# On Finding the Right Sampling Line Height through a Parametric Study of Gas Dispersion in a NVB
## 4 Conclusions  
In this paper, a reasonable value of the Schmidt number corresponding to the application of gas dispersion in the atmospheric boundary was found as a value of 0.2 for the RANS k-omega turbulence model. This value was obtained by comparing the wind tunnel measurements against different RANS simulations with the Sc\({}_{\text{t}}\)-number varying from 0.1 to one. The influence of the Sc\({}_{\text{t}}\)-number on the gas dispersion shown in the literature was confirmed. The higher the Sc\({}_{\text{t}}\)-number, the higher the dispersion rate was, but at the same time, the lower the gas concentration was.  
From our subsequent parameter study, we concluded that for most of the flow conditions considered in our study, the height for the perfect mixing ratio was between 1.5 m and 2.5 m (in our setup, this measurement height corresponded to about 13% to 22% of the building height and 33% to 55% of the opening height). For the most common case of mixed convection, the predicted optimal measurement height was around 1.8 m. This led to two important deductions. First, the influence of the Richardson number and the inlet flow direction was important since even for the range of nearly perfect mixing (1.5-2.5 m), the quotient of the NH\({}_{3}\)/CO\({}_{2}\) mixing ratio could vary from 0.35 to 3.40. Second, very few convection cases corresponded to the current common recommendation of at least a 3 m measurement height for a perfect mixing ratio.  
Another important finding is that with the sampling line placed at the outgoing flow direction of the barn, the perfect mixing condition could be fulfilled (at the right height) with comparable accuracy as with a whole net of sampling points. This means that the commonly recommended line measurements are in principle reasonable. Other solutions of on-farm measurement strategies can be tested; for example, a vertical net of sampling points at the outgoing flow direction of the barn with grid points of 0.1 m \(\times\) 10 m (height \(\times\) length) might be considered to further increase the measurement accuracy with tracer gas methods. Further investigations will be needed in order to deepen our understanding of the mixing gas in NVBs. In the present study, the considered barn had a fixed width/length ratio and openings without curtains. The influence of the building and opening designs on the gas mixing ratio at different evaluation heights should be considered in future studies.  
Conceptualization, E.M.D., D.J., Q.Y., and [PERSON]; methodology, E.M.D., D.J., Q.Y., and S.H.; software, E.M.D.; validation, E.M.D.; formal analysis, E.M.D., D.J., Q.Y., and S.H.; investigation, E.M.D.; writing--original draft preparation, E.M.D.; writing--review and editing, D.J., Q.Y., G.Z., T.A., M.K., and S.H.; visualization, E.M.D.; supervision, T.A., M.K., and S.H.;project administration, S.H.; funding acquisition, S.H. and D.J. All authors read and agreed to the published version of the manuscript.  
The research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), Grant Number 397548689. We further thank [PERSON] for his support in typesetting the paper.  
Not applicable.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} CFD & Computational fluid dynamics \\ NVB & Naturally ventilated barns \\ RANS & Reynolds-averaged Navier-Stokes \\ ABLWT & Atmospheric boundary layer wind tunnel \\ AOZ & Animal-occupied zones \\ \end{tabular}