Lagrangian model with heat-carrying particles

The dispersion of pollutants in the atmosphere, whether from industrial emissions, wildfires, or other sources, poses significant challenges to air quality management and environmental protection. Understanding the behavior of plumes is crucial for predicting their dispersion patterns and potential impacts on human health and the environment. In this work, we present a new plume rise scheme based on heat transport. The idea at the basis of the new algorithm is the same as the actual scheme embedded in the Lagrangian Particle Model SPRAY-WEB. The temperature difference between the ambient and the plume and the vertical velocity of the plume are expressed on a fixed Eulerian grid. The particles are assigned with an equivalent momentum, temperature, mass, and density, transported as scalar quantities with the particles following the Lagrangian description of the motion. This allows us to reproduce the entrainment phenomenon as a mixing of two fluids (environmental air and plume) with different temperatures: the resulting temperature is given by Richmann’s law. The results obtained with the old plume rise algorithm and the new one are compared with Briggs (1975) analytical curve in the case of an idealized atmosphere with a neutral stratification and a constant horizontal wind and with experimental data. From the comparison in an ideal atmosphere, it emerged that with the new algorithm, the plume reaches a higher height than with the old one and the asymptotic trend obtained with both models follows the Briggs curve. As for the comparison with the measurements, the results obtained with the new algorithm are in better agreement with the experimental data than the old one.