# On Finding the Right Sampling Line Height through a Parametric Study of Gas Dispersion in a NVB
## 3 Results and Discussion  
### Influence of the Sct-Number  
In Figure 7, the simulated dispersion rates are presented in term of tables filled with colors using the \"colors scale\" of the Microsoft Excel \"conditional formatting\" tool. For both tables (k omega and k epsilon), each row corresponds to the simulated dispersion rate for different Sct-numbers with, at the far left, the measured dispersion rate from the wind tunnel experiment (denoted \"Meas.\" and without color). Within each row, the simulated dispersion rates are compared with the measured dispersion rate, which serves as a reference (denoted \"meas. dis. rate\" in the color bar). The result of this comparison is color-coded. The greener the cell in the table is, the closer is the simulated value listed there to the associated measurement. The larger the deviation between the simulated dispersion rate and the measured dispersion rate is, the more red the cell becomes. The extreme values (i.e., color red) of the color bar are zero (minimum, as the dispersion rate cannot be negative) and at least twice the measured dispersion rate (for the maximum). The left table corresponds to the k-omega model, and the right table corresponds to the k-epsilon model. Overall, it can be seen that the higher the Sct-number is, the higher is the dispersion rate, reaching the maximum value of about 65 for the k-omega model and about 170 for the k-epsilon model, both for a Sct-number equal to one. Considering the k-omega model result, the dispersion rates matching the measurement values best are those of the Sct-number equal to 0.2. In the case of the k-epsilon model, it is the Sct-number equal to 0.1 that has the most suitable dispersion rates. We took another look at the results, but this time at the absolute gas concentration, in terms of percentage, from the numerical simulation relative to the measured concentration at each point i for comparison, see Equation (5). As representative examples, we chose to show, in Figure 8, the values at the points of the middle Lines 2 and 5 (see Figure 2). Figure 7: Comparison between the measured and simulated dispersion rate. Overall, we noticed an overprediction of the absolute concentrations for both models, but the k-epsilon concentrations were 10 times higher than the ones from k-omega. \[\mid C_{(i,simulated)}-C_{(i,measured)}\mid/C_{(i,measured)}\cdot 100 \tag{5}\]  
The high sensitivity of the concentration relatively to the Sct-number can be noted, as this was already shown in numerous previous studies recalled in the Introduction of this paper [7]. Our results showed that the lower the Sct-number, the higher was the overestimation of the concentration. A higher Sct-number, which means lower diffusion in order to compensate for the overestimation, led to more accurate concentrations. [PERSON] et al. [17] came to the same conclusion when analyzing high-buoyancy gas dispersion with the RANS model. As another telling example, [PERSON] et al. [18] also found a high discrepancy (three to five times) between the RANS model and the measurement when modeling pollution dispersion in a street canyon. On the one side, for the k-omega model, the concentrations for a Sct-number of 0.2 in violet (the value of the Sct-number matching at best the measured dispersion rate)  
Figure 8: The influence of the turbulent Schmidt number on the simulated absolute concentration of gas relative to the measured concentration; evaluation at the points of Lines 2 and 5; left, the result of the k-epsilon model, and right, the result of the k-omega model. were almost constant around 600-700%. On the other side, for the k-epsilon model, the concentrations for a Sc\({}_{\rm t}\)-number of 0.1 in blue (value matching at best the measured dispersion rate) varied greatly from one point to another from 4900-7300%. Those results led us to the conclusion that the k-omega model with the Sc\({}_{\rm t}\)-number equal to 0.2 can be retained for the study. This was because with this setup, the dispersion rates had a good match with the measurements.