H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 9 Article Theoretical analysis of the performance and optimization of indirect flat evaporative coolers Hamidreza Asemi1, Rahim Zahedi2*, Sareh Daneshgar3 1Faculty of Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran 2Department of Renewable energy and Environmental Engineering, University of Tehran, Tehran, Iran 3Faculty of Electrical Engineering, Iran University of Science and Technology, Tehran, Iran A R T I C L E I N F O Article history: Received 13 July 2022 Received in revised form 16 August 2022 Accepted 22 August 2022 Keywords: Indirect Evaporative Cooling, Exergy, Optimization *Corresponding author Email address: Rahimzahedi@ut.ac.ir DOI: 10.55670/fpll.fuen.2.1.2 A B S T R A C T External-cooling indirect evaporative coolers with different configurations and working air sources are incomprehensively analyzed and compared so far. This paper investigates the mechanism and theory of operation of indirect flat-panel evaporative coolers based on X-analysis. Then, based on the second law of thermodynamics analysis, the entropy production rate of the flat-plate heat exchanger of the cooler is calculated. As a result of this analysis, the optimal energy efficiency-evaporation efficiency and cooling capacity values are presented in terms of effective parameters in the design. 1. Introduction One of the most common methods used to cool environments is the passage of hot air over wet surfaces at low temperatures, called "evaporative cooling." This method is considered compared to mechanical (compression) cooling systems due to its cheaper and non-use harmful refrigerant in the ozone layer [1]. An essential drawback of this type of cooling is the lack of proper control of ambient humidity. This form is produced by the indirect evaporative cooling method to a large extent, and cooling with the desired quality is prepared. Mode of operation as shown in Figure 1, indirect evaporative coolers have two primary and secondary airflows. The initial air has no contact with moisture and enters the desired environment after cooling. Suppose the secondary air is in direct contact with the water film. In that case, this action causes the water film to evaporate and the transformer plates to cool down, eventually removing heat from the primary air. The mixture of these two breaths of air provides favorable conditions for the environment. Rawabawale and Sapali [2] analytically evaluated the influence of size variation of the cooling tower on exergy loss and found that the cooling tower with a larger length than height yields smaller exergy loss with higher thermal efficiency. Kiyaninia et al. [3] experimentally and theoretically investigated the exergoeconomic performance of a solar photovoltaic-based direct evaporative air-cooling system. The results showed that for an inlet air with a temperature of 30oC and relative humidity of 30%, the maximum system exergy efficiency was obtained at about 20%. Martineza et al. [4] and Nada et al. [5] studied the energy and exergy performance of different wet pad materials of evaporative coolers through experiments and found that the exergy efficiency was between 70% and 94% under different pad thicknesses. This research comparatively analyzes the energy and exergy performance of indirect flat evaporative coolers on the basis of a verified numerical model and experimental correlation. 2. Thermal analysis The control volume is considered for thermal analysis of the cooler according to Figure 2. It is worth mentioning that the analysis of the mass heat transfer process of this type of air conditioner is complex. Therefore, in the thermal study, it is necessary to consider hypotheses to do the calculations quickly. Hypotheses are: • Lewis number: 1 = Le • Mass heat transfer coefficients are assumed to be constant. Future Energy Open Access Journal https://doi.org/10.55670/fpll.fuen.2.1.2 February 2023| Volume 02 | Issue 01 | Pages 09-14 Journal homepage: https://fupubco.com/fuen ISSN 2832-0328 mailto:Rahimzahedi@ut.ac.ir https://doi.org/10.55670/fpll.fuen.2.1.2 https://fupubco.com/fuen H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 10 • The effect of mass heat transfer between secondary air droplets is considered to be negligible. • Saturation enthalpy changes with humid secondary air temperature are linear. • The plates are considered completely wet. • Heat transfer to the environment is negligible. Figure 1. Isometric view of indirect evaporation cooler Figure 2. Control volume of an indirect evaporative cooler 2.1 Energy balance for primary air According to Figure 2, the primary air loses its heat significantly, so: 𝑈0(𝑡 − 𝑡𝑤) = �̇�𝑃𝑐𝑃 ⅆ𝑡 (1) As a result, after integration, the number of primary air units using X-theory is as follows [6]. (𝑁𝑇𝑈)𝑝 = 𝑈0𝐴 𝑚𝑃𝑐𝑃 = −ln ( 𝑡2−𝑡1 𝑡1−𝑡𝑤 ) (2) The initial air impact factor will be as follows. 𝜀𝑃 = 1 − 𝑒𝑥𝑝(𝑁𝑇𝑈)𝜌 = 𝑡1−𝑡2 𝑡1−𝑡𝑤 (3) 2.2 Energy balance for secondary air In Figure 2, a differential element from the air contact surface shows a wet surface. Thermal balance for the earth element from [7]: ℎ𝐷(ℎ𝑤 − ℎ) ⅆ𝐴 = �̇�𝑠 ⅆℎ (4) By integrating equation (5) (𝑁𝑇𝑈)𝑠 = ℎ𝐷𝐴 �̇�𝑠 = ℎ𝐷𝑐𝑃𝐴 �̇�𝑠𝑐𝑃 = −ln ( ℎ0−ℎ𝑤 ℎ0−ℎ𝑖 ) (5) After arranging the above equation, the coefficient of the effect of the secondary air is as follows: 𝜀𝑠 = 1 − 𝑒𝑥𝑝(−𝑁𝑇𝑈)𝑠 = ℎ𝑖−ℎ0 ℎ𝑖−ℎ𝑤 (6) According to the linear proportion of changes in the enthalpy of humid air with the ratio of temperatures [8]: 𝑐𝑤𝑏 = ℎ0−ℎ𝑖 𝑡𝑤0− 𝑡𝑤𝑖 (7) Cwb is the specific saturation temperature of equation (7) as follows. 𝜀𝑠 = 1 − 𝑒𝑥𝑝(−𝑁𝑇𝑈)𝑠 = 𝑡𝑤0− 𝑡𝑤𝑖 𝑡𝑤𝑖− 𝑡𝑤 (8) Assuming 1 = Le (i.e., assuming that the rate of penetration of the rate of heat transfer and mass diffusion are the same at the contact surface of air-water): 𝐿𝑒2∕3 = ℎ𝐶 ℎ𝐷𝐶𝜌 → ℎ𝐶 = 𝐶𝜌ℎ𝐷 (9) With replacement (9) in (5): (𝑁𝑇𝑈)𝑠 = ℎ𝑐𝐴 �̇�𝑠𝑐𝑃 = −ln ( 𝑡𝑤0− 𝑡𝑤 𝑡𝑤𝑖− 𝑡𝑤 ) (10) 2.3. Energy balance between the primary and secondary air By defining the coefficient of cooling effect in indirect evaporative coolers [9]: 𝜀𝑠 = 𝑡1−𝑡2 𝑡1− 𝑡𝑤𝑖 (11) The energy balance equation between the primary and secondary air will follow: �̇�𝑝𝑐𝑃(𝑡1 − 𝑡2) = �̇�𝑠 (ℎ𝑂 − ℎ𝑖) (12) Incidentally, according to equation (7) 𝑡2 = 𝑡1 − 𝑐𝑚𝑎𝑥 𝑐𝑚𝑖𝑛 (𝑡𝑤0 − 𝑡𝑤𝑖) (13) While Cmin and Cmax are: 𝑐𝑚𝑖𝑛 = �̇�𝑝𝑐𝑃 (14) 𝑐𝑚𝑎𝑥 = �̇�𝑠𝑐𝑤𝑏 (15) By placing equation (13) in equation (2): H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 11 𝜀𝑃 = 𝑐𝑚𝑎𝑥 𝑐𝑚𝑖𝑛 ( 𝑡𝑤0− 𝑡𝑤𝑖 𝑡1− 𝑡𝑤 ) (16) By placing equation (6) in equation (5), water temperature 𝑡𝑤 = 𝜀𝑠( 𝑐𝑚𝑎𝑥 𝑐𝑚𝑖𝑛 )+𝜀𝑃+𝑡1 𝜀𝑠( 𝑐𝑚𝑎𝑥 𝑐𝑚𝑖𝑛 )+𝜀𝑃 (17) By placing equation (17) in equation (2), the coefficient of the cooling effect of the cooler is: 𝜀𝐶 = 1 1 𝜀𝑃 + 1 𝜀𝑆 ( �̇�𝑝𝑐𝑃 �̇�𝑠𝑐𝑤𝑏 ) (18) In addition, to calculate the heat transfer coefficients of the primary and secondary air passages and the sticky surface, respectively [10] are: 𝑁𝑢 = 0.023𝑅𝑒𝐷ℎ 4/5𝑃𝑟1/2 𝑅𝑒 > 2300 (19) 𝑁𝑢 = 7.54 𝑅𝑒 ≤ 2300 (20) Where: 𝑅𝑒𝐷ℎ = 4�̇� 𝛱𝐷𝜇 , 𝐷ℎ = 2𝑏 2.4. Calculate the drop in air flux by multiplying the capacity of the air conditioner The pressure drop of the whole system due to local friction drops is calculated according to the following equations [11]. 𝛥𝑃𝑓 = 𝑓 𝐿 𝐷ℎ 𝑣2𝜌 2 (21) 𝛥𝑃𝑙 = ∑ 𝐾 𝑣2𝜌 2 (22) 𝛥𝑃𝑡 = 𝛥𝑃𝑓 + 𝛥𝑃𝑙 (23) As a result, the required power of the device blower, assuming ηm =1, is [12]: 𝑤 = �̇�𝑃𝛥𝑃𝑃 𝜂𝑃 + �̇�𝑠𝛥𝑃𝑠 𝜂𝑠 (24) 2.5. Calculating the energy efficiency ratio The energy efficiency ratio of EER is equal to 𝐸𝐸𝑅 = 𝑄𝑐 𝑤 (25) Where Qc is the cooling capacity of the indirect air conditioner can be calculated from the following equation. 𝑄𝑐 = �̇�𝑝𝑐𝑃(𝑡1 − 𝑡2) (26) 2.6. Analysis of the second law for indirect plate evaporative coolers There are several evaluation criteria for the optimal operating conditions of thermal systems. One of the most reliable criteria is the second law analysis or exergy analysis. Figure 2 shows that an indirect plate air conditioner is like a plate heat exchanger with the opposite flow for secondary airflow and cross-flow for primary air. In order to obtain a statement to calculate the initial airflow exergy rate, we assume that the surface temperature of the plates is constant throughout the length of the plate, which is a reasonable assumption for this type of cooler. The rate of production of primary exergies of such plates is as follows, which includes two parts: output and output [13, 14]. (𝑒𝑡,𝑝) 𝑖𝑛 = 𝑅𝑎𝑡1ln (1 + 1.6)𝜔𝑜 (27) (𝑒𝑡,𝑝) 𝑜𝑢𝑡 = 𝑐𝑃𝑡0 ( 𝑡2 𝑡0 − 1 − 𝑙𝑛 𝑡2 𝑡0 ) + 𝑅𝑎𝑡0 ln (1 − ∆𝑃 𝑃0 ) + 𝑅𝑎𝑡𝑜ln (1 + 1.6)𝜔𝑜 (28) Moreover, entropy production for secondary air is in equations (29) and (30). In addition to heat transfer and friction, it also has the mass transfer term due to evaporation, which consists of input and output. (𝑒𝑡,𝑆) 𝑖𝑛 = (𝑐𝑃 + 𝜔𝑐𝑃𝑣)𝑡0 ( 𝑡𝑊𝑖 𝑡0 − 1 − 𝑙𝑛 𝑡𝑊𝑖 𝑡0 ) + (1 + 1.6𝜔𝑜)𝑅𝑎𝑡0 ln ( 𝑃 𝑃0 ) + 𝑅𝑎𝑡0[(1 + 1.6𝜔𝑜)𝑙𝑛 1+1.6𝜔𝑜 1+1.6𝜔 + 1.6𝜔𝑜 ln 𝜔 𝜔0 ] (29) (𝑒𝑡,𝑆) 𝑜𝑢𝑡 = (𝑐𝑃 + 𝜔𝑜𝑢𝑡𝑐𝑃,𝑣)𝑡0 ( 𝑡𝑊𝑜 𝑡0 − 1 − 𝑙𝑛 𝑡𝑊𝑜 𝑡0 ) +(1 + 1.6𝜔𝑜𝑢𝑡) 𝑅𝑎𝑡0 ln (1 − ∆𝑃 𝑃0 ) + 𝑅𝑎𝑡0[(1 + 1.6𝜔𝑜𝑢𝑡)𝑙𝑛 1+1.6𝜔𝑜 1+1.6𝜔𝑜𝑢𝑡 + 1.6𝜔𝑜𝑢𝑡 ln 𝜔𝑜𝑢𝑡 𝜔𝑜 ] (30) As a result, the total entropy production rate is calculated as follows: 𝑠𝑔𝑒𝑛 = 1 𝑇0 {[�̇�𝑃𝑒𝑡𝑝 + �̇�𝑠𝑒𝑡𝑠] 𝑖𝑛 −[�̇�𝑃𝑒𝑡𝑝 + �̇�𝑠𝑒𝑡𝑠] 𝑜𝑢𝑡 } (31) Based on the entropy production equations (27 to 31), the design method of indirect coolers mentioned in the first part of the article, the functional relationship of the total entropy production rate is as follows: �̇�𝑔𝑒𝑛 = 𝑓(�̇�𝑝, �̇�𝑠, 𝐿, 𝑤) (32) 3. Results and Discussion A computer code has been prepared to calculate the design values such as the temperature of the air leaving the air conditioner, the energy efficiency ratio, and to observe the effect of effective parameters such as plate length and mass flow rate on the EER according to Figure 3. Figures 3 and 4 result from these calculations. As shown in Figure 4, the initial outlet air temperature of the T2 model was compared with the experimental reference results [4]. The difference between the modeling results and the experimental results is about 3%, and this difference is due to ignoring the effects of environmental parameters in modeling. Figure 5 compares the cooling effect of X with the experimental results [4]. After designing the system according to equations (27) to (32), the entropy produced by the system is investigated. It is evident that the system, based on the design conditions, is faced with limitations in selecting the values of W and L. Due to these limitations, the mentioned values must be considered in a specific range. The variables are examined by keeping the other parameters constant on the entropy production rate of the system, and finally, the optimal values of the system design are obtained. It is worth noting that the optimization of design variables by the exergy method (the second law of thermodynamics) is not economically optimal for systems. Therefore, in practice, in order to optimize the systems, both thermo economic studies should be done. H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 12 Figure 6 shows the entropy production rate in terms of the secondary air flow rate changes at a constant value of the primary airflow rate. The design shows that the maximum and minimum point distance values are minimal. Figure 7 shows the entropy production rate of initial airflow. As shown in this figure, the maximum and minimum entropy production points are not within the design range. This trend indicates the low sensitivity of the entropy production rate to the initial air flow rate. Figure 4. Comparison of the initial air outlet temperature of the model with experimental results Figure 5. Comparison of the cooling coefficient of the model air conditioner with the experimental results Figures 8 and Figure 9 show the entropy production rate in secondary air discharge in different primary discharges and the entropy production rate in secondary air discharge in different primary discharges, respectively. As can be seen, at a certa in amount of primary or secondary air flow rate, the minimum entropy production can be achieved by selecting another reasonable flow rate. Figure 10 also shows the entropy production rate in terms of plate length. It is observed that the longer the plate lengths are selected in this type of short coolers, the more the entropy production rate Figure 3. Flowchart design of direct evaporative coolers H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 13 increases. As a result, the length of the pages should be selected by the primary and secondary discharges for maximum efficiency. Figure 6. Entropy production rate in terms of secondary air flow Figure 7. Entropy production rate in terms of initial air flow Figure 8. Entropy production rate in terms of primary air discharge in secondary discharges Figure 9. Entropy production rate in terms of secondary air flow in primary flows Figure 10. Entropy production rate in terms of plate length in secondary discharges 4. Conclusions In this study, the energy and exergy performance of cooling indirect flat evaporative coolers and direct evaporative coolers are compared and analyzed on the basis of the developed mathematical model. The main conclusions are given as follows: 1) Indirect evaporative coolers have better performance than direct evaporative coolers in dry areas. 2) Exergy analysis is an excellent tool to optimize the parameters affecting the performance of indirect evaporators. The increased fresh air flowrate reduces the cooling efficiency and exergy efficiency of all evaporative coolers. Ethical issue The authors are aware of and comply with best practices in publication ethics, specifically with regard to authorship (avoidance of guest authorship), dual submission, manipulation of figures, competing interests, and compliance with policies on research ethics. The authors adhere to publication requirements that the submitted work is original and has not been published elsewhere in any language. Data availability statement Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study. Conflict of interest The authors declare no potential conflict of interest. H Asemi et al. /Future Energy February 2023| Volume 02 | Issue 01 | Pages 09-14 14 Abbreviations and Greek symbols A Effective heat transfer surface (m2) B The distance between the two cooler plates (m) Cmax Maximum heat transfer capacity(W/oC) Cmin Minimum heat transfer capacity(W/oC) Cp Specific heat capacity to air (KJ/Kg oC) Cpv Specific heat capacity of water vapor (KJ/Kg oC) Dh Hydraulic diameter (m) et,p Primary air exergy (W/KgK) et,s Secondary air exergy (W/KgK) hi Enthalpy of secondary air inlet (KJ/Kg) ho Enthalpy of secondary air outlet (KJ/Kg) hw Enthalpy of air saturation at the common air and water level (KJ/Kg) K Local drop coefficient L The length of the plates of indirect evaporators (m) Le Louis Number �̇�𝑎 Air mass flow (Kg/s) �̇�𝑝 Primary air flow (Kg/s) �̇�𝑠 Secondary air flow (Kg/s) EER Energy efficiency ratio f Friction coefficient hc Conduction heat transfer coefficient (W/m2oC) hD Mass transfer coefficient (Kg/m2s) Nu Nusselt number 𝛥𝑃𝑓 Pressure drop due to friction (Pa) 𝛥𝑃𝑙 Local pressure drop (Pa) 𝛥𝑃𝑝 Initial pressure drop 𝛥𝑃𝑠 Secondary pressure drop Pr Prandt number Re Reynolds number Sgen Production entropy t1 Dry bubble temperature of the primary air inlet t2 Dry bubble temperature of the primary air outlet twi Wet bubble temperature of secondary air inlet two Wet bubble temperature of secondary air outlet tw Saturation temperature of the joint surface of air and water to Ambient temperature ṁw Mass flow of water NTUp Number of primary air transfer units NTUs Number of secondary air transmission units U0 The total heat transfer coefficient between the primary air and the common surface of the secondary air of water 𝜀𝐶 Cooler effect coefficient 𝜀𝑝 Primary air impact coefficient 𝜀𝑠 Secondary air impact coefficient ρ Air density 𝜂𝑝 Fan efficiency of the first part 𝜂𝑠 Secondary fan efficiency 𝜇 Adhesion coefficient ω𝑜𝑢𝑡 Humidity for secondary exhaust air ω0 Humidity for the environment References [1] Y. 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