A Parametric Study of an Indirect Evaporative Cooler Using a Spray Dryer Model

Abstract

Indirect evaporative coolers (IECs) are becoming a viable alternative to the more energy-intensive traditional HVAC systems for space cooling, especially in arid regions. In this work, a recently developed computational model of an IEC was used to conduct a parametric study. The model employs a spray dryer model to track the flow path and evaporation rate of droplets. The key parameters investigated were the temperature of the droplets, a bypass effect where the amount of exhaust air and water was reduced to as low as 10%, and the length of the heat exchanger. The results suggest that the wet bulb efficiency could be increased from the previously observed 35% to 72.5% if the water temperature is decreased to 16 °C. In order to drastically increase the performance, the heat exchanger length should be increased from 50 cm to 100 cm, which could still end up in a more compact design overall as fewer plates are required. The bypass study resulted in peak performance when 40% of the secondary air flow was used as working air in conjunction with a proportional reduction in water usage. Overall, the computational model has been employed in an attempt to reduce the bulkiness, increase the efficiency and reduce the water consumption of such a system.

1. Introduction

Indirect evaporative cooling has been identified as a potential key technology for reducing the energy consumption required for cooling buildings [1,2,3]. The operational principle is that fresh air from the outside is cooled down in a counter-flow heat exchanger by a stream of used air from the inside into which liquid water is sprayed. A schematic of the operating principle of such an apparatus is shown in Figure 1.

The comfort level of the inside air is a maximum relative humidity of 60% and a maximum temperature of 26 °C, so that the air droplets will in part evaporate and cool down the air stream leaving the building. This cooler air will then be used to cool down the air that is entering the building. The latter is usually termed primary or supply air, while the air stream leaving the building is called the secondary or working air.

The operating conditions shown in Figure 1 represent a worst case scenario where the working (secondary) air stream is at the limiting comfort level. The temperatures and relative humidities listed lead to a desired wet bulb efficiency ${\eta }_{wb}$ of

$${\eta }_{wb}={\displaystyle \frac{T_{db,in}-T_{db,out}}{T_{db,in}-T_{wb,in}}}={\displaystyle \frac{26-21}{26-20.28}}=87.4\%$$

(1)

where all temperatures refer to the primary, supply air stream and the subscript $db$ refers to dry bulb temperature, while $wb$ refers to the wet bulb temperature, respectively.

In the original hardware described in reference [4], the primary air stream will not be further processed and enter the air conditioned space as is. The corresponding process is shown in a psychrometric diagram in Figure 2.

A modification of this general IEC technology is the M-cycle, where a fraction of the supply air is redirected and used as working air. This cycle is also called dew-point evaporative cooler. An overview of his technology was given by Taler et al. [5].

Recently, a computational model of an IEC has been created [4]. It is based on the formerly commercial software package CFX-4.4 (Ansys Inc., Canonsburg, PA, USA), and by using the built-in spray dryer model. It employs a so-called Lagrangian model to track the water droplets added to the secondary air stream. In addition, a porous media model to simulate the corrugated heat exchanger plates was included [4]. The mathematical details of the model will be described in Section 2.

In that previous study, the effect of the mass flow rate of liquid water and the droplet size was evaluated, and it was found that a notable effect on efficiency occurred only when the average droplet size was 25 microns or smaller. However, for the maximum droplet flow rate and the lowest droplet size of 25 microns, the predicted efficiency was still a mere 38%. In all the cases, the temperature of the water droplets was equal to the temperature of the secondary air at the inlet, 26 °C. This was done in order to isolate the evaporation from other effects such as heating of the droplets when the water temperature is below the working air temperature. In that model, a distinction was made between droplet evaporation and wall evaporation, and it was assumed that the heat exchanger walls on the wet side were completely covered with a thin water film.

Historically, there have been numerous modeling efforts to simulate heat and mass transfer in an IEC. Zhao et al. [6] conducted a numerical analysis of a counter-flow regenerative IEC by subdividing the heat exchanger geometry into control volumes and applying analytical heat and mass transfer equations. In 2010, Chen et al. [7,8] developed a different method by extending the transport theory that emerged out of the analogy between heat and mass transfer to account for the transport of moisture. Later on, Lee et al. [9] investigated the performance of different flow arrangements in the regenerative design with and without corrugated cells. This group employed the number of transfer units ($ϵ$-NTU) method to calculate the performances of a flat plate, a corrugated plate and a finned type heat exchanger. They concluded that the finned type heat exchanger enabled the most compact design.

In their paper from 2010, Riangvilaikul and Kumar [10] showed the differences between a direct evaporative cooler, an indirect evaporative cooler, and a dew-point evaporative cooler where a fraction of the supply air is diverted and serves as working air stream. They used their model to study the bypass effect, i.e., the effect of the ratio between working air and supply air, and they compared their modeling data with experiments conducted on a heat exchanger of 120 cm length and achieved very good agreement.

In 2013, Woods and Kozubal [11] conducted both modeling and experimental studies on a liquid desiccant air conditioner comprising two stages: a liquid desiccant dehumidifier and an indirect evaporative cooler. They developed fluid-thermal numerical models for each stage and validated them with experimental prototypes, achieving a high degree of agreement with experimental results.

In the following year, Anisimov et al. [12] created a comprehensive network model to analyze heat and mass transfer in a dew-point evaporative cooler. This model was later expanded by Pandelidis et al. [13,14] to explore various design options.

Also in 2014, Cui et al. [15] were the first group to utilize computational fluid dynamics (CFD) methods, employing commercial software ANSYS Fluent 14.0 and the Euler–Lagrangian model for particle tracking. However, their study did not provide detailed information on droplet sizes and quantities, and the problem was simplified to a one-dimensional model. Despite these limitations, the model was validated against experimental data, showing good agreement.

Consequently, Xu et al. [16] employed CFD to determine optimal flow velocities in a dew-point evaporative cooler in 2016. Their findings indicated a 30% performance improvement with an irregular design compared to a flat plate design. They also found that the optimal ratio between working air and product air was 0.3. Later, Xu et al. [17] reported experimental results of a super-performance dew-point air cooler achieving a wet bulb effectiveness of 114% under specific operating conditions.

In 2017, Wan et al. [18] published a two-dimensional CFD model to simulate coupled heat and mass transfer processes in an evaporative cooler. They then applied a one-dimensional model to analyze average Nusselt and Sherwood numbers on both the fluid stream and cooling air sides. In a subsequent study, Wan et al. [19] introduced a novel method to determine heat transfer coefficients in an NTU–Le–R model and developed a two-dimensional CFD model to simulate the evaporative cooling process and compute outlet data.

Moreover, De Antonellis et al. [20] proposed a phenomenological model for indirect evaporative coolers in data centers, where indoor air temperatures can significantly exceed outdoor temperatures. Their study considered separate air streams and accounted for the wettability of the heat exchanger surface area, although heat conduction inside the heat exchanger plates was neglected. The model showed excellent agreement with experimental results. Further simulations of a cross-flow heat exchanger under different operating conditions also yielded very good agreement between the model and experiments [21]. Additionally, this group published experimental data on various heat exchanger arrangements of similar size to those considered in their work [22], with measured wet bulb efficiencies ranging from 45% to 85% depending on flow conditions.

Around the same time, Lin et al. [23,24] developed a counter-flow heat exchanger model incorporating longitudinal heat conduction, mass diffusion, and latent heat transfer between working air and water film. They also explored a cycle where outlet air is partially redirected as working air, highlighting the need for better understanding of local heat and mass transfer coefficients in IECs. In 2019, Oh et al. [25] investigated purge configurations, finding that longer channel lengths and a purge ratio around 35% resulted in lower product air temperatures and higher dew-point effectiveness.

Still in 2017, Jafarian et al. [26] used the CFD tool OpenFOAM to model undeveloped flow regions in a dew-point evaporative cooler, proposing a new boundary condition for water flux in secondary channels. Their 2D and 3D simulations showed minor differences, with all water evaporating from the wet channel wall. In 2019, Min et al. [27] developed and validated a 2D model for cross-flow IECs, considering condensation and optimizing channel geometry. Also in 2019, Liu et al. [28] developed a two-dimensional numerical model for a dew-point evaporative cooler, integrating momentum, mass, and energy equations. This model, validated against experimental data, was used to assess the impact of various operating conditions on an improved cooler design featuring a corrugated surface heat and mass exchanger. Subsequently, Liu et al. [29] investigated the performance of a high-efficiency dew-point evaporative cooler with optimized air and water flow arrangements.

Finally, in a recent study, Zhu et al. [30] developed a three-dimensional model in COMSOL Multiphysics 5.6 (https://www.comsol.com/) to simulate the airflow and moisture content transport in a regenerative dew-point evaporative cooler, also accounting for regions where the wet wall was dry. Overall, they had excellent agreement with experimental results.

The current study follows up on the previous work by Berning et al. [4], which utilized a numerical model to simulate droplet evaporation in IECs. Earlier analyses focused on the effects of water mass flow rate and droplet size, revealing that wet-bulb efficiencies approached 40% for droplet sizes around 25 microns. However, these simulations assumed droplet temperatures equal to the secondary air stream temperature, isolating the phase change effect. Here, the impact of droplet temperature on IEC performance is investigated. Next, the bypass effect where the working, exhaust air is only a fraction of the supply air is quantified. Finally, the effect of the plate length is modeled. The overall goal is to increase the efficiency in order to reduce the bulkiness and cost of IECs. Reducing water usage is another objective, which is particularly important in arid regions facing water scarcity.

2. Model Description

A detailed model description was given in reference [4]. In this study, the formerly commercial computational fluid dynamics solver CFX-4.4 (Ansys Inc.), was employed to model droplet evaporation on the exhaust side of an indirect evaporative cooler. This software offers built-in physical models for flow in porous media, multiphase flow, and multi-species flow, along with numerous customization capabilities through user subroutines, enabling manipulation of transport equations and parameters.

2.1. Computational Grid

The model employs a Eulerian grid to solve for the air flow in both sides of a counter-flow heat exchanger with specified inlet velocities to match experimental conditions. Liquid water droplets are sprayed into the secondary air stream at the inlet, and the flow paths of these droplets are tracked by a Lagrangian approach which yields information about the droplet mass and diameter, its temperature, its coordinates and the velocity components in three dimensions. In case the droplet hits the heat exchanger wall, it is taken out of consideration. Heat transfer between droplets and the background air is also taken into account. The numerical grid is shown in Figure 3.

The mesh contains 48,000 control volumes in a cartesian grid. It can be seen that the grid quality is very good in the straight channel section while there is some distortion in the edges where accuracy is less important because the majority of the phase change and heating or cooling occurs in the straight channel section. In the base case, the channel length is 250 mm. If longer channels are investigated, the current grid is merely stretched in the x-direction, leaving the number of cells unchanged so that the last solution can be used as initial guess for the new case.

The near-triangular inlet and outlet sections have a combined length of 250 mm. The height of a half-channel is 2.5 mm at both supply and exhaust side. Owing to the symmetry conditions that are applied at the side of the computational domain, the total channel depth is thus 5 mm. Finally, the metal sheet is assumed to have a thickness of 0.5 mm.

2.2. Assumptions

Same as in reference [4], the following assumptions are made:

• The problem is steady-state.
• The air behaves like an ideal gases.
• The flow is laminar.
• The water droplets in the exhaust region are entering at random positions at the exhaust inlet.
• The droplets are prevented from bouncing off the walls by invoking an appropriate command. A droplet hitting the wall is taken out of consideration.
• At the surface of the exhaust side wall (“wet wall”), water is assumed to exist in an infinitely thin layer.

2.3. Modeling Equations

The equations solved were explained in detail in reference [4], and for the sake of brevity they are only repeated in brief here.

2.3.1. Gas Phase

In the gas phase, the continuity equation is solved:

$$\nabla ·\left(\rho ϵ\mathbf{U}\right)=S_{\mathrm{m}}$$

(2)

along with the three-dimensional momentum equation:

$$\nabla ·(\rho ϵ\mathbf{U}\otimes \mathbf{U})=\mathbf{B}+\nabla \times \sigma$$

(3)

where $\sigma$ is the stress tensor:

$$\sigma =-p\delta +(\zeta -{\displaystyle \frac{2}{3}})\nabla ·ϵ\mathbf{U}\delta +\mu ϵ·(\nabla \mathbf{U}+{\left(\mathbf{U}\right)}^T)$$

(4)

and B denotes the body force:

$$\mathbf{B}={\mathbf{B}}_{\mathbf{F}}-({\mathbf{R}}_{\mathbf{C}}+{\mathbf{R}}_{\mathbf{F}}|\mathbf{v}{|}^{\alpha })\mathbf{v}$$

(5)

with the constant resistance:

$${\mathbf{R}}_{\mathbf{C}}=32\times \mu /d_h^2$$

(6)

where $d_h$ represents the hydraulic diameter of the channels, here taken to be $4.24$ mm. The porosity in the channel regions is set to $ϵ=0.75$, and this leads to an acceleration in the fluxes in the channel region compared to the inlet region. All symbols and units are listed in the Nomenclature below.

The energy equation reads:

$$\nabla ·\left(\rho ϵ\mathbf{U}H\right)-\nabla (\lambda ϵ\nabla \mathbf{T})=S_H$$

(7)

where H is the total enthalpy that depends on the static enthalpy $h(T,p)$ according to:

$$H=h+{\displaystyle \frac{1}{2}}{\mathbf{U}}^2$$

(8)

In the solid region, the energy equation simplifies to:

$$\nabla ·({\lambda }_s\nabla \mathbf{T})=0$$

(9)

The system of equations is closed by the ideal gas law:

$$\rho ={\displaystyle \frac{pW}{RT}}$$

(10)

where W is the molecular weight of air (28.84 g/mol) and R is the universal gas constant. In addition to these conservation equations, one species equation is solved for the water vapour in air:

$$\nabla ·\left(\rho \mathbf{U}{Y}_{H_{2}O}\right)-\nabla ·(\rho D_{H_{2}O-air}\nabla Y_{H_{2}O})=S_i$$

(11)

where $Y_{H_{2}O}$ indicates the mass fraction of water vapour and $D_{H_{2}O-air}$ is the binary diffusion coefficient of water vapour in air, given by [31]:

$$D_{H_{2}O-air}=1.87\times {10}^{-10}\times {\displaystyle \frac{T^{2.072}}{P}}$$

(12)

where P is the total pressure in [atm] and T is the temperature in [K].

At the wet wall, the amount of evaporative cooling is calculated by the diffusion of water vapour from the wet wall into the first numerical cell, leading to a source term in the water vapour transport equation and an according sink term in the energy equation [4]. A comparison of the different spray dryer models was given in reference [32].

2.3.2. Liquid Phase

The liquid phase is described as droplets with a given size distribution. As usual in the Euler–Lagrangian formulation, the volume of the droplets is neglected, and this approach holds if the volume fraction in general is below 10%. The size of the droplets, however, plays a role in the determination of the rate of evaporation and the drag coefficients for the interaction with the continuous phase.

As described in reference [4], the equation for the position of a particle is:

$${\displaystyle \frac{\xi }{dt}}=\mathbf{C}$$

(13)

where $\xi$ is the computational position, t is time and $\mathbf{C}$ is computational velocity. The latter is obtained from the physical velocity of the particles $\mathbf{u}$ according to:

$$\mathbf{C}={\left({\displaystyle \frac{dx}{d\xi }}\right)}^{-1}\mathbf{u}$$

(14)

The momentum equations for the dispersed phase result directly from Newton’s second law:

$$m\left({\displaystyle \frac{d\mathbf{u}}{dt}}\right)=\mathbf{F}$$

(15)

where $\mathbf{F}$ is the force on the particle and m is its mass. The major component of the force term is the drag exerted on the particle by the continuous phase:

$${\mathbf{F}}_{\mathbf{D}}={\displaystyle \frac{1}{8}}\pi d^2\rho C_D\left|v_R\right|v_R$$

(16)

where the drag factor is given by the Schiller–Naumann equation [33]:

$$C_D={\displaystyle \frac{24}{Re}}(1+0.15R{e}^{0.687})$$

(17)

and the particle Reynolds number is defined as:

$$Re={\displaystyle \frac{\rho |v_R|d}{\mu }}$$

(18)

In addition to the drag force, the buoyancy force is accounted for:

$${\mathbf{F}}_{\mathbf{B}}={\displaystyle \frac{1}{6}}\pi d^2({\rho }_P-\rho )\mathbf{g}$$

(19)

The vapor pressure is calculated via Antoine’s equation:

$$P_{vap}=\exp \left(A-{\displaystyle \frac{B}{T+C}}\right)$$

(20)

If the saturation pressure is given in [Pa] and the temperature T in [K], then the coefficients for water are A = 23.296, B = 3816.44 and C = $-46.13$, respectively.

When the particle temperature is above the boiling point, the mass transfer is determined by the convective heat transfer:

$${\displaystyle \frac{dm}{dt}}=-{\displaystyle \frac{Q_c}{r_{evap}}}$$

(21)

where $r_{evap}$ is the heat of vaporization ($2.44\times {10}^6{\displaystyle \frac{\mathrm{J}}{\mathrm{kg}}}$).

The rate of convective heat transfer is given by:

$$Q_c=\pi d\lambda Nu(T_g-T)$$

(22)

where $\lambda$ is the thermal conductivity of the fluid, $T_g$ and T are the temperature of the fluid and the particle and $Nu$ is the Nusselt number given by [34]:

$$Nu=2+0.6\times R{e}^{0.5}{\left({\displaystyle \frac{\mu c_p}{\lambda }}\right)}^{0.333}$$

(23)

where $c_p$ is the specific heat of the fluid (4186 J/kg). When the particle is below the boiling point, condensation occurs and the mass transfer is given by:

$${\displaystyle \frac{dm}{dt}}=\pi d\rho D_{H_{2}O-air}Sh\left({\displaystyle \frac{W_C}{W_G}}\right)\log \left({\displaystyle \frac{1-X}{1-X_G}}\right)$$

(24)

Here, $W_C$ and $W_G$ are the molecular weights of the vapour and the mixture in the continuous phase, while X and $X_G$ are the molar fractions in the drop and in the gas phase. Finally, the Sherwood number $Sh$ for a droplet with the diameter d is given by the analogy between heat and mass transfer:

$$Sh=2+0.6\times R{e}^{0.5}{\left({\displaystyle \frac{\mu }{\rho D_{H_{2}O-air}}}\right)}^{0.333}$$

(25)

The above equations are easily invoked in CFX-4 where a spray dryer model is pre-implemented. This model required the droplet size distribution as input parameter, and for the simulations conducted here, a Rosin–Rammler distribution was chosen. In this case, the volume fraction (VF) of particles that exceed a certain diameter d is given. The mathematical function is

$$VF(diam>d)=e^{-{(d/d_{mean})}^n}$$

(26)

CFX-4 requires the mean diameter $d_{mean}$ and the exponent n as input parameter. Figure 4 shows exemplarily a Rosin–Rammler distribution.

In CFX-4, the partial differential equations for the flow calculation are solved before the ordinary differential equations (PDEs) for the particle transport model. Hence, the particle transport model forms an extra loop in the solution procedure outside the flow calculation. After solving the particle transport equations, the source terms in the fluid flow and mass fraction equations are updated and the PDEs are solved again. It usually takes a few hundred iterations for the outside loop to converge, and the number of iterations on the particle transport equations is around 6–10. Altogether, it takes a few thousand iterations to converge. When using a prior solution as initial guess, it took around 1 h to obtain a converged solution on a laptop computer with a 2.6 GHz CPU.

2.4. Operating Conditions

In the current study, several operational and geometrical parameters were varied. The base case conditions were the same as in reference [4], and they are summarized in

Table 1. Summary of inlet boundary conditions for base case [4].

Property	Value	Unit
Supply temperature	26	°C
Exhaust temperature	26	°C
Droplet temperature	26	°C
Supply relative humidity	60	%
Exhaust relative humidity	60	%
Average droplet diameter	50	microns
Droplet flow rate	20, 40, 50	mL/s
Supply velocity	2.44	m/s
Exhaust velocity	2.44	m/s

. The supply inlet temperature of 26 °C was arbitrarily chosen and represents an average summer day in Denmark. The exhaust inlet temperature of 26 °C represents the maximum comfort level for a room temperature, and by choosing the water temperature to be 26 °C as well, all cooling had to be done in the form of evaporation.

In the parametric study presented here, the following parameters were changed individually, while all other properties were at base base:

• Step-wise reduction in the droplet temperature from 26 °C to 16 °C.
• Step-wide reduction in the exhaust inlet velocity by introducing a bypass factor from 1.0 to 0.1.
• Step-wise increase in the channel length from 25 cm to 75 cm.

The final simulation was conducted that included a combination of all best parameters.

3. Results

As was described in detail in a previous publication [4], there are two separate cooling effects accounted for at the exhaust side (secondary air stream):

• The droplet evaporation effect as described above which leads to a cooling of the air around the droplets pathways and thus to an increased relative humidity of the air.
• A wall evaporation effect that is accounted for in the first computational cell near the wall at the exhaust side.

Both these effects are competing and thus are affecting each other. In a previous study [4], it was found that only for a droplet size in the order of 25 microns and below, there is a notable increase in the cooling power, which means that the wall effect is dominant for larger droplet sizes. The supply air stream does not experience any phase change and is merely cooled down by passing over the cold wall. The overall cooling effect is divided between exhaust stream and supply stream, but it is observed that the majority of the cooling takes place in the supply stream, as is intended. In the following, the effect of the three parameters that were varied will be discussed in detail.

3.1. Effect of the Droplet Temperature

The water temperature was varied from 16 °C to 26 °C (base case). In all cases, the average droplet diameter was taken to be 50 microns. It was shown in reference [4] that under normal conditions, a droplet size of 90–100 microns could be expected, while a significant, positive effect of the droplet size started around 25 microns. The results are summarized in Figure 5. The channel length was the base case of 25 cm which is comparatively short, and this is reflected in the results.

As the air conditions were the same as in Figure 1, the anticipated temperature drop is 5.72 °C. However, even for a water flow rate of 50 mL/s and a water temperature of 16 °C, the predicted temperature drop is only in the region of 2.7 °C which corresponds to a wet bulb efficiency of 48%. The results show a linear dependency of the wet bulb efficiency and the temperature drop on the water temperature.

It was mentioned above that there is a combined cooling effect of the wall and of the droplet evaporation, and these are working in opposite directions: the higher the cooling effect due to droplet evaporation, the smaller is the cooling effect of the wall. The combined cooling effect is then divided between the working, secondary air stream and the supply, primary air stream, and the majority of cooling should ideally be found in the supply air. Figure 6 shows a comparison between the droplet cooling effect and the wall cooling power. Overall, the wall cooling is only weakly affected by the droplet flow rate and temperature, while the cooling power due to droplet evaporation depends strongly on the water flow rate. The wall cooling is lowest for the highest water flow rate and highest for the lowest water flow rate, as could be expected. Even at an average droplet diameter of 50 microns as was investigated here, there is a strong effect of the water flow rate, as seen in Figure 6, left. A question, however, is, how much of this added cooling ends up in the “right” air stream, the primary air stream. This will be investigated below.

It can also be seen that the cooling power due to droplet evaporation decreases with decreasing droplet temperature. This is owing to an effect that has not been discussed so far: the heating up of the droplets to the surrounding air temperature before evaporation can occur. In the model, convective heat transfer is captured by Equation (23). This provided a third cooling effect that is smaller than wall cooling and droplet evaporation, but becomes important when the droplets are entering at a lower temperature, as seen in Figure 7 which shows a comparison between the added effect of droplet evaporation and wall cooling compared to the amount of cooling that ends up in both air streams. The difference between these total enthalpy differences is the sensible heat of the droplets plus numerical inaccuracies. When the droplets enter the domain sub-cooled, they generally provide an added cooling effect, as is indicated by the blue arrows.

On the other hand, when the droplets enter at the same temperature as the air stream, they actually cool down from inlet to outlet, releasing sensible heat which works in opposite directions of the cooling effect due to wall and droplet evaporation. Thus, in case the droplets enter the domain at the same temperature as the air stream, the combined effect of wall and droplet evaporation exceeds the combined cooling down of the air streams, shown by the red arrows in Figure 7. The lines cross at a droplet inlet temperature around 23 °C, and in this case there is no effect due to the sensible heat of the droplets. In all simulations where the droplet temperature is the same as the air inlet temperature, the droplets are cooling down and release sensible heat which counteracts the combined cooling effect of the evaporation of the wet wall and of the droplets.

Finally, the question is, how much of the cooling effect actually ends in the exhaust stream versus the supply stream. Obviously it is the supply stream that should ideally experience the larger amount of cooling. Figure 8 shows a comparison between the cooling of the exhaust stream versus the supply stream.

While an increase in the water flow rate from 20 m/s to 50 mL/s leads to a strong increase in the cooling of the exhaust stream, the effect on the supply stream is weaker. Overall, the predicted cooling power is in the order of 2.2 W–2.7 W per half-channel that is simulated here, hence twice these values for a full channel. This, however, depends on the operating conditions. Because the cooling of the supply stream is proportional to its temperature drop and the system efficiency, the lines in Figure 8 correspond to the lines shown in Figure 5.

3.2. Bypass Effect

Next, the bypass effect was investigated. A bypass means that only a fraction of the exhaust air is used as working air, and the other part is directly expelled to the environment without being passed through the heat exchanger. Clearly, the overall amount of air that enters the space to be cooled must be equal to the amount of air leaving. The bypass concept was already investigated by Xu et al. [16]. In our case, the mass flow of the exhaust air was step wise reduced. In order to obtain comparable results, the amount of water sprayed into the exhaust air was also reduced, which means that the amount of water listed is the equivalent rate compared to the base case with no bypass. Therefore, the case of 50 mL/s water injected at a bypass ratio of 0.4 is the same amount of water as 20 mL/s with no bypass, and the case of 20 mL/s at a bypass ratio of 0.4 would correspond to the same water rate as 8 mL/s with no bypass. A bypass ratio of 0.4 means that only 40% of the exhaust air compared to the case with no bypass is streaming through the exhaust side of the heat exchanger. The results are summarized in Figure 9.

It is interesting to note that the efficiency actually increases until a bypass ratio of 0.4 compared, then the performance gradually starts to decline, and below a bypass ratio of 0.3 there is a steep decline because the thermal mass at the exhaust side becomes too low. This agrees well with the results from Xu et al. [16], who found that the optimum value for the ratio between working (exhaust) air and product (supply) air is 0.3 under different operating conditions. Another comparison can be made with the modeling work by Jafarian et al. [26], and they also found that the efficiency increases when the velocity of the exhaust air decreases.

3.3. Effect of the Channel Length

Adiabatic coolers are generally very bulky and it is highly desirable to increase the efficiency so that the number of plates and thus the overall volume can be reduced. On the other hand, it was mentioned by Duan et al. [2] that a reason for the limited efficiency of these devices is a lack of heat transfer area. A longer heat exchanger may thus lead to a higher efficiency and a lower amount of plates. In our base case, the channel length was only 25 cm, and the calculated efficiency was accordingly low, in the range of 30–40% [4] which agrees well with values summarized by Riangvilaikul and Kumar [10]. Therefore, the effect of an increased channel length was investigated, and the channels were step-wise stretched to 35 cm, 45 cm, 55, cm, 65 cm, and up to 75 cm. Together with the length of the inlet and outlet sections, the overall length in the last case is thus 1 m. The results are summarized in Figure 10.

As could be expected, there is a clear increase in the cooling performance with a predicted efficiency of nearly 60% or a temperature drop of 3.4 °C of the supply air for the longest channel length and the higher water flow rates. In a prior study, Jafarian et al. [26] compared their three-dimensional model to experiments, and the system they investigated had a channel length of 120 cm. Depending on the mass flow rates, the predicted efficiency was as high as 80%, and it was in very good agreement with experimental data.

In the context of the study on the channel lengths, the pressure drops shall be discussed as well, because clearly the longer channels lead to a higher predicted pressure drop. It was noted for all the cases investigated that the pressure drop on the primary, supply air stream was always fairly low, below 100 Pa, while on the secondary, working air stream it was typically more than one order of magnitude larger, caused by the drag and the evaporation effects. In the case of the 75 cm long channel, the maximum predicted pressure drop was 5.3 kPa on the exhaust side without a bypass and with the maximum water flow of 50 mL/s. This compares to a pressure drop of 1.8 kPa for a channel length of 25 cm with 50 mL/s water flow, which is reduced to 1.79 kPa when the water flow rate is 20 mL/s. Therefore, the water flow rate has only a small impact on the predicted pressure drop. Overall, however, the importance of the bypass is stressed again because the pressure drop is clearly reduced by using a bypass.

3.4. Combination of Best Parameters

Finally, one case where the best parameters are combined shall be investigated in detail. Thus, the longest channel length is taken together with a droplet inlet temperature of 16 °C and a bypass ratio of 0.4. The mean droplet size was 50 microns and the flow rate was equivalent to 50 mL/s at base case, hence 20 mL/s. The detailed results of the CFD analysis are shown below.

Figure 11 shows the temperature and relative humidity distribution at mid-channel of the exhaust stream. The temperature is given in Kelvin, and it drops substantially in the first half of the plate, i.e., the exhaust air is coldest in the middle of the plate. This must be attributed to the bypass effect because in prior simulations in reference [4], the temperature at mid-channel of the exhaust side dropped from inlet to outlet. The relative humidity of the flow at the exhaust side increases immediately upon entering the heat exchanger and is around 80–90% throughout most of the domain.

Figure 12 shows the temperature and relative humidity distribution at mid-channel of the supply stream. Similar to previous results, the temperature drops steadily from inlet to outlet [4], in the current case by almost 5 °C. The relative humidity of the supply stream increases, but the flow remains below the dew point such that no condensation is expected.

Figure 13 and Figure 14 show the results near the wet wall.

The temperature here is close to the minimum temperature found in the entire domain, and it is lowest near the supply outlet, which is very beneficial for the performance. The relative humidity is above 95%. In Figure 14, owing to the conventions in CFX-4, the values for the amount of water evaporating and the associated energy sink term are per unit volume.

The calculated efficiency in this case was 72.5% which corresponds to a temperature drop of 4.15 °C. The pressure drop on the working air side was 2.1 kPa, hence substantially lower than without the bypass. A last calculation where the average droplet size was reduced to 25 microns resulted in an efficiency of 77.5%.

4. Discussion

In this work, the role of three different parameters on the performance of an indirect evaporative cooler has been investigated. Under otherwise base case conditions, reducing the droplet temperature from 26 °C to 16 °C resulted in an efficiency increase in the added cooling effect due to the sensible heat absorbed by the droplets. At the lowest temperature investigated, 16 °C, the efficiency increases to 47.6% compared to 39.5% when the flow rate was 50 mL/s.

The bypass effect showed an increase in dry bulb efficiency when the flow ratio was 40% of the supply stream. A further reduction in the exhaust air stream yielded a decrease in performance due to the small thermal mass. The maximum dry bulb efficiency was 40.76% when the flow rate was equivalent to 50 mL/s with no bypass, i.e., 20 mL/s. The droplet temperature here was at base case, 26 °C. This shows that applying a bypass can save water in regions where water consumption is a problem.

Increasing the channel length leads to a drastic, if nonlinear, increase in efficiency. For the longest channel length of 75 cm which means that the overall heat exchanger length is 100 cm, the efficiency for base case conditions increased to 60.26%. Overall, it must be carefully considered whether the number of plates in the heat exchanger should be reduced and the length of the plates should be increased in order to make the system less bulky and heavy. It is also noted that when the number of plates is reduced, the overall water consumption will be reduced as well.

A combination of the best parameters, i.e., the lowest droplet temperature combined with a bypass ratio of 0.4 and the longest channel length of 75 cm yielded an efficiency of 72.5% for an average droplet size of 50 microns. This efficiency further increased to 77.5% when the droplet size was reduced to 25 microns. These values are well in line with general numbers cited by Riangvilaikul and Kumar [10].

Clearly, experiments are in order to validate the model. In a prior project, the measurement data produced was in part contradicting. It was also found that the amount of water used greatly exceeded the required amount which was not a problem because it was recirculated. In practice, however, this meant that the device was a liquid to gas heat exchanger rather than an evaporative cooler, and for the model it means that the underlying assumption of having negligible liquid phase volume fraction was violated. Therefore, the modeling results presented here have successfully been compared to available data from the literature. In the future, the physical evaporative cooler described in reference [4] could be modified or the water amount used adjusted to provide data for model validation.

5. Conclusions

Employing a formerly developed computational fluid dynamics model, a parametric study of an internal evaporative cooler has been carried out. The goal was to shed fundamental understanding of the effect of the droplet temperature, the bypass effect where the amount of exhaust air was only a fraction of the incoming air, and the channel length. The results show that subcooling the incoming water has a strong effect on the predicted performance, especially when the amount of water entering is high. The reason is the added cooling effect due to sensible heating of the droplets. Investigation of a bypass effect showed a clear maximum in performance when the exhaust air stream was only 40% of the incoming air stream. As the amount of water has been proportionally reduced, this would be an opportunity to save water in arid regions. Finally, an increase in overall heat exchanger length from 50 cm (including inlet and outlet section) to 100 cm yielded a clear increase in the predicted performance, as could be expected. Thus, fewer, longer heat exchanger plates can be used to handle the same air stream which will likely reduce the overall volume and will certainly reduce water consumption. Overall, it was shown that there are possibilities to further improve and optimize the design of such IECs, and the usefulness of the methods of CFD and the spray dryer model in designing such devices. However, such modeling work alone without experimental validation is of limited value, and therefore, future work will focus on validating these findings.