Plume rise model for merging plumes

To correctly reproduce the dispersion of pollutants the plume rise modeling is fundamental to obtain the injection height, i.e. the altitude at which the majority of the smoke burden is released into the surrounding atmosphere, because from this depends how the plume from fire emissions are ultimately transported In 2013 Alessandrini et al. proposed a method for the buoyant plume rise computation in which a scalar transported by the particles and representing the temperature difference between the plume and the environment air is introduced. As a consequence, no more particles than those inside the plume have to be released to simulate the entrainment of the background air temperature. A second scalar, the vertical plume velocity, is assigned to each particle. In this way the entrainment is properly simulated and the plume rise is calculated from the local property of the flow. However, the method may have some drawbacks when two plumes from different sources cross, as in the case of two neighbouring chimneys or scattered fires. In this case, the scheme can lead to non-physical situations that lead to an increase in temperature. To avoid this problem, the scheme has been modified. In the new model, the particles do not carry the temperature difference but the temperature and mass so that the transport of the heat quantity can be simulated. 
The model is  tested against data from two laboratory experiments in neutral and stable stratified flows. The comparison shows a good agreement. Then, we teste the model in the case  of two plumes from adjacent stacks combining during the rising stage. The results are presented in terms of statistical indeces and plots.