# Performance Analysis of the Demand-Based Ventilation in a Nordic Apartment Building
## 2 Materials and Methods
### Simulation Model  
The performance of the ventilation system was analyzed by using the ductwork topology presented in Figure 2. The physical properties, components and settings are described in Tables 2 and 3. The ductwork was modelled, and the airflow distribution was simulated by using a HIT Balance tool, which is a tailored version of the simulation tool MagiCAD [31]. The ideal control of the constant static pressure in the supply and exhaust plenums was assumed. Ductwork is assumed to be ideal without leakages. In Equation (1), the exponent was assumed to be 0.5, according to most HVAC parts manufacturer documentation recommendations [31]. The other possible local resistances, e.g., apartment control dampers, are presented as an additional pressure loss to the branch. The principles for calculating the pressure drops are given below, along with the used equations [31; 32]. K-values for the components of the system were taken from the manufacturer data for designed airflows. The following equation was used for the volumetric airflow rate:  
\[\mathrm{q}_{\mathrm{v}}=\mathrm{k}\cdot\sqrt{\Delta p}, \tag{1}\]  
where \(\mathrm{q}_{\mathrm{v}}\)--volumetric airflow rate, \(\Delta p\)--component pressure drop. The resistance coefficient for the duct was calculated with:  
\[\frac{1}{\sqrt{\lambda}}=-2\cdot\lg\biggl{(}\frac{k}{d\cdot 3.71}+\frac{2.51}{ Re\cdot\sqrt{\lambda}}\biggr{)} \tag{2}\]  
where \(d\)--roughness number, \(Re\)--Reynolds number, \(\lambda\)--friction coefficient. The duct pressure drop equation for \(90^{\circ}\) circular bends was obtained from:  
\[\Delta\mathrm{p}=0.32\cdot\mathrm{v}^{1.8} \tag{3}\] \begin{table}
\begin{tabular}{l c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Room**} & \multicolumn{4}{c}{**4-Room Apartment**} & \multicolumn{4}{c}{**3-Room Ap.**} & \multicolumn{4}{c}{**2-Room Ap.**} & \multicolumn{4}{c}{**Studio Ap.**} \\ \cline{2-13}  & **Size** & **Airflow** & **L/s** & **K-Value** & **Size** & **Airflow** & **K-Value** & **Size** & **Airflow** & **K-** & **Size** & **Airflow** & **K-** \\  & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** \\ \hline \multirow{3}{*}{Bathroom} & \multirow{3}{*}{\(\mathcal{O}\)250} & N 1  & B  & 25.94 & \(\mathcal{O}\)250 & N  & B  & 26.83 & \(\mathcal{O}\)200 & N  & B  & 36.68 & \(\mathcal{O}\)200 & N  & 76 & 76 & 17.00 \\ \cline{1-1} \cline{3-13} Storage or W.C. & \multirow{3}{*}{\(\mathcal{O}\)200} & & & & & & & & & & & & & \\ Kitchen & & & & & & & & & & & & & & \\ Living/ & & & & & & & & & & & & & & \\ bed- & & & & & & & & & & & & & & \\ room & & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Airflow rates of the branch-level balancing damper, k values and ductwork sizes. \begin{table}
\begin{tabular}{l c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Room**} & \multicolumn{4}{c}{**4-Room Apartment**} & \multicolumn{4}{c}{**3-Room Ap.**} & \multicolumn{4}{c}{**2-Room Ap.**} & \multicolumn{4}{c}{**Studio Ap.**} \\ \cline{2-13}  & **Size** & **Airflow** & **K-L/s** & **Size** & **Airflow** & **K-L/s** & **Size** & **Airflow** & **K-** & **Size** & **Airflow** & **K-** \\  & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** & **mm** & **L/s** & **Value** \\ \hline \multirow{3}{*}{Bathroom} & \multirow{3}{*}{\(\mathcal{O}\)250} & N 1  & B  & 25.94 & \(\mathcal{O}\)250 & N  & B [FONOTE:2]Footnote 2: footnotemark: [ENDFOOTNOTE] & 26.83 & \(\mathcal{O}\)200 & N  & 116 & 56 & 36.68 & \(\mathcal{O}\)200 & N  & 76 & 76 & 17.00 \\ \cline{1-1} \cline{3-13} Storage or W.C. & \multirow{3}{*}{\(\mathcal{O}\)215} & & & & & & & & & & & & \\ Kitchen & & & & & & & & & & & & & \\ Living/ & & & & & & & & & & & & & & \\ bed- & & & & & & & & & & & & & & \\ room & & & & & & & & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Pressure drop equations for T connections. where _v_flow velocity.