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4 .4
EXPIRIENCES WITH DYNAMIC TESTING ilfiTTF{ .*DS AI THI [\4CLTThI -SALT RTACTSR TXPIRIMTT$T
€ &
t
st 3
$
T.
'W. KERLIN, S.
KEYWORDS: reoc tivity, (se-, cruency, plwef , lesfi:n j, per-
(ormonce, sign al s, MSPE
J..PALL, R. C. STBFFYT* and M. R. BUCKNER**
Oah R'idge Nation.al Laborato.ry, Aah Ridge, Tennessee 37830
Received Ltay 23, 19?O Revised Septemi:er L4,
LgT 0
A series of y'eactiuitSt-to-power frequarcy ,1,€sponse nteasuvenzents ?,uas made on the hloltensalt Reactor ExP erintent. Tlzis u)as clone for 233 ry and 235 [/ fuels, for a vange af op erating power leu els, at s eu eral points i,n the sysl e?n ofi erati.ng Itistoyy, and ./'or seue]'ttl, different test pt oced"u?,es. A cornparison oJ' experirnental resu,lts utith prior theoreti.cdl predi.ctions confirmecl the uatirtity of the theoretical prerii"ctiorzs. The test p?-ogram included n?easu,rernents using fize pseu.clorarz.do.ftz bina. 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.
!....
reassessed if necessary and so that confirrnec methods could be established. f or anaryzing future, high -performance mortensalt reactors
3. to evaluate techniques f or perf orniing dy narnics experimcnts and mefirods of data anaiysis
.
Tests were performed at several differ.ent power ievels, &t several different times in the system,s operati:rg history, ancl for the reactor fueled u'ith 235u and with 233u. Items 1 and z were the main objectives of the test proglarn, but ilris paper €rrrphasizes item 3 since it should be of general interest to those planning dynamics tests in other systems. Those interested only in the perfor * manee of the MSRE could skip secs. f[ ancl III ancl proceed directlSr to the results in Sec. IV.
I. INTRODUCTION An extensive dynamics testing progr?r,r was carried out at the Molten-Salt Reactor Experiment (usRn ). t The tests consisted of reactivity to power frcquency response measurenrents. The purpose of the test program was: ,
1. to demonstrate the safety the system
ancl
operability of
2. to check the valiciiiy of ilre theoretical analysis so that the safety of the plant coulct, be
+Present addressl Tennessee Valtey Authority, Chattanocgar, Tennessee.
*tUtrivcrsity of Tennessee, Knoxville, Tenne$see. f)resertt adrlress: Savannalr Iliver Lstboratory, Aiken, South Cnrolirra.
NUCLIiAIt l'l'ICIINOLOGY VOL. 10
tsEIlIttlAItY lg?r
II.
PLANNINIG THE TESTS
A.
Objective
The primary test objective was to ureasure the reactivity-to-power frequency response over the ran€le of frequencies where im1:ortant system cly namic effects occurred. Inspection of the fre quency response predictions (see Figs. B and 14 of Ref . U inclicated that nl.easurem ent.s clown to '- 0.005 rad/.sec at the low frequency encl were needed. It would have been dcsirable tq .arry the hish frequency end of the measurements out to about 50 racl/sec if $re zero-power reactor kinetics effe.cts were to be observed. If ilre interest were in feeclback effects, the upper frequency neecl rrot have been greater ilran -0.b racl/sec. The approach used hcre was to deternrine ilre high frequeney ( 1.0 to 100.00 ract/sec ) response by noise t03
Kerlin et al.
ExpERIENcEs wITrI DyNAIuIc TESTING
nreasurements during z,eto-power operation. Subsecluent at -power measurements concentratccl on
the
0' 005-
to
0. 5
-rad/sec rangc wler€ feeclback
effects tvere inrportant,
B. Equipment used in Experimentaf
ftlleasurements
The selection of the experinental methods for the MSRB dynamics tests was based on the information required and on the capabilities of the available equipment. Fortunately, the emphasis on low frequency results ( 0.0c5 to 0. b rad/sec ) made it possible to obtain the important part of the system frequency resparrs€ using the standard MSRB control rods to int'oduce the input reactivity perturbations. The MsItB has three identical control rods, each with an active rength of sg.4 in. one rod is normally designated as the regulating rod a'd is used for fine control. The other two rods are used as shinr rods for coarse adjustrnents. The rods
are actually flexible,
stainless
C.
Test Signals
1. tntroduction Test signal selection was influ-
enced by considerations of accuracy requirements, frequellcy range over which information was
need€d, and harclware capabilities. The following input 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 input spectrum)
g. multifrequency binary sequence (prewhit_ ened output spectrum).
-steel
hoses on Pulse and step tests are easy to implement, but which are strung gadoliniurn oxide poisori cylinthese signals give results with limited accuracy. ders. The rods are mounted in thimbles which This is because the signals are nonperiodic, illd have two 30-deg offsetting be*ds so that the rocls therefore have a continuous frequency spectrum can be centrally located even though ilrere is no a'd resulting low signal ene-rgy in the neighborroom for the control-rod clrive assemblies above hood of a frequency of interest. the central a:<is of the core. The murimum rod The other five signals are more trouble to imspeed is - 0. 5 in. /see. Typical rod travel in the plement, but they permit more accurate results. experiments was - 0. b in. for most of the 23s u This is bbcause they are periodic, and therefore tests and 0.3 in. for most of the 233U tests. This concentrate the signal energy in discrete harmon_ gave a reactivity change of in the ic frequencies. -0.025Vo 0g) 235u rn alr of the tests using periodic tests a'd -0.02vo (izg) in the *ru tests. signals, the period is determined by the lowest v Figure 1 shows the contror-rod and drive fl,s- desired frequency: sembly. The position indication for eacrr rod was obtained from a synchro geared to the rod drive 2T T = (t)r mechanisrn. A coarse synchro (b-deg rotation per inch of rod travel) was used in u""ly tests and fine synchro (60-deg rotation per inch of roda where T = period travel) was used in rater tests. The signar from the position synchro was anrplified and 1ow-pass ut = lowest desired frequency filtered ( l-sec time constant) to eliminate high For example, the required period for a test in frequency noise and ilre accompanying aliasing .i_ fect prior to input into the Bunker Ramo computer, which the lowest required frequency is 0.01 rad/sec in 628 sE-c. All other harmonics would be BR-340, where the signal was digitized eue"y 0.25 sec and recorded on magnetic tape. at integer multiples of 0.01 rad/sec. The accuracy of the results is improved by using input sigThe nuclear power level signal was furnished nals consisting of tnore than 1 cycle. In the MSRE by the output of a compensated ion charnber located acliacent to the core. This signal was also measurements 2 to 10 cycles were used. amplified, low-pass filtered (l-sec iinre constant), digitized at 0.zs-sec intervals, a'd recorded on 2. Properties of htfutt Signals. rnagnetic tape. The BR-940 computer was also used in con_ a. htlse. The energy density e of a pulse of junction with a portable analog computer duration r and arnplitude A at frequency,i" g*", for generation of the input sigrral for the test. A com- by: puter program was prepared for on-line generatio* of each test signal used in the teJts (the e= leilteT/z)-l ' signals are described in Sec. f[.C .Z), L vTTTJ '
ry 2n a
104
NUCLEAR TECIINOLOGY VOL.
TO FEBRUARY
19?I
KCTlin et al .
E,Y.PERIENCES WITI"I DYNAMIC TESTING
REVERS|BLE DRIVE MOTON COOLANT TO DRIVE ASSEMELY
TCOOLING
GAS INLET
COOLING GAS COf.lTAlN€R
IhDICATOR SYNCHRO TRANSTiITTER -POSITION
FIXED DRIVE SUPPORT AND UPPER LIMIT
3
swtTcH
-
in. CONTAINiv€NT TUBE
ANT TO POISON ELEMENTS
DRIVE UIJIT SPACER
*
LOWER LIMIT
swrTcH
in.o. D.-3o4 s. s.- FLExTBLE HOSE CABLE
SPRING LOADED ANTIBACKLASH HEAD AND IDLER GEAR
3-in. x 2-in.
ECCENTRIC
REDUCER
l6-in.
COOLANT EXHAUST
RADIUS x 3O" BEND
-_-_*O--
BEADED POISON ELEMENTS
2- in
Fig,
CONTAINMENT THIMBLE
1. Control-rod drive
2. Note that the amplitude i.s expressecl as energy spectral density (energy per unit frequerlcy). This spectrum appears in Fig.
b. Step. A step input may be thought of as a pulse whose duration has gone to infinity. The step test is suitable only for systems rvhose r€sponse settles to some constant value after the NUCLEAR TECHNOLOGY VOL.
a,
10
TEBRTIANY 1971
assembly,
step input. This requires that the systemts zetofrequency gain be a finite constant (including zero). In principle, the step input contains an infinite amount of ener€ry, but this energy is'concentrated in the low frequencies where it is of little use.
c. Pseudorandont Binary Sequ.ence. The pseudorandom binary sequence (PRBS) is often used t05
$ I srs
Kerlin et al.
EXPERIENCI'S WITTI DYNAMIC TESTINC
greatest arnplitucler (thereby furnishing a measure of the ban.Iu'idth of il^rc signal): hp =0.44N
(2)
,
wher e ht, = harmonic nurnber of the harmonic with
half the pcwer as the harmonic with the greatest po\,vei'. Thus, if the lowest frequency is (oL rad/sec, and the required highest frequency is @tt rad/sâ&#x201A;Źc, then the number of bits is given by:
()
z
u, :) a lr, E ft
tr z. :)
N
F
A,
J[ = 2.27 uh &)r
E.
lrl o. (9 E,
(3)
.
The bit duration
lrj Zt
1rr
quenclr of
A I is fixecl by the interest. The relation is
highest fre -
Lt = 2'77cnl
(4)
of course, these are just rules of thumb. ff
!r.l
I DIMENSIONLESS FREOUENCy
Fig.
2.
(
o
T)
Energy spectrum of a square pulse.
d. Pseudorando?n Ternary sequence. The pseudorandom ternary sequenceo (pRTs) is similar to the PRBS, but three levels of the input signal are
for frequency response measurements and for approximate impulse response measurements. The methods for generating the pRBs are well known."t These methods $ve periodic sequences of +lts and - lts (each member of the sequence is called a bit). The total number of bits in ilre sequence N must be 2z 1 for any integer value of z, The period of the signal is given by the product of the number of bits N and ilre bit time interval
the
total signal enerry is too small, the signal enerry per harmonic may be too small even for the harmonic with the largest amplitude.
lO
3 DENOTES HARMONIC FREQUENCY BASIS
-
SAFNE TCTAL DURATION
ALL
FOR
SIGNALS
At.
The spectrum of the pRBs with pulse arnplitude A and total test duration I is given by:
A, = arwt 2 (N + 1)A,r rr&
fgl#.4Dl
A"=#
,
o.f (\t lr',
o
:)
ror
te
/
oos
L J
a
(L
O
=
for k
-0,
(1)
lrj a J
:)
O O cro oooo
63 BIT
o.02
(L
where Ap = amplitude of the energy spectrurn at
the &'th harmonic frequency. The spectra for several sequences are shown in Fig. g. Note that
the short sequences concentrate rnost of the signal enerry in the first few harrnonics and ilre longer sequences spread the signal power among more harmonics. In planning a test, one must select the periocl to give the reqtrired lorvest frequency. The required upper frequency fixes the sequence length N or equivalently (since the periocl i.q fixect) ttre bit duration. The following relation specifies ilre harmonic nunrber at which the signal power is half as Iarge as the amplitude of the harnronic with the t06
x F
o.or
3I
(J
c
BIT
trj
z
lrJ
o.oo5 a_
.l
(o
il tl
o.oo2
o
oor
a
tz,5to?o50too
rr lf li
HARMONIC NUMEER
Fig.
3.
Energy spectrum for severar PRBS signals.
NUCLI'AR TECTINOLOGY VOL.
10
FEBRUARY T9?I
' re'il
KCTIin et
used (-1r 0, +1). The numiler of shifts in thesequence is given by N = $z - 1) f or integer values of Z . The spectrum of the PRTS with pulse amplitude A and total test duration 7'is given by:
ou=&eiffi14#Pl' Ap = 0
rorpodd for&even.
odd harmonics are non -zeto and they have an amplitude u'hich is one-third larger than the corr€sponding amplitude of a PRBS harnronic f or a sequence with the salne value of N. Figure 4 shows a cornparison of these signals. The properties given in'Eqs. (2) trrrough (4) for the PRBS also apply for the PRTS. The PRTS is of interest because it has the advantage that it cliscriminates against nonlinear effects. This may be advantageous because it allows one to use large amplitude sigrrals in frequency response measurements. The PRTS has the disadvantage that in the MSRE (and in many other reactor systerns ) a three -level input is harder to implement with system hardware than a two-Ievel signal. e . n-sequence. Thc n-sequenceu is obtained. by a sirnple rirocii{ication of the PRtsS. T}re mociifica-
tion consists of inverting every other bit in a PRBS. Since the number of bits /V in a PRBS is
6
r.o
o F o tr,
IJ J
= o z E,
lr,
) tr
o
o.t
-
o-
o.ol
o.r
O.Or
I
NORIT|ALIZED HARMONIC NUMBER ( k/N)
Flg.
4.
Envelope of amplitude spectra and rr-sequence.
NUC I,DAIT
r,rlF
I'ECIINOLOGY
\IO
for IlItBS, PIiTS,
L. IO FEI}IIUAIIY
I $?
I
EXI,T]RIf]NCHS WITII DYNAIVIIC TtsSTING
always odd, the number obtainecl by nrc-.lification The spectrum of the pulse arnplitude A, anC
of bits in an
n-sequence
of an N-bit PRBS is 2N. tt-sequence with N bits, total test duration T is
given by:
(5) ao=t!!;i)AtlW'
This shows that the shape of the PRTS spectrum is the sarne as for the PRBS. However, only the
P o-
aI.
Ap
-0
rorftodd (6)
for
& even.
Figure 4 shows a eomparison of the spectrum for the n-sequence zurd the PRBS and PRTS. Since the shape of the amplitude spectrum is the same as for the PRBS, the bandrvidth relations lgqt . (2) through (4)] stilt apply. The n.-sequence discriminates against nonlinear effects as in the case of the PRTS signal. f . Multifrequency Binary Sequence (MFBS) I'lat Sfectrum. In all frequency response lrleasurements, a major obj ective is to select input
signals with a large fraction of the total available signal energy concentrated in the f requencies selected f or measurement. Generally, it is desirable to space the harmonics evenly on a logarithmic scale except in regions where more resolution is needed. Since the harmonics of the PRBS, PRTS, and n-sequence are evenly spaced on a linear scale, the spacing of the harmonics is too dense at the higher frequencies (see F'ig. 3). This constitutes a waste of siEral energy irr identifying nearby harmonics which are only sliglrtly different from one another, An alternate procedure is to design a test signal rvhich maximizes the fraction of the total signal energy in harrnonics selected by the experimenter. A sigrral of this type can be obtained by a computer optimization of the polarities of the pulses in 4 pulse chain of fixed length. The objective functiotr, rvhich is minimized in the optimization, is the differerlce between the desired spectrum and the spectrum obtained for a given pulse chain. Experience shows that as much as 65 to 75Vo of the total signal power can be concsrltratecl in selectecl harmonics.u" Furthermor€, the signal can be desig:red so as to discriminate against nonlinear effects. A typical signal used in the MSRE experiments appears in Fig. 5.
g. It'Iultifr.equency Binary Sequence (lvlFBS)Prepltitened S\ectrunt. One of the main reasons for interest in the PRBS, PRTS, and rr-sequence is flrat the amplitude spectrum can be made quite flat over a wide frequency ran€le. This is important in measurements rvith large noise contamination of the input sigtral. The procedure for such a system woutrcl be to use as nruch input signal energry as possible (withln limits set lly system operating r07
Kerlln et al.
-l
EXPERIENCES WITH DYNAMIC TESTING
a. open-Loop Rod Positicming. This procedure was used in the early tcsts. The desired input signal generated by the BR- 340 computer was used to actuate vrithdraw and insert signals to the control -rod drive motor. The withclraw and insert times were different because the coasting characteristics of the rod were different f or with drawals and insertions. The withdraw and insert times were adjusted manually during the beginning of the test to grve the desired pulse shapes. This procedure worked well when the control rocls v/ere new, but the wear associated with long-term operation caused difficulty in later tests.
Jl*arrSrc
(o} THE INPUT
SIGNAL
(o g,
}IOTE; THE TW€LVE OESIRED HARMOHICS
I|J
z rd J z I v, J rda F o F
coilrAlH 75.3 %
OF
THE TOTAI. STGHAL EilERGY
t!
o
= o tr ct
O O
E t!
I
DESIRED HAR'{ONICS
b. Flux Deneand. The flux demand procedure was used to overcome the problerns associated with open-Ioop tests. The procedure was to feed the test sequence in as a ftux demand signal for the flux-servo system. This caused the control rods to move to satisfy the flux demand. In ilris test, the spectrum of the flux signal had the approximate shape of the spectrum of the test . quence. The amplitude of the spectrum of "Lthe input was approximately the amplitude of the flux signal divided by the amplitude of the system frequency response at that frequency. This procedure worked satisfactorily for the final tests with the 235u loading. The only ccndition was that the flux servo systein had to be ad-
OTHER HARMOHICS
oercw. scALE
-
ldl to-2 FREeUENcv (rad/lec)
(b}
ENERGY SPECTRUM
Fig. 5. MFBS flat spectrunr signal and its spectrurn.
conditions and nonlinear effects ) anO to divide this energy evenly among the desired harmonics so that the signal-to-noise ratio would be as high as possible at each measurement frequency. In systems in which the predominant noise contanrination is in the out/tut signal, the same observations apply as were mentioned above in connection with an input-noise problem. That is, each. output harmonic srroulcl contain the muimum possible sigrral energy. Thus, for systems with output noise problems (a common case) trre output amplitude spectrum should be flat. This can be accomplished by using an input signal whose &rrrplitude spectrum ha^s a shape which is the reciprocal of the amplitude spectrum of the system freqriency response. A method has been developed? for obtaining a flat output spectrum if preliminary estimates of the amplitude of the system frequency response are available from theoretical calculations or from preliminary measurements. The procedure is the same as described in the previous section, except that the desired anlplitude spectrum used in the optimizatiorr has the shape of the reciprocal of the expected shape of the amplitucle of the system frequency response. The amputucle spectrum of a typicat input signal for a prewhitened MFBS test is shown in Fig. 6.
3. signal hput Procedures; Three different procedures were used in the tests. The changes were required to overcorne probrems rvith ilre control rods and with the system background flux noise. t08
-'l
JLA'
=
3
sec
THE INPUT SIGNAL
I
to-t
LJ
z 14,
J
ri.
z I ln
NOTE: THE SIX DESTRED HARMONICS CONTAIN 727"/O
OF THE TOTAL SIGNAL
J
x? o
ENERGY
F
|ro z I
to-a
() (r lr
o DESIR€D HARMONICS O OTHEFI HARMONICS
I arrow
scALE
fO-'25tO-lZSr9o?5rc FREQLTENCy
(D} ENERGY
Flg.
6.
(rodlsccl
SP€CTRUM
MFBS prewhitened signal and
NUCLEAR TECIINOI.OGY VOL.
IO
its spectrum. FDBRUARY I9?I
*:+uilFql ,,s
Kerlin et al.
justed to avoid hunting by the control rod. This was necessary because of loose coupling in the rod drive mechanism (see Fig 1), which caused an error in every indicated rod position change. If each rod position change was llreceded by a change in the opposite direction, then each reading was in error by a multiplicative factor. When rod position changes in arbitrary directions were made, the indicated position error was not a simple factor and it was impossible to obtain r€liable rod position indications. When the reactor operated with 233U fuel , a change in system characteristics made the flux demand procedure unacceptable. Shortly after operation began rvith 233U fuel, tlr€ voicl fraction in the fuel salt increased significantly with an &ceompanying increase in flux noise. This noise component in the error signal in tlre servo caused excessive rod motion. This was unaccepta"ble because of the problem with erroneous rod position signals.
c. Closed-Loop Rod Positioning. The problems with the flux demand test led to the closedloop rod positioning procedure. In this procedure, the flux signal from the ion chamber was disconnected from the servo system and was replaced by the rod position signal. Then, the error signal rvhich actuated the control-rod drive wa,s the difference b€frv€€n acfual and desired rod position signal. This procedure was satisfactory in all tests,
III.
DATA ANALYSIS
IUIETHODS
Three different digital computer codes were used in the data analysis. These are described briefly below: 1. FOURCO. s This cocle computes the Fourier transform of the output signal and the input signal, ard computes their ratio to give the frequency response.
2. CPSD.S This code is based on a digital simulation of bandpass filters. The filters have adjustable bandwidths, as opposed to the other two analysis methods in which the effective bandwidths are determined by the duration of the data record analyzecl. 3. CABS.ro This code cornputes the autocorrelation function of the input, the autocorrelation function of the output, and the cross-correlation function for input and output. These are then Fourier transformed (using FOURCO) to give the input power spectrum, th€ output power spectrunt, and the cross power spectrum. The frequency response is given by the ratio of the cross power spectrum to the input power spectrulll. NUCLEAR TECHNOI.,OGY VOL.
10 FEI]RUARY T9?1
IV.
EXPERIENCES WITII DYNAMIC TESTING
RESULTS
The large number of clifferent tests (over 50) makes it impossible to show all the results in this paper'. Instead, some typical results will be shown, and t comparison with theoretical results will 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 early tests, the inlrut consisted of a reactivity pulse, a reactivil;y step, of a pseudorandom binary reactivity input. The input procedure was the openIoop rod positioning procedure, and all three data analysis methods were used, Figure shows the zeto-power frequency response for the "uu-fueled reactor with fuel salt stationary. This figure also shows the noise analysis results 12 at high f requency. The comparison of the magnitude with calculations is quite good. The phase results are Iess satisfactory. - Figure B shows the frequency response at 2.5 MW. The agreement between the shape of the measured frequency response and the shape of the predicted frequency response is good for magnitude and phise. The differences between the theoretical and experimental results for the absclute value of this magnitude are not compietely understood, but it is suspected that the problems with accurate rod position indications and with establishing the true power level by heat balances are largely responsible for the differences. (The frequency response is a strong function of power level. See Figs. B and 14 of Ref. 1.) fne autocorrelation function of the rod position signal and the cross-corr€lation function for the 2.5 MW test appear in Figs. 9 and 10. The blips near each end are due to asymmetry in the pulses (the positive pulses do not have exactly the same shape as the negative pulses). These blips are predictable from the theoretical properties of pseudorandom binary signals with asymmetrical pulses.tt These blips were not observed during the first tests (before the power was increased to 2.5 MW), but they have been observed intermittently in subsequent tests. They cause no problems in obtaining frequency response results. They are included here to illustrate,an unexpected feature in the test results which were bothersonle until the cause was
understood.
.
Figrrre 11 shows the results at ?.5 MW. From this figure, it appears that the dip in the amplitude at *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 recirculation effectsrt it appears ttrat tnore mixing of the t09
Kerlin et al.
EXI)EINIENCES WITII DYNAN,TIC TESTING toa 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 4 NOISE ANALYSIS
ei. -l.o
6
<=
7?
(,
c,, FREQUENCY
(rody'ec)
o
-20 Ctl
o .|t trj a I (L
-40 ZERO POWER 7-sec PULSE , TEST NO. t r 7-sec PULSE , TEST NO. Z l 3.5-sec PULSE . TEST NO. 3 a 3.5-sec PULSE.TEST tiO. 4 o
-60 -80
o.or
o rr,r,
Fig.
7.
activity perturbation. The comparison of the experimental results with theoretical predictiops (see Fig. I of Ref. 1) appeals in Fig. LZ.
b. 235 ry FueI, Intermed.iate Issfs. Measurements were made again afier 1 year of power operation (2100 e q u i v a I e nt full-power hours). Pseudorandonl binary sequerlce inputs were trsed at porver levels of 1, 5 , and 7 MW. The opel)- loop rod positioning procedure was used. These tests shorved rlo significant changes in the dynarnic characteristics due to aging. ry I'rrcI , Fittal lesfs. A final set of rneasurements for the ?3su-fuelecl system were nracle after llrore than 9000 equivalent full-power hours of operation. Input steps, pseuclorurdorn binary
lt0
2s6
t.o
rod/secl
Frequency response at zera power; fuer static.
fuel salt in the external loop should be inctuded in the theoretical model. A measure of the adequacy of the theoretical model is its ability to predict the natural period of oscillation of the power response following a re-
c.
t
FREQUENCY (
sequences, and pseudorandotn ternary sequences were. used. The last attempts at open-loop rod positioning were made in some of ilre PRBS tests. This procedure worked occasionally, but it was not reliable. The fltx demand method was usecl for most of these tests to overcorne problerns encountered with th€ open-loop roC positioning method. Figure 13 shows results from flux clemand tests using one of the few satisfactory PRTS signals. These results show flrat there were llo aging effects which caused significant changes in the power hours of operation. 11 lluel , Irtitial Operation. plans were to use the flu:i demand technique in the clynamics tests for the 233U loacling, but this proce-
d.
233
made
dure pro\red unacceptable because of the problelns mentioned in Sec. fr.C.3. This led to the use of the closecl-loop rod positioning nreilrod, which proved to be satisfactory, and rvhich was used in all subsequent tests. Pseudoranclom binary s€quences and pseudorandorll temary sequences NUCLEAR TI'CIINOI,OCY VOL.
rO
FNBRUAITY 19?1
EXI;IIRIENCI]S WITTI DYNAM IC TESTTNC
Kerlin et al.
i-
lq.
cVa tl.o <=
z
a (,
o 127-?tT PRES -CPSD ANALYSlS c 1?7 -8]'T PRBS-CABS ANALYSIS A sil -81T PRES - CPS0 ANALY9:3 l 5II - BIT PRB S - CA 8S A NAL Y5I S v I
t0?
0.01
0.001
0.02
FREQUENCY 90
0.05
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IO
FEBRUAITY I9?I
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EXPERIENCI.]S WTTH DYNAMIC TESTING
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NUCLEAR TECIINOI,OGY VOL.
10 FEBRUARY
I9?T
KCTIin
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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 results shown in Fig . 14 arc in good agreement with theory and the scatter is small. The theory still shows too large a dip at A.24 rad/sâ&#x201A;Źc , indicating too little rnixing in the theoretical model. The PRTS results shown in Fig. 15 have the same general form a^s the PRBS results, but the scatter is excessive. This is apparently due to the probIems in determining the rod position accurately for the three-level signal (see Sec. If .C.3).
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IO
FEBRUAITY I9?I
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Kerlin et al.
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FEBITUANY T97T
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EXPERIENCTjS
wI'rH DYNAMIC
TESTING
u'ere used. Results are shorvn in Figs. 16 through 19. These results again clemonstrate ilrat there was no significant change in system dynamics due to agrng. In these tests, cornparisons were rnade of the different test signals, In general , the aclsantage of the IvIFBS was demonstrated. ir is not possibte to present the cletails of the comparison here (see Ref. ?), but some typicai results are shown in Table I. This table shows re sults f or a PRIIS test and an MFBS test. Each test ccnsisted of B cycles and each cycle was analyzeo separately to give an independent estimate of the frequency re.sponse. The lorver percent deviations for the MFBS tests are due to the higher signal-to-noise ratio at each measurement frequency, rvhich occur because the input signals concentrate the available energy in thes e frequencies. The prervhitening technique was of little benefit because the amplitude of the MSRE frequency response did not change very much over the frequency range of interest.
TABLE I Pereent Deviations in Measured Magnitude Ratios
Persent Deviationa Frequency (rad/,sec)
MFBS
PRBS
0.01 6 0.0 49
16.0
34.0 16.4
7.3
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5.8
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The main conclusion as far as the MSRE program is concerned is that the dynamic characteristics of the MSRE were found to be satisfactory and essentially as predicted, for both the 235U ancl the 233 U fuel loadings. Conclusions having to do with experiences ln performing dynamics tests on a system with no special provision for test equipment are:
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1. By proper matching of the testing method to the system characteristics and to the characteristics of normal system hardware, it was possible to-f
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19. hISRE frequency
response-MFBs with prewhitened output speetrllm. NUCLIIAII TECHNOI.,OGY VOL. 10
FEBRUARY 19?1
KETIin et
to rneasure the systern frequency response without the expense of installing an oscillator rod. 2. A thorough undcrstanding of the properties of test signals is a great help in selecting the optimum test signal for a particula.r application. Our experience suggests that the M fBS signal rnay have the widest general utilrty of the rnethods used in the MSRE tests. ACKNOS'I-EDGilIEIUIS
This research was sponsored by the U.S, Atomic Energy Commission under contract with the Union Carbide Corporation.
5, 1
aI.
EXPERIENCES WITII DYNAMIC TESTTNG
H. R. SIMPSON, Proc.IEE, 113, 12,2A75 (December
966).
6. A, Van Den BOS , "Construction of Binary Multifrequency Test Signals,t' IFAC Symlr. on ldentificati.on in 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 for Frequeney Response Testing,tt Doctoral Dissertation, University of Tennessee, Knoxville (1970). 8. S. J. BALL, "A Digital Filtering Technique for Bfficient Fourier Transform Calculations," USAEC Report ORNL-TM-1662, Oak Ridge National Laboratory (1e6 ?).
1. T. 'W, KERLIN, S. J. BALL, and R. C. STEFFY, 'oTheoretical Dynamics Analysis of the Mo1ten-Salt Reactor llxperiment," Nu.cI. Techrwl., 10, 118 (19?1), 2. P. A. N.
K. R.
GODFREY, and. P, H. HAMMOND, "Estimation of Proeess Dynamic CharacBRIGGS,
teristics by Correlation Methods Using Pseudo-Random Signals,tt IFAC Synzp. on ldentnfication in Automati.e
Control, Systems, June 72-17, 1967, Pragzter, Czechoslnuaki.a, Part II, pp. 3.1-3.L2, Academic, Prague (Jwre 1 96
7).
3. T. 'W. KERLIN, "The Pseudorandom Binary Signal for Frequency Response Testing," USAEC Report ORNLTM-1662, Oak Ridge National Laboratory (1966).
4. R. J.
HOOPER and E. P. GYFTOPOULOS, "On the
Measurernent
of Characteristic Iiernels of a Class of
Nonlinear Systerns," Proc. Symt. an Neutron (1
NUCLEAR TIiCFINOLOGY
967).
VOL. IO
USAEC Report ORNL-TM-L647, Oak Ridge National Laboratory (1966).
10. T. 'W. KERLIN and J. L. LUCruS, "CABS-A Fortran Computer Program for Calculating Correlation Functions, Power Spectra, and the Frequency Response USAEC Report ORNL-TM1663, Oak Ridge National Laboratory (1966).
from Experirnental Data,"
11. R. C. STEFFY, "Frequency
Response Testing of the Molten-Salt Reactor E>qperiment," Thesis, University of Tennessee, Nuclear: Engineering Department (Novernber 1969); and tISAEC Report ORNL-TM-2823, Oak Ridge National Laboratory (1970).
12. D. P, ROUX and D. N. FRY, Oak Ridge National Laboratory, Fersonal Communication.
Noi,se,
Waues and hr,Ise Propagation, Conf. 660206, IJ.S. Atomic
Enerry Commission
'W. KERLIN and S. J. BALL, "Experimental Dynamic Analysis of the Molten-Salt Reactor E>periment,"
9. T.
REFERE UCES
FNL\RUAITY 19?I
13. K. R. GODFREY and W. MURGATROYD, Proc. IEE,
tlz,
3, 565 (March 1965).
lr7