Time-Dependent Contaminant Transport in Ventilating Air from a Moving Source

Abstract

A new method which combines the Eulerian, fixed control volume with a moving, Lagrangean flow channel is described for the solution of the conjugate, advection-diffusion problem for modeling transport processes of contaminant species. The transport model is presented as a conservative mass balance equation in a state-flux, species transport form in the space-time domain. A fully-implicit, general solution scheme is formulated with matrix operators in the space-time domain. The particular solutions for specific initial and boundary conditions and source term are constructed with the help of a single, inverse matrix operator, A -1 , which has to be calculated only once for all possible particular problems. Although A -1 involves a large number constants, all are independent from the initial, boundary, and source term input vectors. The multi-level, state-flux, space-time (SFST) scheme brings a significant computational acceleration since A -1 has to be calculated only once, such as in mine ventilation cases involving long drifts with constant air flow velocities. Such application is shown in an example for analyzing the transport and concentration distributions of diesel particulate matter (DPM) in the ventilation air at the working area with the interactions between ventilation and a moving diesel loading machine. Comparison between simulation and in situ DPM monitoring results suggests that reliable evaluation of average exposure of DPM to mine workers may be accomplished directly from tailpipe DPM emission data, ventilation air velocity, and mine geometry with the use of the SFST model even in a highly dynamic working area, potentially reducing the need for real-time DPM monitoring.