## 2 Materials and Methods
### Methodology
#### 2.3.4 Calculation of Indoor Carbon Dioxide Concentration  
This research uses the calculated natural ventilation mode in _DesigbuilderTM_ with a discharge coefficient of 0.65. The CO\({}_{2}\) concentration equations are described in the EnergyPlusTM Engineering Reference [47]. _The Carbon Dioxide Predictor-Corrector_ is based on the following Transient Mass Balance Equation (see Equation (3)). Each element of Equation (2) is detailed in Appendix A.  
\[\rho_{air}\ V_{Z}\ C_{\text{CO2}}\ \frac{dC_{Z}^{t}}{dt}=\sum_{i=1}^{N_{zi}}kgmass_{ sched\ load}*1.0\ ^{6}+\sum_{i=1}^{N_{ones}}m_{i}\left(C_{zi}-C_{z}^{t}\right)+\left(C_{\infty}-C_{ z}^{t}\right)+m_{sys}(C_{SUP}-C_{Z}^{t}) \tag{2}\]  
As described in Appendix A, the CO\({}_{2}\) concentration depends on internal CO\({}_{2}\) loads, the zone air density and volume, CO\({}_{2}\) due to outdoor infiltration and ventilation, which  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{3}{c}{**Windward/Northeast Windows**} & \multicolumn{3}{c}{**Leeward/Southwest Windows**} \\ \multicolumn{3}{c}{**59 cm Height \(\times\) 134 cm Wide**} & \multicolumn{3}{c}{**WW\({}_{\text{eq}}\)R \({}^{1}\)**} \\ \hline \multicolumn{3}{c}{**Opening Conditions**} & \multicolumn{3}{c}{**as Equation (1)**} & \multicolumn{3}{c}{**Opening Conditions**} \\ \hline
**Wide (cm)** & **Wide (\%)** & **WWR (\%)** & & **WWR (\%)** & **Wide (cm)** \\ \hline
2 & 1.5\% & 0.23\% & 0.23\% & 0.54\% & 1.9\% & 2 \\
4 & 3.0\% & 0.46\% & 0.45\% & 1.07\% & 3.0\% & 4 \\
8 & 6.0\% & 0.92\% & 0.87\% & 2.14\% & 6.0\% & 8 \\
15 & 7.5\% & 1.72\% & 1.54\% & 4.02\% & 11.2\% & 15 \\
22 & 11.2\% & 2.53\% & 2.16\% & 5.90\% & 16.4\% & 22 \\
30 & 15.2\% & 3.45\% & 2.80\% & 8.04\% & 22.3\% & 30 \\
51 & 47.7\% & 6.78\% & 4.10\% & 10.99\% & 44.0\% & 41 \\ \hline \hline \end{tabular}  
* equivalent ratio calculated with Equation (1) considering windows at both sides (wind and lee).  
\end{table}
Table 4: WWR and WW\({}_{\text{eq}}\)R depending on opening configuration.  
Figure 6: DNVP for optimal IAQ during the winter season.  
are present in this simulation, and also on CO\({}_{2}\) transferred from other zones and CO\({}_{2}\) from the air supply stream, which are not present.  
The standard _EnergyPlusTM__epw weather file_[48] has been modified to establish the average wind speed and direction for a typical morning in December, with direction 260\({}^{\circ}\), speed 2.6 m/s.  
The _DesignBuilderTM_ simulation includes a scheduled ventilation protocol which is not within the current options of the software capabilities. To ensure the proper function of the DNVP, the authors used the EMS runtime scripting tools described in _The Application Guide for EMS_[47]. The scripting code is presented in Appendix B. The EMS script is acting over the openings to ensure the CO\({}_{2}\) remains under 800 ppm, as described in the DNVP in Figure 4. The EMS window-opening actuator is connected to two variables/sensors: _Air_CO2_Concentration_ and _TrendDirection_. _TrendDirection_ evaluates whether the CO\({}_{2}\) concentration is rising or decreasing.  
It is expected that slight variations will be found between the simulation forecast and the real-time monitoring data. This is provided by the expected delay between the software simulation and the human management of the windows.  
Finally, the monitoring process introduces an evaluation TC according to the method described in the UNE-EN 16798-1:2020 [27], Section A.2.2. UNE. The adaptative comfort is based on the following Equation (3):  
\[\theta_{rm}=(1-\alpha)\times\left\{\theta_{ed-1}+\alpha\cdot\theta_{ed-2}+ \alpha^{2}\cdot\theta_{ed-3}\right\} \tag{3}\]  
\(\theta_{rm}\)Outdoor running mean temperature for the considered day  
\(\theta_{ed-1}\)Daily mean outdoor air temperature for the i-th previous day