Performance Analysis of the Multi-Stage Dew-Point Indirect Evaporative Air Cooler

Abstract

In this study, a multi-stage regenerative-cross-flow dew-point evaporative cooler performance is analyzed and compared to the performance of a regenerative dew-point evaporative cooler. The most beneficial configuration of the proposed exchanger was established on the basis of its geometry and performance analysis using validated numerical models. For specific outlet air parameters, it was found that the multi-stage cooler with a working-to-primary air-flow ratio equal to 0.3 reaches 5.6% lower outlet air temperatures and 10.2% higher cooling capacity when compared to the regenerative unit. The proposed cooler provides lower outlet air temperatures for all average outdoor air parameters in selected locations, for both dry and humid outdoor air parameters (e.g., Denver (USA) and Izmir (Turkey)).

1. Introduction

During the last fifty years, climate changes have occurred, including an increase in average outside air temperatures. Climate change is having an impact on the energy sector as the cooling season is lengthening and the heating season is shortening. This is confirmed by scientists worldwide who are studying climate change and its effects. For example, trends have been observed both in Europe (Mediterranean [1], Poland [2], and Europe [3]), and in countries of South and North America (Brazil [4], Canada [5], and USA [6]). As a result, the energy consumption of air-conditioning systems (AC) has been increasing for years and will be increasing until 2050, as predicted by the scenarios and analyses conducted by the International Energy Agency described in the Future of Cooling report [7]. The use of more efficient air-conditioning technologies can significantly reduce the energy consumption associated with the rise in temperature, and the development of alternative air-conditioning systems based on renewable energy is crucial. One widely studied device is based on indirect evaporative dew-point cooling. There are reviews of the literature and summaries of achievements in this field of science. General conclusions are presented in

Table 1. Conclusions for future research based on recent literature reviews in the field of indirect evaporative cooling.

Reference	Main Findings
[8]	There is a need to evaluate the cooling capacity of hybrid systems based on indirect evaporative cooling devices implemented in different cooling applications.
[9]	Single-stage indirect evaporative coolers (IEC) and multi-stage IEC have a potential to substitute for mechanical AC systems in hot, dry regions.
[10]	Novel dew-point evaporative cooling (DPIEC) unit structures should be considered for intensifying heat-transfer area between the dry and wet channels.
[11]	There is need to develop a cooler structure and channel geometry in terms of effective water distribution and air distribution. There is potential for improving water distribution in indirect evaporative coolers regarding materials development. Adaptation of DPIEC in sorption air conditioning systems is crucial in alternative air-conditioning system development.
[12]	New structures of the exchangers are expected to be developed to simultaneously increase heat-transfer surface and decrease the exchanger geometric size. New porous materials should be further investigated to enhance water evaporation and improve water distribution strategies.

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Boudia et al. [13] compared two dew-point coolers with the regenerative and the combined configurations. It was found that performance of the second cooler configuration showed 5% higher cooling capacity and higher water consumption. Kashyap et al. [14] analyzed different types of flow and water schemes in indirect evaporative cooling devices by comparing their key performance indicators obtained numerically. They found the influence of geometrical and operational parameters on cooling capacity, effectiveness, and COP, and crossing temperature depends on the configuration of parallel/counter and cross-flow. Wan et al. [15] studied the dew-point evaporative cooler with counter-flow closed-loop configuration with two different water flows to supply air-flow directions. In the case of each configuration, a two-dimensional computational fluid dynamics model was developed to compare the performance of a typical indirect evaporative cooler with standard flow distribution to that of two proposed coolers with new flow distribution. They found that water flow to supply the air-flow direction influences the cooler performance, and the first configuration achieved the highest latent and wet-bulb efficiencies and enlargement coefficient.

It is a fact that multi-stage and combined indirect evaporative cooling units are considered by researchers as promising devices for the purpose of air-conditioning systems. Basic variants of such units are cross-flow dew-point evaporative coolers [16]. This study is dedicated to analyzing the structure of a multi-stage evaporative cooling unit based on the combination of cross-flow and regenerative counter-flow, and compares its performance to the typical regenerative dew-point evaporative cooler performance (Figure 1a,b).

This paper presents an analysis of the efficiency of a combined evaporative exchanger (Figure 1a), which is characterized by cross-regenerative flow in wet channels. The efficiency of the proposed variant is compared with the efficiency of the regenerative indirect evaporative cooler. Because of this objective, numerical simulations are performed for the air-flow parameters equal to t_1i = 30 °C and RH_1i = 45%. Selected air parameters correspond to the average temperature and relative humidity found in a temperate climate during the summer season. The ratio of working air flow to primary air flow in the cross-flow part varied between 0.3 and 1.0 and in regenerative part from 0.1 to 0.5.

2. Materials and Methods

Numerical simulations are performed with mathematical models based on the convective heat transfer coefficient. The general assumptions regarding this modeling method are presented in [18]. Generally, the heat exchange with the surroundings is negligible, the operation is steady-state, air flow is an incompressible gas, the water used for evaporation keeps the plate surface in a saturated state, the mass-flow force follows from the humidity ratio gradient, kinetic properties of air stream and water are constant and assumed equal, and the bulk average value of air-flow heat capacity is much larger than that of water. Model validation is presented in Appendix A.

The unit studied can be divided into two main heat and mass transfer zones: the cross-flow zone and the counter-flow zone. In these two areas, the process of heat transfer needs to be described with different sets of equations: ordinary and partial.

The sensible heat balance for the primary air flow for the regenerative and cross-flow parts [18] are described as:

$${\dot{G}}_1·c_{p1}·\frac{\partial t_1}{\partial X}dX=-d{Q}_1^s,$$

(1)

where:

• ${\dot{G}}_1$ —partial air mass flow rate: ${\dot{G}}_1=\left(\frac{dY}{L_Y}\right)·G_1$, kg/s
• $c_p$—specific heat capacity of moist air, J/(kg K)
• $t$—temperature, °C
• $d{Q}_1^s$—sensible heat transfer rate, W
• $L_Y$—channel length in Y direction, m
• X—coordinate along the supply air-flow direction, m

Regarding the regenerative part [18]:

• The sensible heat balance for the working air flow:

  $$-{\dot{G}}_2·c_{p2}·\frac{\partial t_2}{\partial X}dX=-d{Q}_2^s+c_{g2}·\left({t^{\prime }}_{p2}-t_2\right)·d{M}_2,$$

  (2)
• The sensible mass balance for the working air flow:

  $$-{\dot{G}}_2·\frac{\partial x_2}{\partial X}dX=d{M}_2,$$

  (3)
• The total heat balance:

  $$d{Q}_1^s-d{Q}_2^l-d{Q}_2^s=0,$$

  (4)

  where:
  • ${\dot{G}}_2$—partial moist air mass flow rate: ${\dot{G}}_2=\left(\frac{dY}{L_Y}\right)·G_2$, kg/s
  • $dM$—mass transfer rate of water vapor, kg/s
  • ${t^{\prime }}_{p2}$—plate temperature, °C
  • $d{Q}_2^l$—latent heat transfer rate, W

Regarding the cross-flow zone [18]:

• The sensible heat balance for the working air flow:

  $${\dot{G}}_3·c_{p3}·\frac{\partial t_3}{\partial Y}dY=-d{Q}_3^s+c_{g3}·\left({t^{\prime }}_{p3}-t_3\right)·d{M}_3,$$

  (5)

  where:
  • ${\dot{G}}_3$—partial moist air mass flow rate: ${\dot{G}}_3=\left(\frac{dX}{L_X}\right)·G_3$, kg/s
  • $L_X$—channel length in X direction, m
  • Y—coordinate along the working air-flow direction, m
• The mass balance for the working air flow:

  $${\dot{G}}_3·\frac{\partial x_3}{\partial Y}dY=d{M}_3,$$

  (6)
• The total heat balance:

  $$d{Q}_1^s+d{Q}_3^l+d{Q}_3^s=0,$$

  (7)

The boundary conditions are presented below on the base of Figure 2. Air-flow parameters at the entrance to the dry channels in the regenerative part:

$$\begin{array}{c}{t}_1\\ \\ \end{array}|\begin{array}{c}=t_{1i}\\ \overline{X}=0.0\\ \overline{Y}=\left(0.0\dots 1.0\right)\end{array}& & \begin{array}{c}{x}_1\\ \\ \end{array}|\begin{array}{c}=x_{1i}\\ \overline{X}=0.0\\ \overline{Y}=\left(0.0\dots 1.0\right)\end{array}$$

Air-flow parameters at the entrance to the working channels in the regenerative part:

$$\begin{array}{c}{t}_2\\ \\ \end{array}|\begin{array}{c}=t_{2i}=t_{1o}\\ \overline{X}=1.0\\ \overline{Y}=\left(0.0\dots 1.0\right)\end{array}\begin{array}{c}{x}_2\\ \\ \end{array}|\begin{array}{c}=x_{2i}=x_{1o}=x_{1i}\\ \overline{X}=1.0\\ \overline{Y}=\left(0.0\dots 1.0\right)\end{array}$$

Air-flow parameters at the entrance to the working channels in the cross-flow part:

$$\begin{array}{c}{t}_3\\ \\ \end{array}|\begin{array}{c}=t_{3i}\\ \overline{X}=\left(0.0\dots X_{cross}\right)\\ \overline{Y}=0.0\end{array}\begin{array}{c}{x}_2\\ \\ \end{array}|\begin{array}{c}=x_{3i}\\ \overline{X}=\left(0.0\dots X_{cross}\right)\\ \overline{Y}=0.0\end{array}$$

The model also includes an empirical equation that describes the water vapor saturation pressure as a function of temperature [19]. Numerical models of typical regenerative air coolers (DPIEC 3) are identical to the model of the regenerative zone of the combined cross-regenerative cooler. The equations presented above were solved using the developed algorithm that was implemented in a digital computer program. The accuracy of the numerical method was checked by computing the identical variants on various space-domain grids. The number of grid nodes found with the minimum time of computation was reached at a step size of 0.01 in the X and Y directions [19]. The tolerance of accuracy was 0.5% thermal and mass balance error. Numerical simulations were performed for the cross-regenerative exchanger. The characteristic dimensions of the analyzed device are presented in

Table 2. Analyzed dew-point evaporative cooler operating parameters.

Parameter	DPIEC 1 and DPIEC 2 Multi-Stage Dew-Point Evaporative Cooler	DPIEC 3 Regenerative Dew-Point Evaporative Cooler
Cooler length	1.0 m	1.0 m
Cooler width	1.0 m	1.0 m
Cooler channel height	3.0 mm	3.0 mm
Inlet velocity	3.0 m/s	3.0 m/s
NTU1	6.38	6.38

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3. Results and Discussion

Until now, the analysis of indirect evaporative dew-point exchangers allowed for a good understanding of their operation characteristics for various operational parameters. Generally regenerative counter-flow evaporative heat exchangers achieve higher dew-point efficiencies, while cross-flow heat exchangers based on the Maistotsenko-cycle achieve higher cooling capacities [20].

To calculate the cooling capacity of the unit, the inlet air flow was assumed to be $\dot{m}=1.0$ kg/s. In Figure 3a,c,e, the influence of the ratio of the working to the primary air flow in each section is presented. The counter-flow and cross-flow parts are marked as 2 and 3, respectively. The influence of the relative length of the cross-part on the outlet air temperature is presented. Based on the temperatures obtained, the cooling capacity of the device was calculated for various configurations, which are shown in Figure 3b,d,f. It can be noticed that in the case of W₂/W₁ = 0.1, the cross-section of the proposed exchanger allows for lowering the air temperature after the exchanger. It follows from the fact that until the cross-flow section achieves 0.7, the outlet temperature decreases. The minimum air temperature at the exit of the exchanger occurs when the cross-flow section length is equal to 0.7. In general, lower temperatures are observed for a higher working-to-product air-flow ratio in the cross-flow section (W₃/W₁). Nevertheless, for W₃/W₁ equal to 0.5, 0.7, and 1.0, the temperature values fluctuate by 0.5 °C. By increasing the W₂/W₁ ratio from 0.1 to 0.3 and 0.5, there is a possibility to achieve lower outlet air temperatures. For different lengths of the cross-section and W₂/W₁ = 0.1 and W₂/W₁ = 0.3, the outlet air temperatures are in the range 20.6–24.8 and 18.8–20.3 °C, respectively. According to Figure 3, for working-to-product air-flow ratio W₂/W₁ = 0.5, the exchanger achieves the lowest values of the outlet temperatures in the range 17.9 °C–21.3 °C.

By analyzing the different relative lengths of the cross-section for the three ratios, W₂/W₁ = 0.1, W₂/W₁ = 0.3, and W₂/W₁ = 0.5, the minimum outlet temperatures are obtained for different lengths of the cross-section. For example, for parameters W₂/W₁ = 0.1 and W₃/W₁ = 1.0, the air temperature behind the exchanger is the lowest for X_cross = 0.7; for W₂/W₁ = 0.3 and W₃/W₁ = 1.0, the air temperature behind the exchanger is the lowest for X_cross = 0.4; and for W₃/W₁ = 0.5 and W₃/W₁ = 1.0, the air temperature after the exchanger is the lowest for X_cross = 0.1. It follows that the higher the value of the air flow that is reversed to the working channel, the smaller part of the exchanger can be devoted to the cross-section.

It can be seen in Figure 3b that the proposed exchanger achieves a maximum cooling power ranging from 5.6 to 8.6 kW for the ratio W₂/W₁ = 0.1, even though the air is cooled less effectively in this case. Because of the limitation of the mainstream (W₂/W₁ = 0.5), the cooling power varies from about 5.2 kW to about 6.1 kW when changing the relative length of cross-flow section (see Figure 3f). It comes from the fact that the value of the cooled air flow mainly affects the level of cooling power achieved by the proposed exchanger.

Based on the analysis presented above, two different exchanger configurations were selected to compare their operation with the operation of the regenerative dew-point exchanger. The first configuration of the exchanger (DPIEC1) selected is characterized by parameters W₂/W₁ = 0.1, W₃/W₁ = 0.5, and X_cross = 0.7. This is the case for which the device achieves a relatively high cooling capacity of 8.3 kW. The second variant (DPIEC2) of the exchanger has a cross-section length of X_cross = 0.4, and the ratio of the auxiliary inlet air in each section is W₂/W₁ = 0.3 and W₃/W₁ = 0.5. In this case, the regenerative part has a length equal to 0.6. This is the case for which the average level of cooling efficiency and the average level of cooling power are obtained and compared to the other analyzed variable flow and geometric parameters of the exchanger. The usefulness of the application of variants I and II is verified by comparing it with the most common variant of the evaporative indirect exchanger, for which the characteristic parameters are summarized in Table 2. A previously optimized G ratio equal to 0.3 was chosen for the regenerative exchanger [21].

On the basis of the considerations presented above, the following operating conditions were established:

• The relative length of the cross-flow part X_cross is equal to 0.7 and 0.3 for DPIEC 1 and DPIEC 2, respectively;
• The working-to-primary air ratio in the regenerative counter-flow part W₂/W₁ equals 0.1 and 0.5 for DPIEC 1 and DPIEC 2, respectively;
• The working-to-primary air ratio in the cross-flow part W₃/W₁ in each case equals 0.5 for DPIEC 1 and DPIEC 2.

Comparison of the Multi-Stage Unit with Typical Regenerative DPIEC

In this section, proposed multi-stage arrangements of dew-point evaporative coolers are compared with the original regenerative dew-point evaporative cooler (configuration shown in

Table 3. Characteristic parameters of the exchangers.

	Type of Exchanger	W3/W1	W2/W1	${\mathit{X}}_{\mathit{cross}}$	${\mathit{X}}_{\mathit{regenerative}}$
DPIEC 1	Combined cross-regenerative counter-flow heat and mass exchanger	0.5	0.1	0.3	0.7
DPIEC 2		0.5	0.3	0.3	0.7
DPIEC 3	Regenerative dew-point evaporative cooler	-	0.3	-	1.0

). The regenerative device (DPIEC 3) is characterized by the same NTU₁ as DPIEC 1 and 2 (shown in Table 2).

A set of numerical simulations was performed to establish the impact of outdoor air conditions on the cooling performance of the proposed units. The analysis was performed under variable inlet temperature (25, 30, and 35 °C) at constant relative humidity established at 45%. The results are presented in

Table 4. The results of exchanger comparison for outdoor air relative humidity RH = 45%.

Outdoor Air Temperature, °C	Outlet Air Temperature, °C			Cooling Capacity, kW
	DPIEC 1	DPIEC 2	DPIEC 3	DPIEC 1	DPIEC 2	DPIEC 3
25	17.2	15.3	16.2	7.1	6.8	6.2
30	20.8	19.0	19.7	8.4	7.8	7.2
35	24.0	22.8	23.4	9.9	8.6	8.2

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The outdoor air parameters t_1i = 30 °C and RH_1i = 45% are assumed to be representative for temperate European climate conditions [22]. Regarding these parameters, the temperature obtained by DPIEC 1, DPIEC 2, and DPIEC 3 is 20.8, 19.0, and 19.7 °C, respectively. Multi-stage configuration DPIEC 2 achieves the lowest temperature of outlet air for the parameters considered, while the highest cooling capacity is obtained for DPIEC 1. The lowest cooling capacity is reported for regenerative DPIEC 3 (6.2 kW). The proposed configuration of multi-stage cooler (W₃/W₁ = 0.3) obtains lower outlet air temperatures and higher cooling capacities, as shown in Table 4. The differences in outlet temperatures between coolers are the highest for the low outlet temperature (5.6% lower than regenerative cooler) and cooling capacity (10.2% higher than regenerative cooler).

The development of evaporative exchangers is directed at decreasing air outlet temperatures. The efficiency of the exchangers strongly depends on the inlet air parameters that are related to the system location. The average outdoor air parameters for the hot season were assumed for eight cities. The performance of two dew-point indirect evaporative coolers DPIEC 2 and DPIEC 3 was simulated for each set of outdoor air parameters. The simulation results are presented in

Table 5. Performance of the dew-point indirect evaporative coolers analyzed for the selected cities.

City	Inlet Air Temperature	Inlet Air Relative Humidity/(Air Humidity Ratio)	Air Dew-Point Temperature	DPIEC 2		DPIEC 3
				Outlet Air Temperature	Dew-Point Effectiveness	Outlet Air Temperature	Dew-Point Effectiveness
-	°C	%/(g/kg)	°C	°C	%	°C	%
Athens	33.8	31/(10.3)	14.4	17.9	82.0	18.8	77.3
Beijing	37.4	45/(18.5)	23.6	24.7	92.0	25.2	88.4
Denver	33.0	25/(7.9)	10.5	15.6	77.2	16.8	71.8
Helsinki	26.7	46/(10.2)	14.1	16.8	78.6	17.6	72.2
Izmir	35.5	55/(20.4)	25.1	25.9	92.3	26.2	89.0
Madrid	36.1	29/(11.0)	15.4	18.8	83.6	19.71	79.2
Prague	27.7	42/(9.9)	13.6	16.6	78.7	17.5	72.3
Warsaw	32.0	50/(15.1)	20.3	21.8	87.2	22.3	82.9

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The lowest air temperature (15.6 °C) was achieved for Denver by the proposed variant of DPIEC 2. On the other hand, for the average parameters occurring in Izmir, the outlet air temperature equaled 25.9 °C. In general, the indirect evaporative cooling potential is higher in dry climates and lower in moderate and humid climates.

For each city analyzed, the multi-stage unit (DPIEC 2) achieves lower supply air temperatures and higher dew-point effectiveness in comparison to DPIEC 3. The highest difference between effectiveness is observed for the humid (20.0 g/kg) Izmir air parameters and the lowest for the dry air (7.9 g/kg) parameters of Denver.

4. Conclusions

In this study, the structure of a multi-stage evaporative cooling unit based on a combined cross-flow and regenerative counter-flow unit was analyzed. The most beneficial configuration was established on the basis of its geometry and performance analysis using validated numerical models. Based on the analysis performed, the following operating parameters and DPIEC 1 were chosen to achieve the highest cooling capacity: the relative length of the cross-flow part X_cross equals 0.7, the working-to-primary air ratio in the regenerative and cross-flow part equals 0.1 and 0.5, respectively. To achieve a compromise between the highest possible cooling capacity and the lowest outlet air temperature, DPIEC 2 was proposed. For DPIEC 2, the relative length of the cross-flow part X_cross equals 0.4, and the working-to-primary air ratio in the regenerative and cross-flow part equals 0.3 and 0.5, respectively. To find the proposed coolers’ functionality, their performance was compared to the typical regenerative dew-point evaporative cooler performance. Despite DPIEC 1’s highest cooling capacity, it reaches higher temperatures than the regular regenerative unit, while DPIEC 2 reaches even lower outlet air temperatures and lower cooling capacity. Hence, in the final analysis for various locations, DPIEC 2 and the regenerative cooler were compared by simulating their performance. In general, the proposed multi-stage cooler configuration provides lower outlet air temperatures for all average outdoor air parameters in selected locations in comparison to the regenerative unit. For locations with higher air humidity (i.e., Izmir; see Table 5—bold values), the differences between the achieved dew-point efficiencies of the devices are higher than for locations with air parameters indicating a dry climate (Denver; see Table 5—bold values).