Plume rise and spread in buoyant releases from elevated sources in the lower atmosphere

Abstract

This study focuses on the influence of emission conditions—velocity and temperature—on the dynamics of a buoyant gas release in the atmosphere. The investigations are performed by means of wind tunnel experiments and numerical simulations. The aim is to evaluate the reliability of a Lagrangian code to simulate the dispersion of a plume produced by pollutant emissions influenced by thermal and inertial phenomena. This numerical code implements the coupling between a Lagrangian stochastic model and an integral plume rise model being able to estimate the centroid trajectory. We verified the accuracy of the plume rise model and we investigated the ability of two Lagrangian models to evaluate the plume spread by means of comparisons between experiments and numerical solutions. A quantitative study of the performances of the models through some suitable statistical indices is presented and critically discussed. This analysis shows that an additional spread has to be introduced in the Lagrangian trajectory equation in order to account the dynamical and thermal effects induced by the source conditions.

Appendix

The evaluation of the accuracy of a model requires defining some parameters in order to quantify the differences between numerical solutions and experimental data. In this study we have applied the criteria proposed by Chang and Hanna [7]. The global error is split into a systematic error and a local error. The first is related to the general ability of the model to underestimate or overestimate the measures. The second provides an evaluation of the differences between the single predictions and the mean behaviour of the model. The systematic and local errors are evaluated by the AFB and the NMSE, respectively:

$$\begin{aligned}&AFB=\frac{1}{M}\mathop \sum \limits _{i=1}^M \left[ {2.0\frac{\mathop \sum \nolimits _{j=1}^N \left| {C_{exp} ( j)-C_{mod} ( j)} \right| }{\mathop \sum \nolimits _{j=1}^N ( {C_{exp} ( j)+C_{mod} ( j)})}} \right] _i\\&NMSE=\frac{1}{M}\mathop \sum \limits _{i=1}^M \left[ {\frac{\frac{1}{N}\mathop \sum \nolimits _{j=1}^N ( {C_{exp} ( j)-C_{mod} ( j)})^2}{\frac{1}{N}\mathop \sum \nolimits _{j=1}^N C_{exp} (j)\frac{1}{N}\mathop \sum \nolimits _{j=1}^N C_{mod} (j)}} \right] _i \end{aligned}$$

where $C_{exp} (j)$ and $C_{mod} (j)$ are, respectively, the experimental measure and the computed value evaluated at each measure point $j$ and for each plume $i$; $N$ and $M$ are the number of measurements and the number of plumes, respectively.

If the data are distributed on several orders of magnitude, AFB and NMSE give a larger weight to the higher values. In order to balance this effect we define two logarithmic indices, the MG for the systematic error and the VG for the local error:

$$\begin{aligned}&MG=\frac{1}{M}\mathop \sum \limits _{i=1}^M \left\{ {\hbox {exp}\left[ {\frac{1}{N}\left( {\mathop \sum \limits _{j=1}^N \ln C_{exp} (j)-\mathop \sum \limits _{j=1}^N \ln C_{mod} (j)}\right) } \right] } \right\} _i\\&VG=\frac{1}{M}\mathop \sum \limits _{i=1}^M \left\{ {\hbox {exp}\left[ {\frac{1}{N}\mathop \sum \limits _{j=1}^N ( {\ln C_{exp} ( j)-\ln C_{mod} (j)})^2} \right] } \right\} _i \end{aligned}$$

The fraction of observations within a FAC2 is related to the ability of the model to provide results without exceeding an upper bound. The FAC2 is defined as the fraction of data having the property $0.5\le C_{exp} /C_{mod} \le 2$.

The criterion of acceptance of the model performances is provided by the validity ranges of the statistical indices [7]:

• $FAC2\ge 0.5;$

• $AFB\le 0.3;$

• $0.7\le MG\le 1.3;$

• $NMSE\le 1.5;$

• $VG\le 4.0.$