# Performance Analysis of the Multi-Stage Dew-Point Indirect Evaporative Air Cooler
## 1 Introduction  
During the last fifty years, climate changes have occurred, including an increase in average outside air temperatures. Climate change is having an impact on the energy sector as the cooling season is lengthening and the heating season is shortening. This is confirmed by scientists worldwide who are studying climate change and its effects. For example, trends have been observed both in Europe (Mediterranean [1], Poland [2], and Europe [3]), and in countries of South and North America (Brazil [4], Canada [5], and USA [6]). As a result, the energy consumption of air-conditioning systems (AC) has been increasing for years and will be increasing until 2050, as predicted by the scenarios and analyses conducted by the International Energy Agency described in the Future of Cooling report [7]. The use of more efficient air-conditioning technologies can significantly reduce the energy consumption associated with the rise in temperature, and the development of alternative air-conditioning systems based on renewable energy is crucial. One widely studied device is based on indirect evaporative dew-point cooling. There are reviews of the literature and summaries of achievements in this field of science. General conclusions are presented in Table 1.  
[PERSON] et al. [13] compared two dew-point coolers with the regenerative and the combined configurations. It was found that performance of the second cooler configuration showed 5% higher cooling capacity and higher water consumption. [PERSON] et al. [14] analyzed different types of flow and water schemes in indirect evaporative cooling devices by comparing their key performance indicators obtained numerically. They found the influence of geometrical and operational parameters on cooling capacity, effectiveness, and COP, and crossing temperature depends on the configuration of parallel/counter and cross-flow. [PERSON] et al. [15] studied the dew-point evaporative cooler with counter-flow closed-loop configuration with two different water flows to supply air-flow directions. In the case of each configuration, a two-dimensional computational fluid dynamics model was developed to compare the performance of a typical indirect evaporative cooler with standard flow distribution to that of two proposed coolers with new flow distribution. They found that water flow to supply the air-flow direction influences the cooler performance, and the first configuration achieved the highest latent and wet-bulb efficiencies and enlargement coefficient. It is a fact that multi-stage and combined indirect evaporative cooling units are considered by researchers as promising devices for the purpose of air-conditioning systems. Basic variants of such units are cross-flow dew-point evaporative coolers [16]. This study is dedicated to analyzing the structure of a multi-stage evaporative cooling unit based on the combination of cross-flow and regenerative counter-flow, and compares its performance to the typical regenerative dew-point evaporative cooler performance (Figure 1a,b). This paper presents an analysis of the efficiency of a combined evaporative exchanger (Figure 1a), which is characterized by cross-regenerative flow in wet channels. The efficiency of the proposed variant is compared with the efficiency of the regenerative indirect evaporative cooler. Because of this objective, numerical simulations are performed for the air-flow parameters equal to \(t_{1i}=30\,^{\circ}\)C and RH\({}_{1i}=45\%\). Selected air parameters correspond to the average temperature and relative humidity found in a temperate climate during the summer season. The ratio of working air flow to primary air flow in the cross-flow part varied between 0.3 and 1.0 and in regenerative part from 0.1 to 0.5.