## 2 Methodology
### Numerical Simulation
#### 2.3.4. Evaluation Indices  
To evaluate the SV performance, the following evaluation indices were used:  
1. Effective draft temperature for SV (EDTS);
2. Air diffusion performance index (ADPI);
3. Local mean age of air (LMAA);
4. Energy utilization coefficient (EUC).  
In addition to the widely used PMV model [46], the EDTS index is also frequently used for evaluating SV. It was proposed by [PERSON] [47] and was found to be reliable for evaluating thermal comfort of SV. When \(-1.2\) K \(<\) EDTS \(<\) 1.2 K, the thermal comfort is evaluated as satisfactory. EDTS was calculated using Equation (14).  
\[EDTS=(t_{x}-t_{room})-(v_{x}-1.1) \tag{14}\]  
where \(t_{x}\) is the local air temperature (\({}^{\circ}\)C), \(t_{room}\) is the average room temperature (\({}^{\circ}\)C), and \(v_{x}\) is the local air velocity (m/s).  
The ADPI was used to assess the uniformity of air velocity and temperature distributions and their contribution to thermal comfort [48]. The more comfortable the thermal environment, the larger is the ADPI. The ADPI was calculated using Equation (15).  
\[ADPI=\frac{n_{i}(-1.2\text{K}<EDTS<1.2\text{K},\ 0<v<0.8m/\text{s})}{n} \tag{15}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Case** & **T\({}_{0}\)** (\({}^{\circ}\)**C)** & **V\({}_{0}\) (m/s)** & **L (mm)** \\ \hline
1 & & & 500 \\
2 & & & 650 \\
3 & & & 800 \\
4 & & & 950 \\
5 & & & 1100 \\
6 & & & 1250 \\ \hline \hline \end{tabular} Note: T\({}_{0}\) = supply air temperature; V\({}_{0}\) = supply air velocity; L = air inlet spacing.  
\end{table}
Table 5: Simulated cases.  
Figure 6: Comparison of different grid numbers: (a) air temperature; (b) air velocity.  
where \(n\) represents the number of nodes in the occupied zone [49], and \(n_{i}\) represents the number of nodes when the EDTS of the nodes is in the comfort range.  
The local mean age of air was defined as the average time between air particles entering a room to arriving at a certain point indoors. It is an effective index for measuring the freshness of indoor air and is widely used in evaluating the indoor air quality of buildings [50]. The smaller the air age, the higher the air freshness. It can be solved as an additional transport scalar; the transport equation is [38]  
\[\frac{\partial}{\partial t}(\rho\tau)+\frac{\partial}{\partial x_{j}}\big{(} \rho u_{j}\tau\big{)}=\frac{\partial}{\partial x_{j}}\Big{(}\Gamma_{\tau}\frac{ \partial\tau}{\partial x_{j}}\Big{)}+S_{0} \tag{16}\]  
where \(\tau\) is the local mean air age (s) of all micro-masses at that point, \(\Gamma_{\tau}\) is the diffusion coefficient, and \(S_{0}\) is the source term.  
The energy utilization efficiency can be quantified by comparing the air temperature in the occupied zone and the exhaust air temperature. A larger EUC value indicates a better energy-saving effect. The EUC was calculated using Equation (17).  
\[\varepsilon_{t}=\frac{T_{p}-T_{s}}{T_{o}-T_{s}} \tag{17}\]  
where \(T_{p}\) represents the exhaust air temperature (\({}^{\circ}\)C), \(T_{s}\) represents the supply air temperature (\({}^{\circ}\)C), and \(T_{o}\) represents the average temperature in the occupied zone (\({}^{\circ}\)C).