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i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3

Available o

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journal homepage: www.elsevier .com/locate/ i j refr ig

Calculations on performance characteristics of counterflowreversibly used cooling towers

Quan Zhang a,b, Jiasheng Wua,b, Guoqiang Zhang a,b,*, Jin Zhou a,b, Yonghui Guo a,b,Wei Shen a,b

aCollege of Civil Engineering, Hunan University, Changsha 410082, ChinabKey Lab of Building Safety and Energy Efficiency, Hunan University, Ministry of Education, China

a r t i c l e i n f o

Article history:

Received 1 August 2011

Received in revised form

23 October 2011

Accepted 29 October 2011

Available online 6 November 2011

Keywords:

Cooling tower

Reversible

Counterflow

Heating

Heat transfer

Mass transfer

Numerical analysis

* Corresponding author. College of Civil Engi88821005.

E-mail address: gqzhang@188.com (G. Zh0140-7007/$ e see front matter ª 2011 Elsevdoi:10.1016/j.ijrefrig.2011.10.016

a b s t r a c t

This paper aims at developing an analytical model for the coupled heat and mass transfer

processes in a counterflow Reversibly Used Cooling Tower (RUCT) based on operating

conditions, which is more realistic than most conventionally adopted Merkel approxima-

tions. Temperature and moisture content differences are chosen as the driving forces of

heat and mass transfer correspondingly and a system of specific difference equations is

developed to solve the model more efficiently. The model is investigated by using an

iterative algorithm, which is validated with the experimental data reported. The analytical

model also accommodates the direct and quick calculation of air and water temperature

profiles, moisture content of air and the water mass flow rate change along the vertical

length of the RUCT. With the aid of the developed model, the thermal behavior of the

counterflow RUCT under various operating and environmental conditions is also studied in

this paper. The results reveal that the proposed model can provide a theoretical foundation

for practical design and performance evaluation of counterflow RUCT.

ª 2011 Elsevier Ltd and IIR. All rights reserved.

Calcul des caracteristiques de performance des tours derefroidissement reversibles a contre-courant

Mots cles : Tour de refroidissement ; Reversible ; Contre-courant ; Chauffage ; Transfert de chaleur ; Transfert de masse ; Analyse

numerique

neering, Hunan University, Changsha 410082, China. Tel.: þ86 731 88825398; fax: þ86 731

ang).ier Ltd and IIR. All rights reserved.

Nomenclature

A area (m2)

Patm atmospheric pressure (kPa)

a surface area per unit volume (m�1)

cp specific heat at constant pressure (J kg�1 K�1)

cda specific heat of dry air (J kg�1 K�1)

cv specific heat of water vapor (J kg�1 K�1)

cp,a specific heat of moist air (J kg�1 K�1)

ma mass flow rate of moist air (kg s�1)

mda mass flow rate of dry air (kg s�1)

mw mass flow rate of water (kg s�1)

mw,i mass flow rate of inlet water (kg s�1)

mw,o mass flow rate of outlet water (kg s�1)

hc heat transfer coefficient (W m�2 K�1)

hm mass transfer coefficient (kg m�2 s�1)

i specific enthalpy (J kg�1)

isv(Tw) specific enthalpy of water vapor condensating to

the water (J kg�1)

L length (m)

H width (m)

Z width (m)

Q heat absorption capacity (kW)

T temperature (�C)Ta air temperature (�C)Ta,i air inlet temperature (�C)Ta,o air outlet temperature (�C)Twb,i wet bulb temperature of the inlet air (�C)Tw water temperature (�C)Tw,i water inlet temperature (�C)Tw,o water outlet temperature (�C)ua humidity ratio of saturated moist air (kgw kgda

�1)

us humidity ratio of saturated moist air at water

temperature (kgw kgda�1)

ua,i air inlet humidity ratio (kgw kgda�1)

ua,o air outlet humidity ratio (kgw kgda�1)

r0 latent heat of condensation of water at 0 �C (J kg�1)

rw(Tw) latent heat of condensation of water at water

temperature (J kg�1)

r correlation coefficient (dimensionless)

R2 absolute fraction of variance (dimensionless)

RMSE root mean square error

ANN Artificial Neural Network

Le Lewis number

Greek symbols

u humidity ratio (kgw kgda�1)

h heating efficiency (dimensionless)

Subscripts

a moist air

da dry air

db dry-bulb

wb wet-bulb

s saturation

c convective

i inlet

o outlet

v water vapor

sv saturated water vapor

w water

Superscripts

i the ith control unit

j the jth control unit

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3 425

1. Introduction

Mechanical draft cooling towers are generally employed in

large scale air-conditioning systems to release the heat

withdrawn from the building (Hajidavalloo et al., 2010; Jin

et al., 2007; Khan et al., 2003; Lemouari and Boumaza, 2010).

However, a mechanical draft cooling tower may also be

reversibly used as part of a heat pump system extracting free

heat from ambient air in cold seasons to generate hot water

for buildings (Deng et al., 1998). Recently, a number of new

desuperheater heat recovery systems that include a Revers-

ibly Used Cooling Tower (RUCT) have been installed in Main-

land China, and have been operating satisfactorily for several

years (Song et al., 2011; Wu et al., 2011a; Zhang et al., 2010).

The heat and mass transfer characteristics of a standard

water cooling tower have been well understood and docu-

mented when it is normally used to dissipate heat to the

atmosphere (Al-Waked and Behnia, 2006; Heidarinejad et al.,

2009; Klimanek and Bialecki, 2009; Milosavljevic and

Heikkila, 2001; Ren, 2008). However, when it is operated in

a reverse mode to extract heat from the ambient air as part of

a heat pump system for hot water supply, its operational

characteristics are expected to be significantly different from

that of a standard water cooling tower, and should be

investigated (Tan and Deng, 2002; Wen et al., 2011). These

differences include reduced latent heat exchange and

increased chilled water flow rate when chilled water exits

from a RUCT. Previous related work included carrying out an

extensive literature review on applying desuperheater to

recover heat for hot water supply (Tan, 2000) and for devel-

oping an analytical method for evaluating the heat and mass

transfer characteristics in a RUCT (Tan and Deng, 2002).

Furthermore, field experimental results from a RUCT installed

in a sub-tropical region in China indicated that the developed

method could be used to evaluate the thermal performance of

the RUCT with an acceptable error. However, this method

cannot be used to determine the air and water states at any

intermediate horizontal sections along the vertical length of

the RUCT. Tan andDeng (2003) presented a numerical analysis

by which the air and water states at any horizontal sections

along the tower height may be determined. The numerical

analysis is based on the heat and mass exchange within the

tower, which was also partially validated by the on-site

experimental data. However, they did not consider the effect

of Lewis number, and the results are only applicable to Lewis

number equal to one. Wu et al. (2011b) presented an Artificial

Neural Network (ANN) model that can be used effectively to

predict the performance characteristics of the RUCT under

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3426

cross flow conditions, providing a theoretical basis on the

research of heat and mass transfer inside RUCT. To under-

stand the heating process and the related heat and mass

exchanges for accessing optimal operating conditions, it is

necessary to develop a realistic model for predicting the

thermal behavior of the counterflow RUCT.

The objective of this paper is to develop a model for anal-

ysis of the combined heat andmass transfers in a counterflow

RUCT. In this model, the effects of Lewis number, the aire-

water interface temperature, the variation of water mass flow

rate, and the effect of water vapor condensation on the air

process states, and along the vertical length of the RUCT are

considered together. Furthermore, a comparison of analytical

and numerical results will be provided, which reveals good

agreements with experimental data reported by Tan andDeng

(2002). The proposed model will also be used to analyze the

distribution of the water and air temperatures inside the

RUCT aswell as the air humidity and to predict the quantity of

the water gain during the condensation phase. Finally, the

thermal behavior of the RUCT under various operating and

environmental conditions is also studied.

2. Mathematical model and solution ofcounterflow heat and mass transfer process

In a counterflow RUCT, inside of the tower is packed with

packing material providing a large surface area for heat and

mass transfer from air to water droplets, as shown in Fig. 1,

the chilled water to be heated is sprayed into an upward

flowing air stream using a number of nozzles. The nozzles are

arranged in such a way that the water is uniformly distributed

over the fill material. Due to heat and mass transfer, the

temperature of water is increased while the air enthalpy

decreases because the air is cooled and dehumidified by the

water as it flows up.

2.1. Assumptions

The theoretical model of the RUCT is based on the following

assumptions and simplifications:

Fig. 1 e Schematic of heat andmass transfer in counterflow

RUCT.

1. The thermal effects of the RUCT packing material are

negligible.

2. Both air andwater inlet flow rates are steady and uniform.

3. Both the air and chilled water have constant physical

properties.

4. The interface of contact between the water and air is

considerable.

5. No thermal losses from all sides of the RUCT.

6. Temperature has no influence on the transfer coefficients.

7. Thermal dispersion effects are negligible in both air and

chilled water domains.

8. Operating parameters of the RUCT are varying only in the

vertical direction.

9. The variation of water mass flow due to condensation

cannot be neglected.

10. The interface temperature between water film and air is

assumed to be equal to the water film temperature.

2.2. Governing equations of heat and mass transfer inthe RUCT

The driving potential for mass transfer is the humidity ratio

difference between the saturated air at the airewater inter-

face and the moist air, thus dmw can be written as

dmw ¼ hmðua � usÞdA (1)

where us is the humidity of air at the water temperature, ua is

the air humidity in the bulk air flow and hm is mass transfer

coefficient.

On the other hand, the quantity of water vapor con-

densated is equal to the air flowmultiplied by the air humidity

variation. The air side water-vapor mass balance can be

written as (Stabat and Marchio, 2004)

�mdadua ¼ hmðua � usÞdA (2)

At steady-state conditions, the energy balance between air

and water, including condensation, is given by the following

relation

�mdacdaTa;iþmdaua;i

�cvTa;iþr0

���½mdacdaTa;oþmdaua;oðcvTa;oþr0Þ�¼mdadua

�cvTw;iþr0

�þhcðTa�TwÞdA(3)

Then, equation (3) can be reduced as�cdamdaTa;i þ cvmdaua;iTa;i

�� ðcdamdaTa;o þ cvmdaua;oTa;oÞ¼ cvmdaduaTw;i þ hcðTa � TwÞdA (4)

The energy transferred from the air to water due to conden-

sation of mass and heat convection is balanced with the

increase of the enthalpy of the water

cwmw;oTw;o � cwmw;iTw;i ¼ hcðTa � TwÞdAþ dmwisvðTwÞ (5)

dQ ¼ hcðTa � TwÞdAþ dmwhsvðTwÞ (6)

where isv(Tw) is the enthalpy of water vapor condensating to

the water. This quantity is evaluated at the bulk water

temperature Tw and can be expressed as

isvðTwÞ ¼ cwTw þ rwðTwÞ (7)

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3 427

Substituting equation (7) into energy balance equation (5)

produces

cwmw;i

�Tw;o � Tw;i

�þ cwðTw;o � TwÞdmw

¼ hcðTa � TwÞdAþ rwðTwÞdmw (8)

By substituting Tw,i for Tw into equation (8), we can obtain

cwmw;i

�Tw;o�Tw;i

�þcw�Tw;o�Tw;i

�dmw

¼hcðTa�TwÞdAþrwðTwÞdmw (9)

By substituting dTw¼Tw;o�Tw;i into equation (9), we can obtain

cwmw;i

�Tw;o�Tw;i

�þcwdmwdTw¼hcðTa�TwÞdAþrwðTwÞdmw (10)

dmwdTw is infinitesimal of higher order, which is negligible.

Equation (10) is then modified to

cwmw;i

�Tw;o � Tw;i

� ¼ hcðTa � TwÞdAþ rwðTwÞdmw (11)

The water and air energy balance in terms of the heat and

mass transfer coefficients is given by equation (11).

The equations (1), (2), (4) and (11) are the basic heat and

mass transfer equations between water and air in a counter-

flow RUCT. The heat transfer coefficient hc and mass transfer

coefficient hm reflect the intensity of the thermal-hydraulic

process within the RUCT, which can be calculated as follows

(Wang et al., 2010)

hc ¼cp;a,ma,

�Ta;i � Ta;o

�ðTa;av � Tw;avÞ,A (12)

Ta;av ¼ �Ta;i þ Ta;o

��2 (13)

Tw;av ¼ �Tw;i þ Tw;o

��2 (14)

cp;a ¼ 1:005þ 1:842,ua (15)

where ua is the moisture content of inlet air stream deter-

mined by air inlet dry and wet bulb temperature.

hm ¼ mw

k,V

ZTw;i

Tw;o

cwh00 � h

dT (16)

Fig. 2 e Directions of water and air flows, divided segment

of padding.

where “h” is the enthalpy of saturated water vapor evaluated

at Tw, k is a coefficient determined by Tw,o and is resulted from

water vapor condensated from the tower which can also get

a portion of heat. The expression of k for the whole tower is

given by Shi (1990)

k ¼ 1� cp;w,Tw;o

586� 0:56ðTw;o � 20Þ (17)

2.3. Numerical method

To depict air and water temperature profiles, moisture

content of air and the water mass flow rate change within the

RUCT, as shown in Fig. 2, we divided the whole process into

finite sections, each with an area of dA. Sectionm is filled with

water which enters the section at the temperature of Twi and

exit at Twiþ1. Section n is filled with water at the inlet temper-

ature of Twj and outlet temperature of Tw

jþ1, which has no

influence on computational results as operating parameters of

the counterflow RUCT vary only in the vertical direction. In

each stage, an iterative computation is developed in each

differential section according to the initial conditions. The

governing equations could be cast in the form of differential

equations and solved by a finite difference method (Hao et al.,

2003; Qi et al., 2007). In each differential section, the outlet

parameter can be obtained according to the inlet parameter.

After solving all steps, we can get the condition parameter of

the water and air in each position. Only if the step length is

short enough and in the vertical direction, the method is

dependable. In each step, the foregoing equations can be

discretized and solved using the finite difference method.

Eventually, water temperature, water mass flow rate and

moisture content for the air at each spot within the counter-

flow RUCT can be obtained.

The conservation equations are accompanied with two

relationships describing the kinetics of condensation through

the airewater interface of the water film. The area of the

interface is

dA ¼ Ai;j ¼ Ln� Hm

(18)

The equations (1)e(2), (4) and (11) can be reformulated as

miþ1;jw �mi;j

w ¼ hm

�ui;j

a � ui;js

�Ai;j (19)

mda

�uiþ1;j

a � ui;ja

� ¼ hm

�ui;j

a � ui;js

�Ai;j (20)

�cdamdaT

iþ1;ja þ cvmdau

iþ1;ja Tiþ1;j

a

���cdamdaT

i;ja þ cvmdau

i;ja T

i;ja

�

¼ cvmda

�uiþ1;j

a � ui;ja

�Ti;jw þ hc

�Ti;ja � Ti;j

w

�Ai;j (21)

cwmi;jw

�Tiþ1;jw � Ti;j

w

�¼ hc

�Ti;ja � Ti;j

w

�Ai;j þ ri;jw

�miþ1;j

w �mi;jw

�(22)

The number of model equations above (equations (19)e(22))

is four, but the number of variables is six, and because the

humidity ratio of saturated moist air at water temperature us

and latent heat of condensation of water at water temperature

rw are the function of Tw (Hao et al., 2003), the function relation

to us, rw and Tw must be obtained by simulation. It is known

that humidity ratio of saturated moist air and latent heat of

Table 1 e Comparison of the measured and calculatedresults obtainedwithmethod by Tan andDeng (2002) andpresented approach.

La Ga Tdba Twb

a Tw,ia Ta,o

a Tw,oa Tw,o

b Db Tw,oc Dc Lec

kg/s kg/s �C �C �C �C �C �C �C �C �C

1.48 9.2 11.8 10.7 7.3 9.8 8.7 8.93 0.23 8.98 0.28 0.91

1.48 9.2 15.2 13.5 7.5 11.8 10.0 10.58 0.58 10.78 0.78 0.91

1.48 9.7 17.5 16.6 7.6 14.8 12.5 12.93 0.43 12.88 0.38 0.91

1.48 9.9 21.7 20.7 7.6 18.4 17.6 16.02 1.58 15.63 1.97 0.91

1.48 10.2 25.5 23.5 7.2 20.4 18.3 18.37 0.07 18.36 0.06 0.91

2.22 9.0 11.8 10.7 7.5 9.5 8.6 8.86 0.26 8.70 0.10 0.91

2.22 9.0 15.2 13.5 7.8 11.4 9.8 10.38 0.58 10.60 0.80 0.91

2.22 9.3 17.5 16.6 7.9 14.1 12.4 12.47 0.07 12.74 0.34 0.91

2.22 9.5 21.7 20.7 8.3 17.5 17.0 15.51 1.49 15.64 1.36 0.91

2.22 9.9 25.5 23.5 7.8 19.7 17.9 17.54 0.36 17.47 0.43 0.91

2.96 8.7 11.8 10.7 7.6 9.2 8.4 8.80 0.4 8.50 0.10 0.91

2.96 8.8 15.2 13.5 8.0 11.0 9.7 10.29 0.59 10.33 0.63 0.91

2.96 9.0 17.5 16.6 8.1 13.8 12.4 12.18 0.22 12.42 0.02 0.91

2.96 9.0 21.7 20.7 9.4 16.8 16.4 15.55 0.85 15.94 0.46 0.91

2.96 9.3 25.5 23.5 8.9 18.6 17.5 17.37 0.13 17.84 0.34 0.91

3.70 8.5 11.8 10.7 7.8 9.0 8.5 8.84 0.34 8.47 0.03 0.90

3.70 8.3 15.2 13.5 8.5 10.9 9.5 10.45 0.95 10.17 0.67 0.90

3.70 8.4 17.5 16.6 8.7 12.8 12.9 12.26 0.64 13.09 0.19 0.90

3.70 8.5 21.7 20.7 11.1 16.1 16.5 16.16 0.34 16.90 0.40 0.91

3.70 9.0 25.5 23.5 10.2 17.8 17.6 17.63 0.03 18.43 0.83 0.91

4.44 8.5 11.8 10.7 8.2 9.0 8.8 9.05 0.25 9.21 0.41 0.90

4.44 8.0 15.2 13.5 8.9 10.5 9.6 10.60 1.00 10.29 0.69 0.90

4.44 7.9 17.5 16.6 9.8 13.0 13.0 12.74 0.26 13.27 0.27 0.90

4.44 8.1 21.7 20.7 12.0 15.6 16.8 16.40 0.40 17.28 0.48 0.90

4.44 8.6 25.5 23.5 12.2 17.6 17.8 18.39 0.59 18.13 0.33 0.90

a The experimental values by Tan and Deng (2002).

b The calculated values by Tan for the RUCT water outlet

temperature.

c The calculated values by improved model for the RUCT water

outlet temperature.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3428

evaporation of water at water temperature are related to

temperature as well as pressure, leading to difficulty in three

dimensions regression. However, generally pressure of the

tower is 101.325 kPa, which makes the usage of two dimen-

sions regress feasible. Two regression equations related to us,

rw and Tw, obtained by Matlab software at the pressure of

101.325 kPa and thewater temperature between 0 �C and 60 �C,

are as follows

ui;js ¼

h0:0144

�Ti;jw

�4�0:7461

�Ti;jw

�3þ33:6887

�Ti;jw

�2þ50:0495 Ti;j

w

þ 4266:8615i� 10�3 ð23Þ

ri;jw ¼h� 2:377

�Ti;jw

�þ 2500:6737

i� 103 (24)

The accuracy of the results obtained from regression

formulas is evaluated through comparison between the

calculated values and the standard values in ASHRAE

Handbook (2009a, 2009b). Therein, the results of us obtained

from equation (23) yield a correlation coefficient (r) of 0.9999,

an absolute fraction of variance (R2) of 0.9999 and a Root Mean

Square Error (RMSE) of 0.23 g kg�1 with the standard values

(ASHRAE Handbook, 2009a). And an r of 0.9999, a R2 of 0.9999

and an RMSE of 0.34 kJ kg�1 are revealed between rw obtained

from equation (24) and the standard values (ASHRAE

Handbook, 2009b).

Combining equations (19)e(24) gives

miþ1;jw ¼ mi;j

w þ hm

�ui;j

a � ui;js

�Ai;j (25)

uiþ1;ja ¼ ui;j

a þ hm

mda

�ui;j

a � ui;js

�Ai;j (26)

Tiþ1;ja ¼

�cdaþcvu

i;ja

�mdaT

i;ja þcvmda

�u

iþ1;ja �u

i;ja

�Ti;jwþhc

�Ti;ja �Ti;j

w

�Ai;j

�cdaþcvu

iþ1;ja

�mda

(27)

Tiþ1;jw ¼ Ti;j

w þhc

�Ti;ja � Ti;j

w

�Ai;j þ ri;jw

�miþ1;j

w �mi;jw

�

cwmi;jw

(28)

Equations (25)e(28) are iteratively solved from top to bottomof

the counterflow RUCT.

3. Model validation

To validate the proposed model, the outputs of the improved

model are compared with model provided by Tan and Deng

(2002). The experimental parameters of the RUCT are given

as follows:

Table 1 lists the calculated value of water outlet tempera-

tures (Tw,ob ) by Tan and (Tw,o

c ) by improved model at various

chilled water flow rates under five different inlet air temper-

atures. Furthermore, Table 1 also lists the measured water

outlet temperatures (Tw,oa ) from the field experimental work on

the RUCT by Tan and Deng (2002). Results of Lewis number

ðLe ¼ hc=ðhm,cdaÞÞ are also presented in Table 1, in order to

demonstrate the improvement of accuracy with the analytical

procedure presented in this paper implemented. The results

reveal that Lewis number varies from 0.90 to 0.91.

The accuracy of the model was evaluated based on the

regression analysis between the calculated values and the

experimental values. Figs. 3 and 4 present the comparison

between the experimental values and calculated values by

twomodels respectively. In order to depict the accuracy of the

models, Figs. 3 and 4 are provided with a straight line indi-

cating perfect prediction and a �5% error band. As shown in

Fig. 3, the calculated water outlet temperatures by Tan yield

an r of 0.9885, a R2 of 0.9772, and an RMSE of 0.53 �C with the

experimental data. Comparison of the RUCT water outlet

temperatures by proposed model with experimental data is

showed in Fig. 4. For this parameter, the improved model

yields an r of 0.9862, a R2 of 0.9726 and an RMSE of 0.60 �C with

the experimental data. According to the Figs. 3 and 4, the

results of two models are almost the same.

However, the accuracy of current model is slightly lower

than that of the model proposed by Tan and Deng (2003). In

order to simplify the calculation of the current model, it

assumes that water side heat transfer resistance in the RUCT

can be neglected and the watereair interface temperature is

approximately equal to water temperature. Therefore, the

enthalpy of saturated air at interface is evaluated at water

temperature. However, in the model proposed by Tan and

Fig. 3 e The calculated values by Tan for the RUCT water

outlet temperature vs. the experimental values.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3 429

Deng (2003), the water side heat transfer resistance is signifi-

cant and cannot be neglected. The hypothesis is proposed that

the interface temperature is an algebraic average of the bulk

air temperature and the bulk water temperature. The slight

discrepancy should be due to the application of different

integration techniques, the governing differential equations

of the counterflow RUCT are discretized by finite difference

method in this research. Another source of discrepancy may

be different functions representing temperature dependence

Fig. 4 e The improved model calculated values for the

RUCT water outlet temperature vs. the experimental

values.

of specific heats and saturation pressure. However, presented

validation of heat and mass transfer model conducted on the

entire counterflow RUCT analysis show good agreement

between data obtained with the model proposed by Tan and

Deng (2003) and the proposed approach. This confirms that

the proposed approach is properly implemented and equiva-

lent to the Tan and Deng (2003) analysis and can also predict

the performance of the RUCT very well.

In summary, the advantages of the proposed model are

simple, flexible, relative accurate, and easy for engineering

applications.

4. Results and discussion

4.1. Performance characteristics of the counterflowRUCT

Heat absorption capacity and heating efficiency of the RUCT

are adopted to describe the heat and mass transfer perfor-

mance (Wu et al., 2011b). In a counterflow RUCT analysis, the

heat transfer rate obtained by Merkel approach isQ ¼ mwcp;w

�Tw;o � Tw;i

�(29)

where the effect of the change in chilled water mass flow rate

is not considered in the energy balance. If the air is super-

saturated inside the counterflow RUCT, then the mass flow

rate of the condensated water could be determined by the

following equation

mv ¼ mda

�ua;i � ua;o

�(30)

where ua,i and ua,o represent the specific humidity of air at the

entry and the exit of the RUCT.

However, another equation for the heat absorption

capacity, according to the Merkel approach, in which the

water gain, due to condensation, is considered in the energy

equation

Q ¼ mwcp;w�Tw;o � Tw;i

�þmvcpwTw;o (31)

The heating efficiency (h) of the counterflow RUCT, is the ratio

of the actual water temperature variance of the water passing

through the counterflow RUCT to its variation under ideal

conditions, which is

h ¼ Tw;o � Tw;i

Twb;i � Tw;i(32)

where Tw,i and Tw,o are the inlet and outlet water temperature

respectively, Twb,i is the wet bulb temperature of the inlet air

stream, which is also the heating limit of circulating water.

4.2. Detailed numerical analysis within the counterflowRUCT

The proposed analytical model can be used to determine the

water and air states at any intermediate horizontal sections

along the tower height within the counterflow RUCT.

The boundary conditions at the bottom of the RUCT (Z¼H )

are the air inlet temperature (Ta,i ¼ 17.5 �C), inlet humidity

ratio (ua,i ¼ 11.4 gw kgda�1) and the air inlet mass flow rate

(ma,i ¼ 9.0 kg s�1) (Tan and Deng, 2003). The boundary

Fig. 5 e Air and water temperature distributions in the fill. Fig. 7 e Water mass flow rate distribution in the fill.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3430

conditions at the top of the RUCT (Z ¼ 0) are the inlet water

temperature (Tw,i ¼ 8.1 �C), and the water inlet mass flow rate

(mw,i¼ 2.96 kg s�1) (Tan andDeng, 2003). The RUCT volume can

be divided randomly. 10 to 20 sections will suffice for the

required accuracy of the calculation results (Ismail and

Mahmoud, 1994; Tan and Deng, 2003). In this study, the

RUCT fill height was equally divided into 10 portions. The

results of the analysis are graphically plotted versus the RUCT

height and shown in Figs. 5e7.

As can be seen from Fig. 5, the temperature of air flowing

upwards steadily decreases to the top, and the temperature of

water increases continuously as it flows downwards to the

bottom so that the heating process continues. Fig. 6 shows the

humidity ratio distributions. The humidity ratio of air flowing

upwards also steadily decreases to the top. The distribution of

the mass flow rate of the water is plotted in Fig. 7, which

increases from the top of the fill to bottom. Since the water

vapor partial pressure at the interface between the air and the

water is lower than the water vapor partial pressure in the air,

there is a transfer of water vapor into the water. This mass

transfer brings a heat transfer related to the condensation,

Fig. 6 e Distribution of air humidity ratio in the fill.

which is called transfer of latent heat. At the same time,

because of the difference in temperature between surface of

the water and the air, there is transfer of heat by convection.

4.3. Effect of inlet parameters on the performance

The proposed analytical model of the heat and mass transfer

process in the RUCTwas verified by applying the experimental

data of Tan (Tan, 2000; Tan and Deng, 2002). The comparison

of the results obtained by proposed method and by Tan

showed very good agreement in the validation computations.

Therefore, the proposed model can be used to predict the

properties of the water outlet temperature, water mass flow

rate change and heating efficiency of the counterflow RUCT

for given design and operating conditions.

The performance of a counterflow RUCT will change with

environmental conditions, which will affect the water outlet

temperature. Investigation of the thermal behavior of the

RUCT at different environmental conditions allows the

prediction of its performance at different atmospheric

conditions. Fig. 8 shows the effect of the air inlet wet bulb

Fig. 8 e Effect of air inlet wet bulb temperature on water

outlet temperature at different watereair flow rate ratios.

Fig. 9 e Effect of air inlet wet bulb temperature on heating

efficiency at different watereair flow rate ratios.

i n t e rn a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3 431

temperature on water outlet temperature at different water-

eair flow rate ratios. Fig. 9 is a plot between heating efficiency

(h) and air inlet wet bulb temperature, for different values of

themass flow rate ratio (mw/ma). Fig. 10 shows the effect of the

air inlet wet bulb temperature on water mass flow rate at

different watereair flow rate ratios. These plots are generated

based on the following input data: Patm ¼ 101.325 kPa;

Tw,i ¼ 7 �C; Ta,i ¼ 20 �C; ma ¼ 8 kg s�1.

As shown in Fig. 8, when the air inlet wet bulb temperature

is 10 �C and mw/ma ¼ 1.5, the RUCT can supply water at

a temperature of 7.73 �C. With an increase of 10 �C in the air

inlet wet bulb temperature (20 �C), the temperature of

the water from the tower increases to 9.70 �C. However, for

mw/ma ¼ 0.5, when the air inlet wet bulb temperature is 10 �C,the supply water temperature is 8.92 �C, then with an increase

of 10 �C in the air inlet wet bulb temperature (20 �C), the water

outlet temperature increases to 13.92 �C. It is obvious that the

water outlet temperature increases as the air inlet wet bulb

temperature increases at different watereair flow rate ratios.

Futhermore, Fig. 8 implies that the changes in watereair flow

Fig. 10 e Effect of air inlet wet bulb temperature on water

mass flow rate at different watereair flow rate ratios.

rate ratio has relatively more effect on water outlet tempera-

ture compared to changes in the air inlet wet bulb tempera-

ture for the same RUCT.

The variation of heating efficiency of the RUCT is shown in

Fig. 9 for the above input simulated data. This figure shows

thatwhen thewatereair flow rate ratio reduces from1.5 to 0.5,

the heating efficiency of the RUCT increases obviously.

However when the watereair flow rate ratio remains

unchanged, the variations of the air inlet wet bulb tempera-

ture have little influence on the value of heating efficiency. On

the other hand, in contrast to the water outlet temperature as

shown in Fig. 8, the changes in watereair flow rate ratio also

have relatively more effect on heating efficiency compared to

changes in the air inlet wet bulb temperature for the same

RUCT.

Fig. 10 offers the opportunity to understand the change of

inlet and outlet of water mass flow rate. At the air inlet of the

RUCT, the incoming moist air meets chilled water from

evaporator. Depending on the dew point temperature of the

entering moist air, it may experience two different processes

in the RUCT (Aya and Nariai, 1991; Celata et al., 1991; Ibrahim

et al., 1995; Lekic and Ford, 1980; Li et al., 2006; Shah et al.,

2010; Song et al., 2009). Basically, the heat and mass transfer

between the moist air and the chilled water in an RUCT

depends on the temperature difference of the two fluids and

the vapor partial pressure difference between the water

surface and the moist air.

As shown in Fig. 10, the RUCT inlet water temperature

remains constant (7 �C) and the air inlet dry-bulb temperature

remains constant (20 �C), the values of the air inlet wet bulb

temperature vary from 20 to 10 �C. Fig. 10 shows that when

mw/ma ¼ 0.5 and mw/ma ¼ 1.5, the increase in the quantity of

condensedwater are 0.027 and 0.032 kg s�1, respectively, given

the air inlet wet bulb temperature is 20 �C. The quantity of

condensed water increases as the mass flow rate ratio

increases.

As the air inlet wet bulb temperature decrease, the reduc-

tion in condensed water quantity is close to zero. This is

reasonable because the temperature of inlet water is close to

dew point temperature of the entering moist air. As the wet

Fig. 11 e Effect of watereair flow rate ratio on heat

absorption capacity at different water inlet temperature.

Fig. 12 e Effect of watereair flow rate ratio on heating

efficiency at different water inlet temperature.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 5 ( 2 0 1 2 ) 4 2 4e4 3 3432

bulb temperature of inlet air continually decreases, the water

loss continues due to water evaporation. As explained above,

the water vapor condensation in the RUCT occurs when the

inlet water temperature is lower than the air dew point

temperature; otherwise, the evaporation of water occurs.

The heat absorption capacity of the counterflow RUCT

versus watereair flow rate ratios at different water inlet

temperatures is shown in Fig. 11. These plots are generated

based on the following data: Patm ¼ 101.325 kPa; Ta,i ¼ 20 �C;Twb,i ¼ 18 �C; ma ¼ 8 kg s�1. In this case, it demonstrates that

when the watereair flow rate ratio is 0.5, the heat absorption

accomplished by the RUCT is 127.36 kW at a water inlet

temperature of 3 �C, and the heat absorption is 54.60 kW for

a water inlet temperature of 12 �C at the same watereair flow

rate ratio. In conclusion, the rate of heat absorption capacity

continues to decrease at higher water inlet temperatures. In

other words, when the inlet chilled water has a low temper-

ature and relative highwatereair flow rate ratio, the RUCT can

absorb more heat from the air.

Fig. 12 shows the performance of RUCT in terms of heat

absorption efficiency and watereair flow rate ratios at

different water inlet temperatures. The input data used in this

figure is the same as that in Fig. 11. A high degree of the RUCT

effectiveness corresponds to a better heating performance

and higher heat absorption. It can be seen in Fig. 12 that when

the inlet chilled water has a low temperature and high

watereair flow rate ratio, the value of heating efficiency

decreases rapidly.

5. Conclusions

Based on the findings of this work the following conclusions

can be drawn:

1. A more realistic detail mathematical model based on heat

and mass transfer characteristics is found to be practically

applicable to a reversibly used mechanical draft cooling

tower under counterflow conditions for the steady-state

operation. In this model, we have considered the effects

of the airewater interface temperature, the water vapor

condensation, the variation of water mass flow rate along

the vertical length of the RUCT and the non-unity of the

Lewis number.

2. The proposed heat and mass transfer model of RUCT was

validated with the experimental data reported by Tan and

Deng (2002). Furthermore, the comparison between the

results by the proposedmodel and by Tan showed very good

agreement in the validation computations. Furthermore, the

model alsoaccommodates thedirect andquick calculationof

air and water temperature profiles, moisture content of air

and thewatermassflowrate changealong thevertical length

of the RUCT. It can be concluded that themodel developed in

this work can provide a theoretical foundation for practical

design and performance evaluation of counterflow RUCT.

3. When the temperatures of the entering chilled water and

the air dry-bulb are constant, the water outlet temperature

and heating efficiency of the RUCT aremainly controlled by

the mass rate ratio of water and air along with the air inlet

wet bulb temperature. The changes in watereair flow rate

ratio has relatively significant effect on water outlet

temperature and heating efficiency compared to changes in

the air inlet wet bulb temperature. When the temperatures

of the entering air dry-bulb and wet bulb are constant, the

heat absorption capacity and heating efficiency of the RUCT

are mainly controlled by the temperature of the entering

chilled water and the watereair flow rate ratio. With low

temperature inlet water and relative high watereair flow

rate ratio, the RUCT can absorb more heat from the air,

while the heating efficiency decreases.

Acknowledgements

The research reported herein has been carried out with the

help of the National Key Technologies R&D Program of China

during the 11th Five-year Plan Period (No. 2006BAJ04A13) and

Research Project from Guangdong Province (No.

2010B090400301). Besides, we are grateful to Prof. Deng

Shiming and Dr. Tan Kunxiong of Hong Kong Polytechnic

University for their helpful experimental results and sugges-

tions in the mathematical model elaboration, and Dr. Ding Jie

of Texas Tech University for his advice on language expres-

sion. These supports are gratefully acknowledged.

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