19 research outputs found
Some remarks on modelling the PDF of the concentration of a dispersing scalar in turbulence
The paper deals with the probability density function (PDF) of the concentration of a scalar within a turbulent flow. Following some comments about the overall structure of the PDF, and its approach to a limit at large times, attention focusses on the so-called small scale mixing term in the evolution equation for the PDF. This represents the effect of molecular diffusion in reducing concentration uctuations, eventually to zero. Arguments are presented which suggest that this quantity could, in certain circumstances, depend inversely upon the PDF, and a particular example of this leads to a new closure hypothesis. Consequences of this, especially similarity solutions, are explored for the case when the concentration field is statistically homogeneous
On the early development of dispersion in flow through a tube with wall reactions
This is a study on numerical simulation of the
convection-diffusion transport of a chemical species in steady flow
through a small-diameter tube, which is lined with a very thin layer
made up of retentive and absorptive materials. The species may be
subject to a first-order kinetic reversible phase exchange with the wall
material and irreversible absorption into the tube wall. Owing to the
velocity shear across the tube section, the chemical species may spread
out axially along the tube at a rate much larger than that given by the
molecular diffusion; this process is known as dispersion. While the
long-time dispersion behavior, well described by the Taylor model,
has been extensively studied in the literature, the early development of
the dispersion process is by contrast much less investigated. By early
development, that means a span of time, after the release of the
chemical into the flow, that is shorter than or comparable to the
diffusion time scale across the tube section. To understand the early
development of the dispersion, the governing equations along with the
reactive boundary conditions are solved numerically using the Flux
Corrected Transport Algorithm (FCTA). The computation has enabled
us to investigate the combined effects on the early development of the
dispersion coefficient due to the reversible and irreversible wall
reactions. One of the results is shown that the dispersion coefficient
may approach its steady-state limit in a short time under the following
conditions: (i) a high value of Damkohler number (say Da ≥ 10); (ii) a
small but non-zero value of absorption rate (say Γ* ≤ 0.5).link_to_OA_fulltex
Importance of advective zone in longitudinal mixing experiments
One- dimensional Fickian dispersion models such as the advection diffusion equation ( ADE) are commonly used to analyse and predict concentration distributions downstream of contamination events in watercourses. Such models are only valid once the tracer had entered the equilibrium zone. This paper compares previous theoretical, experimental and numerical estimates of the distance to reach the equilibrium zone with new experimental values, obtained by examining the change of skewness in a tracer profile, downstream of a cross- sectionally well mixed source. Closer agreement was found with Fischers' theoretical estimate than prior experimental and numerical studies