Extension of a fluctuating plume model of tracer dispersion to a sheared boundary layer and to a large array of obstacles

Abstract

Fluctuating plume models provide a useful conceptual paradigm in the understanding of plume dispersion in a turbulent flow. In particular, these models have enabled analytical predictions of higher-order concentration moments, and the form of the one-point concentration probability density function (PDF). In this paper, we extend the traditional formalism of these models, grounded in the theory of homogeneous and isotropic turbulent flow, to two cases: namely, a simple sheared boundary layer and a large array of regular obstacles. Some very high-resolution measurements of plume dispersion in a water channel, obtained using laser-induced fluorescence (LIF) line-scan techniques are utilised. These data enable us to extract time series of plume centroid position (plume meander) and dispersion in the relative frame of reference in unprecedented detail. Consequently, experimentally extracted PDFs are able to be directly compared with various theoretical forms proposed in the literature. This includes the PDF of plume centroid motion, the PDF of concentration in the relative frame, and a variety of concentration moments in the absolute and relative frames of reference. The analysis confirms the accuracy of some previously proposed functional forms of model components used in fluctuating plume models, as well as suggesting some new forms necessary to deal with the complex boundary conditions in the spatial domain.

Dispersion of a Passive Scalar Fluctuating Plume in a Turbulent Boundary Layer. Part II: Analytical Modelling

“…By means of experimental measurements, Gailis et al (2007) showed that the lateral and vertical profiles of i cr exhibit large variations on the y-z plane. Based on these measurements, they proposed to parametrize i cr as a function of the mean relative concentration c r ,…”

“…The dependence of this parameter on the flow dynamics and emission conditions however has been rarely characterized either experimentally or numerically. As far as we know, the only attempt to measure this parameter is that of Gailis et al (2007), who studied the dispersion of a passive scalar with optical measurement techniques within both a turbulent boundary layer and an obstacle array. Given this lack of information, most of the meandering plume models found in the literature (Luhar et al 2000;Yee and Wilson 2000;Franzese 2003;Mortarini et al 2009) adopt quite simple models for i cr , which is generally assumed to be dependent on the x-coordinate only.…”

“…More complex parametrizations of i cr have been proposed only recently. Gailis et al (2007) introduced a three-dimensional model of i cr to predict the concentration PDF within a dispersion plume in a group of obstacles. This same parametrization was used by Ferrero et al (2013) to compute the concentration statistics of two reactive chemical species within a convective boundary layer.…”

Prediction of high concentrations and concentration distribution of a continuous point source release in a semi-idealized urban canopy using CFD-RANS modeling

“…For this reason, the Gamma distribution is selected as it is one of the widely known distributions for this kind of studies and has been validated by many researchers (e.g. Lung et al, 2002;Yee et al, 1993;Gailis et al, 2007;Gailis and Hill, 2006). The PDF of the Gamma distribution for concentration C is given as follows:…”

“…Usually researchers select known distributions to describe the measured concentration (e.g. Lung et al, 2002;Mylne and Mason, 1991;Gailis et al, 2007). The peak concentrations are predicted by using predefined confidence intervals/thresholds or the Extreme Value Theory and the Generalized Pareto Distribution (e.g.…”