# Performance Analysis of the Multi-Stage Dew-Point Indirect Evaporative Air Cooler
## 3 Results and Discussion
(**d**) Cooling capacity for \(W_{2}/W_{1}\) equal to 0.3. (**e**) Outlet air temperature for \(W_{2}/W_{1}\) equal to 0.5. (**f**) Cooling capacity for \(W_{2}/W_{1}\) equal to 0.5.  
less effectively in this case. Because of the limitation of the mainstream (\(W_{2}/W_{1}=0.5\)), the cooling power varies from about 5.2 kW to about 6.1 kW when changing the relative length of cross-flow section (see Figure 3f). It comes from the fact that the value of the cooled air flow mainly affects the level of cooling power achieved by the proposed exchanger. Based on the analysis presented above, two different exchanger configurations were selected to compare their operation with the operation of the regenerative dew-point exchanger. The first configuration of the exchanger (DPIEC1) selected is characterized by parameters \(W_{2}/W_{1}=0.1\), \(W_{3}/W_{1}=0.5\), and \(X_{cross}=0.7\). This is the case for which the device achieves a relatively high cooling capacity of 8.3 kW. The second variant (DPIEC2) of the exchanger has a cross-section length of \(X_{cross}=0.4\), and the ratio of the auxiliary inlet air in each section is \(W_{2}/W_{1}=0.3\) and \(W_{3}/W_{1}=0.5\). In this case, the regenerative part has a length equal to 0.6. This is the case for which the average level of cooling efficiency and the average level of cooling power are obtained and compared to the other analyzed variable flow and geometric parameters of the exchanger. The usefulness of the application of variants I and II is verified by comparing it with the most common variant of the evaporative indirect exchanger, for which the characteristic parameters are summarized in Table 2. A previously optimized \(G\) ratio equal to 0.3 was chosen for the regenerative exchanger [21]. On the basis of the considerations presented above, the following operating conditions were established:  
* The relative length of the cross-flow part \(X_{cross}\) is equal to 0.7 and 0.3 for DPIEC 1 and DPIEC 2, respectively;
* The working-to-primary air ratio in the regenerative counter-flow part \(W_{2}/W_{1}\) equals 0.1 and 0.5 for DPIEC 1 and DPIEC 2, respectively;
* The working-to-primary air ratio in the cross-flow part \(W_{3}/W_{1}\) in each case equals 0.5 for DPIEC 1 and DPIEC 2. Comparison of the Multi-Stage Unit with Typical Regenerative DPIEC  
In this section, proposed multi-stage arrangements of dew-point evaporative coolers are compared with the original regenerative dew-point evaporative cooler (configuration shown in Table 3). The regenerative device (DPIEC 3) is characterized by the same NTU\({}_{1}\) as DPIEC 1 and 2 (shown in Table 2). A set of numerical simulations was performed to establish the impact of outdoor air conditions on the cooling performance of the proposed units. The analysis was performed under variable inlet temperature (25, 30, and 35 \({}^{\circ}\)C) at constant relative humidity established at 45%. The results are presented in Table 4. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Outdoor Air** & \multicolumn{3}{c}{**Outlet Air Temperature**, \({}^{\circ}\)**C**} & \multicolumn{3}{c}{**Cooling Capacity, kW**} \\ \cline{2-7}
**Temperature**, \({}^{\circ}\)**C** & **DPIEC 1** & **DPIEC 2** & **DPIEC 3** & **DPIEC 1** & **DPIEC 2** & **DPIEC 3** \\ \hline
25 & 17.2 & 15.3 & 16.2 & 7.1 & 6.8 & 6.2 \\
**30** & **20.8** & **19.0** & **19.7** & **8.4** & **7.8** & **7.2** \\
35 & 24.0 & 22.8 & 23.4 & 9.9 & 8.6 & 8.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of exchanger comparison for outdoor air relative humidity RH = 45%. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Type of Exchanger** & \(W_{3}/W_{1}\) & \(W_{2}/W_{1}\) & \(X_{cross}\) & \(X_{regenerative}\) \\ \hline DPIEC 1 & Combined cross-regenerative & 0.5 & 0.1 & 0.3 & 0.7 \\ \hline DPIEC 2 & counter-flow heat and mass exchanger & 0.5 & 0.3 & 0.3 & 0.7 \\ \hline DPIEC 3 & Regenerative dew-point evaporative cooler & - & 0.3 & - & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Characteristic parameters of the exchangers.