Mathematical Modeling of Hybrid Cooling Tower

8/12/2019 Mathematical Modeling of Hybrid Cooling Tower

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No.20,2012Vol.30,Eng. & Tech. J ournal,

3616

Mathematical Modeling of Hybrid Cooling Tower for

Steam Power Plant

Dr. Hashim A.Hussain

Electromechanical Engineering Department,Univercity of Technology/ Bagdad

Email:[email protected]

Received on:5/6/2012 & Accepted on:4/10/2012

ABSTRACTAn economical and environmental requirements of hybrid cooling tower in

steam power plant are represented by decreasing of outlet water temperature,reducing of water and energy consumption, and working without mist formation.

The present work is devoted to study and determine the best contact method of dryand wet tower to build hybrid cooling tower.A three suggested models differs in

contacting method of air and water are studied. Analysis of these models aredependent on the basic principles of thermodynamics ,mass and heat transfer withconsidering of initial and boundary conditions. The best model must be givingaccepted values in economical and environmental requirements. A Computer

program by Matlab is used for solving the governing equations and determining thesuitable mathematical model. The results are indicated that the third model (air in

series and water in parallel) is the best in contacting method which satisfied the

economic and environment requirements .The results are recorded and represented

by graphs.

Keywords: Cooling Towers, Steam Power Plants, Energy.

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Mathematical Modeling of Hybrid CoolingNo.20,2012,Eng. & Tech. J ournal, Vol.30

Tower for Steam Power Plant

3617

List of symbols

UnitsDescriptionSymbol

)( 2msurface area of heat exchangeA

)( 2msurface area of heat transferA

)( 2msurface area of mass transferA

)./( KkgkJheat capacity of dry airpa

C

)./( KkgkJ

heat capacity of vaporPVC

)./( KkgkJ

heat capacity of waterwC

)/( kgkJ

specific enthalpyh

)/( kgkJ

difference enthalpy evaporationvh

)./( 2 KmWtotal heat coefficientK

-Vapor numberVK

-ratio of air mass flow rate of dry

toweramamaL W

./&=

-ratio of water mass flow rate of wet

towerwmwmL WW

&& /=

-ratio of air to wateroL

)/( skgtotal mass flow rate of airam&

)/( skgtotal mass flow rate of waterwm&

)/( skgmass flow rate of water

evaporationwvm&

-Coefficient n ( partial load)noCtemperature of wet airmt

)( aPpressureP

)( 3mvolumeV

)(3

mvolume of heat transfer by

convectionV

)( 3mvolume of mass transfer by

evaporationV

)/( kggair humidityaX

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Greek symbol

Abbreviations

INTRODUCTIONhe theory of cooling water coming from condensation process, i.e.incoming or outgoing from the condenser is based on exposing to air or

more accurately exposing the surface of water to the air only. This

process would cool the air, however, slowly, and this is similar to thecooling of water available on the pool and swamps surfaces. There is a faster

way made by spraying water in the air. Both ways include exposing the water

-Cooling tower efficiency+

-Condenser efficiencyc

)./( 2 KmWheat transfer coefficient by

convection

)/( smrate of mass transfer

)/( smcoefficient of mass transfero(%)humidity ratio

DefinitionSymbolDry cooling towerDCT

Hybrid cooling towerHCT

Wet cooling towerWCT

inlet water temperature to dry tower1wDt

inlet air temperature to dry tower1Dat

mass of air to dry tower1Dam&

mass of air to wet tower1Wam&

air humidity at entrance of dry tower1DaXair humidity coefficient at entrance of wet

tower1WaX

outlet water temperature to dry tower2wDt

outlet air temperature to dry tower2Dat

outlet water temperature to wet tower2wWt

T



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surface to air[1].Cooling towers are used with condensers cooled by water to

decrease the temperature of the water used as a medium of condensation when

it acquires the thermal power lost from the condenser. Pump the hot wateroutgoing from the condenser to enter to the cooling tower from the upside,

then distributed equally in drops form, and it contacts the air incoming to the

tower as shown in the figure (1). Cooling process is performed inside thetower as a result of evaporating a portion of water while contacting the air heat

transfer by load process, carrying the steam ejected to outside the tower, andthus leads to high air humidity. In addition to that, a portion of the sensed heattransfers from air to air, and therefore, the temperature of the air outgoing

from the tower increases. The efficiency of the cooling tower depends

significantly on the humid temperature of the air incoming to the tower, and

whenever the temperature of the wet air while coming inside is low, theefficiency of the tower will be increased. [2,3]. The average of the heattransfer in the tower depends on the degree of the wet temperature of the

incoming air. Reasons of using the cooling towers: in huge cooling andcondensation units, such as the power stations and central air conditioning,

where it is necessary to have huge amounts of water to cool the cooling liquid.

If the temperature of the water coming inside the condenser is relatively high,

then we need huge amount of water whether the cooling unit is medium orlarge. The efficiency of the cooling tower depends on the following: the wet

temperature of the air while coming inside the tower, the area of the water

surface exposed to air, period of exposure and the speed of air flow in thetower and the direction of the air flow compared to the falling water (parallel ,

contrast or crossing) [4] .The wet type is more common in large cooling

towers, such as in electrical power generation. It is a direct contact heatexchanger, in which hot water from the condenser and cooling air come into

direct contact. The water flows in either open circuit or closed circuit. In open

circuit, cooling water is pumped into a system of pipes, nozzles, and sprayerswithin the tower. Air from the atmosphere enters the tower from the bottom ofthe tower and flows upward through the falling water [5]. The water is

collected at the bottom of the tower and then re circulated to remove more heatfrom the condenser. The temperature of the cold water entering the condenserwill determine the steam condensate temperature and, hence, the backpressure,

which impacts the efficiency of the whole power generation system [6].

The mist is considered as a basic factor in the wet cooling tower as a resultof evaporating low rate of water while cooling, and this leads to form mist.

This has the following negative impacts: complaints and protests from the

local residence. It creates corrosion and ice in the adjacent areas. Problemsappear in the adjacent areas from traffic roads (roads and railways) in case ofhuge cooling towers [7]. Figure (3) illustrates the thermal representation of

the psychometric drawing of the hybrid tower as shown in the figure (2).The external air enters to the wet portion represented at point 1. Air comes

out from the wet portion at point 2 upon cooling water. We notice mist

formation (outside saturation curve) . Hot air leaves the dry portion of thethermal exchanger at point 3 after cooling water at fixed humidity level, and

then mixes with air outgoing from the wet portion. Mixed air currents leave



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from the dry and wet parts represented at the point 4 outside the tower. We

notice that the mixing line (1-4) (resulted from mixing the surrounding air with

the ejection air) if not crossed with the saturation curve (humidity = 100%)then there will not be condensed outgoing water, and therefore, not mist will

appear [9,10].

Mathematical model of the hybrid cooling tower (HCT)This model consists of three elements:-

Mathematical model for wet cooling tower operation (WCT)Mathematical model for dry cooling tower operation (DCT).Determination of xa2, ta2, tw2 when coming out from the tower, i.e. two

temperatures when water and air currents are outgoing with the humidity

content of the air upon leaving (xa2).

In order to facilitate the calculations of the hybrid cooling tower, take intoconsideration the following : the tower is considered as adiabatic system withthe surrounding atmosphere, in case of steady state of the tower related ,

distribute regularly air and water amounts to the tower profile surface .Mathematical model of wet cooling tower (WCT)

The mathematical model of the wet cooling tower operation shall be studied

according to Merkal relations [3]. The wet tower effectiveness might be

expressed as : -

In order to determine the evaporation number Kv, we may start from thethermodynamic basic of heat and mass transfer and to equalize water and air

state . Figure (4) explains the cycle of air and water in cooling tower for steam

power plant.From equations of water equilibrium and energy balance[3] :-

wdm

adX.

am = .(2)

wmdwh

wdh

wh

wdhwma

dha

m.

.....

. ++=

.(3)

dA

aX

gXwmd )(

.=

.(4)

dA

aX

gXdQ )( =

.(5)

dHdQadham += &

.(6)

wmd.

vghd &=

.(7)

)11

/()21

(m

tw

tw

tw

tc

= (1)



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wmdwhwmdvghdQ && +=

.(8)

wmd

wh

vghdQ &)( +=

.(9)

dA

wh

vgh

aX

gXdA

at

gt

wdh

wm )).(()(. +=&

.(10)

=

Wm

dA

vK

&

.

.(11)

AAA ==

.(12)

))(()(w

hvg

ha

Xg

Xa

tg

t

wdh

wm

dA

+=

&

.(13)

+

=)()(.

.

wh

vgh

at

gt

paC

paC

wdt

wC

vK

pac

Z

=

)

wgagwgagag

pa

ag

wv

hXXhXXhh

chh

dhK

++= )()))(((

1.

)1.

()(

.(14)

(15)

(16)

==

ah

gh

wdh

wm

dA

vK

&

. .(17)

Mathematical model of dry cooling tower (DCT)

The model of the dry cooling tower operation shall be studied according tonature of flow heat exchange. The dry tower effectiveness might be expressed

as per the following relations [13,14]:



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The dry and wet tower contacting depends on type of hybrid cooling tower andon the calculation of the main parameters and according to basic of physics,

mathematical relations and boundary conditions[15,16,17] .

Dry part calculation

a-saturation state

11

21

atwt

wt

wt

=

(18)

(19)

(20)

(21)

.(22)

b- without saturation )(22 aDsaD

tXX

(23)

))}.

.exp(1).exp((1{

.

.

wC

wm

AK

paC

am

wC

wm

wC

wm

paC

am

&&

&

&

&

=

)).

.1)(

.exp((

.

.1

)).

.1).(exp((1

paC

am

wC

wm

wC

wm

AK

paC

am

wC

wm

paC

am

wC

wm

wC

wm

KA

&

&

&&

&

&

&

&

=

)

).

exp(1

.

).

exp(1

.

/(.

.

paC

am

AK

paC

am

AK

wC

wm

AKw

Cw

mAK

wC

wm

AK

&

&

&

&

&

+

=

)( 22 aDsaD tXX

2)2(2

2)2(22

..))(

)..((.

aDwtaDsaD

VaDPVtaDsaDpaaD

tCXX

htCXtCh

++=

)..(. 2222 VaDPVaDaDpaaD htCXtCh ++=

222 .)1(. aDaaawaaaa hmLXmLXm &&& +=



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Wet part calculation

(26)

Suggested models

There are several methods for contacting of air and water flow . In this workwe shall test three models to find the best that give the economical andenvironmental requirements. Figure (5) explains the schematic diagram of

hybrid cooling tower contact with thermal station

Boundary conditions of suggested models

aaa

wWwwwWw

aaaaaa

aaaaaa

wwwwww

www

mmm

mLmmmLm

XXXXXX

tttttt

mttmtt

ttt

WD

DDW

WDDW

DWDW

WWDD

DW

&&&

&&&&&

&&

==

===

====

====

==

11

21

21

22

1

)1(,.

,

,,

),,,(

211

2121

2211

2212

11

222 .)1(. aDaaawaaaDa hmLhmLhm &&& +=)( 1221 aaawwww XXmmmmm v === &&&&&

aaaaaa

Wwww

aaaaa

aaaa

aaaaaaa

aaa

wwwww

mLmmLm

mmmm

LXXXX

XXXX

XXttLtt

ttt

tttttt

DW

DDW

W

DDW

WDW

WD

WwDWD

&&&&

&&&&

)1(,.

,

),,(

),,,,(

,,

1

122

1

122

1

121

2

211

222

11

222111

==

===

===

=

==

===

Model 1

aaa

wwww

aWaDaaa

aaaaaaW

wwwww

mmm

mmmm

XXXXXX

tttttt

tttttt

WD

DDW

DaW

DwD

WDwWD

&&&

&&&&

==

==

====

===

===

1

221

211

21

121

211

211

2211

,

,

,,,,

Model 2

Model 3

skgmw /83=& ,oCt

w50

1 =

,

Working conditions



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3624

Computer program

The governing equations are solved by Mat lab language which is used the

psychometric diagram with applied the boundary and working conditions.Figure (9) shows the flow chart of a computer program steps of solution:

RESULTS AND DISCUSSIONFigure (10) explain the outlet temperature tw2 as function of Xa2 . It shows

a comparison of tw2 for models 1, 2 and 3, the model 3 is the best modelbecause it gives a lower water outlet temperature tw2 than others modelsTables (1) and (2) show the comparison of thermal parameters between

model 1 and model 3.Model 1 gives outlet water temperature tw2=36.5 at Xa2

=19.292 while for model 3 at Xa2= 19.292 gives tw2= 35.55 . Table (3)

shows the results of model 3 which are ,outlet water temperature, evaporationlosses and evaporation rate at different air humidity. From the abovecomparison, we take model 3 is the best, because tw2 is a lower, so that model

3 has to studied in deep since it is shown to be the best in achieving of aneconomical and environmental requirements .

Figure (11) shows the working state for model 3 parameter load n = ( 0.4 -

0.8) . There is no effect of n on the outlet water temperature when Lw = 1,

but there is an effect at small value of LwFigure (12) represents the effect of partial load state for wet tower on

cooling water temperature and evaporation rate for model 1. Also there is no

effect at La=1. The comparison at the same conditions between curves ofmodels 1and 3, show that model 3 give best working conditions than model 1

according to cooling water temperature as shown in figures (11and12)

Figure (13) represents the evaporation losses for model 1and 2 .Model 1 giveevaporation losses lower than model 3 when water temperatures are equal

and tw2 increase slowly at decreases La Figures (14 and 15) represent a

comparison of evaporation losses rate for model 3 with different temperaturesta1=25 C and ta1=30C ,it is notice that, the evaporation losses rate not exceeds1.67% which equal to evaporation losses rate for model 1 The effects of partial

load parameter for wet tower on outlet water temperature are given through theindex (n) by following relation [12] :-

(27)Table (4) shows the effect of Kv on outlet water temperature for wet tower

to comparison with dry tower so that, It can be seen that tw2 decreased at Kv

increasing ( Kv = 0.36 leads to tw2 =45 C while when Kv =2.0 , tw2 = 25 C).Figure(16) explain the comparison results of model 3 and 1 with increasingof Kv, while leads to tw2 always lower for model 3 than model 1. Model 3

is better since tw2 more decreasing with increasing of kv than for model 1.This produce high effectives for model 3 than model 1 .

7.0,20 11 == oCta ) 11 ,at

nG

oo

G

VV llKK )/(=



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3625

Table (1) results of model 1 of thermal parameters

)(

2

akg

wg

aX

)

2

( oC

at

)

2

( oC

wt

)/(

2

skg

XaW

)(

2

oC

taW

)

2

( oC

aDt

)(

2

oC

wDt

aL

19.29239.4236.539.235.904344.50.30

25.53538.2131.3034.4333.5347.4046.200.60

27.51136.2030.1733.4633.1948.7147.230.70

28.35534.6229.3332.66232.5649.6348.220.80

29.24933.5328.5632.73432.4549.9448.520.90

30.19632.4927.7232.29032.6650.0049.320.95

31.34531.8227.9532.02932.1250.0049.550.95

Table (2) results of model 3 of thermal parameters( 11

,at )

7.0,20 11 == oCta

)/( skg

wvm&

)(

2

akg

wg

aX

)

2

( oC

at

)

2

( oC

wt

)

2

( oC

wWt

)

2

( oC

aDt

)(

2

oC

wDt

wL

4.01819.29239.0335.5518.5524.3342.140.30

6.65525.59638.5230.0723.1827.8639.620.60

7.56727.37637.8428.5524.4329.8637.770.70

8.45328.36036.5528.2525.3930.7635.780.80

8.61529.72935.5327.7726.3330.8934.540.90

9.05830.47134.1027.4726.5531.2933.160.95

9.25231.16632.2327.2127.3331.6832.560.95



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Table (3) results of model 3 outlet water temperature, evaporation lossesand evaporation rate.

4.0,20 11 == oCta

0.1,20 11 == oCta

)(

2

akg

wg

aX

)(

2

oC

at

)(

2

oC

wt

)/(

2

skg

XaW

)(

2

oC

taW

)

2

( oC

aDt

)(

2

oC

wDt

aL

26.51638.1333.2238.15034.8845.6644.91050.

28.68337.1632.0137.48434.2046.9845.910.60

30.35235.8131.0736.42433.8548.3846.550.70

32.23134.3430.3035.66933.5849.6647.760.80

32.56933.4329.9135.33833.4449.9448.230.90

33.10932.8829.5535.13433.3750.0048.990.95

34.15233.3429.2434.65633.1850.0049.550.95

)(

2

akg

wg

aX

)(

2

oC

at

)

2

( oC

wt

)/(

2

skg

XaW

)(

2

oC

taW

)

2

( oC

aDt

)(

2

oC

wDt

aL

20.49338.6431.3533.11633.4045.7445.57050.

22.49837.6329.6932.01732.3347.4346.160.60

24.41236.2028.6231.02932.1749.5546.900.70

26.39234.6327.7730.19431.6649.7747.990.80

26.79033.3226.9529.89431.2049.9548.550.90

27.65432.2526.6929.63031.0450.0048.990.95

28.21731.1626.1329.49330.8151.0049.440.95



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0.1,30 11 ==

o

Cta

2.0,30 11 == oCta

0.1,25 11 == oCta

%W

W

m

mV

&

&

)/( skg

Vwm&

)(

2

oC

wtW

L

0.862.59043.000.70

0.932.8042.800.80

0.972.9042.600.85

1.003.2741.901.00

%W

W

m

mV

&

&

)/( skg

Vwm&

)(

2

oC

wtW

L

1.405.70037.000.70

2.006.70036.100.80

2.216.27235.500.85

2.427.26034.101.00

%W

W

m

mV

&

&

)/( skg

Vwm&

)(

2

oC

wt

WL

0.852.55036.000.30

0.892.64035.800.40

0.912.73035.700.50

0.952.95035.400.60

1.003.02035.100.70

1.063.18934.800.801.113.33034.400.85

1.153.47034.200.90

1.23.60033.900.95

1.263.75033.601.00



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3628

7.0,25 11 == oCta

Table (4) calculated wet part parameters to comparison.

CONCLUSIONSResults of this study indicated that, the contacting method of air in series

and water in parallel for hybrid cooling tower give outlet water temperature

lower than others of contacting methods, this leads to choose model 3 is the

best model, since it satisfied the ecumenical and environmental requirements.Also the contact of air in series and water in parallel for hybrid cooling tower

decreased the energy consumption ( low of co2 gases) and working conditions

without mist formation. So that we can know there is mist or not bydetermination of this is a very important requirement in steam power plant.

There is no effect of the partial load coefficient (n) on the outlet water

temperature when Lw = 1, but there is an effect at small value of Lw . Finally,there is no effect of ( n) in state of working wet cooling tower.

.REFRENCES[1] . ASHRAE Handbook-Fundamentals (SI), 2005.[2]. Bosnjakovic, F. Technische Thermodynamik Verlag Steinkopff, Dreden

1965.[3]. Merkel, F. Verdunstungsk ,VDI-Forschungsheft (1929).

%W

W

m

mV

&

&

)/( skg

Vwm&

)(

2

oC

wt

WL

0.631.90837.620.30

0.661.98037.520.40

0.672.0137.380.50

0.722.1637.280.60

0.752.25336.950.70

0.792.3736.820.80

0.812.4436.520.85

0.852.5536.310.90 0.892.6636.130.95

0.942.7935.921.00

G

VKG

oL

octa1octm1

octW2octW1

0.3631.515103545

1.271.315122438

1.8981.520182545

2.0361.022252535



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3629

[4]. Poppe, M. W. rme und Stoffubertragung bei der Verdunstungsk im

Gegen-

[5]. Heat Transfer Fluids and Systems for Process and EnergyApplications,Jasbir Singh,1edition, january,1985.

[6]. M.A.dos S.Bernardes,Technische,konomische und kologische Analyse

von Aufwindkraftwerken, 2004.[7] . Air-Conditioning and Refrigeration Mechanical Engineering

Handbook Ed. Frank Kreith,2008.[8]. MATLAB7 -- simulink toolbox Help, version 7(R14), 2004.

[9]. HVAC Water Chillers and Cooling Towers- Fundamentals, Application,

and Operation, Herbert W. Stanford III. 2007.

[10]. American Society of Heating, Refrigerating and Air-Conditioning

Engineers, Refrigeration Handbook, Atlanta, Georgia,1986.[11] Heat Transfer Text Book Third edition, John H. Lienhard IV / John H

venhard, 2003.

[12] Refrigeration and Air-Conditioning Third edition A. R. Trott and T.Kelley, 2004.

[13] Randall W.Jameson, SPX Cooling Technlogies, 2010.

[14] Paul A.Lindhl,Jr. Plume Abatement and Water Conservation with the

wet/dry Cooling Tower, 2010.[15] http://www.enviromission.com.au .

[16] http://www.cubicekballoons.cz

[17] http://www.science direct.com

Figure (1) Condenser and cooling tower contact in steam power plant

(Didacta- Italia).

http://www.enviromission.com.au/http://www.cubicekballoons.cz/http://www.science/http://www.pdffactory.com/http://www.pdffactory.com/http://www.pdffactory.com/http://www.science/http://www.cubicekballoons.cz/http://www.enviromission.com.au/


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3630

Fi ure 2 H brid coolin tower.

Figure (3) Thermal cycle of hybrid cooling tower on the

psychometric diagram.

Figure (4) The schematic diagram of the cooling tower subsystem for the

steam power plant.



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Figure (5) Schematic diagram of hybrid cooling tower contact with

thermal station.

Figure (7) Model 2 for hybrid cooling tower (air and water in series).

Figure (6) Model 1 for hybrid cooling tower (air in parallel and water in series).



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Figure (8) Model 3 for hybrid cooling tower

(air in series and water in parallel).

Read data

( load the psychometric file to the ram)

Determination of the governing equation

required

Generate an arbitrary transformer

distributed regularly and represents the

changeable to imitate

For each value of the arbitrary transfer,

solve the previous equation and save the

result

Drawing of the required

curve

Figure (9) Shows the flow chart of Solution steps.



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3633

Figure (11 ) working state at partial load for

model 1.

Model 1 (air and water inseries)

Model 2 (air parallel, water

series)

Model

ModelModel

Figure (10) Comparison of outlet water

temperature for models 1, 2 and 3.



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3634

Figure (13 ) Comparison of evaporation losses for model 1and 3.

Figure (12) working state at partial load for model 3.



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3635

Figure (15) outlet water temperature with evaporation rate

atoCt 30= for model 3.

Figure (14 ) Outlet water temperature with evaporation rate

atoCta 251 = for model 3.



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3636

Figure (16) Effect of wet part on cooling water temperature

for models 1 and 3.

Mathematical Modeling of Hybrid Cooling Tower

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