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Applied Thermal Engineering 40 (2012) 294e303

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Numerical study of a power plant condenser tube arrangement

Hui Zeng, Ji’an Meng, Zhixin Li*

Key Laboratory of Thermal Science and Power Engineering of Ministry of Education, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China

a r t i c l e i n f o

Article history:Received 19 July 2011Accepted 13 February 2012Available online 18 February 2012

Keywords:Power plant condenserTube arrangementHeat exchangerNumerical simulation

* Corresponding author. Tel.: þ86 10 62772919; faxE-mail address: lizhx@tsinghua.edu.cn (Z. Li).

1359-4311/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.applthermaleng.2012.02.028

a b s t r a c t

The flow and heat transfer performance of a power plant condenser for a 300 MW unit was numericallyanalyzed using a porous medium model. Three typical tube arrangements were considered. The analysisindicates that none of these three tube arrangements satisfies the Heat Exchange Institute Standards (HEIStandards) with lower overall average heat transfer coefficients in the condenser and higher backpressures. A new tube arrangement was developed based on the modeling results for the velocity, heattransfer coefficient and air mass fraction distributions in the condenser. This tube arrangement givesbetter condenser performance than the HEI Standards.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Power plant condenser (a huge complex shell-and-tube heatexchanger) is one of the most important auxiliary equipments ina power plant. Increases of the condenser heat transfer rate willincrease the plant thermal efficiency by reducing the turbineexhaust pressure. A higher heat transfer coefficient will also reducethe condenser sizes.

A condenser has a large number of cooling tubes (a condenserfor a 300 MW unit has approximately 20 000 tubes) with thecondenser flow and heat transfer performance highly dependenton the tube arrangement. If the tubes are not well arranged, theoverall heat transfer coefficient will be reduced and the turbineexhaust pressure, which is equal to the condenser back pressure,will be increased. Therefore, the tube arrangement must be opti-mized for a good condenser design. Many companies have devel-oped high-performance tube arrangements. Some are now widelyused, such as the cap-shaped tube arrangement developed by theAlsthom Corporation of France, the double-peak-shaped tubearrangement developed by the Balcke-Durr Corporation ofGermany, the lozenge-shaped tube arrangement developed byWestinghouse of the USA, the church-window-shaped tubearrangement developed by ABB of Switzerland, and the AT-shapedtube arrangement developed by Toshiba of Japan.

The power plant condenser design is traditionally based onrecommendations by the condenser manufactories founded onprevious designs and experimental tests, often based on the

: þ86 10 62781610.

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standards developed by the Heat Exchange Institute (HEI Stan-dards) [1]. However, this method does not take a number of factorsthat affect the heat transfer rate into account, including the tubearrangement. Improved computers and numerical simulationshave now made it possible to solve for the fluid flow and heattransfer distributions in condensers numerically. In 1972, Patankarand Spalding [2] developed a calculational procedure based on theporous medium concept to analyze the transient behavior of shell-and-tube heat exchangers which greatly reduced the computingtime as well as the storage, and provides an easy way of exploitingthe extensive experimental data. Numerical simulations of the flowand heat transfer in condensers have now been conducted bymanyresearchers. Davidson and Rowe [3] took into account the effect ofnon-condensable gases using a single-phase model. Al-Sanea et al.[4] and Bush et al. [5] used a two-dimensional two-phase modelwith comparisons to experimental data to show that the predic-tions agreed well with the experimental data in the lower half ofthe condenser but had some discrepancies near the top of the tubenest. Zhang et al. [6e9] did a series of studies from a two-dimensional single-phase model to a quasi-three-dimensionaland two-phase model. Malin [10] used a three-dimensionalapproach in PHOENICS to model a marine condenser with thecomputed overall condensation rate in excellent agreement withmeasured data. Ormiston et al. [11,12] analyzed the convergence ofcondenser simulation models and found that new algorithms couldobtain solutions in just a few time steps. Hu and Zhang developeda modified k-epsilon turbulence model for condenser simulations[13], and later assessed the effects of different closure correlationson the numerical simulations [14,15].

These models have been used for tube arrangement analyses.Sato et al. [16] numerically estimated the performance of an AT-

Fig. 1. Three typical tube arrangements for the condenser of a 300 MW unit.

Fig. 2. Condenser cross-section.

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303 295

shaped tube arrangement condenser, showing that the heattransfer performance of the condenser with the new tubearrangement was up to 20% higher than with the former design,which was confirmed by hydraulic analog tests. Roy et al. [17]numerically calculated the performance of a steam condenserwith a lozenge-shaped tube arrangement and studied the effects ofvarious operating parameters on the condenser performance.Ramon et al. [18] analyzed the influence of the condenser pressureand the overall heat transfer coefficient for a church-window-shaped condenser for various operating parameters andcompared the results with the HEI Standards. Prieto et al. [19]compared the predictions of the HEI Standards for the samecondenser and results of numerical simulations using two-dimensional and three-dimensional models to recommend use ofnumerical models for improving tube arrangement. Gong et al. [20]analyzed the condenser’s tube arrangement of the Daya bay nuclearpower station through tow-dimensional calculation program. Theresult indicates that the new type tube arrangement of the BeDcompany makes great improvement in many ways than the oldone. Wang et al. [21] studied the thermal performance of an N-11220-1 power plant condenser and pointed out that the condensercan be improved by means of either replacing the tube arrange-ment or increasing the sizes of steam lanes around the tube bundle.Zhou et al. [22] introduced a means of installing guide plate toimprove flow and heat transfer characteristics in the condenser,which is confirmed by the calculation.

Though there are now many high-capacity power units, thereare still many 300 MW units used around the world. Sincecondensers for 600 MW and 1000 MW units are similar to those of300 MW units, a good condenser tube arrangement for a 300 MWunit can give guidance for designs of large units. This study analyzesthe flowand heat transfer in a power plant condenser for a 300MWunit. Three typical tube arrangements are considered to study theimpact of the tube arrangement on the condenser performance. Anew tube arrangement is then developed with numerical resultsshowing that the new tube arrangement gives significantlyimproved condenser performance.

2. Physical and numerical model

2.1. Physical model

Fig. 1 shows three typical tube arrangements for the condenserof a 300 MW units. Type A is a cap-shaped tube arrangement, type

B is a double-peak-shaped tube arrangement, and type C isa lozenge-shaped tube arrangement. All three tube arrangementsare now widely used in power plants. Since all condensers aresymmetric across their center planes, Fig. 1 only shows a half of thetube bundle.

Fig. 2 shows the entire cross section of the condenser withtube arrangement A. There are two distinct flow regions in thecondenser with one region where the cooling tubes areconcentrated is the tube bundle region and the free flow region.The steam from the turbine exhaust enters the condenser at thetop of the shell and flows through the bundle region tocondense. There are vents in the center of each bundle to extractthe non-condensable gases (mainly air) and the non-condensedsteam. In addition, baffles guide the steam flow in the tubebundle. Some tube arrangements have an independent bundlebefore the vent, which is separated from the main condensationregion by baffles. This region is named as air cooling region dueto the high air mass fraction. The condenser is double tube-passes, so each tube bundle is divided into two parts with anequal numbers of tubes. Cooling water enters into the lowertube bundle and then exits from the upper tube bundle. Thecondenser geometric and operating parameters are listed inTable 1.

Table 1Condenser geometric and operating parameters.

Geometric parameters Operating parameters

Tube material TP 304L Inlet steam mass rate 658.08 t/hTube number 23 002 Inlet steam dryness fraction 0.9Tube length 10.84 m Air in-leakage mass fraction 4.65 � 10�5 [1]Outer tube diameter 25 mm Outlet venting rate 3516 m3/h [1]Inner tube diameter 24 mm Cooling water flow rate 39 254 t/hTube pitch 32 mm Inlet cooling water temperature 20 �C

Tube cleanliness factor 0.9

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303296

2.2. Numerical model

As in previous studies, a two-dimensional single-phasenumerical model was used to analyze the flow and heat transfer ina condenser to save computer time. The tubes were modeled asa porous medium with the complex multi-phase and multi-component flow on the shell side simplified into a single-phaseflow of a mixture of steam and air. The condenser geometry andthe boundary conditions are symmetric, so only the left half of thecondenser was simulated.

The tube bundle porous medium uses an isotropic porosity, b,defined as the ratio of the volume occupied by the fluid to the totalvolume. In the present work, bf is set equal to 1 in the free flowregion, while in the tube bundle regionwhere the tubes are laid outin an equilateral triangular pattern, bb is defined as [9]

bb ¼ 1� p

2ffiffiffi3

p�Do

Pt

�2

(1)

where Do is the tube outer diameter and Pt is the tube pitch.The two-dimensional steady-state governing equations for

mass, momentum, and air mass fraction in the Cartesian coordinatesystem are as follows [9].

Mass conservation equation for the steam and air mixture:

v

vxðbruÞ þ v

vyðbrvÞ ¼ �b _m (2)

Momentum conservation equations for the steam and airmixture:

v

vxðbruuÞþ v

vyðbrvuÞ ¼ v

vx

�bðmtþmÞvu

vx

�þ v

vy

�bðmtþmÞvu

vy

�

�bvPvx

�b _mu�bFu (3)

v

vxðbruvÞþ v

vyðbrvvÞ ¼ v

vx

�bðmtþmÞvv

vx

�þ v

vy

�bðmtþmÞ vv

vy

�

�bvPvy

�b _mv�bFv (4)

Conservation of air mass fraction:

v

vxðbruYaÞ þ v

vyðbrvYaÞ ¼ v

vx

�brðDt þ DÞ vYa

vx

�

þ v

vy

�brðDt þ DÞ vYa

vy

�(5)

where _m is the steam condensate rate per unit volume, Fu and Fv arethe flow resistance force components in x and y directions due tothe tube bundle, m is the dynamic viscosity, D is the diffusivity of airin the vapor, mt is the turbulent dynamic viscosity and Dt is the

turbulent diffusivity of air in the vapor, and Ya is the air massfraction.

The steam condensate rate per unit volume _m, is calculated byequating the enthalpy reduction of the steam to the internal energyincrement of the cooling water as

_mLV ¼ ðTs � ToÞ � ðTs � TiÞln�Ts � ToTs � Ti

� AR

(6)

where L is the latent heat of condensation, Ti is the inlet coolingwater temperature, To is the outlet cooling water temperature, andTs is the steam temperature calculated as the saturation tempera-ture corresponding to the steam pressure.

The total thermal resistance R, is

R ¼ RwDo

Diþ Rf þ Rt þ Rc þ Ra (7)

where Rw, Rf, Rt, Rc and Ra are the individual thermal resistances forthe water side, fouling, tube wall, condensate and air. Rw, Rt, Rc andRa are obtained from various semi-empirical heat transfer correla-tions [9]. The fouling resistance, Rf, is based on a cleanliness factor,FC, with the overall heat transfer coefficient, ha, predicted using theHEI Standards as

Rf ¼�1FC

� 1�

1ha

(8)

The RNG k-ε model [23] was used to model the turbulencethrough the turbulent viscosity, mt, and the turbulent diffusivity ofair, Dt, in the vapor.

The boundary conditions for the computational domain were:Steam inlet: The velocity and air mass fraction were specified at

the inlet boundary.Vent: The total volumetric venting rate was fixed. The pressure

at the vent was uniform and if therewasmore than one vent, all thevents had the same pressure.

Walls: The shell walls and baffles of the condenser wereassumed to be non-slip and impermeable.

Symmetry plane: Along the center symmetry line the deriva-tives with respect to the cross-stream direction of all field variableswere set to zero.

The simulation was performed using the commercial softwareFLUENT 6.2. The discretization is based on the SIMPLEC algorithm,with the QUICK scheme used to discrete the governing equations.

3. Simulation results

The performance of the condenser for a 300 MW unit wasnumerically analyzed using three different tube arrangements.Engineering experience has shown that a good tube arrangementleads to high and uniform heat transfer coefficient, prevents airfrom concentrating in the main condensation region and preventssteam leakage, i.e., prevents the steam from directly reaching theair cooling region (or the vent) without flowing through the maincondensation region.

3.1. Condenser performance with tube arrangement A

Tube arrangement A is a cap-shaped tube arrangement. Thehalf of the condenser that was analyzed has only one tubebundle. The tubes are arranged as a continuous closed bundlewhich is curved to form branch channels for the steam inlet. Thevent and the air cooling region are in the center of the tubebundle.

Table 2Grid independence test results.

Element number 374 684 618 061 952 343 1 498 328

ha/W m�2 K�1 2265 2199 2169 2151Pb/kPa 5.74 5.83 5.87 5.89

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303 297

A non-uniform quadrilateral grid was generated using Gambit2.0, with fine elements in the tube bundle region and coarseelements in the external free flow region. Calculations withdifferent size elements tested the grid independence. The overallaverage heat transfer coefficient and condenser back pressure forthe different element sizes are in Table 2. The results showed thatthe 4.5 mm elements in the tube bundle regionwas sufficiently fineto result in a grid-independent solution. This grid size was alsoapplied to the other tube arrangements.

Fig. 3 shows the simulation results for the condenser with tubearrangement A. The streamlines in Fig. 3(a) show that the steamenters into the condenser at the top with a uniform downwardvelocity, flows around the tube bundle through the main channels,

Fig. 3. Simulation results for the cond

and enters into the tube bundle from all around the periphery. Dueto the effect of the side wall, the flow resistance in the left mainchannel is larger than in the right main channel where thesymmetry plane has no effect on the flow resistance. The steamflowing through the right main channel turns into the bottomchannel and then flows upward into the left main channel untilreaching the middle part of the lower tube bundle. The branchchannels link with the main channels to guide the steam flowdeeper into the tube bundle and tomake the steammore uniformlyenter into the bundle region. The disadvantage of the flow patternof tube arrangement A is that some vortices occur near the rightside of the tube bundle where the pressure is lower causing steamflow reversal from inside the tube bundle to the vortex region. Inaddition, part of the steam leaks directly to the air cooling regionthrough the steam flow channel in the middle of the upper tubebundle.

The velocity distribution in the condenser with tube arrange-ment A is shown in Fig. 3(b). Themaximumvelocity is about 120m/s at the beginning of the right main channel as the steam flowsdownward. In the tube bundle region, the maximum velocity

enser with tube arrangement A.

Fig. 4. Simulation results for the condenser with tube arrangement B.

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303298

occurs at the top of the upper tube bundle and in the left part of thelower tube bundle, with velocities greater than 20 m/s. As thesteam flows through tube bundle towards the vent, its velocitydecreases rapidly due to condensation. The velocity drops to lessthan 1 m/s in the region near the vent. The contours also indicatethat a low velocity region in the right part of the lower tube bundlewith velocities of less than 1 m/s.

The air mass fraction distribution in the condenser with tubearrangement A is presented in Fig. 3(c). The air mass fraction ismuch less than 0.01 inmost of the tube bundle region and increasesas the steam is condensed. Fig. 3(c) also shows a sharp increase ofthe air mass fraction in the air cooling region to about 0.3 at thevent. The flow pattern with vortex flows and a low-velocity regionin the right part of the lower tube bundle have a significantly higherair concentrations region there, with the air mass fraction is as highas 0.3, the same as at the vent.

The heat transfer coefficient distribution in the condenser withtube arrangement A is shown in Fig. 3(d). The heat transfer coef-ficient is highest in the peripheral bundle region where the steambegins to condensate and the air mass fraction is not very high, with

values up to 4000 W m�2 K�1. The air mass fraction is high insidethe tube bundle region, so the heat transfer coefficient is the lowest,with values less than 100 W m�2 K�1. The large air mass fractionleads to a large thermal resistance to the steam condensation.Therefore, the heat transfer coefficient is also very low in the highair concentration region in the right part of the lower tube bundle.

In summary, the steam flow in the condenser with tubearrangement A is reasonable. This arrangement makes the steamuniformly enter into the tube bundle region all around the tubes,with the branch channels making the steam too much deeper intothe tube bundle for condensation. The air cooling region also worksreasonable. However, the vortex flows, the air concentration regionand the steam leakage into the air cooling region will reduce theheat transfer performance.

3.2. Condenser performance with tube arrangement B

Tube arrangement B is a double-peak-shaped tube arrangementwith half of the condenser having the same two tube bundles. Sincethe two tube bundles are parallel, half of the condenser has three

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303 299

vertical main channels, including the one between the two tubebundles. The double-peak-shaped tube bundle also has a branchchannel between the two peaks, which extends to inside the tubebundle. The vent and the air cooling region are at the end of thebranch channel. The vertical main flow channels and the branchflow channels between the two tube bundles are all tapered.

Fig. 4 shows the simulation results for the condenser with tubearrangement B. The streamlines in the condenser in Fig. 4(a) showthat the steam first flows downward through the middle and rightmain channels, then enters into the bottom main channel, andfinally flows upward through the left main channel to the top-leftcorner of the tube bundle. The steam then enters the tube bundleat different positions all along the flow channels. The branchchannels of the condenser with tube arrangement B are not ascomplex as those of tube arrangement A, with vortices only underthe baffles between the upper and lower tube bundles. The steamdirectly leaks to the air cooling region through the channels at thetwo corners of the lower part of each tube bundle.

Fig. 5. Simulation results for the cond

The velocity distribution in the condenser with tube arrange-ment B is shown in Fig. 4(b). The maximum velocity occurs in themiddle of the right main flow channel, with a velocity about 130 m/s. The velocity distribution in the tube bundle is more uniform thantube arrangement A, especially in the upper tube bundle. However,low velocity regions in the lower tube bundle show the steam flowsin the two tube bundles may be disturbed by each other. Thevelocities in the low velocity regions are not as low as those withtube arrangement A.

The air mass fraction distribution in the condenser with tubearrangement B is plotted in Fig. 4(c). The numerical results show airconcentration regions in the lower tube bundle, but the air massfractions are not high, with maximums less than 0.1.

The heat transfer coefficient distribution in the condenser withtube arrangement B is shown in Fig. 4(d). The heat transfer coefficientdistribution is more uniform thanwith tube arrangement A, and thehighheat transfer coefficient region is larger. Even so, the vortexflowsand the high air concentration reduce the heat transfer performance.

enser with tube arrangement C.

Table 3Condenser performance with different tube arrangements.

Tubearrangement A

Tubearrangement B

Tubearrangement C

HEIStandards

ha/W m�2 K�1 2169 3062 2020 3172Pb/kPa 5.87 4.91 6.37 4.90

Fig. 6. New tube arrangement.

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303300

The numerical results for the tube arrangement B with thetapered main channels and branch channels indicate that this isa good design with uniform steam flow into the tube bundles andless vortices. The air mass fraction in the air concentration regionsis not high and the heat transfer coefficient distribution is moreuniform than with tube arrangement A. The shortcomings of tubearrangement B are that the steam flows in the two tube bundlesmay attract each other, and there is still some steam leakage fromthe main channels to the air cooling region.

3.3. Condenser performance with tube arrangement C

Tube arrangement C is a lozenge-shaped tube arrangement withhalf of the condenser having two tube bundles which are similarbut not the same. The two tube bundles vertically placed so there isa horizontal main channel between the two tube bundles. Eachtube bundle is approximately lozenge-shaped with tubes removedin the tube bundle peripheral to form tiny secondary branchchannels. This design results in no independent air cooling regionin tube arrangement C.

Fig. 5 shows the simulation results for the condenser with tubearrangement C. The streamlines in Fig. 5(a) show that the steamflows all the way down in the right main channel, but in the leftmain channel the steam only flows half way down, and then turnsinto the horizontal main channel and flows to the right mainchannel. The two steam flows mingle and flow around the lowertube bundle until reaching its left-top corner. The steam enters allaround the tube bundle, but the steam does not flow directly to thevent. The flow has three vortices in the down-left part of the uppertube bundle and in the upper-left and lower-right parts of the lowertube bundle, which make the steam flow turn away from the ventsin these areas.

The velocity distribution in the condenser with tube arrange-ment C is shown in Fig. 5(b). Themaximumvelocity is located in themiddle horizontal flow channel with a velocity about 100 m/s. Alarge low velocity region exists in center of each tube bundle nearthe vents and the vortex flows.

The air mass fraction distribution in the condenser with tubearrangement C in Fig. 5(c) shows that the maximum air massfraction is not located at the vents, but in the center of the vortices.Thus, the air concentration is very high there and the air suction isvery poor.

The heat transfer coefficient distribution in the condenser withtube arrangement C is depicted in Fig. 5(d). Along the periphery, theheat transfer coefficient is as high as 4000Wm�2 K�1, but in the airconcentration region, the heat transfer coefficient falls rapidly witha large low heat transfer coefficient area.

Tube arrangement C has no independent air cooling region, sothe air mass fraction is relatively low near the vents and very highin the vortex flow regions. The flow pattern near the vents is dis-rupted by the vortices, which creates a large area with low heattransfer coefficients, so the condenser performance with tubearrangement C is not as good. However, tube arrangement C makesthe steam enters all around the tube bundle so the steam flow isuniform except in the high air concentration regions. If the exhaustcapacity is strong enough to avoid high air concentrations, thecondenser performance with tube arrangement C will be greatlyimproved.

3.4. Comparison of the three tube arrangements

The condenser performance is mainly indicated by the overallaverage heat transfer coefficient and the back pressure. A higheroverall average heat transfer coefficient will create a lowercondenser back pressure and, consequently, a better turbine

thermal efficiency. The condenser performance with three tubearrangements are listed in Table 3 for a fixed venting capacity withthe values obtained using the HEI Standards method also listed forcomparison. All three tube arrangements have shortcomings, withthe condenser performance with tube arrangement B a little lowerthan the HEI Standards results and with the other two tubearrangements beingmuch lower than the HEI Standards results, i.e.,the overall average heat transfer coefficients are lower and the backpressures are higher. Thus, tube arrangement B has the best results.Since tube arrangement C has no independent air cooling region,the condenser performance with tube arrangement C is the worst,with an overall average heat transfer coefficient only 63.7% of theHEI Standards result and a back pressure of 6.37 kPa, about 1.5 kPaabove HEI Standards.

4. New condenser tube arrangement

The new tube arrangement shown in Fig. 6 was developed toimprove the condenser performance. This tube arrangement usesa natural tree branch shape for reference, with the tube bundlearranged in a double-tree-shape. Seen from Fig. 6, the tubearrangement has tapered channels, with many secondary taperedbranch channels around the tree-shaped tube bundle which allowmore uniform steam flow into the tube bundle. The vent is at thecenter of the tube bundle. The steam condensation is increased byhaving the air cooling region converge as the flow approaches thevent. Also, the tubes are carefully arranged to eliminate steamleakage channels. The tubes are arranged in one tube bundle toeliminate the flow disturbances caused by multiple tube bundles.

The predicted results for the new tube arrangement are shownin Fig. 7. The streamlines in the condenser in Fig. 7(a) show thatthere is no upward flow in the left channel and the steam flow

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303 301

through the right main channel flows only into the bottom mainchannel. The secondary branch channels play a key role guiding thesteam flow into the tube bundle with no obvious vortices. There-fore, the steam is forced to very uniformly enter into the tubebundle and to the air cooling region.

The velocity distribution in the condenser with the new tubearrangement is shown in Fig. 7(b). The velocity distribution in thetapered channels is more uniform than in the other three tubearrangements, with the steam more uniformly entering into thetube bundle as the steam flows through the gradually shrinkingchannels. In the tube bundle, the velocity distribution is centeredon the air exhaust channels and the vent, indicating that the steamcondensation in the tube bundle is also very uniform.

Fig. 7(c) shows the air mass fraction distribution in thecondenser with the new tube arrangement. The air mass fractioncontinuously increases from the outer surface of the tube bundle tothe air cooling region. The air mass fraction rises sharply from 0.01to above 0.3 as the steam and air mixture flows through the aircooling region, which shows that the effect of the air cooling region

Fig. 7. Simulation results for the condens

is quite good. Since the boundary conditions are not symmetric,a locally highmass fraction region appears in the lower-right part ofthe tube bundle, but the air mass fraction is only about 0.01, whichdoes not seriously affect the condenser performance.

The heat transfer coefficient distribution in the condenser withthe new tube arrangement is given in Fig. 7(d). Fig. 7(d) showsa more uniform heat transfer coefficient distribution over thewhole tube bundle region than for tube arrangement B, with themain condensation regions having higher heat transfer coefficients.In the lower right part of the tube bundle the heat transfer coeffi-cient is lower than in the other condensation regions due to theincreased air concentration.

Thus, the new tube arrangement is very effective with a betterflow pattern and more uniform heat transfer coefficient distribu-tion thanwith the other tube arrangements. For the same operatingconditions, the overall average heat transfer coefficient is3709 W m�2 K�1 and the back pressure is 4.68 kPa. Therefore, thecondenser performance with the new tube arrangement is betterthan the HEI Standards results. The heat transfer coefficient is more

er with the new tube arrangement.

Table 4The measured data of the rebuilt and old condensers with different tube arrangements.

Old condenser (tube arrangement C) Rebuilt condenser (new tube arrangement)

No. 1 2 3 4 5 1 2 3 4 5G/MW 300.9 300.2 301.6 297.3 299.1 299.9 281.6 329.4 330.1 330.3Ti/�C 18.03 20 22 24 26 24.08 22.015 23 24 26To � Ti/�C 10.13 10.01 10.22 9.93 10.09 10.21 8.86 10.12 9.96 10.14Pb/kPa 6.56 6.74 7.24 7.95 8.43 6.45 5.37 6.05 6.25 6.79PD/kPa 6.80 6.49 6.22 6.37 6.03 5.00 5.12 4.98 4.95 4.77PD/kPa 6.38 4.96

H. Zeng et al. / Applied Thermal Engineering 40 (2012) 294e303302

than 80% higher and the back pressure is 1.7 kPa less than for tubearrangement C.

The new tube arrangement has already applied in the Xibaipopower plant, Hebei Province, China. The condenser No. 2 wasrebuilt with the developed new tube arrangement. The measuredgeneration power, inlet temperature and temperature rise ofcooling water, and back pressure of the rebuilt condenser No. 2with new tube arrangement and the old one with the tubearrangement C under different operating conditions are listed inTable 4. In order to compare the condenser performance with thetwo tube arrangements, the back pressures under the designoperating condition, PD, are calculated based on the measured data.The average of PD of the condenser with the new tube arrangementis 4.96 kPa, which is 1.42 kPa lower than that of the old one. Theseresults show that the condenser performance with the new tubearrangement is significantly improved and indirectly confirmed theabove mentioned numerical results.

5. Conclusions

The flow and heat transfer performance of a condenser fora 300 MW power plant has been numerically analyzed for threetypical tube arrangements. Among these three tube arrangements,tube arrangement B is the best, with an overall average heattransfer coefficient and a back pressure close to the HEI Standards.Tube arrangement C is the worst, with an overall average heattransfer coefficient only 63.7% of the HEI Standards and a backpressure of 6.37 kPa, 1.5 kPa above the HEI Standards.

The three typical tube arrangements were analyzed to developa new tube arrangement design. Numerical simulations showedthat the new tube arrangement forces the steam to more uniformlyenter the tube bundle with no significant air concentration region,and the condenser performance with the new tube arrangement isbetter than the HEI Standards. This new tube arrangement can alsobe used with higher power units.

Acknowledgements

This work was financially supported by the National BasicResearch Program of China (2007CB206901) and the NationalNatural Science Foundation of China (51036003).

Nomenclature

A area (m2)D diffusivity of air in vapor (m2 s�1)Dt turbulent diffusivity of air in vapor (m2 s�1)Di tube inner diameter (m)Do tube outer diameter (m)FC cleanliness factorFu, Fv flow resistance force in the momentum equations

(N m�3)G generation power (MW)

ha average heat transfer coefficient (W m�2 K�1)L latent heat of condensation (J kg�1)_m condensation rate per unit volume (kg m�3 s�1)Pb back pressure (kPa)PD back pressure under design operating condition (kPa)Pt tube pitch (m)R total thermal resistance (m2 K W�1)Ra air film thermal resistance (m2 K W�1)Rc condensate thermal resistance (m2 K W�1)Rf fouling thermal resistance (m2 K W�1)Rt tube wall thermal resistance (m2 K W�1)Rw water side thermal resistance (m2 K W�1)Ti inlet cooling water temperature (◦C)To outlet cooling water temperature (◦C)Ts steam temperature (◦C)u velocity component in the x direction (m s�1)v velocity component in the y direction (m s�1)V volume (m3)x, y coordinates (m)Ya air mass fraction

Greek symbolsb local volume porositybb porosity in tube bundle regionbf porosity in free flow regionm dynamic viscosity (kg m�1 s�1)mt turbulent dynamic viscosity (kg m�1 s�1)r density (kg m�3)

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