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Binding Energy per nucleon Excess binding energy is released in any nuclear reaction in which heavy-mass nucleus is broken into two intermediate-mass nuclei. Combining two light-mass nuclei into a heavier nucleus also releases binding energy. Radioactive decay is the release of binding energy as a nucleus decays to a more stable isotope. most stable nuclei

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Page 1: Binding Energy per nucleon - Michigan Tech IT Support …pages.mtu.edu/~jstallen/courses/MEEM4200/lectures/nuclear/nuclear... · Binding Energy per nucleon ... Steam, 40th ed., Babcock

Binding Energy per nucleon

Excess binding energy is released

in any nuclear reaction in which

heavy-mass nucleus is broken into

two intermediate-mass nuclei.

Combining two light-mass nuclei

into a heavier nucleus also

releases binding energy.

Radioactive decay is the release of

binding energy as a nucleus decays

to a more stable isotope.

most stable nuclei

Page 2: Binding Energy per nucleon - Michigan Tech IT Support …pages.mtu.edu/~jstallen/courses/MEEM4200/lectures/nuclear/nuclear... · Binding Energy per nucleon ... Steam, 40th ed., Babcock

Fission Probability

[K&R, 1993]

Neutron Cross Section

[Culp, 1991]

2

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Types of Neutron Reactors

Fundamentals of Nuclear Science and Engineering, 2nd ed., Shultis and Faw, CRC Press, 2008.

3

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U.S

.N

ucl

ear

Pow

er

React

ors

4

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Babcock & Wilcox

lowing general description applies to Oconee Unit 1, although it is generally applicable to all U.S. B&W plants;the concepts are applicable to all PWRs.

Containment buildingFig. 2 is a vertical section of the reactor containment

building. The structure is post-tensioned, reinforced concrete with a shallow domed roofand a flat foundation slab.The cylindrical portion is prestressed by a post-tensioningsystem consisting ofhorizontal and vertical tendons. Thedome has a three way post-tensioning system. The foundation slab is conventionally reinforced with highstrength steel. The entire structure is lined with 0.25 in.(6.3 mm) welded steel plate to provide a vapor seal.

The containment building dimensions are: inside di-

ameter 116 ft (35.4 m); inside height 208 ft (63.4 in); wallthickness 3.75 ft (1.143 m); dome thickness 3.25 ft (0.99m); and foundation slab thickness 8.5 ft (2.59 m). Thebuilding encloses the reactor vessel, steam generators,reactor coolant loops, and portions of the auxiliary andsafeguard systems. The interior arrangement meets therequirements for all anticipated operating conditions andmaintenance, including refueling. The building is designed to sustain all internal and external loading conditions which may occur during its design life.

Reactor vessel and steam generatorsAlso shown in Fig. 2 are the reactor vessel and the two

vertical steam generators, each of which produces approximately 5.6 x 106 lb/li (705.6 kg/s) of steam at 910

1

OnceThroughSteam Generators (2)

fl

/

/Reactor coolant

Pumps (4)Pressurizer

I

Fig. 3 B&W nuclear steam supply system.

Reactor Vessel

47-4 Steam 40 / Nuclear Installations for Electric Power

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Thium, was designed and subsequently built. Italy andr Japan also built versions of these British designs.

The Soviet Union developed a graphite-moderated,boiling water-cooled, enriched uranium reactor from itsearly Obninsk power station design. A major differencein this reactor from similar Western designs was that itdid not include a sturdy reactor containment buildingThe early Soviet goals included the development of na*val propulsion reactors based upon the PWR conceptwhich was then applied to civilian use. This PWR designwas exported to several Soviet bloc countries and Finland. The Soviet PWR was similar to the U.S. designsexcept it generally provided significantly lower electrical output

The excellent moderator characteristics of deuteriumoxide (heavy water) became the basis for the very successful Canadian deuterium (CANDU) reactors. Thesenatural uranium-fueled reactors were first operated in1962 (25 MW Nuclear Power Demonstration reactor at

1: Rolphton, Ontario), and subsequent designs increasedoutput to 800 MW. CANDU designs have been built inIndia, Pakistan, Argentina, Romania and South Korea.

In Japan, electric utilities were experimenting withseveral types ofimported nuclear generation plant designs.They ordered gas-cooled reactors from the U.K., and BWRand PWR designs from the U.S. The Japanese governmentalso began sponsorship of a breeder reactor design.

The Germans were actively involved in designs primarily associated with high temperature gas reactor

J concepts. In 1969, the formation of Kraftwerk Union introduced German PWR and BWR designs based on U.S.

• technology. The intent was to construct a series of theseplants to achieve economies of scale. However, unlike theFrench program, few plants were constructed. SeveralGerman PWRs were exported to Brazil, Spain, Switzerland and the Netherlands

The energy crisis of the mid 1970s caused significantreductions in worldwide electric usage growth rates, and

Steam 40/ Nuclear Installations for Electric Power

structure between reactor buildings 1 and 2. Corresponding equipment for Unit 3 is located separately. The fol

47-3

Fig. 2 PWR containment building, sectional view.

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rWilcox —

NSSS. The first of these lainto operation in 1987 at thstation in West Germany. Tder construction in the U.S

The NSSS for a typical sewater reactor consists of thsteam generators, coolant rpiping to connect these comsimplified schematic provi’sists of two water flow circuses pressurized water tot,core to the steam generatireactor coolant pump. Thprimary loop pressure higeneration in the reactor eThe steam generators provmary coolant loop and theflow loop. In the B&W desiwater enters the steam gedheated steam, which is sonduce power. The primary Rsupplying the energy to goinformation is included in

Fig. 6 shows a reactor vetsteam generators inside a ciselis constructed oflowaflcless steel cladding. Externtis 20.75 ft (6.32 m) with an Im) including the closure Ihead is held in place by Mihigh tensile alloy steel stuivessel and closure head is

The vessel has six majiflow (two outlet hot leg ancant water enters the vestnozzles located above theflows downward in the amtor vessel and the internathe core and upper plenulthe upper portion of the vhot leg nozzles. Fkr 7 finia nuclea

Babcock &

Fig. 4 Reactor containment building, ground floor plan view.

psi (62.7 bar) and 595F (313C). This provides GOF (33C)of superheat. The B&W nuclear steam supply system(NSSS) (Fig. 3) is the only large scale commercial designthat provides the added benefit of superheated steamoutput. A plan view ofthe containment building is shownin Fig. 4. The concrete shielding around the NSSS components is also shown. Table 1 provides a listing of theimportant design parameters for the Oconee-type NSSS.Adso provided are the design parameters for a larger B&W

PrimaryFlow Loop

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•r i’c”? r—U IImnd1 o.’-fl_ primary loop press1j rnw’ngeneration in the reactorThe steam generators provide the Iimary coolant loop and the power pflow loop. In the B&W design, subecwater enters the steam generator anheated steam, which is sent to the siduce power. The primary side watersupplying the energy to generate U,information is included in Table 1 a

Fig. 6 shows a reactor vessel beingsteam generators inside a containmesel is constructed oflow alloy steel wiless steel cladding. External diametis 20.75 ft (6.32 m) with an internal hm) including the closure head. Thhead is held in place by sixty R 5 ir,high tensile alloy steevessel and closure he

The vessel has sbflow (two outlet hot leg and tour muant water enters the vessel throu;nozzles located above the midpointflows downward in the annular spator vessel and the internal thermathe core and upper plenum, downthe upper portion of the vessel andhot leg nozzles. Fig. 7 shows a reacta nuclear power plant site.

Fig. 4 Reactor containment building, ground floor plan view.

psi (62.7 bar) and 59SF (313C). This provides 60F (33C)of superheat. The B&W nuclear steam supply system(NSSS) (Fig. 3) is the only large scale commercial designthat provides the added benefit of superheated steamoutput. A plan view ofthe containment building is shownin Fig. 4. The concrete shielding around the NSSS components is also shown. Table 1 provides a listing of theimportant design parameters for the Oconee-type NSSS.Also provided are the design parameters for a larger B&W

Inlet

Steam Outlet

To Turbine— —--- —. —

— — — ——--.-

From LastFeedwater Heater

Baffle

t Loop4 4 4

system Containment

515—Safety Injection System

Fig. 5 Simplified schematic of primary and secondary loops.

———

Secondary coolant Loop

Steam 40 / Nuclear Installations for Electric Power

Fig. 6 Reactor vessel pk

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Page 9: Binding Energy per nucleon - Michigan Tech IT Support …pages.mtu.edu/~jstallen/courses/MEEM4200/lectures/nuclear/nuclear... · Binding Energy per nucleon ... Steam, 40th ed., Babcock

Reactor Concepts Manual Pressurized Water Reactor Systems

USNRC Technical Training Center 4-20 0603

REACTOR COOLANTSYSTEM

CONTAINMENT

CORE

S/G

PZR

RCP

CONTAINMENT SUMP

SAFETYVALVES

MOISTURE SEPARATORREHEATER (MSR)

THROTTLEVALVE

MAIN STEAMISOLATION VALVE

(MSIV) HP LP LP

MAINTURBINE ELECTRIC

GENERATOR

MAINCONDENSER

CIRC.WATER

CIRC.WATER

LPHEATER

CLEAN UPSYSTEM

CONDENSATEPUMP

MAINFEEDWATER

PUMP

HPHEATER

LPHEATER

The major secondary systems of a pressurized water reactor are the main steam system and thecondensate/feedwater system. Since the primary and secondary systems are physically separated from each other(by the steam generator tubes), the secondary system will contain little or no radioactive material.

The main steam system starts at the outlet of the steam generator. The steam is routed to the high pressure mainturbine. After passing through the high pressure turbine, the steam is piped to the moisture separator/reheaters(MSRs). In the MSRs, the steam is dried with moisture separators and reheated using other steam as a heatsource. From the MSRs, the steam goes to the low pressure turbines. After passing through the low pressureturbines, the steam goes to the main condenser, which is operated at a vacuum to allow for the greatest removalof energy by the low pressure turbines. The steam is condensed into water by the flow of circulating waterthrough the condenser tubes.

At this point, the condensate/feedwater system starts. The condensed steam collects in the hotwell area of themain condenser. The condensate pumps take a suction on the hotwell to increase the pressure of the water. Thecondensate then passes through a cleanup system to remove any impurities in the water. This is necessarybecause the steam generator acts as a concentrator. If the impurities are not removed, they will be left in thesteam generator after the steam forming process, and this could reduce the heat transfer capability of the steamgenerator and/or damage the steam generator tubes. The condensate then passes through some low pressurefeedwater heaters. The temperature of the condensate is increased in the heaters by using steam from the lowpressure turbine (extraction steam). The condensate flow then enters the suction of the main feedwater pumps,which increases the pressure of the water high enough to enter the steam generator. The feedwater now passesthrough a set of high pressure feedwater heaters, which are heated by extraction steam from the high pressureturbine (heating the feedwater helps to increase the efficiency of the plant). The flow rate of the feedwater iscontrolled as it enters the steam generators.

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Reactor Concepts Manual Pressurized Water Reactor Systems

USNRC Technical Training Center 4-18 0603

RELIEFNOZZLE

HEATER SUPPORTPLATE

SURGE NOZZLE

SUPPORT SKIRT

ELECTRICAL HEATER

INSTRUMENTATIONNOZZLE

LOWER HEAD

SHELL

LIFTINGTRUNNION

(LOAN BASIS)

INSTRUMENTATIONNOZZLE

UPPER HEAD

MANWAY

SAFETY NOZZLE

SPRAY NOZZLE

Cutaway View of a Pressurizer

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ower Plant Engineering

97,600 gpm (6.15 m3Is)280 ft (85.3 m)2,500 psia (17.2 MPa)650° F (343° C)28 ft (8.5 m)1,1896ft-5 in. (196 cm)7,000 hp (5,220 kW)

ssure parts are carbon or low-alloy steel. Areasreactor coolant contact are clad with stainless steel

tghouse and Combustion Engineering use U-tubeierators. Thç steam generators used by Babcock &t vertical, straight tube and shell exchanges. Reacit enters at the top of the steam generator and slowsd through the Inconel tubes and exits at the bottomtin generator. Feedwater enters the steam generatormiddle and flows down an annulus between theDerator shell and tube baffle and enters near therhe water, as it passes up the steam generator, isIto steam. The steam is superheated before leavinggenerator. Since the steam is superheated, moisture

s and dryers are not used.ses or decreases in the generating plant electrical;e fluctuations in the reactor coolant pressure. Ar on one of the RCS loops is used to limit pressureluring load transients and to maintain constant coolm pressure during steady-state operation. Figure,ws a typical pressurizer. The pressurizer contains

creases above the pressurizer’s capability. Both relief andsafety valves vent to a pressure relief tank that containscooler water for condensing steam. A pressurizer for a largefour-loop design has a typical height of approximately 53 ft(16.2 in), with an 8 ft (2.3.m) diameter, and contains approximately 75 immerser heaters with 1,800 kW of power. Thepressurizer is low-alloy steel with stainless steel interior

8. Typical Design Parameters and Data for Componentsof a Large Four-Loop PWR

SPRAYNOZZLE

RELIEFNOZZLEolant pump

atureheight

ngrpmdiameter

erator (U-tube)height

shell diameter (outside)shell diameter (outside)pressure (tube side)ng pressure (tube side)e (shell side)pressure (shell side)

How ratecoolant flow ratecoolant inlet temperaturecoolant outlet temperature

ight

67 ft-8 in. (20.6 m)14 ft-7¼ in. (4.5 m)11 ft-3 in. (3.4 m)2,500 psia (171.2 MPa)2,250 psia (15.5 MPa)1,000 psia (6.9 MPa)1,200 psia (8.3 MPa)3.8 x 106 lbih (480 kgls)35 x 106 lb/h (4,419 kg/s)621°F (327° C)558°F (292°C)346 tons (314 tonnes)

stinghouse 1984.

NOZZLE

MAN WAY

UPPER HEAD

INSTRUMENTATIONNOZZLE

TEMPORARYLIFTING

TRUNNION

SHELL

ELECTRICALHEATER

INSTRUMENTATIONNOZZLE

HEATERSUPPORT

PLATE

LOWER HEAD

SURGE

Fig. 23-12. Pressurizer for a large PWR design. (From Westinghouse.Used with permission.)

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Reactor Concepts Manual Pressurized Water Reactor Systems

USNRC Technical Training Center 4-19 0603

RCS

RCS

SPRAYVALVES

SAFETIES

RELIEFS

PRESSURIZER

HEATERS

SURGE LINE

REACTOR COOLANTSYSTEM (RCS)

PRESSURIZERRELIEF TANK

DRAIN

VENT

COOLINGSPRAY

Pressurizer and Pressurizer Relief Tank

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t[IWdI .sm-a+tari steam then passes through moisture separators in the upper

Fig. 23-li. Steam generator for a large PWR. (From Westinghouse.Used with permission.)

Steam Nozzlewith IRestrictor

MIXINGVANES

DASHPOTREGION

DIMPLE

THIM8LESCREW

17 Fuel assembly with control rod cluster. (Fromsed with permission.)

pical Reactor Fuel Parameters for a Large PWRmr-Loop Design

FeedwaterNozzle

steam generator shell, where the entrained liquid is removed.The steam then passes through steam dryers to raise thesteam quality to 99.75%. Table 23-8 shows typical parameters and other data for reactor coolant pumps and steamgenerators used in a large four-loop PWR design. The steamgenerator U-tubes are made of Inconel, and the shell and

SecondarySeparator

Manway

Upper Shell

PrimarySeparator

Feedwater Ring

AntivibrationBars

Tube Support Plate

Lower Shell

Handhole

Slowdown PipeTubesheet

Tube BundleWrapper

Tube Bundle

Parameter Value

12 ft (3.66 m)diameter 0.36 in. (0.914 cm)

g thickness 0.0225 in. (0.0572 cm)il Zircaloy 4Bter 0.3088 in. (0.7844 cm)

0.496 in. (1.26 cm))d arrangement 17)< 17Lssembly 264i a core 50,952ol rod cluster assemblies 53

Channel Head

‘Se 1984.

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nail tflat in a I’WR, with the fuel temperatures roughly comparable. Because Waterand vapor coexist in the core, a BWR produces saturated steam at about 545°F (285°C).The coolant thus serves The triple function of coolant, moderator, and working fluid.In its simplest form (Fig. 10-15), a boiling-water-reactor powerplant consists ofa reactor, a turbine generator, a condenser and associated equipment (air ejector,cooling system, etc.), and a feed pump. Slightly subcooled liquid enters the reactorcore at the bottom, where it receives sensible heat to saturation plus some latent heatof vaporization. When it reaches the top of the core, it has been converted into a verywet mixture of liquid and vapor. The vapor separates from the liquid, flows to theturbine, does work, is condensed by the condenser, and is then pumped back to thereactor by the feedwater pump.The saturated liquid that separates from the vapor at the top of the reactor or ina steam separator flows downward via downcomers within or outside the reactor andmixes with the return condensate. This recirculating coolant flows either naturally, bythe density differential between the liquid in the downcomer and the two-phase mixturein the core, or by recirculating pumps in the downcomer (not shown in the figure).This is similar to what happens in modern large fossil-fueledsteam generators. Modernlarge boiling-water reactors are of the internal, forced recirculation type.The ratio of the recirculation liquid to the saturated vapor produced is called therecirculation ratio. It is a function of the core average exit quality [Eq. (10-9), below].Boiling-water core exit qualities are low, between 10 and 14 percent, so that recirculation ratios in the range of 6 to 10 are common. This is necessary to avoid largevoid fractions in the core, which would materially lower the moderating powers of

Saturatedsteam to turbine

mg

(a)(b)

Figure 10-15 Schematic of a BWR system: (a) internal and (b) external recirculation.

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VI

THERMAL-HSSION REACTORS AND PORPLANTS 421

:iThis state of affairs has been corrected by one of several methods: by-pass control,

a dual-pressure cycle, an overmoderated reactor in which voiding results in a reducedloss of neutrons due to water absorption and hence increased power, and recirculationcontrol [3] . The last method is the one adopted in current designs. It is described inthe next section.

10-8 BWR LOAD FOLLOWING CONTROL

The recirculation control method is based on a direct cycle but with variable recirculation flow in the downcomer, It is shown schematically in Fig. 10-17. Equation(10-17) is rewritten with the help of Eqs. (lO-8a) and (10-9) as

Qt = ?etZi(hg — hd) (10-18)

hg, the saturated steam enthalpy at the system pressure, and hd, the feedwater enthalpy,are both weak functions of load. Thus the plant load Qt is therefore proportional tothe product of e and ñz, the flow in the downcomer.

STEAM DRYERS

STEAM SEPARATORS

DRVINGFLOW —.-

MAIN STEAM FLOWTO TURBINE

MAIN FEED FLOWFROM TURBiNE

RECI RCULATIONPUMP

Figure 10-17 BWR reactor vessel internal flow paths.

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Reactor Concepts Manual Boiling Water Reactor Systems

USNRC Technical Training Center 3-2 0400

Jet Pump

ReactorVessel

SteamLine

Steam Dryer&

MoistureSeparator

Reactor Core

RecirculationPump

ThrottleValve

ElectricalGenerator

Turbine

Condenser

PumpContainment Suppression Chamber

Turbine Building

To/FromRiver

Containment/Drywell

Boiling Water Reactor Plant

Inside the boiling water reactor (BWR) vessel, a steam water mixture is produced when very pure water(reactor coolant) moves upward through the core absorbing heat. The major difference in the operationof a BWR from other nuclear systems is the steam void formation in the core. The steam-water mixtureleaves the top of the core and enters the two stages of moisture separation, where water droplets areremoved before the steam is allowed to enter the steam line. The steam line, in turn, directs the steamto the main turbine causing it to turn the turbine and the attached electrical generator. The unused steamis exhausted to the condenser where it is condensed into water. The resulting water is pumped out ofthe condenser with a series of pumps and back to the reactor vessel. The recirculation pumps and jetpumps allow the operator to vary coolant flow through the core and change reactor power.

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Reactor Concepts Manual Boiling Water Reactor Systems

USNRC Technical Training Center 3-4 0400

BWR 6 Reactor Vessel

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750 Power Plant Engineering

Fig. 23-15. Pressure vessel for a BWR. (From

Company. Used with permission.)

and flows back into the annulus region where it mixes with

entering feedwater.The steam leaves the separators at the top flowing up

wards and outwards through a series of drying vanes in the

steam dryer where additional separated water is recovered.

The steam then leaves the pressure vessel at the steam outlet

nozzle and passes to the turbine—generator through the main

steam lines. The steam separator assembly sits on the top

flange of the core shroud and forms the top of the core

discharge plenum. The steam dryer assembly is supported by

pads extending from the pressure vessel wall above theml 1 t,A k,1A,, il-in otoni

which fits intofor transfen-jnjsigns manufacix 9 and Jo <

designs are ccoverseas.

Three typesstandard fuelouter edge oflower and uppassembly dunfuel assemblyclad tubes willThe water rodremaining 5kslightly enriciinto anchor hoa BWR than falong Ihe fueling. Each fuechannel. Thethe fuel rods -

Control rotypical contrashape and cosheath. Eachwith each tubing. Each coiControl rods

STEAM OUTLET

CORE SPRAY INLET

LOW PRESSURECOOLANT

INJECTION INLET

CORE SPRAY SPARGER

JET PUMP ASSEMBLY

FUEL ASSEMBLIES

JET PUMP/RECIRCULATIONWATER INLET

VESSEL SUPPORT SKIRT

CONTROL ROD DRIVES -

IN-C OREFLUX MONITOR

CORE PLATE

RE CIRCU tAT ID NWATER OUTLET

SHIELD WALL

CONTROL ROD DRIVEHYDRAULIC LINES

General EleCtricBAIL

HANDLE

UPPERTIE PLATE

FUELBUNDLE

FUEL RODINTERIM

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