Bozorgmehr 2 Modeling

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American Institute of Aeronautics and Astronautics092407

1

Modeling, Evaluation and Application Potential of Two

Stage Indirect/Direct Evaporative Air Coolers

Ghassem Heidarinejad1

and Mojtaba Bozorgmehr2

Department of Mechanical Engineering, Tarbiat Modares University, P.O. Box 14115-143, Tehran, Iran

Two-stage indirect/direct evaporative air cooler can provide summer comfort conditions

as an environmentally clean, fresh supply air and energy efficient cooling system for some

regions with wide variety climatic conditions. In this paper, a general mathematical heat and

mass transfer model for evaporative devices, which take into account surface wetting factor

and non-unity Lewis factor is developed and presented. This model then has been adapted

for indirect and direct evaporative air coolers. Cross flow configuration in which dry and

wet air streams travel perpendicularly to one another is the most straightforward way to

prevent mixing air streams in an indirect evaporative air cooler. An iterative numerical

solution used to predict cooling performance of the cross flow indirect cooler; while for the

direct cooler, solution reduces to a simple analytical one. Factors affecting on coolingperformance of this system consists of operational and geometrical parameters and climatic

conditions. Results show that the operational parameters which mainly control the cooling

performance of the indirect stage are number of transfer units in both dry and wet

airstreams in addition to air stream mass flow ratio and that of the direct stage is only

number of transfer units. Whereas poor wetting degrades cooling efficiency, water flow rate

should be enough low to keep the surface wet. A climatic condition zone has been specified in

which this cooling system provides comfort condition and so fills the gap between direct

evaporative cooling system and conventional vapor compression cooling system extending

the application of the evaporative cooling in multi climatic conditions such as Iran.

Nomenclature

A = area [m2]cp = specific heat at constant pressure [kJkg

-1C

-1]

Cf = fluid to air heat capacity rate ratio (=mfcpf/macpa), [-]

Cw = water to air capacity rate ratio (=mwcw/macpa), [-]

h = convective heat transfer coefficient [kWm-2

C-1

]

hfg = evaporation heat of water at reference temperature [kJkg-1

]

i = specific enthalpy [kJkg-1

]

Km = convective mass transfer coefficient [kgm-2

s-1

]

La,Lf,Lw = flow lengths in the directions of secondary air, primary air and spray water, respectively [m]

Le = Lewis number (=/D), [-]

Lef = Lewis factor (=h/Kmcpa)

m = mass flow rate [kgs-1

]

NTU = number of heat transfer units (=hAa/macpa)

R = a ratio of sensible heat transfer capacitances (=UAf/hAa), [-]Rva = water vapor to dry air specific heat capacity ratio (=cpv/cpa)

Rwa = water to dry air specific heat capacity ratio (=cpw/cpa)

S = spacing between plates [m]

t = temperature [C]

U = overall heat transfer coefficient between primary air and water film [kWm-2

C-1

]

1Associate Professor, Department of Mechanical Engineering, Email: [email protected], AIAA Member.

2PhD Student, Department of Mechanical Engineering, Email: [email protected].

6th International Energy Conversion Engineering Conference (IECEC)28 - 30 July 2008, Cleveland, Ohio

AIAA 2008-569

Copyright 2008 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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w = Humidity ratio of moist air [kg(water) kg(air)-1

]

xa,xf,xw = coordinates of secondary air, primary air and spray water from inlets, respectively [m]

= thermal diffusivity coefficient [m2s

-1]

= cooling effectiveness %

= surface wettability factor

Subscripts

a = secondary air asw = saturated air at water temperature

f = primary air

in = inlet

out = outlet

v = vapor

w = water

I. Introduction

vaporative air conditioning is an environmentally friendly and energy efficient method for cooling buildings andis being used increasingly in residential and commercial applications worldwide. This method of cooling can

provide comfort conditions in the areas with dry and hot climate and supplies superior indoor air quality incomparison with vapor compression systems since fresh outdoor air is supplied. Two main different methods are

used, the direct and the indirect one. In the direct method, air passes through a wetted media in an adiabaticsaturation process. In the indirect method, a wet surface heat exchanger is used in which a non-adiabatic evaporationtakes place. Parallel plate indirect evaporative heat exchangers have alternating wet and dry airflow passages, whichare separated from each other. Primary air, which flows in dry passages, is cooled sensibly without adding water,while the secondary air flowing in wet passages carries away the heat energy from the primary air. The surface ofwet passages is wetted by spray water, so that water film evaporates into the secondary air and decreases thetemperature of the wall. Therefore, heat is transferred from primary to secondary air without introducing moistureinto the primary air stream. The air leaving the dry side of the cooler has a lower wet-bulb temperature than theambient.

As shown in Fig. 1 depending on the condition of secondary air, there are four possible cycles of indirect stage.Figure 1(a) shows an indirect cooler in which evaporation of water occurs out of heat exchanger and then coldsaturated air removes heat from supply air in an air-to-air heat exchanger. In Fig. 1(b) a wet surface heat exchangeris used. As the air at the outlet of the indirect stage dry side has a lower temperature than the ambient, consequentlyit would be advantageous to extract a fraction of this cooled air and pass it through the wet side of the heatexchanger instead of using ambient air. This type of cooler is referred to as a regenerative indirect evaporativecooler and is shown in Fig. 1(c). If regenerative evaporative cooler units were placed in series, the cooled air leavingthe last unit would approach the ambient dew point temperature, but each additional stage would lower the dry sideair mass flow rate resulting lower cooling capacity. Recently some novel designs have been developed and studiedwhich approach dew point temperature. Secondary air could be supplied from outdoor or room exhaust or a mixingof both. If room exhaust is used for secondary air, it is so-called recovery and is shown in Fig. 1(d).

There are some restrictions on both direct and indirect methods, which limit their applications if each one is usedalone. Direct evaporative cooling has the disadvantage that if the ambient wet-bulb temperature is higher than 21C,the cooling effect is not sufficient for indoor comfort cooling applications. In addition, as mentioned above in anindirect evaporative cooler, a heat exchanger is used and it has been suggested that only 50-60% of the incomingsecondary air wet bulb temperature can be achieved. It means that the cooling effectiveness of the indirect systems isnot high enough to be used alone for air conditioning purposes.

One way to overcome these restrictions in order to increase the cooling capacity is combining indirect and direct

evaporative stages. If a first indirect stage is added to a second direct stage, a two stage indirect/direct cooler isobtained which further cools the air. A two stage air-conditioner combining indirect and direct processes is gainingpopularity in places where the higher wet-bulb temperatures (i.e., higher ambient humidity) does not permitsufficiently low indoor temperatures from a simple direct air-conditioner. In this system, the outside air is precooledin an indirect stage and then further cooled in a subsequent direct stage. The first stage cools the air without addingmoisture and in the second stage moisture is added. The result is that the final air temperature leaving the air-conditioner is lower than what could be achieved with a direct air-conditioner only in a lower level of moisturecontent. This expands the application of evaporative air-conditioning considerably to areas with slightly higher wet-bulb temperatures.

E


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Figure 1. Indirect evaporative cooler in different cycles.

Two-stage systems are capable of providing cooling that is equivalent to, or even superior to mechanical airconditioners. A two stage indirect/direct evaporative cooler is shown schematically in Fig.2. This paper deals withthe modeling of such a cooler.

In comparison with indirect and direct evaporative cooling, there is not much enough reported work on two stageevaporative cooling. El-Dessouky et al.

1constructed an experimental rig of two-stage evaporative cooling unit and

tested in the Kuwait environment. The system was formed of an indirect evaporative cooling unit (IEC) followed by

a direct evaporative cooling unit (DEC). During the summer season of Kuwait with dry bulb temperatures higherthan 45C the system was operated. The system was operated as a function of the packing thickness and water flowrate of the DEC unit. Other parameters include the water flow rate to the IEC unit and the mode for operating theIEC heat exchangers. Results showed that the effectiveness of the IEC/DEC varies over a range of 90120%.Similarly, the effectiveness of the IEC unit was varied over a range of 2040%. The effectiveness of the DEC unitwas over a range of 6393%. Scofield and DesChamps2 studied characteristics of direct and indirect evaporativecooling units, which utilize plate type air-to-air heat exchanger. The first stage of the system contains an indirectevaporative cooling unit, which includes a plate type heat exchanger. In this unit, ambient air, with low wet bulbtemperature is sprayed with water before it flows in the plate heat exchanger against indoor air (primary air). Thisresults in reduction of the primary air temperature. Further conditioning of the primary air is achieved in aconventional cooling tower. Operation of this system shows monthly savings of 30% in the energy cost overconventional refrigeration systems. Al-Juwayhel et al.3 studied the performance of an indirect/direct evaporativecooling system and the effect of coupling the system with a cooling tower. Results show that the highest thermal

efficiency is obtained for the combined system, which is followed by a two-stage indirect/direct evaporative coolingunit. The lowest thermal efficiency is reported for the direct evaporative cooling system. In the combined system,the cooling tower removes the thermal load added to the system during air precooling and as a result, higher thermalefficiency is achieved. Review of literature shows that two stage evaporative cooling systems are being paid moreattention recently in most of the regions for residential and commercial applications.

d) Recovery cycle indirect evaporative coolerc) Regeneration cycle indirect evaporative cooler

a) Separated saturator and heat exchanger

Primary air

Extracted air from indirect stage

Secondary air

Primary air Air to airheat exchanger

Conditioned

space

Direct

saturator

Indirect heat

exchanger

Conditioned

space

Secondary air

Primary air Indirect heatexchanger

Conditioned

space

b) Conventional indirect evaporative cooler

Return air

Primary air Indirect heatexchanger

Conditioned

space


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Figure 2. Two stage indirect/direct evaporative cooler.

As an early work on modeling of indirect cooling, Maclaine-Cross and Banks 4 analyzed the evaporative heattransfer in an indirect cooler. They suggested a simplified analysis model assuming that water film is stationary and

continuously replenished with water at the same temperature and saturation line is a linear function of temperature.The resulting decoupled equations describing the wet and the dry passages of the cooler were solved by defining anew independent variable: wet bulb depression, which is the difference between dry bulb and wet bulb temperatures.This model then could be used to predict the cooler performance by analogy to dry surface heat exchangers.

Hsu et al.5 investigated three basic types of wet surface heat exchangers. They found that cooling effectivenessof each configuration increases with increasing dry channel NTU (Number of Transfer Units) and reaches maximumvalues asymptotically at some large values of NTU. They assumed that the non-circulating water is locallyreplenished and its local temperature was calculated from the mass and energy balance equations. They took intoaccount the effect of longitudinal plate conduction. Their results showed that it has almost no effect on the co-current and counter-current configurations and its degrading effect on efficiency of cross flow is accelerated whenthe ratio of dry passage length to that of the wet passage is large.

Pescod6

proposed a simple design method for indirect evaporative cooler using parallel plastic plates with smallprotrusions. Although the thermal conductivity of plastic is very low, the heat transfer resistance across a thin plastic

plate would be less than of the thermal resistance between the air and plate in dry side.Predictions of the efficiencies of Pescods wet surface plate heat exchanger were found to be higher than theexperimental data. Thus, incomplete wetting of plate surfaces was suspected. Kettleborough and Hsieh

7described a

counter flow indirect evaporative cooler with configuration of upward flow of the primary air and downward flowsof secondary air and water. Numerical analysis was utilized to study the thermal performance of the unit. Byapplying wetting factor better agreement between calculated and measured performance data qualitatively wasachieved.

Erens and Dreyer8 purposed three different models describing evaporative indirect cooler: (1) Poppe model-considering a variable Lewis factor, spray water evaporation rate and modeling over saturation in the secondary air;(2) Merkel model- can be derived from Poppe model by assuming a Lewis factor of unity and negligible effect ofspray water evaporation and assuming that the secondary air never becomes over saturated; (3) Simplified model-assuming that the water temperature is constant through out the cooler. They concluded that simplified model issuitable for small units and for initial design purpose.

Chengqin and Hongxing9

developed an analytical model for the indirect evaporative cooling with parallel andcounter flow configurations. Similar to any other analytical model, humidity ratio of air in equilibrium with watersurface assumed as a linear function of the surface temperature. Effects of spray water evaporation, spray watertemperature variation along the heat exchanger, non-unity surface wettability and Lewis factor were considered inthe model. Results of analytical solutions found to be in good agreement with those of numerical integrations.

The principles underlying all of the indirect evaporative cooling devices such as indirect evaporative air andfluid cooler and closed-wet cooling tower is the same. So the resulting set of the equations for the mathematicalmodeling could be obtained in a general form10,11. The differences are due to geometrical and flow configuration,heat, and mass transfer coefficients. For an indirect evaporative air cooler, cross flow configuration is best suitedwith parallel plate wet surface heat exchanger. Review of the previous researches show that simplified models


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consider either constant water temperature or neglect effect of water evaporation rate. In this paper using a realcurve fitted saturation line, variation of water temperature and its evaporation rate, non-unity Lewis factor andsurface wetting factor are taken into account to model a cross flow evaporative indirect air cooler.

II. Modeling

A. Physical description of cross flow indirect coolerVarious designs for the indirect evaporative cooler have been developed12

. Indirect heat exchangers must bedesigned such that the dry and wet airstreams do not mix. The most straightforward way to prevent mixing is to usea cross flow pattern, in which the dry and wet airstreams travel perpendicularly to one another; and all four heatexchanger edges are available as airflow inlets and outlets. Conventionally, in cross flow designs, wet passageairflow considered vertical and dry passage airflow is horizontal. Counter flow heat exchangers are typically moreeffective than those of cross flow design. This is because the average temperature difference between the twoairstreams, which is directly proportional to the heat transfer rate, is greater for counter flow than it is for cross flow.But as presented by Heidarinejad and Bozorgmehr13, because of simultaneous interaction of latent and sensible heattransfer, good enough efficiencies could be obtained with cross configuration in comparison with that of counterflow configuration.

A typical design consists of a series of parallel plates in which one is open for primary airflow and the other oneis open for water and secondary airflows. Circulation water sprayed onto the top of the heat exchanger and flowsdownward along wall surfaces of wet channels. Primary air flows in the alternative channels. As can be seen fromFig. 3 each repeated section of the cooler consists of a half of dry channel, plate wall and a half of wet channel.Whereas in the cross flow configuration, primary air and secondary air flow in perpendicular direction, the heatexchanger is divided into a series of two-dimensional elements, each of the surface area dA as shown in Fig. 3.

The following assumptions here are considered:-There is no diffusion in the flow direction;-Unit is insulated from the surrounding;-Heat and mass transfer coefficients are constant;-Lewis factor is not unity;-Spray water is circulated;-Plate wall, bulk water and air/water interface have the same temperature.

Figure 3. Model section and differential element.

B. Governing equations of heat and mass transferHeat and mass transfer occur simultaneously in an indirect evaporative heat exchanger. For a differential element

as shown in Fig. 3, by applying principles of mass and energy conservation, a set of differential equations obtainedas follows.

1/2Sf 1/2Sa

Secondary air

Platewall

Secondary air in

a a a am , t , i , w

Water in

w wm ,t

Primary air out

f f f m ,t dt +

Primary air in

f fm ,tdA

Secondary air out

a a a a a a am ,t dt , i di ,w dw+ + +

Water out

w w w wm dm ,t dt + +

a) Model section and its adjacent section b) Differential element

Water

PrimaryAir


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Energy balanceEnergy balance equation for the secondary air:

a a c w a v m asw a a am di =[h (t -t )+i K (w -w ) ]A dx (1)

Energy balance equation for the primary air:

f pf f w f f f m c dt =U(t -t )A dx (2)

With the assumption of varying water flow rate, energy balance equation for the streams flowing inside theelement shown in Fig. 3 is as follows:

w w w w w w f pf f a am c dt +c t dm +m c dt +m di =0 (3)

Mass balanceThe mass balance for the element gives the rate of spray water evaporation.

a a m asw a a am dw =K (w -w ) A dx (4)

In above equations aaa Ldxxd /= , w w wdx =dx /L , and f f f dx =dx /L represent differential dimensionless

coordinates with respect to the flow lengths. Equations (1)-(4) govern heat and mass transfer in an indirectevaporative cooler. Some manipulation to the above equations results the following set of coupled ordinaryequations:

a va asw a w a aa va

1dt =[ ](1+R (w -w ))(t -t )NTUdx

(1+w R ) Le

(5)

a asw a adw =(w -w ) NTUdxLe

(6)

f w f f

f

Rdt =(t -t ) NT U dx

C(7)

w f w f w a a fg pa w va wa asw a a

w w w

R 1 1dt =NTU.[ (t -t )dx - (t -t )dx -[h /c +t (R -R )] (w -w )dx ]

C C C Le

(8)

Equations (5)-(8) form a set of coupled ordinary differential equations, which can be solved simultaneously,using a multi step numerical integration procedure.

Water circulation conditionSpray water temperature varies inside the heat exchanger. Because of water circulation, the inlet spray-water

temperature w int will equal the outlet spray-water temperature w outt .

w in w out t t (9)

Equation (9) sets the condition for inlet and outlet water temperature due to the circulation of water.

C. Procedure of integrationThe integration procedure starts from the element in which both inlet conditions of primary and secondary air

streams are known and proceeds throughout the cooler. In practice, water is normally circulated, so ignoring heat


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loss in the water circuit, inlet, and averaged outlet water temperature are the same, and this temperature has to befound iteratively.

For down flow case which secondary air and water both flow downwards, integration starts from the top of thecooler where the inlet air conditions are known with an assumed water temperature. The integration proceedsdownwards to the bottom of the cooler. The averaged water temperature at the bottom is compared to the assumedinlet water temperature and is corrected to obtain equal inlet and outlet temperatures.

In the case of up flow, because secondary air enters from the bottom, integration starts from the bottom with anassumed outlet water temperature and proceeds upwards. This procedure leads to a water temperature distribution atthe top, which is not constant. The difference between inlet and outlet water temperature in each vertical column ofelements is used to update assumed outlet water temperature. The solution is iterated until constant watertemperature at the top and equal water temperature at the inlet and outlet is achieved.

D. Physical description of direct coolerIn a direct evaporative cooler, the heat and mass transferred between air and water decreases the air dry bulb

temperature (DBT) and increases its humidity, while the enthalpy would be essentially constant in an ideal process.The minimum temperature that can be reached is the wet bulb temperature (WBT) of the incoming air. Wet porousmaterials or pads provide a large water surface in which the air is moistened and the pad is wetted by dripping water.Cooling water is sprayed or simply poured from the top to effect falling film at the surface of cellulose papers ofpad. Cellulose paper is a good packing for pads because it is porous and durable for repeated wetting and drying,and has a very large pore surface for a given packing volume in comparison to commercial fibers. The main merits

of this type of pad are: (1) large pressure loss can be avoided and good effect of evaporation can be ensured, sincethe process air flows in a straight channel; (2) the evaporative cooler is compact in size and less in weight due to itshigh surface density. Considering the humid airflow close to a wet surface, according to Fig. 4, the heat transfer will

occur if the surface temperature wt is different from the draft air temperature at . If the absolute humidity

(concentration) of the air close to the surface asww is different from the humidity of the draft aw , mass transfer will

also occur. It is assumed that the makeup water entering the sump to replace evaporated water is at the sameadiabatic saturation temperature of the incoming air. For a differential element as shown in Fig. 4, by applyingprinciples of mass and energy conservation, a set of differential equations can be obtained as follows

Figure 4. An element of direct evaporative cooler.

Energy balanceEnergy balance equation for the air

a a c w a v m asw am di =[h (t -t )+i K (w -w ) ]dA (10)


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Mass balanceMass balance equation for the air is the same as equation (4). In a direct evaporative cooler, water is added in

small quantities and attains the wet bulb temperature of the incoming air condition and its temperature is essentiallyconstant within the device. For such a case, taking into account that the water flow direction is irrelevant, and withan additional assumption that Le =1, based on a general mathematical model developed by Halasz 10 the governingequations of mass and energy could be obtained as follows.

a

ca W B a WB

a p

hd(t -t )=- (t -t )dA

m c(11)

a

ca W B a W B

a p

hd(w -w )=- (w -w )dA

m c

(12)

These equations can be integrated over the whole surface to yield:

a

a, o W B c

a,i W B a p

t -t h A=exp(- )

t -t m c(13)

a

a,o W B c

a,i W B a p

w -w h A=exp(- )w -w m c

(14)

Therefore, the effectiveness of a direct evaporative cooling device defined as the following simple equation:

a

a,i a,o c

a,i WB a p

t -t h A=1-exp(- )

t -t m c = (15)

III. Results and discussion

As can be seen from the equations for modeling indirect stage, the system is well described by fivedimensionless parameters, which are NTU, Cf, Cw, R and /Le. This form is suitable for describing the results and

conditions with just a few dimensionless parameters. Profiles of the primary air and water temperature for typicalconditions are illustrated in Fig. 5(a) for secondary air up-flow and Fig. 5(b) for secondary air down-flow. Thisfigure shows the effect of flow configuration on the distribution of temperature on the surface of heat exchanger.

These figures represent the two-dimensional distribution of primary air and water temperature. Typicalexperimental data from a test set up which has been designed and constructed for investigation of operationalparameters and climatic conditions effects on cooling performance has been used to validate modeling results. Theresult for a sample case has been presented in Fig. 6. As can be seen modeling result has a good agreement withexperimental data both in value and the shape of the outlet temperature profile. It is concluded that the presentedapproach is capable to provide a two dimensional picture of temperature distribution on the heat exchanger surface.

The experimental set up is capable to provide a wide variety range of climatic conditions and operationalparameters. It has been designed modular and consists of four main modules as follows.

Primary air humidity and temperature simulator

Secondary air humidity and temperature simulator

Two stage indirect/direct evaporative cooling system Control unit to set climatic and operational conditions


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Figure 5. Profiles of water and primary air temperature in indirect cross flow configuration.

NTU=3.0, Cf=2.0, Cw=4.0, R=1.5, /Le=1.0tf,i=30C, ta,i= 30C, wa,i=0.01

Figure 6. Results of temperature profiles of primary air in sample test of indirect cross flow cooler.

Tf

0 1

0

1

xa

/La

xf/Lf0

0.2

0.4

0.6

0.8

1

20 25 30 35 40

Temperature

No

ndimentiontioalheight

Inlet

Model Outlet

Experiment

+5%

-5%

a) Model temperature distribution b) Comparison between model and experimental outlet

temperature profiles

TwTf

xf/Lf

xa/La

xw/Lw

xf/Lf1

0

0 1

1

0

10

Tf Tw

xf/Lf

xa/L

a

a) Secondary air flows up

xw/Lw

xf/Lf

0

0 1

1

1

0 1

0

b) Secondary air flows down


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A schematic diagram of test set up has been illustrated in Fig. 7. As mentioned above the purpose of test set updevelopment is to research the application potential of two stage indirect/direct cooling system for a country withmulti climatic condition such as Iran. The results of these tests will be presented in upcoming papers to support theprevious predicted data14.

Figure 7. Schematic diagram of test set up.

As can be seen from previous figures water temperature is not constant and its variation must be taken intoaccount. The effect of water flow rate on the averaged water temperature profile in the direction of its flow has beenshown in Fig. 8. It could be seen that increasing rate of circulating water increases its average temperature on thesurface of heat exchanger, although sump water temperature decreases. As can be seen, increasing water flow rateflattens its temperature profile and increases its average temperature value. As water flow rate increases, because ofincreasing average water temperature, cooling efficiency decreases. So it could be concluded that increasing waterflow rate lowers cooling efficiency and flattens water temperature profile while decreasing water flow rate causes

increasing cooling efficiency with a gradient in the water temperature profile. Then water flow rate should be kept asminimum as possible, but lowering water flow rate may cause incomplete wetting. This effect has been shown inFig. 9. As can be seen cooling efficiency exponentially deteriorates due to incomplete wetting. For a specifiedcooling system there could be found a minimum water flow rate which keeps the surface wet enough. Effect of NTUon indirect cooling effectiveness in different air flow ratios is shown in Fig. 10. As can be seen cooling effectivenessis under the control of primary to secondary air flow ratio and this parameter determines the shape of this curve.Cooling effectiveness in direct cooling based on Eq. (15) has been shown in Fig. 11. Comparing this simpleanalytical equation with experimental data

15for a cellulose pad shows good agreement.


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21

22

23

24

0 0.2 0.4 0.6 0.8 1

Tw

[C]

xw/L

Cw=0.4

Cw=1.0

Cw=2.0

Cw=4.0

Figure 8. Effect of water flow rate on averaged water temperature profile.NTU=3.0, Cf=1.0, Cw=0.4~4.0, R=1, /Le=1.0

tf,i=30C, ta,i= 30C, wa,i=0.01

30

35

40

45

50

55

60

65

70

75

80

1 1.5 2 2.5 3

Coolingeffe

ctiveness%

Cf

Sigma/Le=1.0

Sigma/Le=0.75

Sigma/Le=0.5

Figure 9. Effect of surface wetting on cooling effectiveness versus airflow ratio.NTU=3.0, Cf=1.0~3.0, Cw=2.0, R=1, /Le=0.5~1.0

tf,i=30C, ta,i= 30C, wa,i=0.01


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0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6

Coolingeffectiveness%

NTU

Cf=1.0

Cf=2.0

Cf=3.0

Figure 10. Effect of NTU on indirect cooling effectiveness in different air flow ratios.NTU=1.0~6.0, Cf=1.0~3.0, Cw=4.0, R=1, /Le=1.0

tf,i=30C, ta,i= 30C, wa,i=0.01

Figure 11. Cooling effectiveness in direct cooling based on equation (15)

compared with experimental data [Ref. 15].

IV. ConclusionUsing the general mathematical heat and mass transfer model for evaporative devices, which takes into account

water temperature and flow rate variation, modeling of a cross flow two-stage evaporative cooler has beenpresented. The indirect stage is well described by the numerical solution of energy and mass balance equations whilethe direct stage effectiveness is determined by an analytical simple equation, which is suitable for cellulose paperpads. Two-stage evaporative cooler could provide comfort conditions in some major cities of Iran where directcooling system is unable to meet comfort requirements.


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References1El-Dessouky, H., Ettouney, H., Al-Zeefari. A., Performance analysis of two-stage evaporative coolers, Chemical

Engineering Journal, Vol. 102, 2004, pp. 255266.2Scofield, C. M., DesChamps, N. H., Indirect evaporative cooling using plate type heat exchangers ASHRAE Trans, Vol.

90, 1984, pp. 148153.3Al-Juwayhel, F. I., Al-Haddad, A. A., Shaban, H. I., El-Dessouky, H. T. A., Experimental investigation of the performance

of two-stage evaporative cooler Heat Transfer Eng, Vol. 18, 1997, pp. 2133.4Maclaine-Cross, I. L., Banks, P. J., A general theory of wet surface heat exchangers and its application to regenerative

cooling ASME J. Heat Transfer, Vol. 103, 1981, pp. 579-585.5Hsu, S.T., Lavan, Z., Worek, W. M., Optimization of wet surface heat exchangers, Energy, Vol. 14, 1989, pp. 757-770.6Pescod, D., A heat exchanger for energy saving in an air conditioning plant, ASHRAE Trans, Vol. 85, 1979, pp. 238-251.7Kettleborough, C. F., Hsieh, C. S., The thermal performance of the wet surface plastic plate heat exchanger used as an

indirect evaporative cooler, ASME J. Heat Transfer, Vol. 105, 1983, pp. 366-373.8Erens, P. J., Dreyer, A. A., Modeling of indirect evaporative air cooler, Heat Mass Transfer, Vol. 36, 1993, pp. 17-26.9Chengqin, R., Hongxing, Y., An analytical model for the heat and mass transfer processes in indirect evaporative cooling

with parallel/counter flow configurations, Heat Mass Transfer, Vol. 49, 2006, pp. 617-627.10Halasz, B., A general mathematical model of evaporative cooling devices, Rev. Gen. Therm, Vol. 37, 1998, Elsevier,

Paris, pp. 245255.11Hasan, A. A. Performance analysis of heat transfer processes from wet and dry surfaces: cooling towers and heat

exchangers, Doctoral dissertation. Helsinki University of technology, 2005.12Watt, J. R., Brown, W. K., Evaporative air conditioning handbook. Lilburn: Fairmont Press. 1997.13Heidarinejad, Gh., Bozorgmehr, M., Modeling of indirect evaporative air coolers, Proceeding of 2nd PALENC and 28th

AIVC conference, Crete island, Greece,Vol. 1, 2007, pp. 416420.14

Heidarinejad, Gh., Bozorgmehr, M., Heat and mass transfer modeling of two stage indirect-direct evaporative air coolers,ASHRAE JOURNAL (Thailand Chapter) Vol. 1, 2007-2008, pp. 2-8.

15Camargo, J. R., Ebinumab, C. D., Silveira, J. L., Experimental performance of a direct evaporative cooler operating duringsummer in a Brazilian city, International Journal of Refrigeration, Vol. 28, 2005, pp. 11241132.

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