## 2 Methodology
### Theory of Multiple Parallel Jets  
The jet interaction with multiple jets arranged in parallel is shown in Figure 3. The spacing between the air inlets is L, and the air inlets have the same diameter and supply air volume. The momentum of the jet from each air supply inlet is \(P_{i}\) (\(i\) = 1, 2, 3..., _n_). It is assumed that the infinitesimal area vertical to the cross-section of the jet is d\(F\). The radius of the infinitesimal area is \(R\). According to the law of conservation of momentum [34], the momentum on the cross-section is the sum of the momentum of all jets flowing through the cross-sectional area. \[dP=dP_{1}+dP_{2}+dP_{3}+\cdots\cdots+dP_{n} \tag{1}\]  
where  
\[dP=\rho v^{2}dF,dP_{1}=\rho_{1}v_{1}^{2}dF,\cdots\cdots,dP_{n}=\rho_{n}v_{n}^ {2}dF \tag{2}\]  
where \(v_{1},v_{2},\cdots,v_{n}\) is the average velocity of each jet passing through the section (m/s); \(\rho_{1},\rho_{2},\cdots,\rho_{n}\) is the density of each single jet (kg/m\({}^{3}\)); \(v\) is the velocity at the study point (m/s). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Instrument** & **Measuring Location** & **Parameter** & **Range** & **Accuracy** & **Sampling Frequency** \\ \hline WZY-1 & Room air & Temperature & & & 0.2 Hz \\  & Envelope & Temperature & & & 0.003 Hz \\ \hline Swema 03+ & Supply air and all the measurement points in the occupied zone and jet area & Velocity & 0.05–10 m/s & \(\pm\)0.03 m/s \(\pm\) 3\% & 8 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Information on the measurement instruments. The air densities at each supply air inlet can be regarded as equal. The equation can be simplified as  
\[v^{2}=v_{1}^{2}+v_{2}^{2}+\cdots\cdots+v_{n}^{2}=\sum\limits_{i=1}^{n}v_{i}^{2} \tag{3}\]  
According to the sectional velocity of a single jet proposed by [PERSON] [35], the equation is defined as  
\[\frac{v_{x}}{v_{c}}=\exp\left[-\frac{1}{2}\left(\frac{r}{c\pi}\right)^{2}\right] \tag{4}\]  
where \(v_{c}\) is the axial velocity of the single jet at \(x\) from the supply air inlet (m/s), \(r\) is the distance from the study point to the axis of the single jet (m), \(v_{r}\) is the velocity at a distance \(r\) from the axis coordinate \(x\) (m/s), \(c\) is a constant (0.082 in this study). On the premise of uniform supply air at each supply air inlet of the SV, the axial air velocity of each jet can be considered to be the same. The equation can be deduced as  
\[v=v_{x}\sqrt{\sum\limits_{i=1}^{n}\exp\left[-\left(\frac{r_{i}}{0.082x}\right) ^{2}\right]}=K_{v}\cdot v_{x} \tag{5}\]  
where  
\[K_{v}=\sqrt{\sum\limits_{i=1}^{n}\exp\left(-\left(\frac{r_{i}}{0.082x}\right) ^{2}\right)} \tag{6}\]  
Overlapping correction coefficient of velocity \(K_{v}\) was established on a Shapelev normal distribution. As three equally spaced supply air inlets were arranged in the experiment, the velocity attenuation formula of the axis of the central air outlet can be expressed as  
\[v=k_{v}\cdot v_{x}=\sqrt{2\exp\left[-\left(\frac{l}{0.082x}\right)^{2}\right] }\cdot v_{x} \tag{7}\]  
There are many semi-empirical attenuation formulas for the axial velocity \(v_{x}\) at different downstream distances in previous studies. [PERSON] [36] obtained the following formula for calculating the axial velocity attenuation of multiple parallel jets:  
\[\frac{v_{x}}{v_{0}}=3.347A_{r}^{-0.147}\left(\frac{x}{a_{0}}\right)^{-1.151} \tag{8}\]  
where \(Ar\) is the Archimedes number, and \(d_{0}\) is the diameter of the nozzle (m). [PERSON] [37] obtained the formula through dimensional analysis:  
\[\frac{v_{x}}{v_{0}}=\frac{0.48}{a_{0}^{2}+0.145} \tag{9}\]  
where \(a\) is a turbulence coefficient affected by nozzle type. Figure 3: Multiple parallel jets. The modified formula is obtained by neglecting the short distance from the intersection point to the edge of the air inlet:  
\[\frac{\frac{\
u_{x}}{\
u_{0}}}{\
u_{0}}=\frac{1.13\times 0.48\sqrt{F_{0}}}{ax} \tag{10}\]  
where \(F_{0}\) is the area of the air inlet (m\({}^{2}\)).