Probabilistic Model for Concentration Fluctuations in Compact-Source Plumes in an Urban Environment

Abstract

A comprehensive model for the prediction of concentration fluctuations in plumes dispersing in the complex and highly disturbed wind flows in an urban environment is formulated. The mean flow and turbulence fields in the urban area are obtained using a Reynolds-averaged Navier-Stokes (RANS) flow model, while the standard k-turbulence model (k is the turbulence kinetic energy and is the viscous dissipation rate) is used to close the model. The RANS model provides a specification of the velocity statistics of the highly disturbed wind flow in the urban area, required for the solution of the transport equations for the mean concentrationc and concentration variance c 2 (both of which are formulated in the Eulerian framework). A physically-based formulation for the scalar dissipation time scale t d , required for the closure of the transport equation for c 2 , is presented. This formulation relates t d to an inner time scale corresponding to "internal" concentration fluctuation associated with relative dispersion, rather than an outer time scale associated with the entire portion of the fluctuation spectrum. The two lowest-order moments of concentration (c and c 2 ) are used to determine the parameters of a pre-chosen functional form for the concentration probability density function (clipped-gamma distribution). Results of detailed comparisons between a water-channel experiment of flow and dispersion in an idealized obstacle array and the model predictions for mean flow, turbulence kinetic energy, mean concentration, concentration variance, and concentration probability density function are presented.

CFD simulation of near-field pollutant dispersion in the urban environment: A review of current modeling techniques

“…However, in compensation, a model solving the transport equation of the concentration variance has been known as the prediction method of concentration fluctuation in RANS model (Launder, 1978). With the availability of measurements of concentration fluctuation in a plume dispersing in an urban area, efforts to model the concentration variance for urban plumes have been undertaken by several researchers Hsieh et al, 2007;Mavroidis et al, 2007;Wang et al, 2009;Milliez and Carissimo, 2008;Yee et al, 2009). Generally, it has been demonstrated that these models can be used to reproduce concentration variance in an idealized urban area under laboratory conditions.…”

Chemical Source Localization Fusing Concentration Information in the Presence of Chemical Background Noise

“…The total PDF is composed of a mixed fluid part due to in-plume mixing of eddies containing the target substance (the first term on right-hand side), and an unmixed ambient fluid part (the second term on right-hand side) caused by plume meandering which produces intermittent periods of zero concentration for a fraction of time (1 − γ ), being γ the intermittency factor. Although Equation (3) is specified in terms of four parameters, it can be uniquely modeled by the mean (M) and the standard deviation (SD) of a series of readings [28]. There is a simple relation among M, SD, and the plume intermittency; thus, γ is determined as: $\gamma =\gamma false(k*,s,\lambda false)=\frac{\Gamma \left(k*;\lambda /s\right)}{\Gamma false(k*false)}=\min \left(1,\frac{3}{K_{\mathrm{int}}{}^2+1}\right)$ where $\Gamma \left(v;c\right)$ corresponds to the incomplete gamma function and $K_{int}$ is the ratio between the SD and the mean of the series of readings at a fixed position.…”

“…For a specified value of $K_{int}$, the parameters $\lambda$, $k^{*}$ and $s$ can be obtained solving a set of transcendental equations, thus making Equation (3) totally defined. The details for computing these parameters are given in [28]. …”

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

“…The full mixing hypothesis is not a physical solid theory for the development of a plume from a point source and some researchers have provided innovative parameterizations (Hsieh et al, 2007;Wang et al, 2007Wang et al, , 2008Yee et al, 2009). In some cases the pollutant travel time is used which is a key turbulence time scale of the plume near the source.…”