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EXPIRIENCES WITH DYNAMIC TESTINGilfiTTF{ .*DS AI THI [\4CLTThI -SALTRTACTSR TXPIRIMTT$TT. 'W. KERLIN, S. J..PALL,Oah R'idge Nation.al Laborato.ry,

Received Ltay 23, 19?ORevised Septemi:er L4, LgT 0

R. C. STBFFYT* and M. R. BUCKNER**Aah Ridge, Tennessee 37830

A series of y'eactiuitSt-to-power frequarcy ,1,€-

sponse nteasuvenzents ?,uas made on the hlolten-salt Reactor ExP erintent. Tlzis u)as clone for 233 ryand 235 [/ fuels, for a vange af op erating powerleu els, at s eu eral points i,n the sysl e?n ofi erati.ngItistoyy, and ./'or seue]'ttl, different test pt oced"u?,es.A cornparison oJ' experirnental resu,lts utith priortheoreti.cdl predi.ctions confirmecl the uatirtity ofthe theoretical prerii"ctiorzs. The test p?-ogram in-cluded n?easu,rernents using fize pseu.clorarz.do.ftzbina. ry s eque?zc e, f>s eudorartdo'm ternary seq:uer?,c e,n- sequ,ettce, and the multifrequency binary se-

, guence.

:.!i. i!i'i.a. !....

I. INTRODUCTION

An extensive dynamics testing progr?r,r wascarried out at the Molten-Salt Reactor Experiment(usRn ).

t The tests consisted of reactivity topower frcquency response measurenrents. Thepurpose of the test program was: ,

1. to demonstrate the safety ancl operability ofthe system

2. to check the valiciiiy of ilre theoretical anal-ysis so that the safety of the plant coulct, be

+Present addressl Tennessee Valtey Authority, Chat-tanocgar, Tennessee.

*tUtrivcrsity of Tennessee, Knoxville, Tenne$see. f)res-ertt adrlress: Savannalr Iliver Lstboratory, Aiken, SouthCnrolirra.

Syo {j,+,*

KEYWORDS: reoc tivity, (se-,cruency, plwef , lesfi:n j, per-(ormonce, sign al s, MSPE

reassessed if necessary and so that con-firrnec methods could be established. f oranaryzing future, high -performance morten-salt reactors

3. to evaluate techniques f or perf orniing dy -narnics experimcnts and mefirods of dataanaiysis .

Tests were performed at several differ.ent powerievels, &t several different times in the system,soperati:rg history, ancl for the reactor fueled u'ith235u and with 233u. Items 1 and z were the mainobjectives of the test proglarn, but ilris paper €rrr-phasizes item 3 since it should be of general in-terest to those planning dynamics tests in othersystems. Those interested only in the perfor *manee of the MSRE could skip secs. f[ ancl III anclproceed directlSr to the results in Sec. IV.

II. PLANNINIG THE TESTS

A. Objective

The primary test objective was to ureasure thereactivity-to-power frequency response over theran€le of frequencies where im1:ortant system cly -namic effects occurred. Inspection of the fre -quency response predictions (see Figs. B and 14of Ref . U inclicated that nl.easurem ent.s clown to'- 0.005 rad/.sec at the low frequency encl wereneeded. It would have been dcsirable tq .arry thehish frequency end of the measurements out toabout 50 racl/sec if $re zero-power reactor kinet-ics effe.cts were to be observed. If ilre interestwere in feeclback effects, the upper frequency neeclrrot have been greater ilran -0.b racl/sec. The ap-proach used hcre was to deternrine ilre high fre-queney ( 1.0 to 100.00 ract/sec ) response by noise

NUCLIiAIt l'l'ICIINOLOGY VOL. 10 tsEIlIttlAItY lg?r t03

Kerlin et al. ExpERIENcEs wITrI DyNAIuIc TESTING

nreasurements during z,eto-power operation. Sub-secluent at -power measurements concentratccl onthe 0' 005- to 0. 5 -rad/sec rangc wler€ feeclbackeffects tvere inrportant,

B. Equipment used in Experimentaf ftlleasurements

The selection of the experinental methods forthe MSRB dynamics tests was based on the infor-mation required and on the capabilities of theavailable equipment. Fortunately, the emphasison low frequency results ( 0.0c5 to 0. b rad/sec )made it possible to obtain the important part ofthe system frequency resparrs€ using the standardMSRB control rods to int'oduce the input reacti-vity perturbations.

The MsItB has three identical control rods,each with an active rength of sg.4 in. one rod isnormally designated as the regulating rod a'd isused for fine control. The other two rods are usedas shinr rods for coarse adjustrnents. The rodsare actually flexible, stainless -steel hoses onwhich are strung gadoliniurn oxide poisori cylin-ders. The rods are mounted in thimbles whichhave two 30-deg offsetting be*ds so that the roclscan be centrally located even though ilrere is noroom for the control-rod clrive assemblies abovethe central a:<is of the core. The murimum rodspeed is - 0. 5 in. /see. Typical rod travel in theexperiments was - 0. b in. for most of the 23s utests and 0.3 in. for most of the 233U tests. Thisgave a reactivity change of -0.025Vo 0g) in the235u tests a'd -0.02vo (izg) in the *ru tests.

Figure 1 shows the contror-rod and drive fl,s-sembly. The position indication for eacrr rod wasobtained from a synchro geared to the rod drivemechanisrn. A coarse synchro (b-deg rotation perinch of rod travel) was used in u""ly tests and afine synchro (60-deg rotation per inch of rodtravel) was used in rater tests. The signar fromthe position synchro was anrplified and 1ow-passfiltered ( l-sec time constant) to eliminate highfrequency noise and ilre accompanying aliasing .i_fect prior to input into the Bunker Ramo computer,BR-340, where the signal was digitized eue"y 0.25sec and recorded on magnetic tape.

The nuclear power level signal was furnishedby the output of a compensated ion charnber loca-ted acliacent to the core. This signal was alsoamplified, low-pass filtered (l-sec iinre constant),digitized at 0.zs-sec intervals, a'd recorded onrnagnetic tape.

The BR-940 computer was also used in con_junction with a portable analog computer forgeneration of the input sigrral for the test. A com-puter program was prepared for on-line genera-tio* of each test signal used in the teJts (thesignals are described in Sec. f[.C .Z),

104

C. Test Signals

1. tntroduction Test signal selection was influ-enced by considerations of accuracy requirements,frequellcy range over which information wasneed€d, and harclware capabilities. The followinginput signals were used during the testing pro-gram:

a. pulse

b. step

c. pseudorandom binary sequence

d. pseudoranclom ternary sequence

€. n-sequence

f . multifrequency binary sequence (flat inputspectrum)

g. multifrequency binary sequence (prewhit_ened output spectrum).

Pulse and step tests are easy to implement, butthese signals give results with limited accuracy.This is because the signals are nonperiodic, illdtherefore have a continuous frequency spectruma'd resulting low signal ene-rgy in the neighbor-hood of a frequency of interest.

The other five signals are more trouble to im-plement, but they permit more accurate results.This is bbcause they are periodic, and thereforeconcentrate the signal energy in discrete harmon_ic frequencies. rn alr of the tests using periodicsignals, the period is determined by the lowestdesired frequency: v -

T = 2T(t)r

where

T = period

ut = lowest desired frequency

For example, the required period for a test inwhich the lowest required frequency is 0.01rad/sec in 628 sE-c. All other harmonics would beat integer multiples of 0.01 rad/sec. The accura-cy of the results is improved by using input sig-nals consisting of tnore than 1 cycle. In the MSREmeasurements 2 to 10 cycles were used.

2. Properties of htfutt Signals.

a. htlse. The energy density e of a pulse ofduration r and arnplitude A at frequency,i" g*",by:

a

e = ry leilteT/z)-l '2n L vTTTJ '

NUCLEAR TECIINOLOGY VOL. TO FEBRUARY 19?I

UPPER LIMITswtTcH

DRIVE UIJITSPACER

LOWER LIMITswrTcH

3-in. x 2-in. ECCENTRICREDUCER

KCTlin et al . E,Y.PERIENCES WITI"I DYNAMIC TESTING

REVERS|BLE DRIVE MOTON

COOLANT TO DRIVEASSEMELY

TCOOLINGGAS INLET

COOLING GAS

COf.lTAlN€R

-POSITION IhDICATOR

SYNCHRO TRANSTiITTER

FIXED DRIVE SUPPORT AND3 - in. CONTAINiv€NT TUBE

ANT TOPOISON ELEMENTS

* in.o. D.-3o4 s. s.- FLExTBLE

HOSE CABLE

SPRING LOADED ANTIBACKLASHHEAD AND IDLER GEAR

l6-in. RADIUS x 3O" BEND

COOLANTEXHAUST -_-_*O--

BEADED POISON ELEMENTS

2- in CONTAINMENT THIMBLE

Fig, 1. Control-rod drive assembly,

This spectrum appears in Fig. 2. Note that theamplitude i.s expressecl as energy spectral density(energy per unit frequerlcy).

b. Step. A step input may be thought of as apulse whose duration has gone to infinity. Thestep test is suitable only for systems rvhose r€-sponse settles to some constant value after the

NUCLEAR TECHNOLOGY VOL. 10 TEBRTIANY 1971

step input. This requires that the systemts zeto-frequency gain be a finite constant (including zero).In principle, the step input contains an infiniteamount of ener€ry, but this energy is'concentratedin the low frequencies where it is of little use.

c. Pseudorandont Binary Sequ.ence. The pseu-dorandom binary sequence (PRBS) is often used

a,

t05

$Isrs Kerlin et al. EXPERIENCI'S WITTI DYNAMIC TESTINC

!r.l I lO

DIMENSIONLESS FREOUENCy ( o T)

Fig. 2. Energy spectrum of a square pulse.

for frequency response measurements and for ap-proximate impulse response measurements. Themethods for generating the pRBs are wellknown."t These methods $ve periodic sequencesof +lts and - lts (each member of the sequence iscalled a bit). The total number of bits in ilre se-quence N must be 2z 1 for any integer value ofz, The period of the signal is given by the prod-uct of the number of bits N and ilre bit time in-terval At.

The spectrum of the pRBs with pulse arnplitudeA and total test duration I is given by:

A, = 2 (N + 1)A,r fgl#.4Dl ,

ror te / arr& arwt

greatest arnplitucler (thereby furnishing a measureof the ban.Iu'idth of il^rc signal):

hp =0.44N ,

wher e ht, = harmonic nurnber of the harmonic withhalf the pcwer as the harmonic with the greatestpo\,vei'. Thus, if the lowest frequency is (oL

rad/sec, and the required highest frequency is @ttrad/s€c, then the number of bits is given by:

J[ = 2.27 uh .

&)r

The bit duration A I is fixecl by the highestquenclr of interest. The relation is

Lt = 2'77-cnl

of course, these are just rules of thumb. ff thetotal signal enerry is too small, the signal enerryper harmonic may be too small even for the har-monic with the largest amplitude.

d. Pseudorando?n Ternary sequence. The pseu-dorandom ternary sequenceo (pRTs) is similar tothe PRBS, but three levels of the input signal are

o.f

oos

o.02

o.or

o.oo5

o.oo2

o oortz,5to?o50too

HARMONIC NUMEER

Fig. 3. Energy spectrum for severar PRBS signals.

NUCLI'AR TECTINOLOGY VOL. 10 FEBRUARY T9?I

(2)

N

FA,

()zu,:)alr,Efttrz.:)E.lrlo.

(9E,lrjZt1rr

(3)

fre -

(4)

A"=# for k -0, (1)

(\t

lr',o:)LJ(L

=lrjaJ:)(L

xF

(JctrjzlrJ

where Ap = amplitude of the energy spectrurn atthe &'th harmonic frequency. The spectra forseveral sequences are shown in Fig. g. Note thatthe short sequences concentrate rnost of the signalenerry in the first few harrnonics and ilre longersequences spread the signal power among moreharmonics.

In planning a test, one must select the periocl togive the reqtrired lorvest frequency. The requiredupper frequency fixes the sequence length N orequivalently (since the periocl i.q fixect) ttre bit dur-ation. The following relation specifies ilre har-monic nunrber at which the signal power is half asIarge as the amplitude of the harnronic with the

t06

3 DENOTES HARMONIC FREQUENCY

BASIS - SAFNE TCTAL DURATIONFOR ALL SIGNALS

O O O cro oooo 63 BIT

3I BIT

.la_ a(o

iltlrrlf

li

'

re'il

ou=&eiffi14#Pl' rorpodd (5) ao=t!!;i)AtlW' rorftodd (6)

used (-1r 0, +1). The numiler of shifts in these-quence is given by N = $z - 1) f or integervalues of Z .

The spectrum of the PRTS with pulse amplitudeA and total test duration 7'is given by:

Ap = 0 for&even.This shows that the shape of the PRTS spectrumis the sarne as for the PRBS. However, only theodd harmonics are non -zeto and they have an am-plitude u'hich is one-third larger than the corr€s-ponding amplitude of a PRBS harnronic f or asequence with the salne value of N. Figure 4shows a cornparison of these signals. The proper-ties given in'Eqs. (2) trrrough (4) for the PRBS alsoapply for the PRTS.

The PRTS is of interest because it has the ad-vantage that it cliscriminates against nonlineareffects. This may be advantageous because itallows one to use large amplitude sigrrals in fre-quency response measurements. The PRTS hasthe disadvantage that in the MSRE (and in manyother reactor systerns ) a three -level input isharder to implement with system hardware than atwo-Ievel signal.

e . n-sequence. Thc n-sequenceu is obtained. bya sirnple rirocii{ication of the PRtsS. T}re mociifica-tion consists of inverting every other bit in aPRBS. Since the number of bits /V in a PRBS is

o.olO.Or o.r I

NORIT|ALIZED HARMONIC NUMBER ( k/N)

KCTIin et aI. EXI,T]RIf]NCHS WITII DYNAIVIIC TtsSTING

always odd, the numberobtainecl by nrc-.lification

The spectrum of thepulse arnplitude A, anCgiven by:

of bits in an n-sequenceof an N-bit PRBS is 2N.tt-sequence with N bits,total test duration T is

Ap - 0 for & even.

Figure 4 shows a eomparison of the spectrum forthe n-sequence zurd the PRBS and PRTS. Since theshape of the amplitude spectrum is the same asfor the PRBS, the bandrvidth relations lgqt . (2)through (4)] stilt apply.

The n.-sequence discriminates against nonlin-ear effects as in the case of the PRTS signal.

f . Multifrequency Binary Sequence (MFBS) -I'lat Sfectrum. In all frequency response lrlea-surements, a major obj ective is to select inputsignals with a large fraction of the total availablesignal energy concentrated in the f requenciesselected f or measurement. Generally, it is de-sirable to space the harmonics evenly on a loga-rithmic scale except in regions where moreresolution is needed. Since the harmonics of thePRBS, PRTS, and n-sequence are evenly spaced ona linear scale, the spacing of the harmonics is toodense at the higher frequencies (see F'ig. 3). Thisconstitutes a waste of siEral energy irr identifyingnearby harmonics which are only sliglrtly differentfrom one another,

An alternate procedure is to design a test sig-nal rvhich maximizes the fraction of the totalsignal energy in harrnonics selected by the ex-perimenter. A sigrral of this type can be obtainedby a computer optimization of the polarities of thepulses in 4 pulse chain of fixed length. The ob-jective functiotr, rvhich is minimized in the opti-mization, is the differerlce between the desiredspectrum and the spectrum obtained for a givenpulse chain. Experience shows that as much as 65to 75Vo of the total signal power can be concsrl-tratecl in selectecl harmonics.u" Furthermor€, thesignal can be desig:red so as to discriminateagainst nonlinear effects.

A typical signal used in the MSRE experimentsappears in Fig. 5.

g. It'Iultifr.equency Binary Sequence (lvlFBS)-Prepltitened S\ectrunt. One of the main reasonsfor interest in the PRBS, PRTS, and rr-sequence isflrat the amplitude spectrum can be made quite flatover a wide frequency ran€le. This is important inmeasurements rvith large noise contamination ofthe input sigtral. The procedure for such a systemwoutrcl be to use as nruch input signal energry aspossible (withln limits set lly system operating

6P r.oo-oFotr,IJJ

=E,ozlr,o)tr o.to--

Flg. 4. Envelope of amplitude spectra for IlItBS, PIiTS,and rr-sequence.

NUC I,DAIT I'ECIINOLOGY \IO L. IO FEI}IIUAIIY I $? I r07

r,rlF

(og,I|JzrdJzIv,JFoFt!o=otrctEt!

Kerlln et al. EXPERIENCES WITH DYNAMIC TESTING

-lJl*arrSrc

(o} THE INPUT SIGNAL

rda

ldlto-2

FREeUENcv (rad/lec)

(b} ENERGY SPECTRUM

Fig. 5. MFBS flat spectrunr signal and its spectrurn.

conditions and nonlinear effects ) anO to divide thisenergy evenly among the desired harmonics sothat the signal-to-noise ratio would be as high aspossible at each measurement frequency.

In systems in which the predominant noisecontanrination is in the out/tut signal, the sameobservations apply as were mentioned above inconnection with an input-noise problem. That is,each. output harmonic srroulcl contain the muimumpossible sigrral energy. Thus, for systems withoutput noise problems (a common case) trre outputamplitude spectrum should be flat. This can beaccomplished by using an input signal whose &rrr-plitude spectrum ha^s a shape which is the recip-rocal of the amplitude spectrum of the systemfreqriency response.

A method has been developed? for obtaining aflat output spectrum if preliminary estimates ofthe amplitude of the system frequency responseare available from theoretical calculations orfrom preliminary measurements. The procedureis the same as described in the previous section,except that the desired anlplitude spectrum usedin the optimizatiorr has the shape of the recipro-cal of the expected shape of the amplitucle of thesystem frequency response. The amputucle spec-trum of a typicat input signal for a prewhitenedMFBS test is shown in Fig. 6.

3. signal hput Procedures; Three different pro-cedures were used in the tests. The changes wererequired to overcorne probrems rvith ilre controlrods and with the system background flux noise.

t08

a. open-Loop Rod Positicming. This procedurewas used in the early tcsts. The desired inputsignal generated by the BR- 340 computer wasused to actuate vrithdraw and insert signals tothe control -rod drive motor. The withclraw andinsert times were different because the coastingcharacteristics of the rod were different f orwith drawals and insertions. The withdraw andinsert times were adjusted manually during thebeginning of the test to grve the desired pulseshapes. This procedure worked well when thecontrol rocls v/ere new, but the wear associatedwith long-term operation caused difficulty inlater tests.

b. Flux Deneand. The flux demand procedurewas used to overcome the problerns associatedwith open-Ioop tests. The procedure was to feedthe test sequence in as a ftux demand signal forthe flux-servo system. This caused the controlrods to move to satisfy the flux demand. In ilristest, the spectrum of the flux signal had the ap-proximate shape of the spectrum of the test

"L-. quence. The amplitude of the spectrum of theinput was approximately the amplitude of the fluxsignal divided by the amplitude of the system fre-quency response at that frequency.

This procedure worked satisfactorily for thefinal tests with the 235u loading. The only ccndi-tion was that the flux servo systein had to be ad-

fO-'25tO-lZSr9o?5rcFREQLTENCy (rodlsccl

(D} ENERGY SP€CTRUM

Flg. 6. MFBS prewhitened signal and its spectrum.

NUCLEAR TECIINOI.OGY VOL. IO FDBRUARY I9?I

I to-tLJz14,

J ri.

zIlnJx?oF|r-o to-azI()(rlr

}IOTE; THE TW€LVEOESIRED HARMOHICScoilrAlH 75.3 % OFTHE TOTAI. STGHALEilERGY

O DESIRED HAR'{ONICS

O OTHER HARMOHICS

-I oercw. scALE

-'l

JLA' = 3 sec

THE INPUT SIGNAL

NOTE: THE SIX DESTREDHARMONICS CONTAIN 727"/OOF THE TOTAL SIGNALENERGY

o DESIR€D HARMONICSO OTHEFI HARMONICS

I arrow scALE

*:+uilFql ,,s

justed to avoid hunting by the control rod. Thiswas necessary because of loose coupling in therod drive mechanism (see Fig 1), which causedan error in every indicated rod position change.If each rod position change was llreceded by achange in the opposite direction, then each read-ing was in error by a multiplicative factor. Whenrod position changes in arbitrary directions weremade, the indicated position error was not asimple factor and it was impossible to obtain r€-liable rod position indications.

When the reactor operated with 233U fuel , achange in system characteristics made the fluxdemand procedure unacceptable. Shortly afteroperation began rvith 233U fuel, tlr€ voicl fractionin the fuel salt increased significantly with an &c-eompanying increase in flux noise. This noisecomponent in the error signal in tlre servo causedexcessive rod motion. This was unaccepta"ble be-cause of the problem with erroneous rod positionsignals.

c. Closed-Loop Rod Positioning. The prob-lems with the flux demand test led to the closed-loop rod positioning procedure. In this procedure,the flux signal from the ion chamber was discon-nected from the servo system and was replacedby the rod position signal. Then, the error signalrvhich actuated the control-rod drive wa,s the dif-ference b€frv€€n acfual and desired rod positionsignal. This procedure was satisfactory in alltests,

III. DATA ANALYSIS IUIETHODS

Three different digital computer codes wereused in the data analysis. These are describedbriefly below:

1. FOURCO. s This cocle computes the Fouriertransform of the output signal and the input sig-nal, ard computes their ratio to give the frequen-cy response.

2. CPSD.S This code is based on a digitalsimulation of bandpass filters. The filters haveadjustable bandwidths, as opposed to the othertwo analysis methods in which the effective band-widths are determined by the duration of the datarecord analyzecl.

3. CABS.ro This code cornputes the autocorre-lation function of the input, the autocorrelationfunction of the output, and the cross-correlationfunction for input and output. These are thenFourier transformed (using FOURCO) to give theinput power spectrum, th€ output power spectrunt,and the cross power spectrum. The frequencyresponse is given by the ratio of the cross powerspectrum to the input power spectrulll.

NUCLEAR TECHNOI.,OGY VOL. 10 FEI]RUARY T9?1

Kerlin et al. EXPERIENCES WITII DYNAMIC TESTING

IV. RESULTS

The large number of clifferent tests (over 50)

makes it impossible to show all the results inthis paper'. Instead, some typical results will beshown, and t comparison with theoretical resultswill be madc. (tfre reader may consult Refs.7 r 9,and 11 for more details on test results.)

Fr equency Re sponse Results

a, 235U Fuel, hi.tial OBeratf.on. For these earlytests, the inlrut consisted of a reactivity pulse, areactivil;y step, of a pseudorandom binary reac-tivity input. The input procedure was the open-Ioop rod positioning procedure, and all three dataanalysis methods were used, Figure shows thezeto-power frequency response for the "uu-fueledreactor with fuel salt stationary. This figure alsoshows the noise analysis results 12 at high f re-quency. The comparison of the magnitude withcalculations is quite good. The phase results areIess satisfactory.

- Figure B shows the frequency response at 2.5MW. The agreement between the shape of themeasured frequency response and the shape of thepredicted frequency response is good for magni-tude and phise. The differences between thetheoretical and experimental results for the absc-lute value of this magnitude are not compietelyunderstood, but it is suspected that the problemswith accurate rod position indications and withestablishing the true power level by heat balancesare largely responsible for the differences. (Thefrequency response is a strong function of powerlevel. See Figs. B and 14 of Ref. 1.) fne autocor-relation function of the rod position signal and thecross-corr€lation function for the 2.5 MW test ap-pear in Figs. 9 and 10. The blips near each endare due to asymmetry in the pulses (the positivepulses do not have exactly the same shape as thenegative pulses). These blips are predictablefrom the theoretical properties of pseudorandombinary signals with asymmetrical pulses.tt Theseblips were not observed during the first tests (be-fore the power was increased to 2.5 MW), but theyhave been observed intermittently in subsequenttests. They cause no problems in obtaining fre-quency response results. They are included hereto illustrate,an unexpected feature in the test re-sults which were bothersonle until the cause wasunderstood. .

Figrrre 11 shows the results at ?.5 MW. Fromthis figure, it appears that the dip in the amplitudeat *0.24 rad/sec in the preclicted frequency r€-sponse is too large irr the theoretical predictions.Since this calculated dip was due to fuel recircu-lation effectsrt it appears ttrat tnore mixing of the

t09

Kerlin et al. EXI)EINIENCES WITII DYNAN,TIC TESTING

toa

ei. 6-l.o<=7?(,

ZERO POV/ER

7-sec PULSE, TEST NC {

7-sec PULS€, j IST NO 2

3 S-sec PULSE, TI.SY nro 3

3 S-sec PULSE, TEST NO 4NOISE ANALYSIS

c,, FREQUENCY (rody'ec)

o.or o t t.o

rr,r, FREQUENCY ( rod/secl

Frequency response at zera power; fuer static.

Ctlo.|t

trja

I(L

o

-20

-40

-60

-80

Fig. 7 .

fuel salt in the external loop should be inctuded inthe theoretical model.

A measure of the adequacy of the theoreticalmodel is its ability to predict the natural period ofoscillation of the power response following a re-activity perturbation. The comparison of theexperimental results with theoretical predictiops(see Fig. I of Ref. 1) appeals in Fig. LZ.

b. 235 ry FueI, Intermed.iate Issfs. Measure-ments were made again afier 1 year of poweroperation (2100 e q u i v a I e nt full-power hours).Pseudorandonl binary sequerlce inputs were trsedat porver levels of 1, 5 , and 7 MW. The opel)- looprod positioning procedure was used. These testsshorved rlo significant changes in the dynarniccharacteristics due to aging.

c. 2s6 ry I'rrcI , Fittal lesfs. A final set of rnea-surements for the ?3su-fuelecl system were nracleafter llrore than 9000 equivalent full-power hoursof operation. Input steps, pseuclorurdorn binary

lt0

sequences, and pseudorandotn ternary sequenceswere. used. The last attempts at open-loop rodpositioning were made in some of ilre PRBS tests.This procedure worked occasionally, but it wasnot reliable. The fltx demand method was useclfor most of these tests to overcorne problernsencountered with th€ open-loop roC positioningmethod. Figure 13 shows results from flux cle-mand tests using one of the few satisfactory PRTSsignals. These results show flrat there were lloaging effects which caused significant changes inthe power hours of operation.

d. 233 11 lluel , Irtitial Operation. plans weremade to use the flu:i demand technique in the cly-namics tests for the 233U loacling, but this proce-dure pro\red unacceptable because of the problelnsmentioned in Sec. fr.C.3. This led to the use ofthe closecl-loop rod positioning nreilrod, whichproved to be satisfactory, and rvhich was used inall subsequent tests. Pseudoranclom binary s€-quences and pseudorandorll temary sequences

ZERO POWER

7-sec PULSE , TEST NO. t r7-sec PULSE , TEST NO. Z l3.5-sec PULSE . TEST NO. 3 a3.5-sec PULSE.TEST tiO. 4 o

NUCLEAR TI'CIINOI,OCY VOL. rO FNBRUAITY 19?1

Kerlin et al. EXI;IIRIENCI]S WITTI DYNAM IC TESTTNC

i-lq.

cVatl.o<=za(,

127-?tT PRES -CPSD1?7 -8]'T PRBS-CABSsil -81T PRES - CPS05II - BIT PRB S - CA 8S

0.01 0.02 0.05

FREQUENCY kadlsecl

ANALYSlSANALYSIS

ANALY9:3A NAL Y5I S

I

ocAlv

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Fig. 8. Frequency respons€, Fower = 2.5 MW.

400 800 1200

CORRETATTON TIME (t"")

Fig. 9. Input autocorrelation function for a 51l-bit PRBS test et 2.5 MW.

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Kerlin et al. EXPERIENCI.]S WTTH DYNAMIC TESTING

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CORREI.ATION TIME (sec)

I'ig. 10, Cross-correlation function for a 511-bit PRBS test at 2.b MW.

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il2 NUCLEAR TECIINOI,OGY VOL. 10 FEBRUARY I9?T

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KCTIin ET AL. NXPERIENCES WITII DYNAMIC TEST-ING

v/ere used, Typical results are shown in Figs . L4

and 15 for PI?,BS and PRTS tests. The PRIIS re-sults shown in Fig . 14 arc in good agreement withtheory and the scatter is small. The theory stillshows too large a dip at A.24 rad/s€c , indicatingtoo little rnixing in the theoretical model. ThePRTS results shown in Fig. 15 have the samegeneral form a^s the PRBS results, but the scatteris excessive. This is apparently due to the prob-Iems in determining the rod position accuratelyfor the three-level signal (see Sec. If .C.3).

e. 233 ry FueI, Final Tests. A finat series oftests was run ^.-g months later. For the finaltests, the PRBS, the n-sequencer the MFBS-flatspectrum, and the MFBs-prewhitened spectrum

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Kerlin et al. EXPERIENCTjS wI'rH DYNAMIC TESTING

u'ere used. Results are shorvn in Figs. 16 through19. These results again clemonstrate ilrat therewas no significant change in system dynamics dueto agrng.

In these tests, cornparisons were rnade of thedifferent test signals, In general , the aclsantage ofthe IvIFBS was demonstrated. ir is not possibte topresent the cletails of the comparison here (seeRef. ?), but some typicai results are shown inTable I. This table shows re sults f or a PRIIS testand an MFBS test. Each test ccnsisted of B cyclesand each cycle was analyzeo separately to give anindependent estimate of the frequency re.sponse.The lorver percent deviations for the MFBS testsare due to the higher signal-to-noise ratio at eachmeasurement frequency, rvhich occur because theinput signals concentrate the available energy inthes e frequencies.

The prervhitening technique was of little benefitbecause the amplitude of the MSRE frequency re-sponse did not change very much over the fre-quency range of interest.

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TABLE I

tBasedlon B cyeles of datz. Both signals had same arn-plitude and bit duration. The MFBS hact LzB bits and thePRBS had L27 bits.

v. coNclu$torus

The main conclusion as far as the MSRE pro-gram is concerned is that the dynamic character-istics of the MSRE were found to be satisfactoryand essentially as predicted, for both the 235U

anclthe 233 U fuel loadings.

Conclusions having to do with experiencesperforming dynamics tests on a system withspecial provision for test equipment are:

1. By proper matching of the testing method tothe system characteristics and to the characteris-tics of normal system hardware, it was possible

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I t6 NUCLIIAII TECHNOI.,OGY VOL. 10 FEBRUARY 19?1

to rneasure the systern frequency response withoutthe expense of installing an oscillator rod.

2. A thorough undcrstanding of the propertiesof test signals is a great help in selecting theoptimum test signal for a particula.r application.Our experience suggests that the M fBS signalrnay have the widest general utilrty of the rnethodsused in the MSRE tests.

ACKNOS'I-EDGilIEIUIS

This research was sponsored by the U.S, AtomicEnergy Commission under contract with the UnionCarbide Corporation.

REFERE UCES

1. T. 'W, KERLIN, S. J. BALL, and R. C. STEFFY,'oTheoretical Dynamics Analysis of the Mo1ten-SaltReactor llxperiment," Nu.cI. Techrwl., 10, 118 (19?1),

2. P. A. N. BRIGGS, K. R. GODFREY, and. P, H.HAMMOND, "Estimation of Proeess Dynamic Charac-teristics by Correlation Methods Using Pseudo-RandomSignals,tt IFAC Synzp. on ldentnfication in Automati.eControl, Systems, June 72-17, 1967, Pragzter, Czechosln-uaki.a, Part II, pp. 3.1-3.L2, Academic, Prague (Jwre1 96 7).

3. T. 'W. KERLIN, "The Pseudorandom Binary Signalfor Frequency Response Testing," USAEC Report ORNL-TM-1662, Oak Ridge National Laboratory (1966).

4. R. J. HOOPER and E. P. GYFTOPOULOS, "On theMeasurernent of Characteristic Iiernels of a Class ofNonlinear Systerns," Proc. Symt. an Neutron Noi,se,Waues and hr,Ise Propagation, Conf. 660206, IJ.S. AtomicEnerry Commission (1 967).

KETIin et aI. EXPERIENCES WITII DYNAMIC TESTTNG

5, H. R. SIMPSON, Proc.IEE, 113, 12,2A75 (December1 966).

6. A, Van Den BOS , "Construction of Binary Multi-frequency Test Signals,t' IFAC Symlr. on ldentificati.onin Autonzatic Control Systents, June 12-7V, 7967, Prague,C zechoslnuakia, Part II, p;r. 3.1-3 .L2, Academic, Prague(June L9671.

7. M. R., BUCKNER, "Optirnum Binary Signals forFrequeney Response Testing,tt Doctoral Dissertation,University of Tennessee, Knoxville (1970).

8. S. J. BALL, "A Digital Filtering Technique forBfficient Fourier Transform Calculations," USAEC Re-port ORNL-TM-1662, Oak Ridge National Laboratory(1e6 ?).

9. T. 'W. KERLIN and S. J. BALL, "Experimental Dy-namic Analysis of the Molten-Salt Reactor E>periment,"USAEC Report ORNL-TM-L647, Oak Ridge NationalLaboratory (1966).

10. T. 'W. KERLIN and J. L. LUCruS, "CABS-A For-tran Computer Program for Calculating CorrelationFunctions, Power Spectra, and the Frequency Responsefrom Experirnental Data," USAEC Report ORNL-TM-1663, Oak Ridge National Laboratory (1966).

11. R. C. STEFFY, "Frequency Response Testing of theMolten-Salt Reactor E>qperiment," Thesis, University ofTennessee, Nuclear: Engineering Department (Novernber1969); and tISAEC Report ORNL-TM-2823, Oak RidgeNational Laboratory (1970).

12. D. P, ROUX and D. N. FRY, Oak Ridge NationalLaboratory, Fersonal Communication.

13. K. R. GODFREY and W. MURGATROYD, Proc. IEE,tlz, 3, 565 (March 1965).

NUCLEAR TIiCFINOLOGY VOL. IO FNL\RUAITY 19?I lr7