Modelling pollution dynamics of longitudinally ventilated road tunnels

This paper develops a mathematical model in various forms to describe the dynamic response between vehicle exhaust emissions, air flow and the resulting pollutant concentrations in a longitudinally ventilated tunnel. Starting with the well-known "advection-diffusion" partial differential equation, several innovations in analysis are presented to finally create a simple estimator usable in predictive control algorithms. These innovations include; i) a variable time step numerical method of solution, ii) a discrete time (z-domain) model of the system, iii) a linear analytical solution for harmonic inputs which leads to a frequency domain description of the system dynamics for small perturbations about a mean operating condition, iv) a continuous time (s-domain) transfer function model, derived from the frequency domain analysis.