IEEE Transactions on Nuclear Science, Vol. NS-26, No. 1, February 1979

TRAINING SIMULATORS FOR NUCLEAR POWER PLANTS

Dr. Wei L. Chen

Abstract--This paper is a short introduction tothe power plant training simulator. The topics underits coverage include description of training simula-tors in terms of their implementation and functions;the mathematical models for simulating the plant sys-tems; and the performance testing of the simulatorsas contrasted and compared to actual plant operatingcharacteristics.

THE SIMULATOR AND ITS FUNCTIONS

A nuclear power plant simulator consists of aduplicate of the actual plant control room instrumen-tation which provides proper indications in responseto operator control actions, thus permitting operatortrainee interaction with the instrumentation in realtime. In addition to control room instrumentation,the simulator consists of a computer complex andinput/output interface equipment as well as theattendant computer programs. A basic simulatorconfiguration is shown in Figure 1, and photographsof instrumentation panels in two simulators are shownin Figures 2 and 3.

|COMPUTER lCOMPLEX

, -,-M --F2INSTRUCTOR ICONTROLS I. OPERATORS

: INTERFACE CONTROLS &UNITS INSTRUMENTS

The interactive capability of control roominstrumentation is the end result of continual realtime computation of mathematical models (implementedvia computer programs) which simulate the dynamicsand logical behavior of a specific power plant.

Simulators for training nuclear power plantoperators have been in use since the late 50's.Through the years these simulators have grown in thescope of plant system coverage and in the complexityof simulation techniques. The sophistication ofsimulator implementation is still rapidly evolving inboth the areas of simulation models and instrumenta-tion. For example, simulators for power plantsequipped with advanced control rooms require moresophisticated instrumentation. Such advanced controlrooms make extensive use of computer-controlled CRTdisplay systems. The capability of computer moni-toring and display allows the operators access tomore information both in terms of the number ofobservable plant system states as well as plantreference and logged data. This added plant capa-bility can be directly translated into increasedsimulator complexity. However, the purpose and thebasic functions of such a simulator stay essentiallyunchanged.

Simulators which have been delivered or arebeing developed by all manufacturers for both domes-tic and international customer/owners are listed inTables 1 and 2, respectively.

NRC REQUIREMENTS FOR NUCLEAR PLANT OPERATOR TRAINING

The use of Nuclear Power Plants is regulated andgoverned under the licensing power of NRC.

The Code of Federal Regulations (CFR) Title 10,Part 50 further requires that the controls of anyreactor licensed under Part 50 can only be operatedby licensed operators or licensed senior operators.

INSTRUCTOR

Figure 1. Basic Simulator Configuration

Figure 2. TVA's Browns Ferry BWR Plant SimulatorInstrumentation Panels with Instructor

Console in Foreground

The author is Engineering and Research DepartmentDirector at The Singer Company, Link Division, SilverSpring Operations, 11800 Tech Road, Silver Spring,Maryland 20904.

Figure 3. Consolidated Edison's PWR Plant SimulatorInstrumentation Panels

0018-9499/79/0200-0016$00.75 D 1979 IEEE

Part 55 of Title 10 establishes the proceduresand criteria for licensing of operators and senioroperators.

The NRC issues two types of licenses: operatorand senior operator. In representative control roomoperating conditions, a shift of operating personnelmay consist of a senior licensed operator who directsthe operation in the capacity of a shift supervisor,two licensed operators who manipulate the reactorcontrols, and two auxiliary or equipment operatorswho assist the operators. The licenses remain validfor a period of two years after the date of thei ssue.

Licensing Examinations

The NRC licensing examination consists of bothwritten and operating tests. The written tests per-tain to principles of reactor operation, instrumenta-tion and controls, operation procedures and theunderstanding of plant characteristics and design

features. The operating test seeks to demonstratethe applicant's ability to interpret instrumentreadings, to manipulate the controls, and to operateother facility equipment. The applicant must alsodemonstrate knowledge of radiological safety prac-tices and radiation monitoring equipment.

The operating tests are further subdivided into"cold" and "hot" examinations. The cold examinationspertain to operators for plant start-up.

After the plant achieves criticality, licensingrequirements can be met by one of three "hot" exami-nation methods:

1) Through the use of actual plants, and gothrough start-ups.

2) Combined use of simulator maneuvering andmanipulation of actual plant control sthrough power changes or reactivity changes;not necessarily start-ups.

TABLE 1. POWER PLANT SIMULATORS - DOMESTIC

CUSTOMER/OWNER

A.E.P.

Babcock & Wilcox

Carolina Power & Light

Combustion Engineering

Consolidated Edison

Duke Power Company

General Electric

TVA

TVA

TVA

VEPCO

Westi nghouse

Arizona Public Service

Pennsylvania Power& Light

Washington Public PowerSystem Supply

SNUPPS

GE

GE

Public Service ofNew Hampshire

General Physics forPhiladelphia Electric

Southern Services

MANUFACTURER

EAI

Singer

Singer

Singer

Singer

Singer

General Electric

Singer

Singer

Singer

EAI

Westinghouse

EAI

Singer

Singer

Westinghouse

Singer

Singer

Singer

Singer

C-E (EAI)

INSTALLED

12/73

12/69

6/77

6/70

12/73

3/76

6/68

6/76

10/76

6/77

4/78

2/72

No

No

No

No

No

No

No

No

No

PLANT SIMULATED TYPE

Johm Amos III

Rancho Seco

Shearon Harris

Calvert Cliffs

Indian Point #2

McGuire

Dresden II

Browns Ferry

Sequoyah

Cumberl and

North Anna I

Zion I

Palo Verde I

Susquehanna I

Handford/Richl andI & IV

Callaway I

Black Fox

Perry

Seab rook

Limerick

Scherer

II I Il_ _ I

ULLIVLKYDATE

10/69

6/75

4/72

12/73

11/75

6/68

12/75

4/76

8/76

7/77

8/79

10/79

10/79

CONTRACT--DATE______

_I

7/68

7/73

8/70

2/72

1/74

1/67

2/74

2/74

2/74

7/75

8/76

10/76

4/77

1/78

1/78

5/78

6/78

7/77

Fossil

PWR

PWR

PWR

PWR

PWR

BWR

BWR

PWR

Fossil

PWR

PWR

PWR

BWR

PWR

PWR

BWR

BWR

PWR

BWR

Fossil

17

I inri Ttsr-v-rI I- -- ---- ----t

3) Through the use of a certification programas follows: Participation in an NRC-approved training program utilizing a nu-clear power plant simulator, and obtaininga certificate from the simulator trainingcenter attesting to the applicant's abilityto cope with start-up and overall controland alarm conditions. The applicant mustalso have manipulated controls during fivesignificant reactivity changes; not neces-sarily start-up. Reactor start-up will notbe required as part of the test if theabove certification program is used.

License Renewal

Licenses can be renewed by means of reexamina-tion or by participating in a requalification pro-gram. The program requires that a licensee must havemanipulated the reactor controls through at least 10reactivity changes during the 2-year period. Thisrequirement can be met by the use of simulators thathave operating characteristics, controls, and instru-mentation similar to those of the subject plant.

NRC Position on Control Room Simulation

There are presently three differentiatingcharacteristics among the simulators as shown below,with ANSI 3.5 defining the simulator tolerances andperformance characteristics of all three categories:

1) Commerical/GenericOperated by Manufacturers

2) Plant SpecificOperated by Utilities

3) Control Room InstrumentationConventional, Advanced Controls, Hybrid.

However, in addition to these obvious differences,NRC determines the adequacy of any given simulatoras part of a training or recertification program interms of:

1) The completeness and accuracy of plantsimul ation.

2) The extent and types of control room expe-rience provided by the simulator. This in-cludes normal start-up and shut-down as wellas various abnormal operating conditions.

3) The operating experience of simulatorinstructors.

NRC Experience in the Use of Simulators

The NRC examiners have found that (1) indivi-duals trained using simulators have a better under-standing of plant responses to transient conditionsand abnormal situations and are also more confident

TABLE 2. POWER PLANT SIMULATORS - INTERNATIONAL

CUSTOMER/OWNER

AKU (Sweden)

EDF (France)

GE-Tai Power (Taiwan)

Kansai Electric (Japan)

KWS (Germany)

KWS (Germany)

Ontari o-Hydro(Canada)

Tai Power - Gibbs &Hill (Taiwan)

VTT (Finland)

Tokyo Electric(Japan)

Tecnatom

Tecnatom

KWU

Iran

Nucl ebras

a v _ _ _ _ _ _ _ _ _ _ _ i i .fr ^I %

I| LAJ^^i1_^ ^ .^ tACNTRACT DELIVERYMANUFACTURER INSTALLED PLANT SIMULATED TYPE DATE DATE

Asea-Atom Sweden

LMT France

Si nger

Westinghouse/Mitsubishi

Singer

Singer

CAE (Canada)

EAI

Nokia (Finland)

General Electric/Toshiba

Singer

Singer

Singer

LMT

LMT

No7/75

Yes

2/76

11/73

5/77

7/77

Yes

Yes

Yes

Fall'73

6/78

No

3/78

No

No

Ringhal s IOskarsham I & II

Bugey

Chi n-Shan

Takahama

Biblis A

Brunsbuttel

Pickering 5-8

Talin

Loviisa I

Fukushimo

Lemoni z

Cofrentes

Biblis A

Bugey (Copy)

Angra II

PWRBWR

PWR

BWR

PWR

PWR

BWR

PHWR

Fossil

PWRRussi an

BWR

PWR

BWR

PWR

PWR

PWR

7/71

4/75

11 -12/73

8-9/74

8-9/75

Wi nter1973-74

11/73

6/75

2/76

2/76

3/77

1/78

5/75

6/76

7/76

8/75

6/78

12/78

3/78

I I II___I _ L

a_ _

18

I

in answering questions that require prediction ofplant responses to postulated situations, (2) simu-lators are extremely effective for examining andevaluating indviduals, and (3) there has been excel-lent correlation between the results of the licensingexaminations and the performance at the simulator forgiven individuals.

The NRC believes that simulators, used in con-junction with comprehensive training programs, areeffective training devices and intends to encouragetheir use in future training programs.

MATHEMATICAL MODELS & MODELING

Mathematical models are a collection of mathema-tical equations. Solutions to these equations repre-sent the behavior of the simulator as a function oftime and operator actions.

The main body of the math model consists of setsof coupled differential equations which bear formalanalogies to the physical plant systems being simu-lated. These equations pertain to all simulatedplant system states such as temperatures, pressures,levels, reactor power and turbine speed.

Scope of Simulation

The process of modeling starts with a definitionof the scope of simulation. The scope specifies thechoice of states that must be included in the models(or equations to be solved). It further specifiesthe modes of operation and system functions themodels must depict and satisfy the time behavior(dynamic) within tolerance (ANSI 3.5). A core modelis presented in the Appendix as an illustration.

Objectives of Models

Casual observation indicates that the model isnot anywhere comparable in complexity to the variousreactor codes for analysis and design use. The basicparameters and equation forms are preserved, but thespacial distribution has been much simplified. Inother words, the trainer core model has been simpli-fied by lumping the distributed parameters to a muchgreater extent than that by the codes.

This immediately raises the important questionas to the "adequacy" of the proposed model. Inanswering this question, one must examine the objec-tives or the intended use of the model.

The proposed trainer model is obviously notsuitable for reactor design analysis or performance"prediction". However, for training purposes, themodel is satisfactory in that it correctly exhibitsthe expected and "known" behavior of the reactorunder various important phases of operation. Speci-fically, the instrumentation indicates proper re-sponses and trends as a function of operator actionsand operation history (initial conditions or previousstates). The design objectives specific to a train-ing device exerts similar influence in the modelingof almost all subsystems, both in the primary steamsystem areas and the balance of plant areas; as tobe expected.

It can thus be said that trainer models oftenrepresent a simplified version of engineering ordesign analysis models. However, in the trainerenvironment, there are additional requirements andconstraints that are not pertinent to engineeringmodels.

Models in Trainer Environment

The two major requirements imposed by the train-ing environment are the need to provide for completeman/machine interaction and the ability of thesimulator to respond in real time. These addedrequirements present no conceptual difficulty, butthey carry significant cost implications. In orderto obtain a closer understanding of the trainermodeling process, it would again be meaningful toobserve the difference between the engineering modelsand those for trainer use.

The objectives of an engineering simulation areusually very specific and limited in scope. In otherwords, an engineering simulation effort, if success-ful, must answer some very specific questions posedduring the course of engineering design and analysis.As such, given finite computational (or budget)resources, simplifications and assumptions will bemade, and the operating range and modes will belimited to those directly relevant to the properlyposed questions. For example, a simulation task mayhave the specific objective of predicting hot spotsin a distributed medium such as the inside of areactor core. For the sake of economy, a priorknowledge of operating conditions likely to cause hotspots can be used to limit the range and mode ofoperation that the model must cope with. Also, theestimation of coefficients and parameter selectioncan also be simplified or limited to suit the speci-fic application, and it is obviously unnecessary toinclude the remainder of the nuclear steam system orany of the balance of plant.

In a trainer, the capabilities of math modelsof individual subsystems must satisfy the dual con-straint of "full mission capability" and "integratedsystem capability." Full mission capability requiresthat the individual model must satisfy the trainingrequirements in all operating modes. In the caseof the core model, it must be able to respond tooperators actions and show correct indications on allrelated control room instrumentation. This has to betrue throughout the operating mission of startingfrom cold start-up, going through criticality andpower range changes. This model must also respond toany of the selected malfunction incidents occurringat any state of operation. The full mission capa-bility thus increases the complexity of a trainermodel over that for engineering models.

The trainer must also provide interactive train-ing capability for the entire plant. This greatlyincreases the scope of simulation, but the task ofintegrating the many subsystem models into a trainerrepresents by far the most difficult and one of themost time-consuming aspects of power plant simulatorimplementation.

Due to the complexity and closely coupled inter-actions among power plant systems, the dynamic beha-vior of the integrated simulator models is extremelydemanding on the accuracy and flexibility of thesubsystem model s. The integrated model s must notonly be functionally correct, but must exhibit theproper sequence of events, especially under plantmalfunctioning conditions, so that negative trainingis avoided.

Another major difficulty often encountered stemsfrom various problems related to the design database. The most obvious problem that often occursduring the initial phase is the lack of data. Simu-lators are required to operate before the start-up

19

of the plant itself, so that trained operators willbe available for start-up. Through the courseof power plant construction, new data may becomeavailable and various changes may be introduced suchthat updating of models becomes necessary. An evenmore difficult problem is the frequent need toresolve and reconcile among conflicting data. Thisrequires personnel with strong insight in power plantperformance and mathematical modeling techniques.

SIMULATOR PERFORMANCE TESTING

The simulators are subjected to extensivetesting per established acceptance test procedures.The acceptance test procedures (ATP) comprise twomain parts. the first part consists of functionaltests that pertain to the various simulator systemcomponents such as computers, controls, instrumenta-tion, and the system and support software. Thesecond part consists of performance tests pertainingto the simulation models. The performance tests arefurther grouped into:

1) Mission Tests during which the simulatorgoes through various normal operating sequences fromthe appropriate initial conditions. This alsoincludes a "full mission" test, going from cold startthrough 100% power and complete shut down.

2) Plant Malfunction Tests during which allthe plant malfunctioning conditions are exercised onthe simulator.

FEEDWATER PUMPS TRIPPED

/ L L SWELL

I50 INI ..,e100 4i

\. \'OWER s

80 4 \0 LVLWATER LV

60 A

40

20

3) Major Transient Tests during which thesimul ator demonstrates various plant condi tionswhere major disturbances occur due to operator mal-operation or for the sake of demonstrating conse-quences of drastic operator actions.

The following is a sample case of BWR simulatorperformance test data as obtained during the accep-tance testing phase for the Taiwan Power Company'sChin Shan Power Plant Simulator. The test caseincludes plots of data indicating the results of thefollowing events presented in the identified figures:

1) Steamline Rupture Outside Drywell(In Tunnel) - Figure 4

2) Pressure Regulator Fail Open - Figure 5

3) Single Recirculation Pump Trip - Figure 6

4) Manual Trip of Both Recirculation Pumps -

Figure 7

5) Main Steam Line Isolation ValvesManual Closure - Figure 8

6) Power Response to Feedwater Flow by ChangingLevel Set Point - Figure 9

7) Flow-Power Relation - Figure 10.

POWER

.----..VESSEL LVL(rN.ABOVE FEEDWATER SPARGER)(NORMAL= 124.7")

t/ll X I/t DOME PRESSURE 100 A

10 20 40TIME AFTER RUPTURE (SEC)

Figure 4. Steam Line Rupture Outside Drywell (In Tunnel)

20

110/ FLOW LIMIT

--A-- % POWER-- -o-- DOME PRESSURE

20 40 60 80TIME (SEC)

Figure 5. Pressure Regulator Fail Open

--0-- 0 I/

POWER

CORE FLOW

change of scale fro here on

10 20 30 80 130TIME AFTER PUMP TRIP (SEC)

Figure 6. Single Recirculation Pump Trip

180 230

100

% POWER

VLV

100

so

% POWEROR

% FLOW

60

40

20

21

%t

- o--o-- % CORE FLOW

---A----- % POWER

0'

-0-a - - -- -

N TURAL RECIRCULATION

=HANGE OF SCALING FRDM HERE 0N

10 20 30 so 130 180TIME AFTER PUMP TRIP (SEC)

Figure 7. Manual Trip of Both Recirculation Pumps

230

I %

I 'I'I1140 1 .1

I 0

i I_-

- 1100

-IU5LJ T0

1060 /low

F-1040

1/01020

- lAnn

----A-- POWER-. o - -o DOME PRESSURE

ral11-~~~relief valves open

120

100

% POWER

so

60

40

20

^ I I a La 1 L- L J- La a122*~5 _, _ 0 _ 5 2

Figure 8.

I I

I

!I > DOME PRESSURE (PSIA)

I IfO.- _ 1 1

11IIIII '

,0

I.,o0

I.Iik I

I 0

_ _ ~~~ ~ ~~~~I_ _ _ _-.lvvvDOMEPRESSURE(PSIA)

IPOWER

__________ 1

S 1 0 IS 20TIME AFTER MSIV CLOSURE (SEC)

Main Steam Line Isolation Valves Manual Closure

100-

80

60% POWER

OR% FLOW

40

20

22

i

I,I

n--=

L- a o% aho% --"wr N .0

- -o-. *"-O-

. 0

_- -A- _-_% POWER

-- ° . FEEDWATER FLOW ( lb/sec)

80TIME (SEC)

NOTE: START WITH NORMAL WTRLVL 1247 IN.ABOVE FEEDWATERSPARGER. AT TI CHANGE LVLSETPOINT TO 130 IN. ABOVEFWS. AT T2 CHANGE SET-

_-POINT TO 116.5 IN.AOV FWS.

Figure 9. Power Response to Feedwater Flow Variation by Changing Level Set Point

A- B= ROD PATTERN FIXED, INCREASING PUMP SPEEDB-C= INSERTING RODC-D= ROD PATTERN FIXED, DECREASING PUMP SPEED TO MIN (20%)

0.2 0.4

NORMALIZED CORE

W A~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'o

.._J.. _ AI.-.

- -ACHIN HAN FSAR

0.6 0.8 1.0

FLOW((% RATED FLOW)

Figure 10. Flow-Power Relation

23

Tl

100 -

% POWER

95 -

go 4

100

80

% POWER

60

40

20

0

-- ---

o- OIMVL'p4 I Cu rNCOUL.

I I i I I

A

DSlMlUlJATFn RFqIII T-

APPENDIX

TYPICAL PWR CORE MODEL

The following sets of equations are represen-tative of a PWR Core model for simulator implementa-tion. The solution in real time to these coupledequations exhibits the dynamic behavior of thereactor core. Interfaces between the core model andthe neighboring systems are illustrated in FigureA-1. The simplified flow chart shown in Figure A-2defines the computational procedure.

Thermohydraul ics / h}outI fI///,/,/// / I

CORE mFUEL ROD & A COOLANT

_CLADDING ,1 + I

/AVE. TEMP T/ HEAT TRAN. QHEAT GEN. QT V///

L hfinf

M dTfM .Cp t=QT-Q

whe re:

M = Total Mass of Fuel & Clad.

MCp= Specific Heat of F & C

Q = K W0.7 (T - TM)where:

W = RCS Flow through Core

TM = Ave. Moderator Temp.

QT KT + QDF + QDSdQDF (0.03 -a- QDF)dt T

dQDS (0.03 -a- QDS)dt TS

where: a= Ave. Neutron Flux

QDF = Fast Decay Heat

QDS m Slow Decay Heat

Coolant Temperature Inz

0 C olant Pressure Ino« o> Coolant Mass Flow Rate

uR Coolant Temperature Out

K4 Coolant Quality at Outlet

THERMOFYDRAULICS BLOCK

Saturation TemperatureSpecific Heat ofModerator

Core Outlet TemperatureAverage Moderator

TemperatureVoid FractionSpecific Heat ofVaporization

Moderator QualitySpecific Volume of GasSpecific Volume of FluidNormalized Moderator

amDe ietreVOIDS, PRESSURE,TEMPERATURE

Boron REACTIVITY BLOCKCVCS Concentration

Doppler EffectReactivity Due to Boron ConcentrationCoefficients for Moderator

Insertion Depth Temperature Effectof RCCA Groups Void, Pressure, Rod Insertion Effects

TOTAL REACTIVITYWITHOUT EFFECTSOF XE,SM

en

H

z0U

00K4

POINT KINETICS BLOCK

Concentration of 3-Group NeutronPrecursors

Concentration of Iodine,Promenthium, Xenon, Samarium

Neutron flux level

POWER LEVEL, a1

0

K0E-4

0

0

SPATIAL EXTENSION BLOCK

Insertion Depth Instantaneous Flux Coefficients &of RCCA Groups Residual Flux Coefficients

(Functions of Rod Group Positions)PowerDoppler Heat RateModerator Heat Rate

Request Aeroball Readings

z Thermocouple Readings

| i i Aeroball Readings

U En En In-Core Detector Readin sD z >dH U)

Ex-Core Detector Readings

DNBR

REACTORPROTECTIONSYSTEM

Ial, a2,a3,a4, POWER

FLUX-DEPENDENT QUANTITIES

InstrumentationAeroball Channel ReadingsThermocouple SignalsPower Range Ex-Core Detector

SignalsStationary In-Core Detector

Signals

Figure A-2. Simplified Core Model Flow Chart ShowingComputational Paths and Interfaces

24

Figure A-1. System Block Diagram withCore Model Interface

_~~~~~ I

;1

i

-

hOut = n QMhf =hf W

where:

C = Specific Heat of Coolant.

Iodi ne

dC

dt V*RO9 a- IcIYI I

where:

Reactivity

Pt Po + PDP + PM + PCB + PRod + PXe + PSm

where:PO= Excess Reactivity

PDp = Doppler Reactivity

PM= Moderator Reactivity

PCB = Boron Concentration

PRod = Total Rod Reactivity

PXe = Xenon Reactivity

Psm = Samarium Reactivity.

The reactivities are derived from data such as:

o Doppler Coef. (Temp)

o Moderator Coef. (Temp)

o Boron Worth

e Rod Worth.

Point Kinetics

Neutron Flux

ddt tS+ Pt -

dt[=+V V9a -

6 dC ]

i =1where:

Average Neutron

Average Neutron

Average Neptron

Flux

Speed

Generation Time

C =

yIXI =

V =

Xenon

DCXed-t-

Iodine Concentration

Iodine Yield per Fission Neutron

Iodine Decay Constant

Average Neutron Yield per Fission.

yXe XvOO0X* a + XICI - XXecXe -

aXe *cxe "a

where:

C = Xenon ConcentrationXe

YXe = Xenon Yield Per Fission Neutron

XXe = Xenon Decay Constant

0Xe = Xenon Absorption Cross-Section.

Promethium

dC PM YPMdt V.tv - PM

Samarium

dCSM-t APMCPM - cSMCSM a

Spatial Extension

*(x,y,z,t) = v(x,y,z,Life) * (t) -

(1 + ax sin BXX + ay sin BYY + az sin BzZ)v(x,y,z,Life) is the basic 3-D Flux Shape for given'Life'.

aX'yM az, are Flux Tilt Functions

p = Total Reactivityt

C = Group i Delayed Neutron Precursor1 Concentration

S = Neutron Source.

Delayed Neutron Precursor

dCi 1 - -dt - 7-- i x1Ci

where:

ai = Yield of Group i per fission Neutron

xi = Decay Constant of Group i

i = 1, 2, . . . 6.

a (t) = 1 . O(Z+) - O(Z-)z sin B Z O(Z+) + -(Z-)

~ (t) = 1 . -*(Z+) - -(X-)x sin B Y *(X+) + f(X-)

a (t) = 1 . O(Y+) - #(Y-)y sin B 7 -(Y+) + o(Y-)

y

v(x,y,z,Life) = Y(x,y) v(z,Life)

25

where T(z,Life) is average Neutron Flux along z,and typically

z

I 7(Z ,MOL)

z

If~(Z,EOL)

and so on.

Flux Detectors

In-Core

in(x,y,z,t) = *(x,y,z,t) RLd(X,7,Z)

T(x,y) can be approximated from T(x,y,z) and iT(z)data or design code analysis.

Flux Tilt Functions

1W(Z+,t) = . *(x,y,z,t)dVz<O

-1$(Z-,t) = - f *(x,y,z,t)dVz<O

Consider 8 zone example

If1 = Vr *(x,y,z,t)dVX>Oy>OZ>O

=8$2 = v f (xy,z,t)dV

x<Oy>Oz>O

and so on.

Thus:

*(Z+,t) = ($+ + $2 + $3 + ¢J/4

*(Z-,t) = (¢s + $6 + $7 + +9)/4

W(X+,t) = (¢1 + $3 + $, + ¢7)/4

d137b5-b8

where RL (X,Y,Z) is the Rod Tip Effect.

J Fl ux1

Z

NO ROD

1

AFTER INSERT

Ex-Core

ex(x,y,z,t) = [a *.i + (1 - 8) Ej* RE

where 8 is a weighting factor < 1

and RE is the edge rod effect to the Ex-coreod is detectors.

e.g. The effect of flux change due torod 1 is much greater than thatdue to rod 2.

0

z

7

26