A PDF propagation approach to model turbulent dispersion in swirling flows

A computationally efficient approach that solves for the spatial covariance matrix along the dense particle ensemble-averaged trajectory has been succ essfully applied to describe turbulent dispersion in swirling flows. The pr ocedure to solve for the spatial covariance matrix is based on turbulence i sotropy assumption, and it is analogous to Taylor's approach for turbulent dispersion. Unlike stochastic dispersion models, this approach does not inv olve computing a large number of individual particle trajectories in order to adequately represent the particle phased a few representative particle e nsembles are sufficient to describe turbulent dispersion. The particle Lagr angian properties required in this method are based on a previous study (Sh irolkar and McQuay, 1998). The fluid phase information available from pract ical turbulence models is sufficient to estimate the time and length scales in the model. In this study, two different turbulence models are used to s olve for the fluid phase - the standard k-epsilon model, and a multiple-tim e-scale (NITS) model. The models developed here are evaluated with the expe riments of Sommerfeld and Qiu (1991). A direct comparison between the dispe rsion model developed in this study and a stochastic dispersion model based on the eddy lifetime concept is also provided. Estimates for the Reynolds stresses required in the stochastic model are obtained from a set of second -order algebraic relations. The results presented in the study demonstrate the computational efficiency of the present dispersion modeling approach. T he results also show that the NITS model provides improved single-phase res ults in comparison to the k-epsilon model. The particle statistics, which a re computed based on the fundamentals of the present approach, compare favo rably with the experimental data. Furthermore, these statistics closely com pare to those obtained using a stochastic dispersion model. Finally, the re sults indicate that the particle predictions are relatively unaffected by w hether the Reynolds stresses are based on algebraic relations or on the tur bulence isotropy assumption. (C) 2001 Editions scientifiques et medicales E lsevier SAS.