Assessment of Puff-Dispersion Variability Through Lagrangian and Eulerian Modelling Based on the JU2003 Campaign

Abstract

In the framework of the Urban Dispersion International Evaluation Exercise (UDINEE) project coordinated by the European Commission’s Joint Research Centre, a case study was conducted of the Joint Urban 2003 (JU2003) experimental campaign in the central area of Oklahoma City, USA. The UDINEE project concerned the cases of puff dispersion of the JU2003 campaign, which are of special interest to scenarios related to security studies, such as explosions of radiological dispersal devices. Starting from the fact that puff-dispersion variability is substantial, especially in complex urban areas, even for puffs released under similar meteorological conditions, a methodology is presented for assessing this variability, which is applied to the dispersion of puffs in two of the intensive operation periods of the JU2003 campaign. Lagrangian and Eulerian dispersion models are applied for the simulations. For the Lagrangian model, variability is assessed by repeating the computations a large number of times. For the Eulerian model, variability is assessed by constructing probability density functions of concentrations on the basis of the dispersion-model results. Peak concentrations, dosages, puff-arrival times and puff durations are considered. Percentiles calculated by the Lagrangian model for all the above quantities and by the Eulerian model for peak concentrations and dosages are compared with the measurements. The results are encouraging since in several cases the measured and computed ranges of values overlap.

Appendices

Appendix 1

The velocity and turbulence profiles used as inlet boundary conditions for the three-dimensional flow simulations have been calculated by a separate one-dimensional run of the CFD model. The one-dimensional (only in the z-direction) momentum equation was solved, while adjusting in each case the wind velocity at the top boundary so as to obtain the corresponding average wind velocity measured by the PWIDS No. 15 anemometer 40 m above the ground. The k and ε transport equations were also solved in this one-dimensional computation. The calculated wind speed, turbulent kinetic energy and turbulent kinetic energy dissipation rate are shown in Fig. 9.

Fig. 9

Calculated profiles of wind speed, turbulent kinetic energy and turbulent kinetic energy dissipation rate used as inlet boundary conditions for the three-dimensional flow simulations corresponding to the dispersion of the four puffs in IOP3 and IOP7

Appendix 2

The validation of the computed flow fields is based on the comparison of simulated velocity components and turbulent kinetic energy with the corresponding quantities measured by the sonic anemometers in the downtown area during the puff dispersion. The locations of the 20 sonic anemometers in the city centre during the JU2003 campaign are shown in Fig. 10. According to Hanna et al. (2007), the sonic anemometers were located about 5 m or more from the nearest building, and were sited near street intersections.

Fig. 10

Location and numbering of the 20 sonic anemometers of the JU2003 campaign; building heights are also indicated

The measured u- and v-velocity components and the standard deviations of the u-, v- and w-components have been temporally averaged for each anemometer for the time period of each puff dispersion in IOP3 and IOP7. The averaged standard deviations of the three velocity components were used to calculate the turbulent kinetic energy. The averaged velocity components and the turbulent kinetic energy were compared with the corresponding simulated values interpolated at the exact anemometer locations in Figs. 11 and 12.

Fig. 11

a Calculated versus measured u-velocity component, bv-velocity component, c turbulent kinetic energy at the 20 sonic-anemometer locations and for the four puffs of IOP3

Fig. 12

a Calculated versus measured u-velocity component, bv-velocity component, and c turbulent kinetic energy at the 20 sonic-anemometer locations and for the four puffs of IOP7

The v-velocity component (south–north) is captured by the model better than the u-component (west–east), but there are some outlier u values in each IOP. The turbulent kinetic energy is systematically underestimated by the model, especially in IOP7, which is an aspect of the k–ε closure observed previously by the authors in several similar modelling studies. Therefore, we performed sensitivity calculations in the framework of this project using a one-equation k–l turbulence closure, which gives values of turbulent kinetic energy in better agreement with the observations and without a systematic bias. However, these computations show that the overall results of the dispersion model do not seem to be influenced by the selection of the turbulence closure scheme. Apparently, the k–ε model may underestimate the value of k, but this is compensated by a similar underestimation of the value of ε in the final calculation of the turbulent diffusivity. In a previous work (Efthimiou et al. 2017a) where flow and dispersion of a tracer from a continuous release in an urban environment was simulated, the use of the k–ε turbulence model gave very reasonable agreement with the experimental data.

Appendix 3

3.1 Beta Probability Density Function and Parametrization

The beta function is selected as the p.d.f. for the time-averaged concentration $\bar{C}\left( {\Delta \tau } \right)$, whose general formulation in this case is expressed as

$$ {\text{p}}.{\text{d}}.{\text{f}}.\left( X \right) = \frac{1}{{B\left( {\alpha ,\zeta } \right)}}X^{\alpha - 1} \left( {1 - X} \right)^{\zeta - 1} , \,{\text{where }}\,0 \le X \le 1 $$

(7)

$$ X = \frac{{\bar{C}\left( {\Delta \tau } \right)}}{{C_{ \text{max} } \left( {\Delta \tau } \right)}}, $$

(8)

where $B\left( {\alpha ,\zeta } \right)$ is a normalization constant to ensure that the total probability integrates to one. Here, the exponents $a$ and $\zeta$ are estimated using the mean concentration $\bar{C}$, variance $\sigma_{C}^{2}$ and $C_{ \text{max} } \left( {\Delta \tau } \right)$ from the relationships derived from the beta-function properties,

$$ a = \frac{1}{1 + \eta }\left( {\frac{\eta }{I} - 1} \right), $$

(9)

$$ \zeta = \eta \alpha , $$

(10)

$$ \eta = \frac{{C_{ \text{max} } \left( {\Delta \tau } \right)}}{{\bar{C}}} - 1, $$

(11)

with $I = \sigma_{C}^{2} /\bar{C}^{2}$ the concentration fluctuation intensity.

For the estimation of the extreme value $C_{ \text{max} } \left( {\Delta \tau } \right)$, the approach introduced by Bartzis et al. (2008) is adopted at this stage, where

$$ C_{ \text{max} } \left( {\Delta \tau } \right) = \bar{C}\left[ {1 + 9I\left( {\frac{\Delta \tau }{{T_{C} }}} \right)^{ - 0.3} } \right], $$

(12)

and $T_{C} = 0.5k/\varepsilon$ is the concentration integral time scale.