—— — — — = — — — = = — e . ~ CENTRAL RESEARCH LIBRARY DOCUMENT GOLLEGTION [ 1 OAK RIDGE NATIONAL LABORATORY I o operated by (BN UNION CARBIDE CORPORATION m | NUCLEAR DIVISION for the U.S. ATOMIC ENERGY COMMISSION | ORNL- TM- 2823 " LIRART ! | /23 3 445k 0514033 5 | | | | 9 | 4 2 FREQUENCY-RESPONSE TESTING OF THE MOLTEN-SALT REACTOR EXPERIMENT (Thesis) R. C. Steffy, Jr. | | [ % Submitted to the Graduate Council of the University of Tennessee in partial fulfillment i for the degree of Master of Science. ORNL-TM-2823 Contract No. W-7405-eng-26 REACTOR DIVISION FREQUENCY-RESPONSE TESTING OF THE MOLTEN-SALT REACTOR EXPERIMENT R. C. Steffy, Jr. Submitted to the Graduate Council of the University of Tennessee in partial fulfillment for the degree of Master of Science. MARCH 1970 OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee operated by UNION CARBIDE CORPORATION for the U.S. ATOMIC ENERGY COMMISSION flO(.‘IKHliEDIMAHTN ENERGY RESEARCH LIBRARIES 3 44bE 0514033 5 H TABLE LIST OF TABLES + o &« & « & & LIST OF FIGURES . . . . . . ACKNOWLEDGEMENTS . . . . . ABSTRACT . . . . . . . « . . I. IT. ITT. V. INTRODUCTION . . . . . . SYSTEM DESCRIPTION . . . Physical Description. Theoretical Predictions EXPERIMENTAL PROCEIURE . Test Patterns . . . . iii OF CONIENTS * [} . . . » . - . a * Pseudorandom binary sequences. . . . . Pseudorandom ternary sequences . . . . . . Choice of Pseudorandom sequence . . . . Signal Generation . . Rod-jog tests . . Flux-demand tests. Rod-demand tests . Data Acquisition . . Data Analysis Methods Computing schemes Comparison of data EXPERIMENTAL RESULTS . . 235U Fuel Loading . Rod-jog tests . Flux-demand tests, £33 Fuel Loading . . Flux-demand tests, Rod-demand tests . LIST OF REFERENCES . . . . APPENDIX . * . * . . . . . . CONCLUSIONS AND RECOMMENDATIONS., o o o o o o o & viii ix 10 13 13 13 18 20 2l 25 26 30 32 3k 34 35 51 51 52 57 6 Qb 103 106 110 iv LIST OF TABLES TABLE PAGE I. Composition of MSRE Fuel Salt . . . . . v +v v v o v o v . L IT., DNeutronic Characteristics of MSRE with 23 and 235U Fuel Salt at 1200°F. & v v v v v e e e e e e e e e . 6 IIT. Results of Different Analysis Techniques at 0.016L49 rad/sec When Applied to Eight Periods of Data . . . . . . . . . Lo IV. Results of Different Analysis Techniques at 0.4gLTh rad/sec When Applied to Eight Periods of Data . , . . . . . . . L1 V. Results of Different Analysis Techniques at 0.989L47 rad/sec When Applied to Eight Periods of Data ., ., . . . . . . . L2 VI. Results of Analysis at a Harmonic Frequency (0,3298 rad/sec) kk VII. Results of Analysis at a Non-Harmonic Fregquency (O.3h63 rad/SeC). v v v w4 e e e e e e e e e e e e e e e e e L5 VIII. Pertinent Information Related to Each Test Performed for This Study . . o ¢ & v 0 v v i e e e e e e e e e e 111 LIST OF FIGURES FIGURE 1. Basic MSRE Flow Diagram . . + « & o o & o o o o o o o o o o 2. Electromechanical Diagram of MSRE Contrcl Rod Drive Train . 3. MSRE Control-Rod Drive Unit Power Transmission Diagram. . 4., Theoretical Frequency Response of Z>°U-Fueled MSRE for Several Power Levels . . 4 o o o o o o o o o o o o o o 5. Theoretical Frequency Response of £°-Fueled MSRE for Several Power Levels . .« ¢ & ¢ ¢ o o o o & o o o o s o 6. Example of a Pseudorandom binary sequence, {a) Time Behavior, (b) Autocorrelation Function, and (c¢) Power Spectrum. . . T. Example of a Pseudorandom Ternary Sequence, (a) Time Behavior, (b) Autocorrelation Function, and (c) Power SPecTrUmM & v v ¢ ¢ ¢ o o 4 o 4 o & o o s & s s s e o s 8. Range Over Which the Power Content of a PRBS or PRIS is Essentially Flat for Sequences of Various Length and Bit Times . & v 4 o & o o & o o o o o o o o o o o o o o o 9. Control-Rod Position and Flux for a Typical PRBS Rod-Jog Test, A Typical PRBS Flux-Demand Test and a Typical PRTS Flux- Demand Test . . . ... « o e s s s s 4 s o s s s e s s e e 10. Circuitry Used for Generating the Pseudorandom Signals for the Flux-Demand Tests . . . . + ¢« ¢ v ¢ v ¢ o o o o o« o & 11, Natural Filters for One-Period Analysis and for Eight- Period Analys is * . . . * . . . . * * » - * o . . . . * 2 PAGE 11 12 15 19 23 27 29 37 vi FIGURE PAGE 12, Shape of the Analysis Filter Employed by the CPSD Technique for Various Values of the Damping Factor, ¢ . . . . . . . L8 13. [Frequency-Response Results Obtained by Analyzing a Test Case Using the CPSD Analysis Scheme with Various Values of the Damping Factor, £ . « v v ¢ v v v v v v 0 0 o o v o v v Lg 14, Correlation Function and Power Spectrum Results from a Rod-Jog Test., . & v 4 4 & o v v v v 6 6 v v e o v e e e 53 15. Frequency-Response Results from Rod-Jog Tests . . . . . . . o7 16. Correlation Function and Power Spectrum Results from a Flux- Demand Test Using a PRBS Test Pattern . . . . . . . . . . 59 17. Frequency-Response Results from a Flux-Demand Test with the Reactor at 5 Mw with U-235 Fuel . . . . . . . . . . . . . 62 18. Frequency-Response Results from a Flux-Demand Test with the Reactor at 2 Mw with U-235 Fuel . . . . . . .« . . . . . . 66 19. Correlation Function and Power Spectrum Results from a Flux-Demand Test Using a PRTS Test Pattern . . . . . . . 67 20. Frequency-Response Results from a Flux-Demand Test Performed on the £®U-Fueled Reactor .Using a PRTS Test Pattern, . . 70 21, Correlation Function and Power Spectrum Results from a Flux- Demand Test Using a "Non-Symmetric!" PRTS Test Pattern . . 72 22, Frequency-Response Results from Flux-Demand Tests Performed on the £2°U-Fueled Reactor Using "Non-Symmetric'" PRTS Test Patterns . v v v v ¢ o o o o o « . c e e e e e e 5 vii FIGURE 23, Examples of the Uncontrolled Neutron Flux During Periods of 8 Mw Power Operation for the 23°U Fuel loading and the 233] Fuel T10adiNg o o o o o o o 0 0 . e s 4 e s 0 e e e s ol,, Frequency-Response Results from Flux-Demand Tests Using PRES Test Patterns Performed on the £>%-Fueled Reactor . 25, Frequency-Response Results from Flux-Demand Tests Using PRTS Test Patterns Performed on the £°AJ-Fueled Reactor . 26. Frequency-Response Results from Rod-Demand Tests Using PRBS Test Patterns Performed on the £>%U-Fueled Reactor. . . . 27. Frequency-Response Results from Two Periods of a Rod-Demand Test Using a 242 x L PRTS Test Pattern. . . . . . . . . . PAGE 78 79 86 95 100 viii ACKNOWLEDGEMENT The author wishes to thank Dr. T, W. Kerlin for his guidance in the direction, for his expert instruction in the theoretical phases of this study, and for his assistance in the data-interpretation, Mr, S. J. Ball was responsible for the design of much of the electronic circuitry used in the testing, was a helpful consultant for all prhases of the testing, and was very helpful when computer-related problems occurred. His assistance is gratefully acknowledged. The author wishes to acknowledge Mr. J. L, Lucius for his help with computer problems. The cooperation of the entire staff at the MSRE is appreciated, ix ABSTRACT Tests to determine the neutron flux-to-reactivity frequency response were performed on the Molten Salt Reactor Experiment with the reactor at various power levels between zero and full power and with the reactor fueled with a 22U fuel mixture and a 2337 fuel mixture, Test patterns employed were pseudorandom binary sequences (PRBS) and pseudorandom ter- nary sequences (PRTS) of various sequence lengths and minimum-pulse- duration times. 1In some tests reactivity (control-rod position) was forced to follow the test pattern, and in other tests the neutron flux was forced to follow the test pattern. The experimental results were analyzed by several different methods and the results were compared. The frequency response of the uncontrolled reactor system was found to be in good agreement with theoretical predictions for both the 2357 ana 233 fuel loadings. There were no indications of response characteristics that might cause control or safety problems. The power spectra for the various sequences were flat over the ex- pected ranges and variations in the sequence specification changed the power spectra in the expected manner with no anomalous changes. A diagram is presented which makes specification of the spectral characteristics for a particular sequence immediate. For the 75U fuel loading, results of the flux-controlled testing using PRBS's and PRIS's were adequate, but for the 7%y fuel loading, additional system noise coupled with equipment limitations caused ex- cessive scatter in the frequency-response results for both type sequences, For the ©°2U fueled system, a closed-loop method of positioning the control rod and use of a PRBS was necessary to obtain acceptable results. Use of a PRTS with this method of control-rod positioning caused intro- duction of errors in the indicated control-rod position rendering the test results unacceptable. Experimental data were purposely analyzed at non-harmonic frequencies showing that careful specification of the analysis frequency is necesgary for meaningful results, 1In data containing a large amount of noise, the results of analysis of the same data by the different techniques were found to contain anomalous differences, particularly at the first few har- monic frequencies, Analysis of the data by the different methods for low- noise tests gave results which were in excellent agreement. Keywords: frequency-response testing, MSRE, pseudorandom binary se- quences, pseudorandom ternary sequences, signal generation, Fourier analysis, 235y 23 ’ CHAPTER T INTRODUCTION The dynamic response of a nuclear reactor may be characterized by several methods.l* One of the more useful methods is the determination of the power-to-reactivity frequency response of the uncontrolled reactor. Mathematical models are usually formulated which predict the frequency response before the reactor is in operation., These same models are frequently used in application of.stability criteria, such as the Tamiliar Nyquist stability criterion® or determination of the eigen- values of the system matrix. 2,3 Stability criteria can seldom be "measured" so the adequacy of the mathematical models must be determined by some other means. Determination of the adequacy of a model is important since it is entirely possible that analysis of a mathematical model will show a reactor to be stable yet the mathematical model may be incapable of accurately describing the actual response of the system. One method by which the adequacy of a model may be determined is to compare the theoretical frequency response with the experimentally de- termined frequency response. Perhaps more important is that, regardless of the agreement between the predicted and observed response, once the *Superscript numbers refer to similarly numbered references in the IList of References. experimental frequency response is determined the dynamic response char- acteristics of the actual system are known and this is the information of primary interest, The frequency response of the €357J-fueled Molten-Salt Reactor Experi- ment (MSRE) was predicted by Ball and Kerlin® and the results of the initial, experimental, frequency-response tests were reported by the same authors.® The purpose of the work reported herein was to continue the experimental tests throughout reactor operation with €357 ag the fissile material and then to continue the testing program throughout reactor operation with £33 as the fissile material. Variations were made in testing signals and testing techniques and the effects of these variations on the experimentally determined frequency response were noted. CHAPTER IT SYSTEM DESCRIPTION I. PHYSTICAL DESCRIPTION The MSRE is a liquid-fueled, graphite-moderated, thermal reactor. The ligquid fuel is composed of the fluorides of uranium, zirconium, lithium, and beryllium in the proportions shown in Table I. The liquid in the secondary loop is composed entirely of LiF (70 mole percent) and BeFo. At full power, the reactor produces about 8 Mw of power which is dissipated to the atmosphere by an air-cooled radiator through which about 2 x 10° cfm of air is forced. Figure 1 shows the basic flow diagram for the MSRE, The basic differences between the dynamic behavior of the MSRE and most other #%U-fueled reactors arise due to the circulating fuel. The most apparent effect of the fuel circulation is the birth of delayed neu- trons in the external loop; indeed, the fuel circulation lowered the effective fraction of delayed neutrons born in the core from .0067 to .00kL for the U-235 fuel loading and from .0026 to .0017 for the U-233 fuel loading.® It requires about 17 sec for fuel leaving the core region to reenter the core, and at higher powers the effects of fuel salt reentering the core with a temperature which is representative of the power level 17 sec earlier also has a pronounced effect on the dynamic behavior of the neutron flux., Table IT lists certain important facts about the neutronics of the MSRE, particularly those which affect the dy = namic response of the reactor. TABLE T COMPOSTTION OF MSRE FUEL SALT 2357 Fuel Loading £33] Fuel Loadingb (Mole %) (Mole %) LiF 65 6L.5 BeF o 29.1 30.2 ZrF 5 5.2 UF, 0.9 0.1k ISOTOPIC URANTUM CONCENTRATIONS (Atom %) (Atom %) 2337 0 8h.7 234y 0.3 6.9 235U 35 2.5 2363 0.3 0.1 2387 6L, b 5.8 a. Molten-Salt Reactor Program Semiannual Progress Report, July 31, 1964, USAEC Report ORNL-3708, Oak Ridge National Laboratory, p. 231, (November 1964). b. Molten-Salt Reactor Program Semiannual Progress Report, February 28, 1969, USAEC Report ORNL-4396, Oak Ridge National Laboratory, p. 130, ' Il REACTOR || VESSEL FUEL . PUMP 0 || o0 HEAT EXCHANGER ¢ (o = X1 o =\ [1100°F OVERFLOW TANK FREEZE FLANGE | 1 F=-T\ 1175°F 1200 gpm REACTOR CELL ——— — — == === | oraIN T 1| '|TANK | CELL FREEZE L I 1 VALVE | I [ [ ! | ] | | | | I SPARE FILL AND FLUSH FILL AND DRAIN TANK TANK DRAIN TANK (73 cu ft) (73 cu ft) (73 cu tt) FIGURE 1. — . I [l 1025°F ORNL-LR-DWG. 56870R{ 850 gpm T 5 I =) AlR 200,000 cfm 100°F Basic MSRE flow diagram, RADIATOR COOLANT COOLANT PUMP COOLANTIl CELL I I I I I I [ I I I I 300°F ORAIN TANK (449 cu ft) TABLE IT NEUTRONIC CHARACTERISTICS OF MSRE WITH 73U and 75U FUEL SALT at 1200°F £33 Fuel 2357 Fuel Minimum Critical Uranium Loadinga . b Concentration (g U/liter salg) 15.82 33.06d Total Uranium Inventory (kg) 32.8 207.5 Prompt Neutron Generation Time (sec) L.o x 107% 2.4 x 107 Reactivity Coefficients® Fuel Salt Temperature (°F)~1 -6.13 x 107° k.1 x 10°° Graphite Temperature [(°F)~1] -3.23 x 1073 -L.0 x 10°° Total Temperature [(°F)~1] -9.36 x 107° -8.1 x 107> Fuel Salt Density +. 4L 0.182 Graphite Density +.54hLY 0.767 Uranium Concentration +.389 0.234 Effective Delayed Neutron Fractions Fuel Stationary 2.64 x 10773 6.66 x 1073 Fuel Circulating 1.71 x 1072 L.k x 1073 Reactivity Change Due to Fuel Circulation (% 3k/k) -.093 -0.222 “Fuel not circulating, control rods withdrawn to upper limits. b 2357 only. “Rased on 73.2 ft° of fuel salt at 1200°F, in circulating system and drain tanks. dBased on a final enrichment of 33% #7°U, e e eas V) . . At initial critical concentration. Where units are shown, coefficients for variable x are of the form &k/kdx; otherwise, coef- ficients are of the form xak/ksx. inghly enriched in the fissionable isotope (91.5% 23U or 93% =7°U). Source: Haubenreich, P. N. et al,, "MSRE Design and Operations Report, Part V-A, Safety Analysis of Operation with 237U, " USAEC Report ORNL-TM- 2111, Oak Ridge National Iaboratory, p. 41, (February 1968). Since the reactivity perturbations for the experimental tests re- ported herein were introduced by control rod movement, a brief description of the control mechanism will be given, The reactor is controlled by three control rods which are positioned in thimbles near the vertical centerline of the core and are inserted into or withdrawn from the core as demanded. Normal rod movement (as opposed to a rod scram) is achieved by activating a single-phase reversible-drive motor. This, in turn, drives a chain which is attached to a flexible cable that is threaded with beads of the poison, gadolinium oxide. The cable maneuvers around two 30° bends in the thimble before reaching the core centerline position. The three control rods are essentially identical in every respect; however, during operation, bne of the rods is positioned farther into the core and is used as a regulating rod., It was through movement of this rod that reactivity perturbations for the dynamics tests were introduced, A schematic diagram of the control-rod drive train is shown in Figure 2, and a detailed schematic of the drive unit assembly is shown in Figure 3. These are shown in detalil in order to give the reader a feel for the complexity of the control rod assembly so that the problems encountered in trying to determine the exact position of the lower end of the control rod might be better appreciated. A complete description of the MSRE physical plant is given in Reference 7, and a description of the instrumentation is given in Reference 8. ORNL-OWG 63 -8334R INPUT TO SIZE 18 SYNCHRQ CONTROL TRANSFORMER, PART OF TORQUE AMPLIFYING ROD POSITION TRANS- — MITTER IN SHIM REGULATING ROD LIMIT SWITCH ASSEMBLY INPUT SIGNAL TO Q-2360 TORQUE AMPLIFIED ROD POSITION POTEN- TIOMETER DRIVES IN LOGGER- COMPUTER ROOM a— FINE TO POSITION READOUTS SYNCRO NO.2 IN CONTROL ROOM | — cOARSE 60° PER INCH OF ROD MOTION POSITION POTENTIOMETER ROO POSITION INPUT TO SAFETY SYSTEM b TO SAFETY B SYSTEM REDUCTION GEARING e FAN SYNCHRO NO.1 MOTOR 5% PER INCH OF ROD MOTION _ TACH SERVD MOTOR DRIVE ELECTROMECHANICAL SPROCKET (m] CLUTCH ,E REDUCTION \EOUAL RPM o SPROCKET GEARING [ . 1-TO-¢ GEARS CHAIN INCLUDES _f 1t REVERSE LOCKING AIR FLOW OVERRUNNIN £ ¢ TO COOL ROD CLUTCH FLEXIBLE TUBULAR ROD SUPPORT-/ v=0.35in/sec I T X% POISON ELEMENTS THIMBLE — HORIZONTAL GRAPHITE BARS — GRID PLATE CORE VESSEL—™ FIGURE 2. Electromechanical diagram of MSRE control rcd drive train. RATIOS: POT. ROTATION _ 5° ORNL-DWG 66-39154a FINE SYNCHRO ROTATION _ 60° ROD TRAVEL ~ in. COARSE_SYNCHRO ROTATION __ 5° 52T, 32op ROD TRAVEL in, , POTENTIOMETER 30T, 320P /c\ SINGLE TURN ROD TRAVEL — in. 52T, 32DP (/ " 1000 7 T P @ " " °T 320 @a COARSE" SYNCHRO 26T, 320P 02 A ‘ SIZE 31 26T, 320P &7 Ysi¥<= <57 390p 78T, 32DP “3\‘ , 32D TS Q‘ SPROCKET, 64T PITCH "FINE" SYNCHRO CIRCUMFERENCE SIZE 18 4.00 INCHES — : ELECTROMAGNETIC SPROCKET CHAIN proocET , CLUTCH, 32 v dc 3~ in. /, 0.24 omp, ELECTROID CO. 26T, 320P C NO. 2EC-26CC-8-8 / 54T, 24DP 54T, 24DP OVERRUNNING CLUTCH FORMSPRAG TYPE FS/05 WORM, 24DP, SINGLE THREAD WORM WHEEL 52T, 24DP u 54T, 24DP 41T, 24DP ' 40T, 24DP 14T, 24DP 14T, 240P SERVO MOTOR, 115 v, 25 2¢ — - DIEHL cO. MoToR | S0 ¢PS» 25w, 2¢ BASIC ASSEMBLY NO. FPF 49-91-1 ac TACHOMETER BLOWER 24T, 2LDP means 24 teeth on diametral pitch of 2k. FIGURE 3. MSRE control-rod drive unit power transmission diagram. 10 IT. THEORETICAL PREDICTIONS OF FREQUENCY RESPONSE The mathematical model® which was used to predict the frequency response of the 235J-fueled MSRE divided the reactor core into 18 fuel lumps and 9 graphite lumps. The external loop (coolant system and heat exchanger included) was also modeled using a lumped parameter model. Results of the initial dynamics tests® were in excellent agreement with the predictions, so the same basic model was used to predict the response of the 23j-fueled system,-> Figures 4 and 5 show the theoretical neutron level-to-reactivity frequency responses for the two fuels. In general, the theoretical curves will also be shown with the experimental data and are shown here for comparison purposes. For the higher power levels, an outstanding feature of these plots is the dip in the magnitude-ratio curves at about 0.2k rad/sec and on ’ No-8k ’ the associated "bumps'" in the phase angle. The frequency at which these occur corresponds to the time required for the fuel to circulate completely around the primary loop (25 sec) and is caused by the return to the core region of fuel which has temperature representative of the power level 25 sec earlier. With the £7°U fuel, the dips in the magnitude-ratio curves were relatively small and were not verified in the initial testing program,® but for the #37U fuel, the predicted dips were larger and it was hoped that these could be verified. For a given fuel loading, the mag- nitude of the dip is a function of the salt mixing> that occurs during the circulation around the primary system. More mixing causes a less pronounced dip. 11 ORNL-DWG 69-12243 ZERO POWER T g I 104 + 30 5 Mw P AN \ N M % — PHASE (deq) O \ -30 T " %E ";;fiLN\ | -60 / ZERO POWER -90 E 1073 1072 107! 109 101 FREQUENCY (rad /sec) FIGURE 4, Theoretical frequency response of 275U-fueled MSRE for several power levels. 12 4 ORNL-DWG 69-12244 ZERQO POWER 3n - éo N N 30 \\ 'g' \SiMw :\ g N\ Ll 0 gt) 1Mv‘v\ \ \\ I N U a N ™ N By -30 \‘--r, P X 1T N -60 — ZERO POWER 5 N AT T -390 3 -2 - 0 { 10 2 5 10 2 5 10 2 5 10 2 5 {0 FREQUENCY (rad/sec) FIGURE 5, Theoretical frequency response of 2337-fueled MSRE for several power levels,. 13 CHAPTER ITI EXPERIMENTAL PROCEDURE In all experimental frequency-response tests which utilize a de- terministic inputrsignal, the same general procedure must be followed: (1) the pattern of the input signal which is to be used must be determined, (2) the input signal must be imposed upon the system, (3) the values of the input signal and the resulting output must be determined and recorded, and (4) the record signals must be analyzed, While there is great variety as to how each of these steps may be performed, they must each be per- formed before an experimental frequency-response determination can be made, In this section, the method by which we satisfied each of these require- ments will be discussed. TI. TEST PATTERNS The basic test patterns which were used in the experimental determi- nation of the frequency response of the MSRE were the bseudorandom binary sequence (PRBS) and the pseudorandom ternary sequence (PRTS). Pseudorandom Binary Seguences!© * Certain periodic, binary (two-level) sequences of square-wave pulses (bits) are known to have the following important mathematical properties: * The two levels which a PRBS assumes are O and +1 during the genera- tion stages, particularly if the shift register technique mentioned later 1s used., However, the values a PRBS assumes in practice are +1 and -1. 14 (1) The autocorrelation function of the sequence has a spike at lag time equal zero and an identical spike at lag times of nT (n is an integer and T is the period length). The value of the auto correlation function is slightly less than zero between the spikes. (2) The power spectrum of the sequence is flat over a wide frequency range. The particular frequency range over which the spectrum is flat depends on the particular sequence and the pulse width, An example of a PRBS, its autocorrelation function, and power spectrum are shown in Figure 6. The analytical expression for the autocorrelation function of a PRBS is: Z + 1 Cir(t) = 1 - (57, 0=t =T/7; Cii(7) = - 1/z, T/z; Z T Cll(T) = l:_[l"T'f‘l-Z, T‘ZSTST * In generating the ternary signal the levels normally used are 0,1,2, but in actual application the levels used are 0,1,-1. Note that the levels 0,1,2 correspond to 0,1,-1, not to =1,0,+1 as is sometimes quoted in the literature.®® Effects of this difference are shown in Sect. 1 of Chap Iv. 19 ORNL-DWG €69-9523R 0 2 4 6 8 10 12 14 TIME INCREMENT ‘ T ‘—-T/Z-_—’4 0 - 1 c =3 - o = 0 o o (&) | O 2 4 6 8 10 12 14 CORRELATION TIME 1.0r—* ] ° 0.5 () * 0 2 4 © 8 10 12 14 FREQUENCY (harmonic number) FIGURE 7. Example of a pseudorandom ternary sequence, (a) time behavior, (b) autocorrelation function, and (c) power spectrum. 20 where the symbols have the same meaning as before. Note that the auto- correlation function is normalized to equal 1 at 1t = Q. The amplitudes of the power spectrum at the harmonic frequencies are given by A(k) = o for k = 0 or even and cin _}Efll o 8(Zz + 1 Z Alk) = _L‘j;-l' — for k = odd. z Knt 3 Z A PRTS has an average value of zero while the average value of a PRBS is non-zero (but is small). For zero-power reactors or for systems in which variable drift is a problem, the zero average value of a PRTS may be a distinct advantage, particularly for short seguence tests in which the deviation of the average value of the PRBS is farther from zero. Another advantage of the PRTS is that it discriminatesZ0 against system nonlinearities and therefore gives a better estimate of the "linearized" system response, This should be particularly useful for testing systems which are strongly nonlinear. The primary disadvantage of the PRTS is the three levels. In practice it is often considerably more difficult to achieve three levels with available system hardware than it is two. More information about the properties of pseudorandom ternary se- quences may be found in References 11, 1k, 19, 20, 21, and 22. Choice of Pseudorandom Sequence The anticipated response of the system under investigation usually dictates the desired frequency spectrum of the input signal. One usually 21 desires to have a spectrum with sufficient signal power over the range where the system has a resonance peak or other interesting characteristic. For a periodic signal, the lowest freguency containing information is, of course, the fundamental frequency, fo = 2£/T , (1) where fo 1 fundamental frequency (rad/sec), and T period length, sec. For a pseudorandom binary or ternary sequence, a 'rule of thumb"” for the highest frequency at which one should plan to obtain useful information is the harmonic frequency at which the signal power is equal to one-half the power in the fundamental harmonic. This is not a physical limitation, but serves as a guide in planning tests. The actual physical high- frequency limit for obtaining realistic results 1s based on the noise level in the system and data-sampling rate. Tt can be shownl® that the harmonic with about one-half the ampli- tude of the fundamental harmonic is given approximately by the relation, k, = 0.4z, where n harmonic number of the harmonic with one-half the amplitude of the fundamental, and i 1 Z, number of bits in the sequence. Tt follows that and H i 0.447 2x/T (3) 22 Rearranging this expression yields .88 T/Z = T (4) but T/Z is just the duration of one bit so . . . . 88n basic bit duration = T/7 = T (5) This implies that specification of = high-frequency limit also specifies the basic bit duration. Note that the upper frequency limit is indepen- dent of all other properties of the sequence. With these basic relations, the graph shown in Figure 8 can be con- structed. This graph presents all of the information one needs to deter- mine the properties of the sequence he must use to obtain information from a single test which will cover the frequency range of interest. The funda- mental frequency line is a plot of the relation given in (1). The half-power frequency lines which are parallel to the fundamental frequency line were calculated from equation (3). The basic bit duration lines were determined from equation (5). Use of this graph is perhaps best illustrated using an example. Sup- pose one had a system for which he desired to know the frequency response in the fregquency range between 0.0l and 0.5 rad/sec. From the graph we see that the period required to give a fundamental frequency of 0.01 rad/sec is about 630 sec. So that the signal power at the higher fre- quencies is not less than half the signal power at the lower frequencies, a bit time of about 5 seconds or less is necessary. The only remaining para- meter to specify is the sequence length, A 127-bit PRBS would fit nicely with the hypothesized conditions to give results over the required fre- quency range. With the specified bit time, shorter sequences would 23 ORNL-DWG 69-9524R2 POSSIBLE PRBS OR PRTS m-SEQUENCES BASIC BIT DURATION (sec) ~ & -9 PO & FY 10 5 2 1 05 0201005 109 HALF-POWER FREQUENCY LINES —~ PERIOD (sec) 102 FUNDAMENTAL — FREQUENCY —*" 101 103 102 101 100 To} 102 FREQUENCY (rad/sec) FIQURE 8. Range over which the power content of a PRBS or PRIS is essentially flat for sequences of various length and bit times. 2l increase the fundamental frequency, but shifting to longer sequences would lower the fundamental frequency and probably be acceptable to the experimentor, It is apparent from this example that there is g spectrum of accept- able sequences, bit times, and /or period lengths available for each par- ticular application. It is this variety which emphasizes the utility of a diagram such as that in Figure 8., The effect on the other parameters caused by changing one item in a test specification may be directly ob- served. This diagram was found to be very useful in planning the dynamic tests reported herein, IT. SIGNAL GENERATION There are two stages in imposing the desired signal on a system. First, the signal itself must be generated in some manner and then the system hardware must be forced to follow the signal. Since a Bunker-Ramo- 340 digital computer was a part of the equipment at the MSRE site, it pre- sented the opportunity for generating either a PRBS or PRTS using the shift register technique. A machine language program was written by S. J. Ball of the Instrumentation and Controls Division at Oak Ridge National ILaboratory that allowed the use of a variety of different se- quence lengths for both the PRBS and PRTS. The consequence of this pro- gram was the opening and closing of relays in the BR-340. By applying the appropriate voltages across these relays and summing them,a pseudo- random signal could be generated easily, 25 There were three distinctly different methods used for getting the generated sequence into the reactor system. The methods for implementing these signals will be presented in this section with brief discussion of the advantages and/or disadvantages of each, but most of the discussion will be deferred to the results section (Chapter IV). Rod-Jog Tests The rod-jog method was used extensively during the early testing program by Kerlin and Ball.® The BR-340 was used to generate the desired sequences and integrator and comparator circuits on an Electronic Associates, Inc., Model TR-10, analogue computer were used to determine "on" times for the control rod drive motor. When switching from a positive to a negative position in the sequence, the rod was required to insert for x sec., where the time, x, was adjustable. The inverse jump in a sequence instigated a withdraw of y sec., where y was adjustable and separate from x. Since there was no automatic feedback from the rod position, the rod-jog tech- nique was an open-loop procedure. Details of the rod-jog method are given in the report by Kerlin and Ball,® The rod-jog technigue worked when the control-rod system was new and tight. However, as the system aged, frequent adjustments became neces- sary on the timing circuits to keep the rods jogging at the same average position without drifting. This method was attempted several times near the end of operation with the ®7°U-fuel and, with one exception, produced unacceptable rod positions. 26 Flux-Demand Tests Since the rod-jog method was not able to provide accurate and repro- ducible rod bositions, it was necessary to either change the testing method or discontinue the testing program. This led to development of the flux-demand technique, At low powers (<1 Mw) the servo system in the MSRE compares the neu- tron flux as indicated by the compensated ion chambers with g manually- demanded flux and moves the control rod as necessary to meet the demand, At powers greater than 1 Mw, the neutron flux is compared with a "computed" flux-demand and the servo again moves the rod to meet the demand. (The computed flux-demand is based on temperature drop across the core, neu- tron flux, and core-outlet temperature.) Since the servo moved the con- trol rod to match the actual flux with the demand, the flux could be forced to simulate any reasonable test pattern by putting in a false flux-demand at low-power levels or a false computed flux-demand at high powers., This was the reverse of the normal brocedure in that the predeter- mined signal shape was imposed on the output and the input (rod position) became the dependent variable, Figure 9 shows control rod position and flux plotted as a function of time for representative rod-jog and flux- demand tests. In the rod-jog example, the rod position resembles the shape of an ideal PRBS and the flux is determined by the system characte- ristics; whereas, the plots of the flux-demand tes+t show that flux follows the test pattern and the rod is the free agent. The two levels of the PRBS flux-demand are apparent and may be compared with the three levels of the PRTS flux-demand signal, 27 ORNL-DWG 68-9668 T o ST ROD POSITtON ALY ) UL e atv M v “H\_ 7 \-' "' % _-" 5 '.“ % ; \ 4 S . Y ow ] s " s ‘\u‘ N AL A AL St NS "‘-:." s st Noazants FLUX \/\ PRBS ROD - JOG 1 | | I T I - ROD POSITION = l‘ ~\ AOA A i i A -fv'\. N f » . \' . '.' . - \‘“‘ : vy, s ; . -A-r-ru-._‘ « ‘ 1 ~ . .. o - L p L : . voA . j A . s, * e K % o < - v’ . v L W . Yo X 0 E Z > )_ x g FLUX [, - o, M ™, : - @ P .'/\'. :,\'- ;f 3 ./\', ) ;s i . o s s * ;- .’ S : < : " S . : . < |y s o5y v : I Doy : WS viOA S Y\ f VoG N _ \/ N/ OV \J o —~ PRBS FLUX- DEMAND | | | I T [ ROD POSITION ~ ~ . o Y % In >N & TN ~, :’5 “" '\_\)""3 “1. g "'9' v"f ™. Voo o ! '\ f%) . Lo s y . . & " . - 3 N < w 7 v @ff\gw 2 , J ;‘; "\: - FLUX :’\/\. : " ! \J .’ L PRTS FLUX - DEMAND Lo Lo 1 | ey o 0 0.5 1.0 1.5 : 2.0 TIME (min) FIGURE 9, Control-rod position and flux for a typical PRBS rod-jog test, a typical PRBS flux-demand test and a typical PRTS flux- demand test,. 28 For the flux-demand technique, the pseudorandom signals were generated with the circuits shown in Figure 10, Reference voltages from the TR-10 were fed to the BR-3L0-operated relays. The relays were off-on type so they either fed the reference voltage or zero voltage back to the TR-10. For the PRBS, 1f the relay were closed the up part of the sequence was created, Opening the relay formed the down part of the sequence. For the PRTS, two relays were operated with the following results: relay No. 1 and No.2 open created the down pulse, No, 1 open and No. 2 closed formed the middle position, and No. 1 closed and No. 2 open caused the up part of the sequence. Both relays closed was not allowed. Attenuator No. 9 reduced the signal to the voltage which was needed for the particular test. At the start of a test, attenuator No. 9 was normally set at zero and then increased slowly until the desired signal magnitude was achieved. Normally the flux was allowed to deviate from steady state by 5 to 10%. Attenuator No. 11 was adjusted so that the output of the second amplifier corresponded to the steady-state flux with the pseudorandom sequence imposed on 1t, This voltage was inserted into the servo circuits at the indicated point in Figure 10c. The flux-demand method offered distinct advantages over the rod-jog technigue. During testing, adjustments of the times which the rod with- drew and inserted were not necessary and there were no problems with sys- tem drift since the servo automatically maintained the actual flux approxi- mately equal to the demanded flux. The basic disadvantage of this tech- nique was that it worked the control rods rather vigorously, especially after the more responsive £ fuel was added to the system. While exer- cising the control rods 1s not in itself particularly undesirable, design 29 ORNL~-DWG 69— 9525 PRBS SIGNAL GENERATOR ———— e 0 TO -10v F.5, (a) TO SERVO CIRCUITS PRTS SIGNAL GENERATOR | ] -5 5 | . “:\\\\47 0 TO —10y F.S. —_ (2) | I | SERVO | I 10 l CIRCUITS _____ 1 -10 | BR-340 | | LRz _SSs.Bws _ SIMPLIF{ED SERVO CIRCUITRY SERVO oM ‘0 100k AMPLIFIER L A 1[\ A 92.5 aROVE ¢ W L~ W +6v OPERATES CIRCUITRY o : v R-237 * i R-252 RODS FLUX (c) CLAMPS (-0.33 T0 6v) REF. ORNL DWG FROM 30k RC 13-12-53 ION & YW CHAMBER R-250 y OPERATIONAL AMPLIFIER __.l :>_ X = GAIN —MA— RESISTOR —o— SWITCH Y= IDENTIFICATION NUMBER ——{::}a AT TENUATOR 1l gerav Y = IDENTIFICATION NUMBER T FIGURE 10. Circuitry used for generating the pseudorandom signals for the flux-demand tests. 30 of the rods in the MSRE provided loose coupling between the actual and indicated rod positions and every rod movement carried with it the in- herent probability of an erroneous indication, The problems encountered while using the flux-demand technigue were primarily a result of hardware limitations in the MSRE and do not repre- sent an inherent flaw in the technique; however, excessive noise contami- nation in the frequency range near a resonance peak can cause erratic results when the flux is being controlled to give a flat power spectrum. This will be discussed in Chapter IV in relation to some of the experi- mental results. When using this technique, the experimental testing was less laborious for the experimentors and equipment set-up time was less than when testing with the other methods. For zero-power reactors or for reactors in which power drift tends to be a problem, this technique would appear to be particularly advantageous. Since the flux is the con- trolled parameter, it cannot drift and if the system is at steady state initially, pseudorandom perturbations of the flux about the steady-state value will not cause an Imbalance between power and flux, Rod-Demand Tests The disadvantages of the flux-demand tests caused a final change in technique back to rod-controlled testing. However, instead of controlling the rod position indirectly by adjusting the time the drive motor remained activated, the technique was changed to directly control the rod position. This was achieved by comparing the actual rod position with a demanded position and keeping the drive motor activated until the desired position was realized. Since there was feedback from the rod position, this was a 31 closed loop system, The result of this technique was to yield rod po- sitions which were like those obtained from an ideal rod-jog test and to circumvent the problem of excessive rod motion that was present with the flux-demand technigue, Since the control-rod servo 1s really a comparator circuit, it was well suited for comparing actual rod position with demanded position, and 1t was already wired to move the control rods if the input voltages (normally flux and flux-demand) were unbalanced. Tt was necessary to disconnect the normal inputs to the servo system and to replace them with actual and demanded rod positions. The circuits for generating the pseudorandom perturbations were basically the same as those used with the flux-demand technique (Fig. 10). The ion-chamber connection in Figure 10c was replaced with a signal deter- mined by the actual rod position and attenuator 11 in Figure 10a or Figure 10b was adjusted so that the output of the servo amplifier was approximately zero before starting a test, One operational problem related to the rod-demand technique should be pointed out. The rod was moved when the actual rod position was out- side the deadband around the demanded position. When the demand shifted at the start of a new pulse, the rod moved until the voltages were again matched, at which time the rod would start coasting to a stop. The servo circuits could be adjusted to start the stopping process so that the road did not coast through the deadband and instigate an adjustment in the opposite direction. When a PRBS test signal was being employed, the po- sition at which the rod stopped within the deadband was not important, 32 hence the adjustments were simple., (The important point was that the rod did stop within the deadband and at the same position each time.) However, the three levels of a PRTS signal caused this adjustment to become more involved. The middle position of the PRTS might occur after a pulse with plus or minus polarity. If the rod tended to coast nearly through the deadband before actually stopping, then the middle position of the PRTS was satisfied by two different actual rod positions. The only adjustment which resulted in a unique value for the middle position was a setting which caused the rod to stop midway of the deadband. There were also slight differences in the upper and lower positions depending on whether the rod had started from the middle position or the extremity position. For the MSRE, the rod-demand technique meshed with equipment limi- tations in such a way that it was the most effective method for frequency- response testing. ITI. DATA ACQUISITION For all of the tests the reactivity perturbations were initiated by control rod movement. As described earlier, contrcl rod movement 1s con- trolled by a drive motor, and a series of gears connects the rod drive to the position synchros. These indicators feed a voltage to the position indicators in the control room snd to the on-line BR-3L0 digital computer. For the dynamics tests, the signal gcing to the BR-340 was intercepted and fed into an analog computer (TR-10) where the signal was amplified by a factor of ~ 10 and low-pass filtered using a filter with a l-sec time constant, This amplified and filtered signal was then 33 fed back into the BR-340 where it was digitized every 0.25 sec and re- corded on magnetic tape. This frequency of digitization made possible the storing of useful information which had frequency components as high as ~ 12 rad/sec; however, most of the test patterns we employed had little signal power above 1 rad/sec, A filter with a l-sec time constant was used to attenuate high-frequency information and prevent aliasing effects, The nuclear power was determined by recording the signal supplied by a compensated ion chamber, The primary purpose of this chamber was to feed the linear-power recorders which are located in the main control room. This signal was also fed into the TR-10 and amplified (by ~ 10) and filtered using a l-sec time constant. The signal was then fed to the BR-340 where it was digitized and recorded every 0.25 sec, along with the rod position. The rod position and flux signals were not digitized si- multaneously. There was actually about 0.08-sec difference between the digitizations. This causes the calculated phase angle to be in error by 0.5° at 0.1 rad/sec and 5.0° at 1,0 rad/sec. This error was not recog- nized until after most of the results had already been obtained and since this was not a significant error in the frequency range of interest, the calculations were not repeated, In order to be compatible with the analysis programs, the data were retrieved from the magnetic tapes and stored on punched cards., 3k TV. DATA ANALYSIS METHODS The purpose of the dynamics tests was the determination of the power-to-reactivity frequency response. After the data from a par- ticular test was reduced to a stack of IBM cards, there were three methods for gleaning the desired information. Computing Schemes FOURCO. The most direct and fastest method for determining the frequency response was to immediately Fourier transform the digitized data and then divide the transformed output (flux) by the transformed input (rod position) for the desired result. This was accomplished using a computer code called FOURCO23 which uses a digital simulation of an 24 Analysis of 8 cycles of analog method reported by Broome and Cooper. a 127-bit PRBS with a 3-sec bit time (12,192 input and output data points) required only 1.1 min on the IBM 360/75 for calculation of the frequency response at 60 different frequencies. CPSD. This analysis method utilized a digital simulation of an ana- log filtering technique for obtaining cross-power spectral density, CPSD, functions.®s®> This code calculated the power spectrum of the input sig- nal and the cross-power spectrum of the input and output signals and di- vided the cross-power spectrum by the input power spectrum toc obtain the frequency response at each frequency of analysis, The key feature of this ccde is an adjustable filter width about the analysis frequency. Analysis time for 8 cycles of a 127-bit PRBS with a 3-sec bit time on the IBM 360/75 was 2.0 min for analysis at 60 frequencies, 35 CABS.®® The third calculational procedure was more involved., The autocorrelation functions of the input and output signals were calculated and the cross-correlation ffinction of the signals was calculated. These were then Fourier transformed to obtain the input, output, and cross- power spectra. The input power spectfum was then divided into the cross- power spectrum to obtain the frequency response. The correlation functions, power spectra and frequency response were then machine plotted. Calculation time using CABS for the previously mentioned case was 10 minutes, Comparison of Data Analysis Methods CARS and FOURCO. If an experimental test is composed of several consecutive periods of the same sequence, there are several cholces available for analyzing the data. One method is to evaluate a single Fourier integral of all the data. Alternatively, the data may be split into segments (each consisting of one or more periods of data) and a Fourier integral for each segment can be determined, and the resulting estimates can be averaged. The basic difference between analyzing one period of data at a time or several periods of data as one period is to change the effective filter, or spectral-window, width. I a Fourier analysis is performed at frequency «,, where ay is a harmonic frequency, the magnitude of the harmonic will actually be composed of all the signal strength under the filter area. The "natural filter,™ H(w,), 1s®’ H(w,) = Si%mgmi &)m%me ’ 36 where Tm = the time duration of the data being analyzed, n W frequency (rad/sec), and frequency of analysis, Wi This function has a maximum value when @ equals w,; and has null points where (w; - ) Tm equals an even multiple of . Suppose Tm is equal to one period, T, of a periodic signal then every second null point occurs on an adjacent harmonic; however, if eight cycles of data were analyzed, there would be 16 null points between the harmonic frequencies (see Figure 11)., For an ideal periodic signal either filter would be suitable since there would be spectral power at only the harmonic frequencies. However, actual signals are not ideal and there is always random noise contamination at every frequency; furthermore, if the harmonic frequencies are not specified very precisely, contamination resulting from the side lobes and the adjacent harmonics not intersecting at a null point may be significant. Using the "eight-period" filter tends to discriminate against noise contamination except very close to the actual harmonic frequency but causes large errors if the frequency at which the analysis is beling performed is not the actual harmonic frequency. ©Note that performing an analysis at a frequency which is midway between adjacent harmonics would not allow any of the signal strength of the periodic signal to enter into the result since the filter would null at every harmonic frequency; hence, analysis at these frequencies apparently provides a means of calculating the system noise level which was present during the testing. However, for this type analysis to be valid, 1t is necessary that the frequencies which are midway between the true harmonics of the minimum period length actually be harmonic frequencies also. For example, if only one period 37 ORNL— DWG 6911726 EIGHT-PERIOD FILTER 08 ! ‘ TYPICAL SPECTRAL ' ONE-PERIOD FILTER POWER FROM IDEAL PERIODIC SIGNAL\ 0.6 Vv 04 0.2 FILTER MAGNITUDE -0.2 N N -04 ' 3n 2m _r T ar 3w W= T W T W= T wj Wty Wty wtT FIGURE 11. Natural filters for one-period analysis and for eight- period analysis. 38 of data is available, analysis at mid-harmonic frequencies is not mean- ingful; however, if two periods of data are analyzed, the frequencies mid- way between the adjacent power-containing harmonics are harmonics of the total period and analysis at these frequencies is allowed. For the direct Fourier analysis method (FOURCO), application of the preceding argument is straight-forward, but for the CABS program it is more complex, With the CABS program, it is normal to work with at least two cycles of data, since correlation functions are usually calculated for lag times as long as one period. Calculation of the correlation functions immediately reduces the data to one period length (fixing the filter shape) which is then Fourier analyzed. Using more periods of data in the correlation function determination improves the statistics of the correlation function. The alternate method of using fewer periods in the correlation function analysis yields worse statistics for the correlation function but more power spectrum results at the same frequency, which may then be ensemble averaged. The choice is whether to ensemble average before or after Fourier transforming. Mathematically, at least for ideal signals, the end result 1is the same. Since the correlation functions are informative in themselves, the usual method is to reduce the data to correlation functions of one-period length before Fourier analyzing. To determine the effect of varying the periods of data which were analyzed, eight periods of a 127-bit PRBS with a 3-sec bit time (this will be written as 127 x 3 in the remainder of this text) were analyzed several different ways, All eight periods were analyzed as one period — giving a very narrow filter — then four periods were analyzed as one 39 period and the two answers averaged. This was repeated using two periods and one period of data at a time, The results are shown in Tables III, TV, and V for different analysis frequencies, For the calculations in which the data were separated into smaller segments, there is significant scattef in the data; however, the averages agree fairly well with CABS appearing to exhibit a slight trend upward in magnitude ratioc as the data are more finely divided, With FOURCO, the final averaged result does not appear to be significantly affected by per- forming the analyses on one period at a time even though the individual results for the analysis which used one period at a time are very erratic, particularly at the lower frequencies. The coherence-function values listed in Tables IIT, IV, and V for the CABS analysis are a measure of the degree to which an output of a system is related to a certain input. Mathematically the coherence * function is defined®® by the relation, 2 L) - 2 c, (1) &, (F) where y = the coherence function, G. (f) = the Fourier transform of the cross-correlation function * at frequency f, Gx(f) = the spectral power of the input signal (rod position in this text) at frequency f, and Gy(f) = the spectral power of the output signal (flux) at frequency f. ¥ Tn this text, only the positive root of y© is considered to have physical meaning, Lo TABLE IIT RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.016L491 RAD/SEC WHEN APPLIED TO EIGHT PERIODS OF DATA No. of Periods Analyzed As One CARS FOURCO Phase Phase M.R." (Deg.) cor’ M.R.” (Deg,) 8 356 69 .95 360 70 L 373 63 .96 37k 6L 327 (L .98 322 8 Avg.© 365 67 .97 363 71 Std. Dev.d 11 6 L1h 16 10 2 430 Lg .91 361 69 435 50 1.00 393 kg 361 61 .99 395 T2 28l 67 .88 310 11 Avg. 378 60 .9l 365 69 Std. Dev. 71 6 .06 Lo 8 1 530 o9 235 99 Lol 52 333 69 336 80 451 77 312 66 319 _86 Avg. 372 7h Std. Dev. 98 15 “Magnitude Ratio bCoherence Function C Average dStandard Deviation RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.4947L4 RAD/SEC WHEN APPLIED TO EIGHT PERIODS OF DATA 41 TABLE IV No. of Periods Analyzed : As One CABS FOURCO g Phase o Phase M.R. (Deg.) Coh. M.R. (Deg.) 8 671 -26 1.00 670 -26 b 69k -28 1.02 667 -27 ‘ 663 -2l 1.01 672 -2k Avg.© 679 -25 1.02 670 -26 Std, Dev. 22 5 .01 L 2 2 650 -27 1.01 Lhop -22 775 -29 1.01 ThT -31 585 -21 1.02 600 -23 120 -30 £.00 T45 -2k Avg. 690 -27 1.01 671 -25 Std. Dev. 88 L .01 87 L 1 6hs -9 574 =37 768 ~28 729 -35 575 -20 62k ~25 748 -2 43 =27 Avg. 676 -25 Std. Dev. 80 9 Magnitude Ratio bCoherence Function CAverage dStandard Deviation Lo TABLE V RESULTS OF DIFFERENT ANALYSIS TECHNIQUES AT 0.98947 RAD/SEC WHEN APPLIED TO EIGHT PERIODS OF DATA No. of Periods Analyzed As One CARBS FOURCO o Phase b a Phase M.R. (Deg.) Coh. M.R. (Deg.) 8 509 -L6 1.02 536 -L6 L 511 -43 .99 512 -L45 51b -29 97 549 =48 Avg.© 513 -47 .98 531 -47 Std. Dev.d 2 5 .01 26 2 D 510 -46 .93 539 -h3 533 -43 1.04 L85 =47 Lo -63 .97 513 -48 52k =60 95 582 -L8 Avg. 510 -53 97 530 -Lt Std. Dev, 27 10 .0L b1 2 ] 580 -hp 500 -43 500 -48 470 -L7 L87 -Iis5 548 -51 566 -4k 603 -52 Avg. 532 -L7 Std. Dev. Lg n "Magnitude Ratio bCoherence Function CAverage dStandard Deviation L3 For a causal system in which there is only one input and one ouput and no noise contamination, the measured coherence function should be unity. For real systems in which ideal conditions do not exist, the co- herence function should be between 0 and 1. If two totally unrelated signals were analyzed, the coherence ffinction would be zero. Some of the experimentally-determined values for the coherence function shown in Tables III, IV, and V are slightly greater than 1.0. This is theoretically impossible and the reason for these values being greater than 1,0 is not understood. The CPSD code, which also calculated coherence functions, also occasionally gave results which were slightly greater than unity. These anomalously high values did not destroy the general usefulness of the coherence function calculations which were, in general, lower for tests in which the results contained excessive scatter (indicating noise contamination) than for the smoother results. Analyses at non-harmonic frequencies yielded coherence functions which were erratic and often had values as large as 500. In an effort to demonstrate the effect of the analysis filter, the same data were also analyzed by FOURCO at frequencies which were offset from the harmonic frequencies by 10% of the difference between harmonics. Table VI lists both the real and imaginary parts of the input and output signals for a harmonic frequency and Table VII lists the same information for the nearest adjacent non-harmonic frequency. The analyses were per- formed with 1, 2, 4, and 8 periods of data as one with the appropriate results averaged, as before. For the analysis at a harmonic frequency, the average value of both the real and imaginary parts of the signals Ll TABLE VT RESULTS OF ANALYSIS AT A HARMONIC FREQUENCY (0.3298 RAD /SEC) Periods of Data Analyzed Input Signal Output Signal As One Real Imaginary Resl Imaginary 8 -177 388 -193 I L - 87 192 -107 25 - 86 198 - 84 20 Avg.D - 87 195 - 95 23 Std. Dev.b 1 L 16 3 2 - L 96 - 56 11 - 43 96 - 52 15 - kg 100 - Lk 6 - L1 100 - 4o 1L Avg. - 43 o8 - 48 11 Std. Dev, 2 2 T L 1 - 20 L9 - 28 5 - 22 L8 - 27 6 - 20 L9 - 29 3 - 21 L - 23 13 - 27 51 - 17 1 - 21 48 - 28 Y - 20 50 - 19 1 - 19 _20 - 21 _2 Avg - 21 Lo - 24 5 Std. Dev. 3 1 5 L aAverage bStandard Deviation TABLE VII RESULTS OF ANALYSIS AT A NON-HARMONIC FREQUENCY (0.3463 RAD/SEC) Periods of Data Analyzed Input Signal Qutput Signal As One Real Imaginary Real Imaginary 8 87 - 31 2kl 35 4 91 120 - 26 7L 3& 117 - 16 60 Aveg.? 93 119 - 21 67 Std. Dev.b 3 2 7 10 2 3 93 - L2 30 L 92 - 37 30 5 9> - 31 2l I 92 - 29 25 Avg. 5 93 - 35 27 Std. Dev. 2 2 6 3 1 -12 L - 26 9 -1k 46 - 2l 9 -12 L7 - 27 7 -13 L6 - 20 13 ~13 Lg - 1k -5 -13 L3 - 29 10 -12 L8 - 17 10 -1 b7 -1 2 Avg, -13 L7 - 21 T Std. Dev. 1 1 7 6 aAverage bStandard Deviation L6 approximately doubles* each time the number of periods being analyzed as one doubles. This indicates that most of the calculated signal energy was resulting from a source which was unaffected by the changing filter shape. Of course, this source was the spectral energy of the signal at the analysis (harmonic) frequency. For the analysis at a non-harmonic frequency, there is no apparent relation between the average values of the signals as the number of periods being analyzed is changed. This should be expected since the changing filter shape is weighting the sig- nal energy in the nearby harmonic, as well as those farther away, in an entirely different manner with each filter change. CPSD. The advantage of the CPSD technique is that the filter shape may be specified at the time the analysis is performed, The filter specified by the code has the transfer functionl® H(s) = 0302 -+ E;Ujos + 52 * The doubling occurs because the integral being used to calculate the signal energy is: T F(jo) = [ £(t) e 0% at ~0 where H: Eamme ot S } the time signal, frequency (rad/sec), = \/_l) time, and the total time of the recorded data. ] H &+ £ 1 The integral is not normalized by 1/T; therefore, for data sets containing the same power at frequency w, the calculated F(jw) will be twice as large if the number of sets analyzed is doubled. L7 where wo = the center frequency of the filter, s = the Laplace transform variable, and L = the damping factor. Figure 12 shows H(s) for various values of t. As g takes on smaller values, the peak in the transfer function becomes very narrow, If{ is set too wide, the contribution from other frequencies becomes significant, but if § is set too narrow, a slight discrepancy between the harmonic frequency and the calculational frequency will cause a large error in the calculation of the signal magnitude at the harmonic. The complete fre- guency response plot for the test case (8 periods, 127 x 3 PRBS) is shown in Figure 13 for various values of §. When { is equal to 0.5, the data is smoothed to the extent that it does not portray the actual frequency- response shape in the regions of sharp curvature. Damping factors of 0.05 and 0.001 give essentially the same shape; however, there is more scatter in the data with the 0.001 damping factor. Comparison of the CPSD method with a damping factor of 0.05 with the CABS and FOURCO results revealed that the results were usually within 5% of each other with occasional deviations of 10%. There were a few tests in which there was large discrepancy between the analysis techniques at a few frequencies., Since these appear to be a function of the testing technique, they will be discussed in the appropriate section (Chapter 1v, Section II), Unless otherwise specified the data reported herein used the fol- lowing analysis criteria: L8 > ORNL-DWG 69-11727 FILTER MAGNITUDE 90 ———]EHEL 3 ORNL —NWG 69— 12248 0.060 2 s nam 0.046 1 ’ s 0.032 F 0.018 # . 0.004 AUTOCORRELATION FUNCTION (arbitrary units) | ; | -0.010 b 0 140 280 420 560 700 ' CORRELATION TIME {sec) POWER SPECTRUM (arbitrary units) FREQUENCY (rad /sec) (a) Autocorrelation function and power spectrum of the control-rod position. Periods of data analyzed — L Type sequence — 127 x 5 PRBS FIGURE 14 Correlation function and power spectrum results from a rod-jog test, 54 ORNL-DWG 69-12054 2.0 1.4 +— —4 i — — 0.8 - + : — e - e 0.2 \ ‘ _ | L 1 AUTOCORRELATION FUNCTION ( arbitrary units) s | | 04 L 1 | | _ _10 —— e ok —— A ; 0 140 280 420 560 700 CORRELATION TIME (sec) FPOWER SPECTRUM (arbitrary units) 1072 2 5 10™ 2 5 10° FREQUENCY {rad/sec) (b) Autocorrelation function and power spectrum of the neutron flux. Periods of data analyzed — 4 Type sequence — 127 x 5 PRBS FICURE 14. (continued) 55 ORNL-DWG €9—12053 0.30 0.22 T 044 [- e = 0.06 -0.02 \ e, CROSS~- CORRELATION FUNCTION (arbitrary units) 0 140 280 420 560 700 CORRELATION TIME (sec) CROSS—-POWER SPECTRUM (arbitrary units) 2 5 1072 2 5 10~ FREQUENLCY (rad/sec) (c) Cross-correlation function and cross-power spectrum of the control- rod position and neutron flux. Periods of data analyzed — L Type Sequence = 127 x 5 PRBS FIGURE 1L, (continued) 56 Figure lhkc. Since the reactivity input was a PRBS (flat power spectrum), the envelope of the points in the first part of the cross-correlation function approximately defines the impulse response of the system,®® The results of primary interest, magnitude ratio and phase, are shown in Figure 15. Over most of the frequency range there is 1little scatter in the data and the experimentally determined points follow the theoretical curves very well., The scatter in the magnitude ratic at frequencies greater than 0.6 rad/sec is due to the low power content of the input signal in this frequency range (Figure lha). The low magnitude of the power in the input signal causes a low signal to noise ratio and a large amount of scatter in the results. In addition, the timing method used with the rod-jog technique did not produce the exact period lengths which were desired. This made specification of the fundamental frequency tedious, and for a four-cycle test an average period length was used, This inac- curacy may decrease the signal to noilse ratio even more because the fre- guencies at which the analyses are performed may not be the exact harmonic frequencies, Also shown in Figure 15 are results of a similar test which was per- formed during the initial testing program of the MSRE. There 1is very little difference between the results which leads to the conclusion that the dynamic characteristics of the MSRE were not changed by about 9000 equivalent-full-power hours of nuclear operation, 2. Flux-Demand Tests Ten dynamics tests utilizing the flux-demand technique were per- formed with the #7°U fuel loading., Two of these ten yielded completely 27 ORNL-DOWG 69-12256 103 b ] < 0 ®lo * POWER LEVEL-8Mw 2 o TEST PERFORMED DURING EARLY POWER OPERATION, CPSD ANALYSIS, DATA FROM REFERENCE {6 e TEST PERFORMED NEAR END OF OPERATION WITH U-235 FUEL, CABS ANALYSIS 102 100 60 1 | o] | N | 4 ! . ! < <0 J' Y T P [ l 3 | ; | s S = E -20 “ s \ L/_.._\ l - i 1 9 . n\j 1 * 4 ! j I -0‘3."&19-.‘&---."'- ll Jo > ‘ ; LT iy B Poomio ol o | B O s o | L - — f e N -100 | il . 10~2 2 5 Tom 2 5 10 FREQUENCY (rad/sec) Periods of data analyzed — L Type sequences — 127 x 5 PRBS FIGURE 15. Frequency-response results from rod-jog tests,. 58 unusable results due to a faulty magnetic-tape unit which was supposedly recording the data. In fact, the computer was malfunctioning throughout this entire phase of the testing program and there were numerous bad data points dispersed randomly throughout the data. In general, these bad points were easy to distinguish in that they read either very large or very small in comparison with the bulk of the data, A computer program was written which scanned the data and discarded these points which were obviously in error and replaced the bad points with points derived from a linear interpolation between the two nearest good points. Three test patterns were employed during this phase of the testing program. These were the PRBS, PRTS, and the "non-symmetric" PRTS. The difference between the PRTS signals will be discussed in the appropriate section. In this section, we will find that the flux-demand tests were un- suitable for the required measurements, Nevertheless, the experience with these tests is described to illustrate the problems and to show the considerations which led to the third (and successful) technique described in Section 3 of this chapter. PRBS Test Patterns Figures 16 and 17 are plots of a set of results from a 127 x 5 PRBS test performed with the reactor at 5§ Mw. DNote that the flat power spec- trum is associated with the autocorrelation of the flux signal rather than the rod-position signal. The cross-correlation (Figure 16¢) is not indicative of the impulse response of the system since the autocorrelation of the input (Figure 16a) does not have a flat power spectrum. The 59 ORNL-OWG 89-12249 0.30 0.22 o > o & M' P A o AP ns 'vM -0.02 |5 : AUTOCORRELATION FUNCTION (arbitrary units) LTEY] Skt g o 140 280 420 560 700 CORRELATION TIME {(sec) POWER SPECTRUM (orbitrary units) o N w» 03 2 5 1072 2 5 0! 2 5 1P FREQUENCY (rad /sec) (a) Autocorrelation function and power spectrum of the control-rod position, Pericds of data analyzed — 5 Type sequence — 127 x 5 PRBS FIGURE 16, Correlation function and power spectrum results from a flux- demand test using a PRBS test pattern., 60 ORNL- DWG 69 -12250 8 » o te = 5 _-'E b o —— 4 - = o — Q =z o [V > 2 o % - T & f 8 o VA— - v —'v“ 3 [ \ = i 2 4 @ = \ N w 4 TN I N o 20 4 N - 4 1 9 \_/ W . " \H- .”a- -60 —-100 t0~3 2 5 10°2 2 5 10~ 2 5 100 FREQUENCY (rad/sec) Periods of data analyzed — 5 Type sequence — 127 x 5 PRBS FIGURE 17. Frequency-response results from a flux-demand test with the reactor at 5 Mw, 63 magnitude-ratio and phase plots are shown in Figure 17. There is more scatter in the data near the peak in the magnitude ratio than was evident in the rod-jog test. This is probably a result of the testing technique. Since the output power spectrum is flat (Figure l6b), there must be a minimum in the input power spectrum (Figure 162) in order to achieve a peak in the magnitude-ratio plot. For a system with a relatively-white noise input, this implies that the signal-to-noise ratio of the input signal 1s worse at the minimum than at any other point; hence, the sta- tistical confidence one should place in the values at the peak in the magnitude ratio plots is the lowest of any region on the plot. The autocorrelation functions of the test patterns as implemented by the different techniques are shown in Figures 1llha and 16b. While they are 1in general agreement, there are two noticeable differences. The small negative spike which occurs at both ends adjacent to the large positive spike in the autocorrelation function in Figure 16b is caused by a deadband in the servo system. With the rod-jog technique, the rod was moved and then held stationary until time for a pulse of different polarity, With the flux-demand technique, the rod would move the flux until the flux-demand was satisfied and then stop. The flux would con- tinue to change and would move on through the "satisfied" state and would have to be brought back by rod movement in the other direction. A dead- band in the flux signal may be observed by careful inspection of Figure 9, page 27. The width of this deadband was found to determine the magnitude of the negative spike. Some tests were performed in which the deadband was very narrow and the spikes were all but eliminated. 6l The small positive spikes which occur at lag time equal to 278* sec in the autocorrelation function in Figure 16b are thought to be a result of the shape of the flux signal when going from a low to high value not being the inverse of the flux signal when going from a high to low value, Similar spikes were noted at both 35 sec and 278 sec on most other 127 x 5 PRBS flux-demand tests., Only spikes at lag times of 35 sec were reported in similar tests with the rod-jog testing technique. One 127 x 5 rod-demand test had a small spike at ~ 33 sec with no other anomalous spikes. The occurrence of a spike at 35 sec is predictable (References 13, 30, 31) and is a function of the time between the longest run of consecutive positive bits and negative bits for the particular sequence being used. The additional spikes at 278 sec which appeared with the flux-demand technique are thought to be caused by the same type of phenomenon that caused spikes at 35 sec, but this has not been proven. The spike at 33 sec with the rod-demand technique was small and should not be considered as strong disagreement with the predicted time of 35 sec. Spikes were also observed in PRBS tests of other length and in PRTS tests. No theoretical work could be found which related the position of the spikes to the properties of the PRTS, but it is likely that they are caused by the same type phenomenon. *The autocorrelation functions are very nearly symmetric about the half-period time. There were corresponding spikes in the second half of the autocorrelation functions at the appropriate times, but only the spikes during the first half are mentioned in the text, for clarity of presentation. 65 The magnitude-ratio and phase-angle plots for a 127 x 5 PRBS with the reactor at 2 Mw is shown in Figure 18, The theoretical and experi- mental data are in adequate agreement at this lower power, PRTS Test Patterns The faulty magnetic tape unit malfunctioned on two out of three tests which employed PRTS test patterns. The results of the successful PRTS test (242 x T7.25 at 8 Mw) are shown in Figures 19 and 20. The auto- correlation function of a PRTS waveform is obvious in Figure 19b and the assoclated power spectrum is relatively flat over nearly twe decades in frequency. The curvature in the autocorrelation of the rod position (Figure 19a) is unusual compared to those previously shown. The plot indicates that the rod position was not a true periodic signal since it was not symmetric about the half-period time. These tests were performed in February and March when changes in atmospheric conditions were rapid. Ambient air temperature and/or wind velocity changes affect the heat-removal rate at the radiator which ultimately forces a reactivity change in the core. Since the flux was being controlled during these tests, the outside dis- turbances were shown by changes in control rod position which were, in turn, reflected in the correlation function calculations, While temperature effects account for the non-symmetrical shape of the autocorrelation function in Figure 19a, the general "bowed'" shape must be explained by other means. The period of this test (2Lk2 x 7.25) was long compared to most other tests performed, hence the fundamental 66 ORNL-DWG 69-12055 POWER LEVEL-2 Mw ANALYS!S METHOD ¢ CABS ~— THEORY 3 No'alr 100 = 20 > y \ 8 .-*‘::I 5 > 002 3 o ! ‘ J 5 ; : ' = ' o - w 5 -0.02 ._ I | wl @ @ 3 S -0.06 o «J -0.10 0 400 800 1200 1600 2000 CORRELATION TIME (sec) POWER SPECTRUM (arbitrary units) 2 5 1072 2 5 107! FREQUENCY (rad/sec ) (a) Autocorrelation function and power spectrum of the control-rod position. Periods of data analyzed — 2 Type sequence — 242 x T7.25 PRIS FIGURE 19. Correlation function and power spectrum results from a flux- demand test using a PRTS test pattern. 68 ORNL—DWG 69-12254 2.0 1.2 0.4 %""J"’""*"’JF-‘“ Mty fl-—%—w AUTOCCRRELATION FUNCTION (arbitrory units) ~-0.4 -1.2 -2.0 0 400 800 1200 1600 2000 CORRELATION TIME (sec) 102 POWER SPECTRUM (arbitrary units) C)l N 1 0 z 2 5 10~ FREQUENCY (rad/sec) 10”3 2 5 1o 2 5 10 (b) Autocorrelation function and power spectrum of the neutron flux. Periods of data analyzed — 2 Type sequence — 242 x 7.25 PRTS FIGURE 19. (continued) 69 ORNL-DWG 69-12255 0.30 » +— S 0.18 ey o : b x E p _~ 0.06 o 3 O : : 2 . % 5 : ?anyiavvv-nfiflf ) 3 -0.06 - g — w 1.4 o 3 i -0.18 o) ) o o O -0.30 0 400 800 1200 1600 2000 CORRELATICN TIME (sec) CROSS-POWER SPECTRUM ({arbitrary units) 10°3 2 5 107 2 5 10~ 2 5 10° FREQUENCY (rod /sec) (c) Cross=-correlation function and cross-power spectrum of the control- rod position and neutron flux. Periods of data analyzed — 2 Type sequence — 242 x 7.25 PRTS FIGURE 19. (continued) 70 ORNL-DWG 69-42257 POWER LEVEL-8Mw ANALYSIS METHOD * CABS — THEQRY 300 220 > o PHASE (deg) N Q 1072 2 5 1072 2 5 o 2 5 10 FREQUENCY (rud/sec) Periods of data analyzed — 2 Type sequence — 242 x 7.25 PRTS FIGURE 20. Frequency-response results from a flux-demand test performed on the £7°U-fueled reactor using a PRTS test pattern. 71 frequency was exceptionally low. The reactor was at full power so the amplitude of the frequency response was expected to be low at the low frequency., Since the spectral power of the flux was flat, the power in the rod-position signal at the fundamental frequency must be relatively high to give the low value in the amplitude of the frequency response. Note that the power content of the lowest harmonic in Figure 19a is a factor of about 20 higher than most of the other harmonics. The relative high power content in the fundamental frequency necessarily yields a function similar to one period of a sine wave, "Non-Symmetric" PRTS Test Patterns One property of a PRTS is that its autocorrelation function has a negative spike at lag time equal to T/2 which is equal in magnitude to the positive spikes at lag times equal to zero and T (see Section I of Chapter II). This is possible only if the second half of the sequence is the negative of the first half, For example, if the first two bits in a PRTS are positive, the first two bits of the second half of the sequence will be negative. The results of the first attempts at using a PRTS are shown in Figures 21 and 22. These were surprising in that the autocorrelation function of the flux signal (Figure 21b) did not assume the expected shape of a PRTS. The reason for the unexpected correlation function was found to be the manner in which we assigned voltage to the PRTS signal which was generated by the on-line computer (BR-340). Instead of using a signal which had the same number (n) of plus and minus pulses with (n-l) intervals at zero level, as is the case for a true PRTS, we were actually 70 ORNL— DWG 69—12258 0.20 Z § 2 014 5 2 - s X & oo08 '_ Q = 3 o T L T z i 2 ooz i < - | 2 MMMV\M P\N\ !V\N-N\/\J’V\M“V*—‘-“W < i3 O - % ¥ o . = -004 = 2 i i -0.10 0 160 320 480 640 800 CORRELATION TIME (sec) POWER SPECTRUM (arbitrary units) 73 2 5 1072 2 5 T 2 5 10 FREQUENCY (rad /sec) (a) Autocorrelation function and power spectrum of the control-rod position. Periods of data analyzed — L Type sequence — 80 x 10 "non-symmetric' PRTS FIGURE 21. Correlation function and power spectrum results from a flux- demand test using a "non-symmetric" PRTS test pattern. T3 ORNL—-DWG 69—12259 20 » S 14 > s | = - s z 8 © — Q z > H 2 fi & e 5 i : - JL'- ~ ‘\fnflu\-—~h—uflqd bvfl,-—-urufiufla* ~ e & v S o -4 — > < -10 0 160 320 480 640 800 CORRELATION TIME {(sec) POWER SPECTRUM (arbitrary units) i 2 2 5 10" FREQUENCY (rad/sec) 2 5 10 (b) Autocorrelation function and power spectrum of the neutron flux. Periods of data analyzed — k Type sequence — 80 x 10 '"non-symmetric' PRTS, FIGURE 21, (continued) Th ORNL-DOWG 69 -42260 20 o = 2 > 1.4 ° = s ; = : S 08 - QO = 3 [T = . : 9 O 2 . :: = . : 3t < : ] E ‘[L,-‘. ~ ‘N\dV\MP’\M W\/\-MN\NP\MM ] @ { V 2 Q i O : J -04 e 9 ¥ Q —{.0 0 160 320 480 640 800 CORRELATION TIME (sec) 102 6—- S o - CROSS-POWER SPECTRUM ({arbitrary units) 61 192 1073 2 5 1072 2 5 107! 2 5 10° FREQUENCY (rad/sec) (c) Cross-correlation function and cross-power spectrum of the control- rod position and neutron flux, Periods of data analyzed — L Type sequence = 80 x 10 '"non-symmetric' PRTS FIGURE 21. (continued) 5 ORNL~DWG 69-12261 POWER LEVEL ~2 Mw & BC x 10 PRTS, CABS ANALYSIS o 242 x 7.25 PRTS, CABS ANALYSIS —— THEORETICAL a&n Ny - Bk 140 PHASE (deg) 20 A N . \\\ d /(.F’ 40 el : n‘t - N1 & - 4K g Topoe, 00 s g0 salos ] ¢} 4 ' a“‘ .flE. la' ‘P?n.’;lfia\;?;b-: 1 .o.o -100 . 1073 2 5 1072 2 5 107" 2 5 10 FREQUENCY (rad/sec) FIGURE 22, Frequency-response results from flux-demand tests performed on the £7°U-fueled reactor using "non-symmetric' PRTS test patterns. 76 using a signal with the same number (n) of plus and zero pulses with (n-1) minus pulses, which resulted in the autocorrelation function not being sym- metric about the half-period time. Calculation of the power spectra for this type of signal showed that 3/” of the signal power was concentrated in the even harmonics with the remainder in the odd harmonics., This is still a valid signal for frequency-response determination, but it defeats one of the purposes of using the PRTS — the concentration of all the signal power in the odd harmonics. The magnitude-ratio and phase-angle plots for two tests which utilized this type signal are shown in Figure 22, Most of the scatter in the data is due to including the values obtained by analyzing the data at all harmonic frequencies instead of just on the even harmonics which contain most of the signal power. II. =°% FUEL LOADING While the results of tests which utilized the flux-demand technique during the 75U testing were less than ideal, they were adequate and certainly better than no results. Hence, the plans for the 237U testing program were to perform the dynamics tests using the flux-demand tech- nigue. Both the PRBS and PRTS test signals were to be utilized with a general shift to shorter bit times so that the signals would have more signal power at higher frequencies., This was desired due to the shift in the freguency response of the reactor with the fuel change (see Figures L and 5 for a comparison of frequency responses). While compensation for the changes in the frequency response of the reactor was not difficult, there were other changes in the ”pefsonality” of the reactor which did present problems, First, the control rods were T worth more® (about 30%) which meant that it would require less movement to obtain the same change in reactivity. Since the control rod was suspected of having caused problems in the U testing program, it was anticipated that the effect of moving the rod less (0.3 in. instead of 0.5 in.) would tend to magnify any inherent discrepancies which existed between indicated and actual control-rod position. Second, with the £35U fuel the reactor had been an exceptionally noise-free system, but shortly after operation began with the 37U fuel, the void fraction increased from sbout 0.05% to about 0.6%. This caused a large change in the background neutron noise. An example of the uncon?rolled neutron level for both the €PU fuel loading and the 2% fuel loading is shown in Figure 23. Typical correlation functions for the various types of signals em- ployed in the testing were shown in Section I of Chapter IV and these will not be repeated for each test,. 1. Plux-Demand Tests PRBS Test Patterns The first tests on the 77U fuel loading were performed while the reactor was at zero* power, The results of this test are shown in Figure 2La. While these results do not disprove the theoretical pre- diction, the scatter is such that they do not verify it either. Not only is there considerable scatter in these results, but at low frequencies * . Zero power implies a neutron level which is low enough so that no significant temperature changes occur but which is high enough not to be significantly affected by the neutron sources other than fission. 78 K/\ ORNL-DWG 69-12230 — «— 1.5 Mw hg——— — 5 min TIME — 233 FUEL 235, FUEL ot e A WYL i Pty VM A A A AAUAA M P et T e A i/ o) 30 40 50 60 70 30 40 50 60 70 POWER LEVEL (percent of 15 Mw) FIGCURE 23, Examples of the uncontrolled neutron flux during periods of 8 Mw power operation for the 225U fuel loading and the 27U fuel loading. 79 ORNL-DWG 69-12043 104 5 2 s A3 «:é?1() 5 POWER LEVEL-ZERO ANALYSIS METHODS a FOURCO ENSEMBLE > o FOURCO ® CABS o2 — THEORY 0 o Q Z -30 L w < I o ~60 -90 | 1073 2 5 4072 2 5 407! 2 5 100 FREQUENCY (rad/sec) (a) Results from four periods of a 127 x 5 PRBS with the reactor at zZero power, FIGURE 24, Frequency-response results from flux-demand tests using PRBS test patterns performed on the €2 -fueled reactor. 80 ORNL-DWG 69-12052 _x Q00 K .o 3 POWER LEVEL-ZERO ANALYSIS METHODS o FOURCO ENSEMB e CABS — THEORY = Q o -60 L w) <{ I a -90 [»] ~120 o I 10 2 5 4072 2 5 40t 2 5 40° FREQUENCY (rad/sec) (b) Results from three periods of a 127 x 5 PRBS with the reactor at Zero power, FIGURE 24, (continued) 81 ORNL-DWG 69-12051 POWER LEVEL-1Mw ANALYSIS METHODS © FOURCO e CABS = THEORY SO e | ? \\\ 101 248 \ 0 60 \ 30 PHASE (deg) o ° ¢ e O ® \\\Q. +.O Q;n.o ® o % -60 0 ¢ -120 -90 - 0> 2 5 102 2 5 10 2 FREQUENCY (rad/sec) (c) Results from four periods of a 127 x 5 PRBS with the reactor at 1 Mw, FIGURE 24, (continued) 82 ORNL -DWG 69-12050 FUEL STATIONARY POWER LEVEL - ZERO 3n Ny 84 ANALYSIS METHODS « CPSD s FOURCO ENSEMBLE — THEORY — /—"‘ > —30 P o ‘/ S ’fl W rcItIv: gfh;fi‘!fi'fi*h n «SKL fi‘ f fl T A4 < / £ B I -60 o d,w”/’ 3 ,’ T =] q -90 103 2 5 402 2 5 10! 2 5 40° FREQUENCY (rad/sec) (d) Results from four periods of a 127 x 5 PRBS with the reactor at zero power and the fuel not circulating. FIGURE 24, (continued) 83 the different analysis schemes often yielded results which were radically different. Analysis at higher freguencies tended to decrease the scatter in the data as well as in the differences between analysis method. Typically, after about eight harmonics for a 127 x 5 test the differences between the analysis methods were negligible, An example of the strong disagreement between analysis schemes is evident in the magnitude ratio results shown in Figure 2ha. At the first harmonic (.00989 rad/sec) the CABS analysis resulted in a value of 230, FOURCO using a fine filter gave 2850, and the ensemble average of results from the four periods cof data analyzed separately (broad filter) by FOURCO was 5200, The CPSD analysis (not shown) was 894, The coherence function was 0.17 as calculated by CABS and was 0.65 according to the CPSD analysis. The CABS result is obviously a low-confidence number and the CPSD coherence of .65 does not indicate strong relationship between the measured input and output signals. Why the analysis techniques yielded different results when analyzing the same data i1s not completely resolved; however, there are clues which indicate that it is related to system noise, First, this problem was not pronounced except when testing with the flux-demand technique, and, as will be discussed later, the flux-demand technique caused an amplification of errors in the control-rod position indication., Second, 1in each case where there was a large discrepancy between analysis techniques, the CABS calculation of the power spectrum of the input signal was found to have a large phase angle (-89° for the point being discussed), Since only the cross-power spectra can contain phase information, the input power spec- tra calculations are obviously in error. The input power spectrum is 8L actually calculated by Fourier transforming the autocorrelation function of the input signal, and noise will make the autocorrelation function slightly non-symmetric about the half-period time since it prevents the signal from being exactly periodic., It is thought that this non- periodicity of the autocorrelation function was the cause of the erroneocus CABS results. At least, when the result was in error, the coherence function signaled a warning to beware of placing confidence in the calcu- lation. | Results of another zero-power test (3 cycles of a 127 x 5) are shown in Figure 24b. The differences between the results of different analysis schemes are not as pronounced; however, the general scatter in the re- sults is greater. This is probably due to using only 2 periods of data in the analysis, One curious feature of these results is the consistent roll-off of the experimentally determined phase angle at frequencies above about 0.4 rad/sec, even though the theoretical calculations predict an increase. This feature was apparent in all of the results and was not dependent on the type signal nor the testing technique. The implication is that either the theoretical predictions were inadequate in this aspect, or that there was an inherent phase lag between the actual and indicated rod position at the higher frequencies. Since the indicator was nearer the drive motor than the lower end of the rod and was separated from the lower end of the rod by several feet of flexible hose, it seems reasonable to expect a phase lag in the actual position at the higher frequencies. The results from 4 cycles of a 127 x 5 PRBS which was performed with the reactor at 1 Mw are shown in Figure 24c. The typical scatter at all 85 frequencies and the discrepancies between analysis techniques at the low frequencies is apparent. The low phase-angle values at the higher fre- quencies are also present. With the fuel not circulating, the dynamic characteristics of the MSRE approach those of solid-fuel reactors. The results of a frequency- response test which was performed with the fuel not circulating are shown in Figure 2ld, page 82. The scatter in these results is much less than the scatter in the results for the circulating-fuel tests. The magnitude-ratio results are in general agreement with the theoretical prediction, but the bPhase angle is below the theoretical at the higher frequencies, PRIS Test Patterns If some type of system noise were the cause of the éxcessive scatter in the results of tests which utilized a PRES test signal, it does not seem logical that going to a three-level signal would improve the results, This logical deduction was verified by the results of tests at zero power and at 5 Mw, The results of three different tests at zero power are shown in Flgures 25a, 25b, and 25c. Two of the tests are 80 x 3 sequences and the third is a 242 x 5 sequence. There are not any significant differences between the results of these tests, and each is characterized by the same type scatter which was apparent in the PRBS flux-demand tests, While there is some variation between results obtained from the different analysis methods, the differences are not as pronounced as they were in the results obtained in séme of the PRBS tests. However, since all of the PRBS tests did not exhibit large differences in results for the 86 ORNL —DWG 69—142049 POWER LEVEL - ZERO ANALYSIS METHODS e CABS 4 FOURCO ENSEMBLE THEQORY 0 e 4 . =30 on e - T ] 0 .—‘-—"‘—_—_"‘ / 5 — ~ % * /// z : N a ‘Bj —60 yd a P //////,/' d ‘ ° a Oy A . ° o2 4 % -90 102 2 5 10°" 2 5 10 FREQUENCY (rad /sec) (2) Results from four periods of an 80 x 3 PRIS with the reactor at zero power. FIGURE 25, Frequency-response results from flux-demand tests using PRTS test patterns performed on the £°3-fueled reactor. 87 4 ORNL—-DWG 69— 1412048 POWER LEVEL -ZERO ANALYSIS METHOD o FOURCO THEORY O O ’;’ -30 U5 o T o o //’ ~ o '_,.p""_—_—_-'"\-f /f‘ o Q o l('j;[)" 0 // o q GP o) o | T -60 A 02y ol / w O 0 o5 o% ///’J 9 o // / —90 _ | | 0% 2 5 (0% 2 5 10" 2 5 10° FREQUENCY (rad/sec) (b) Results from two periods of a 242 x 5 PRTS with the reactor at Zero power. - FIGURE 25. (continued) 88 ORNL-DWG 69--12047 POWER LEVEL — ZERO ANALYSIS METHOD 4 FOURCO ENSEMBLE THEORY — / A a4 AJ g N 3 1 w A O w T T —90 o —120 A 100" 2 5 107" 2 5 10° FREQUENCY (rad/sec) (c) Results from three periods of an 80 x 3 PRTS with the reactor at Zero power, FIGURE 25. (continued) 89 ORNL-DWG 69-12046 104 POWER LEVEL~ 5Mw S ANALYSIS METHODS o CARBS, FOURCO, CPSD {ALL GAVE SAME RESULTS) ~— THEORY 102 60 30 > 0 Q T Ll o) 30 = b w ¢ \- w 1‘\ T o0 \ a ¢ N .‘ 9 ® -30 ® -60 103 2 5 102 2 5 0! 2 5 10° FREQUENCY (rad/sec) FIGURE 27. Frequency-response results from two periods of a rod-demand test using a 242 x 5 PRTS test pattern. 101 frequency response of the MSRE, The results do tend to be scattered around the theoretical curve and normalization of the results was not necessary. The coherence functions calculated from these data generally scat- tered in a band between about .94 and 1.08 over the frequency range at which the signal power was relatively constant. The coherence functions at the fundamental frequency were considerably below this scatter band (0.65 for the results shown in Figure 27), but after a few harmonics, the values were within the normal scatter. Discussion When a PRBS test pattern was used, the results from the rod-demand technique were very encouraging. Normalization factors were often neces- sary to get the experimental results to agree with the theoretical pre- dictions, but the shapes of the two were in accord. When a FRTS test pattern was employed with the rod-demand technique, there was excessive scatter in the results. Since there is considerable interest in the PRTS test pattern, it is unfortunate that these results were of poor quality; however, the failure of these tests did provide another clue toward bet- ter understanding of the MSRE. The postulated reasons for failure of the flux-demand technigue to provide adequate results was the behavior of the control-rod assembly, and the results of the rod-demand tests tend to verify the postulate. When the rod was moved in a manner which simulated a PRBES waveform, it would be inserted, held stationary for a few seconds, withdrawn, held stationary, and then inserted again. This pattern was repeated with the only variation being in the length of time it remained stationary. An 102 insertion was always followed by a withdrawal and vice versa, If the bottom end of the rod did not actually move the distance the gear train indicated, as might be the case if any of the several possible high- friction conditions mentioned on pages 92 and 93 actually existed, then the waveform would still be well represented, but the indicated magnitude of the perturbations would be in error. This certainly fits with the results of the PRBS tests when used with the rod-demand technique and explains the necessity of use of a normalization factor. With the PRTS wave form, each movement of the control rod is not necessarily the opposite of the previous movement. An insertion may follow an insertion, and a withdrawal may follow a withdrawal., If, after a single insertion, the rod had moved to a high-friction position which was slightly hindering its motion, another insertion would force it on through this spot‘and it might or might not end near a similar spot after the second insertion. The effect of sub- sequent withdrawals and insertions is unclear since the insertions may originate from two different positions and those from the middle position may be following an insertion or withdrawal. If the rod-position indi- cator was not able to provide accurate information during at least part of these movements, then the test results would be expected to contain scatter. This fits the results of the PRTS tests when the rod-demand technique was used. Tt is important to note that these explanations for the results of the different type teste have not been proven but are offered as reasonable explanations which fit the experimental observations. 103 CHAPTER V CONCIUSIONS AND RECOMMENDATIONS The purpose of this work was to experimentally measure the freguency response of the MSRE and to determine the effects of varying the testing technigque and test signal specification. The experimental results veri- fied the predictions and were adequate to provide a recommendation for improving the theoretical model. The dip in the magnitude ratio which was predicted at about 0.24 rad/sec is present in the experimental results, but it is not as pronounced as expected, Since the magnitude of the dip has been shown> to be a strong function of the salt mixing as it circulates around the primary system, I conclude that the theoretical models need to allow for more mixing of the fuel salt. Tn the course of the testing program, three different testing tech- niques were used, The rod-jog technique, an open-loop method of rod con- trol, worked well when the rods were free-moving. OSince there was no feedback, any imbalance between the withdrawal and insertion times re- sulted in drift of the average position. The flux-demand technique im- posed the test pattern on the flux rather than rod position. The results from this type test contained more scatter than rod-controlled testing but for the U fuel loading gave adequate results. The faster response of the £3J-fueled reactor, coupled with the increased noise level and more aging of the control rod assemblies, gave results which contained such scatter that they were of little value in determining the frequency 104 response of the MSRE., For a system in which the rod position is well de- fined, this technique should work well and has advantages which might make it preferred over rod-controlled testing for certain applications. The rod-demand technigue, a closed-loop method of rod control, when used with a PRBS, meshed with the physical limitations of the MSRE to give the best results of the testing program, Normalization of the re- sults was sometimes necessary but the shapes were in good agreement with the theory. Various PRBS and PRTS sequences were used, The PRBS was found to give better results with the rod-controlled testing and neither type sig- nal was adequate when the flux-demand technique was used with the £33 fuel loading. The failure of the PRTS signal when used with the rod- demand technique is thought to be an extension of the problems associated with the control-rod position indication. Sequence lengths varied between 80 and 242 bits and the basic bit duration varied between 3 and 10 seconds. The expected distributions of signal power as a function of frequency were found and there were no anomalous effects noted for the different sequence specifiications, As one would expect, it was found that better statistical precision was obtained for sequences which were repeated several times. Analysis techniques gave consistent results when applied to data which contained a relatively low noise level but differed radically at the low frequencies, typically the first five‘to ten harmonics, when the data contained high noise content, such as during the flux-demand tests. No systematic study was made to determine the reasons for these differences which leaves this as an area in need of additional work. 105 The experience gained in this work emphasizes the need to plan the testing of a system to match the test procedure to the characteristics of that system. In particular, the difficulty in obtaining accurate indications of rod position changes dictated that all unnecessary rod movement be eliminated. In the £3J-fueled system with a high noise level in the flux signal, the rod-demand method proved to be the best testing procedure, Some areas in which more work is needed are: ln Determination of the cause of the difference between analysis schemes at the low frequencies when a large amount of noise is present,. Investigation into the meaning of the coherence function when applied to periodic sequences and explanation for the experimentally determined coherence functions which were greater than 1.0. Complete verification of the hypothesis that proper analysis at frequencies midway between adjacent harmonic frequencies of the minimum periocd length will provide a measure of the system noise level that was present during the testing. LIST OF REFERENCES 10. 11, 107 LIST OF REFERENCES Buckner, Melvin R,, "A Study of the Application of System Identifi- cation Techniques in the Analysis of Nuclear Reactor Dynamics, " Unpublished Masters Thesis, Nuclear Engineering Department, University of Tennessee, Knoxville, Tennessee (December 1968). Ball, 5. J. and Kerlin, T, W,, "Stability Analysis of the Molten-Salt Reactor Experiment," USAEC Report ORNL-TM-10T70, Oak Ridge National Laboratory, (December 1965), Steffy, Jr., R. C. and Wood, P. J., "Theoretical Dynamic Analysis of the MSRE with U-233 Fuel," USAEC Report ORNL-TM-2571, Oak Ridge National Laboratory (July 1969). Haubenreich, P. N. et al., "MSRE Design and Operations Report, Part V-A, Safety Analysis of Operation with £33, " USAEC Report ORNL-TM-2111, Oak Ridge National Laboratory, p. 41, (February 1968). Molten-Salt Reactor Program Semiannual Progress Report, July 31, 1964 USAEC Report ORNL-3708, Oak Ridge National Laboratory, p. 231, (November 1964), 2 Molten-Salt Reactor Program Semiannual Progress Report, February 28, 1969, USAEC Report ORNL-4396, Oak Ridge National Iaboratory, p. 130, (August 1969). Robertson, R. C., "MSRE Design and Operations Report, Part 1, Description of Reactor Design,' USAEC Report ORNL-TM-728, Cak Ridge National Laboratory, (January 1965). Tallackson, J. R., '"MSRE Design and Operations Report, Part II-A, Nuclear and Process Instrumentation," USAEC Report ORNL-TM-729, Part II-A, Oak Ridge National Laboratory, (February 1968). Kerlin, T. W. and Ball, S, J., "Experimental Dynamic Analysis of the Molten-Salt Reactor Experiment," USAEC Report ORNL-TM-16L47, Oak Ridge National Laboratory, (October 1966). Kerlin, T. W. '"The Pseudo-Random Binary Signal for Frequency Response Testing," USAEC Report ORNL-TM-1662, Oak Ridge National Iaboratory, (1966). Elspas, Bernard, 'The Theory of Autonomous Linear Sequential Net- works, " Transactions of the I.R.E. on Circuit Theory, CT-6: L5-60 (1959). 12, 13. 1k, 15, 16. 170 18. 19. 20. 2l. 22, 23. 108 Everett, D., "Periodic Digital Sequences with Pseudonoise Properties," General Electric Company (Limited of England) Journal of Science and Technology, 33(3): 115-126 (1966). Godfrey, K. R. and Murgatroyd, W., "Input-Transducer Errors in Binary Cross-correlation Experiments,' Proceedings of the Institute of Electrical Fngineers, 112(3): (March 1965). Briggs, P. A. N., Godfrey, K. R., Hammond, P, H., "Estimation of Process Dynamic Characteristics by Correlation Methcods using Pseudo Random Signals,” TFAC Symposium on Identification in Automatic Control Systems, 12-17 June, 1967, Prague, Czecho- slovakia, Part II, pp. 1 - 12, Academia-Prague (June 1967). Zierler, Neal, "Linear Recurring Sequences," Journal of the Society of Industrial Applied Mathematics, 7(1): (March 1960). Simpson, H., C., "Statistical Properties of a Class of Pseudorandom Sequences, " Proceedings of the Tnstitute of Electrical Engineers, 113(12): 2075, (December 1966). Turin, G. L., "An Introduction to Matched Filters,'" Institute of Radio Engineers Transactions on Information Theory, IT-6: p. 311 (1960). Roberts, P, D. and Davis, R. H., "Statistical Properties of Smoothed Maximal-Length ILinear Binary Sequences," Proceedings of the Institute of Electrical Engineers, 113(1): 190 (January 1966). Kerlin, T. W., "Frequency-Response Testing," Nuclear Safety, 8(L). 339-345, (Summer, 1967). Hooper, R. J. and Gyftopoulos, E., P,, "On the Measurement of Characteristic Kernels of a Class of Nonlinear Systems," Neutron Noise, Waves, and Pulse Propagation, Proceedings of Symposium at University of Florida, February 14 - 16, 1966, R. E. Uhrig, Editor, AEC-Symposium Seriles No, 9, USAEC-DTIE, Oak Ridge National Laboratory, (1967). Godfrey, K. R., "Three-Level m-Sequences," Electronic Letter, 2. U1 (1966). Briggs, P. A. N, and Godfrey, K., R., "Pseudorandom Signals for the Dynamic Analysis of Multivariable Systems,'" Proceedings of the Institute of Electrical Engineers, 113(7): (July 1966). Ball, S, J., "A Digital Filtering Technique for Efficient Fourier Transform Calculations," USAEC Report ORNL-TM-1662, Oak Ridge National Laboratory (July 1967). 24, 25. 26, 27, 28. 29. 30. 31. 109 Broome, P. G. and Cooper, G. C., "Fourier Spectrum Analysis by Analog Methods, " Instrumentation and Control Systems, 35(5): 155-60 (May 1962). Ball, S. J., Instrumentation and Control Systems Division Annual Progress Report, September 1, 1965, USAEC Report ORNL-3875, pp. 126 - 127, Oak Ridge National Laboratory (September 1965), Kerlin, T. W. and Lusius, J. L., "CABS — A Fortran Computer Program for Calculating Correlation Functions, Power Spectra, and the Frequency Response from Experimental Data," USAEC Report ORNIL- TM-1663 (September 1966). Thie, J. A,, Reactor Noise, Rowan and Littlefield, Inc.,, New York (1963). Bendat, J. S. and Piersol, A. G., Measurement and Analysis of Random Data, John Wiley and Sons, Inc., New York (1966). Balcomb, J. Douglas, Demuth, H. B,, and Gyflopoulis, E.P., "A Cross- correlation Method for Measuring the Impulse Response of Reactor Systems," Nuclear Science and Engineering, 11: 159-166 (1961). Godfrey, K. R., Everett, D., and Bryant, P. R., "Input-Transducer Errors in Binary Crosscorrelation Experiments - 2," Proceedings of the Tnstitute of Electrical Engineers, 113(1): 185-189 (January 1966). Godfrey, K. R., "Input-Transducer Errors in Binary Crosscorrelation Experiments — 3," Proceedings of the Institute of Electrical Engineers, 113(6): 1095 - 1102 (June 1966). APPENDIX TABLE VIIT PERTINENT INFORMATION RELATED TO EACH TEST PERFORMED FOR THIS STUDY Power Number Results Tape Level Test Test of in “Analysis Number™ Fuel (Mw) Method Signal Periods Text Methods 27333 U-235 8 Mw rod-jog 127 x 5 PRBS L Fig. 1k,15 CABS (a) Regular analysis at har- monic frequencies (b) Analysis at harmonic and mid-harmonic frequencies FOURCO 27328 U-235 8 Mw flux-demand 242 x 7.25 PRTS 2 Fig. 19,20 CABS FOURCO 27324 U-235 8 Mw flux-demand 127 x 5 PRES 3 No CABS FOURCO 27327b U-235 8 Mw flux-demand 80 x 10 PRTS No None 27337 U-235 5 Mw flux-demand 80 x 10 non- L No CABS sym.2 PRTS 27336° U-235 5 Mw flux-demand 2L2 x 5 PRTS 3 No CABS (a) All data (b) Two periods of data (c) Two periods after at- tempting to correct bad data FOURCO (a) All data (v) Two periods of data TTT TABIE VIITI (continued) Power Number Results Tape Level Test Test of in Analysis Number ™ Fuel (Mw) Method Signal Periods Text Methods 27338 U-235 5 Mw flux-demand 127 x 5 PRBS 5 Fig. 16,17 CABS FOURCO 27325b U-235 2 Mw flux-demand 242 x 7.25 PRIS 2 No CABS FOURCO 07332 U-235 2 Mw flux-demand 242 x T7.25 non- 2 Fig. 22 CABS sym. PRTS FOURCO 27340 U-235 2 Mw flux-demand 80 x 10 non-sym L Fig. 21,22 CABS PRTS FOURCO 27343 U-235 2 Mw flux-demand 127 x 5 PRBS 5 Fig. 18 CABS FOURCO o732L U-233 8 Mw flux-demand 127 x 5 PRBS 7 No CABS +27330 CPSD FOURCO (2) Using 5 periods of data (b) Using 7 periods of data 27325 U-233 5 Mw flux-demand 80 x 3 PRIS 12 Fig. 25(d) CABS (a) At harmonic and mid-- harmonic frequencies FOURCO (a) Regular (b) Ensemble CPsD cTT TABLE VIII (continued) Power Number Results Tape Level Test Test of in Analysis Number Fuel (Mw) Method Signal Periods Text Methods 27339 U-233 1 Mw flux-demand 127 x 5 PRBS L Fig. 2k(c) CABS FOURCO 27340 U-233 1 Mw flux-demand 242 x L4 PRTS 3 No CABS 2T3h3f U-233 1 Mw flux-demand 80 x 3 PRTS -—-- No -——— 27326 U-233 Zero flux-demand 127 x 5 PRBES L Fig. 2L(a) cABS (1oow) (a) Regular (b) Analyzed first two and last two periods of data . and averaged results & FOURCO (a) Regular (b) Ensemble CPSD 27334 U-233 Zero flux-demand 80 x 3 PRTS L Fig. 25(a) CABS (50w) FOURCO (a) Ensemble 27334 .U-233 Zero flux-demand 127 x 5 PRES 3 Fig. 24(b) CABS (50w) FOURCO (a) Ensemble 273355 U-233 Zero flux-demand 127 x 5 PRES b Fig. 2L(d) CABS (50w) CPSD FOURCO (a) Ensemble TABLE VITI (continued) Power Number Results Tape Level Test Test of in Analysis Number Fuel (Mw) Method Signal Periods Text Methods o7342% U-233 Zero flux-demand 80 x 3 PRTS I Fig. 25(e) CABS (50w) FOURCO (2) Ensemble 27336 U-233 Zero flux-demand 242 x 5 PRTS 2 Fig. 25(c) CABS (50w) FOURCO (a) Ensemble 27336 U-233 Zero flux-demand 80 x 3 PRTS 3 Fig. 25(b) CABS (50w) FOURCO (a) Regular (b) Ensemble 27329 U-233 8 Mw rod-demand 127 x 5 PRBS 5 Fig. 26(d) CABS FOURCO CPSD 27330 U-233 8 Mw rod-demand 242 x 5 PRTS O Fig. 27 CABS FOURCO 27343 U-233 8 Mw rod-demand 242 x L PRTS 3 No FOURCO 27337 U-233 8 Mw rod-demand 127 x 3 PRBS 3 No CABS o734l U-233 8 Mw rod-demand 127 x 3 PRBS 8 Fig. 13 CABS and 26(c) (a) Two periods analyzed then averaged results HTT TABLE VIII (continued) Power Number Results Tape g Level Test Test of in Analysis Number Fuel (Mw) Method Signal Periods Text Methods 27341 (continued) Tables ITI, (b) Four periods analyzed, v,v,VvI, then averaged results VIT (c) Regular CPSD (a) £ = 0.001 (b) £ =0.05 (c) ¢ =0.5 FOURCO (a) Regular (b) Two periods analyzed then averaged results (c) Four periods analyzed then averaged results (d) Same as a,b,c except analysis at non-harmonic frequencies 27327 U-233 5 Mw rod-demand 127 x 5 PRES 11 Fig. 26(b) POURCO +27331 (a) Using only 5 periods of data (b) All data CABS (a) Analysis at harmonic freguencies (b) At harmonic and mid- harmonic frequencies qTT TABLE VIIT (continued) Power Number Results Tape Level Test Test of in Analysis Number Fuel (Mw) Method Signal Periods Text Methods X-8205 U-233 Zero rod-demand 127 x 5 PRBS 3 Fig 26(a) CABS (10kw) FOURCO CPSD a. Recorded here to aid in future reference to the data. b. Computer malfunctioned during data-recording making results meaningless. c. The raw data for this test was destroyed and was not available for further analysis. d. Non-symmetric. e. The results from this test were very peculiar and did not resemble the expected frequency response at all, The reason for this bad test has not been explained, but it was noted that there was excessive drift in the fuel-salt temperature during the test, Attempts to correct for this drift were unsuccessful. fo g. Amplifiers saturated during test. Fuel not circulating for this test. 9TT 1. N. J. Ackermann 2. R. G. Affel 3. J. L. Anderson 4L, C. F. Baes 5. S. J. Ball 6. H. F, Bauman 7. 5. E. Beall 8. E. S. Bettis 9. R. Blumberg 10. E. G. Bohlmann 11, C. J. Borkowski l12. G. E. Boyd 13. R. B, Briggs 14, R. A. Buhl 15. 0. W. Burke 16. F. H. Clark 17. W. B. Cottrell 18, C. W. Craven 19, J. L. Crowvley 20. F. L, Culler 21, S. J. Ditto 22, W. P, Eatherly 23. J. R, Engel 2L, D. E, Ferguson 25. L. M. Ferris 26. A, P. Fraas 27. D. N. Fry 28. W. K. Furlong 29. C. H. Gabbard 30. R. B. Gallaher 31. W. R, Grimes 32. A. G. Grindell 33. R. H. Guymon 3k, P. N. Haubenreich 35. A. Houtzeel 36. T. L. Hudson 37. P. R. Kasten 38-42. T. W, Kerlin 43. R. J. Kedl Ly, H. T. Kerr 103-10kL, 105-106. 107-109. 110. 111, ORNL Patent 117 INTERNAL DISTRIBUTION L5 L6, L7 L8 49 50 51 Office ORNL-TM-2823 S. S, Kirslis A, I, Krakoviak T, S. Kress Kermit Laughon, AEC-0SR Ry Qu@mertHtEHY Pt D DO DO =24 g > - LIZLIU';UC—lU';Uf"IZ.E: G Central Research Library (CRL) Y-12 Document Reference Section (DRS) Laboratory Records Department (IRD) Laboratory Records Department — Record Copy {LRD-RC) . P EdEaoarraE=EsoHOEHOGZE HE n QEIOED QNG m— D Tucius Iundin . Lyon MacPherson MacPherson Martin McCoy . McCurdy McIntosh, AEC-Washington McNeese Miller Moore Nicholson Oakes Perry Piper . Prince Ragan Redford . Robinson Rosenthal Roth, AEC-ORO Savolainen ap Scott . 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