NAT_MSREdynamicsTesting.txt

 

7 s e
Aol

»

*

cluded measurvements using the

\»

EXPERIENCES WITH DYNAMIC TESTING

S‘/D filfin, L

 

METHODS AT THE MOLTEN-SALT

REACTOR EXPERIMENT

reachufy, fre~
quency, power, testing, per~
formance, signals, MSRE

KEYWORDS:

. W. KERLIN, S. J. BALL R. C. STEFFY, *andM R. BUCKNER**
Oak Ridge National Labowatm'y, Oak dede, Tennessee 37830

Keceived May 23, 1970 |
Revised September 14, 1970 -

 

A series of veactivity-to-power frequency re-

sponse measuremenis was made on the Molten-
Salt Reactor Experviment. This was done for P30
and #°U fuels, for a range of operating power
levels, at several points in the sysiem opervaling
history, and for several different test procedures.
A comparison of expevimental resulis with prior
theoretical predictions confirmed ithe validity of
the theoretical predictions. The test program in-
pseudorandom
binary sequence, pseudorandom ternary sequence,
n-sequence, and the multifrequency binary se-

 

I. INTRODUCTION

An extensive dynamics testing prograra was
carried out at the Molten-Salt Reactor Experiment
(MSRE)." The tests consisted of reactivity to
power f{rcquency response measurements. The
purpose of the test program was: T

1. to demonstrate the safety and operability of
the system

2. to check the validity of the theoretical anal-
ysis so that the safety of the plant could be

 

*Present address:
tanocga, Tennessee,

**University of Tennessee, Knoxville, Tennessee. Pres-
ent address: Savannah River Laboratory, Aiken, South
Carolina,

Tennessee Valley Authority, Chat-

NUCLEAR TECHNOLOGY =~ VOL. 10 FEBRUARY 1971

reassessed if necessary and so that con-
firmed methods could be established for
analyzing future, high- performance molten-
salt reactors

3. to evaluate techniques for performing dy-
namics experiments and methods of data
analysis.

Tests were performed at several different power
levels, al several different times in the system’s
operating history, and for the reactor fueled with
U and with ***U. Items 1 and 2 were the main
objectives of the test program, but this paper em-
phasizes item 3 since it should be of general in-
terest to those planning dynamics tests in other
systems. Those interested only in the perfor-
mance of the MSRE could skip Secs. II and III and
proceed directly to the results in Sec. IV.

Il. PLANNING THE TESTS
A. Objective

The primary test objective was to measure the
reactivity-to-power frequency response over the
range of frequencies where important system dy -
namic effects occurred. Inspection of the fre-
quency response predictions (see Figs. 8 and 14
of Ref. 1) indicated that measurements down to
~0.005 rad/sec at the low frequency end were
needed. It would have been desirable to carry the

-high frequency end of the measurements out to

about. 50 rad/sec if the zero-power reactor kinet-
ics effects were to be observed. If the interest
were in feedback effects, the upper frequency need
not have been greater than ~0.5 rad/sec. The ap-
proach used here was to determine the high fre-
quency (1.0 to 100.00 rad/sec) response by noise

103
 

 

 

Kerlin et al.

measurements during zero-powar operation. Sub-
sequent at-power measurements concentrated on
the 0.005- to 0.5-rad/sec range where feedback
effects were important.

B. Equipment Used in Experimenta! Measurements

The selection of the experimental methods for
the MSRE dynamics tests was based on the infor-
mation required and on the capabilities of the
available equipment. Fortunately, the emphasis
on low frequency results (0.005 to 0.5 rad/sec)
made it possible to obtain the important part of
the system frequency respouse using the standard
MSRE control rods to introduce the input reacti-
vity perturbations.

The MSRE has three identical control rods,
each with an active length of 59.4 in. One rod is
normally designated as the regulating rod and is
used for fine control. The other two rods are used
as shim rods for coarse adjustments. The rods
are actually flexible, stainless-steel hoses on
which are strung gadolinium oxide poison cylin-
ders. The rods are mounted in thimbles which
have two 30-deg offsetting bends so that the rods
can be centrally located even though there is no
room for the control-rod drive assemblies above
the central axis of the core. The maximum rod
speed is ~0.5 in./sec. Typical rod travel in the
experiments was ~0.5 in. for most of the 2%y
tests and 0.3 in. for most of the 2**U tests. This
gave a reactivity change of ~0.025% (7¢) in the
**U tests and ~0.02% (12¢) in the 2%V tests,

Figure 1 shows the control-rod and drive as -
sembly. The position indication for each rod was
obtained from a synchro geared to the rod drive
mechanism. A coarse synchro (5-deg rotation per
inch of rod travel) was used in early tests and a
fine synchro (60-deg rotation per inch of rod
travel) was used in later tests. The signal from
the position synchro was amplified and low-pass
filtered (1-sec time constant) to eliminate high
frequency noise and the accompanying aliasing ef-
fect prior to input into the Bunker Ramo computer,
BR-340, where the signal was digitized every 0.25
sec and recorded on magnetic tape.

The nuclear power level signal was furnished
by the output of a compensated ion chamber loca-
ted adjacent to the core. This signal was also
amplified, Jow-pass filtered (1-sec time constant),
digitized at 0.25-sec intervals, and recorded on
magnetic tape. | '

The BR-340 computer was also used in con-
junction with a portable analog computer for
generation of the input signal for the test. A com-
puter program was prepared for on-line genera-
tion of each test signal used in the tests (the
signals are described in Sec. II.C.2).

104

 

EXPERIENCES WITi{ DYNAMIC TESTING

C. Test Signals

1. Introduction. Test signal selection was influ-
enced by considerations of accuracy requirements,
frequency range over which information was
needed, and hardware capabilities. The following
input signals were used during the testing pro-
gram:

a. pulse

c

. step

. pseudorandom binary sequence

QL o

. pseudorandom ternary sequence

@

. n-sequence

bty
.

multifrequency binary sequence (flat input
spectrum) |

g. multifrequency binary sequence (prewhit-
ened output spectrum).

Pulse and step tests are easy to implement, but
these signals give results with limited accuracy.
This is because the signals are nonperiodic, and
therefore have a continuous frequency spectrum
and resulting low signal energy 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 because they are periodic, and therefore
concentrate the signal energy in discrete harmon-
ic frequencies. In all of the tests using periodic
signals, the period is determined by the lowest
desired frequency:

ro2
where
T ='period
w1 = lowest desired frequency.

For example, the required period for a test in
which the lowest required frequency is 0.01
rad/sec in 628 séc. All other harmonics would be
at integer multiples of 0.01 rad/sec. The accura-
cy of the results is improved by using input sig-
nals consisting of more than 1 cycle. In the MSRE
measurements 2 to 10 cycles were used,

2. Properties of mput Signals.

a. Pulse. The energy density e of a pulse of
duration T and amplitude A at frequency w is given
by:

‘e _A*T? [sin(wT/Z)] 2
2r L wT/2 |
FEBRUARY 1971

NUCLEAR TECHNOLOGY VOL. 10

 
 

'NUCLEAR TECHNOLOGY

Kerlin et al.

FXPERIENCES WITH DYNAMIC TESTING

REVERSIBLE DRIVE MCTOR

  
   
    

SOLENOID ACTUATED
RELEASE

GEAR AND ARM
' \, .
/ 4

 

 

 

A l
SWITCH i ]
DRIVE UNIT —// ‘
SPACER lg
{
LOWER LIMIT L?
SWITCH '-3

 

 

3~in. x 2~in. ECCENTRIC
REDUCER

GUIDE BARS, ——_]

4 AT 90°

BEADED POISON ELEMENTS—< |

2~in. CONTAINMENT THIMBLE —-

 
 
 
 

y | | ‘1 ("'

COOLANT TO DRIVE
ASSEMBLY

/'—“COOUNG

\O/ GAS INLET
L
\ //’

"
o~

COOLING GAS
CONTAINER

-~

 

——POSITION INDICATOR
SYNCHRO TRANSMITTER

FIXED DRIVE SUPPORT AND
3~ in. CONTAINMENT TUBE

COOLANT TO
POISON ELEMENTS

%in.0.D0.-304 S.S.- FLEXIBLE
HOSE CABLE

 

a0
~—— SPRING LOADED ANTIBACKLASH
HEAD AND IDLER GEAR

oi™

 

    
 

I6-in. RADIUS x 30° BEND

 

 

 

Fig. 1. Control-rod drive assembly,

This spectrum appears in Fig. 2. Note that the
amplitude is expressed as energy spectral density
(energy per unit frequency). | ' |

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 whose re-
sponse settles to some constant value after the

VOL. 10

FEBRUARY 1971

step input. This requires that the system’s zero-
frequency gain be a finite constant (including zero).
In principle, the step input contains an infinite
amount of energy, but this energy is concentrated
in the low frequencies where it is of little use.

¢. Pseudorandom Binary Sequence. The pseu~
dorandom binary sequence (PRBS) is often used

105

 

 

 

 
Lot o
Naatag

 

 

Kerlin et al.

0.1

w = FREQUENCY (rad/sec)
T = PULSE DURATION (sec

0.01

ENERGY PER UNIT FREQUENCY
AZ T2

 

 

0.00!

 

Q.4 | 10 100
DIMENSIONLESS FREQUENCY (w T)

Fig. 2. Energy spectrum of a square pulse.

for frequency response measurements and for ap-

proximate impulse response measurements. The
methods for generating the PRBS are well
known.”? These methods give periodic sequences
of +1’s and -1’s (each member of the sequence is
called a bit). The total number of bits in the se-
quence N must be 22 - 1 for any integer value of
Z. The period of the signal is given by the prod-
uct of the number of bits N and the bit time in-
terval At

The spectrum of the PRBS with pulse amplitude
A and total test duration T is given by:

 

 

2 . 2
py =2 WADET (G (g
2 |
A0=;1VzT for k=0, (1)

where A; = amplitude of the energy spectrum at
the A’th harmonic frequency. The spectra for
several sequences are shown in Fig. 3. Note that
the short sequences concentrate most of the signal
energy in the first few harmonics and the longer
sequences spread the signal power among more
harmonics. |

In planning a test, one must select the period to
give the required lowest frequency. The required
upper frequency fixes the sequence length N or
equivalently (since the period is fixed) the bit dur-
ation. The following relation specifies the har-
monic number at which the signal power is half as
large as the amplitude of the harmonic with the

106

EXPERIENCES WITH DYNAMIC TESTING

A Py Y A e L gratuam. e, oet ) - A
T Ay s R T R AT

'y 2 Y . e LUl S R SN s M.
e o T O v Tl O o iy R R R B AR
Ref T B NI TR e e s ST | PO L IO LR ]

L R S A  F o T T e A E N

-

greatest amplitude’ (thereby furnishing a measure
of the bandwidth of the signal):

kr =0.44N , (2)

where 2, =harmonic number of the harmonic with
half the power as the harmonic with the greatest
power, Thus, if the lowest frequency is ;
rad/sec, and the required highest frequency is wy,
rad/sec, then the number of bits is given by:

N =227 %L (3)
w1
The bit duration A is fixed by the highest fre-
quency of interest. The relation is

At = — | (4)

Of course, these are just rules of thumb. If the
total signal energy is too small, the signal energy
per harmonic may be too small even for the har-
monic with the largest amplitude. .

- d. Pseudovandom Tevnary Sequence. The pseu-
dorandom ternary sequence* (PRTS) is similar to
the PRBS, but three levels of the input signal are

 

1.0
DENOTES HARMONIC FREQUENCY
BASIS ~ SAME TOTAL DURATION
0.5 FOR ALL SIGNALS
0.2
0.1
.
w
O
2 005
4
o
s
g
Wi
9% 002
D
a
x .
—
LS 0.0t
o
ac.
2
w 0.005 -
-t
T 4
| '
1 °
0.002 .
o i
L] i
' o @
! y
0.001%

1 2 5 10 20 50 100
HARMONIC NUMBER

Fig. 3. Energy spectrum for several PRBS signals.

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

 
 

AMPLITUDE (NORMALIZED TO PRBS)

used (-1, 0, +1). The number of shifts in these-
quence is given by N = (37‘ - 1) for integer
values of 7.

The spectrum of the PRTS with pulse amplitude
A and total test duration I'is given by:

 

8 (N +1)A°%T [sin(kfr/N)]2 .
A = & : for % odd
3 2 kRu/N
A’ / (5)
Ay =0 for k& even.

This shows that the shape of the PRTS spectrum
is the same as for the PRBS. However, only the
odd harmonics are non-zero and they have an am-
plitude which is one-third larger than the corres-
ponding amplitude of a PRBS harmonic for a
sequence with the same value of N. Figure 4
shows a comparison of these signals. The proper-
ties given in-Egs. (2) through (4) for the PRBS also
apply for the PRTS.

- The PRTS is of interest because it has the ad-
vantage that it discriminates against nonlinear
effects. This may be advantageous because it
allows one to use large amplitude signals in fre-
quency response measurements. The PRTS has
the disadvantage that in the MSRE (and in many
other reactor systems) a three-level input is
harder to implement with system hardware than a
two-level signal.

e. n-Sequence. The n-sequence’ is obtained by
a simple modilication of the PRBS. The modifica-
tion consists of inverting every other bit in a
PRBS. Since the number of bits Nin a PRBS is

o

o

 

0.01
0.0t O.1 | 10

NORMALIZED HARMONIC NUMBER (k/N)

Fig. 4. Envelope of amplitude spectra for PRBS, PRTS,
and n-sequence, '

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING

always odd, the number of bits in an n-sequence
obtained by nicdification of an N-bit PRBS is 2N.

The spectrum of the n-sequence with N bits,
pulse amplitude A, and total test duration T is
given by: |

 

| A2 e (T \K:
4, = AN+ DA% [sm(k/r/N)J for b odd
N? kw/N 1 ©)
A =0 for & even.

Figure 4 shows a comparison of the spectrum for
the n-sequence and the PRBS and PRTS. Since the
shape of the amplitude spectrum is the same as
for the PRBS, the bandwidth relations [Egs. (2)
through (4)] still apply.

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

f. Multifrequency Binary Sequence (MIFBS)—
Flat Spectrum. In all frequency response mea-
surements, a major objective is to select input
signals with a large fraction of the total available
signal energy concentrated in the frequencies
selected for measurement. Generally, it is de-
sirable to space the harmonics evenly on a loga-
rithmic 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 Fig. 3). This
constitutes a waste of signal energy in identifying
nearby harmonics which are only slightly different
from one another.

An alternate procedure is to design a test sig-
nal which maximizes the {raction of the total
signal energy in harmonics selected by the ex-
perimenter. A signal of this type can be obtained
by a computer optimization of the polarities of the
pulses 'in a pulse chain of fixed length. The ob-
jective function, which is minimized in the opti-
mization, is the difference between the desired
spectrum and the spectrum obtained for a given
pulse chain. Experience shows that as much as 65
to 75% of the total signal power can be concen-
trated in selected harmonics.®”’ Furthermore, the
signal can be designed so as to discriminate
against nonlinear effects.

A typical signal used in the MSRE experiments
appears in Fig. 5.

g. Multifrequency Binary Sequence (MFBS)—
Prewhitened Spectrum. One of the main reasons
for interest in the PRBS, PRTS, and ii-sequence is
that the amplitude spectrum can be made quite flat
over a wide frequency range. This is important in
measurements with large noise contamination of
the input signal. The procedure for such a system
would be to use as much input signal energy as
possible (within limits set by system operating

107

 

 
T R AR it it 45N

S TR AT NSNS R TR W TN e

FRACTION OF TOTAL SIGNAL ENERGY -
: 5'
nN

- At o, — _ - ‘
B#gfl?maw&ys LR N e SRR O I PR 2 a7 o 3 AR e PPNy
L T G N R L s e N el R SR R ¥ S ;- T P G B LG S Ao L A N T A R R Er
: T N e O By i e e R Rogee ¥y B TS e T e S G IR AT i g ) e Rl M g Y g ¥, £
] U TR ;;1;"?5“, Y ST ¥ I T 4: ..; P Y L 3 ?;:}‘;;,‘, i P u :‘ " > 5 e

Kerlin et al.

 

M e M0k
L U0 UUJHU”U”UU e

 

 

 

 

 

 

 

 

 

 

“l Ate3 sec 7
(o) THE INPUT SIGNAL

io~!

 

NOTE. THE TWELVE
DESIRED

CONTAIN 753 %, OF
THE TOTAL SIGNAL

ENERGY

O DESIRED HARMONICS
D OTHER HARMONICS
BELOW SCALE

  

1073
10

 

0~} 10° 10!
FREQUENCY (rad/sec)
(b) ENERGY SPECTRUM

| Fig. 5. MFBS flat spectrum signal and its spectrum,

- conditions and nonlinear effects) and 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
contamination is in the output signal, the same
observations apply as were mentioned above in
connection with an input-noise problem. That is,
each output harmonic should contain the maximum
possible signal energy. Thus, for systems with

output noise problems (a common case) the output

amplitude spectrum should be flat. This can be
accomplished by using an input signal whose am-
plitude spectrum has a shape which is the recip-
rocal of the amplitude spectrum of the system
frequency 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 amplitude spectrum used
in the optimization has the shape of the recipro-
cal of the expected shape of the amplitude of the

- system {requency response. The amplitude spec-

trum of a typical input signal for a prewhitened
MFBS test is shown in Fig. 6.

3. Signal Input Procedures. Three different pro-
cedures were used in the tests. The changes were
required to overcome problems with the control
rods and with the system background flux noise.

108

 
   

EXPERIENCES WITH DYNAMIC TESTING

a. Open-Locp Rod Positioning. This procedure

was used in the early tests. The desired input

signal generated by the BR-340 computer was
used to actuate withdraw and insert signals to
the control-rod drive motor. The withdraw and
insert times were different because the coasting
characteristics of the rod were different for
withdrawals and insertions. The withdraw and

insert times were adjusted manually during the

beginning of the test to give the desired pulse
shapes. This procedure . worked well when the
control rods were new, but the wear associated
with long-term operation caused difficulty in
later tests.

b. Flux Demand. The flux demand procedure
was used to overcome the problems associated
with open-loop tests. The procedure was to feed
the test sequence in as a flux demand signal for
the flux-servo system. This caused the control
rods to move to satisfy the flux demand. In this
test, the spectrum of the flux signal had the ap-
proximate shape of the spectrum of the test se-

.quence. The amplitude of the spectrum of the

input was approximately the amplitude of the flux
signal divided by the amplitude of the system fre-
quency response at that frequency.

This procedure worked satisfactorily for the
final tests with the ?**U loading. The only condi-
tion was that the flux servo system had to be ad-

 

A

:

T 0N
AT Ooon

"‘"* Ot = 3 sec

(@) THE INPUT SIGNAL

 

 

 

 

 

 

 

 

 

 

NOTE: THE SIX DESIRED
HARMONICS CONTAIN 72 7%
OF THE TOTAL SIGNAL
ENERGY

FRACTION OF TOTAL SIGNAL ENERGY

O DESIRED HARMONICS
0 OTHER HARMONICS

BELOW SCALE

 

03" _
1002 2 5 107! 2 5 10°® 2 5 10!
FREQUENCY (rod/sec)

(6) ENERGY SPECTRUM

Fig. 6. MFBS prewhitened signal and its spectrum,

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

o=

 
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 preceded by a
change in the opposite direction, then each read-
ing 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 re-

liable rod position indications.

When the reactor operated with °°U fuel, a
change in system characteristics made the flux
demand procedure unacceptable. Shortly after
operation began with ***U fuel, the void fraction
in the fuel salt increased significantly with an ac-
companying increase in flux noise. This noise
component in the error signal in the servo caused
excessive rod motion. This was unacceptable be-
cause of the problem with erroneous rod position
signals.

- ¢. 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 replaced
by the rod position signal. Then, the error signal
which actuated the control-rod drive was the dif-
ference between actual and desired rod position
signal. This procedure was satisfactory in all
tests.

Hi. DATA ANALYSIS METHODS

Three different digital computer codes were
used in the data analysis. These are described
briefly below:

1. FOURCO.? This code computes the Fourier
transform of the output signal and the input sig-
nal, and computes their ratio to give the frequen-
cy response.

2. CPSD.? 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 band-
widths are determined by the duration of the data
record analyzed.

3. CABS.'® This code computes the autocorre-
lation 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, the output power spectrum,
and the cross power spectrum. The frequency
response is given by the ratio of the cross power
spectrum to the input power spectrum.

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING

IV. RESULTS

The large number of different tests (over 50)
makes it impossible to show all the results in
this paper. Instead, some typical results will be
shown, and 2 comparison with theoretical results
will be made. (The reader may consult Refs. 7, 9,
and 11 for more details on test results.)

Frequency Response Results

a. 250U Fuel, litial Operation. For these early
tests, the input consisted of a reactivity pulse, a
reactivity step, or a pseudorandom binary reac-
tivity input. The input procedure was the open-
loop rod positioning procedure, and all three data
analysis methods were used. Figure 7 shows the
zero-power frequency response for the **°U-fueled
reactor with fuel salt stationary. This figure also
shows the noise analysis results'? at high fre-
quency. The comparison of the magnitude with
calculations is quite good. The phase results are
less satisfactory. | |

. Figure 8 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 magni-
tude and phase. The differences between the
theoretical and experimental results for the absc-
lute 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. 8 and 14 of Ref. 1.) The autocor-
relation function of the rod position signal and the
cross-correlation function for the 2.5 MW test ap-
pear 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.'® These

blips were not observed during the first tests (be-

fore the power was increased to 2.5 MW), but they
have been observed intermittently in subsequent:
tests. They cause no problems in obtaining fre-
quency response results. They are included here
to illustrate an unexpected feature in the test re-
sults which were bothersome until the cause was
understood. : :

Figure 11 shows the results at 7.5 MW. From
this figure, it appears that the dip in the amplitude
at ~0.24 rad/sec in the predicted frequency re-
sponse is too large in the theoretical predictions.
Since this calculated dip was due to fuel recircu-
lation effects,’ it appears that more mixing of the

109

 
 

Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING

104

0.0t 01

 

ZERO FOWER

T-sec PULSE, TEST NC 1
7-sec PULSE, TEST NO 2
3.5-sec PULSE, TES™ NO 3
3 5-sec PULSE, TEST NO 4
NOISE ANALYSIS

10

w, FREQUENCY (rod /sec)

20

'
N
o

-40

PHASE (deg)

=100

0.001 0.0t

 

ZERO POWER

7-sec PULSE , TEST NO. |
7-sec PULSE , TEST NO. 2 A
3.5-sec PULSE ,TEST NO. 3 &
3.5-sec PULSE ,TEST KO. 4 ©

0.1

w, FREQUENCY (rad/sec)

Fig, 7.

fuel salt in the external loop should be included 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-
activity perturbation. The comparison of the
experimental results with theoretical predictions
(see Fig. 9 of Ref. 1) appears in Fig. 12.

b. ¥°U Fuel, Intermediate Tests. Measure-
ments were made again after 1 year of power
operation (2100 equivalent full-power hours).
Pseudorandom binary sequence inputs were used
at power levels of 1, 5, and 7 MW. The open-loop
rod positioning procedure was used. These tests
showed no significant changes in the dynamic
characteristics due to aging.

c. ¥5U Fuel, Final Tests. A final set of mea-
surements for the ***U-fueled system were made
after more than 9000 equivalent full-power hours
of operation. Input steps, pseudorandom binary

110

Frequency response at zero power; fuel static,

sequences, and pseudorandom ternary sequences
were used. The last attempts at open-loop rod
positioning were made in some of the PRBS tests.
This procedure worked occasionally, but it was
not reliable. The flux demand method was used
for most of these tests to overcome problems
encountered with the open-loop rod positioning
method. Figure 13 shows results from flux de-
mand tests using one of the few satisfactory PRTS
signals. These results show that there were no
aging effects which caused significant changes in
the power hours of operation.

d. 23U Fuel, Mitial Operation. Plans were
made to use the flux demand technique in the dy-
namics tests for the ?**U loading, but this proce-
dure proved unacceptable because of the problems
mentioned in Sec. II.C.3. This led to the use of
the closed-loop rod positioning method, which
proved to be satisfactory, and which was used in
all subsequent tests. Pseudorandom binary se-
quences and pseudorandom ternary sequences

NUCLEAR TECHNOLOGY

VOL. 10 FEBRUARY 1971

 

 
 

 

Kerlin et al. EXFERIENCES WITH DYNAMIC TESTING

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

\ |
T T 3
RN
. c/ofv iE\a f ;
— i,. ‘|
T o) b AR E e N
®| o PPl e o
c 1&g togO®
Tv .2
S o 4
= .4,,.0/ - X
T 5
O o /s v
. ° / )
g ,éwy..,.,POWER LEVEL -~ 2.5 MY
o STEP TEST o g ;
, I 127-BIT PRBS-CPSD ANALYSIS ®© LY i
. 127-BIT PRBS—CABS ANALYSIS & PRy
X 511-BIT PRBS-CPSD ANALYS!S A 1
511-BIT PRBS-CABS ANALYSIS ©
0.001 0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0
FREQUENCY (rod/sec) '
90
) POWER LEVEL — 2.5 mW
s STEP TEST o
70 127-BIT PRBS-CPSD ANALYSIS @
50 127-8IT PRBS-CABS ANALYSIS A
511-BIT PRBS-CPSD ANALYSIS A
50 511-8IT PRBS-CABS ANALYSIS V
40
S 30
LY
X 20
§ 10
r o — .
Q
-10 -THEORETICAL
-20 '
-30
-40
-50
-60
-70
0.001 0.002  0.005 0.01 0.02 005 01 2.2 0.5 1.0
FREQUENCY (rod/sec)
Fig. 8. Frequency response, power = 2,5 MW,
- i
s
=
D
> .
e
£ |
=
[
z .
Z
O
-
U
Z
5 |
% x
.'w
o
o
O
O
O 3
= »
D
< | X . .
o actouet e I R o
RIS PR SRR - WP
0 400

Fig. 9. Input

NUCLEAR TECHNOLOGY VOL. 10

800 1200 1600
CORRELATION TIME (sec)

autocorrelation function for a 511-bit PRBS test at 2.5 MW,

FEBRUARY 1971 ' » 111

 

NN RS PR R N
T e ST S R T A A T Ci s e

A
o
m&
 

E
l »  Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING
!

 

 

»

x X x X

 

xy X X
"

 

 

 

CROSS~-CORRELATION FUNCTION (Arbitrary Units)

 

 

 

 

 

 

 

 

 

 

 

 

0 400 800 ’ 1200 1600
CORRELATION TIME (sec)

Fig. 10. Cross-correlation function for a 511-bit PRBS test at 2.5 MW,

— T
Q

C o -

w| o vo %
= sy

L - 7.5 MW TRL

z STEP TEST o

o 127-BIT PRBS-CPSD ANALYSIS e

127-BIT PRBS-CABS ANALYSIS A
S11-BIT PRBS-CPSD ANALYSIS A
, S511-BIT PRBS-CABS ANALYSIS ¥
0002 0005 Q.01 002 005 o1 0.2 05 10
FREQUENCY (rad/sec)

 

80
70

60

40

PHASE (deg)

.30 |JPOWER LEVEL - 7.5 MW
STEP TEST |

-40 1427-BIT PRBS-CPSD ANALYSIS

_so | 127-BIT PRBS-CABS ANALYSIS
511-BIY PRBS-CPSD ANALYSIS

-60 } 511-BIT PRBS-CABS ANALYS!S

0.001  0.002 0.005 0.01 0.02 0.05 0.1 0.2 0.5 1.0

FREQUENCY (rod/sec)

 

Fig. 11, Frequency response, power = 7.5 MW,

112 A NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

   
 

Kerlin et al. FXPERIENCES WITH DYNAMIC TESTING

~were used. Typical results are shown in Figs. 14
soermenta|  and 15 for PRBS and PRTS tests. The PRBS re-
sults shown in Fig. 14 arc in good agreement with
theory and the scatter is small. The theory still
shows too large a dip at 0.24 rad/sec, indicating
too little mixing in the theoretical model. The
PRTS results shown in Fig. 15 have the same
general form as the PRBS results, but the scatter
is excessive. This is apparently due to the prob-
lems in determining the rod position accurately
for the three-level signal (see Sec. II.C.3).

PERIOD OF OSCILLATION (min)

 

e. ¥ Fuel, Final Tests. A final series of

2).02 005 Ot 02 05 1.0 20 50 100 :
POWER LEVEL (MW) | tests was run ~9 months later. For the final
tests, the PRBS, the n-sequence, the MFBS-flat
Fig. 12, MSRE natural periods of oscillation. spectrum, and the MFBS-prewhitened spectrum
10°

POWER LEVEL - 8 Mw

ANALYSIS METHOD
o CABS
5 ——THEORY

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

2
S
c Q
«i o
<
< 102
<
<
o
5
2
10!
140
/ Py °
- 60 - 2
o
3 ~d °l P
w .
N
v .\ o
q O
X \\\% o
* -20 e N\
oood’o % q\
OWM;O%°EM
-100
1073 2 5 1072 2 5 107! 2 5 100

FREQUENCY (rad/sec)

Fig. 13. Frequency-response results from a flux-demand test performed on the ?**U-fueled reactor using a PRTS
test pattern., ’ | -

VNUCLEAR TECHNOLOGY VOL. 16 FEBRUARY 1971 113

 

 

   
 

Kerlin et al.

EXPERIENCES WITH DYNAMIC TESTING

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

il -1 m
AT
= ' ANA
— » /4« LYSIS METHODS
£ 2 ./ o FOURCO, CABS,CPSD —
S P (EACH GAVE SAME RESULTS) 45
o '
1 - —HEQY = POWER LEVEL - 8MW
90 >
< ANALYSIS METHOD
A - © « CABS
| - THEORY
60 n\i‘“‘ 111
. ch . ’
T \é
13 :30 1 3
w @\
< s
R il
Rogrin N
D \N
B
-30 }— . -
H 3
L
1073 2 5 102 2 5 107t 2 5 100 9
I
a

FREQUENCY (rad/sec)

Fig. 14. Results from a 127-bit PRBS with the reactor
at 8 MW,

 

103

THEORETICAL

)

3n
nogp

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0% 2 5 102 2 5 10' 2 5 10°
FREQUENCY (rad/sec)

Fig. 15. Frequency-response results from a rod-
demand test using a 242-bit PRTS test pattern.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

— 102
Z
o 5
2
10!
10°3 2 5 1072 2 5 10t 2 5 100
FREQUENCY (rad/sec)
90
.\
60 \\\
30 \\
~ ° o\, THEORETICAL
g "N »
L O \>\ O O OQ‘\\
7] VO
;:I \\cl‘}é OO(ZDO\\\
a Ox]:b%%\\\
-30 \\
) - \\\
-60 ™S
N
-90
1072 2 5 10! 2 5 109 2 5 10!
- FREQUENCY (rad/sec)
Fig. 16. MSRE frequency response—PRBS signal,
114

 

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

N X
Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING ‘
’ {
90
\\ B
60 , \\ ,
» \\\
= N : THEORETICAL
8 ON (
= N |/
O 0
2 \od!o ococc\r\\
I %%NN
Q. '\
-30 * \,\
'\\
\'\
-60 ’ '\\
-90
1072 2 5 107! 2 5 109 2 5 10!
FREQUENCY (rod/sec) f
103
° |
!
2 %
t:f&)Q~ . §
S1°% THEORETICAL ,
C 2 L
— 10 :
z 3
S 0
@ S POWER LEVEL - 7 MW
5
2
10 —_— 2
10 2 5 102 2 5 10!t 2 5 100 | £l® THEORETICAL
c
FREQUENCY (rod/sec) - 107
Z
Fig, 17. MSRE frequency response—n-sequence. s 5
2
10!
103 -2 5 102 2 5 o' 2 5 10°
FREQUENCY (rad/sec)
%0
N\
O
30 \\
S ' N “THEORETICAL
@ o N
= SN 1/
w O o5
% K/ 0 oo:\NN
o ]
- N~
~
..60 \\
-90 1
10-2 2 5 107! 2 5 100 2 5 10

NUCLEAR TECHNOLOGY VOL. 10

FEBRUARY 1971

. FREQUENCY (rod/sec) o .

Fig. 18. MSRE frequency response—MJFBS with flat input spectrum.

115

 
Pt Tt T o L SR b 2L i

AENIE R - g L

Kerlin et al. EXPERIENCES WITH DYNAMIC TESTING

were used. Results are shown ir Figs. 16 through
19. These results again demonstrate that there
was no significant change in system dynamics due

to aging.

In these tests, compariscns were made of the
different test signals. In general, the advantage of
the MFBS was demonstrated. it is not possible to
present the details of the comparison here (see
Ref. T), but some typical results are shown in
Table I. This table shows results for a PRBS test
and an MFBS test. Each test censisted of 8 cycles
and each cycle was analyzed separately to give an
independent estimate of the frequency response.
The lower percent deviations for the MFBS tests
are due to the higher signal-to-noise ratio at each
measurement frequency, which occur because the
input signals concentrate the available energy in
these frequencies.

The prewhitening technique was of little benefit
because the amplitude of the MSRE frequency re-
sponse did not change very much over the fre-
quency range of interest. ’

0%

102 THEORETICAL

GAIN ([;;L'gfl)

 

10!
103 2 5 102 2 5 10V 2 5 10°

FREQUENCY (rod/sec)

 

 

 

TABLE I

Percent Deviations in Measured Magnitude Ratios
Percent Deviation?

Frequency (rad/sec) MFBS PRBS
0.016 16.0 34.0

0.049 7.3 16.4

0.082 4.1 7.3

0.12 ‘ 4.6 9.2

0.15 7.0 6.6

0.21 4.4 17.8

0.28 ° 3.9 16.6

0.35 4.0 9.5

0.41 3.9 9.8

0.48 3.6 5.1

0.54 1.8 7.9

0.61 3.3 5.8

 

 

 

 

 

“Based on 8 cycles of data. Both signals had same'am-
plitude and bit duration. The MFBS had 128 bits and the
PRBS had 127 bits.

V. CONCLUSIONS

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 satisfactory
and essentially as predicted, for both the ?**U and
the ***U fuel loadings.

Conclusions having to do with experiences in
performing dynamics tests on a system with no
special provision for test equipment are:

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

 

S0

T

oI\

 

60

 

N

\ /THEORETICAL
N

 

30

N

AN

/N

 

PHASE (deg)
o

G

o
/ ~
Y
NN

o

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

-90 . '
1072 2 5 10!

2

5 10° 2 5 10}

FREQUENCY (rod/sec)

.Fig. 19. MSRE {requency response—MFBS with prewhitened output spectrum.

116

 

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971
 

to measure the system frequency response without
the expense of installing an oscillator rod.

2. A thorough understanding of the properties
of test signals is a great help in selecting the
optimum test signal for a particular application.
Our experience suggests that the MI'BS signal
may have the widest general utility of the methods
used in the MSRE tests.

ACKNOVLEDGMENTS

This research was sponsored by the U.S, Atomic
Energy Commission under contract with the Union
Carbide Corporation,

REFERENCES

1. T. W, KERLIN, S. J. BALL, and R, C. STEFFY,
‘““Theoretical Dynamics Analysis of the Molten-Salt
Reactor Experiment,’”’ Nucl. Technol., 10, 118 (1971).

2. P. A. N. BRIGGS, K. R. GODFREY, and. P. H.
HAMMOND, ‘‘Estimation of Process Dynamic Charac-
teristics by Correlation Methods Using Pseudo-Random
Signals,”” IFAC Symp. on Identification in Automatic
Control Systems, June 12-17, 1967, Prague, Czechoslo-
vakia, Part II, pp. 3.1-3.12, Academic, Prague (June
1967).

3. T. W. KERLIN, ‘““The Pseudorandom Binary Signal
for Frequency Response Testing,”’ USAEC Report ORNL-
TM-1662, Oak Ridge National Laboratory (1966).

4, R. J. HOOPER and E., P. GYFTOPOULQS, ‘On the
Measurement of Characteristic Kernels of a Class of
Nonlinear Systems,’”’ Proc. Symp. on Neutron Noise,
Waves and Pulse Propagation, Conf, 660206, U.S. Atomic
Energy Commission (1967).

NUCLEAR TECHNOLOGY VOL. 10 FEBRUARY 1971

Kerlin et al.

EXPERIENCES WITH DYNAMIC TESTING

5. H. R. SIMPSON, Proc. IEE, 113, 12, 2075 (December
1966).

6. A. Van Den BOS, ‘“Construction of Binary Multi-
frequency Test Signals,”’ IFAC Symp. on Identification
in Automatic Control Systems, June 12-17, 1967, Prague,
Czechoslovakia, Part II, pp. 3.1-3.12, Academic, Prague
(June 1967),

7. M. R. BUCKNER, ‘‘Optimum Binary Signals for
Frequency Response Testing,”” Doctoral Dissertation,
University of Tennessee, Knoxville (1370),

8. S. J. BALL, ‘‘A Digital Filtering Technique for
Efficient Fourier Transform Calculations,”” USAEC Re-
port ORNL-TM-1662, Oak Ridge National Laboratory
(1967).

9. T. W. KERLIN and S. J. BALL, ‘‘Experimental Dy-
namic Analysis of the Molten-Salt Reactor Experiment,”’
USAEC Report ORNL-TM-1647, Oak Ridge National
Laboratory (1966).

10. T. W. KERLIN and J. L. LUCIUS, ‘““CABS—A For-
tran Computer Program for Calculating Correlation
Functions, Power Spectra, and the Frequency Response
from Experimental Data,”” USAEC Report ORNL-TM-
1663, Oak Ridge National Laboratory (1966).

11. R. C. STEFFY, ‘“Frequency Response Testing of the
Molten-Salt Reactor Experiment,”’ Thesis, University of
Tennessee, Nuclear Engineering Department (November
1969); and USAEC Report ORNL-TM-2823, Oak Ridge
National Laboratory (1970).

12, D. P. ROUX and D. N, FRY, Oak Ridge National
Laboratory, Personal Communication,

13. K. R. GODFREY and W. MURGATROYD, Proc. IEE,
112, 3, 565 (March 1965). |

117