International Journal of Heat and Mass Transfer 53 (2010) 1156–1163

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International Journal of Heat and Mass Transfer

journal homepage: www.elsevier .com/locate / i jhmt

Condensation in a vertical tube bundle passive condenser – Part 2:Complete condensation

Gavin Henderson, Wenzhong Zhou, Shripad T. Revankar *

School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907, USA

a r t i c l e i n f o a b s t r a c t

Article history:Received 26 May 2009Accepted 20 October 2009Available online 28 November 2009

Keywords:Passive condenserTube bundleComplete condensationNon-condensable gasHeat and analogy model

0017-9310/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.ijheatmasstransfer.2009.10.040

* Corresponding author. Tel.: +1 765 496 1782; faxE-mail address: shripad@ecn.purdue.edu (S.T. Reva

An experimental study of the tube bundle effect on heat removal capabilities in complete condensationmode of a passive condenser was performed. A full scale test section, with four condenser tubes, wasdesigned and constructed to simulate operating conditions of a passive containment cooling system.For complete condensation analysis, pure steam was supplied to the test section and heat transfer prop-erties were measured for pressure from 100 to 280 kPa. The condensation heat transfer results were sim-ilar to the findings from single tubes, except for a slightly higher condensate mass flux. This wasdetermined to be a result of turbulent mixing in the secondary boiling water caused by the tube bundle.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Condensation is an important mode of heat transfer that iswidely applicable in the power industry due to its ability to achievehigh heat transfer coefficients. General Electric’s economic simpli-fied boiling water reactor (ESBWR) includes a passive heat exchan-ger to depressurize the containment by condensing steam invertical tubes through a pool of water [1]. This heat exchanger iscalled a passive containment cooling system (PCCS). The PCCS con-denser must provide enough heat removal to keep the pressure inthe containment less than the design pressure after a design basisaccident, such as a loss of coolant accident (LOCA). A detailedknowledge of the PCCS heat transfer capabilities is necessary inpredicting the containment pressure following a design basisaccident.

The PCCS condenser has three modes of operation: throughflow, cyclic venting, and complete condensation mode [2]. Theoperational mode depends on the noncondensable (NC) gas massfraction and the pressure difference between the dry well (DW)and the suppression pool (SP). The pressure difference betweenthe DW and the SP serves as the driving force for the PCCS. Steamand NC gas from the DW pass through the PCCS and the condensedwater is directed back to the gravity driven cooling system (GDCS)pool and then to the reactor pressure vessel (RPV). Uncondensedsteam and NC gas from the PCCS are vented to the SP. At the begin-ning stages of an accident, the pressure difference between the DWand the SP will be relatively high, and the PCCS will be in through

ll rights reserved.

: +1 765 494 9570.nkar).

flow mode. In this mode, uncondensed steam and NC gas passthrough the PCCS with the condensed water. When the pressuredifference between the DW and the SP becomes comparable tothe head of the submerged vent line, the vent path from the PCCSto the SP is closed. While the vent path is closed, NC gas and uncon-densed steam accumulate in the condenser causing a decrease incondensation mass flow and an increase in DW pressure. Afterthe pressure becomes high enough to overcome the head of thesubmerged vent line, the path to the SP is opened until the pres-sure difference is less than the vent line head in the SP. Openingthe pathway to the SP allows the accumulated NC gas to be ventedout of the condenser to start the cycle over again. This operationalmode is called the cyclic venting mode, and it continues untilalmost all of the NC gas in the DW has been vented to the SP. Inthe late stages of an accident, there will be very little NC gas inthe DW and the PCCS will work in complete condensation mode.During complete condensation mode, the pressure differencebetween the DW and SP is always less than the head of thesubmerged vent line and all of the steam in the PCCS is condensed.The complete condensation mode of operation is similar tothermosyphon where the steam produced in the reactor vessel iscondensed in the PCCS and the condensate returns to the reactorvessel.

Experiments have been carried out by several researchers oncondensation with and without the presence of NC gas in a verticaltube [3–11]. Most of these experiments use forced convection forthe heat removal mechanism. However, the PCCS condenser usespool boiling as the method for heat removal. Kim and No [7] diduse pool boiling, but in a large rectangular tank and the experi-ments did not involve the presence of NC gas. Oh and Revankar

Nomenclature

A areabf blowing parameter for momentum transferd diameterDAB diffusion constantf friction coefficientg gravitational constantH heighth heat transfer coefficienthfg latent heat of vaporizationk thermal conductivityM molecular weightm00 mass flux_m mass flow rate

P pressure_Q heat transfer rateq00 heat fluxRe Reynolds numberSh Sherwood numberT temperaturet timeU overall heat transfer coefficientu axial velocityy dependent variable

Greek symbolsC mass flow rate per unit lengthd film thicknessl dynamic viscositym kinematic viscosityq densityr error term or characteristic length

s shear stressX collision integral

Subscriptsavg averagec condensationcond gas region condensationCT condensate tankD dimensionlessd diameter based quantityf momentum transfer parameterI interfacei insideL liquidm modelmea measuredNu Nusselt solutiono outsideP pool, pressureref referenceSAT saturationsec secondary sidesen sensibleTC thermocoupletube condensing tubev vaporW wall0 quantity at no transpiration

Superscript* dimensionless quantity

G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163 1157

[9,10] carried out tests with a single condensing tube using poolboiling in a cylindrical secondary pool and the presence of air asthe NC gas.

A new multi-tube test facility was designed and constructed toextend work of Oh and Revankar [9,10] as well as to investigate thetube bundle effect on PCCS heat removal capabilities. This paperwill focus on experimental analysis of the complete condensationmode in a multi-tube condenser. The results on through flow modeoperation of PCCS are presented in Part 1 of this paper [12].

2. Experimental program

2.1. Test facility

The multi-tube test facility consists of a steam generator (SG),steam and air supply line, tube bundle test section, secondary pool,condensate tank, SP, and a storage tank. A general schematic of thetest facility is displayed in Fig. 1. For the purpose of complete con-densation experiments, the SP and air supply line are not utilized.The SG is made from a 45.7 cm diameter, 3.05 m height, and sche-dule 40 stainless steel pipe. It is powered by a 100 kW immersiontype sheathed electrical heater, mounted at the lower flange. Asafety relief valve was installed on the top of the SG to relievesteam if the pressure in the tank reaches 1 MPa. At maximumpower, the SG can produce steam at a flow rate of 50 g/s. Fromhere, the steam is directed through the steam line which leads tothe entrance of the test section.

The steam supply line directs the vapor to the test section.Schedule 40 stainless steel piping, with a diameter of 50.8 mm

was selected. It is installed with two vortex flow meters, a pressuretransducer, and a thermocouple for determining the flow condi-tion. The vortex flow meter sizes are 38.1 mm and 19.1 mm. Twoflow meters are used so a larger range of steam flows can be mea-sured. The 19.1 mm vortex flow meter can measure small steamflow rates, while the 38.1 mm meter can measure steam flow upto the maximum design flow rate of 50 g/s. Each vortex flow meteris installed on parallel steam lines. The steam will only be directedthrough the flow meter that corresponds to the desired flow rate.Globe valves are used to control the direction of the steam flow.

The specific design of the bundle test section was based on thescaling results from the prototype design. The method of scalingthe tube bundle test facility, based on the PCCS prototype, is ex-plained in Part 1 of this work by Zhou et al. [12]. The bundle ismade of four condenser tubes arranged as a square so that the boil-ing condition in the center of the bundle can be well achieved. Thetube inner diameter and length are the same as the prototype. Thepitch between two tubes was selected according to the standardvalue of a commercial bundle condenser. On the top of the con-denser there is a 1 m long insulation part, which is used to measurethe pool water level change. This part is also used to minimize theinlet effect. After the insulation part, a top header was designed todistribute the incoming steam into four condenser tubes. The vol-ume of the header was calculated from the volumetric ratio be-tween test loop and prototype. To keep the volumetric ration aswell as the header length, the header is comprised of two parts:the upper cylinder and lower cylinder. The 4-tube condensationbundle is connected right after the top header. Each tube is5.08 cm in diameter and has a length of 1.80 m, which is the sameas the prototype design. The pitch between two tubes is 6.35 m and

Fig. 1. Schematic of test facility.

1158 G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163

p/D = 1.25. The bottom header, which is the last part of the con-denser, is connected with the tube bundle. The structure anddimension of the bottom header is exactly the same as the topheader. An axial and cross sectional schematic of the bundlecondenser is displayed in Fig. 2. The condensed steam, from thecondenser tubes, leads out of the test section to a condensate tank.

Fig. 2. Axial and cross sectional schematic of tube bundle test section (all units incm).

The condensate tank is made of 1.5 m tall, 30.5 cm diameter sche-dule 40 stainless steel pipe, and is mounted vertically under thetest section.

The outer tube, which is also displayed in Fig. 2, represents thesecondary pool. As steam passes through the condenser tubes, heatis transferred to the water inside the secondary pool. This heattransfer process results in steam being condensed inside the con-denser tubes and water boiling off in the secondary pool. The sec-ondary pool is made of schedule 10 stainless steel pipes consistingof a 25.4 cm diameter bottom section and a 40.6 cm diameter topsection. The two different size pipes are welded together by areducing section that bridges the two sizes. The total length ofthe entire secondary pool is 4.1 m.

The storage tank serves as a heat and mass sink for the system.Water in this tank can be pumped to the SG, secondary pool, andSP. Likewise, water can also be drained from the SG, condensatetank, secondary pool, and SP to the storage tank. Water from thestorage tank is continuously pumped into a heat exchanger to pre-vent the water in the tank to become saturated. The steam pro-duced in the secondary pool is directed to the storage tank byvent lines to maintain an atmospheric pressure condition in thesecondary pool. Blowdown steam discharge, from the SG reliefvalve, is also directed to the storage tank.

All of the tanks in the test facility are equipped with a DP cell,pressure gauge, and thermocouples. The DP cells measure the pres-sure differential in the tanks, which is essential in determining thechange in water level over time. The pressure gauges and thermo-couples are used to determine the steam properties in each of thetanks. Thermocouples were installed at seven different axial loca-tions in the secondary pool to record the pool water temperature.The test section thermocouples are positioned at 10 different axiallocations. There are 14 thermocouples at each axial position,making a total of 140 thermocouples used on the test section.

10

20

30

40

50

onde

nsat

ion

Mas

s Fl

ow

(g/s

)

G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163 1159

The locations of the thermocouples, indicated as red dots, can beseen in Fig. 21. Each of the thermocouples was soldered to the outerwall of the condenser tubes.

2.2. Test procedure

For complete condensation experiments, there is no NC gaspresent and the vent line to the SP is kept closed. The experimentis initiated by starting up the data acquisition system and heatingup the SG. The valve above the SG is kept closed during the heatingperiod. When the pressure in the SG is high enough to start con-ducting an experiment, the valve is then opened to bleed any airout of the system. The air is bled through the steam line and testsection then out the bottom of the condensate tank to the storagetank. After all the air has been bled out of the system, a valve belowthe condensate tank is shut. Once this valve is shut, the systempressure increases as more steam accumulates and the secondarywater pool heats up. The experiment begins when the water inthe secondary pool reaches saturation temperature and the pres-sure becomes a steady state condition. Data is taken with the dataacquisition system as long as the pressure remains at a steady stateor until a sufficient amount of data has been recorded.

2.3. Data reduction

The desired heat transfer quantities are the condensation massflow rate, overall HTC, secondary HTC, and condensation HTC. Thecondensation mass flow rate ð _mcÞ can be calculated using thefollowing relationship:

_mc ¼DHCT

DtqcACT ð1Þ

The condensate tank water level difference (DHCT), in Eq. (1) isdetermined by time averaging the condensate tank DP cell waterlevel readings. The condensate density (qc) is taken as the densityof saturated water at the steam pressure in the system. The con-densation heat transfer rate ð _QcÞ can then be calculated as follows:

_Q c ¼ _mchfgðPSATÞ ð2Þ

where the latent heat of vaporization, hfg(PSAT), from Eq. (2) is takenat the steam pressure in the system.The overall, secondary, and con-densate HTC are defined as followed:

U ¼_Q c

AiðTSAT � TPÞð3Þ

hsec ¼_Q c

AoðTWo � TPÞð4Þ

hc ¼_Q c

AiðTSAT � TWiÞð5Þ

The inner and outer areas of the condensing tube are known,and the condensation heat transfer rate is calculated by Eq. (2).The temperature of the outside condensing wall (TWo) and the sec-ondary pool temperature (TP) can be average from thermocouplereadings. These values can then be inserted into Eqs. (3) and (4)to obtain the overall and secondary HTC. However, since therewere no thermocouples attached to the inside wall of the condens-ing tube, the temperature of the inside condensing wall (TWi) in Eq.(5) is an unknown value.

The overall HTC, U, can be written as a function of heat transferresistances in the following way [13]:

1 For interpretation of references in color in Fig. 2, the reader is referred to the webversion of this article.

U ¼ 1hcþ 1nðdo=diÞdi

2kWþ di

hsecdo

� ��1

ð6Þ

By substituting Eqs. (3) and (4) into Eq. (6) and solving for the con-densation HTC, the following expression can be reached [13]:

hc ¼2kW _mchfg

2kWpdiHtubeðTSAT � TWoÞ � _mchfg1nðdo=diÞdið7Þ

The condensation HTC (hc) can then be calculated in Eq. (7) andsubstituted back into Eq. (5) to solve for the inside condensing walltemperature.

3. Results and discussion

3.1. Tube bundle data

Temperature data is continuously recorded during steady stateoperation with thermocouples. The temperature is recorded at theSG, steam supply line, secondary pool, outer wall of the condens-ers, and condensate tank. The SG has two thermocouples, thesteam supply line has one, the secondary pool has seven, the outerwall of the condensers has 140, and the condensate tank has two.The temperature readings were averaged for tanks that containedmore than one thermocouple. The SG, steam supply line, and con-densate tank are at a higher temperature than on the secondaryside because they are pressurized. The temperature differencebetween the outer wall of the condensers and the secondary pooldetermines the secondary HTC. The experiments were conductedunder the conditions of the average calculated liquid film Reynoldsnumber is 50-1265.

In complete condensation mode, the condensation mass flowrate increases as a function of system pressure, as shown inFig. 3. Without the presence of NC gas, the condensate mass flowrate is only a function of the incoming steam flow rate, whichdirectly determines the system pressure. If the steam flow rate in-creases, the system pressure must increase to condense all of thesteam in the condenser [14]. Thus in Fig. 3, it can be seen thatthe condensation mass flow rate increases with the system pres-sure. To perform a heat balance, the condensation heat transferrate is compared with the secondary heat transfer rate, shown inFig. 4. The condensation heat transfer rate is calculated from thecondensate mass flow rate and latent heat of evaporation at thesteam saturation temperature. The secondary heat transfer rate iscalculated from the secondary boil off rate and latent heat of evap-oration at the pool saturation pressure.

The average readings for the pool temperature, outer wall tem-perature, saturation temperature (TSAT), and calculated inner walltemperature are displayed with system pressure in Fig. 5. The pooltemperature and outer wall temperatures are averaged fromthermocouple readings for each experimental test run. The steam

0100 150 200 250 300

System Pressure (kPa)

C

Fig. 3. Condensation mass flow rate as function system pressures.

0

20

40

60

80

100

120

0 20 40 60 80 100 120Condensation Heat Transfer Rate (kW)

Seco

ndar

y H

eat T

rans

fer

Rat

e (k

W)

Fig. 4. Heat balance.

100

105

110

115

120

125

130

135

100 150 200 250 300System Pressure (kPa)

Tem

pera

ture

(C)

Average Tsat

Average Two

Average Tp

Calculated Twi

Fig. 5. Average saturation, outer wall, and pool temperatures for increasing systempressures.

1160 G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163

saturation temperature is determined from the system pressurethat the experimental test is run at. The average outer wall temper-ature and pool temperature stay relatively constant with increas-ing system pressure. Since there are no thermocouples on theinside walls of the condenser, the inner wall temperature can notbe recorded directly. The inner wall temperature is calculated fromthe equation for condensation HTC in Eq. (5). The temperature ofthe inner wall increases with system pressure, but not as rapidlyas the saturation temperature.

The condensation, secondary, and overall HTC for complete con-densation mode are shown in Fig. 6. All of the HTC values aredependent on the heat removal rate and their respective tempera-ture differences. The condensation HTC is dependent on the tem-perature difference between the saturation temperature andinner wall (dTSAT = TSAT � TWi). This temperature difference in-creases faster than the heat removal rate for lower pressures;therefore, the condensation HTC will decrease. The condensation

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

100 150 200 250 300System Presure (kPa)

Ave

rage

HTC

(W/m

2-K

) Condensation

Secondary

Overall

Fig. 6. Average condensation, secondary, and overall HTC for increasing systempressures from tube bundle.

HTC could not be accurately computed for the three lowest pres-sures, due to the very small temperature difference of dTSAT Thesecondary HTC depends on the temperature difference betweenthe outer wall and secondary pool (TWo � Tp). Since this tempera-ture difference stays relatively constant, the secondary HTC will in-crease with the same rate of heat removal. The temperaturedifference that the overall HTC depends on is between the satura-tion temperature and pool water (TSAT � Tp). The overall HTC hasshown to be constant across system pressure, so the temperaturedifference must increase at the same rate of heat removal.

3.2. Comparison with single tube data

Previous research on PCCS condensation has involved a singletube condenser. Oh and Revankar performed experiments with sin-gle tubes of inner diameter 26.6 mm and 50.8 mm with a length of0.98 m. The tube bundle condenser currently being used consists offour full scale condenser tubes of 50.8 mm ID with a length of1.8 m. To compare condensation rates across different sized testsections, the condensation mass flux is calculated. The condensa-tion mass flux is calculated by dividing the condensation mass flowrate with the total area of the inside walls of the condenser tubes.Fig. 7 shows the condensation mass flux for each of the three testsections discussed. Each of the condenser configurations produceda similar trend in condensation mass flux for increasing systempressures. For the single tube condensers, the 26.6 mm ID test sec-tion produced a slightly higher condensation mass flux than withthe 50.8 mm ID test section. This phenomenon is a result of thecondensation HTC being smaller for the 50.8 mm ID test section[13]. The test section with four full height condensers with50.8 mm ID showed the highest condensation mass flux of thethree test sections. This result will be explained by a larger second-ary HTC for a tube bundle condenser.

The condensation, secondary, and overall HTC for the 50.8 mmID single condenser tube is shown in Fig. 8. For the same systempressure, Fig. 9 shows a comparison of the secondary HTC betweenthe tube bundle condenser and single tube condenser. Based on alinear fit for the trends, the single tube secondary HTC is between25% and 35% less than what was recorded for the tube bundle. Thelarger secondary HTC is a result of turbulent mixing of two phaseflow in the secondary water pool. The secondary water is continu-ously boiled off from contact with the condenser tubes. Since thereare four condenser tubes in close proximity, the bubbles interactand create a turbulent two phase mixture at the top of the second-ary pool. Through flow visualization windows on the secondarypool wall, the boiling was observed. Compared to single tube thetube bundle boiling was vigorous with large flow recirculation.

0

0.01

0.02

0.03

0.04

0.05

0.06

100 200 300 400 500System Pressure (kPa)

Con

dens

ate

Mas

s Fl

ux

(kg/

m2-

s)

Single Tube (26.6 mm ID)Single Tube (50.8 mm ID)Tube Bundle

Fig. 7. Condensate mass flux of single tubes (26.6 and 52.5 mm ID) and tube bundlefor increasing system pressures.

0.0E+00

5.0E+03

1.0E+04

1.5E+04

2.0E+04

2.5E+04

100 150 200 250 300 350System Pressure (kPa)

Ave

rag

e H

TC

(W

/m2-

K) Condensation

Secondary

Overall

Fig. 8. Average condensation, secondary, and overall HTC for increasing systempressure from single tube (52.5 mm ID).

0.0E+00

4.0E+03

8.0E+03

1.2E+04

1.6E+04

100 150 200 250 300 350System Pressure (kPa)

Seco

ndar

y H

TC (W

/m2-

K)

Tube BundleSingle TubeSingle Tube TrendlineTube Bundle Trendline

Fig. 9. Comparison of single tube and tube bundle secondary HTC.

G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163 1161

These type of recirculation have been observed in reboilers withtube bundles [15]. This increases the secondary pool temperature,which decreases the temperature difference between the outerwall of the condensing tubes and the secondary pool water. A de-crease in the temperature difference will cause the secondary HTCto be larger. This is the phenomenon that explains a higher second-ary HTC condensation mass flux in the tube bundle test section.

3.3. Error analysis

The results of the condensation, secondary, and overall HTCerror propagation are shown in Fig. 10. The error terms decreaseas the system pressure is increased. For the low system pressures,the error is around 20–30% of the HTC. The error of the HTCdecreases to 1–3% for experiments at high system pressures. Thisresults from the increase in DT with increasing system pressure.Of all the calculations, the average water pool temperature has

0.0E+00

4.0E+03

8.0E+03

1.2E+04

1.6E+04

100 150 200 250 300System Pressure (kPa)

Ave

rage

HTC

(W/m

2-K

) Condensation

Secondary

Overall

Fig. 10. Average HTC from tube bundle with error propagation.

the largest error associated with it. So when the DT becomes small,the error of the HTC calculation increases. This is also the reasonthat the secondary HTC has a higher error than the condensationand overall HTC. The DT between the outer wall of the condensertubes and the water pool is much smaller than the DT used inthe condensation and overall HTC calculation. The highest errorof all the HTC calculations comes in the condensation HTC forthe three lowest system pressures. In these cases, the errors ofthe average temperatures are larger than the DT itself. This causesthe propagation of error to be large and the condensation HTCcalculation becomes extremely inaccurate. For this reason, the con-densation HTC in the three lowest system pressure experimentshas been eliminated from plots. Table 1 provides a summary ofthe relative error produced in these calculations. The largest con-tributor in the error propagation was the average temperaturereadings. The condensation HTC could not be accurately computedin the three lowest pressure conditions because the error of theaverage temperature reading was larger than the DT itself.

4. Heat and mass transfer analogy model

4.1. Methodology

A heat and mass transfer analogy model was used to predict theheat transfer properties of a condenser tube using the same oper-ating conditions as in the complete condensation experiments.This model is based on the heat balance at the interface of the con-densate film and gas, where the heat transfer from the gas bound-ary layer to the liquid film is equated with the heat transferredthrough the liquid film [13]. The interface temperature is solvediteratively to balance the heat transfer between the liquid filmand the gas mixture region. This first is performed at the entranceof the condenser tube until all parameters converge within a spec-ified tolerance. Once the heat balance has converged, the proce-dures are repeated on the next axial node and then for the entirelength of the condenser.

For the heat and mass transfer analogy model, the mixture isassumed to be saturated at the liquid/gas interface. The heat trans-ferred in the gas/steam mixture consists of the latent heat of con-densation and sensible heat transfer. The heat flux can then becalculated using Eq. (8).

q00 ¼ m00c hfg þ hsenðTSAT � TIÞ ð8Þ

The film HTC (hL), gas region condensation HTC (hcond), and sensibleHTC (hsen) are estimated to calculate the total condensation HTC[13]. The inverse of the total condensation HTC is equated in Eq.(9) by the sum of the individual resistances.

1hc¼ 1

hLþ 1

hcond þ hsenð9Þ

Table 1Summary of error propagation.

Pressure (kPa) Relative errors

Qcon hc hsec U

114 0.025 N/A 0.272 0.303124 0.013 N/A 0.218 0.091157 0.008 N/A 0.135 0.029166 0.016 0.059 0.115 0.028183 0.006 0.032 0.087 0.019191 0.008 0.028 0.075 0.018207 0.017 0.035 0.088 0.022225 0.004 0.018 0.065 0.012246 0.011 0.023 0.065 0.014274 0.008 0.017 0.054 0.011

y = 1.1578x

0

2

4

6

8

10

12

0 2 4 6 8 10 12Condensate Mass Flow: Model (g/s)

Con

dens

ate

Mas

s Fl

ow :

Expe

rimen

t (g/

s)

Fig. 11. Comparison between experimental condensate flow rate per tube from thetube bundle to the predicted condensate flow rate from the heat and mass analogymodel.

1162 G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163

In complete condensation mode, the vapor is assumed to be satu-rated and the only heat transfer resistance is the condensate film.

Assuming the liquid film to be laminar, the velocity profile isobtained through a force balance in the control volume.

uLðyÞ ¼ðqL � qÞ � g

lLd � y� y2

2

� �þ sI

lLy ð10Þ

The first term on the right hand side of Eq. (10) represents theNusselt analysis for no interfacial shear, which is a parabolic veloc-ity profile. The second term is a linear velocity profile depending onthe interfacial shear stress. The liquid flow rate can then be deter-mined in Eq. (11) from the velocity profile and balanced with thesum of condensate mass flow rates at each axial node.

_mL ¼Z R

R�duLðrÞ2pdr ¼ 2p

Z d

0uLðyÞðR� yÞdy ¼

Xð _mcÞi ð11Þ

The mass balance in the liquid film can be expressed with thefilm thickness and simplified by the use of dimensionless parame-ters, as shown in Eqs. (12) and (13).

C �_mL

2pR¼ ðqL � qÞg

3mLd3 þ sI

2mLd2 ð12Þ

ReL ¼43ðd�Þ3 þ 2 � s�I ðd

�Þ2� �

ð13Þ

From Eq. (13) the film thickness can be calculated, and if there is nointerfacial shear then the Nusselt film thickness is defined in Eq.(14).

dNu ¼3mLC

ðqL � qÞg

� �1=3

ð14Þ

Momentum transfer balance is used to calculate the frictioncoefficient by combining transport quantities and applying the ef-fect of suction boundary layer.

f � sI

q � ðuavg � uL;avgÞ2=2¼ f0

bf

expðbf Þ � 1ð15Þ

In Eq. (15), f0 represents the friction factor at no transpiration;bf ¼ m00=G1

ðf=2Þ0, represents the blowing parameter for momentum trans-

fer. For turbulent flow this quantity is represented by Eq. (16), andfor fully developed laminar flow this quantity is represented by Eq.(17).

f0 ¼ 0:079Re�0:25d ð16Þ

f0 ¼16Red

ð17Þ

The Sherwood number is calculated in Eq. (18) using a masstransfer balance as follows, where bm represents the mass transferblowing parameter.

Sh � gmdqD¼ Sh0

bm

expðbmÞ � 1ð18Þ

The gas transport properties of dynamic viscosity, thermal con-ductivity, and diffusion coefficient are calculated using Eqs. (19)–(21). For these equations, r represents the characteristic lengthof a molecule (10�10 m), and Xv represents the dimensionless col-lision integral.

l ¼ 2:669� 10�6 ðT �MÞ0:5

r2Xvð19Þ

k ¼ 2:63� 10�3 ðT=MÞ0:5

r2Xvð20Þ

DAB ¼0:00266T3=2

P �M0:5AB r2

ABXD

ð21Þ

5. Results

For this study, the desired outputs of the heat and mass transferanalogy model were the average condensate mass flow rate, axialcondensate mass flow rate, and the axial condensation HTC. First,the average condensate mass flow rate was predicted by the modelfor comparisons to experimental results. Since the model only pre-dicts data for a single condenser tube, the experimental averagecondensate mass flow rate is divided by a factor of four to obtainthe average condensate mass flow rate per tube. Fig. 11 showsthe comparison between the experimental results and model pre-dictions. The red lines represent a +/� 25% agreement between theexperiment and the model. From the trendline shown, with line fit,y = 1.1578x, we can see that the experimental condensate massflow rates are about 16% higher than model predictions on average.This finding is a direct result of the tube bundle effect on conden-sation heat removal. The turbulent mixing on the secondary sidedecreases the DT between pool water and condensing tube, caus-ing an increase in secondary HTC. This increase in secondary HTCis enough to make the condensate mass flow rates higher thanfor a single tube. Since the model only predicts results for a singlecondenser tube, turbulent mixing is not taken into account. This issufficient enough to cause the predicted condensate mass flowrates to be less than in a tube bundle experiment. The only exper-imental data points that are less than the model predictions are thecases of the two lowest condensate mass flow rates. In these twocases, the secondary boil off rate is very low with minimal bubbleinteractions. For boil off rates that are this low, the secondary poolwill not experience any turbulent mixing.

Since there is not a way to measure the condensate mass flowrate at different axial points, the axial profile for condensationHTC could not be directly computed. To estimate the local conden-sation HTC, the heat and mass transfer analogy model was used topredict the axial condensate mass flow rates. These local condensa-tion rates where then applied to experimental data to estimate thecondensation HTC at each of the 10 axial thermocouple locations.The local condensation HTC points where then compared to the ax-ial profiles of condensation HTC predicted by the model. The axialcondensation HTC profiles at two different system pressures fromboth experimental results and model predictions are shown inFig. 12. The experiment and the model produced similar resultsat the entrance and exit of the condenser tube. Just after a distanceof 0.1 m from the entrance of the condensers the experimentshowed a slightly faster drop in condensation HTC than the model.And after about 0.5 m from the entrance of the condensers theaxial HTC profile became flat. This means that along the length ofthe condensers the condensate mass flow rate is increasing at

0.E+00

1.E+04

2.E+04

3.E+04

4.E+04

5.E+04

0 0.3 0.6 0.9 1.2 1.5 1.8Axial Distance from Entrance (m)

Con

dens

atio

n H

TC (W

/m2-

K)

Experiment: 225 kPaExperiment: 274 kPaModel: 225 kPaModel: 274 kPa

Fig. 12. Axial condensation HTC from experimental runs compared with predic-tions of the heat and mass analogy model at different pressures.

G. Henderson et al. / International Journal of Heat and Mass Transfer 53 (2010) 1156–1163 1163

the same rate as the difference in saturation temperature and innerwall temperature. The result suggests that the axial condensationHTC profile in the bottom half of a condenser will have a more flatprofile in a tube bundle than in a single condenser.

6. Conclusions

In this study, the complete condensation mode of a passive con-denser was investigated with a tube bundle. Complete condensa-tion mode, in a PCCS, occurs when pure steam passes throughthe condenser and all of the steam is condensed. A full scale fourtube condenser was designed and constructed to investigate theeffect of a tube bundle on condensation heat removal. Data wasrecorded to analyze condensation mass flow rate and HTC trends.

The system pressure for the experiments was directly deter-mined by the steam flow rate to the tube bundle condenser. Sinceall of the steam is condensed, the system pressure increases withan increase in steam flow rate to condense all of the steam. Forincreasing system pressure, the overall HTC stayed constant, thesecondary HTC increased, and the condensation HTC initially de-creased and then stayed relatively constant. The condensationmass flux of the tube bundle was slightly higher than in a singletube of the same diameter. This was found to be a result of turbu-lent mixing in the secondary water pool, causing a higher second-ary HTC in the tube bundle.

A heat and mass transfer analogy model was used to predict theaxial heat transfer properties of a single PCCS tube under the sameconditions as the complete condensation experiments. For most ofthe experiments, the model under predicted the condensate mass

flow rate. This is a result of the model not factoring the turbulentmixing effect of a tube bundle. The local condensation HTC esti-mates were close to the model predictions at the entrance and exitof the condenser tube. In the middle section of the condenser, theHTC estimates were less than the model predictions with a moreflat profile. This suggests that the local condensation HTC in thebottom half of a tube bundle condenser is closer to constant thanin a single tube.

Acknowledgements

This work was supported by the US Department of Energy(DOE) under Nuclear Energy Education Research (NEER) researchgrant with award number DE-FG07-04ID14605 for which theauthors are grateful.

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