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-ϵ turbulence model (k is the turbulence kinetic energy and ϵ 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 concentration \({\bar{c}}\) and concentration variance \({\overline{c'^2}}\) (both of which are formulated in the Eulerian framework). A physically-based formulation for the scalar dissipation time scale td, required for the closure of the transport equation for \({\overline{c'^2}}\), is presented. This formulation relates td 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 (\({\bar{c}}\) and \({\overline{c'^2}}\)) 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.