Optimization of the performance of M-Cycle indirect evaporative cooling via thermodynamic approach

ABSTRACT For the further energy conservation, the study on the optimizing the M-Cycle indirect evaporative cooling (MIEC) performance is meaningful. With the aim of the optimization, a model of a general MIEC system was established, the thermodynamic entropy production optimization method was used to fully reflect the energy quality and irreversibility. The inlet parameters, supply air ratio, dew point temperature efficiency, unit-cooling capacity and Entropy Production Number were used to analyze and improve the cooling and thermodynamic performance of the general MIEC. A total of 6750 air treatment processes have been studied with the self-programmed FORTRA. It is concluded that when the inlet temperature is high, with the increase in inlet relative humidity, the unit-cooling capacity of the system greatly improves while the Entropy Production Number increases relatively small. When the ambient humidity variation range is large, the irreversible loss of the system can be reduced by coordinating the supply air ratio and dew point temperature efficiency of the MIEC system. Ultimately, the results of this study will provide theoretical reference for the design and operation of the practical engineering of the MIEC.


Introduction
Improving energy efficiency and reducing energy consumption is an important way to deal with the world energy crisis.Technological revolutions on indirect evaporative cooling have recently hit the industrial world.The theory of M-Cycle indirect evaporative cooling was proposed by Dr Valerij Maisotsenko et al. in 2003(Maisotsenko et al. 2003).The M-Cycle indirect evaporative cooling (MIEC) is famous for its outstanding cooling performance, low energy consumption and no environmental pollution.Theoretically, the product air can be cooled to as low as the dew point temperature of the inlet air (Maisotsenko et al. 2003).During the past decade, the M-Cycle indirect evaporative cooling system has application in various fields, such as air conditioning, refrigeration, etc.Much work has been reported recently (Pan De Lidis et al. 2018;Pandelidis 2020;Zhu et al. 2019;Shahzad et al. 2021).Pan De Lidis et al. (2018) analyzed the application of three arrangements of the cross-flow M-Cycle air cooler, where it is used as a heat recovery device in the air conditioning system, and each arrangement is justified depending on the moderate climate.Pandelidis (2020) studied the Maisotsenko cycle cooling tower through numerical modeling.The study confirmed high practical potential of using M-Cycle in water cooling applications.Zhu et al. (2019) investigated two efficient humidified gas turbine cycles, a hybrid cooler of indirect evaporative and Maisotsenko cycle and a conventional indirect evaporative cooler, by simulation in his study.Results show that the application of Maisotsenko cycle-based air saturator could further improve the gas turbine cycle efficiency.Shahzad et al. (2021) took the thermodynamic analysis of the improved evaporative cooling systems (DEC, IEC, MEC) from the viewpoint of heat stress in poultry houses in Multan, Pakistan.
Research on the M-Cycle indirect evaporative cooling systems has attracted many scholars.Additionally, one of the most interesting research topics is the performance optimization of M-Cycle indirect evaporative cooling (Tariq et al. 2018;Shahzad et al. 2018;Li et al. 2021;Fan et al. 2021;Sohani, Sayyaadi, and Hoseinpoori 2016;Zhan et al. 2011;Rogdakis et al. 2014;Pandelidis and Anisimov 2015;Pandelidis et al. 2017).The published information that is relevant to this topic is mainly about evaluating the performance of the MIEC by investigating different types of configurations, arrangement, and size (Fan et al. 2021;Sohani, Sayyaadi, and Hoseinpoori 2016;Zhan et al. 2011;Rogdakis et al. 2014;Pandelidis and Anisimov 2015;Pandelidis et al. 2017).Fan et al. (2021) constructed a novel dew point evaporative cooling tower based on M-cycle and its cooling performance such as outlet water temperature, precooled air temperature and wet bulb effectiveness were experimentally investigated.The results confirmed high practical potential of using M-Cycle in water cooling applications.Sohani, Sayyaadi, and Hoseinpoori (2016) implemented the developed GMDH model for multi-objective optimization of a prototype m-cycle cross-flow indirect evaporative cooler.The average annual values of coefficient of performance and cooling capacity were maximized, simultaneously, while working to air ratio and inlet air velocity were decision variables of optimization.Results of their studies implied that the optimized inlet air velocity for all climates varied between 1.796 m.s −1 and 1.957 m.s −1 , while the optimum WAR was 0.318 for "A" class cities.Moreover, the mean values of the COP and CC were improved 8.1% and 6.9%, respectively.Zhan et al. (2011) studied the cooling performance of the counter-flow and cross-flow heat exchangers through the development of a dedicated computer model and case-by-case experimental testing and validation.The results showed that the counter-flow exchanger offered greater (around 20% higher) cooling capacity, as well as greater (15%-23% higher) dew-point and wet-bulb effectiveness when equal in physical size and under the same operating conditions.The cross-flow system, however, had a greater (10% higher) energy efficiency (COP).In the study of Rogdakis et al. (2014), an alternative geometry of an M-cycle is developed and evaluated.Using a smart network of air channels, a wet-bulb efficiency of about 120% was achieved.The efficiency of the proposed system has been estimated to be about 105%, while the product air temperatures satisfy the cooling demands of buildings at regions of low relative humidity.Pandelidis and Anisimov (2015) investigated the carefully selected geometrical and operational aspects of the cross-flow Maisotsenko cycle heat and mass exchanger used for indirect evaporative air cooling by mathematical simulation.Pandelidis et al. (2017) numerically investigated the performance of three highly efficient, advanced indirect evaporative air coolers: the "classical" cross-flow M-Cycle heat and mass exchangers and two novel combined M-Cycle air coolers proposed by them.As can be seen from the above research results, for the research object is limited to a specific structure, the results of these studies are not generalisable and optimization research on the MIEC mostly starts from the change of structure, and optimization research methods based on thermodynamic methods are relatively rare.In addition, all MIECs were compared in terms of cooling efficiency, COP, energy saving rate, exergy efficiency, exergy efficiency ratio, and exergy destruction.The energy quality and irreversibility in the thermodynamic process cannot fully reflect.Furthermore, the existing research results show that multiple evaluation indexes always have contradictory conclusions (Anisimov and Pandelidis 2015), which makes the optimal design and operation of the MIEC at a loose end to a certain extent.Attempts to resolve these dilemmas have resulted in the development of the thermodynamic entropy production optimization method.
The thermodynamic entropy production optimization method uses the entropy production parameter to reveal the energy quality and irreversibility in the thermodynamic process and optimize the heat exchanger furthermore.However, studies do not give much attention to the unique features of the MIEC.Previous research has shown that this method has a certain application and analysis in the study of heat exchanger optimization (Wang et al. 2018;Farzaneh-Gord, Ameri, and Arabkoohsar 2016;Nima et al. 2019;Sepehr et al. 2018;Guzmán et al. 2018).Wang et al. (2018) studied the transient processes of heat exchangers by entropy generation analyses and the results can guide their designs and operations.Farzaneh-Gord, Ameri, and Arabkoohsar (2016) studied the optimal geometry and operational conditions of helically coiled heat exchangers for both laminar and turbulent flows based on the second law of thermodynamics.Nima et al. (2019) studied the second law features of an innovative nanofluid having hybrid nanoparticles of graphene nanoplatelets-Pt through a ribbed tripletube heat exchanger.Sepehr et al. (2018) numerically investigated heat transfer, pressure drop and entropy generation in shell and helically coiled tube heat exchangers in their study.JEV Guzmán et al. (2018) studied the entropy transportation process inside a plate and tube heat exchanger by numerical simulations.They analyzed and compared the entropy levels around tubes with circular and elliptical cross sections.The purpose of the comparison is to determine how the entropy flux contributes to increase, or decrease, the value of the entropy in certain regions of the flow field.
Recently, a few studies have been conducted on the entropy production optimization on the MIEC (Wang et al. 2019;Lin et al. 2020).Wang et al. (2019) studied the especial dew point air cooler under various operational and structural conditions via the entropy production number parameter.Additionally, the entropy production number is found to be a promising indicator for optimized design.Lin et al. (2020) proposed a robust optimization framework of the dew point evaporative cooler toward favorable dew point effectiveness, cooling capacity and coefficient of performance.Two optimization algorithms, multi-to-singleobjective and multi-objective optimizations, were developed using genetic algorithm.In their study, it was found that the multi-to-single-objective optimization is able to obtain appropriate objective functions according to predefined.Previous work (Wang et al. 2019;Lin et al. 2020) deals only with the working situations of an MIEC with a particular structure.To the author's knowledge, there is little application of the thermodynamic entropy production optimization method to a general MIEC.More research is still required before the final goal of obtaining the optimization method by evaluating the energy quality and irreversibility used in a general MIEC.In this paper, the thermodynamic entropy production optimization method is used in the optimization of the performance of a general MIEC.The entropy production of a general M-Cycle evaporative cooling system was studied, and the research results were used to analyze and improve the operational capability and cooling process of a general MIEC.Ultimately, the results of this study will provide theoretical reference for the design and operation of the practical engineering of the MIEC.

Physical and mathematical models
M-Cycle indirect evaporative cooling system is famous for its outstanding cooling performance.Theoretically, the product air can be cooled as low as the dew point temperature of the working air at inlet. Figure 1 is a schematic of the MIEC.The MIEC is composed of a certain number of working units, and each working unit is made up of a set of dry and wet channels.The working unit of the MIEC is shown in Figure 2. The inlet air (the state 1 in Figure 3) flows into the dry channel, and the temperature of the inlet air decreases for its constantly exchanging sensible heat with the surface of the plate between the dry and wet channels during its flow.The air is divided into two parts at the exit of the dry channel, one part is supplied to the user as product air (State 2), the other part enters the wet channel.The air in the wet channel is continuously humidified and transfers heat to the water film, further reducing the surface temperature of the plate between the dry and wet channel.The air exhausted from the wet channel is at state 4. The psychrometric processes in the MIEC are shown in Figure 3.
Before analyzing the heat and mass transfer in the wet and dry channels, to simplify the mathematical model, first make the following assumptions: The mathematical description of the MIEC is written as follows: Mass conservation equation: Thermal balance equation: In wet channel: In dry channel: Subscripts "1", "2" and "4" represent the air states of the inlet air, the product air, and the exhausted air, respectively.The subscript "3" represents the increased water vapour of air flowing through the wet channel.The subscript "d" or "w" indicates whether the parameter is in the dry or wet channel, respectively.m is the   mass flow rate.ρ is the air density, r is latent heat of evaporation.h w is the mass transfer coefficient, L is the channel length, (d w -d s ) is the moisture content difference between the water film surface and the air in the wet channel.α w is coefficient of heat transfer at the surface of the sheet between the dry and wet channels, α w =Nu s λ s /δ s , λ s is the heat conductivity coefficient of water, δ s is the thickness of the water film.The mass transfer coefficient and the coefficient of heat transfer at plate surface in the wet channels obey the Lewis relation.
Where Le is the Lewis number and it is taken as 1 for the wet channel.

Calculation method of thermodynamic irreversibility
In accordance with the entropy balance for the MIEC shown in Figure 1, total entropy production (S) can be written as: where s 2 and m 2 are, respectively, entropy flow and mass flow rate of product air in the system.Homoplastically, s 4 and m 4 are for the outlet air while s 1 and m 1 are for the inlet air system in the system.
Unit entropy production (S gen ) is defined as the ratio of the total entropy production in the MIEC to the mass flow of inlet air in the cooler, i.e., S gen =S/m 1 .For moist air is assumed to be an ideal gas, unit entropy production of the system can be expressed as: where C pd and C pw are mean specific heat capacity of moist air in dry and wet channels, respectively.Mean specific heat capacity of moist air can be calculated by the following equation.
where C pg is the specific heat capacity of dry air; C pq is the specific heat capacity of water vapor.
The supply air ratio (γ) definition of M-Cycle indirect evaporative cooling system is given.P v4 is partial evaporation pressure of saturated water of outlet air, and d 4 is moisture content of outlet air in the M-Cycle indirect evaporative cooler.The relationship between them can be expressed as: For M-Cycle evaporative cooling system, the pressure drop of the cooler is much lower than that of the resistance consumption of the entire cooling system.Thus, the pressure drop ratio, (P 2 -P 4 )/P 2 , (P 1 -P 2 )/P 1 , (P s -P 2 )/P 2 , in Equation 8 can be ignored.The reference temperature T 0 is taken to be 273.15K and the reference pressure P 0 is considered to be 101.325kPa.On this basis, equation 9, equation 10 and equation 11 are substituted into equation 8 to acquire the unit entropy production in the system.
Unit entropy production reflects the total irreversibility of thermodynamic process involving heat and mass transfers, but the heat transfer rate is not taken into account.The Entropy Production Number (Ns) (Bejan 1977) was introduced for thermodynamic irreversibility analysis of the MIEC.The Entropy Production Number is a parameter describing the thermodynamic perfection degree of M-Cycle indirect evaporative cooling system and it at the same time takes into consideration the influence of entropy production and heat transfer rate, which has practical significance.It is defined as the following: where, T 0 is reference temperature.Q is unit-cooling capacity, which is defined as the ratio of total system cooling capacity to inlet air mass flow.Unit-cooling capacity can be written as:

Research approach
The M-Cycle evaporative cooling system is environmentally friendly and energy efficient for no CFCs and no traditional compressor in used.The temperature of the product air can be cooled as low as the dew point temperature of the inlet air by isohygrometric treatment.Different temperatures of the product air can be obtained via the MIEC with different structures, size, or working conditions.Conventional optimization of the MIEC is to improve the evaporative cooling performance by optimizing the structure, size or working conditions.For instance, the length or width of channel, air supply rate, flow speed, thickness and temperature of the water film, etc.The excellent cooling performance of the MIEC means high dew point efficiency, high cooling efficiency, large cooling capacity, high COP, high energy saving rate, etc. Obviously, the relationship between efficient and energy-saving cooling performance with the inlet parameters, structure, is useful to optimize the M-Cycle evaporative cooling system.
Theoretically, for the M-Cycle evaporative cooling system, the product air can be cooled as low as the dew point temperature of the working air at the inlet.According to the basic theory, research on optimization of the performance of M-Cycle indirect evaporative cooling can be carried out by using a calculation program compiled by Fortran language, as follows.First, parameters of the inlet air are given and parameters of product air and the supply air ratio of the system are pre-setted, then parameters of the exhausted air and the mass flow ratio of product air and exhausted air can be obtained according to Equation 1.In addition, evaporative cooling performance of the system, such as dew point efficiency and unit-cooling capacity, and thermodynamic performance, such as entropy production and the Entropy Production Number, can be obtained according to equations 7-15, 17-18.The characteristic parameter range of high efficiency and energy saving MICE can be obtained by analyzing the relationship between the inlet parameter, supply air ratio, cooling performance and thermodynamic performance.Obviously, this parameter range is of great significance for the optimization of the MICE.
With the aim of performance optimization of the M-Cycle indirect evaporative cooling, 75 kinds of inlet air states with a temperature range of 28℃-42℃ and relative humidity range of 50%-90% were involved.In addition, the expected dew point efficiency is taken the range of 10%-100%, and supply air ratio is taken the range of 0.1-0.9.Ninety air treatment processes occurred for different supply air ratios and dew point efficiency of the system in the condition of a certain inlet air.So, 6750 air treatment processes were studied.Various data needed in the study were obtained from the self-programmed FORTRA.

Validation
The validation on the energy balance is carried out by the energy balance error of different psychrometric processes in the MIEC.The energy balance error is calculated as: where the inlet and outlet of the energy, E in , E out , is the sum of the enthalpy leaving and entering the MIEC.
Dew point temperature efficiency of evaporative coolers is evaluated in accordance with the following equations.
Figure 4 shows the relationship between the energy balance error, inlet temperature t 1 and dew point efficiency η.It is clearly seen that the maximum disequilibrium rate of the energy equation is 0.00052%.Accordingly, the present model is solved with a high degree of precision.

Result and analysis
For the MICE model shown in Figure 1, its cooling performance and thermodynamic performance parameters are obtained through numerical calculation.The applicable ranges of temperature and relative humidity of the inlet air are 28℃-42℃, 50%-90% respectively.The supply air ratio is set to 0.1-0.9, and the expected dew point efficiency is set to 10%-100% when the cooling system is working.

Influence of inlet parameters on unit-cooling capacity
Figure 5 depicts the impact of the inlet air temperature on unit-cooling capacity of the M-Cycle evaporative cooling system.The unit-cooling capacity refers to the ratio of the sum of the cooling capacity produced by the M-Cycle cooler to the inlet mass.
As seen in Figure 5, the unit-cooling capacity increase as the increase in the inlet temperature when the inlet relative humidity is constant and the system works on the same supply air ratio and the same dew point efficiency.The influence of inlet relative humidity on the unit-cooling capacity is analyzed under the same supply air ratio and the same dew point efficiency, the results are shown in Figure 6.As shown in Figure 6, the unit-cooling capacity increases with the decreases of inlet relative humidity when the inlet temperature remains constant.In other words, the unit-cooling capacity increases with the increase in the inlet temperature and the decrease of inlet relative humidity.

Influence of dew point temperature efficiency on unit-cooling capacity
Figure 7 depicts the relationship between the dew point temperature efficiency and unit-cooling capacity on the condition that the inlet parameters are respectively (28℃, 60%), (28℃, 70%), (38℃, 60%), when the supply air ratio is set as 0.6.As shown in Figure 7, the unit-cooling capacity increased with the increase in the inlet air temperature by comparing the curves of inlet parameters as (28℃, 60%) and (38℃, 60%).The comparison of curves of the two inlet parameters, (28℃, 60%) and (28℃, 70%), shows that the greater the humidity, the smaller the unit-cooling capacity.The unit-cooling capacity of the M-Cycle evaporative cooling system increases as the dew point temperature efficiency increases when the inlet parameters are constant.When the system works at the same dew point temperature efficiency, the unit-cooling capacity of the system will increase with the increase in the inlet air temperature and decrease with the increase in the inlet relative humidity.It indicates that the unit-cooling capacity of the M-Cycle evaporative cooling system with lower inlet air relative humidity and higher inlet temperature increases more than that with the higher inlet air relative humidity and lower inlet temperature.

Influence of supply air ratio on unit-cooling capacity
The supply air ratio of MICE is the ratio of the mass flow rate of product air and inlet air, which is less than 1.The smaller supply air ratio will reduce product air and enhance secondary air in the system, which will result in low temperature of the product air and high dew point temperature efficiency.Figure 8 shows the relationship between unit-cooling capacity and supply air ratio, the dew point temperature efficiency when an inlet air with a temperature of 30℃ and relative humidity of 60%. Figure 8 shows that the same unitcooling capacity can be obtained in different supply air ratios and dew point temperature efficiency of the cooling system.Table 1 shows unit-cooling capacity when the inlet air parameters are 30℃ and 60%.As can be seen from Table 1, a unit-cooling capacity of 5.0 ± 0.5 kJ/kg was obtained through the following supply air ratios and dew point temperature efficiency: γ = 0.6, η = 90% or 100%; γ = 0.7, η = 80%; γ = 0.8, η = 70%; γ = 0.9, η = 60%.
Figure 9 depicts the impact of the supply air ratio on unit-cooling capacity of M-Cycle evaporative cooling system with different inlet parameters.As shown in Figure 9, the unit-cooling capacity increases with the increase in the supply air ratio in the condition that the dew point temperature efficiency is constant.Number that occurs in the cooling system increases with the increase in inlet air relative humidity.The irreversible loss of the system decreases largely with the increase in inlet air temperature when the inlet air relative humidity is extremely high.

Influence of inlet parameters on the entropy production number
In Figure 10(a), the Entropy Production Number decreases rapidly as the inlet air temperature rises when the inlet air relative humidity is 80% or 90% and η = 80%, γ = 0.5.The maximum Entropy Production Number occurs when the inlet temperature is taken as 28℃ and its values are 4.621 and 4.577, respectively.The Entropy Production Number increases first and then decreases with the increase in the inlet air temperature when the inlet air relative humidity is 50%, 60% or 70%.For inlet air relative  humidity is 50%, the maximum Entropy Production Number occurs at 35℃ and its value is 4.745; the minimum value occurs at 28℃ is 4.682.For inlet air relative humidity is 60%, the maximum value occurs at 32℃ is 4.790 and the minimum value occurs at 42℃ is 4.688.For inlet air relative humidity of 70%, the maximum value occurs at 30℃ is 4.828 and the minimum value occurs at 42℃ is 4.659.However, the inlet air relative humidity has a substantial effect on the Entropy Production Number of the system.In addition, minimum range of Entropy Production Number with an inlet air relative humidity from 50% to 90% is acquired at 36℃, inlet air temperature.As shown in Figure 10(b)-(d) that the variation curves of Entropy Production Number with inlet parameters when the system works, respectively, under conditions η = 90%, γ = 0.5; η = 80%, γ = 0.6 and η = 90%, γ = 0.6, and the variation trends are consistent with those in Figure 10(a).The limiting values for the Entropy Production Number of the cooling system with different operating parameters are listed in Table 2.The data in Table 2 were obtained under conditions of the MIEC works with inlet air temperatures from 28℃ to 42℃ and relative humidity from 50% to 90%, with a supply air ratio of 0.5 or 0.6 and the dew point temperature efficiency of 80% or 90%.
The influence of the inlet air temperature on the rangeability of Entropy Production Number is investigated in Figure 11.The rangeability of Entropy Production Number is the difference between the maximum and minimum values of the cooling system with a constant inlet air temperature and inlet air relative humidity varying within a certain range.In here, the humidity variation range is 50%-90%.As shown in Figure 11, the variation range of Entropy Production Number of the system is less than 0.06 when the cooling system works in a supply air ratio of 0.5 with inlet air temperature varying from 34℃ to 38℃ or in supply air ratio of 0.6 with an inlet air temperature varying from 35℃ to 41℃.Therefore, for the inlet air within a certain temperature range, the energy consumption of the M-Cycle evaporative cooling system can be reduced by coordinating the supply air ratio and dew point temperature efficiency of the MIEC when the humidity variation range is large.

Influence of dew point temperature efficiency on entropy production number
The relationship between the dew point temperature efficiency and Entropy Production Number is shown in Figure 12.Obviously, the Entropy Production Number increases with the increase in the dew point temperature efficiency.However, the curve slope of Entropy Production Number varies with the dew point temperature efficiency with different inlet parameters.The maximum Entropy Production Number varies with the dew point temperature efficiency.As shown in Figure 12(a) and 12, when the inlet air relative humidity is 50%, the maximum Entropy Production Number is obtained at inlet temperature of 36-37℃.When the inlet temperature is less than 36℃, the Entropy Production Number decreases relatively slowly with an increase in the dew point temperature efficiency.However, when the inlet temperature is greater than 37℃, the Entropy Production Number decreases sharply with the increase in the dew point temperature efficiency.In the condition of the cooling system works in the same dew point temperature efficiency, Entropy Production Number increases with the increase in inlet temperature from 28℃ to 36℃ and decreases with the increase in inlet temperature from 37℃ to 42℃.As shown in Figure 12(c) and (d), when the inlet air relative humidity is 60%, the maximum Entropy Production Number is obtained at inlet air temperatures of 33℃-34℃.When the inlet temperature is less than 33℃, the Entropy Production Number decreases slowly with the increase in the dew point temperature efficiency, but when the inlet temperature is greater than 34℃, the Entropy Production Number decreases sharply.Under the conditions in the cooling system works at the same dew point temperature efficiency, the Entropy Production Number increases with an increase in the inlet temperature from 28℃ to 33℃ and decreases with the increase in the inlet air temperature from 34℃ to 42℃.As shown in Figure 12(e), (f) and (g), when the inlet air relative humidity is 70%, 80% or 90%, the maximum Entropy Production Number is obtained at an inlet air temperature of 28℃ and the Entropy Production Number decreases sharply with the increase in the dew point temperature efficiency.Under the condition in the cooling system works at the same dew point temperature efficiency, the Entropy Production Number decreases with the increase in the inlet temperature from 28℃ to 42℃.

Influence of supply air ratio on entropy production number
Figure 13 depicts the impact of the supply air ratio on the Entropy Production Number of M-Cycle evaporative cooling system with the same inlet air temperature.Figure 13(a), (c) and (e) respectively depict the inlet air temperatures of 28℃, 33℃, 38℃ and the inlet air relative humidity of 50%.It is found that the Entropy Production Number decreases sharply with the increasing of the supply air ratio when the supply air ratio is less than 0.3 and the decrease of Entropy Production Number is slower when the supply air ratio is greater than 0.3.Figure 13(b), (d) and (f) respectively depict the inlet air relative humidity varying from 50% to 90% and the benchmark for comparison is inlet air relative humidity of 50% for the same inlet air temperature.As shown in Figure 13(b), the deviation of the Entropy Production Number from the reference base increases with the increasing supply air ratio and inlet air relative humidity.In Figure 13(d), when the inlet air temperature is 33℃and supply air ratio is greater than 0.5, the deviation of the Entropy Production Number from the reference base increases much more with the increase in the supply air ratio at a higher inlet air relative humidity.In Figure 13(f), when inlet air temperature is 38℃and supply air ratio is less than 0.4, the deviation of the Entropy Production Number from the reference base decreases much more with the increase in the supply air ratio at a higher inlet air relative humidity.It can be further concluded from Figure 13(b), (d) and (f) that when the supply air ratio of the MIEC is set within the range of 0.4-0.7, the inlet parameters have little influence on the Entropy Production Number.Figure 14 depicts the impact of the supply air ratio on the Entropy Production Number of M-Cycle with a constant inlet air relative humidity.The benchmark for comparison is inlet air temperature of 28℃ and the same inlet air relative humidity.Figure 14(a) shows the supply air ratio has a greater impact on the Entropy Production Number with the inlet temperature of 33℃ and 38℃ than with 28℃ for the same inlet air relative humidity of 50%.Moreover, the Entropy Production Numbers at different inlet temperatures of 28℃, 33℃, 38℃ tend to approach as the supply air ratio increases.Figure 14(b) shows that the supply air ratio has a greater impact on the Entropy Production Number with the inlet temperature of 33℃ than with 28℃ but has a smaller impact with 38℃ than with 28℃ for the same inlet air relative humidity of 60%.As shown in Figure 14(c), (d), (e), for the inlet air relative humidity is, respectively, 70%, 80%, 90%, the supply air ratio has a smaller impact on the Entropy Production Number with the inlet temperatures of 33℃ and 38℃ than with 28℃.It is concluded from Figure 14 that the relationship between the supply air ratio and the Entropy Production Number is significantly affected by inlet air relative humidity.The Entropy Production Number decreases with the increase in the supply air ratio in the condition of the cooler works with a constant inlet air temperature and inlet air relative humidity greater than 70%, the supply air ratio less than about 0.6.

Conclusion
With the world's energy dilemma, using energy efficiently is highly respected.The M-Cycle evaporative cooling system is environmentally friendly and energy efficient for no CFCs and no traditional compressors.The primary goal of this research was to optimize the performance of M-Cycle indirect evaporative cooling system.The method used in this research is known as the thermodynamic entropy production optimization.The inlet parameters, supply air ratio, dew point temperature efficiency, unit-cooling capacity and Entropy Production Number and so on are used to analyze the cooling performance and thermodynamic performance of a general M-Cycle evaporative cooling system.The main conclusions are given as follows: (1) The unit-cooling capacity of the M-Cycle evaporative cooling system increases with the increase in the inlet air temperature, dew point temperature efficiency and supply air ratio but decreases with an increase in inlet air relative humidity.temperature and is smoother in a lower inlet air relative humidity, while the curve is more intense in a higher inlet air relative humidity.The Entropy Production Number increases with the increase in air relative humidity at a low inlet temperature.However, the difference in the Entropy Production Number between different inlet air relative humidity decreases when the inlet temperature is high.(4) Inlet relative humidity has little effect on Entropy Production Number under a certain range of supply air ratio, dew point temperature efficiency and inlet parameters.For example, the rangeability of the Entropy Production Number is less than 0.06 when the cooler works in supply air ratio of 0.5 with inlet temperature varying from 34℃ to 38℃ or in supply air ratio of 0.6 with inlet temperature varying from 35℃ to 41℃.
(5) The impact of supply air ratio on the Entropy Production Number is related to inlet relative humidity.The Entropy Production Number decreases with an increase of the inlet temperature for various inlet relative humidity which is greater than 70%, the supply air ratio is less than about 0.6.
The research conducted suggests that the cooling and thermodynamic performance of a general M-Cycle evaporative cooling system is influenced by the inlet parameters, the supply air ratio, the dew point temperature efficiency, etc.It is concluded that the unitcooling capacity improves and the Entropy Production Number reduces with a higher inlet temperature and a lower inlet relative humidity.When the inlet temperature is high, with the increase in inlet relative humidity, the unit-cooling capacity of the system greatly improves while the Entropy Production Number increases relatively small.As for the inlet temperature within a certain range, when the humidity variation range is large, the irreversible loss of the system can be reduced by coordinating the supply air ratio and dew point temperature efficiency of the M-Cycle evaporative cooling system.

Disclosure statement
No potential conflict of interest was reported by the authors.

( 1 )
The unit counter-flow dew-point indirect evaporative cooler is adiabatic; no heat is transferred to the outside; (2) Moisture is evenly distributed on the wet surface; (3) The properties of the air streams are uniform; (4) The heat and mass transfer coefficient of moist air conforms to the Lewis relation; (5) The air and moisture in the wet channel can fully contact.

Figure 2 .
Figure 2. Working unit of the MIEC.

Figure 4 .
Figure 4. Energy balance error with inlet air temperature and dew point effectiveness.

Figure 10
Figure 10 depicts the impact of the inlet parameters on the Entropy Production Number of M-Cycle evaporative cooling system working with a constant supply air ratio and dew point temperature efficiency.As can be seen from Figure 10, the Entropy Production Number first increases and then decreases with the increase in the inlet air temperature and the maximum and minimum Entropy Production Number occurs in the process.Furthermore, the Entropy Production Number changes more dramatically with the inlet temperature in a larger inlet air relative humidity.The inlet air temperature at the maximum Entropy Production

Figure 9 .
Figure 9. Influence of supply air ratio on unit-cooling capacity.

Figure 10 .
Figure10.Influence of inlet parameters on the entropy production number.

Figure 11 .
Figure 11.Influence of the inlet air temperature and the rangeability of the entropy production number.

Figure 12 .
Figure 12.Influence of the dew point temperature efficiency on the entropy production number (with different inlet parameters).
(2) The Entropy Production Number of the M-Cycle evaporative cooling system increases with the increase in the dew point temperature efficiency and supply air ratio.(3) The Entropy Production Number of M-Cycle evaporative cooling system first increases and then decreases with the increasing of the inlet air temperature.The curve of the Entropy Production Number varies with the inlet air

Figure 13 .
Figure 13.Influence of the supply air ratios on the entropy production number (with same inlet air temperature).

Figure 14 .
Figure 14.Influence of the supply air ratios on the entropy production number (with same inlet relative humidity).
Note: 1 Dew point temperature efficiency. 2 Supply air ratio.

Table 2 .
The limiting value for entropy production number and its corresponding inlet parameters.t 1.max and t 1.min are the inlet temperature at maximum and minimum Entropy Production Number.Ns max and Ns min are the value of maximum and minimum Entropy Production Number.
a b