Performance analysis of a conventional two-stage indirect evaporative cooler

Abstract

With the aim of saving a portion of the high-quality energy consumed in mechanical vapor compression systems for air conditioning applications, the present work focuses on utilization of low-quality energy conversion processes due to fluid evaporation. The conventional indirect evaporative cooler is selected based on its preference for further modification compared to a regenerative indirect evaporative cooler. It is configured to be operated with two identical stages in series. This task is achieved by developing a thermodynamic model to analyze the performance of the cooling unit and to indicate the extent of its development compared to the cooler in one stage. Preliminary results show that the best operating condition is when the ratio of primary air to secondary air is 1. The cooling unit produces fairly comfortable air within limited climatic conditions. It delivers air at 26 °C and lower even at climatic temperatures as high as 48 °C, but within a very low relative humidity range. The relative humidity range extends to less than 58% as the outdoor air temperature decreases. At high humidity levels (64 to 80% depending on climate temperature), cool air cannot be obtained at 26 °C, and the cooling unit performance is limited only by what the first stage produces. The average performance of the cooling unit exceeds that of the first stage by 42.6%. Increasing air flow rate leads to an increase in cooling capacity, but it also has a negative impact on supply temperature and effectiveness.

1 Introduction

Direct evaporative cooling is the process of cooling air by converting its sensible heat, as it passes over a wet surface, into latent heat, as the liquid water converted into vapor. This low-grade energy conversion results in a decrease in the temperature of both air and water. The amount of evaporated water will mix along with the air and raise its moisture content. Single-stage direct evaporative cooler (DEC) is the most widely used in domestic cooling applications. In any climate zone, the greater the difference between dry- and wet-bulb temperature (WBD), the more effective evaporative cooling becomes in lowering the air temperature. In their reviews, Porumb et al. [1] provided details regarding direct and indirect evaporative cooling technologies. DEC is an economical device in air conditioning applications. This device is an efficient and sustainable alternative to existing mechanical systems. However, it does not have active control over the air temperature and humidity delivered to the conditioned area with major drawbacks when used in humid areas, and also consumes large amounts of water. The cooler performance can be improved with the help of configuring many components within the system. An indirect evaporative cooler (IEC) is a modified alternative design with different mechanical modes capable of producing different results. This requires adopting several criteria for the purpose of preferential selection, including ease of implementing of construction designs, size, and cost. IEC differs from DEC in that it uses a heat exchanger as the cooling medium. The heat exchanger cools the primary outdoor air by transferring sensible heat to the pre-cooled secondary air. The secondary air is pre-cooled by direct evaporative cooling process using air washer or by direct spraying water into the secondary air duct.

IEC are of different modes, conventional IEC, which supply air with temperature above wet-bulb temperature, single-stage dew-point IEC, and the multi-stage M-cycle IEC. The latter systems can deliver air at a temperature below the wet-bulb temperature. Conventional single-stage evaporative cooler is widely used in domestic applications. In this technology, the air is thermally treated without adding any moisture and the cooling efficiency can be improved with the aid of various designs of the IEC components [2]. Arranging the IEC in a multi-stage cooling unit provides lower air temperatures, which broadens the range of applicable climatic zones, improves thermal comfort, and excludes further vapor compression refrigeration system [3]. Incorporating multi-stage IEC into a mechanical vapor compression (MVC) cycle can reduce energy costs by 57–92% depending on the type of application adopted; it can share 34 to 77% of the cooling load [4]. Evaporative cooling systems can play an important role in reducing carbon emissions, as they have low energy requirements. Extra research is needed to enhance its application and subsequent improvements to energy consumption in buildings [5].

The increasing interest through scientific research in developing indirect evaporative cooling systems indicates the widespread use of this type in many applications. Maheshwari et al. [6] analytically presented the benefit of using single-stage IEC in thermal pretreatment of outdoor air during the summer season. The large differences between dry-bulb and wet-bulb temperatures were the most important basis relied upon in Kuwait in inland and coastal areas where weather data were recorded. It was found that an IEC unit field of 70.8 ${\text{m}}^{3}/\text{h}$ can achieve seasonal energy savings of 12,418 and 6320 kWh, for inland and coastal areas, respectively, compared to the MVC unit when operating alone. Duan et al. [7] reported that their review of the current and future potential of IECs shows that the conventional IEC with humid secondary air channels reduces supply air temperature without moisture accumulation and it causes higher pressure drop compared to dry air channel mode. The current structure of IEC exchanger mainly adopts the stacked flat plate form, which is easy-to-manufacture, low cost, and energy-efficient method for indirect air cooling applications. However, single-stage indirect evaporative coolers are not able to provide adequate cooling of buildings. Therefore, their combination with other cooling devices has become a direction of further technical development, and this may help increase its market share. It has been observed that common operating modes related to IEC are IEC/DEC system, IEC/DEC/MVC system, IEC/dryer system, IEC/chilled water system, and IEC/heat pipe system. Possible future modes may include incorporation of the IEC into fan coil units, air handling units, cooling towers, etc. However, these combinations have higher levels of complexity in the configuration, but in return, it could obtain an increase in cooling efficiency and capacity. These works also help identify remaining problems and obstacles, which in turn encourages further research. Based on the wet secondary air channel, Shahzad et al. [8] proposed a modified generic IEC with multipoint injection of air into the secondary air channel for sensible cooling. A wide cooling unit consisting of a vertical heat exchanger was experimentally tested. The unit was adjusted for best spreading and collecting water. The secondary air is a portion of the cold air and is injected into more than one location in the secondary air channel that contains a water-wet liner. Outdoor air was taken at a temperature of 32 to 40 °C and a relative humidity of 23%. The results showed that with vertical heat exchanger, the air temperature was reduced by 10 °C and the effectiveness was achieved at the level of 0.37 to 0.78 depending on the operating parameters, with a small heat transfer area. Noor et al. [9] studied the feasibility of applying seven air conditioning system structures, including DEC, IEC, and MVC unit, and their potential clusters in Multan (Pakistan). A simulation model was created to explore the proposed system’s performance. The results show that the combination of IEC-DEC-MVC provided a greater temperature gradient (21 °C) than MVC and produced 85% more cooling capacity than DEC. Higher coefficient of performance was achieved by the DEC with relatively lower temperature gradient. The lowest wet-bulb effectiveness and cooling capacity were given by the IEC. The IEC-MVC and IEC-DEC-MVC combinations and MVC has achieved adequate thermal comfort for the study area. Comino et al. [10] designed and constructed a compact multi-stage regenerative IEC (12 dry channels and 11 wet cotton lined channels) using 3D printing techniques. A mathematical model was developed to determine the optimal operational and geometric parameters of the cooler. The ε-NTU numerical method was implemented for the design. The incoming air stream was partially reversed at the end of the dry channels (secondary air) to pass through the wet channels, exchanging heat and mass. The other part of the air flow (primary air) is cooled through dry channels and supplied to the conditioned space without changing its moisture content. The system was tested in an air climate that ranged from 27 to 46 °C with a constant a moisture content of 0.01 kg/kg. The ratio of secondary air to primary air was between 0.25 and 0.395. Results showed that the experimental cooling capacity was 45 kW per unit volume for an outdoor air temperature of 27 °C and air flow rate of 100 m³/h which is higher than those of commercial IEC. The heat capacity was increased with the increasing outdoor air temperature and air flow rate. It was concluded that the highly compact IEC can realize low energy consumption with low environmental impact. Pacak et al. [11] analyzed the performance of regenerative cross-flow dew-point IEC configured in a multi-stage configuration (cross-flow and regenerative counter-flow arrangement). The resulting performance was compared to that of a typical regenerative dew-point IEC. The operating parameters were chosen to achieve a compromise between the best cooling capacity and the lowest air supply temperature. Simulations were performed for average summer outdoor air characteristics of 30 °C and 45% relative humidity in a temperate climate. The air ratio in the cross-flow part was from 0.3 to 1.0 while in the regenerative part it was from 0.1 to 0.5. The results indicated that for the proposed multi-stage cooler with an airflow ratio of 0.3, the outlet air temperature decreased by 5.6%, and the cooling capacity increased by 10.2% compared to the typical regeneration unit. At an air ratio of 0.5, the cooler achieves the lowest possible supply temperatures ranging from 17.9 to 21.3 °C. The supply air temperatures for both dry and humid climates were lower than in the typical regenerative cooler. The construction geometry was the main reason for the benefits achieved from the proposed cooler. Chen et al. [12] provided an overview to investigate the aspects of integrating IEC with MVC systems. IEC has been evaluated as a pre-cooler and as a heat recovery device. Mathematically, it was found that IEC shared about 35 to 47% of the total load. As a pre-cooler and heat recovery ventilator, IEC can cause moisture condensation in the dry channel. It has come to the belief of researchers that IEC is a better alternative to MVC in cooling applications. It requires low-quality energy input to produce water evaporation potential to drive cooling action. IECs are simply designed and operated, but they have significant limitations in that they are greatly affected by increasing climate humidity and have little control over supply air conditions. Previously, the specific energy consumption of MVC remained in the range of 0.85–0.02 kW/t, with the technical difficulty of improving efficiency. Hybrid coolers provide the ability to control both temperature and humidity in different climatic conditions. Experimental and analytical studies have shown that the power consumption of the IEC-MVC hybrid system is 15–55% lower than that of MVC. In humid climates, energy savings are moderate (14–26%), but can reach up to 60% in dry climates.

Many studies have focused on optimizing and selecting the best configuration technique of indirect evaporative coolers for further development of their performance. Attempts included installing cooling units in different component locations and air/water distribution while comparing performance between construction modes. Li et al. [13] conducted a comparative study to numerically investigate the thermal performance of a cross-flow plate heat exchanger for an indirect evaporative cooler oriented in two positions, vertical and horizontal. Water was spread to wet the surfaces of the secondary air passages. The comparison was performed under different operating conditions. According to the findings, the supply temperature in the vertical position was 1.41–2.4 times lower than in the horizontal position. The vertical position had a cooling capacity that was 24–44% more than the horizontal position. This was due to the reduction of the wetted area in the secondary air ducts in the horizontal position. Salman [14] presented a simple thermodynamic analysis approach to compare the performance of conventional indirect evaporative (CIEC) and regenerative indirect evaporative cooler (RIEC) under general operating conditions. The main objective was to determine which of the two units had a higher chance of further design modifications. Each cooler has similar heat exchangers (HX) and air washers (AW) and has been subjected to the same operating parameters. The study showed that CIEC provided superior thermal performance in all performance comparisons, i.e., supply air temperature, wet-bulb effectiveness, and cooling capacity in comparison with RIEC. Accordingly, the researcher concluded that CIEC deserves attention for the purpose of further development to improve its performance. The use of the return air from the room as secondary air was one of the main factors to achieve this result. For both coolers, the increase in outdoor air temperature positively affected the effectiveness and cooling capacity but had a negative effect on the supply air temperature. Table 1 summarizes existing studies on the use of different configuration technique of indirect evaporative coolers to achieve better performance.

Table 1 Summary of existing studies on the use and comparison of different configuration technique for indirect evaporative coolers to achieve better performance

The present study aims at the possibility of replacing cooling devices that use high-quality energy with evaporative coolers that use low-quality energy to produce cooling. IEC was considered an effective and sustainable alternative to existing mechanical systems and are known to be promising devices by researchers for the purpose of air conditioning systems [11]. IECs based on pre-cooling of the wet secondary air channel with counter-flow heat exchanger such as M-cycle were considered the most efficient but have higher levels of complexity in the configuration [7], and were not commercialized due to manufacturing problems [8]. Single-stage conventional IEC lowers the supply air temperature without accumulating moisture, but is not able to provide adequate cooling of buildings [7], and it has proven to be worthy of further development compared to single-stage RIEC [14]. Conventional IEC exchanger based on dry secondary air channel mainly adopts the stacked flat plate form, which is easy-to-manufacture, low-cost, and energy-efficient method for indirect air cooling applications. Hence, in this study, it is proposed to broaden the applicable climate zone of single-stage CIEC operation and to enable it to provide better performance by configure it to operate in a two-similar stage unit integrated in series. The study involves evaluating of the proposed cooling unit in terms of basic thermal evaluation factors which are sensible effectiveness, supply air temperature, and heat duty in hot and humid climates. The evaluation is achieved theoretically by establishing an analytical thermodynamic model. The model is implemented with Microsoft Excel to calculate the performance factors of the two-stage unit under different working conditions and to show the evolution in performance values compared to the first stage of the cooler unit.

2 Description of the conventional two-stage indirect evaporative air cooler

The proposed system shown in Fig. 1 is a structural design of a conventional indirect evaporative cooler in two stages. Figure 1a is the schematic of two-stage CIEC. All components and property points are positioned for the following thermal analysis to calculate the heat duty and corresponding resulting performance. The locations of the property points and process lines for the operating cycle are also depicted on the psychometric chart as in Fig. 1b. Each stage includes a direct evaporative cooler (air washer) and an indirect air-to-air heat exchanger (plate type cross-flow heat exchanger). The outdoor air is supplied at point 1 in two streams (secondary air and primary air streams). The secondary air stream passes through the first air washer (${\text{AW}}_{1}$), where it is humidified in an isenthalpic process and being cooled (process line 1–2). The cold secondary air is then directed to the first heat exchanger (${\text{HX}}_{1}$) to exchange sensible heat with the primary air and then vented at point 3 (process line 2–3). The primary air stream goes directly to ${\text{HX}}_{1}$ where it is sensibly cooled (process line 1–4). The cold primary air at point 4 is then migrated from the first stage to the second stage for further cooling process. In the second stage, all previous processes performed in the first stage are repeated, except that the secondary air for this stage is the air emerging from the conditioned zone. The primary air that has just been cooled is directed to pass through the second heat exchanger (${\text{HX}}_{2}$). It is cooled sensibly (process line 4–5), by exchanging heat with the secondary air of the second stage. The air returning from the conditioned zone exhibits a higher relative humidity, but is still not saturated. It is further humidified and cooled (process line 6–7) in an isenthalpic process in the second air washer (${\text{AW}}_{2}$). Its temperature decreases to approach that of the wet-bulb temperature of the outdoor air, while its humidity increases. The moisture content of the supplied air at point 5 maintains the same as that of the outdoor air even if its relative humidity increases due to the decrease in its temperature. Finally this primary air, at point 5, is supplied to the conditioned zone. There, it is moistened and its temperature rises to some extent depending on the internal thermal load.

Fig. 1

Conventional two-stage IEC, a schematic diagram and b process representation on psychometric chart

3 Thermal analysis and evaluation methodology

This section aims to develop an analytical model for the thermodynamic evaluation of the proposed two-stage CIEC. The model is customized to calculate supply air temperature, heat duty, effectiveness, and the effect of operating variables. Operating parameters and assumptions are first determined and then prevailing equations and formulas are discussed. The analysis is based on a specified volumetric air flow rate with pre-determined inlet characteristics of the primary and secondary air streams. Inlet air characteristics are taken to cover the hot and humid conditions prevailing over a wide range of temperature and humidity, such as in the city of Basra, Iraq. Components such as fixed-plate type heat exchangers and air washers are selected to have known specifications and performance with the following assumptions.

• A plate type cross-flow heat exchanger is used for both stages. Each exchanger effectiveness ($${\varepsilon }_{\mathrm{H}\mathrm{X}}$$) is related to the primary air flow rate, which is represented by the following expression [14, 15], see also Appendix.

$$\varepsilon_\text{HX}=1.0702\;\dot{\mathrm V}^{-0.083}$$

(1)

• An air washer with a wet pad is used for both stages. Its saturation efficiency (E) is considered to be 0.9 [16]. The water flow to be supplied to the AW must vary with the inlet air flow rate to ensure the same efficiency.

• All heat transfer processes are in a steady state.

• Air properties are a function of temperature and relative humidity.

• Air properties through the HX passages are evaluated for each stream at an appropriate mean temperature.

• No heat transfer occurs between the surroundings and the heat exchangers.

• No condensation of moisture in the HX.

• Neglecting fan heat generation.

For computer-aided design purposes using Excel sheet, some algebraic relationships are needed to determine air properties and are obtained from the literature [17,18,19].

The saturation vapor pressure, ${P}_{ws}$ (Pa), at a given dry-bulb temperature, is the vapor pressure within humid air, where the water vapor is in thermodynamic equilibrium with pure liquid water, and is given by,

$${\mathrm P}_{\mathrm{ws}}=\mathrm e^{(77.345+0.0057\mathrm T-\frac{7235}{\mathrm T})}/\mathrm T^{8.2}$$

(2)

where T is the absolute dry-bulb temperature (K).

The moisture content of air, $\omega (\text{kg}/\text{kg}$), is given by:

$$\mathrm w=0.622\frac{{\mathrm P}_{\mathrm v}}{\mathrm P-{\mathrm P}_{\mathrm v}}$$

(3)

where ${P}_{v}$ is the vapor partial pressure in the air (Pa), and P is the total pressure of air (Pa).

The relative humidity of the moist air, ${\varnothing }$, is given by:

$$\varnothing\%=\frac{{\mathrm P}_{\mathrm v,}}{{\mathrm P}_{\mathrm{sat},}}\ast100\%$$

(4)

The air wet-bulb temperature, ${T}_{wb}$ $(^\circ\mathrm{C})$, at any point on the psychometric chart is given by:

$${\mathrm T}_{wb}=\mathrm T\ast\text{Arctan}\lbrack0.151977\ast\left(\varnothing\%+8.313659)^{0.5}\right]+\text{Arctan}\left(\mathrm T+\varnothing\%\right)-\text{Arctan}\left(\varnothing\%-1.676331\right)+0.00391838\ast(\varnothing\%)^\frac32\ast\text{Arctan}\left(0.023101\ast\varnothing\%\right)-4.686035$$

(5)

The dry air density $\left({\rho }_{da}\right)$ (kg/m³) is given by:

$$\rho_{da}={1/\lbrack10}^{-5}\;\mathrm T^2-0.0045\;\mathrm T+1.31\rbrack,0<\mathrm T\leq100$$

(6)

The moist air density ${\rho }_{ma}$ (kg/m³) is given by:

$${\mathrm\rho}_{\mathrm{ma}}={\mathrm\rho}_{\mathrm{da}}\frac{(1+\mathrm w)}{(1+1.609\mathrm w)}$$

(7)

The specific heat of moist air (J/kg·K) is given by:

$${\mathrm c}_{\mathrm p}=1005.7+1884\ast\mathrm\omega$$

(8)

3.1 Analysis of the first stage

For known values of outdoor air flow rates (primary air ${\dot{V}}_{1,p}$ (${\text{m}}^{3}$/h) and secondary air ${\dot{V}}_{1,s}$ (${\text{m}}^{3}$/h)), with known properties, the mass and energy balance equations for ${\text{AW}}_{1}$ can be applied.

The mass flow rate of primary air (${\dot{m}}_{1,p}$) and secondary air (${\dot{m}}_{1,s}$) are:

$${\dot{\mathrm m}}_{\mathrm p1}={\mathrm\rho}_1{\dot{\mathrm V}}_{1,\mathrm p}/3600$$

(9)

$${\dot{\mathrm m}}_{\mathrm s1}={\mathrm\rho}_1{\dot{\mathrm V}}_{1,\mathrm s}/3600$$

(10)

The secondary air temperature ${(T}_{2})$, at the outlet of ${\text{AW}}_{1}$, can be calculated from the definition of the air washer efficiency, that is:

$${\mathrm T}_2={\mathrm T}_1-{\mathrm E}_1\ast({\mathrm T}_1-{\mathrm T}_{1,\mathrm{wb}})$$

(11)

where ${T}_{1,wb}$ is the wet-bulb temperature at outdoor air condition and is calculated using Eq. (5) with the previous set of Eqs. (2), (3), and (4).

The primary air temperature at the outlet of ${\text{HX}}_{1}$ (${T}_{4})$ can be calculated from the heat exchanger effectiveness definition, that is:

$${\mathrm T}_4={\mathrm T}_1-\varepsilon_{\mathrm{HX}}\frac{{\mathrm C}_{\min}}{{\mathrm C}_{\max}}\left({\mathrm T}_1-{\mathrm T}_2\right)$$

(12)

where C is the heat capacity of the air stream.

$$\mathrm C=\dot{\mathrm m}{\mathrm c}_{\mathrm p}$$

(13)

${C}_{min}$, smaller heat capacity (W/K) of the two air streams of ${\text{HX}}_{1}$.

${\text{C}}_{\text{max}}$, maximum heat capacity (W/K) of the two air streams of ${\text{HX}}_{1}$.

The temperature drop through the ${\text{HX}}_{1}$ is ${\Delta T}_{1}$ and is given by:

$$\Delta{\mathrm T}_1={\mathrm T}_1-{\mathrm T}_4$$

(14)

The cooling capacity (${\dot{Q}}_{1}$) of the first stage represents the amount of sensible heat that the HX1 can extract from the primary air:

$${\dot{\mathrm Q}}_1={\dot{\mathrm m}}_1\ast{\mathrm c}_{\mathrm p1}\ast({\mathrm T}_1-{\mathrm T}_4)$$

(15)

The wet-bulb effectiveness ${\varepsilon }_{wb1}$ for the first stage of the cooler unit is given as follows:

$${\mathrm\varepsilon}_{\mathrm{wb}1}=\frac{{\mathrm T}_1-{\mathrm T}_4}{{\mathrm T}_1-{\mathrm T}_{1,\mathrm{wb}}}$$

(16)

3.2 Analysis of the second stage

Air properties at the entrance to the second stage are based on ${T}_{4}$ and on ${\omega }_{4}$ because the primary air undergoes only sensible cooling. The value of ${\dot{m}}_{4}$ is the same as the value of ${\dot{m}}_{1}$.

Assuming the conditioned zone causes a temperature rise of 5 °C and adds 0.002 kg/kg moisture to the air (${T}_{R}={T}_{6}={T}_{5}+5^\circ{\rm C}$ and ${\omega }_{R}={\omega }_{6}={\omega }_{1}+0.002$).

The secondary air temperature ${T}_{7}$ leaving ${\text{AW}}_{2}$ is obtained from the definition of the air washer efficiency, that is:

$${\mathrm T}_7={\mathrm T}_{\mathrm R}-\mathrm E\left({\mathrm T}_{\mathrm R}-{\mathrm T}_{\mathrm R,\mathrm{wb}}\right)$$

(17)

where ${T}_{R,wb}$ is the wet-bulb temperature at room condition and is calculated using Eq. (5) with the previous set of Eqs. (2), (3), and (4).

Since ${\dot{m}}_{4}={\dot{m}}_{7}$ and ${c}_{p}$ are almost the same for both air streams through ${\text{HX}}_{2}$, then:

$$\frac{{\mathrm C}_{\min}}{{\mathrm C}_{\max}}=1$$

(18)

${C}_{min}$, smaller heat capacity (W/K) of the two air streams of ${\text{HX}}_{2}$.

${C}_{max}$, maximum heat capacity (W/K) of the two air streams of ${\text{HX}}_{2}$.

The temperature of the primary air leaving ${\text{HX}}_{2}$ (${T}_{5}$) can be calculated as follows:

$${\mathrm T}_5={\mathrm T}_4-{\mathrm\varepsilon}_\text{HX}\frac{{\mathrm C}_{\min}}{{\mathrm C}_{\max}}({\mathrm T}_4-{\mathrm T}_7)$$

(19)

The temperature drop through the ${\text{HX}}_{2}$ is ${\Delta T}_{2}$ and is given by:

$$\Delta{\mathrm T}_2={\mathrm T}_4-{\mathrm T}_5$$

(20)

The wet-bulb effectiveness ${\varepsilon }_{wb2}$ for the second stage of the cooler unit is given as follows:

$${\mathrm\varepsilon}_{\mathrm{wb}2}=\frac{{\mathrm T}_4-{\mathrm T}_5}{{\mathrm T}_4-{\mathrm T}_{4,\mathrm{wb}}}$$

(21)

where ${T}_{4,wb}$ is the air wet-bulb temperature at entrance of ${\text{HX}}_{2}$.

The second stage cooling capacity (${\dot{Q}}_{2}$) represents the sensible heat that can be exchanged through ${\text{HX}}_{2}$ between the primary air and the secondary air.

$${\dot{\mathrm Q}}_2={\dot{\mathrm m}}_1\ast{\mathrm c}_{\mathrm p1}\ast({\mathrm T}_4-{\mathrm T}_5)$$

(22)

3.3 The two-stage cooling unit performance

The overall temperature drop through the two stages as a single cooling unit is ${\Delta T}_{c}$:

$$\Delta{\mathrm T}_{\mathrm c}={\mathrm T}_1-{\mathrm T}_5$$

(23)

The overall cooling capacity of the two-stage cooling unit is:

$${\dot{\mathrm Q}}_{\mathrm c}={\dot{\mathrm Q}}_1+{\dot{\mathrm Q}}_2$$

(24)

The overall effectiveness of the two-stage cooling unit is:

$${\mathrm\varepsilon}_{\mathrm c,\mathrm{wb}}=\frac{{\mathrm T}_1-{\mathrm T}_5}{{\mathrm T}_5-{\mathrm T}_{1,\mathrm{wb}}}$$

(25)

4 Results and discussion

This study aims to investigate the performance of two-stage CIEC as a modified proposal of single-stage CIEC with the aim of obtaining better thermal performance.

Referring to Fig. 1, the outdoor air is directed towards the first stage in two streams, primary air (${\dot{V}}_{1,p})$ and secondary air ${\dot{(V}}_{1,s})$, with an air ratio (AR) of ${\dot{V}}_{1,s}/{\dot{V}}_{1,p}$. At the beginning of the calculations, it is important to know what is the appropriate value of AR that produces the best output.

Taking any outdoor air condition as ${T}_{1}$ = 40 °C and ${\omega }_{1}$ = 0.015 kg/kg, Fig. 2a shows the variation of the primary air temperature along its paths through the heat exchangers. It is clear that as AR increases, the primary air temperatures ${T}_{4}$ and ${T}_{5}$ decrease at the exit points of ${\text{HX}}_{1}$ and ${\text{HX}}_{2}$, respectively. This is because the heat capacity ratio (${C}_{min}/{C}_{max}$) increases with increasing AR for both exchangers. The lowest temperatures are achieved at the point where the heat capacity ratio reaches its maximum at AR = 1. With the next increase in AR, the heat capacity ratio reversed and falls below its maximum value; thus, ${T}_{4}$ and ${T}_{5}$ increase. Obviously, ${T}_{5}$ has a lower value than ${T}_{4}$ as the primary air is further cooled in the second heat exchanger. The second heat exchanger receives primary air at a lower temperature but higher relative humidity than the first heat exchanger. One important result that can be deduced a priori from Fig. 2a is that the two-stage CIEC has the potential to supply cold air with a temperature $({T}_{5})$ close to the outdoor air wet-bulb temperature (${T}_{1,wb})$, which the single-stage CIEC cannot reach under all operating conditions. The supply temperature ${T}_{5}$ of the cooling unit has approached ${T}_{1,wb}$ by 1.76 times closer than ${T}_{4}$.

Fig. 2

Effect of air ratio (AR) on two-stage CIEC performance factors: a ${T}_{4}, {T}_{5}$, and ${T}_{1,wb}$, b temperature differences, ${\Delta T}_{1}, {\Delta T}_{2}$, and ${\Delta T}_{c}$, c cooling capacity, and d wet-bulb effectiveness

Figure 2b identifies the appropriate value of AR that achieves the highest temperature drop through the heat exchangers, ${\Delta T}_{1}$ and ${\Delta T}_{2}$, and the total temperature drop of the cooling unit ${\Delta T}_{C}$. Concerning the first heat exchanger, it is noted that ${\Delta T}_{1}$ increases with increasing AR until it reaches its maximum value at an air ratio of 1. This is because the temperature at the inlet of the first exchanger $({T}_{1})$ is high and keeps constant, while the temperature of the air leaving the first exchanger (${T}_{4}$) and entering the second exchanger is constantly decreasing. Any further increase in AR more than 1 results in an increase in T₄ and thus in a decrease in ${\Delta T}_{1}$. Concerning the second heat exchanger, it is noted that the relation trend between ${\Delta T}_{2}$ and AR is completely opposite to that of ${\Delta T}_{1}$. This is because the air state at the entrance to the second exchanger is more humid relative to outdoor air state, and ${T}_{4}$ is variable and decreasing more sharply than ${T}_{5}$. This change continues until AR reaches 1, where the lowest temperature difference occurs through the second heat exchanger. Then, ${\Delta T}_{2}$ reverses and increases with the next increase in AR. From what has just been shown, it is important to achieve a compromise and real value for AR to obtain maximum temperature drop through the cooling unit. In this case, a compensatory value of AR corresponding to the maximum overall temperature difference ${\Delta T}_{c}$ should be determined. This relationship is also illustrated in Fig. 2b, where it is seen that AR maintained its value of 1 as ${\Delta T}_{c}$ reached its maximum.

One of the primary variables that control the amount of heat transferred in open systems such as heat exchangers is the ability of the heat exchanger to change the temperature of the fluid. In the present system, ∆T in turn depends on the AR values as discussed in Fig. 2b. Therefore, as shown in Fig. 2c, the amounts of heat transferred in the two heat exchangers rise and fall depending on the change in the AR value. In the first exchanger, ${\dot{Q}}_{1}$ increases with increasing AR until AR reaches its maximum value, then the transferred heat begins to reduce with increasing AR. In the second heat exchanger, according to the change in AR, it was observed that the process is reversed, as ${\dot{Q}}_{2}$ decreases with increasing AR and then increases when AR becomes more than 1. Therefore, at the maximum value of ${\Delta T}_{c}$ at which AR equals 1, the highest cooling capacity ${\dot{Q}}_{c}$ is expected. Accordingly referring to Fig. 2d, the highest effectiveness of the first stage occurs at the highest value of ${\Delta T}_{1}$ where AR = 1, and the lowest effectiveness of the second stage occurs at the lowest value of ${\Delta T}_{2}$ at which AR is also equals 1. Therefore, the compensatory effectiveness of the system occurs at AR = 1. Hence, this value of AR will be adopted in the next thermal analysis.

Note that the two-stage cooler achieved 12.6% lower supply temperature, 47.2% greater cooling capacity, and 47.2% greater effectiveness compared to the first stage at AR = 1.

4.1 Effect of operating parameters

Air temperature and relative humidity are the most important operational factors that affect the performance of IEC. Moreover, there is also a selective factor, as needed, which is the air flow rate.

4.2 Effect of outdoor air temperature

Figure 3 shows the effect of outdoor air temperature on the two-stage CIEC performance factors. The primary air flow rate (${\dot{V}}_{1,p}$) is taken as 500 ${\text{m}}^{3}$/h, AR = 1, and ${T}_{1}$ ranges from 30 to 48 °C where the relative humidity (${\varnothing }_{1}$) ranges from 56.9 to 21.6%, respectively. The humidity ratio (${\omega }_{1}$) is constant and equal to 0.015 kg/kg.

Fig. 3

Effect of outdoor air temperature (${T}_{1}$) on two-stage CIEC performance factors: a ${T}_{4}, {T}_{5}$, and ${T}_{1,wb}$, b temperature differences, ${\Delta T}_{1}, {\Delta T}_{2}$, and ${\Delta T}_{c}$, c cooling capacity, and d wet-bulb effectiveness

Figure 3a indicates that ${T}_{4}$ and ${T}_{5}$ increase with increasing ${T}_{1}$. The cooling unit produces a fairly acceptable supply temperature $(26{^\circ\mathrm{C}})$ for a climate zone where ${T}_{1}$ 31 °C at which ${\varnothing }_{1}$ = 53.7%. This point is highlighted by the yellow circle on the curves. When ${T}_{1}$ is lower than 31 °C, a lower supply temperature can be produced at higher value of ${\varnothing }_{1}$. The cooling unit produces thermally treated air at 25.8 °C, 29.3 °C, and 30.9 °C when ${T}_{1}$ is 30 °C, 42 °C, and 48 °C, respectively. The supply temperature trend of the cooling unit in two stages is always lower than that of the first stage with increasing variance from 1.8 to 19.6%, corresponding to outdoor air temperature range. It is shown that the supply temperature close to the wet-bulb temperature of the outdoor air ${T}_{1,wb}$ even in extremely hot climates.

Accordingly, as shown in Fig. 3b, with increasing ${T}_{1}$, the two-stage cooling unit showed a higher decrease in ${\Delta T}_{c}$ than occurs during the single stage $({\Delta T}_{1})$ with increasing variance. The ability of the cooling unit to reduce the primary air temperature $({\Delta T}_{c})$ is 4.2 °C, 12.7 °C, and 17.1 °C when ${T}_{1}$ is 30 °C, 42 °C, and 48 °C, respectively. The first stage heat exchanger consistently showed a higher temperature drop ${(\Delta T}_{1})$ than the second stage $({\Delta T}_{2})$ due to the relative humidity ${\varnothing }_{4}$ being higher than ${\varnothing }_{1}$ and ${T}_{4}$ being lower than ${T}_{1}$.

The temperature drop of the primary air is the main factor that determines the cooler cooling capacity and effectiveness. Therefore, the same effect of ${T}_{1}$ applies to the results of the evolution in cooling capacity ${Q}_{c}$ versus ${T}_{1}$ as shown in Fig. 3c. The cooling capacity of the cooling unit (${Q}_{c}$) increases with increasing ${T}_{1}$ and the heat exchanger of the first stage contributed a higher cooling capacity compared to the capacity contribution of the second stage. The variation of the unit cooling capacity from the first stage capacity increases by 12.2 to 54.8%, corresponding to the outdoor air temperature range. Figure 3d depicts that the wet-bulb effectiveness remains constant and almost does not change versus ${T}_{1}$ in the first stage while it increases in the second stage. As a result of the operation of both heat exchangers, the wet-bulb effectiveness of the cooling unit improves and shows an increase with increasing ${T}_{1}$. The effectiveness of the cooling unit is 64.5% and 89%, which is 12.2% and 54.8% higher than that of the first stage at ${T}_{1}$ = 30 and 48 °C, respectively.

4.3 Effect of outdoor air relative humidity

The outdoor air relative humidity is an effective factor affecting the performance of evaporative coolers. It is known that saturated air passing over wetted surfaces cannot hold any excess water vapor under constant pressure, while unsaturated air can do so to some extent, depending on the percentage of air saturation. The more water vapor the air can capture, the lower the air temperature obtained, where sensible heat is converted into latent heat. The following review shows the results of the effect of outdoor air relative humidity on the performance of the evaporative cooling unit.

Figure 4 shows that the performance parameters of the evaporative cooler suffer greatly from the increase in ${{\varnothing }}_{1}$, which raises the supply air temperature and lowers all other performance parameters. The flow rate of the primary air (${\dot{V}}_{1,p}$) is taken as 500 ${\text{m}}^{3}$/h, AR = 1, and ${{\varnothing }}_{1}$ ranges from 10 to 74% at ${T}_{1}=40^\circ{\rm C}$. Figure 4a indicates that the temperatures ${T}_{4}$ and ${T}_{5}$ increase with an increase in ${{\varnothing }}_{1}$ with the constant proximity of the supply air temperature ${T}_{5}$ with ${T}_{1,wb}$. The evaporative cooling unit produces an acceptable supply temperature at ${{\varnothing }}_{1}$ = 23.8% and below. The supply air temperature is 20.5 °C, 31.7 °C, and 37.5 °C when ${{\varnothing }}_{1}$ is 10%, 44.2%, and 74.3%, respectively. The trend curve of ${T}_{5}$ is in decreasing variance with ${T}_{4}$ until ${T}_{5}$ equals ${T}_{4}$ where ${{\varnothing }}_{1}=74.3\text{\%}$. This behavior mainly reflects negatively on the temperature drop through the second heat exchanger, and thus on the unit cooling capacity, as shown in Fig. 4b and c, respectively. At ${{\varnothing }}_{1}=10\text{\%}$, the primary air temperature drop is 19.5 °C and at higher values of ${{\varnothing }}_{1}$, the temperature drop diminishes and approaches 2.5 °C when ${{\varnothing }}_{1}$ reaches $74.3\text{\%}$. In this case, the temperature drop through the second heat exchanger is zero, and therefore, it cannot achieve any sharing of cooling capabilities.

Fig. 4

Effect of outdoor air relative humidity (${\varnothing }_{1}$) on two-stage CIEC performance factors: a ${T}_{4}, {T}_{5}$, and ${T}_{1,wb}$, b temperature differences, ${\Delta T}_{1}, {\Delta T}_{2}$, and ${\Delta T}_{c}$, c cooling capacity, and d wet-bulb effectiveness

Figure 4d shows that the wet-bulb effectiveness remains constant and almost unchanged versus ${{\varnothing }}_{1}$ for the first stage, while it constantly decreases in the second stage due to the continued convergence between ${T}_{4}$ and ${T}_{5}$. Therefore, the wet-bulb effectiveness of the cooling unit shows a decrease when ${{\varnothing }}_{1}$ increases. The effectiveness is 0.91, which is 53% higher than the effectiveness of the first stage at ${{\varnothing }}_{1}=10\text{\%}$, and is 0.575, which is the same as the effectiveness of the first stage at ${{\varnothing }}_{1}=74.3\text{\%}$.

To give an idea of the amount of air humidity at the point of entry into the conditioned zone, color-shaded circular marks are highlighted on the characteristic curves in Fig. 4. These marks are intended to identify the operating condition that results in a relative air humidity (${\varnothing }_{5}$) of 50 to 80% as specified by the characteristic curves. It is observed from Fig. 4a that the cooling unit can supply air with a relative humidity of just over 50% and a temperature of 26 °C with an effectiveness of 87.4% (Fig. 4d), but at a low outdoor air relative humidity that should not exceed 23.8%.

To give a more comprehensive view of the impact of external operating factors, it is necessary to create a comprehensive figure that achieves this scene. Figure 5 shows the overall operating limits where the appropriate supply air can be labeled for many desired applications corresponding to different climatic conditions. Figure 5a includes locations where the relative humidity of the supplied air (${\varnothing }_{5}$) is constant by indicating the cross lines superimposed on the performance curves. The ends of the temperature curves at high relative humidity side are connected by a curve representing the termination of the second heat exchanger from participating in cooling production, where ${\Delta T}_{2}=0$. The graphics section below the dashed horizontal line at ${T}_{5}$ = 26 (it could be rather than 26 as desired) identifies the appropriate operating conditions to produce fairly comfortable cold air for human comfort. Cold air can be delivered at 26 °C and below, even at high temperature climate (40 to 48 °C), but within a low relative humidity range (up to 23.8%). The cooling unit produces the same level of air temperature in humid zone up to 58%, but within a limited climatic temperature (below 40 °C). Beyond these limits, the cooling unit can supply air at temperatures above 26 °C with the potential to remove heat loads as shown in Fig. 5b. Such heat load even at higher supply temperature (more than 26 °C) is beneficial when integrating the evaporative cooling unit, for the purpose of pre-cooling, with mechanical air conditioning systems. The cooling capacity and the wet-bulb effectiveness decrease continuously with increasing ${{\varnothing }}_{1}$. The effect of further increase in relative humidity is worsened, causing the cooling unit to operate at its lowest performance, such that the second stage becomes useless. When the ambient air humidity exceeds 80%, the system becomes unsuitable for producing significant cooling, but only by a few degrees as the humidity of the supplied air increases. A 2 °C drop in primary air temperature to 23 °C can be achieved depending on operating parameters.

Fig. 5

A comprehensive representation of the impact of external operating factors on performance factors

4.4 Effect of primary air flow rate

Figure 6 displays the change in cooling unit performance due to the change in the primary air flow rate at different outdoor air temperatures. The increase in air flow rate appears to have little effect on the resulting supply temperature as shown in Fig. 6a, because AR remains constant. The supply temperature rises slightly due to the increase in air velocity, and thus, the time period for air to pass through the heat exchangers is reduced.

Fig. 6

Effect of primary air flow rate (${\dot{V}}_{1}$) on two-stage CIEC performance factors at different values of ${T}_{1}$: a supply temperature (${T}_{5}$), b temperature differences (${\Delta T}_{c}$), c cooling capacity (${\dot{Q}}_{c}$), and d wet-bulb effectiveness (${\varepsilon }_{c,wb}$ and ${\varepsilon }_{1,wb}$)

This, of course, reflects negatively on the temperature drop through the heat exchangers as shown in Fig. 6b. However, cooling capacity increases, as shown in Fig. 6c, because the increase in air mass flow rate greatly overcomes the decrease in temperature drop in calculating cooling capacity. The cooling capacity is the only parameter that is positively affected by increasing flow rate.

Regarding the effectiveness of the cooling unit, at a given outdoor air temperature, since $\Delta {T}_{c}$ decreases as the air flow rate increases, and the wet-bulb depression (${T}_{1}-{T}_{1,wb}$) remains the same, the effectiveness decreases as shown in Fig. 6d.

From all the results obtained through the analysis, the average performance achieved by the cooling unit exceeds the performance of the first stage by an average of 42.6%. By using more efficient heat exchanger, the cooling effectiveness of the system would increase by 10–20% [7].

5 Conclusions

The objective of this work was to modify the conventional single-stage IEC to improve its performance by making it operate in two similar stages. It involves an evolution in performance values compared to the first stage of the cooler unit. The main conclusions of this study are summarized as follows:

• (1) The results revealed that the two-stage CIEC achieves its best performance in terms of low supply air temperature and high cooling capacity, with maximum effectiveness when operating at AR = 1. It produces fairly acceptable supply air within limited climatic zones. It delivers cold air at 26 °C and below even at high temperature climate (40 to 48 °C), but within a narrow ambient relative humidity range (up to 23.8%).

• (2) It produces the same level of supply air temperature in humid climate up to 58%, but within a limited climatic temperature (below 40 °C).

• (3) In other locations outside the above limits, the cooling unit can supply cold air at temperatures above 26 °C with the potential to remove significant thermal loads. It is there for useful for various applications such as poultry houses and for pre-cooling purposes when the two-stage CIEC unit is combined with conventional air conditioning systems.

• (4) When the ambient air humidity exceeds 80%, the system becomes unsuitable for producing significant cooling, but only by a few degrees as the humidity of the supplied air increases. Therefore, further development is needed to overcome this drawback by using a more efficient heat exchanger and/or configuring it with another suitable air conditioning devices.

• (5) A 2 °C drop in primary air temperature to 23 °C can be achieved depending on operating parameters.

• (6) The analytical approach to the results and the format of their presentation were able to provide comprehensive details including the relative humidity of the supplied air. It also clarified the ranges of different cooling application areas corresponding to different climatic conditions.

• (7) The performance of two-stage CIEC has been improved in comparison to its first stage. It is capable to produce higher cooling capacity, lower supply air temperature, and higher wet-bulb effectiveness.

• (8) It has the potential to supply cold air with a temperature close to ${T}_{1,wb}$, which the single-stage CIEC cannot reach under all operating conditions.

• (9) The performance of the cooling unit exceeds that of the first stage by an average of 42.6%.

• (10) The first stage heat exchanger has contributed higher cooling capacity in comparison to the second stage capacity.

• (11) The rise in primary air temperature has negatively affected the supply air temperature but has a positive effect in increasing the wet-bulb effectiveness and cooling capacity.

• (12) The performance parameter of the evaporative cooler suffers significantly from the increase in external relative humidity; it raises the supply air temperature and lowers all other performance parameters.

• (13) The increase in air flow rate appears to have little effect on increasing the resulting supply temperature. However, cooling capacity is significantly increased with the effectiveness decreases.

• (14) To achieve operation over a wide range of operating conditions and obtain better thermal performance, it is recommended to:

  • Using a more efficient heat exchanger to produce comfortable conditions over a wider range of operating conditions.

  • Configuring the CIEC to operate with more than two identical stages in series.

  • Consider integrating CIEC with a dehumidification system.

Appendix

1.1 The relationship between heat exchanger effectiveness and air flow rate

The heat exchanger used in this study is a commercial fixed plate heat exchanger, operating in a cross-flow arrangement. It is used for roof type heat recovery ventilator “BGK 100” and is made of aluminum sheet (56 layers, thickness 0.6 mm). Technical features of the heat exchanger are:

• Dimensions, 370 × 370 × 320

• Transfer area, A = 7.623 m²,

• Surface area to total volume ratio, β = (A/V_p) = 385.28 m²/m³,

• Flow area to frontal area ratio, σ = (A_o/A_fr) = 0.446 m²/m²,

• Surface area to void volume ratio, α = (A/V) = 171.76 m²/m³

The specific expression for the heat exchanger effectiveness (${\varepsilon }_{\text{HX}}$) as a function of air flow rate was represented by [14] and used by [15] and is as follows:

$$\varepsilon_\text{HX}=1.0702\;\dot{\mathrm V}^{-0.083}$$

(26)

Salman [15] obtained this formula experimentally as part of his work in preparing his master’s thesis. The heat exchanger was tested experimentally for use as a heat recovery ventilator in building. A ductwork facility capable of reproducing typical outdoor and indoor conditions with regard to temperature and relative humidity was created and connected to the heat exchanger to build an experimental platform. The work was carried out over wide ranges of outdoor air temperatures and relative humidity. The resulting data was visualized to plot the relationship between heat exchanger effectiveness and air flow rate to obtain a mathematical formula that represents the average results of this relationship, as shown in Fig. 7 [15].

Fig. 7

Relationship between heat exchanger effectiveness and air flow rate [15]