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R. P. RoyMem. ASME

e-mail: [email protected]

M. Ratisher

Department of Mechanical andAerospace Engineering,

Arizona State University,Tempe, AZ 85287

V. K. GokhaleSalt River Project—Navajo Generating Station,

Page, AZ 86040

A Computational Model of aPower Plant Steam CondenserA computational model of a power plant steam condenser which incorporates the eof air in-leakage and removal on the performance of the condenser is reported.condenser interior space is modeled as a porous medium. A quasi-three-dimenapproach is taken in which the steady-state steady-flow conservation equations fsteam-air mixture mass, momentum, thermal energy, and air mass fraction are solva series of two-dimensional grids perpendicular to the circulating water flow directThe air removal system is explicitly modeled. The computational model is used to clate the performance of the steam condenser of a 750-MWe unit at 100 percentSome of the calculated variables are compared with measurements obtained in thdenser. The effects of changing various operating parameters on the condenser pmance at 100 percent load are also studied.@DOI: 10.1115/1.1348336#

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IntroductionAccurate prediction of steam condenser performance is im

tant because the power generated by a steam turbine depstrongly on the condenser pressure. Numerous papers havepublished in recent years on the topics of theoretical modelingsteam condensers and practical prediction of condenser pemance. Theoretical condenser models are based on basicciples such as the Navier-Stokes and energy equations forflowing fluid. Methods of practically predicting condenser perfomance, on the other hand, typically rely on empirical relationsdesign data.

The empirical models of steam condenser performance, forample,@1,2#, will not be reviewed here because our approachmore akin to the theoretical models that have been develoAl-Sanea et al.@3# reported a two-dimensional condenser modin which the steady-state conservations equations for mass,mentum, and air concentration were solved by the commerCFD code PHOENICS. The condenser interior space was meled as a porous medium. Steam inflow, air inflow, and the oflow of steam-air mixture were fixed, meaning that the air conctration at vent pipe exit was known a priori. A similar approawas adopted by Caremoli@4#.

The British utility company PowerGen developed the EPOcode for modeling steam condensers@5#. The model was quasithree-dimensional in that two-dimensional~x, y! conservationequations for the fluid mass and momentum were solvednumber of planes perpendicular to the condenser tube length.effect of air blanketing on the steam condensation rate wascluded by specifying each control volume as having either aair concentration where condensation was unaffected or a higconcentration where condensation was totally inhibited. A threold value of air concentration at which condensation becametally inhibited had to be chosen. The air concentration couldexceed this value.

Zhang et al.@6# developed a quasi-three-dimensional condenmodel in conjunction with a measurement program in a powplant condenser which included steam temperature and presand circulating water outlet temperature at several locations.condenser interior space was modeled as a porous mediumspace was divided into 16 computational slabs, each slab resenting the region between a successive pair of tube support pwhere the flow field was treated as two-dimensional. The steastate, steady-flow conservation equations for the steam-air mix

Contributed by the Advanced Energy Systems Division for publication inJOURNAL OF ENERGY RESOURCESTECHNOLOGY. Manuscript received by the AESDivision, July 19, 1999; revised manuscript received October 25, 2000. AssoEditor: A. M. Jacobi.

Copyright © 2Journal of Energy Resources Technology

loaded 16 Sep 2011 to 129.5.32.121. Redistribution subject to ASME lic

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mass, momentum, and air mass fraction were solved. Steamconsidered to be saturated at its local partial pressure,the steam-air mixture was assumed to behave as an idealOne measured pressure in each slab was used as the refevalue in the model to achieve proper distribution of the stecondensation rate. In an extension of this work@7#, the inletsteam flow rates to the slabs were redistributed until the presdrop between the inlet and the vent pipe was identical forslabs. This work is adopted as the starting point for the presstudy.

In this paper, we report the work performed in the followinsequence: the steam condenser of a 750-MWe unit at the NaGenerating Station~NGS! of Salt River Project in Page, Arizonais briefly described; the computational model for analyzingperformance of this condenser is described; the condenser amoval system model is presented; the computational domain,boundary conditions, and the computational approach arescribed; the measurements made at NGS are listed; and, finthe computational results are presented and compared withmeasurements available.

The NGS CondenserThe condenser has two sections, the low-pressure~LP! section

and the high-pressure~HP! section, Fig. 1. Exhaust steam fromthe low-pressure turbine enters the condenser from the top. Clating water enters at the LP section end and exits from thesection end.

Arrangement of the upper and lower tube bundles on eachof the condenser is shown schematically in Fig. 2. At the centeeach bundle is a vent pipe spanning the length of the condenSteam-air mixture enters each tube bundle around its peripand flows inward. The uncondensed mixture, upon reachingcenter of the bundle, enters the vent pipe through orifices distuted along its length. The orifice size decreases in the directiocirculating water~CW! flow, thus imposing a pressure drop acrothe orifice which increases in this direction. This increaseslocal pressure outside the vent pipe in the CW flow direction apromotes condensation even as the CW becomes warmer. Tare 15 tube support plates. In both the LP and the HP sectionregion between the first two tube plates~counting from the CWinlet end! contains the air cooler section. The steam-air mixturethe HP section of the vent pipe flows out of the pipe and arounbaffle, thus allowing the mixture to come in contact with a feadditional rows of tubes~these comprise the air cooler!, and thenenters the LP section of the vent pipe. The steam-air mixtexiting the LP vent pipe flows through a similar arrangement athen proceeds to the air removal system.

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Table 1 contains some of the geometric and operating pareters of the NGS condenser. In the NGS plant, circulating wexiting the condenser is piped to cooling towers.

The ModelSince the condenser is symmetric when viewed from either e

Fig. 3, it suffices to model one-half of it~either side A or side B!.Exceptions to this symmetry are the locations of the auxiliturbine exhausts. For simplification of the model, these exhaare combined with the main steam exhaust. The total mass

Fig. 1 Side view of the condenser

Fig. 2 Arrangement of the upper and lower tube bundles oneach side „A, B …; also the computational domain

82 Õ Vol. 123, MARCH 2001


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rate of the auxiliary turbine exhausts is approximately seven pcent of the main steam exhaust flow rate. Also shown in Fig. 3the replacement, in the computational model, of the divergcondenser neck by a constant-area section for simplicity.

The steam in the steam-air mixture entering the condensewet steam. We represent wet steam as saturated steam at itspartial pressure mixed homogeneously with the appropramount of water~at saturation temperature!, depending upon thelocal quality. In our model, when the wet steam passes ovecondenser tube, a portion of the wet steam flow joins the condsate inventory and the remainder continues past the tube.portion that joins the condensate inventory consists of the condsate resulting from saturated steam condensing on the tube,the water at the local saturation temperature that had been mwith the saturated steam that condensed. The rate of condensof the saturated steam is determined by the rate at which the

Table 1 Geometric and operating parameters of the NGScondenser

1The computational results presented in this paper corresponds to one vapump in operation. Cases of no pump in operation and two pumps in operationconsidered in the parametric study.

Fig. 3 View of the condenser from the circulating water inletend

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energy is transferred to the circulating water flowing throughcondenser tube. No thermal energy is transferred to the circulawater when the saturated water portion joins the condensateventory. If the variation of pressure in the condenser space isaccounted for by the model, the result will be constant quasteam flow past the condenser tubes.1

The inclusion of the thermal energy equation in the consertion equation set should be noted. Its use in the computatiodiscussed later in the paper.

The condenser interior space is modeled as a porous mediuis divided into 16 slabs or subdomains~numbered 0 through 15beginning at the CW inlet end!, each of which represents thregion between two successive tube plates. In each slab,steam-air mixture flow is considered to be two-dimensional~x, y!as the tube plates restrict flow in the axial~z! direction. Althoughthe CW temperature increases monotonically in the axial dirtion, its temperature within each slab is assumed to be at aform average temperature.

Conservation Equations—Wet Steam-Air Mixture. Thesteady-state, steady-flow, two-dimensional, local volumaveraged equations in a slab are:

Continuity (Mass Conservation) Equation

]

]x~bru!1

]

]y~brv !5bS( msource- 2( msink- D (1)

x and y-component momentum equations~written in the conser-vative form @8#!

]

]x~bru2!1

]

]y~bruv !

52b]p

]x1

]

]x S bmeff

]u

]x D1]

]y S bmeff

]u

]y D1bFx-1bS( ~msource- usource!2( ~msink- usink! D (2)

]

]x~bruv !1

]

]y~brv2!

52b]p

]y1

]

]x S bmeff

]v]x D1

]

]y S bmeff

]v]y D

1bFy-1bS( ~msource- vsource!2( ~msink- vsink! D (3)

Thermal Energy Equation~written in the conservative form!

]

]x~bruh!1

]

]y~brvh!

5]

]x S bkeff

cp

]h

]xD1]

]y S bkeff

cp

]h

]yD1bu]p

]x1bv

]p

]y

1bS( ~msource- hsource!2( ~msink- hsink! D (4)

Air Mass Fraction Equation~written in the conservative form!

]

]x~bruf!1

]

]y~brvf!

5]

]x S brD]f

]x D1]

]y S brD]f

]y D1bS( ~msource- fsource!2( ~msink- fsink! D (5)

1Pressure variation is accounted for in our model.

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The dependent variables in Eqs.~1!–~5! are the velocity com-ponentsu andv, pressurep, enthalpyh—all for the wet steam-airmixture, and the air mass fractionf.

The Source and Sink Terms. Several volumetric source ansink terms appear in the conservation equations.

Continuity Equation. The source terms represent the flowfrom the vent pipes into the appropriate control volumes in thecooler sections~i.e., the terms are nonzero for these control vumes only!.

( msource- 5mpipe,out- (6)

The sink terms are comprised of saturated steam condensand transfer of the associated entrained water to the condensaeach control volume, and the flows into vent pipe from the convolumes adjacent to the pipe.

( msink- 5mc-1mw-1mpipe,in- (7)

From the HP section air cooler, the flow enters the LP section vpipe. From the LP section air cooler, the flow enters the pleading to the air removal system. These are treated as sink tand allow mass to be properly balanced.

Momentum Equations.Because the flow from the vent pipe tthe corresponding air cooler section is in the axial~z! direction,the x andy velocity components of each source flow are zero.

msource- usource50 (8)

msource- vsource50 (9)

For the sink terms

( ~msink- usink!5mc-u1mw-u1mpipe,in- u (10)

( ~msink- vsink!5mc-v1mw-v1mpipe,in- v (11)

The sources associated with the forces are

Fx-52Fdrag,x- 1Fgravity,x- (12)

Fy-52Fdrag,y- 1Fgravity,y- (13)

Thermal Energy Equation

( ~msource- hsource!5mpipe,out- hpipe,out (14)

( ~msink- hsink!5~mw-1mc-!hs1mpipe,in- h (15)

Air Mass Fraction Equation

( ~msource- fsource!5mpipe,out- fpipe,out (16)

( ~msink- fsink!5mpipe,in- f (17)

Auxiliary Equations

Steam Condensation Rate.The volumetric rate of saturatesteam condensation in a control volume is obtained as

mc-5S UAsurf-

hf gD S ~Ts2To!2~Ts2Ti !

lnS Ts2To

Ts2TiD D (18)

Heat transfer from the steam/air mixture to the circulating wain condenser tubes is assumed to be only in the radial direct

MARCH 2001, Vol. 123 Õ 83


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Therefore, a one-dimensional resistance model may be usecalculate an overallcleanheat transfer coefficient

Uclean51

RTOTAL,clean(19)

where

RTOTAL,clean5RINNER1RMETAL1ROUTER (20)

The resistance components are calculated from standard exsions @9#. Of the components,RMETAL has the smallest valuewhile RINNER andROUTER are of the same order of magnitude withe latter typically being somewhat larger.

The fouling resistance is incorporated via the use of a cleaness factor~CF!

U5UcleanCF (21)

where CF is taken to be 0.85.

Heat Transfer Coefficients.The tube inner surface heat tranfer coefficient is calculated from the Dittus-Boelter correlatioAll circulating water properties are obtained at the average ofinlet and outlet temperatures for the control volume.

The condensation heat transfer coefficient at the tube outerface,ho8 , is calculated from Fujii’s@10# modification of the Nus-selt correlation for condensation. The effect of vapor shear iscounted for by this modification. The effect of condensainundation is represented by the expression@11#

ho5ho8S mgen

mdrainD n

(22)

with n520.223.

Fluid Properties. All wet steam/air mixture properties are caculated from the general relation

Q5function~p,h,f! (23)

The partial pressure of steam is obtained as

ps5pMa~12f!

Ma~12f!1Msf(24)

Properties for saturated steam and water are evaluated asteam partial pressure using routines provided in the ASME 1IFC steam table. Wet steam properties, including specific volucan be calculated from

Qs5xQg1~12x!Q f (25)

provided the quality,x, is known.Air properties are evaluated from ideal gas relations for air

its partial pressure and the saturated steam temperature.The wet steam-air mixture specific enthalpy calculated by

thermal energy Eq.~4! is

h5hs~12f!1haf (26)

The specific enthalpy of air evaluated from ideal gas is substituinto Eq. ~26! to obtain the wet steam specific enthalpyhs . Thecorresponding steam quality can now be calculated

x5hs2hf

hg2hf(27)

Using the wet steam condensation process model describedlier, the steam quality changed only slightly in the course offlow through the condenser.

The wet steam-air mixture density is calculated as

r5rs1ra (28)

Other specific properties of the mixture, such as entropy andternal energy, can be calculated as

84 Õ Vol. 123, MARCH 2001


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Effective Viscosity and Thermal Conductivity of the FluThese are given by

meff5m1m t (30)

keff5k1kt (31)

It is assumed that the turbulent viscosity and turbulent therconductivity are about two orders of magnitude larger thancorresponding molecular values. For example

m t5150m (32)

and Prt5cpm t

kt50.9 (33)

Equation~33! gives

kt5cpm t

0.9(34)

The multiplication factor in Eq.~32! does not affect the computational results significantly when in the 100–200 range of valuThe insensitivity of the solution to several-fold changes in tvalues ofm t andkt has been documented earlier@6#.

Vent Pipe Flow Rate. The mass flow rate through a vent pipsegment of lengthLvp is expressed as@12#

mvp5AKvprDpvp (35)

Fig. 4 A schematic diagram of the air removal system

Fig. 5 Model of an air ejector stage



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Fig. 6 Steam and circulating water outlet temperature measurement locations—side A

o

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whereKvp , the pipe admittance, is

Kvp5p2dvp

5

9 f Lvp(36)

The friction factor,f, for the pipe is taken to be twice the value fofully developed flow in a steel pipe. This is a conservative esmate to account for the fact that the flow is not fully develope

The volume flow rate from the condenser interior space intvent pipe through an orifice is calculated as@12#

q5CAorificeA2rDporifice (37)

with C50.6.

Condenser Air Removal System. The air removal system isshown schematically in Fig. 4. During normal operation, tsteam-air mixture flows out of the LP section air cooler into a pleading to the two-stage air ejector and a vacuum pump. A sec

Fig. 7 Pressure measurement locations „side A …

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vacuum pump is available for use during startup of the unit. Tsecond vacuum pump is included in a parametric study repolater in the paper.

We also introduce anexternal air cooler as an option in aparametric study. Circulating water is supplied to this air cooto condense an additional amount of steam from the steammixture before it proceeds to the air removal system. This lowthe condenser pressure under conditions of significant airleakage.

Air Ejector Model. For each air ejector stage, a simpmodel@13# which has been shown to agree well with experimeis used. Figure 5 shows the model. The equations usedconservation of energy and air mass fraction for the stage, enbalances across the nozzle and the diffuser, conservation ofmentum in the mixing section, and nozzle and diffuser isentro

Fig. 8 Axial distribution of mixed-mean circulating watertemperature

MARCH 2001, Vol. 123 Õ 85


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efficiencies. The equations are solved for the ejector stage supressure~location 3!. A perfect intercondenser is assumed in tsense that steam condensation takes place at the coolinginlet temperature and the partial pressure of the steam is redto the corresponding saturation pressure. The main condensasplit between the tube sides of the ejector condensers andgland steam condenser to serve as the cooling fluid.

Assuming that the air in-leakage rate to the condenseknown, the performance of the air removal system can be chaterized by the suction pressure that it can achieve. This preswas measured at the plant. The air ejector nozzle and diffu

Fig. 9 Steam-air inlet flow rate for each computational slab

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tioneatercedte isthe

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isentropic efficiencies are used as tuning parameters to recothe calculated pressure with the measurement. The higher thficiencies, the lower the suction pressure achievable for a gimotive steam flow rate.

External Air Cooler. As mentioned earlier, this is a hypothetcal component which is introduced for a parametric study. Fsimplicity, its performance is characterized by its ‘‘effectivness.’’ The effectiveness is defined as the ratio of the actual stcondensation rate to the maximum possible steam condensrate. The maximum possible steam condensation rate reducesteam partial pressure to the saturation pressure correspondithe CW inlet temperature.

The Computational DomainThe domain measures 4.27 m in thex direction and 8.0 m in the

y direction, Figs. 2 and 3. The computational steam inlet plawas chosen such that the calculated flow field at the plane wthe condenser neck ends and the tube bundle space begins wminimally affected by the simplified neck configuration.

Boundary Conditions. The boundaries of the computationdomain may be divided into two groups: internal and externThe external boundaries are the steam inlet plane, the condewalls and floor, and the symmetry plane. The entries to and efrom the vent pipes constitute the internal boundaries. Theseincorporated via the source and sink terms in the governequations.

Steam Inlet Plane. The steam-air mixture enters the condensat this plane with a known total mass flow rate, steam quality,

Fig. 10 Contours of „a… air mass fraction, and „b… steam condensation rate per computational cell „kg Õs… forSlab 1



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Fig. 11 Contours of „a… air mass fraction, and „b… steam condensation rate per computational cell „kg Õs…for Slab 9

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air mass fraction. In both the LP and HP sections, the pressurequired to be uniform at this plane. That such uniformity of prsure exists was verified by measurements at the plant. Theother constraint on the pressure is

]2p

]y2 50 (38)

This is equivalent to drawing a straight line through the first asecond grid points from the boundary, and obtaining the valuthe boundary by extrapolation.

Condenser Walls and Floor.The walls are considered to bimpermeable. The no-slip condition is not used at the walinstead, an extrapolation similar to the pressure is used to obtafictitious velocity at the wall. Wall shear stress is neglectedcause its effect on the flow field would be small compared todrag due to the tubes.

Symmetry Plane. The x-component of velocityu, and the de-rivatives with respect tox of v, p, h, andf are set to zero at thisplane.

Computational ApproachGoverning Eqs.~1!–~5! are discretized over a two-dimension

~x, y! staggered grid~typically 19336!. The discretization ex-pands on the derivation of the SIMPLER algorithm of Patan@14#, the expanded derivation accounting for the porosity of

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medium, and the source and sink terms. Additionally, a lineariequation set representing the air removal system2 is solved.

An outer iteration loop is employed to converge to the corredistribution of flow to each slab at the steam/air mixture inplane. The slabs are solved in succession from the CW inlet enthe CW outlet end. After each outer iteration, the steam/air mture inlet flow to the slabs are redistributed to achieve a unifopressure distribution at the inlet plane of LP and HP sectionsthe condenser.

An inner solution scheme is used for each slab. The equatisolved are:

~i! the pressure equation, derived from the mass conservaequation;

~ii ! the momentum equations;~iii ! the pressure correction equation;~iv! the velocity correction equations;~v! the thermal energy equation; and~vi! the air mass fraction equation.

An iterative scheme is not used because at small air masstions, the air mass fraction discretization equation violates onthe criteria for convergence of iterative solutions@14#

ap>( aI (39)

2The air removal system is modeled by a set of nonlinear equations@9#.

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Fig. 12 Fluid velocity vectors for „a… Slab 1, and „b… Slab 9

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A direct method of solution for the elliptic system of equationsused. The coefficient matrix being sparse, a routine which utiliLU decomposition of a sparse matrix is employed.

MeasurementsMeasurement instruments were installed in the NGS conde

during the early period of the project. The instruments werefollows:

• Steam temperature—this was measured by resistanceperature detectors~RTD—Omega! in selected condenser tubewhich were plugged. With no water flow in these tubes, the lofluid temperature inside each tube would equal the steam tempture outside. The uncertainty in the RTD measurements wasmated to be60.2°C. The RTDs were installed a few inches dowstream of the CW inlet~S in Fig. 6~a!! and a few inches upstreamof the CW outlet~S8 in Fig. 6~a!!. Figure 6~a! shows side A of thecondenser only.

• CW temperature—RTDs were used for this measument also. The CW inlet temperature was measured atlocation on each side~A, B! of the condenser. The locationwhere the CW outlet temperature was measured on side Ashown in Fig. 6~b!, these being locations just upstream of the tuoutlets.

• Temperature in air removal system—the steam/air mture temperature at the inlet to this system was measuredRTD.

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• Pressure in the condenser—Figure 7 shows the pressurelocations on side A of the condenser. A digital manometer~Me-riam! was used, the uncertainty in the measured pressure b60.04 kPa.

• Pressure in the air removal system—The steammixture pressure at the inlet to this system was also measby a digital manometer~Meriam! with an uncertainty of60.04kPa.

Computational ResultsFigure 8 shows the axial distribution of CW temperature fro

the inlet end to the outlet end. The location of the partition btween the LP and HP sections is also shown. Figure 9 showscalculated steam-air mixture mass flow rate at the inlet planeeach of the 16 computational slabs. The highest flow rate is atCW inlet end of the LP section. The next highest flow rate isthe CW inlet end of the HP section. We note again that the psure at the inlet plane is uniform in each of the two sectionshas different values in them.

As indicated in Table 1, the case being studied has a significair in-leakage rate. We present first the air mass fractionsteam condensation rate results for slab 1. This is followed byresults for slab 9. These slabs were chosen rather than slabs8 because the latter contain the air coolers and hence, woulexpected to differ from the other slabs.

The deleterious effect of air on condensation of steamsignificant only when the air mass fraction is sufficiently hig



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Fig. 13 Contours of pressure „Pa… for „a… Slab 1, and „b… Slab 9

I

‘

nb

Theover0.06isbe

Pierce and Rennie@5# found that a tube bundle can be divideinto two regions: one which is essentially unaffected by the prence of air, and one in which air greatly inhibits steam condention. The extents of the regions, of course, vary along the bunaxis. As the steam-air mixture flows inward through a tubundle, the air mass fraction increases in the freestream.reaches a high value before the mixture has penetrated deepthe bundle, then a large part of the heat transfer surface inbundle interior will contribute only minimally to the condensatioof steam. Such an interior region is usually referred to as an ‘bubble.’’ In Fig. 10~a!, air mass fraction contours at four values—0.0001, 0.001, 0.01, and 0.1—are shown for slab 1. If 0.1 is csen as an arbitrary but reasonable value of air mass fractiomark the beginning of an air bubble, the presence of an air buis seen at the interior of each~upper, lower! tube bundle. Figure10~b! shows the steam condensation rate~per computational cell!

Table 2 Steam temperatures near the circulating water outletplane

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contours for slab 1 at three levels: 0.02, 0.04, and 0.06 kg/s.condensation rate increases from essentially zero to 0.06 kg/sa small distance near the bundle periphery. It decreases fromto 0.02 kg/s also over a small distance in the interior. Thisconsistent with the calculated location of air bubble in each tubundle.

Table 3 Circulating water temperature— „a… at inlet, „b… atoutlet

MARCH 2001, Vol. 123 Õ 89


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Figure 11~a! shows the air mass fraction contours at three vues~0.0001, 0.001, and 0.01! for slab 9. The contour corresponding to 0.1 is calculated to be very close to the vent pipe in bbundles and is not shown. Figure 11~b! shows that the sharp droin steam condensation rate occurs very close to the vent pipboth bundles. Thus, the air bubble is essentially nonexistenslab 9 and the available heat transfer surface area is utilizedmore effectively in this slab compared to slab 1.

Table 4 Steam-air mixture pressure— „a… above tube bundles,„b… below tube bundles

Table 5 Air removal system inlet pressure and temperature

Table 6 Effect of air removal capacity on condenser pressure„all pressures in kPa …—„a… LP section „location: SUB 1 …, „b… HPsection „location: SUB 6 …

Table 7 Effect of air removal capacity on total „condenser andcooling tower … irreversibility rate „MW…

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far

Figures 12~a! and ~b! are plots of the steam-air mixture velocity vectors for slab 1 and slab 9, respectively. In each cathe fluid enters at the top with a uniform downward velocitflows around the tube bundles, and enters them from the pphery. In Fig. 12~a!, a region is seen near the center of eabundle where the fluid velocity is very small. This is insidthe calculated air bubble. This region has shrunk considerablFig. 12~b!.

Figures 13~a! and~b! show the calculated pressure contours~inPascals! for some regions of slab 1 and slab 9, respectively. Tcontours are spaced 250 Pa apart. Only those regions are swhere the pressure gradient is significant. Significant pressuredient is maintained deeper into the tube bundles in slab 9, incating appreciable fluid velocity since the velocity is proportionto the square-root of the pressure drop. This is consistent withvelocity vector plots in Figs. 12~a! and ~b!.

The results shown for slabs 1 and 9 are typical of slabs inLP section and HP section, respectively, of the condenser. Tsuggest that the LP section back pressure is more sensitive tair in-leakage rate and the efficacy of the air removal system tis the HP section back pressure.

Comparison With Test DataThe RTDs that were installed for measuring steam tempera

near the CW inlet plane failed. Table 2 compares the calculaand measured values near the CW outlet plane. The agreemegenerally good.

Tables 3~a! and ~b! contain, respectively, the measured Cinlet temperature and the calculated and measured CW outletperatures. In Table 3~b!, the agreement is good except for thlocations 30W and 60W. Both these locations are inside thedicted air bubble where the steam condensation rate is low anis the calculated rise in CW temperature. The RTD data, howedo not reflect this. This discrepancy, to some extent, may beto the relatively coarse grid in our computation. It has been sgested that transition to high air mass fraction typically occover two to three tube rows and this can be difficult to resolvesome locations with the present grid.

The calculated steam-air mixture pressures are in better agment with the measured pressures for the LP section comparethe HP section, Tables 4~a! and~b!. The pressure taps above anbelow the tube bundles had been located so as to measure prevariation, if any, in the CW flow direction. No such variationapparent from the measured data, and little variation is seen fthe calculation.

Table 5 compares the calculated and measured steam-airture pressure and temperature at the air removal system inlet.agreement is generally good.

Parametric StudyThe parameters studied for their effects on condenser

formance are: air in-leakage rate, circulating water inlet teperature, tube cleanliness factor, external air cooler effectness, and the number of vacuum pumps in operation~;airremoval capacity!. For brevity, only the effects of the air inleakage rate and the number of vacuum pumps in operation~i! the HP section and LP section pressures, and~ii ! the totalsystem ~condenser plus cooling tower! irreversibility rate arepresented here. Three air in-leakage rates are consideredscfm ~0.0295 kg/s!, 20 scfm~0.0116 kg/s!, and 10 scfm~0.0058kg/s!.

Tables 6~a! and~b! contain the calculated results for the LP anHP section pressures. The highlighted values correspond tonormal operating condition at 100 percent load. Thefailed casesare conditions where the air in-leakage rate is beyond the capity of the air removal system—i.e., the high condenser presscauses a plant trip. It should be noted that, in the parameter raconsidered, while the LP section pressure is significantly affec



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by the number of vacuum pumps in operation, such is not the cfor the HP section pressure. This is consistent with the comptional results presented earlier.

Table 7 shows the calculated results for the total irreversibirate. The deleterious effect of air accumulation on condenserformance can be seen.

Concluding RemarksA computational model of a power plant steam condense

developed. The model is capable of analyzing the effects ofin-leakage and removal rates on the performance of the condeThe steady-state steady-flow balance equations for thesteam-air mixture mass, momentum, thermal energy, andmass fraction are solved on a series of two-dimensional grThe condenser interior space is modeled as a porous medThe wet steam is represented as saturated steam at itspartial pressure mixed homogeneously with the appropramount of water~at saturation temperature! depending upon thelocal quality. A simple model for wet steam condensationintroduced.

The computational results are compared with the limimeasurements available. It is found that a condenser wlacks sufficient air removal capacity at any given air in-leakarate will not make proper use of its heat transfer surface arealarge part of the area will be used to condense a small portiothe entering steam. The heat transfer surface area will bemore effectively if the air removal system can maintain a loenough air mass fraction to avoid inhibition of steam condention. Furthermore, the condenser performance is degradebuildup of air occurs in that the system irreversibility rate icreases. Given the significant impact of a small rise in condepressure on the power generation capacity of a steam turbinea condenser model needs to be able to predict this effect in oto be useful.

Representation of the wet steam-air mixture as containing srated steam, entrained water droplets of appropriate size disttion, and air will constitute a significant improvement of thmodel. This work is left for the future.

The configuration of the condenser steam inlet region wsimplified in this study for computational simplicity. A morprecise representation of this region and inclusion of thepressure turbine exhaust path in the model could be worthwimprovements.

More detailed and accurate measurement of pressure, temture, and perhaps air concentration distribution will also be helpfor further improvement of the model.

AcknowledgmentsThis research was funded by Salt River Project, Phoenix, A

zona. The able assistance of Mr. Richard Schumm of Salt RProject Research and Development Department is gratefullyknowledged.

Nomenclature

Asurf- 5 heat transfer surface area per unit volume of tubebundle space@m21#

cp 5 steam-air mixture specific heat at constant pressure@J/kg/K#

dvp 5 vent pipe diameter@m#D 5 mass diffusivity of air in steam-air mixtureh 5 wet steam-air mixture specific enthalpy@J/kg#

hf g 5 latent heat of evaporation@J/kg#

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hs 5 wet steam specific enthalpy@J/kg#Lvp 5 vent pipe segment length@m#

k 5 steam-air mixture thermal conductivity@W/m/K#kt 5 turbulent thermal conductivity@W/m/K#

mc- 5 volumetric rate of saturated steam condensation@kg/m3/s#

mdrain 5 rate of condensate drain from tube@kg/s#mgen 5 rate of condensate generation on tube@kg/s#msink- 5 volumetric mass sink@kg/m3/s#

msource- 5 volumetric mass source@kg/m3/s#mw- 5 volumetric transfer rate of water in wet steam to co

densate inventory@kg/m3/s#M 5 molecular weightp 5 steam-air mixture pressure@Pa#

ps 5 steam partial pressure@Pa#Prt 5 turbulent Prandtl no.@dimensionless#

u 5 x-component of steam-air mixture velocity~m/s!v 5 y-component of steam-air mixture velocity~m/s!b 5 porosity @dimensionless#f 5 air mass fraction@dimensionless#m 5 steam-air mixture viscosity@kg/m/s#

m t 5 turbulent viscosity@kg/m/s#r 5 wet steam-air mixture density@kg/m3#Q 5 any property

Subscripts

a 5 airf 5 saturated waterg 5 saturated steams 5 wet steam

References@1# Tsou, J. L., 1990, ‘‘Condenser Performance Prediction Calculation Pro

dure,’’ American Power Conference, Chicago, IL.@2# Tsou, J. L., 1994, ‘‘New Approaches to Condenser Performance Analys

American Power Conference, Chicago, IL.@3# Al-Sanea, S., Rhodes, N., Tatchell, D. G., and Wilkinson, T. S., 1983,

Computer Model for Detailed Calculation of the Flow in Power Station Codensers,’’Condensers: Theory and Practice, The Institution of Chemical En-gineers Symposium Series No. 75, Pergamon Press, pp. 70–88.

@4# Caremoli, C., 1983, ‘‘Numerical Computation of Steam flow in Power PlaCondensers,’’Condensers: Theory and Practice, The Institution of ChemicalEngineers Symposium Series No. 75, Pergamon Press, pp. 89–96.

@5# Pierce, D. L., and Rennie, E. J., 1993, ‘‘Improving Condenser PerformaUsing the EPOC Code,’’EPRI Condenser Technology Conference, St. Peters-burg, FL.

@6# Zhang, C., Sousa, A. C. M., and Venart, J. E. S., 1993, ‘‘The NumericalExperimental Study of a Power Plant Condenser,’’ ASME J. Heat Transf115, pp. 435–445.

@7# Zhang, C., 1994, ‘‘Numerical Modeling Using a Quasi-Three-DimensioProcedure for Large Power Plant Condensers,’’ ASME J. Heat Transfer ,116,pp. 180–188.

@8# Roache, P. J., 1972,Computational Fluid Dynamics, Hermosa Publishers, Al-buquerque, NM.

@9# Ratisher, M., 1998, ‘‘Development of a Computational Model for PredictionPower Plant Steam Condenser Performance,’’ M.S. thesis, Arizona Stateversity, Tempe, AZ.

@10# Fujii, T., 1981, ‘‘Vapor Shear and Condensate Inundation: An OverviewPower Condenser Heat Transfer Technology, eds., P. J. Marto and R. HNunn, Hemisphere, pp. 193–223.

@11# Butterworth, D., 1981, ‘‘Inundation without Vapor Shear,’’Power CondenserHeat Transfer Technology, eds., P. J. Marto and R. H. Nunn, HemispherNew York, NY, pp. 271–277.

@12# White, F. M., 1986,Fluid Mechanics, Second Ed., McGraw-Hill, New York,NY.

@13# Rao, S. P. R., and Singh, R. P., 1988, ‘‘Performance Characteristics of SinStage Steam Jet Ejectors Using Two Simple Models,’’ Chem. Eng. Comm66, pp. 207–219.

@14# Patankar, S. V., 1980,Numerical Heat Transfer and Fluid Flow, Hemisphere,New York, NY.

MARCH 2001, Vol. 123 Õ 91


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