Two-dimensional numerical study of a heat and mass exchanger for a dew-point evaporative cooler

Accepted Manuscript Two-dimensional Numerical study of a Heat and Mass Exchanger for a Dew-point Evaporative Cooler

Yuting Liu, Jun Ming Li, Xu Yang, Xudong Zhao PII:

S0360-5442(18)32346-6

DOI:

10.1016/j.energy.2018.11.135

Reference:

EGY 14233

To appear in:

Energy

Received Date:

08 October 2018

Accepted Date:

28 November 2018

Please cite this article as: Yuting Liu, Jun Ming Li, Xu Yang, Xudong Zhao, Two-dimensional Numerical study of a Heat and Mass Exchanger for a Dew-point Evaporative Cooler, Energy (2018), doi: 10.1016/j.energy.2018.11.135

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ACCEPTED MANUSCRIPT Two-dimensional Numerical study of a Heat and Mass Exchanger for a Dew-point Evaporative Cooler Yuting Liua, Jun Ming Lia,*, Xu Yanga , Xudong Zhaob a

Key Laboratory for Thermal Science and Power Engineering of Ministry of Education,

Department of Energy and Power Engineering, Tsinghua University, Beijing 100084, China b

School of Engineering, University of Hull, HU6 7RX, UK

* Corresponding author. Tel.: +86 10 62771001; E-mail: [email protected]

ABSTRACT This paper describes a two-dimensional numerical model of heat and mass transfer in a dew-point evaporative cooler that couples the momentum and mass transfer equations with the energy equation using various heat and mass transfer models. The numerical model is validated by experiment results from other studies and is then used to study the impacts of various operating conditions including the inlet volumetric air flow rate, working-to-primary air ratio, inlet water temperature, volumetric water flow rate and the temperature and humidity of the inlet air on the cooling in an improved dew-point evaporative cooler with a corrugated surface heat and mass exchanger. Keywords: Dew-point; Evaporative cooler; Heat and mass exchanger; Numerical study

1. Introduction The energy consumed by buildings accounts for about 23% of the total energy consumption, with the energy consumption by refrigeration air conditioning and the related equipment 1

ACCEPTED MANUSCRIPT accounting for about 55% of the building energy consumption in China [1][2]. The mechanical vapour compression refrigeration systems currently used in most of the air-conditioning market are not very energy efficient or environmentally-friendly [3]. The development of environmentally-friendly and efficient refrigeration air conditioning systems continue to be of great significance. Evaporative cooling, which uses the evaporation of water to cool the air, has been used for air conditioning for many years [4]. Evaporative coolers are more energy efficient (COP in the range of 15-20) and environmentally-friendly than vapor compression systems (COP in the range of 2-4) because evaporative coolers do not need compressors which consume large amounts of electric energy and they use water as the refrigerant which does not pollute the environment [5, 6]. Two types of evaporative cooling systems are used widely at present, direct and indirect evaporative cooling systems. The product air provided by direct evaporative cooling systems simultaneously produce the temperature drop and humidity increase because the air directly contacts the water so the water vapour is added to the air through evaporation. However, the additional humidity can make the room uncomfortable which limits the popularity of direct evaporative cooling systems. For indirect evaporative cooling systems, the product air in the dry channel and working air and the water film in the wet channel are separated by a heat exchanger plate, so such systems lower the product air temperature without adding moisture to the product air. In the wet channel, the working air directly contacts the water with heat and mass transfer between the air and water on the wet channel surface. For direct and indirect evaporative cooling systems, the maximum temperature drop of the product air is the difference 2

ACCEPTED MANUSCRIPT between the dry-bulb and wet-bulb temperatures of the inlet air (40-90% of the wet-bulb effectiveness), which restricts the widespread use of evaporative cooling in the refrigeration market [6, 7, 8]. The cooling efficiency (wet-bulb efficiency) of an indirect evaporative cooling system is closely related to the heat and mass exchanger design. For a dew-point evaporative cooler, the wet and dry channels are connected through some perforations and the intake air in wet channel is taken from the dry channel which has been precooled in the dry channel prior to the entry into the wet channel. Therefore, the product air can be cooled below the wet-bulb temperature but above the dew-point temperature of the inlet air. The increase of the temperature drop of the product air increases the cooling efficiency of the evaporative cooler, so the application of dew-point evaporative coolers are widened. [9-12] The cooling efficiency and the temperature drop of the product air in the dew-point evaporative cooler are mainly influenced by the following factors: (1) the water wettability on the wet channel surface; (2) the system configuration (e.g., counter–flow or cross-flow pattern and the heat and mass exchanger plate design); (3) the heat and mass exchanger geometry (e.g. the channel gap, height, width, and length); (4) the operating parameters (air velocity, working to primary air ratio, water flow rate) and (5) the inlet air conditions (dry-bulb temperature and humidity). There have been many numerical and experimental studies of dew-point evaporative coolers. The water wettability on the wet channel surface is mainly influenced by the wet surface material and many researchers studied the impacts of the wet surface materials on the evaporative cooler performance. Zhao et al. [11] investigated various metals, fibres, ceramics, 3

ACCEPTED MANUSCRIPT zeolite and carbon and identified that the holding ability, durability, compatibility with the water-proof coating, contamination risk and cost are the main properties to be considered when choosing the wet surface material while the thermal properties are not very important. AlSulaiman [12] experimentally studied the cooling performance of three kinds of natural fibers in an evaporative cooler and found that the jute was better than palm and Luffa fibers. Mao and Huang [13] investigated the heat and mass transfer mechanisms in a porous ceramic and identified that the porous ceramic with a high thermal conductivity, high porosity and low volume density was a good material for an evaporative cooler. The cooling efficiency and energy efficiency are influenced by the construction and configuration of the dew-point evaporative cooler. Many researchers have proposed various dew-point evaporative cooler designs. Lee et al. [14] numerically studied three different configurations of regenerative evaporative coolers (another name for dew-point evaporative coolers) with a flat plate and a corrugated plate in cross flow and a finned channel in counter flow, and found that the finned channel type was the most compact structure among the three. The finned channel volume was 1/8 of the flat plate type volume. Pandelidisa et al. [15] numerically studied various types of dew-point evaporative coolers using the counter flow design and investigated the influence of holes connecting the dry and wet channels with one dimensional numerical model. Zhan et al. [16] numerically investigated the cooling performance of cross-flow and counter-flow dewpoint evaporative coolers and found that the cooling capacity of the counter-flow design was around 20% higher than that of the cross-flow design and that the wet-bulb efficiency of the counter-flow design was 15-23% higher than that of the cross-flow design, while the energy 4

ACCEPTED MANUSCRIPT efficiency (COP) of the cross-flow design was 10% higher than that of the counter-flow design. The heat and mass exchanger size, e.g. the channel gap, height, width, and length, and the operating parameters of the dew-point evaporative cooler, e.g. the air velocities in the dry and wet channels, the working to primary air ratio and the water flow rate also significantly impact the cooling and the energy efficiency of dew-point evaporative coolers. Many numerical and experimental studies of these factors can be found in literatures. The applications of evaporative coolers are restricted by the climatic conditions and such coolers must useful in hot, dry regions such as the northwest regions of China. Zhao et al. [17-19] studied the feasibility of using dewpoint evaporative coolers in various regions of China and the UK with analyses of the cooling efficiency, energy efficiency and water consumption of dew-point evaporative coolers for various conditions. Many numerical studies have studied the influence of various factors on the performance of dew-point evaporative coolers and optimization of the design and operating mode of the dewpoint evaporative cooler. Zhao et al. [20] studied the influence of the size and operating conditions of a counter-flow pattern exchanger using a two-dimensional numerical model that assumed (1) no thermal conduction along the air flow direction, (2) uniform air flow across the channel and (3) that the wet surface was saturated with water to show that the cooling efficiency and the energy efficiency were largely influenced by the dimensions of the air flow passages, the air velocity and the working to primary air ratio and were less influenced by the water temperature. Zhan et al. [21] used a similar two-dimensional model to study and optimize the performance of a cross-flow dew-point evaporative cooler. Riangvilaikul and Kumar [22] used 5

ACCEPTED MANUSCRIPT a one-dimensional model to study the influence of the inlet air conditions and the major operating conditions on a counter-flow dew-point cooler with the assumptions that the velocity and the fluid properties were uniform within each differential volume, no thermal conduction along the flow direction and the wet surface was completely saturated with water. Anisimov et al. [23] numerically investigated five different dew-point evaporative exchangers using the modified ε-NTU method based on the assumptions that the kinetic properties of the air flow and water film were constant, thermal conduction was negligible in the air flow direction and the wet surface was saturated with water. Pandelidis et al. [24] developed a one-dimensional model to investigate the influence of the location of perforated holes on a dew-point evaporative cooler based on the same assumptions as in Anisimov et al. [23]. Lin et al. [25] improved the numerical model by considering the longitudinal thermal conduction and the mass diffusion in the air streams but still assumed that the kinetic properties of the air flow and the water film were constant. Although there have been many simulations of dew-point coolers, the numerical models have all been greatly simplified and not very accurate and their different heat and mass transfer models have not been compared. Many numerical studies used one-dimensional models and nearly all the numerical models ignored the effects of longitudinal thermal conduction, mass diffusion in the air and variable fluid properties. According to the studies of Hettiarachchi et al. [26] and Heidarinejad and Moshari [27] on cross-flow designs, the predicted performance may be up to 10% lower when the longitudinal thermal conduction is neglected. The dry channel inlet and outlet are usually located on the sides of the heat exchanger and not on the top and 6

ACCEPTED MANUSCRIPT bottom [37, 41], so the air flow in the dry channel is not uniform and the energy equation solution needs to be coupled with the momentum and mass transfer equation solutions. The heat and mass transfer models calculate the heat transfer coefficient using empirical Nusselt number correlations for laminar flow with the mass transfer coefficient calculated using the corresponding Sherwood number correlations. However, the heat and mass transfer mechanisms on the wet surface of the wet channel differ from those on the dry surface, so the accuracies of the various heat and mass transfer models need to be verified. In addition, the influence of the inlet temperature and volumetric flow rate of the circulating water has not been thoroughly investigated, so there is no theoretical basis for selecting the circulating water flow rate for dew-point evaporative coolers. This paper presents a two-dimensional numerical model that couples the momentum and mass transfer equations with the energy equation to study the impacts of the operating conditions on the cooling performance of a dew-point evaporative cooler with a corrugated heat and mass exchanger.

7

ACCEPTED MANUSCRIPT

(a)

(b)

Fig. 1. Heat and mass exchanger for a dew-point evaporative cooler [37, 41]

2. Numerical model 2.1 Mathematical model

Fig. 2 Physical model of the heat and mass exchanger for a dew-point evaporative cooler The primary air in the dry channel transfers heat to the flowing water film on the wet side 8

ACCEPTED MANUSCRIPT through convective heat transfer in the primary air, thermal conduction through the plate and convective heat transfer in the water film with the water film then transferring the heat from the primary air to the working air stream through evaporation and convection heat transfer. The physical model containing half the channels of the dry and wet channels in the y-z plane is shown in Fig. 2. The air flow direction is controlled by the arrangement of the air inlets and outlets and is not shown in Fig. 2. Since the channel gap in z direction is quirt small compared to channel length in y direction and channel width in x direction, the temperature\velocity and humidity distribution in z direction is of small influence on the whole performance of dewpoint evaporative cooler, so this paper only studied the x-y plane and the heat and mass transfer in z direction is processed as energy and mass source in the numerical model. The model described here is adaptable to all kinds of plate-type heat and mass exchangers for dew-point evaporative cooling. The heat transfer in the dry channel and the heat and mass transfer in the wet channel influence each other, so the energy, momentum and diffusion equations for the primary air, the water film and the working air need to be solved simultaneously. The mathematical model for the heat and mass exchanger was based on the following assumptions: a) The heat and mass transfer is in steady state. b) There is no heat transfer to the surroundings from the exchanger. c) The wetting surface is totally wetted. d) The thermophysical parameters of air in the momentum equation are constant but vary with temperature in the energy and mass transfer equations. e) The water in the tank is recirculated with the evaporated water replenished at the same 9

ACCEPTED MANUSCRIPT temperature as the water in the tank. (1) Primary air in the dry channel The primary air in the dry channel is cooled by the downward flowing water film in the wet channel without adding humidity to the dry channel. The air flow is driven by a fan, so the gravity term is neglected in the momentum equation. The governing equations of the primary air are: Conservation of mass equation: 

(1)

 d   (ud )  0

Momentum equation: 









 d (ud  )ud    [ pd I   d (ud  (ud )T )]

(2)

Energy equation: 

 d c p , d u d   t d    ( k d  t d )  d

d  2

ht (t f  td ) ld

(3) (4)

ht is calculated as: ht 

1 1  pl 1   hd k pl h f

(5)

(2) Downward flowing water film The water film absorbs the heat transferred from the primary air and then transfers the heat to the working air through simultaneous heat and mass transfer processes. The water vapor mass transfer is from the water film surface to the working air after evaporating from the water film with the latent heat added to the water film. High wettability materials such as porous fibres or 10

ACCEPTED MANUSCRIPT paper are widely used on the wet surface of dew-point evaporative coolers to enlarge the contact area between the water and the wet air. The water velocity along the surface of such highwettability materials is lower than along the surface of an ordinary plate because of the capillary force, so the heat transfer coefficients were calculated based on the equivalent film thickness assumption defined from the momentum equation: [28] f  (

3 f  1/3 ) f g

(6)

Where =

mf (n  1)W

(7)

The heat transfer coefficient on the surface of the flowing water film is then calculated using the equation proposed by Wilke as referenced in Stoitchkov NJ, Dimitrov GI: [28] Nuf 

hf  f  1.88 kf

(8)

The energy equation for the water film then: 

(9)

 f c p . f u f  t f    ( k f t f )   f

f 

Where

ht (td  t f ) hw (tw  t f ) hm (d s  d w )  a,w   hla f f f

(10)

d s (kg/kg) is the humidity of the wet air near the water film surface where the partial

pressure of the water vapour equals the saturation pressure at the water film temperature. d s  0.622

ps pw -ps

(11)

The saturation pressure of the water vapour is calculated using the correlation proposed by Goff-Gratch [29], log( ps )  c1(T   1)  c2 log(T  )  c3(10 11

c4(1

1 T

)

 1)  c5(10c6(T



1)

 1)  c7

(12)

ACCEPTED MANUSCRIPT Where T* 

373.16 Tf

(13)

c1=-7.90298, c2=5.02808, c3=-1.3816*10-7, c4=11.344, c5=8.1328*10-3, c6=-3.49149, and c7=log (1013.246) (3) Working air in the wet channel In the wet channel, heat and mass transfer occur simultaneously in the working air. Part of the primary air flowing through the dry channel flows into the wet channel through the small evenly distributed perforations on the heat exchanger plate. The air entering into the wet channel through the small perforations is called the working air. A three-dimensional numerical model to study the velocity distribution in wet channel was conducted using fluent which simulates the process of air flowing in dry channel and flowing in wet channel entering from the perforations located at the top of the plate, the simulation result is shown in Fig. 3. The velocity in x-y plane is nearly uniform because the flow resistance of flowing through small perforations is large compared to flowing in dry channel and wet channel, so the velocity in wet channel became uniform after flowing through the small perforations. So, the working air flow velocity distribution is assumed to be one-dimensional in the wet channel with a constant velocity. The governing equations for the working air are then: Energy equation: 

 w c p ,w vw  tw    (k w tw )  w

w  2

hw  (t f  tw ) lw

Moisture transport in the air: 12

h (d  d w )   a,w  d  hv (tw )  vw w   a,w  2 m s  hv (t f ) y lw

(14) (15)

ACCEPTED MANUSCRIPT  vw  d w =  ( Dab d w )  m

m  2

hm  (d s  d w ) lw

(16) (17)

Fig. 3. Air velocity distribution of the working air

2.2 Heat and mass transfer models The heat transfer mechanism in evaporative coolers has been widely studied with various heat transfer correlations developed and used by many researchers. For dew-point evaporative coolers, the heat transfer in the dry channel can be easily modeled with many researchers directly using the same heat transfer correlations in the wet channel. However, the heat and mass transfer mechanisms in the wet channel are quite different from those in the dry channel and cannot be modeled in the same way. The applicability of various correlations for dew-point evaporative coolers employed by various researchers were evaluated by comparing the simulation results for various heat and mass transfer models with previous experimental data 13

ACCEPTED MANUSCRIPT [37]. Correlation A: [30, 31, 32] Nu  2  0.6 Re1/ 2 Pr1/3 Re 

 De u f  ua 

(18) (19)

Correlation B: [33, 34, 22]

Nu  8.235

(20)

Correlation C: [35, 36] The Nusselt number in the entry region is given by 7.54  0.0499Gz tanh(Gz 1 ) tanh(2.264Gz 1/3  1.7Gz 2/3 ) Nu  tanh(2.432Pr1/ 6 Gz 1/ 6 )

(21)

While the Nusselt number in the developed flow region is given by

Nu  7.54

(22)

Where Gz 

De Re Pr y

(23)

The models in the literature used these heat transfer correlations in the wet channel as well as in the dry channel with the mass transfer coefficient in the wet channel calculated using Lewis relationship in most simulation of dew-point evaporative coolers. However, the water film strongly influences the boundary layer especially when the wet surface is covered by a high-wettability material such as a fibre sheet or paper. Thus, the heat and mass transfer coefficients should be calculated by specific correlations for the working air the surface characteristics in the wet channel. The correlation proposed by Dowdy et al. [38] as shown in 14

ACCEPTED MANUSCRIPT Eq. (24) was obtained from the experiment results of evaporative cooling with the the surface covered by a rigid cellulose media saturated with water and was ever used by some researcher correctly. [39] So the present model used the correlation of Eq. (24) to calculate the heat and mass transfer coefficients in wet channel of the dew-point evaporative cooler. Nu  0.1(

le

 po

(24)

)0.12 Re0.8 Pr1/3

le 

V A

(25)

The mass transfer coefficient is also calculated using the Lewis correlation as hw   w c p , w Le 2/3 hm

(26)

The convective heat transfer coefficient of the primary air in the dry channel is calculated in the present model using the correlation proposed by Awad [40] which applies to high widthto-height rectangular channels which is widely used in heat and mass exchanger designs for dew-point evaporative coolers:  1.490  y*1/3 ) 4.5  8.2354.5  Nu  （

(1/ 4.5)

(27)

Where y* is the dimensionless length. y*  y / (DeRePr)

(28)

2.3 Boundary conditions (1) Boundary conditions for the primary air in the dry channel are as follows. Inlet: td  td ,in , ud  uin , vd  0

Outlet: 15

(29)

ACCEPTED MANUSCRIPT P  0,

td 0 y

(30)

The outside wall is assumed to be adiabatic: u  v  0,

td 0 x

(31)

(2) Boundary conditions for the working air in the wet channel are as follows. Inlet: tw,in  td ,out , d w,in  d d,in

(32)

tw d  0, w  0 y y

(33)

Outlet:

The working air flow in the wet channel is assumed to be uniform.  uw  0, vw  ud  r

(34)

(3) Boundary conditions for the flowing water in wet channel are as follows. Inlet: t f  t f ,in

(35)

Outlet: t f y

0

(36)

2.4 Performance parameters The performance of a dew-point evaporative cooler is usually evaluated using the cooling efficiency and the energy efficiency. The cooling efficiency can be described by either the wetbulb efficiency,  wb , or the dew-point efficiency,  dp , while the energy efficiency is usually given by the coefficient of performance (COP). 16

ACCEPTED MANUSCRIPT

 wb 

 dp 

tdb,in  tdb,out tdb,in  twb,in tdb,in  tdb,out tdb,in  tdp ,in

COP 

Qcooling Pw

 a ,in  c p,a (1  r )  (tdb,in - tdb,out ) Qcooling  m

(37)

(38) (39) (40)

The dew-point evaporative cooler consumes water to cool the air, so the water consumption should also be considered when evaluating the performance of a dew-point evaporative cooler.  w, c  m  a,in  r  (d w, out  d w,in ) m

(41)

2.5 Simulation method The governing equations for the primary air, working air and water film are coupled and must be solved simultaneously. The primary air flow in the dry channel and working air flow in wet channel were assumed to be laminar flow because the Reynolds number is low for flowing in dry and wet channel. The 2D governing equations were discretized using the finite element method and solved using the COMSOL software. The accuracy of the numerical model was then verified by comparing with the experimental data of Riangvilaikul and Kumar [37]. The model and the geometric parameters of the dew-point evaporative cooler used by Riangvilaikul and Kumar [37] are shown in Fig. 1(a) and Table 1. The mesh was generated in COMSOL and the grid independence was evaluated based on the average primary air channel outlet temperature. The results are shown in Fig. 4 which gave a final mesh with 5715 elements. Table 1. Geometric parameters of the dew-point evaporative cooler tested by Riangvilaikul 17

ACCEPTED MANUSCRIPT and Kumar [37] Parameter

Value

Channel length (m)

1.2

Channel width (m)

0.08

Channel gap (mm)

5

Working-to-primary air ratio

0.33

Water mass flow rate (g/h)

60

Product Temperature (oC)

25.4

25.2

25.0

24.8

24.6

24.4

0

1000

2000

3000

4000

5000

6000

Mesh Number

Fig. 4. Grid independence check based on the average primary air channel outlet temperature

3. Model validation The simulation results using the various heat and mass transfer models are compared with the experimental data [37] in Fig. 5 for two air inlet conditions. The results show that the present model are more accurate than the other models with the relative error between the data and the 18

ACCEPTED MANUSCRIPT results of the present model being within 3%. Model B is also reasonably accurate but the predicted primary outlet air temperatures are all higher than the measured outlet temperatures which is not reasonable. Because the heat exchanger is assumed to be adiabatic to surroundings in simulation but actually there is heat transfer from surroundings to heat exchanger actually which will lead to temperature increasing of product air, so the product air temperature of numerical results should be lower than of experimental results.

Present model Model A Model B Model C Exp.

Product Air Temperature/(oC)

29

28

±3%

27

26

25 1

2

3

4

5

6

7

Average Dry Channel Velocity/(m/s)

(a) Inlet air temperature of 34℃ and humidity of 19 g/kg

19

ACCEPTED MANUSCRIPT

Present model Model A Model B Model C Exp.

Product Air Temperature/(oC)

26

24

±2%

22

20

18

1

2

3

4

5

6

Average Dry Channel Velocity

(b) Inlet air temperature of 34℃ and humidity of 11.2 g/kg Fig. 5. Model validation with the measurements of Riangvilaikul and Kumar [37]

o

Product Air Temperature of Simulations ( C)

26

24

+3% 22

-3% 20

18

18

20

22

24

26 o

Product Air Temperature of Experiments ( C)

Fig. 6. Model validation with the measurements of Duan et al. [41] The present model was further validated against the measurements of Duan et al. [41]. The 20

ACCEPTED MANUSCRIPT model and geometric parameters of their dew-point evaporative cooler are given in Fig. 1(b) and Table 2. Duan et al. used a corrugated plate heat and mass exchanger unlike the plain plate heat and mass exchanger used by Riangvilaikul and Kumar. The corrugations were in the horizontal direction, so the heat and mass transfer are similar to the heat and mass transfer for a plain plate heat and mass transfer design. The simulation results using the present model are compared with the experimental data as shown in Fig. 6 with the relative error between the predictions and the experimental data nearly all within 3%. Table 2. Geometric parameters for the dew-point evaporative cooler tested by Duan et al. [41] Parameter

Value

Channel length (m)

0.9

Channel width (m)

0.314

Channel gap (mm)

6

Length of corrugated sheets (m )

0.9

Width of corrugated sheets (mm)

314

Thickness of corrugated sheets (mm)

0.2

Corrugation height (mm)

5.8

Corrugation pitch (mm)

12

4. Improved dew-point evaporative cooler design An improved dew-point evaporative cooler design was then developed based on the 21

ACCEPTED MANUSCRIPT previous studies with the geometric parameters listed in Table 3. The design uses a corrugated plate with the corrugations against in the horizontal direction to improve the heat and mass transfer efficiency by increasing the heat and mass transfer area. The corrugations are shown in Fig. 7 and the entire corrugated plate shown in Fig. 8. The bottom part of the plate is flat for the air inlet. The entire dew-point evaporative cooler layout is shown in Fig. 9. The primary air enters the dry channel from the bottom and flows along the dry channels as it is cooled by the evaporating water films in the adjacent wet channels. Then, part of primary air is delivered to the conditioned space from the upper outlet of the dry channel as the supply air while the rest is diverted to the adjacent wet channel as the working air (secondary air) through the interconnecting perforations along the upper part of the plate. The water flows downwards along the wet surface that is covered with a porous fiber while absorbing heat from the primary air in the dry channel through water evaporation to the working air (secondary air) in the wet channel. The enthalpy and humidity of the working air increase until the air is discharged to the outdoors at the bottom of the wet channel as the exhaust air. Table 3. Dew-point evaporative cooler design parameters Parameter

Value

Channel length (m)

1

Channel width (m)

0.348

Channel gap (mm)

4.3

Inlet length (mm)

125

22

ACCEPTED MANUSCRIPT

Fig. 7. Corrugation design

Fig. 8. Entire corrugated plate

23

ACCEPTED MANUSCRIPT

Fig. 9. Dew-point evaporative cooler system design

5. Results and discussion 5.1 Temperature and velocity distributions The temperature distributions of the primary air, the working air and the water film along the plate are shown in Fig. 10 for an inlet air temperature of 38℃, a relative humidity of 20%, an average primary air velocity in the dry channel of 2 m/s, a working-to-primary air flow ratio of 0.44, a volumetric water flow rate of 0.24 L/h (for one wet channel), and an inlet water temperature of 20℃. The velocity distribution of the primary air in the dry channel is shown in Fig. 11. The temperature distribution is uneven because of the non-uniform primary air velocity distribution which reduces the heat and mass transfer efficiency. The average temperatures of 24

ACCEPTED MANUSCRIPT the primary air, water and working air along the channel length are shown in Fig. 12.

(a)

(b)

(c)

Fig. 10. Temperature distributions in the (a) primary air, (b) water film and (c) working air

Fig. 11. Velocity distribution in the primary air 25

ACCEPTED MANUSCRIPT Near the primary air inlet, the primary air temperature initially increases because of the air velocity distribution. Then, the primary air temperature deceases downstream and then increases again near the primary air outlet because of water temperature decreasing along the flowing direction near the water inlet. The water and working air temperatures (both flow from y=1 to y=0) both quickly decrease near the primary air outlet and then slowly increase along the flowing direction. The heat transfer rates between the water and working air along the channel are shown in Fig. 13. The sensible heat transfer is initially negative near y=1 because the working air temperature is higher than the water temperature, so there is sensible heat transfer from the working air to the water. The latent heat transfer is very large near the water inlet because the humidity of the air coming from the primary air flow is quite low so the water quickly evaporates into the working air. Overall the latent heat transfer is much larger than the sensible heat transfer.

32

32

Primary air Water Working air

30

t (oC)

28

28

26

26

24

24

22

22

20

20

18

18

16

16

14

0.0

0.2

0.4

0.6

y(length direction) (m)

26

30

0.8

1.0

14

ACCEPTED MANUSCRIPT

Heat tranfer rate from water to working air (W/m2)

Fig. 12. Average temperatures along the channel

Sensible heat Latent heat

400

200

0

-200

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

y(length direction) (m)

Fig. 13. Heat transfer rates along the channel

5.2 Influence of the average primary air velocity The primary air velocity distribution is uneven in the dry channel, but the average primary air velocity is only influenced by the air volumetric flow rate. This study analyzed the influence of the average primary air velocity on the product air temperature and the cooling capacity for an inlet air temperature of 38℃, a relative humidity of 20%, a working-toprimary air ratio of 0.44, a volumetric water flow rate of 0.24 L/h and an inlet water temperature of 20℃with the results shown in Fig. 14 to give a reference to choose the best volumetric air flow rate for this dew-point evaporative cooler. The product air temperature and the cooling capacity both increase with increasing 27

ACCEPTED MANUSCRIPT average primary air velocity. As a result, the cooling capacity can be improved by increasing the volumetric air flow rate if the product air temperature is still within an acceptable range.

22.5

Product air temperature (oC)

22.0 21.5

52

Product air temperature

48

Cooling capacity

44 40

21.0

36

20.5 20.0

32

19.5

28

19.0

24

18.5

20

18.0

Cooling capacity (W)

23.0

16

17.5

12

17.0 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4

Average velocity of primary air (m/s)

Fig. 14 Influence of the average air velocity on the product air temperature and the cooling capacity

5.3 Influence of the working-to-primary air ratio The dry and wet channels in a dew-point evaporative cooler are connected by interconnecting perforations with the intake air of the wet channel diverted from the dry channel which has been precooled in the dry channel prior to the entry into the wet channel. The ratio of the working air flow rate to the primary air flow rate influences the cooling efficiency and the cooling capacity of the dew-point cooler. The influence of the working-to-primary air ratio on the product air temperature and the cooling capacity is shown in Fig. 15 for an inlet air 28

ACCEPTED MANUSCRIPT temperature of 38℃, relative humidity of 20%, average primary air velocity in the dry channel of 2 m/s, volumetric water flow rate of 0.24 L/h and an inlet water temperature of 20℃. The product air temperature decreases with increasing working-to-primary air ratio. Therefore, the working-to-primary air ratio should be increased to reduce the product air temperature. The cooling capacity initially increases with increasing working-to-primary air ratio when the working-to-primary air ratio is below about 0.28 and then decreases with further increases of the working-to-primary air ratio. The cooling capacities for various average inlet primary air velocities and various working-to-primary air ratios are shown in Fig. 16. The influence of working-to-primary air ratio on cooling capacity trends are nearly the same for the various air velocities, but the ratio for largest cooling capacity increases a little with increasing inlet air velocity. As a result, the working-primary air ratio should be chosen based on all the flow conditions and the desired product air temperature and cooling capacity. Fig. 15. Influence of the working-to-primary air flow rate ratio on the product air temperature and cooling capacity

29

Cooling capacity per unit (W/m2)

ACCEPTED MANUSCRIPT

42 40 38 36 34 32 30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0.0

v=2 m/s v=1.5 m/s v=1 m/s v=0.6 m/s

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Working-to-primary air ratio

Fig. 16. Influence of the working-to-primary air flow rate ratio on the cooling capacity for various average primary air inlet velocities

5.4 Influence of water inlet temperature and volumetric flow rate Previous studies of dew-point evaporative coolers mostly neglected the influence of the water by neglecting the water or assuming that the water was still. However, the inlet water temperature and volumetric flow rate influence the performance of dew-point evaporative cooler. The influence of the inlet water temperature on the product air temperature is shown in Fig. 17 for an inlet air temperature of 38℃, relative humidity of 20%, average primary air velocity of 2 m/s, and a working-to-primary air flow rate ratio of 0.44. The product air temperature increases with increasing inlet water temperature at different rates for all of the various water flow rates. All the lines intersect at a water temperature of about 23.1℃ as shown 30

ACCEPTED MANUSCRIPT in Fig. 17 for water volumetric flow rates from 0.08 L/h to 2 L/h. Quan [42] experimentally studied the influence of water temperature on product air temperature and found that when the water temperature increased from 18℃ to 24.5℃, the product temperature increased from 20.4℃ to 24℃, which was agreeing with the simulation results. The influence of the volumetric water flow rate on the product air temperature is shown in Fig. 18. When the water temperature is higher than 23.1℃, the product air temperature increases with increasing volumetric water flow rate while for water temperatures lower than 23.1℃, the product air temperature decreases with increasing volumetric water flow rate. For an inlet water temperature of 23.1℃, the product air temperature is nearly constant for all the various volumetric water flow rates. The influence of the water temperature and water flow rate on the product air temperature are shown in Figs. 19 and 20 for inlet air dry-bulb temperatures of 34℃ and 30℃and wet-bulb temperature both of 20.6℃. The temperature at which all the lines cross slightly differs for the different operating conditions, but all are close to 23.1℃. But when the wet-bulb temperature of inlet air is changed and dry-bulb temperature is the same, the temperature at which all the lines cross obviously differs for the different operating conditions as shown in Fig. 21 and 22. Therefore, the crossing temperature is mainly influenced by the wet-bulb temperature of inlet air. The results also show that for water flow rates less than 0.24 L/h, the water flow rate has little influence on the product air temperature, where the product air temperature differences are less than 1℃ for an inlet water temperature variation of 10℃. Actually, the water inlet temperature increases as the dew-point evaporative cooler 31

ACCEPTED MANUSCRIPT continues to operate. At the beginning, the water temperature is usually less than the temperature where the lines cross and as a result the circulating water volumetric flow rate should be relatively large to get a high cooling efficiency and coefficient of performance. When the water temperature is greater than the crossing temperature, the circulating water flow rate should be as low as possible but greater than the water flow rate needed to guarantee that the wet surface is totally wetted.

24.0

m=0.08 L/h m=0.16 L/h m=0.24 L/h m=0.6 L/h m=1 L/h m=2 L/h

Product air temperature (oC)

23.5 23.0 22.5 22.0 21.5 21.0 20.5 20.0 20

22

24

26

28

30

o

Water temperature ( C)

Fig. 17. Influence of the water mass flow rate on the product air temperature for td,db =38℃ and td,wb=20.6℃.

32

ACCEPTED MANUSCRIPT

25

Product air temperature (oC)

twater=20oC twater=23.1oC

24

twater=25oC 23

twater=28oC

22

21

20

19 0.0

0.4

0.8

1.2

1.6

2.0

2.4

2.8

3.2

3.6

4.0

Circulating water volume flow rate (L/h)

Fig. 18. Influence of the inlet water temperature on the product air temperature.

Product air temperature (oC)

22.0

m=0.08 L/h m=0.16 L/h m=0.24 L/h m=0.6 L/h m=1 L/h m=2 L/h

21.5

21.0

20.5

20.0

19.5

16

18

20

22

24

26

o

Water temperature ( C)

Fig. 19. Influence of the inlet water temperature on the product air temperature for td,db =34℃ and td,wb=20.6℃.

33

ACCEPTED MANUSCRIPT

22.0

m=0.08 L/h m=0.16 L/h m=0.24 L/h m=0.6 L/h m=1 L/h m=2 L/h

21.8

Product air temperature (oC)

21.6 21.4 21.2 21.0 20.8 20.6 20.4 20.2 20.0 19.8 19.6 16

18

20

22

24

26

o

Water temperature ( C)

Fig. 20. Influence of the inlet water temperature on the product air temperature for td,db =30℃ and td,wb=20.6℃.

m=0.08 L/h m=0.16 L/h m=0.24 L/h m=0.6 L/h m=1 L/h m=2 L/h

Product air temperature (oC)

21.0 20.5 20.0 19.5 19.0 18.5 18.0 17.5

14

16

18

20

22

24

26

28

30

32

o

Water temperature ( C)

Fig. 21. Influence of the inlet water temperature on the product air temperature for td,db =30℃ and td,wb=18.1℃. 34

ACCEPTED MANUSCRIPT

Product air temperature (oC)

19.0

m=0.08 L/h m=0.16 L/h m=0.24 L/h m=0.6 L/h m=1 L/h m=2 L/h

18.5 18.0 17.5 17.0 16.5 16.0 15.5

14

16

18

20

22

24

26

28

30

32

o

Water temperature ( C)

Fig. 22. Influence of the inlet water temperature on the product air temperature for td,db =30℃ and td,wb=15℃.

5.5 Influence of inlet air temperature and humidity Figures 23 and 24 show the product air temperature and cooling efficiency for various inlet air conditions for an average primary air velocity of 2 m/s, working-to-primary air ratio of 0.44, water flow rate of 0.24 L/h and water inlet temperature of 20℃. As shown in Fig. 23 for an constant inlet air wet-bulb temperature of 20.6℃, the product air temperature and wet-bulb efficiency change little for various inlet air dry-bulb temperatures. As shown in Fig. 24 for a constant inlet air dew-point temperature and humidity (di=8.26 g/kg), the product air temperature and cooling efficiencies both increase with increasing inlet air dry-bulb temperature (increasing inlet air wet-bulb temperature). 35

ACCEPTED MANUSCRIPT The results in Figs. 23 and 24 show that the product air temperature is mostly influenced by the wet-bulb temperature of the inlet air. As a result, the product air temperature can be controlled by controlling the inlet air wet-bulb temperature, which can be a theoretical basis for

22.0

1.2

21.8 21.6

Wet-bulb efficiency Dew-point efficiency 1.1 Dry-bulb temperature of product air

21.4

1.0

21.2

0.9

21.0 0.8

20.8 20.6

0.7

Cooling efficiency

Dry-bulb temperature of product air (oC)

pretreatment of inlet air to get the needed performance of dew-point evaporative cooler.

20.4 0.6

20.2 20.0

26

28

30

32

34

36

38

40

0.5

Dry-bulb temperature of inlet primary air (oC)

Fig. 23. Influence of inlet air temperature on the cooling efficiency for a constant wet-bulb temperature (enthalpy) of the inlet air for an inlet air wet-bulb temperature of 20.6℃.

36

ACCEPTED MANUSCRIPT

1.2

Dry temperature of product air Wet-bulb efficiency Dew-point efficiency

21

1.1 1.0 0.9

20 0.8 0.7

19

Cooling efficiency

Dry temperature of product air (oC)

22

0.6 18

26

28

30

32

34

36

38

40

0.5

Dry temperature of inlet primary air (oC)

Fig. 24. Influence of inlet air temperature on the cooling efficiency for a constant dew-point temperature (humidity) of the inlet air humidity of 8.26 g/kg.

6. Conclusions A two-dimensional numerical model that coupled the momentum and mass transfer equations with the energy equation was used to predict the performance of a dew-point evaporative cooler. The model and three heat and mass transfer models in the literature were evaluated against experiment data in the literature. Then, the model was used to study the impacts of various operating conditions including the inlet air volumetric flow rate, workingto-primary air ratio, water inlet temperature, water flow rate and inlet air temperature and humidity on the cooling performance of an improved dew-point evaporative cooler design using a corrugated heat and mass exchanger surface. The main conclusions are: (1) The present numerical model agreed well with experiment data from various researchers 37

ACCEPTED MANUSCRIPT with differences the experimental and numerical results of less than 5%. (2) The primary air temperature decreases along the channel and then increases a small amount near the primary air outlet. The water and working air temperatures both quickly decrease near the primary air outlet and then increase slowly along the channel. (3) The product air temperature and the cooling capacity both increase with increasing average primary air velocity. The cooling capacity can be improved by increasing the air flow rate as long as the product air temperature is acceptable. (4) The product air temperature decreases with increasing working-to-primary air ratio while the cooling capacity increases with increasing working-to-primary air ratio when the working-to-primary air ratio is less than about 0.28 and then decreases with increasing workingto-primary air ratio when the working-to-primary air ratio is greater than about 0.28. Thus, the working-primary air ratio should be chosen to provide the desired product air temperature and the best cooling capacity. (5) For various volumetric water flow rates, the product air temperature increases with increasing inlet water temperature, but the rates of increase differ for different water flow rates. The crossing temperature is mainly influenced by the wet-bulb temperature of inlet air. For water temperatures greater than crossing temperature, the product air temperature increases with increasing water flow rate, while for water temperatures less than crossing, the product air temperature decreases with increasing water flow rate. For a water temperature of crossing temperature, the product air temperature is nearly constant for various water flow rates. However, when the water flow rate is less than 0.24 L/h, the water flow rate has little effect on 38

ACCEPTED MANUSCRIPT the product air temperature with variations of the product air temperature less than 1℃ for a water temperature variation of 10℃. (6) The product air temperature is most strongly influenced by the inlet air wet-bulb temperature so the desired product air temperature and cooling capacity of the dew-point evaporative cooler can be obtained by controlling the inlet air wet-bulb temperature.

Nomenclature A

Wetted surface area (m2)

COP

Coefficient of performance

cp

Specific heat at constant pressure (kJ/(kg·K))

d

Humidity (kg/kg)

Dab

Mass diffusivity, (m2/s)

De

Equivalent diameter (m)

Gz

Graetz number

h

Convective heat transfer coefficient (W/(m2·K))

hla

Latent heat of water (J/kg)

ht

Overall heat transfer coefficient between primary air and water film (W/(m2•K))

hv (t f )

Specific enthalpy of the water film at temperature tf (J/kg)

hv (tw )

Specific enthalpy of working air at temperature tw (J/kg)

hm

Mass transfer coefficient (kg/(m2·K))

k

Thermal conductivity (W/m·K) 39

ACCEPTED MANUSCRIPT ld

Dry channel gap (m)

le

Characteristic length (m)

lw

Wet channel gap (m)

mf

Water mass flow rate (kg/s)

ma

Air mass flow rate (kg/s)

 w, c m

Water consumption (kg/s)

n

number of channels

Nu

Nusselt number

p

Pressure (kPa)

Pr

Prandtl number

Qcoolling Cooling capacity (W) Pw Fan and water pump power in the dew-point evaporative cooler r

working-to-primary air ratio

Re

Reynolds number

t

Temperature (℃)

T

Temperature (K)

u

Velocity (m/s)

V

volume of wetting media (m3)

Vh,e W

Evaporator volumetric air flowrate (m3) Channel width (m)

40

ACCEPTED MANUSCRIPT Wel

Weber number for the liquid phase

x

Vapour fraction

Greek symbols 

Cooling efficiency

Γ

water mass flow velocity (kg/ m•s)

δ

Thickness (m)



Viscosity (kg/m•s)



Kinematic viscosity (m2/s)



Density (kg/m3)

 a,w

Dry air density of working air in wet channel (kg/m3)



Heat source for energy equation (W/m3)

m

Mass source for mass equation (kg/m3)

Subscripts a

air

d

dry channel air (primary air)

db

dry-bulb

dp

dew-point

f

water film

g

gravity

in

inlet

l

liquid phase 41

ACCEPTED MANUSCRIPT Le

Lewis number

out

outlet

pl

plate

po

porous layer

s

saturation near the water surface

wb

wet-bulb

Acknowledgements This work was supported by the National Key R&D Program of China (Grant No. 2016YFE0133300), European Commission H20202 MSCA programme (for the EU H2020— MSCA-RISE-2016-734340--DEW-COOL-4-CDC

project)

and

Royal

Academy

of

Engineering (for the UK-CIAPP\415 project).

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ACCEPTED MANUSCRIPT [5] Zhang L. Energy performance of independent air dehumidification systems with energy recovery measures. Energy. 2006;31(8-9):1228-42. [6] Duan Z, Zhan C, Zhang X, Mustafa M, Zhao X, Alimohammadisagvand B. Indirect evaporative cooling: Past, present and future potentials. Renewable and Sustainable Energy Reviews. 2012;16(9):6823-50. [7] Boukhanouf R, Ibrahim H, Alharbi A, Kanzari M. Investigation of an evaporative cooler for buildings in hot and dry climates. Journal of Clean Energy Technology. 2014;2(3). [8] Heidarinejad G, Bozorgmehr M, Delfani S, Esmaeelian J. Experimental investigation of two-stage indirect/direct evaporative cooling system in various climatic conditions. Building and Environment. 2009;44(10):2073-9. [9] Maisotsenko V, Gillan LE, Heaton TL, Gillan AD. Method and plate apparatus for dew point evaporative cooler. Google Patents; 2003. [10]Hsu ST, Lavan Z, Worek WM. Optimization of wet-surface heat exchangers. Energy. 1989;14(11):757-70. [11]Zhao X, Liu S, Riffat S. Comparative study of heat and mass exchanging materials for indirect evaporative cooling systems. Building and Environment. 2008;43(11):1902-11. [12]Al-Sulaiman F. Evaluation of the performance of local fibers in evaporative cooling. Energy conversion and management. 2002;43(16):2267-73. [13]Mao Xiuming, Huang Xiang, Wen Li. Discussion on design of porous functional ceramics dew point plate-fin indirect evaporative cooler. Refrigeration and air43

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ACCEPTED MANUSCRIPT 2008;28(14-15):1942-51. [21]Zhan C, Zhao X, Smith S, Riffat S. Numerical study of a M-cycle cross-flow heat exchanger

for

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ACCEPTED MANUSCRIPT courants croises pour refroidissement indirect évaporatif. International Journal of Refrigeration. 1998;21(6):463-71. [29]Junzeng XU, Wei Q, Peng S, Yanmei YU. Error of Saturation Vapor Pressure Calculated by Different Formulas and Its Effect on Calculation of Reference Evapotranspiration in High Latitude Cold Region. Procedia Engineering. 2012;28:438. [30]Ranz WE. Evaporation from drops 1. Chemengprog. 1952;48. [31]W.E. Ranz, W.R. Marshall, Evaporation from drops. 2, Chem. Eng. Prog. 48(1952) 173e180. [32]Cui X, Chua KJ, Yang WM, Ng KC, Thu K, Nguyen VT. Studying the performance of an improved dew-point evaporative design for cooling application. Applied Thermal Engineering. 2014;63(2):624-33. [33]Cengel YA. Heat and Mass Transfer: A Practical Approach. Business & Economics. 2006;13(2). [34]O.M. Necati, Heat Transfer, McGraw-Hill Companies, Inc., Singapore, 1985. [35]Bergman TL, Incropera FP, Lavine AS. Fundamentals of heat and mass transfer. 7th ed. John Wiley & Sons, 2011. [36]Baehr HD, Stephan K. Heat and mass transfer. 2nd ed. New York, Berlin: Springer; 2006. [37]Riangvilaikul B, Kumar S. An experimental study of a novel dew point evaporative cooling system. Energy & Buildings. 2010;42(5):637-44. 46

ACCEPTED MANUSCRIPT [38]Dowdy JA, Reid RL, Handy ET. Experimental determination of heat- and mass-transfer coefficients in aspen pads. ASHRAE Transactions. 1986;92. [39]Camargo JR, Ebinuma CD, Cardoso S. A Mathematical Model for Direct Evaporative Cooling Air Conditioning System. Revista De Engenharia Térmica. 2003. [40]Awad MM. Heat transfer for laminar thermally developing flow in parallel-plates using the asymptotic method. Conference Heat transfer for laminar thermally developing flow in parallel-plates using the asymptotic method. p. 371-87. [41]Duan Z, Zhan C, Zhao X, Dong X. Experimental study of a counter-flow regenerative evaporative cooler. Building & Environment. 2016;104:47-58. [42]Quan Liangjie. The study on dew-point evaporative cooler. Master Thesis, Tsinghua University, Beijing, China, 2011. (in Chinese)

47

ACCEPTED MANUSCRIPT Highlights 1. A two-dimensional numerical model of heat and mass transfer in a dew-point evaporative cooler was proposed. 2. An improved counter-flow dew-point evaporative cooler was designed and studied numerically. 3. The impacts of various operating conditions of the dew-point evaporative cooler were studied. 4. The best operational conditions of dew-point evaporative cooler were suggested.