types of mixing processes and situations. These concepts arise from exact conversation results,1 and the similarity of the velocity fields and the particle displacements in turbulent fields at high Reynolds number, especially in the presence of shear. However, the design and control of mixing, like other kinds of turbulent problems, is usually improved by considering quasideterministic models of how turbulent eddies affect the process. Such models are changing with new computations and experimental studies of turbulence structure. Mixing involves continuously bringing together volumes of fluid with different concentrations on small enough scales to effect mixing between molecules.The Lagrangian statistical analysis of the displacements of fluid elements enables joint moments of concentration to be calculated in terms of initial concentration distributions in the absence of diffusion and reaction.2 This macromixing analysis in conjunction with simple concepts of small-scale mixing leads to models and a new understanding for many mixing processes, e.g., concentration fluctuations, simple chemical reactions, and the effects of varying the mean shear, the velocity spectra and the molecular diffusivity.3–7 Since extreme pollution concentrations and many complex chemical and physical processes can only be understood in a given scalar field, rather than from statistics of scalar fields, it is necessary to understand and model where and how mixing occurs in a single realization of the flow. This requires computing and/or measuring the evolving velocity and scalar fields in turbulent flows. Recent direct numerical simulations8–10 and kinematic simulations,11,12 i.e., velocity fields constructed from random Fourier modes, with observed or idealized two-point, two-time Eulerian and Lagrangian spectra, have shown (i) how surface areas expand exponentially, and volumes elongate only slightly;8,13 (ii) how scalar surfaces are deformed quite differently in different characteristic regions of turbulent flows; viz., vortical, eddy regions (rolling up into "fractal'' surfaces), convergent–divergent, stagnating regions (stretching out, and nonfractal), and streaming regions (where tendrils form);14 (iii) how large volumes of matter disperse in particular events (which cannot be obtained from ensemble average statistics obtained from stochastic models based on displacements of one or two particles).15
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.858030
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