On the application of Thomson's random flight model to the prediction of particle dispersion within a ventilated airspace

Abstract

The correct prediction of mean particle concentrations within ventilated airspaces is an important practical problem. Recently, much progress has been made in understanding how to formulate correctly random flight models for particle trajectories in such inhomogeneous turbulent flows. Thomson showed that random flight models which satisfy the wellmixed condition (i.e. give the correct steady-state distribution of particles in phase space) are essentially correct. Thomson subsequently formulated a random flight model which satisfies the well-mixed condition for inhomogeneous Gaussian turbulence. Prompted by the success of this model in predicting particle dispersion in one-dimensional and two-dimensional inhomogeneous turbulent flows, an assessment is made of the ability of the model to predict correctly mean particle concentrations in a three-dimensional inhomogeneous turbulent flow within a mechanically ventilated airspace. When used in conjunction with the statistical properties of the air flow predicted by the k − ε model, Thomson's model is shown to predict mean particle concentrations in close accord with experimental findings. It is suggested that skewness of the turbulent velocity fluctuations is of secondary importance in determining particle dispersion in highly inhomogeneous turbulent flows, compared to the effects of strong mean streamline straining and large gradients in Reynolds stress. This view is supported by numerical studies undertaken using an extension of Thomson's model, which takes partial account of the skewness of velocity fluctuations. It is further suggested that when predicting particle dispersion in strongly inhomogeneous turbulent flows, it may not be necessary to devise random flight models which satisfy the well-mixed condition for more realistic (i.e. non-Gaussian) probability distribution functions of turbulent velocity fluctuations. This would allow difficulties associated with determining such probability distribution functions and the increased complexity of such models to be circumvented.