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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
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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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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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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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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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[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).
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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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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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Figure (13 ) Comparison of evaporation losses for model 1and 3.
Figure (12) working state at partial load for model 3.
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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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Figure (16) Effect of wet part on cooling water temperature
for models 1 and 3.