Reactors - Power AEC Research and Development Report

ANL-5733 Reac to r s - Power ( T I D - 4 5 0 0 , 14th Ed.)

AEC R e s e a r c h and Development Report

ARGONNE NATIONAL LABORATORY P . O. Box 299

Lemont, Illinois

REACTIVITY TRANSIENTS AND STEADY-STATE OPERATION OF A THORIA-URANIA-FUELED DIRECT-CYCLE LIGHT

WATER-BOILING REACTOR ( B O R A X - I V )

by

B . S . Maxon, O. A. Schulze and J. A. Thie

Reactor Engineering Division

Work pe r fo rmed by:

J . Boland M. Novick G. Brunson O. A. Schulze* J. D. Cerchione A. Solbrig R. N. Cur ran R. W. Thiel F . Kirn R. Wallin B. S. Maxon* G. K. Whitham F . D. McGinnis

*Loaned Employee from Amer ican Machine and Foxondry Co.

F e b r u a r y , 1959

Opera ted by The Univers i ty of Chicago under

Contract W-31-1 09-eng-38

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

TABLE OF CONTENTS

Page

I. INTRODUCTION 5

II. DESCRIPTION OF FACILITY 6

A. General 6 B. Core 9

1. Fuel Assembly 9 2. Control Blades 9

III. PHYSICS STATICS EXPERIMENTS 13

A. Approach to Cri t ica l i ty 13 B. Calibrat ion of Shim and Center Blade(s) 14 C. Flux Distr ibution 20 D. Power Cal ibrat ion 20 E. Tempera tu re Coefficient of Reactivi ty 22

IV. REACTIVITY TRANSIENTS 23

A. Exper imenta l P rocedu re 23 B. Trans ien ts with Water at Atmospher ic Boiling

T e m p e r a t u r e 24 C. Trans ien t s with Water Initially Subcooled 26 D. Summary of Trans ien t Behavior 30

V. ATMOSPHERIC PRESSURE BOILING 33

A. Reactivi ty in Steam Voids 35 B. Centra l Fue l and Clad T e m p e r a t u r e s 35 C. Water-Head Effect 38 D. Self-Induced Oscil lat ions 40

VI. PRESSURIZED BOILING 43

A. Reactivi ty in Steam Voids 43 B . Self-Induced Osci l la t ions 43 C. Product ion of U"^ 46

VII. TRANSFER FUNCTION MEASUREMENTS 47

A. Rod Osci l la tor Exper iments 47 B. Ringing Tes t s 52 C. Power Frequency Spect rum 55

TABLE OF CONTENTS

Page

APPENDICES 59

Appendix A: REACTOR CORE PHYSICS 59

Appendix B: TRANSFER FUNCTION ANALYSIS . . . . . . . . . 65

Appendix C: ANALYSIS OF INHERENT MECHANISMS OF REACTIVITY COMPENSATION DURING EXCURSIONS. 69

Appendix D: CORE HYDRAULICS 73

Appendix E: STEADY-STATE REACTIVITY IN VOIDS 75

ACKNOWLEDGEMENTS . 77

REFERENCES 77

REACTIVITY TRANSIENTS AND STEADY-STATE OPERATION OF A THORIA-URANIA-FUELED DIRECT-CYCLE LIGHT

WATER-BOILING REACTOR SYSTEM (BORAX-IV)

B. S. Maxon, O. A. Schulze and J. A. Thie

ABSTRACT

A s e r i e s of exper iments involving rapid ejections of a control blade from lowpower levels were done at room t e m pera tu re and 20 7°F to obtain information about the inherent self- l imit ing capabil i t ies of light water-boi l ing reac to r s y s t e m s . Per iods down to 83 mil l i seconds were se l f - t e rmina ted without core damage . Theoret ica l analysis showed that the power excurs ion data could be co r re l a t ed by a single energy coefficient of react ivi ty: 0,029 i 0.001% reac t i v i t y /Mw-sec .

Steady-s ta te boiling exper iments at p r e s s u r e s ranging from a tmospher ic p r e s s u r e to 322 psig gave powers up to 4.6 Mw for the fo rmer , and 20,5 Mw for the l a t t e r , p r e s s u r e . A react ivi ty in s team voids of 6.9% was achieved at 322 psig; the corresponding power densi ty was 45 kw/ l i t e r of co r e .

Information on reac to r stabil i ty was obtained from m e a s u r e m e n t s of t r ans fe r function using a rod osc i l l a to r . A sharp resonance was observed, and values of the resonant t r ans fe r function obtained were as much as seven t imes higher than the mid-f requency zero-power t r ans fe r function. Theore t ica l analysis revealed the resonat ing t r ans fe r functions were due to a feedback whose magnitude was of the o rde r of react ivi ty in s team voids, and whose phase was de te rmined by t ime constants of the same o rde r as that of the fuel and the s team bubbles .

Computations based on the theore t ica l initial conver-sion ra t io for U show that 71 gm U were produced as a resul t of in termi t tent exper imenta l operat ion for one year , equivalent to 300 MWD.

I. INTRODUCTION

As of 1956, the s e r i e s of BORAX exper iments ( ca r r i ed out in the re ac tors BORAX-I, -II, - II l )( l -4) had provided vir tual ly all existing knowledg per t inent to the safety and operat ing c ha ra c t e r i s t i c s of boiling r e a c t o r s . However, it was rea l ized the thin a luminum-pla te fuel e lements used in

the respec t ive co re s were not typical of the e lements to be employed in, for example, cent ra l stat ion boiling power r e a c t o r s . It was expected the l a t t e r type would have appreciably longer t he rma l t ime cons tants . Thus ea r ly in 1956 it was decided to design and fabr ica te a core (designated BORAX-IV) of t ho r i a -u ran i a fuel e lements for evaluation in the existing BORAX facility.(5)

The des i rab le fea tures which led to the select ion of the fuel e l e ment we re : (1) t ime constants typical of oxide-fueled power r e a c t o r s (see Appendix B); (2) chemical ine r tness of an oxide fuel in water ; (3) m e t a l lurgical s impl ic i ty and economy in the use of aluminum tube sheets loaded with oxide pe l le t s ; and (4) potential economic advantages assoc ia ted with conversion of thor ium to U ^ .

The philosophy involved in designing the core was based on having a r eac to r available for in termi t tent exper imenta l operat ion for a year or longer . The balance of the sys tem remained as for BORAX-III,'^' '*) c h a r ac te r ized by natura l c i rcula t ion, d i rec t cycle, boiling light water with an e lec t r i ca l power capabil i ty of 2 Mw. The s impl ic i ty of the co re was d e m ons t ra ted by the completion of i ts design and fabricat ion in l e s s than a year : the r eac to r was f i r s t brought to c r i t i ca l i ty on December 3, 1956.

The scope of the exper imenta l p r o g r a m was designed to obtain the maximum information on the safety and s tabi l i ty of u ran ia - thor ia - fue led boiling r eac to r s consis tent with the l imi ted budget al located this re la t ive ly low-cost exper iment . The "ringing" and rod osci l la tor exper iments p e r formed r ep re sen t " f i r s t s " in boiling r e a c t o r s . Also incidental to 300 MWD of exper imenta l operat ion during 1957, a quantity of U^'^ was generated, again a "f i rs t" for e l ec t r i c generat ing nuc lear power p lan ts .

II. DESCRIPTION OF FACILITY

A. General

With the exception that a new design of the fuel e lements was requi red , the BORAX-IV sys tem compr i sed the same components and ins t rumentat ion used in BORAX-III. Consequently, the BORAX-IV expe r i mentat ion was hindered to some extent by (l) res idual radioact ivi ty from high-power level runs per formed l e s s than a year before, and (2) na tu ra l de te r iora t ion of components , including con t ro l - rod dr ives and ins t rument cables , or iginal ly intended for s h o r t - t e r m u s e .

The reac to r and turbine buildings a r e shown in F ig . 1. Referr ing to the simplified plant flow d iagram (Fig. 2), the power c i rcui t cons is ts of a feed-water pump that d i scha rges e i ther condensate from the condenser or f reshly de-ionized water from the make-up sys tem into the annular down-comer of the r e a c t o r . Steam from the r eac to r vesse l flows through a s ix -inch line to e i ther the turbine or to a vent to the a tmosphe re . The p r e s s u r e

7

TURBINE (LEFT^ AND REACTOR (RIGHT) BUILDINGS CABLES IN FOREGROUND LEAD TO CONTROL TRAILER ONE-HALF MILE DISTANT

SPENT FUEL

STORAGE

FEEDWATER PUMP

FEEDWATER STORAGE

REACTOR

CIRC. PUMP ELECTRIC HEATERS

FIG. I

REACTOR AND TURBINE BUILDINGS

-SPENT FUEL STORAGE

-STEAM LINE

REACTOR PIT

PIPING PIT

CONDENSER

I RELIEF 1 STEAM V*IVE T REMOTE

X DUMP

REACTOR BACK PRESSURE

REGULATOR

i AUTOMATIC JL W r , FEED-WATER V K^ CONTROL A

MANUAL FEED-VATER

CONTROL

\ o

U£^

FIG. 2

SIMPLIFIED FLOW DIAGRAM

vesse l may be opened and the s team re l eased to building a tmosphere for s h o r t - t e r m t e s t s . The second c i rcui t , which fea tures a c i rculat ing pump and e lec t r i c h e a t e r s , pe rmi t s p r e s su r i z ing the r eac to r vesse l independently of r eac to r operat ion. It is also useful in performing low-power cal ibra t ion of the nuclear i n s t rumen t s . The th i rd c i rcui t consis ts of f i l ters and ion-exchange columns for cleanup of the r eac to r wa te r .

The ins t rumentat ion and c i r cu i t ry is shown schemat ica l ly in F ig . 3.

B. Core

1. Fuel Assembly

The BORAX-IV fuel a s sembly , p ioneered by the Argonne Metal lurgy Division, ut i l izes u r an i a - tho r i a (U02-Th02) pel le ts f i red in air.*' ' ' The uran ium is enriched in U^ ^ to the extent of 93%. The finished pel le ts have an outer d iamete r of 0.230 in. and va ry in length from about 0.375 in. to 0.75 in. The densi ty is about 9-1 g m / c c , with 0.0559 gm U ^ ^ g m ThOz. The pel lets a re inse r t ed into extruded M-388 aluminum (Al - 1% Ni) tube-p la tes , a mechanical bond being made by filling in the spaces with lead .

Each fuel a s sembly (Fig. 4) contains six tube pla tes (8tubes per plate) or a total of 47 active tubes with one tube available for the i n s e r tion of a bo ron - s t ee l rod . Each a s sembly contains about 5425 gm UO2 - Th02, or about 283 gm U -* , with an active length of about 24 in.

2. Control Blades

F igure 5 is a cutaway view of the r eac to r p r e s s u r e ves se l , showing the core a s sembly and location of the control b l ades . The p r e s sure ves se l is a s ta in less s teel teink, 15 ft - 11 5 in. high with an in ternal d iamete r of 52-2- in. , and a wall th ickness of 3/4 in.

The r eac to r is control led by four bo ron - s t ee l sh im blades (122- in. wide x 3/8 in. thick) with 8-in. long hafnium t ip s . These blades operate upward out of the core in channels which divide the co re into four quadran ts . Two center blade designs a r e avai lable . One 3-in. wide blade can be used as an excurs ion blade, i .e . , it can be pneumat ica l ly ejected downward out of the core for t r ans i en t t e s t s . The second blade, 5 in. wide, opera tes in the s a m e manner as the shim blades during no rma l opera t ion. All of the blades have aluminum fol lowers .

The core gr id plate can accommodate up to 88 fuel a s s e m b l i e s , each with cell d imensions of 3.888 x 4.000 in. The a s s e m b l i e s a r e held in place by a hold-down gr id .

CIRCUIT

PERIOD METER

LINEAR POWER METER

SAFETY

START-UP

HOTWELL GAMMA MONITOR

POWER GALVANOMETER

TELEVISION MONITOR

REACTOR

B'O -COMPENSATED

CHAMBER

BIO • COMPENSATED

CHAMBER

BF,

BF,

BF, PRE AMP

SCINTILLATION

COUNTER

REACTOR

CHAMBER

a y REACTOR STEAM PRESSURE I WATER

LEVEL

INSTRUMENT ROOM

LOG AMP.

HI VOLTAGE

PERIOD SCRAM -

PRE-AMP LINEAR AMP

HI VOLTAGE

^ AMP

HI VOLTAGE

^ SCRAM

AMP

HI VOLTAGE

HI VOLTAGE

\ -

*• AMP

TURBINE ROOM •i

* AMP.

P- •1 BATTERY

BOX

^ INSTRUMENT ROOM

AMP

SYNC.

CONTROL RELAY BOX

CONTROL TRAILER PERIOD METERS

PERJOD AMP

^ <^

LEVEL RECORDER

LEVEL METER

<J) LEVEL

RECORDER

_^ SCRAM INDICATION AND RESET

AMP

COUNT RATE METER

- * i DECADE SCALER

*i 9 C.R.M. SELECTOR

SWITCH

Li DECADE SCALER

W GAMMA LEVEL

METER

GAMMA LEVEL

RECORDER

IS: GALVANOMETER

TELEVISION MONITOR

CAMERA CONTROL UNIT

F I G . 3

INSTRUMENTATION AND CIRCUITRY

V-V Vw/* '^^ '^^ V_^ V->' '^-y \ y

v y ^y ^y ^^ ^^ ^^ ^^ ^

^K /"N / ^ /'N /--s /-^ / - s /^'s

\ y "^^ \ y Ky "^^ "^y Ky <y

"^y "^--^ "^^ K^ \^ K^ K^ ^y

STEAM EXIT

CENTER BLADE

FEED WATER INLET

CORE SUPPORT PLATE

DRIVE RODS

F I G . 5

CORE ASSEMBLY IN REACTOR VESSEL

REACTOR.PIT SHIELD PLUG

CORE SUPPORT

STRUCTURE

SHIM BUDES

FUEL ASSEMBLY HOLD-DOWN GRID

FUEL ASSEMBLY

SHIM BLADE GUIDE

SHIM BLADE FOLLOWER

A more detailed descr ipt ion of the design and physics charac te r i s t i c s of the core is given in Appendix A.

III. PHYSICS STATIC EXPERIMENTS

A. Approach to Cri t ical i ty

The approach to cr i t ica l i ty was made by adding one fuel a s s e m bly at a t ime to the water-f i l led reac tor p r e s s u r e vesse l . As the loading p rogressed , the count ra tes from two 'vVestinghouse fission counters wêre measured with all shim blades inser ted in the co re . The shim blades were then removed slowly, one at a t ime , and the count ra tes measu red again. This procedure was repeated after each fuel a ssembly addition, with r e positioning of the source as required, until c r i t ica l i ty was reached.

Cri t ical i ty was obtained with a core loading of 28 fuel a s s e m blies (7.92 kg U^ ) in the pat tern d iagrammed in F ig . 6. With all the shim blades in their maximum out-position, this loading had an asymptotic period of 18 min. As more excess react ivi ty was required for the la ter exper i ments , fuel assembl ies were added to the per iphery of the co re . The worth of these assembl ies is also shown in F ig . 6.

SOURCE FUEL POSITION DESIGHATIOM

RATIO OF LOCAL TO AVERAGE FLUX

WORTH IN » REACTIVITY 68°F.

CENTER BUDE

F I G . 6

FLUX DISTRIBUTION AT VERTICAL CENTER OF FUEL ELEMENTS (30-ELEMENT CORE). CROSSMATCHED

AREA INDICATES CRITICAL LOADING WITH ALL BLADES WITHDRAWN

B. Calibration of Shim and Center Blade(s)

A differential worth cal ibrat ion of the four shim blades was performed by the usual method of measur ing the asymptotic period after withdrawing the shim blades as a "bank" a short distance from thei r c r i t i cal posi t ions . The cr i t ica l position was var ied by adjustment of the center blade, by the addition of fuel assembl ies to the per iphery of the core or by addition of bor ic acid to the reac tor water .

The initial cal ibrat ion of the shim blades was performed at room tempera tu re (68°F) and at saturat ion (20 7°F) in a core consisting of between 29 and 31 fuel a s s e m b l i e s . The differential worths as a function of position for these two t empera tu re conditions a r e given in F ig . 7. The integral worth as a function of position is shown in F ig . 8.

0.3fl

a o-'«

t

-

\-

-

-

-

1

TEH _2F

20

1

1

\

1

^ J X

1

P . , « 0 . FUEL iSSEHBLIES

3 «-3l

1

1

N,

1

1

K \

1

1

fUP" POSIT ION-

\

\

1

V \

-

-

-

-

-

-

-

18 19 20 21 22 23 n 25

POSITION INOICATOD PEAOINS, In.

FIG. 7

DIFFERENTIAL WORTH OF FOUR SHIM BLADES

1.0

fc 0.8

a « 0.6

-

-

-

-

-

-

^

-

/

1

TE

20

TOP OF FU

y

1^-'

1

" P . . NO F ASS

r

EL

A

/} 1

1

FUEL EMBLIES .

1

3 0 - 3 1 ^

/

A 1

/ ' I / /

1

/ /

/

-

-

1

2S.S 2H.S 23.S 22.S 21.5 20.5

POSITION INOICATOD iUDINO. In.

FIG. 8

INTEGRAL WORTH OF FOUR SHIH BLADES

The cal ibrat ion of the center blade was made by the same method employed for the shim blades . The differential worth and integral worth as a function of position are shown in F i g s . 9 and 10. In F ig . 10, the worth of the excursion blade as obtained from the t rans ient t es t s is also given for comparison. In both figures the position indicator reading is the number of inches the blade has been lifted from its fully "out" position b e low the core . It is to be noted that within experimental e r r o r , the worth of the excursion blade did not change with t empera tu re up to 207°F.

0.10

0.08 c

t 0.06

a 0.04

• » *

0.02

-

-

• y

^

A 1

X • DATA

O

. •

1

L . ^ -«

TEW °F

68 207

1

- ^

P.. N(

•

. FUEL ASSEMBLIE

29-30 30-31

1 1

' ^

s

N. s

1 1

\

FIG. 9

DIFFERENTIAL WORTH OF EXCURSION BLADE

2 4 6 8 10 12 I t 16 18 20 22

POSITION INDICATOR READING. In.

FIG. 10

INTEGRAL WORTH OF EXCURSION BLADE

1.2

1.0

t 0.8

> 5 a 0.6

»»

0.4

0.2

-

1 OF

-

-

-

^

1

NTEGRAL / FIG. 9 l i

^

y 1

EMP., •F 68 07

/ d'

NO. F ASSEME

29-! 30-i

y / ^

UEL LIES

1

/

/

X, /

^

0 = WORTH FROM TRANSIENT TESTS WITH 30-ASSEHBLY CORE

_ L J 1

, ..„ 1, , 1 . 1 1 >

^

—

—

6 8 10 12 14

POSITION INDICATOR READING, In.

The shim blades were r e -ca l ib ra ted pr ior to the measu remen t of the excess react ivi ty held down by s team voids in l a rge r sized cores during osci l lator exper iments at saturat ion t empera tu re (atmospheric p res sure ) . Figure 11 shows the differential worth as a function of position in cores consisting of 39 and 42 fuel a s sembl i e s . The loading a r rangement of the 42-assembly core is shown in F ig . 12. The integral worths for these cores a r e plotted in F ig . 13; the worth in a 30-31 assembly core is also plotted for comparison. For the t ransfe r function t e s t s , the differential worth of the osci l lator rod was measured with the resu l t s shown in F ig . 14. The tip of the osci l la tor rod was not necessa r i ly at the same level as that of a blade for a given posi t ion-indicator reading. The rod consisted of a cadmium tube, 12 in. long, which occupied the lower half of the core in its "in" position.

16

o.w

0.36

0.28

a »» 0.20

1

-

-1

1 1

>IS

-

NOT

1

\ V

ASSEMBLI

CENTER B

E: OSCI

1

1

^

\

E S — ^ LADE ADJUS

LUTOR ROB

1

1 1 1 1

„. 42 FUEL ASSEMBLIES

O CENTER BUDE ADJUSTMENT 1 • BORIC ACID ADJUSTMENT

N - ^ TMENT

AT MID-P

1

>

\

^

OSITION

1

\

'H

1

1

1 "UP" P O S I T I O N ^

1

\ .

S \

\ \

1 1

\

\

-

-

-

-

-

-

A

A

-\

H

17 IB 19 20 21 22 23


24 25 26

FIG. II

DIFFERENTIAL WORTH OF FOUR SHIM BLADES AT 207«F (SATURATION TEMPERATURE, ATMOSPHERIC PRESSURE)

NOTE: B :: ASSEMBLY CONTAINING 0.18 in. DIA. BORON-STAINLESS STEEL ROD.

OR = OSCILLATOR ROD

FIG. 12

U2-ASSEMBLY LOADING ARRANGEMENT FOR OSCILLATOR EXPERIMENTS

17

1.8

1.6

\A

1.2

1.0

O.B

0.6

O.H

0.2

26.B 24.5 23.5 22.5 21.5 20.5 19.5 18.

POSITION INDICATOR READING, in.

FIG. 13

INTEGRAL WORTH OF FOUR SHIM BLADES AT 207°F (SATURATION TEMPERATURE, ATMOSPHERIC PRESSURE)

0.032

0.024

0.016

0.006

_ - ^

4 6 8 10


12

FIG. lU

DIFFERENTIAL WORTH OF OSCILLATOR ROD IN y2-ASSEMBLY CORE AT 207°F (SATURATION TEMPERATURE, ATMOSPHERIC PRESSURE)

18

At reac tor p r e s s u r e s above a tmospher ic , the shim blades were cal ibrated in a core consisting of 59 fuel a s sembl i e s , as shown in F ig . 15.

Each of the center 16 assembl ies contained a boron-s ta in less steel poison rod. The shim blades were cal ibra ted at v a r ious t empera tu re s in the range from 100°F to 420°F (300 psig) . The cr i t ica l position was var ied by addition of bor ic acid to the reac tor water . The differential worth of the blades as a function of position for these t empe ra tu r e s is given in F ig . 16. The integral worth at 100°F and 420°F is given in F ig . 17.

NOTE: CROSSHATCHED ASSEMBLIES REMOVED DURING FLUX DISTRIBUTION MEASUREMENTS.

F I G . I S

Sg-FUEL ASSEMBLY LOADING ARRANGEMENT

The inhour curve (Fig. 18) used in these cal ibrat ions is based on a neut ron lifetime of 5 x 10"^ sec . F o r the range of per iods covered in the blade(s) cal ibrat ion and t rans ien t t e s t s , this curve is insensi t ive to the neutron l i fet ime.

U.b

0.5

0.4

0.3

0.2

0.1

n

O °

o

-

NOI CI C

-

1

• • i ^ ^

^ • ^

^ ^ s - ^

JTER BLADE ( IITICAL P0SI1

[

1

^ . .

^

m. nON VARIED

1

1

^ ^

^

X )Y lORIC ACID

1

1

• D

. A 0

ADDITION.

1

1

PRESS., Pt Ig

300 188 145 95

ATM.

X, >

1

1 TEMP.,

420 382 _ 363 ^ 334 100

"DP

• V

N 1

1

POSITION-^

t 1

\

1 •

-

-

-

1

IS 17 19 21

POSITION INDICATOR READING, i n .

F I G . 16 DIFFERENTIAL WORTH OF FOUR SHIM BLADES IN 59-ASSEMBLY CORE AT

TEMPERATURES AND PRESSURES INDICATED

19

FIG. 17

INTEGRAL WORTH OF FOUR SHIM BLADES IN CORE AT lOCF AND 420° F

9-ASSEMBLY

1 1 1 1

NOTE: CENTER BUDE OUT CRITICAL POSITION ADJUSTED BY

TOP OF

Y

420°F

FUEL

/

1

(300 p s i g l -- ^

1 1 y ' '

1

/

/

1

y ^

^ — lOO-F (ATM. PRESSUREl

BOTTOM OF FUEL

\

1

s ^

21.5 17.5 13.5 9.5

POSITION INDICATOR READING, in.

10-* 10-2 to-'

a I0-*

io-«

-_ -

^

---

-

1 1 1

—

^ . \

1

Ji

n <

, 1

^

l > 1

- ^

1

" ^ -

1 1 1

F I G . 18

EXCESS REACTIV ITY VS ASYMPTOTIC PERIOD

e = 0 . 0 0 7 0 U ; NEUTRON L I F E T I M E = 5 x 1 0 - 5 sec

10' 10'

ASYMPTOTIC PERIOD, sec

10»

C. Flux Distr ibution

The neutron flux distr ibution at room t empera tu re (68°F) was measu red for two core loadings by activations of ba re gold foils attached to foil holders that were suspended between the fuel tube-pla tes at var ious positions in the co re . The gold foils were covered with aluminium foil to prevent contamination by impur i t ies in the r eac to r wate r .

The initial measu remen t of neutron flux distr ibution was made for a core consisting of 30 fuel assembl ies (Fig. 6). The rat io of local to average flux in the radial positions for this loading is given in this f igure. The neutron flux distr ibutions para l le l to the core axis for two fuel pos i tions a r e indicated in F ig . 19 in t e r m s of the sa tura ted foil activity. It is to be noted that the excursion and shim blades a r e par t ia l ly inser ted in the co re . The maxiinum to average flux for this loading was about 1.8.

AXIAL NEUTRON FLUX

FIG. 19

DISTRIBUTION AT 68° F

AT TWO FUEL POSITIONS

25 21 17 13 9 5 I

POSITION INDICATOR READING. In.

The measu remen t s of neutron flux distr ibution were repeated when the core had been built up to 56 fuel assembl ies (see F ig . 15). Each of the central 16 fuel assembl ies contained a boron-s ta in less s teel rod, and the water was poisoned with boric acid. The neutron flux distr ibut ions for the radial and axial posit ions a r e shown in F ig . 20. The maximum to average flux for this loading was about 1.95.

D. Power Calibration

Calibrat ions of the nucleonic ins t ruments were performed by various methods, depending on the power level . During initial s t a r t - up of the r eac to r , measu remen t s of the power level were made by activation of gold foils and from the responses of an absolute fission counter . F o r cal ibrat ion at low power (i .e. , 100 watts) , the reac tor power was taken above the source level and both ba re and cadmium-covered gold foils were

21

6

4

?

I

(621

1

~ ^ - - o

(63, '« ' !

1

(58,

\ 0 ( 6 9 )

\ \ \

(65,0 K (B4)?\

1 q (60,

1

\

(55, O

1 1 1 5 10 15 20 26

RADIAL DISTANCE FROM CORE CENTER. In.

RADIAL AND AXIAL NEUTRON FLUX DISTRIBUTION IN SS-ASSEMBLY CORE AT S 8 ° F .

(PARENTHESIZED NUMERALS INDICATE FUEL POSITIONS,

10 15 20 26

AXIAL DISTANCE BELOW TOP OF FUEL, In.

activated for a known period of t ime . The count ra te on the absolute fission counter was also taken. The gold foils were counted with a cal ibrated counter . The relat ive average thermal neutron flux between the absolute fission counter and the core was measu red by gold foils. The power level was then calculated from these measu remen t s and the U^ ^ content in the core and fission counter . The values measu red by both methods agreed within 40%.

More rel iable power cal ibrat ions were made in the kilowatt range by comparison of the total heating and cooling ra tes between the r e actor and e lec t r ica l h e a t e r s . With the reac tor shut down, the heating and cooling ra tes of the reac tor water were measu red with the e lec t r ica l hea te r s (55 kw) turned on, and then off. The reac tor was then taken to about the same power level as the e lec t r ica l hea te r s had been, and the measu remen t s were repeated. In both instances the reac tor water was circulated continuously through the e lec t r ic heater circui t and the reac tor tank. The power calibrat ion by this method was used for the t rans ient tes t m e a s u r e m e n t s .

22

During s teady-s ta te boiling operat ions at a tmospher ic p r e s sure the reac tor power level was cal ibrated by the ra te of change in the water level with zero feed-water flow, or by the measu remen t of the feed-water flow required to attain a constant water level .

Fo r the p r e s su r i zed power runs , the reac tor power was ca l i bra ted by measur ing the p r e s s u r e drop ac ros s an orifice delivering s team either to the turbine or to the a tmosphere . The feed-water flow required to maintain constant water level served as a check on this method.

E. Tempera tu re Coefficient of Reactivity

The change of react ivi ty with t empera tu re was measu red for core loadings of 30 and 59 fuel a s sembl i e s . These measu remen t s were performed by noting the posit ions of the shim blades and by thermocouple readings as the r eac to r was heated stepwise with the e lec t r ica l h e a t e r s . The change of react ivi ty with position of the shim blades was taken from the integral worth curves measu red at ei ther 68°F (30 elements) or 100°F (59 e lements) .

F igure 21 shows the t empe ra tu r e coefficient as a function of water t empera tu re for the two loadings. The average t empera tu re coefficient for the range between 68°F and 200°F in the 30-element core was -2.47 X 10-5 (Ak/k) /°F.

3

2

1 to 80 100 120 mo 160 180

B o

1 15

10

^

y]

^

, V

L- ' i /

y

/

y / ^ >'

/

--'

FIG. 21 TEMPERATURE COEFFICIENT OF REACTIVITY FOR 30-ASSEH6LY AND S0-ASSEN6LY LOADINGS

100 ISO 200 2S0

»»TE« TEMPERATUIIE. -F

IV. REACTIVITY TRANSIENTS

A. Exper imenta l P rocedure

The responses of the r eac to r power and t e m p e r a t u r e s to step inputs of react iv i ty were investigated to de te rmine the self- l imit ing c h a r ac te r i s t i c s of the reac tor over a range of initial per iods from a few s e c onds to slightly below 100 mi l l i seconds . It was not intended to cover completely and exhaustively the range of in te res t for this r eac to r , but ra ther to explore the t rans ien t behavior so that operat ion at s teady power could proceed with g rea te r confidence. The t rans ien t behavior at a t m o s pher ic p r e s s u r e was investigated with the reac to r water init ially at s a t u r a tion t empera tu re (207°F at 5,000 ft elevation) and init ial ly subcooled (120-160°F).

P r i o r to each t rans ien t (1) the r eac to r was heated to the des i r ed t empera tu re with the e lec t r ica l h e a t e r s , (2) the r eac to r was made c r i t i ca l at a low power ( i .e . , 100 watts) with the excurs ion blade holding down a known amount of excess react ivi ty , and (3) the maximum power t r ips and excurs ion t imer were normal ly adjusted to allow the excurs ion to continue through the peak power level using the inherent reac to r shutdown mechani s m s , before the shim blades would s c r a m the r e a c t o r . When these conditions were met , the a i r - loaded centra l excurs ion blade was ejected downward and out of co re . The excurs ion was recorded on va r iab le - speed Brush and Heiland r e c o r d e r s .

The th ree major types of information recorded during the t r a n sient t e s t s were r eac to r power and the surface and fuel center t e m p e r a t u r e s of a few fuel "bayonets ." A fuel "bayonet" was essent ia l ly an aluminum and lead-encased fuel rod minus the tube sheet for convenience in frequent removal and inser t ion . Chromel -a lumel thermocouples were spot welded to the clad surface of the bayonet. The center fuel thermocouple was inse r ted through a hole dr i l led axially in a fuel pellet and held in place by si l icate cement . As pointed out in Appendix C, this method of m e a s u r e m e n t of the t empe ra tu r e of the fuel center proved re l iable during s t eady-s ta te power t e s t s , but was subject to e r r o r s during t rans ien t t e s t s .

Special fuel "bayonets" were used as a precaut ion against core damage as the excurs ion period was reduced. These bayonets contained fuel pel lets enr iched 2 and 4 t imes (2X and 4X) the normal enr ichment and were inser ted in the core between two fuel p l a t e s . Since the heat genera ted in a pellet is approximately proport ional to the enr ichment , the 4X pel le ts in a posit ion of maximum flux should give advance warning, by reason of noticeable damage, of conditions which could inflict s e r ious damage to the whole co re . The special fuel "bayonets" were inspected after each t r a n sient with a per iod sho r t e r than in any previous t e s t .

Reactor power and the thermocouple response were recorded on a single s t r ip of photographic paper by a Heiland osci l lograph employing high-speed ga lvanometers . Power was normal ly measu red by various ion chambers located at different positions around the core . The ion-chamber cu r ren t s were fed to the Heiland galvanometers through either logar i thmic or l inear ampl i f ie rs .

B. Trans ients with Water at Atmospheric Boiling Tempera tu re

Reactor t r ans i en t s , with periods ranging from a few seconds to 83 mi l l i seconds , were made with the reac tor water at the a tmospher ic boiling t e m p e r a t u r e . Atyp ica l recording of an excursion is depicted in F ig . 22.

0.1 sec

FIG. 22

TYPICAL EXCURSION WITH REACTOR WATER AT ATMOSPHERIC BOILING TEMPERATURE (207''F) AND pH = 1|.I5. INITIAL PERIOD = 0.109 sec

Figure 23 shows the peak powers obtained as a function of the rec iproca l period and the pH of the water . The sharp b reak in the curve is the resul t of a single excursion with an initial period less than 100 mi l l i seconds . The pH of the water was var ied to determine its effect on the self- l imit ing cha rac te r i s t i c s of the r eac to r . It was believed that if radiolytic formation of gas bubbles contributes to the self- l imit ing mechanism, then variat ion of the pH of the water might affect the t rans ient behavior . This was expected since, under equilibriunn conditions, radiolytic production of gas is a function of the pH of the water . It is evident from Fig . 23 that the values of pH investigated, had no detectable effect on the peak power. However , these resu l t s do not rule out the existence of radiolytic formation of gas bubbles since (1) the pH may not have exerc i sed a strong influence on t ransient radiolytic production of gas or (2) the peak power may have been insensit ive to radiolytic production of gas .

10

1

' 1 ' 1 ' 1' 1 pH DATA

6.3 • 6.1 A

— «.I5 A ».io a

DOT HEASUJiEll O

!

1 o / 1 1

/ -

1

.•tf

1

t

1

1 1

1

°4I

1

? / /

J {

10 20

RECIPDOCAL PERIOD (IW, leB"

PEAK POWER VS RECIPROCAL PERIOD FOR EXCURSIONS WITH REACTOR WATER AT ATMOSPHERIC BOILING TEMPERATURE (207°F) AND

pH VALUES INDICATED

Figure 24 shows the burs t shape during three excursions of different pe r iods .

1.0

0.8

0.6

o.t

0.2

11 6 8 10

TIME (PERI0DS1, arbitrary zero

FIG. 2U

BURST SHAPE DURING EXCURSIONS OF DIFFERENT INITIAL PERIODS

The energy (including delayed energy) re leased up to the t ime of peak power is given in F ig . 25 as a function of rec iproca l per iod. F igure 26 shows the maximum r i se of surface t empera tu re of a fuel bayonet located near the core center , as a function of rec iproca l per iod.

26

1

INIT IAL TEMP. = 207«F 1

r ^ - ^ ^ - T ^ )

DATA DH

o ^ • -K 2

O "OT MEASURED ( ' -7 .0 ) A ».I5 • 6.30 • 6.10

1 1

A —2i ..^ •

0

"

c ^

2 4 6 8 10

RECIPROCAL PERIOD, s e c '

F IG . 25

ENERGY RELEASED UP TO PEAK POWER VS RECIPROCAL PERIOD

20

DATA pH DAT

L • 6.3 A r O 1J.I5 D

A t.so 1 1

^

/ ' 1

e^-

1

\_ pH

<t.lO 6.10

^ n

1

rn

1

^^_o__.

*

_ J

^

I i 10 12

RECIPROCAL PERIOD, sec"

FIG. 26 MAXIMUM SURFACE TEMPERATURE RISE OF A FUEL BAYONET NEAR CORE CENTER VS RECIPROCAL PERIOD FOR EXCURSIONS WITH REACTOR WATER AT ATMOSPHERIC BOILING TEMPERATURE (207'>F)

C. Trans ients with Water Initially Subcooled

Excurs ions with the water initially subcooled were performed since there was reason to suspect that a shutdown mechanism other than boiling was occurr ing in the subcooled excurs ions in SPERT-I . '^ ) Because of the long t ime constant of the fuel in BORAX-IV, it was felt that shutdown would occur before the clad surface had reached a t empera tu re equal to the boiling point of water .

The resul ts of a typical subcooled excursion is shown in F ig . 27. F igure 28(a) shows the maximum r i s e of surface t empera tu re for a fuel bayonet at the core center at peak power for various periods in excurs ions from 120°F. The peak power was attained before the t empera tu re of clad surface reached the boiling point of the coolant. This was also observed in excursions from 120-130°F [Fig. 28(c) and (d)]. In excursions from 150°F, the t empera tu re of the clad surface exceeded the coolant boiling point for only the longer periods [Fig. 28(b)].

POWER (LOfl)^

y y

1 1 •- 1 1 1 1 1 r :

/ ^ , . »

P-^ POWER (LINEAR)

" —, . . -1—1. 1 I . I , i . .a. 1 1

SHIM BUDES GOING IN

" 7

\ 1

-SURFACE TEMP. RISE := 3 0 . 6 ° F 1

___—

1 1 1 1

\

^

= II9°F

1 1 1 1 1 1 1 1 1

JLo. .10 sec

TYPICAL PERIOD

SUBCOOLED = 0 .121 sec

EXCURSION WITH

FIG.

REACTOR

27

WATER IN TIALLY AT I20°F AND pH = U 05.

80

60

40

20

-S -

-

- 1

^SATURATIOK

"V

X • ^ SURFACE

1 1 1 1 1 1 1 1

^. J— SATURATIOH

1 _ ^ I I I i 8 10 0


(A)

IMITIAL TEMP. = I20°F (B)

INITIAL TEMP. = ISCF pH : 4.06

£ 60 —

^ u .

- \ \ ^ v, 1

-

1 1

> o -

^

s ^

T C S ^

1

^—SATURATION

^FUEL (TC-7)

" S ^ SURFACE • S ^ T C - 6

^£\ ^

1 1 1 1 1 , 8 10 0


J \ L J I L

(C) INITIAL TEMP. = I20-I25°F

pH = B.5

(0) INITIAL TEMP. = I26-I30°F

pH = 3.98

SURFACE

POWER VS

AND FUEL

FIG

TEMPERATURE RISE OF

RECIPROCAL PERIOD

28

A FUEL

FOR SUBCCOLED

BAYONET NEAR

EXCURSIONS

CORE CENTER AT PEAK

28

Figure 29 presen ts the t empera tu re s of the fuel and surface thermocouples at peak power as a function of l ibera ted energy (including delayed energy). Since in this period range energy inc reases as the period i nc r ea se s , the t empera tu re difference between fuel and cladding inc reases as the period d e c r e a s e s , a resul t which is to be expected. F igure 30, however , does not show this t rend in excurs ions from 150°F. It i s believed that the reading of the fuel thermocouple used in this experiment may not have been proport ional to the actual fuel t e m p e r a t u r e . The readings of the fuel thermocouple a r e , instead, proport ional to the surface t empera tu re s .

100

80

60

w

20

' ^

S'ATURATION' ^ F U E L ( T C - 7 )

LIMITS 0

DATA INITIAL TEMP.

• I20-I25°F O I26-I80°F

pH

5.5 3.98

U-r

-SURFACE (TO-*)

- d ^

^

H 5 ENERGY, Mw-sec

FUEL AND LIBERATED

FIG.

SURFACE TEMPERATURE RISE IN SUBCOOLED EXCURSIONS

1%

AT PEAK POWER FROM I20°F TO

VS 130

TOTAL °F

ENERGY

t »

100

80

60

>K)

20

L DATA

V

-

-

-

1

_pH_

•t.l H.05 6.3

(T(

1

^

SURFAC

-3 AND 4)

1

C

o V

'A FUE

fTC-;

c

f ^ 1

1

A

)

^

1

V ^

A

A

V

1

o ^

A

O ^

1

A

^

1

3 V 5

ENERGY, MM-sec

FIG. 30

FUEL AND SURFACE TEMPERATURE RISE AT PEAK POWER VS TOTAL ENERGY LIBERATED IN SUBCOOLED EXCURSIONS FROM I50°F

29

The peak powers attained in subcooled excursions a r e shown in Fig . 31 as a function of rec iprocal per iod. A slight dependence of peak power on the degree of subcooling is observed; the re is no detectable effect of the pH of the water . Figure 32 shows the power behavior during three typical subcooled excurs ions . The energy l iberated to peak power in the subcooled excursions is given as a function of period in F ig . 33.

poc

DATA

A • 0 A

• D

lth\o--'o

TEMP., -F

120 120-125 126-130 150

150 154

_pH

4.05 5.5 3.98 4.05

4.10 6.3

4 6 8 10 20

RECIPROCAL PERIOD ( = | / T ) , sec"'

F IG. 31

PEAK POWER VS RECIPROCAL PERIOD FOR SUBCOOLED EXCURSIONS FROM I20°F TO I5U°F

1.0

0.8

0.6

0.4

0.2

h

u

h-

u

1

IN IT

1 .

lAL PERIOD =

^ ^

0.22 s e c —

0.54 sec —

,

/

1

f

1

^ /

- 1 . 0 3 sec

1

^

1 4 6 8 10

TIME (PERIODS) ARBITRARY ZERO

14

FIG. 32

POWER VS TIME FOR SUBCOOLED EXCURSIONS FROM I20°F

19

8

6

4

3

S '<> I

i >: 8 (0 Ui uf

6

4

2

I 2 4 6 8 10

RECIPROCAL PERIOD, sec"'

FIG. 33

ENERGY TO PEAK POWER VS RECIPROCAL PERIOD FOR SUBCOOLED EXCURSIONS

D. Summary of Trans ient Behavior

The relat ionships between peak power, energy r e l ea se , and reac tor period for sa tura ted and subcooled excurs ions a re summar ized in Fig . 34. In both types of excursions the peak power attained was p ropor tional to the rec iproca l period ra i sed to a power with a constant exponent down to a period of about 100 mi l l i seconds . The "break" in the curve that occurs at about this period is based on a single 83-mil l isecond excursion from saturat ion. The sharp "break" was also observed for the subcooled excursions on SPERT-I,(8) although it occur red at a period approximately twice that in BORAX-IV. Fo r a given initial period, the peak power inc r ea se s as the initial core t empera tu re is inc reased .

A major difference in t rans ient behavior between subcooled and saturated excursion is noted by comparison of F i g s . 22 and 27. The two excursions shown had about the same initial period and peak power. In the excursion from saturat ion, the power after reaching the peaklevel decreased rapidly, passed through a minimum, and began to r i s e again. This behavior

-

- —-^— ^ ^ . ^ INITIAL 1 ~ ^ ^ . ^ k

DATA TEMP. pH ? \

0 154-F 6.3 T ^ \ . A i50°F 4.06 1 ^

n I60°F 4.10

1 1 1

v ^

D \

1 > i

31

RECIPROCAL PERIOD, sec'i

100

10

^

r

\-

l

p

p

|-

p

/ 1 _J.

IN

IE

i :

•

BORAX-I (v80°F)

PROMPT POWE

TIAL TEMP

207°F

0-l5lf>F

.0-l30°F

j /

y-

1

R ONLY {'Ô.BB P

1 1

\ \ v> \ ^ \

/y; y

/ '

1

f

- S P E R

1

/

y /

T-I

1

' ' ^ '

1/ /

(68°n

1

/ /

/

8

7

6

r X

>-

i ^ 3

2

1

-

" / /

1

INITIAL TEMP.

I20-I5^

n

/

i I

A;

1 •

° ' ^

i •

, / h

^ o -^ l-Of

/ /

/ /

1

1

o

1

^ •

/

/ -207''F

OA 2 ^ 6 8 10

RECIPROCAL PERIOD, sec"*

0 1 2 3

PEAK POWER X PERIOP, Hw-sec

DATA

O

• T A

INITIAL TEMP.

207°F

207''F

207"'F

I20-I25°F

pH

~ '7 6.3 4.15 5.5

DATA

A D

• V

INITIAL TEMP.

125-130°F

I50°F

ISO-F

l5rF

pH

3.98

4.05

4.10

6.3

F I G . 3U

SUMMARY OF TRANSIENT BEHAVIOR OF B O R A X - H AND COMPARISON WITH BORAX-I AND S P E R T - I

was not observed in the subcooled excursion; the power essent ia l ly leveled off at peak power. This difference in t rans ien t behavior was observed for other excurs ions , as shown in F ig . 35.

5 8 10 12 14 16 6 8 10 12 14 16 18 TIME (PERIODS), arbitrary units

SATURATION (207°F) SUBCOOLED (120°F)

CURVE kg, (0) T. sec CURVE kg^ (0) T , sec

a 0.007479 0.128 a 0.007121 0.220 b 0.006635 0.460 b 0.006385 0.S41 c 0.006875 0.936 c 0.005746 1.03

F IG. 35 POWER AND REACTIVITY LOSS VS TIME FOR SATURATED AND SUBCOOLED EXCURSIONS

Figure 36 shows the t imes required to reach peak power as a function of initial period for both subcooled and sa tura ted excurs ions . Fo r a given initial period, the t ime to reach peak power increased slightly with lower initial water t e m p e r a t u r e s . F igure 34 shows that, as the initial pe riod decreased (i .e. , i nc rease in step-input of reactivity), the energy to peak power decreased in both types of excurs ions . This t rend, in the period range tes ted, was also observed for the SPERT-I excurs ions .

A number of subcooled and saturated excursions were analyzed for the react ivi ty loss during the respect ive excursions (see Appendix C). F igure 37 shows the relat ionship of react ivi ty loss and energy re lease at peak power to rec iproca l period for these t e s t s . Two interest ing c h a r a c t e r i s t i c s a re apparent: (1) the fraction of input react ivi ty compensated at peak power decreased as the period decreased , and (2) the react ivi ty loss at peak power was proport ional to the energy r e l e a s e . Fu r the r analyses showed over the range when the power r i se began to deviate from an exponential type, that the react ivi ty compensated was a l inear function of the total energy re l ease , independent of the initial period, and only slightly dependent of the initial t e m p e r a t u r e . Energy coefficients of react ivi ty of

14

12

10

e

6

4

2

SUBCOOLED

i20-l50°F \ ^

"

-

4

-j

II A /

A °/ ro,/

Jo/

^6>

S

J 1 . /

/

/ / "

DATA

• A

SATURATION

207''F

INITIAL TEMP.,

°F

207

165

120

dU

7(1

8

6

1^

2

o

Z^

^ ^

" • ~ v ^

• 0 O

^

- V

o SATURATED (207°?) V SUBCOOLED (laO-F)

1 i l l

r 1

i

--0-J

1

--

-

-

0.30

0.20

0.10

0.08 *"

0.06 I >-

0.04 E

0.5 I 1.5

ASYMPTOTIC PERIOD, sec

2 4 6 8 10

RECIPROCAL PERIOD, s e C '

F I G . 36

TIME REQUIRED FOR POWER TO RISE FROM 100 WATTS TO PEAK VALUE

FIG. 37

ENERGY AND REACTIVITY LOSS TO PEAK POWER

VS RECIPROCAL PERIOD. DELAYED ENERGY NOT INCLUDED

about 0.0 3 and 0.028% (Ak/k) /Mw-sec for subcooled and sa tura ted excurs ions , respect ively, fit the experimental data in the period range between about one second and 100 mil l i seconds , (in this same range SPERT-l(8) gives about 0.067%/Mw-sec.) Calculations (Appendix C) show that the combined effects of radiolytic formation of gas bubbles and of heating of water and fuel accounted for between 45 and 75% of the react ivi ty in these exper iments .

F igure 38 shows the typical appearance of the special enriched fuel pellets that were contained in the fuel bayonets descr ibed on page 23. The aluminum jackets were dissolved in sodium hydroxide. The lead bond was removed with ni t r ic acid.

Examination of the pellets failed to show any preferent ia l de ter iorat ion due to either enrichment or i r rad ia t ion h is tory . Therefore the final appearances of the pellets must be attr ibuted to factors such as firing or other p roper t ies inherent in the p r e - i r r a d i a t e d ma te r i a l , as well as to possible damage due to handling.

V. ATMOSPHERIC PRESSURE BOILING

Upon completion of the t rans ient t e s t s , the reac tor was operated at various power levels and core loadings with the p r e s s u r e vesse l open to the building a tmosphere .

BAYONET N0„ f-e

ENRICHMENT NORMAL

MIN. PERIOD, sec

MAX. POWER, Mw

TOTAL ENERGY, Mw-sec

— 290M

2X

0.50

3.30

335.6

«\j

D

i*x NORMAL

290B

2X

0.070

7*

NOT MEASURED

m

if

•IX

r>

f\j

• • il

ÛNIRRADIATED-

NORMAL 2X

•EXCURSION FROM I Mw POWER

NOTE: TOTAL ENERGY INCLUDES SOME LOW-POWER STEADY-STATE TESTS.

FIG. 38

TYPICAL APPEARANCE OF SPECIAL ENRICHED FUEL PELLETS REMOVED FROM FUEL BAYONET DETECTORS.

35

A. Reactivity in Steam Voids

The react ivi ty held by the s team voids was determined by measur ing the changes in positions of the shim blades using the cal ibrat ion obtained at zero power (207°F). The resu l t s for the various core loadings a re summar ized in F ig . 39.

FIG. 3S

REACTIVITY IN STEAM VS POWER FOR VARIOUS CORE LOADINGS

Figure 40 shows the react ivi ty held in s team voids as a function of average power density. On this bas i s , there a re no detectable differences between the core loadings studied. The sca t te r in data is probably due to e r r o r s in the worths of the shim blades , inaccuracies in zero-power condit ions, and uncer ta int ies in the power ca l ibra t ions . F igure 41 shows that the average power density coefficient of react ivi ty (Ak/AP) increased as the power increased . The highest average power level attained during this s e r i e s of t e s t s was about 4.6 Mw (42 fuel assembl ies ) , with slightly less than 1.6% react ivi ty held by the s team (Fig. 42).

B. Fuel and Clad Tempera tu res

F igure 43 shows the maximum measu red and calculated t e m pera tu re r i s e s of the fuel and surface of abayonet located in the center of the

1.6

1.4

1.2

1.0

DATA NO. OF FUEL ASSEMBLIES

<

0.8

S 0.6

0.4

0.2

V D A O

30 31

39 (WITH OSCILLATOR) 42 (WITH OSCILUTOR)

(57

V V

-w^ o

tn

d

a n

^ CO

^ ^

V O o

(t

J _

10 IS 20 25

POWER DENSITY, kw/liter of coolant

F IG. UO

REACTIVITY IN STEAM VS POWER DENSITY

30 35

POWER POWER

FIG. 141

DEPENDENCE OF THE RECIPROCAL OF THE DENSITY COEFFICIENT OF REACTIVITY

37

- ONE CYCLE

OSCILLATOR POSITION

^ R n n niiT ^-u

POWER (LOG), Mw: 4 .57 (AV6.)

ROD OUT ^ROD IN

9.59 r-17.4

l l l l l l l l l l l l l l H l l l l l l l l l l l l l l l l l l l l l l l l l l

-38.8 v - 6 6 . 4

SCRAM

i i i i i i i i n i i i i i i i i i l i i i i i i i i i l i i i i i i i i i l i i i i i i i i i l i i i i i i i i i l i i i i i i i i i - ^ | - ^ 0.1 sec

WATER HEIGHT ABOVE FUEL = 4 .25 f t . REACTIVITY IN STEAM = l.535?l A k / k .

F I G . U2

U.57-MW POWER TEST WITH OSCILLATOR IN lt2-ASSEMBLY CORE

THEORETICAL

25

20

15

10

5

0

O

_ • A

_

A A

^ O

•

—

TC-4

TC-5

TC-6

A

•

1

^ h J

A

A

0 •

IN CORE CENTER

A

•8 •

o

1

A

^ ^ ^ A A AA A A cu

0 * o • • oo

SURFACE

1 1 1

•

O

• A

1

8

A

1 0.5 1.0

POWER, MM

2.0 3.0 4.0

MAXIMUM 30-AND

MEASURED TEMPERATURE 31-ASSEMBLY CORES

RISE IN

FIG.

FUEL AND DURING STEADY-STATE

H3

SURFACE

POWER

OF TESTS

FUEL BAYONET AT CENTER OF

38

core during s teady-s ta te power t e s t s . The calculated curve was based on the following t empera tu re differentials in the fuel bayonet:

Power, Mw

1 2.5 4

Temp

Fi lm

14.7 21.5 24.1

e ra tu re

Al

0.53 1.32 2.11

Difi °F

"erentia

P b

1.38 3.53 5.64

1(AT)

Fuel

40.6 105 176

Total Tempera tu re Differential,

°F

57.2 131.4 207.9

The d iscrepancies between the measured and calculated values can be a t tr ibuted to uncertainty in the the rmal conductivity of the fuel, possible small air gaps, and the sys temat ic experimental e r r o r s associa ted with the difficult a r t of measur ing fuel t empera tu re s by thermocouples . It has been es t imated that a gap in the fuel region occupied by the thermocouple can resul t in an e r r o r of ~4°F.

C. Water-Head Effect

F igure 44 shows the effect of water height above the fuel on the power densi t ies for various core loadings. Fo r a given loading, the react ivi ty held by the s team voids was maintained constant. It appears

10 15 20

POWER DENSITY, ku/llUr of coolant

IS 20

(kw/llterl / ( Ak In stou

FIG. VI

EFFECT OF WATER HEIGHT ABOVE FUEL ON POWER DENSITY AND THE RECIPROCAL OF ITS REACTIVITY COEFFICIENT

39

that water heights g rea te r than about four feet above the fuel had li t t le effect on the power output. However, the power decreased rapidly as the water level dropped to two feet (to the top of r i s e r ) . This is to be expected because of the consequent dec rease in rec i rcula t ion ra te and, pe rhaps , the change in core boiling boundary effected by the stat ic head. The slight inc rease in power density with a water head g rea t e r than four feet may be due to the resul tant increase in average core p r e s s u r e .

F igure 45 is a l inear ins t rument recording of the flux behavior as the top reflector was boiled off. The oscil lat ions became more p r o nounced as the water level fell below the top of the r i s e r , despite the smal l react ivi ty held in the s team.

INITIAL CONDITIONS

POWER = 2.52 Mw WATER HEIGHT ATOP FUEL = 5.75-4.33 ft

SHIM BLADES GOING IN 1.69 Mw

2.08 ft.

UNSTABLE

FIG. H5

OPERATION RESULTING FROM (REACTIVITY IN STEAM

BOIL = 0.

-OFF 695%

OF TOP Ak/k)

REFLECTOR

Heiland recordings of the central fuel and clad surface t e m pe ra tu re s and of the reac tor power during the reflector boil-off wêre used to determine the reac tor power - to - t empera tu re t r ans fe r function, A T / ( A P / P ) . The resul ts for these oscil lat ions where

AP _ amplitudes P average power = 0.5

and the f r e q u e n c y was 0.495 c y c l e / s e c o n d , a r e g iven in Tab le I. The p h a s e s i nd i ca t e t ha t the t e m p e r a t u r e l a g s beh ind the p o w e r .

T a b l e I

P O W E R - T O - T E M P E R A T U R E T R A N S F E R FUNCTIONS [ A T / ( A P / P ) ] ~~"

Clad Sur face F u e l

Magn i tude , °F

5.64 10.22

P h a s e , d e g r e e s

- 44.6 -141 .2

D. Se l f - Induced O s c i l l a t i o n s

As in the p r e v i o u s BORAX r e a c t o r s , ( 1 " ^ ) SPERT-I,("^^ and EBWR,\ ' s e l f - i n d u c e d o s c i l l a t i o n s o c c u r r e d above a c e r t a i n p o w e r t h r e s h old. The t h r e s h o l d i s def ined a s the p o w e r l e v e l at which a s e q u e n c e of two o r m o r e o s c i l l a t i o n s of the s a m e f r e q u e n c y a p p e a r above the bo i l ing n o i s e b a c k g r o u n d . The t h r e s h o l d for the 3 1 - a s s e m b l y c o r e w a s —1.8 Mw or 0.4% r e a c t i v i t y in s t e a m . F i g u r e 46 shows a t y p i c a l r e c o r d i n g of r e a c t o r o p e r a t i o n wel l above the o s c i l l a t o r y t h r e s h o l d . (This t e s t was u s e d for the s p e c t r a l a n a l y s i s d i s c u s s e d in Sec t ion VI -C. )

UJ

A.

24 22 20 18 16 \^ 12 10 8

TIME, sec

FIG. U6

SELF-INDUCED OSCILLATIONS DURING OPERATION WITH 31-ASSEMBLY CORE AT 3.13 Mw AND ATMOSPHERIC PRESSURE WITH 0.915% REACTIVITY IN STEAM

F i g u r e 47 shows the r a t i o of a m p l i t u d e to a v e r a g e p o w e r i s a funct ion i n c r e a s i n g with a v e r a g e p o w e r . Using the z e r o - p o w e r t r a n s f e r funct ion at the a v e r a g e f r e q u e n c y of 1 c y c l e / s e c ,

- ^ = 109.2 N dk

41

The ordinate of F ig . 47 can be converted to the Ak associa ted with the o s cillation. Dividing this value by the react iv i ty in s team gives the osc i l la tion fraction of react ivi ty (Fig. 48). If the oscil lating fraction of react iv i ty is in terpre ted as an oscil lation of void content, then the void osc i l la tory fraction is typically about 0.1 for smal l osc i l la tory operat ion.

0.20

FIG. 1(7 AMPLITUDE OF NATURAL OSCILLATIONS DIVIDED BY AVERAGE POWER VS. AVERAGE POWER FOR A 31-ASSEMBLY CORE

0.1428

0.1071

3P a,a 0.07m

-

-

-

i 1 /

/

/ 1

rfi / o

1 1

)

1

,-o-

1 1 0.2 0.1) 0.6 0.8 1.0 1.2 I.It I.

REACTIVITY IN STEAM. « ik/k

OSCILLATING FRACT

OF REACTIVITY IN

ION OF

STEAM

FIG. >I8

REACTIVITY IN STEAM AS A FUNCTION

The his tory of oscil lation studies shows that, when the r e a c tivity amplitudes in osci l la tory behavior a re somewhat l ess than 0.75% Ak, their waveforms a r e ei ther sinusoidal or very non-sinusoidal . The la t te r type is r a r e but has been observed in the EBWR.(l°) The BORAX-IV data is p resumed to have given evidence only of the former type.

When the power level is sufficiently above the se l f -osc i l la tory threshold, the amplitude of the oscil lat ions can become quite l a rge .

42

Figure 42 shows the 42-assembly core , with the rod osci l la tor , reaching an unstable point at 4.57 Mw, which is well above the threshold for this core loading. The oscil lat ions produced by rod cycling are negligible by comparison with the noise and self-induced oscil lat ions even before the final d ivergence. F igure 49 compares the power with the corresponding react ivi ty at the end of this t e s t . It should be noted that the react iv i ty peaks a r e in the vicinity of prompt c r i t i ca l . Eventually about one-half the react iv i ty in s team (Fig. 42 shows 1.535% Ak/k) appears as excess react ivi ty at the peak. This might be in terpre ted that one-half of the equil ibrium voids disappear from the r eac to r . The violent osci l lat ions a re evidence of a t rend toward lower frequency, a conclusion obtained by compar ison with the smal le r oscil lat ions at the beginning of the t es t . P r e sumably the shift in frequency, along with the limiting amplitudes attained, eventually might be understood in t e r m s of the nonlinear effects which ent e r into the hydraul ic relat ionships of natural circulat ion boiling.

1.2

0.8

0.4 + 0

t -

£ 0.8 o iS

" 1.2

1.6

2.0

2.4

.4

1.2 1.6

TIME, sec

FIG. 90 DIVERGENT REACTIVITY AND POWER OSCILLATIONS AT END OF 11.57-M* TEST (Fid. 42).

Another example of l a rge self-induced oscil lat ions is shown in Fig. 31. The apparent contradiction of the reac tor becoming less stable as the power dec reases is eas i ly explained: the osci l la tory threshold dec reased more rapidly than the average power upon loss of water height above the fuel.

VI. P R E S S U R I Z E D BOILING

With one excep t ion , p r e s s u r i z e d o p e r a t i o n s (in the r a n g e f r o m 70 to 300 ps ig ) w e r e p e r f o r m e d wi th a c o r e load ing of 59 fuel a s s e m b l i e s ( F i g . 15) o r wi th the m a x i m u m a m o u n t of r e a c t i v i t y c o n t r o l l e d by the c o n t r o l b l a d e s at r o o m t e n n p e r a t u r e . One t e s t was conduc ted with a c o r e l o a d ing of 69 a s s e m b l i e s at a p r e s s u r e of 322 p s i g . In t h i s load ing , the b o r o n r o d s w e r e r e m o v e d f r o m the c e n t r a l a s s e m b l i e s , and b o r i c ac id at r o o m t e m p e r a t u r e was added to a s s i s t in c o m p e n s a t i n g for the e x c e s s r e a c t i v i t y . The m e t h o d s of o p e r a t i o n w e r e e s s e n t i a l l y the s a m e as for BORAX-I I I .

In m o s t c a s e s , the p o w e r s w e r e c o m p u t e d f rom a hea t b a l a n c e b e t w e e n r e a c t o r h e a t , s t e a m flow, and f e e d - w a t e r flow, the m a i n s t e a m and feed w a t e r - f l o w r a t e s be ing equal du r ing s t e a d y - s t a t e o p e r a t i o n .

A. R e a c t i v i t y in S t e a m Voids

The r e a c t i v i t y in s t e a m vo ids is def ined as tha t r e a c t i v i t y c o r r e s p o n d i n g to the p e r i o d tha t would be g e n e r a t e d if a l l t he s t e a m voids d i s a p p e a r e d . [This i s equ iva len t to u s ing the r e s u l t s of the c a l i b r a t i o n (4 s h i m s a s a bank) , ob ta ined at o p e r a t i n g p r e s s u r e but z e r o v o i d s , of the con t r o l b l a d e s . The two con t ro l b l ade p o s i t i o n s , i . e . , a t z e r o power and at p o w e r , a r e then u s e d with t h i s c a l i b r a t i o n . ]

F i g u r e 50 shows the d e p e n d e n c e of r e a c t i v i t y in the voids on the p o w e r l eve l and p r e s s u r e . It i s obvious tha t a p p r e c i a b l y h i g h e r s t a b l e p o w e r s and p o w e r d e n s i t i e s can be a t t a i ned at e l e v a t e d p r e s s u r e s . Thus for a g iven p o w e r d e n s i t y the s t ab i l i z i ng inf luence of p r e s s u r e in B O R A X -IV is s t r o n g e r t han the l o s s of s t a b i l i t y e x p e c t e d f r o m l a r g e r n e g a t i v e void coef f ic ien ts at h igh p r e s s u r e s ( see Appendix B) .

B . Self-Induced O s c i l l a t i o n s

The s e l f - i n d u c e d o s c i l l a t i o n s w e r e of the s a m e type o b s e r v e d d u r i n g the t e s t s at a t m o s p h e r i c p r e s s u r e . The o p e r a t i n g c h a r a c t e r i s t i c s of BORAX-IV and the p r e v i o u s BORAX sys tenns a f f i rm tha t l o w e r p r e s s u r e s and h i g h e r p o w e r s a r e m o r e conduc ive to s e l f - i n d u c e d o s c i l l a t i o n s . F i g u r e 51 shows the o n s e t of o s c i l l a t i o n s as the p o w e r is i n c r e a s e d with c o n s t a n t p r e s s u r e at 100 p s i g . By the def in i t ion u s e d h e r e , the o s c i l l a t o r y t h r e s h o l d is about 6 Mw at 100 p s i g . The r e s o n a n t f r e q u e n c i e s i n c r e a s e d wi th p o w e r ( F i g . 52), which i s a l s o in a g r e e m e n t with p r e v i o u s BORAX o p e r a t i o n s . The f r e q u e n c i e s w e r e s o m e w h a t h i g h e r t han o b s e r v e d du r ing the t e s t s at a t m o s p h e r i c p r e s s u r e .

P e r h a p s the f i r s t s u c c e s s f u l a p p l i c a t i o n of a p e r i o d s c r a m to the o p e r a t i o n of bo i l ing r e a c t o r s w a s d e m o n s t r a t e d by the t e r m i n a t i o n of

44

22

20

18

16

l i t

::: 12

S 10 o

\-

u

h -

\—

\—

\—

'[—

DATA

• O /

l-

L • A

1

i

•

NO. OF FUEL ASSEMBLIES

59 &9 69

A A

1

• / A

1

P

y

^

1

RESSURE. psio

296 300 322

/ A /o

o

/

1

—

/

A

o/ /

/

1

A

1 3 It

REACTIVITY IN STEAM, %, Ak

F I G . 50

REACTIV ITY IN STEAM AS A FUNCTION OF POWER AND PRESSURE

45

W\f''''^^^''Â^JWA>v^^

r " 7 J' • F

i f :: I : 6.48 Mw

. . ; . ; 8.55 Mw

Hi i n :;!.

-JU I sec TIME, sec

ONSET POWER

OF AND

SELF-

FIG. 51

-INDUCED OSCILLATIONS CONSTANT PRESSURE AT 100

WITH psio

INCREASED

FIG. 52

RESONANT FREQUENCY OF SELF-INDUCED OSCILLATIONS

DURING OPERATION WITH 59-ASSEMBLY CORE AT CONSTANT

PRESSURE (100 PS is)

7 POWER, HH

a test at 8.55 Mw and 70 ps ig . As shown in F ig . 53 the rat io of power o s cillations to randonn noise was re la t ively high during the course of the t es t . At the t ime of period s c r a m the reac tor was on a half-second per iod for about a quar te r second, the condition requi red for s c r amming .

PERIOD SCRAM 10.8 MM

TIME, sec

PRESSURE POWER DENSITY REACTIVITY IN VOIDS

70 psig

33.4 kw/liter of coolant

5.8(

LINEAR POWER TERMINATED BY

FIG.

TRACE OF PERIOD-

53 8.55-M* INDUCED

OPERATION SCRAM.

A significant observat ion made during this s e r i e s of t e s t s was that the ra te of r i se of the envelope of the annplitudes was not excess ive . In a region of increasing amplitudes the variat ion in react iv i ty associa ted with the power oscil lat ion can be re la ted by the express ion

ko e' a t sin cot

where the damping constant, a, is slightly negative and also t ime dependent. Theoret ical considerat ions indicate that a should become strongly negative as the react ivi ty in void becomes more negative. Previous BORAX reac to r s with l ess react ivi ty in voids have shown substantial ly s t ronger negative values of a . The inference is that the hydraul ics and hea t - t r ans fe r cha rac te r i s t i c s of BORAX-IV a re less conducive to d iver gent oscil lations for a given react ivi ty in voids.

Production of U 233

Figure 54 shows the total loss in react iv i ty as a resul t of intermittent experimental operation for one year , equivalent to 300 MWD. The loss includes effects due to burnup of U^ ^ and boron rods , as well as the production of U^^ , s amar ium, and miscel laneous fission products . Computations based on the theoret ical initial conversion rat io for U^^ :

0.227 atom U"^ generated atoms U^ 5 destroyed

show that 71 gm U were produced

I o.a

100 ISO 200

IRMOItTIOII. Had

FIG. Btt

CUMULATIVE REACTIVITY LOSS OURINGrRRADIATION

VII. TRANSFER FUNCTION MEASUREMENTS

A. Rod Osci l lator Exper iments

The reac tor t ransfe r function, G (to) = (n/'N)/"kj^^, is defined experimental ly as the rat io of osc i l la tory power amplitude to average power, n/N, caused by a driving osci l la tory react ivi ty amplitude, ki^ , having a frequency 00/2TT. All quantities a r e complex, i .e . , having both a magnitude and a phase . An equivalent, although more elegant and fundamental , definition is that G(co) is the Fou r i e r Transform of the kerne l , B(a), in the convolution

^ (t) = jB{a) kin (t -CJ) da N

Figure 12 shows a typical loading used for the rod osci l la tor exper iments at a tmospher ic p r e s s u r e . The osci l la tor rod assembly consis ted of a water-f i l led cadmium tube (12 in. long) with an aluminum tube extension. The extension tube was connected to a drive mechanism designed to generate a sinusoidal rod s t roke (up to 9 in.) and thus to produce a sinusoidal variat ion in react ivi ty . Since the osci l la tor rod replaced a fuel assembly and consequently introduced a water hole in the core , it is

probable that the nuclear and hydraulic cha rac t e r i s t i c s of these loadings differed from those of the smal le r c o r e s . However, for a given power density. F ig . 40 shows the react ivi ty in voids is about the same for all cores during operat ions at a tmospher ic p r e s s u r e . The magnitude and phase of n /N were determined by the tedious method of reading the chart recording for many amplitudes and phases , and averaging the r e s u l t s . F igure 55 shows a typical recording . The disadvantage of this method is the loss of p rec is ion because of the poor s ignal - to-noise ra t io at high powers . An improved analytical technique is to compute the c ros s c o r r e l a tion function between the control rod and the reac tor power. This can be done ei ther by analog or digital methods . Unfortunately, the n e c e s s a r y equipment was not readi ly available to p rocess the BORAX-IV data.

NOTE: PIPS OCCUR WHENEVER OSCILUTOR ROD OF 0.5055i Ak AMPLITUDE IS AT THE TOP OR BOTTOM OF ITS STROKE.

FIG. 55

TYPICAL OSCILLATOR ROD TEST WITH .25* REACTIVITY IN STEAM AT ATMOSPHERIC PRESSURE.

The value of k^^ was de termined from a period generated by moving the osci l la tor rod a fraction of a cycle from cr i t ica l i ty at zero power.

The measured values of the amplitude and phase of the t r a n s fer function are plotted in F i g s . 56 and 57. The d iscrepancies between

190

180

_ 1 7 0

Jl60

— 150

^ U O

< "~I30 - 120 •<

110

100

90

60

HO

30

20

£ 20

30

W

50 .1

(A)

MEASURED

— ^ fB =

1

^ ^ ____

EOR^TIi:

.0081*5

1 1

.^^

AL 1

1

(F)

260

2110

220

200

180

160

I W

120

100

80

60

50

W

30

20

ASSEMBLIES:

POWER, Mw:

% Ak(voids1: i Ak AMPLITUDE OF ROD:

112

.0018 t .0016

0

.0935 i .0505

(a)

39

.78

.15

.100

\ \

\ , V

1

\ \ .

(B)

N , s

1

• ^

1 1

200

190

180

170

16C

150

140

130

120

110

100

50

W

30

20

r 1 i \

\ \

\ ^ \

\

1 1 1

\ \ V \

, , \ (CI

(H)

FREOUEHCY, cps

HZ .81

.145

.0505

240

220

200

180

160

140

120

100

80

60

40

50

40

30

20

20

30

40

50

(U

42

.87

.10

.0933

N s

\ ^ k ;

(D)

V ..

1

• ^

_ L J -1 1

240

220

200

180

160

140

120

100

80

60

40

50

40

30

20

\

(E)

\

V

> \ , \

1

\ r^r^

1 ' 1

• > ^

11

(J)

42

1.48

.25

.0505

F I G . 56

SUMMARY OF ROD OSCILLATOR TESTS FROM ZERO POWER TO I .U8 Mw

o

260

240

220

tj200

< 180

^ 1 6 0

^ 1 4 0

120

; 100 <9

80

60

40

50

40

30

20

20

30

40

50

/

r-1 /

'

i_

s, \

1

\ \

1

1

\ \

(A)

^ \ ^

1

^^

1 -1 1

(F)

ASSEMBLIES:

POWER, MM: « AkfVOIDSl:

% Ak AMPLITUDE OF ROD:

42 1.77 .32 .0505

280

260

240

220

200

180

160

140

120

100

80

60

50

40

30

20

/ /

/ / /

1

V \

1

v

,

-

(B)

\ \

\

1

\

1

\

,.,L

•v

X

(G)

39

1.96

.37

.100

280

260

240

220

200

180

160

140

120

100

80

60

70

60

SO

40

30

20

/ /

/ / /

1

K \

1 1

\ j

11 (C)

\ \

\

K \ \

1111

\\ w N

1 hi

(H)

FREQUENCY, cps

39

2.54

.55

.IOC

360

340

320

300

280

260

240

220

200

180

160

140

80

70

60

50

40

30

20

1 I \

1 , ,

\

\ \

M \

, N

20

(D)

111

\

\

1 1 1 1

\ \ 1 1 N !

, i , > (I)

39

3.29

.77

.100

540

500

460

420

380

340

300

260

220

180

140

100

50

40

30

20

+

0

20

30

40

50

(

^ A v\

/

1 1 1

\

K r 1

(E)

1

\ \ \ \

\ \\

\ 1 1

\ \ \

11

(J)

42 3.40

.725

.0505

F I G . 5 7

SUMMARY OF ROD OSCILLATOR TESTS FROM 1 . 7 7 Mw TO 3 . H O Mw

51

the measu red and calculated zero power t ransfe r function (Fig. 56) may be due to chamber location or to phase shifts in the electronic sys tem (see Appendix B).

The rod osci l la tor m e a s u r e m e n t s , the f i rs t of their kind p e r formed on boiling r e a c t o r s , a re considered to be a major s tep forward in the understanding of the se l f -osc i l la tory tendencies of boiling r e a c t o r s . A sharp resonance in the t ransfer function was observed in the region of the se l f -osc i l la tory frequency. F igure 58(a) shows that the resonant gain increased with power. The half-width of the resonance decreased as the power inc reased . Finally, as shown in Fig . 58(b), the resonant frequency increased with power, the same effect observed for the self-induced o s ci l la tory frequency.

.006

.007

.006

3 | . 0 0 5

i.003

.002

k

\

(A)

\

\

\

\ \

O

\

\

-

\ y

^ ^ \

^

\

\

2 a

POWER, H H

/

(B)

° 1

/ /

,f U 6,

/

/ / o

H

/ ;

I 2 3 4 5 6

POWER, MM

F I G . 5 8

BEHAVIOR OF GAIN AND FREQUENCY OF THE TRANSFER FUNCTION WITH POWER

Experience with the rod osci l la tor technique in BORAX-IV (and subsequently in EBWR) affirmed that the method may be used to obtain information on boiling reac tor stabil i ty at low power levels without incurr ing the r i sk associa ted with l a rge , self-induced chugs at the unstable point at high power l eve l s . When a completely sa t is factory theory of instabili ty exis t s , the constants can be evaluated by low-power t ransfe r function measu remen t s , and the theory then applied to higher powers . If all that exists is a phenomenological theory, then it can at leas t be used to predict t ransfe r functions at powers slightly above those me a s u re d .

Finally, F ig . 59 shows than an empir ica l relat ionship exis ts between the rec iproca l of the resonant gain and the rec iproca l of the o s c i l la tory amplitude divided by the average power. Such a cor re la t ion can

52

£ _ .0016

S i K M

^2 .0012

[-

l-

l-

[-

[- y /

a / ^

K y

y y

y / "

FIG. se

OSCILLATION GAIN tND HtXIHUH SELF-INDUCEO

OSCILLATION FOR THE SAME Ak IN STEAM VOIDS

2 t t S 10 12 I t 16

l / (AN/ l l ) OF SPORTANEOUS OSCILLATIONS IN SI-ASSENtLY CORE

be used to es t imate self-induced osc i l la tory amplitudes at higher powers , provided that the t ransfer function data at lower powers can be extrapolated sat isfactor i ly by the theoret ical method d iscussed in Appendix B.

B. Ringing Tests

In its general form, the ringing tes t consis ts of introducing a sudden step disturbance into a system and measur ing the resul tant response of the sys tem. The t e r m "ringing" is derived from the populari ty of such tes ts on resonant acoustical sys tems in which an audible ring resu l t s from a step input. The ringing tes t has been proposed by Bethe( l l ) for fast r e ac to r s .

As applied to BORAX-IV, the ringing tes ts consisted of a s e r i e s of ejections of the central blade at var ious initial powers , the procedure otherwise being s imi la r to the conduct of excurs ions from essent ia l ly zero power. The resu l t s of this s e r i e s of t es t s a r e typified in F ig . 60. It was found from many such tes t s under var ious conditions that the damping of the dis turbance decreased as the power increased . This is to be expected since the peak in the t ransfe r function "sharpened" as the power inc reased .

The t ransfer function from a ringing tes t is given by

^ " ^ " N(0) ko j N(°°) - N(0) + iiA [N(t) - N(<x))] e-i^t dt (1)

where N(t) is the reac tor power that is disturbed by the step input of r e activity, ko, at t = 0. F igures 61 and 62 show the amplitude and phase of

53

1.0

0.8

0.6

to

i > : o.H — h-.o —

<d —

ul 12

0.2

0.2

- / \ \ \

--

~ r\ - / N J —

— -

- /

-

~ l 1 1

/-POWER

T / INI I IAL = 1.33 MW \ y FINAL = 2.79 Mw

\

\

\

\

\ " "

\

V/ \

\

\ ^

1 1 1

^ — '

-REACTIVITY

y ^^-^

1 1 1

/

/ /

/

/ /

/

1 1 1

y /

/

y^

1 1 1 1 1 1

^

v _____

1 1 1 1 1 1

^

^ - ^

1 1 1

-

-

_

-

..^

-

-

1 . I 2 3

TIME, sec

F I G . 60

RINGING TEST ON 31-ASSEMBLY CORE AT ATMOSPHERIC PRESSURE. STEP INPUT OF REACTIVITY = 0.1(5%

1200

1100

1000

900

800

700

600

500

400

300

200

100

-

-

-

-

-

-

-

-

-

-

—-

c

1

o

o

V

1

/

1

\

\

-

DATA

o

^ . 7 5 ) 1 A

V J

RINGING TEST

ROD OSCILUTOR

I (VOIDS)

^ . 3 * Ak

i

VOIDS

1

)

1 1 0.1

i)/2jt :: FREOUEHCY, cps

AMPLITUDE

OSCILLATOR

F I G . 61

OF TRANSFER FUNCTION

AND BY RINGING TEST DETERMINED

{ F l o . 6 0 ) .

BY ROD

to

30

20

10

I * I 0 Ul

i 10

20

30

to 0 ,1 0 . 2 O . t 0 .6 0.8 I 2

<,)/2ii = FREQUENCr. cps

PHASE

BY ANGLE

RINGING

OF TEST

FIG TRANSFER FUNCTION

( F I G . 60)

62 DETERMINED BY ROD OSCILLATOR A D

the t rans fe r function determined by Eq. (1), using the resu l t s of Fig . 60. Transfer functions determined by the rod osci l la tor technique a re included for compar ison.

The resu l t s obtained by the two methods did not agree for severa l r ea sons . The respect ive core volumes differed by about 30%. The core for the rod osci l la tor tes t contained a l a rge water hole. The step input of react ivi ty in the ringing tes t was somewhat la rge for s t r ic t application of Eq. (1). Fu r the r , because of the reac tor noise, the resu l t s of a ringing experiment a re somewhat s ta t is t ical ly uncertain, unless many such experiments a re averaged. Finally, the t ransfe r function m a y b e amplitude dependent.

Because of its s implici ty and rapidity of execution, the ringing tes t affords approximate stabili ty information via the reac tor t r ans fe r function. The analysis need not be involved provided an approximate m a x imum value of the t rans fe r functions is sufficient for immediate purposes . Fo r example, if the power for t >0 is r epresen ted approximately by a fit of the form

N(t) = N(0) + A sin (o)'t + 0) e" °*

then at

1

RlRoma TEST ~ ^

1 ^

\

1 ROD OSCILLAT(

. 3 * REACTIVI

^ ^

R /

y IN VOIDS

1

V \

\

^ ^

0

1

1

ROD

11

OSCILLATOR

' . 7 6 * REACTIVITY

IN VOIDS 1

1

v \

A r*"""

\ \

1

\ \

00 = CD'» a ( i .e. , at a sharp resonance) ,

t he m a x i m u m va lue for E q . ( l ) i s :

, ,. ~ AO)' 2 N(0) a ko

C. P o w e r - F r e q u e n c y S p e c t r u m

Moorei-'-^) h a s s u g g e s t e d tha t the u s e of a u t o c o r r e l a t i o n m e t h o d s to ob ta in the p o w e r - f r e q u e n c y s p e c t r u m m a y a l s o y ie ld i n f o r m a t i o n about the r e a c t o r t r a n s f e r funct ion . In t h i s r e s p e c t bo i l ing r e a c t o r s a r e idea l s y s t e m s s ince the r e s o n a n t c h a r a c t e r i s t i c of the t r a n s f e r funct ion can be e x p e c t e d to " s h a p e " the bo i l ing n o i s e so tha t t he p o w e r - f r e q u e n c y s p e c t r u m wil l a l s o h a v e a r e s o n a n c e .

The f i r s t s t e p in ob ta in ing the s p e c t r u m i s to c o m p u t e the a u t o c o r r e l a t i o n funct ion , 0 ( T ) , for v a r i o u s c o r r e l a t i o n t i m e s , T, f r o m the p o w e r t r a c e of an u n d i s t u r b e d s t e a d y - s t a t e bo i l ing t e s t :

2 n ( t . ) n ( t . + T )

^('^^ - Z n ( t . ) n ( t . ) '

w h e r e n(ti) r e p r e s e n t d e v i a t i o n s of the p o w e r at t i m e s , tj^, f r o m the a v e r a g e va lue of the p o w e r . T h u s 2 n (tj ) = 0.

i The a u t o c o r r e l a t i o n funct ion of a t y p i c a l p o w e r t r a c e ( F i g . 46)

i s shown in F i g . 6 3 . Since s t a n d a r d a u t o m a t e d t e c h n i q u e s for ob ta in ing th i s funct ion w e r e not a v a i l a b l e , only 200 po in t s in a 2 0 - s e c o n d i n t e r v a l w e r e u s e d . The s t a t i s t i c a l u n c e r t a i n t y of the c u r v e d e t e r m i n e d f r o m 200 po in t s i s l e s s t han would be o c c a s i o n e d by the u s e of only 49 p o i n t s . Suff ic ien t p r e c i s i o n e x i s t e d , h o w e v e r , to o b s e r v e tha t the a u t o c o r r e l a t i o n funct ion was a s t r o n g l y d a m p e d c o s i n e funct ion d u r i n g the f i r s t s e c o n d of c o r r e l a t i o n t i m e .

By W i e n e r ' s t h e o r e m , the F o u r i e r t r a n s f o r m of 0 ( T ) i s the f r e q u e n c y s p e c t r u m of the p o w e r d e v i a t i o n s , n :

W(f) = / 0 ( T ) cos 27TfTdT

As e x p e c t e d . F i g s . 64 and 65 show tha t W and v W p e a k s h a r p l y in the r e gion of the r e s o n a n c e f r e q u e n c y of the r e a c t o r . The quan t i ty v W m a y have s p e c i a l s i g n i f i c a n c e , as po in ted out by Moore . \ 1^ ) If the bo i l ing n o i s e b e f o r e be ing " s h a p e d " by the r e a c t o r t r a n s f e r funct ion i s "wh i t e " ( i . e . , i t s f r e q u e n c y s p e c t r u m is a c o n s t a n t ) , then -/W i s p r o p o r t i o n a l to

2.5

2 .0

1.5

1.0

M 0.5

0.5

1.0

j-

[-

1 (

h

>

L

• V i l 1 1 1

L

\.

1 1 1 1

DATA

O

D

A

• A

r r A

1 1 1 1

BASED ON

200 POINTS

1st 49 POINTS

2nd 49 POINTS

3rd 49 POINTS

4th 49 POINTS

A

J 1 1 1 1

A \

1 1 1 1 2 3

CORREUTION TIME ( T K sec

AUTOCORRELATION

AT 3.13 Mw (FIG

FIG.

FUNCTION

. U6)

63

FOR TYPICAL POWER TRACE

^ 0.6

-

I

r

r 1 1 1° 1

i I r

0.4 0.6 0.8 I FREQUENCY, cps

REACTOR CONPITIONS

ATMOSPHERIC BOILING

POWER 3 . 1 3 Nu

K Ak (VOIDS) . 9 1 5

NO. ASSEMBLIES 31

FOURIER INTEGRATION OVER 3 CYCLES

FOURIER INTEGRATION OVER 4 CYCLES

FIG. 64

FOURIER TRANSFORM OF BORAX-II AUTOCORRELATION FUNCTION

REACTOR CURVE CURVE • CONDITIONS (A) fB)

ATMOSPHERIC BOILING POWER, MM 3.13 4.18 % Ak (VOIDS) .915 .91 NO.ASSEMBLIES 31 42

'BY ROD OSCILLATOR TECHNIQUE

0.4 0.6 0.8 I 2

FREQUENCY, cps

F I G . B 5

BORAX- IT TRANSFER FUNCTION BY AUTOCORRELATION

the amplitude of the t ransfe r function. For purposes of compar ison, a r e -normal ized rod osci l la tor t ransfe r function is included in F ig . 65.

If not constant, the input boiling noise spec t rum should vary slowly in the resonance region; thus the square root of the output frequency spect rum should be a good approximation of the reac tor t ransfe r function.

In summation, Four i e r analysis of the reac tor autocorre la t ion function can provide data on reac tor t r ans fe r functions w ith a minimum of experimental work. Fu r the r , with appropria te automating p rocedures , the data analysis can be quite rapid and effor t less .

I .U

w

c

.a

f 0.6

0.2

-

-

-

-

(B)

/

/

1 1

1 f

(A)

\

\ \

V

I . U

58

APPENDIX A

REACTOR CORE PHYSICS

Cri t ical i ty Calculations

Phys ics calculat ions made p r io r to initial c r i t ica l i ty had ove r es t imated the react iv i ty of the core . Two-group theory predic ted a cold, clean cr i t ica l core of 15.5 fuel a s s e m b l i e s , whereas BORAX-IV f i r s t achieved cr i t ica l i ty with a core loading of 28 a s s e m b l i e s . The d ispar i ty between theory and exper iment may be a t t r ibuted to (1) the calculat ions which ignored the effects on react ivi ty of control rods in the top ref lec tor and the s ta in less steel t ie-down rods in the core center , and (2) the c r i t i ca l r eac to r size which is quite sensi t ive to smal l react iv i ty e r r o r s .

The reac to r c h a r a c t e r i s t i c s r epor ted he re a r e based on pos t -cr i t ica l i ty calculat ions rev i sed to include the above effects. In addition, the slowing-down kerne l of two-group theory has been replaced by the F e r m i slowing-down kerne l , and the two-group cr i t i ca l equation rep laced by the age-diffusion c r i t i ca l equation.

Core Descr ipt ion

The active core section consis ts of four quadrants separa ted by rec tangular channels in which four control blades opera te . The core support plate can accommodate up to 88 a s semb l i e s in a s y m m e t r i c a l a r r a y . The dimensions and composit ions of the fuel a s semb l i e s a r e given in Table II.

Core Volume F rac t ions

Due to the p r e sence of the channels , followers and guides for the control b lades , the volume fract ions of the var ious core const i tuents a r e a function of the core s ize . Table III l i s t s the volume fract ions calculated for co re s consist ing of 28 and 59 fuel a s s e m b l i e s .

Nuclear P a r a m e t e r s

The nuclear p a r a m e t e r s for the var ious conditions studied a r e summar i zed in Table IV.

The the rma l macroscop ic c r o s s sect ions {^Q_C) a r e based on Maxwel l ian-averaged t h e r m a l mic roscop ic c r o s s sect ions r epor t ed in B N I J - 3 2 5 at effective neutron energ ies of 0.03232 ev, 0.04092 ev, and 0.0539 ev, corresponding to mode ra to r t e m p e r a t u r e s of 68°F, 207°F, and 421°F.

Table II

COMPOSITION AND DIMENSIONS OF BORAX IV F U E L ASSEMBLIES

Fue l Tube P l a t e Ma te r i a l Fue l Channels pe r pla te Width (before forming)

End plate Other P l a t e s

Th ickness of webs be tween channels P l a t e edges

Th ickness Width

End p la tes Other p la tes

O.D. of fuel channels I.D. of fuel channels In te rna l r i b s in channel

Number pe r channel Radius

Side P l a t e s Ma te r i a l Width Th ickness O v e r - a l l length

F u e l P e l l e t s Composi t ion O.D. of pe l le t s Length Pe l l e t dens i ty G r a m s U^^^ pe r g r a m Th02

Al - 1 8

4. 4, 0.

0,

0. 0. 0. 0.

6 0.

w t -

,688 in. ,781 in. ,0875 in.

,043 in .

,660 in. ,508 in. ,2975 in. 256 in.

,005

Al - 1 3.828 0.051 31.80

in .

wt-in. in. in.

% Ni

% Ni

UO2 + Th02 0.230 in. 0.375 to 0.75 ir 9.1 g m / c c 0.0556

Fue l A s s e m b l y No. tube p la tes Width Th ickness Act ive fuel length No. fuel tubes fil led (in 6 p la tes ) G r a m s UO2 and ThOj (average) G r a m s U^^^ (average) Lead bond th i ckness

Unit Cel l Width Th ickness

3.828 3.875 24 tg-4 7 5425 283 0.013

4.000 3.888

in . in . ' = i n

in .

in . in .

Table III

CORE VOLUME FRACTIONS AT ROOM T E M P E R A T U R E

Region

Control Blade Ch;

Fue l As

T ie -Do

Boron

T e m p e r a t u r e (°F)

Void m Coolant (%)

Bora ted-SST Rods

r)U"=

U235 u^35 absorp t ion Total absorp t ion

P

e

k<„

Tc (cm^)

iJi, (cm^)

âc (^™') Ref lec tor savings (cm)

i sembly

wn Rods

68

0

0

2.053

0.6792

0.9738

1.0121

1.3742

47.96

3.500

0.07148

7.11

innels

M a t e r i a l

Al - 1 wt-% Ni H2O

Al - 1 wt-7o Ni UO2 + Th02 Pb H2O

SST

SST - 2 wt-% B

Table IV

NUCLEAR CONSTANTS

20 7

0

0

2.053

0.6798

0.9728

1.0120

1.3739

51.00

5.181

207 421

10

0

2.053

0.6905

0.9699

1.0116

1.3908

59.96

5.793

0.06249 0.06153

7.79 8.38

0

0

2,

0,

No. of A s s e m b l i e s

28 59

0.0665 0.0433 0.0227 0.0150

0.1273 0.1317 0.0872 0.0902 0.0536 0.0554 0.6414 0.6636

0.0013 0.0006

0.0004

421 421

0 10

16 0

,053 2.053 2,

,7029 0.6830 0,

0.9687 0.9687 0,

1,

1,

6 1 .

6,

0,

8,

,0115 1.0115 1,

,4140 1.3740 1,

.053

,7138

,9653

,0112

,4303

.47 61.47 72.65

,282 6.104 7,

.05594 0.05757 0,

,005

,05545

,79 8.79 9.53

4 2 1

10

16

2.053

0.6934

0.9653

1.0112

1.3895

72.65

6.805

0.05708

9.53

The thermal disadvantage factors for the fuel and modera to r were obtained from diffusion theory cor rec ted by the rat io of P3 to diffusion theory resul ts for s imi la r cases studied previously. The effect of the borated steel rods was es t imated by diffusion theory, assuming the rods to be black to the rmal neut rons . Per turbat ion theory was then ennployed to take into account the fact that the rods were l imited to 16 center fuel assembl ies in a 59-assembly co re .

The effective resonance integral for the thor ia -u ran ia fuel was determined from the effective resonance integral reported^•'•^) for thorium meta l , co r rec ted for the additional resonance scat ter ing in thor ia . F o r a thor ia density of 9.1 g m / c c , the effective resonance integral obtained is

K f f ^ = 10-14 {1 + 0.1214

Ro + 0.020 -7}

62

where RQ is the rod radius in cen t ime te r s . The slowing down c ros s s e c tion (|21 ) used for light water was 1.353 cm"' ' .

The core age was de termined from the exper imenta l r e su l t s for var ious a luminum-to-wate r ra t ios cor rec ted for the slowing down effect of the thor ia -u ran ia fuel and lead bonding.

F a s t fission factors were es t imated from the resu l t s for u r an ium-H2O la t t ices and the thor ium and uraniiim fast c ro s s sec t ions .

The ref lector savings were de termined from an empi r i ca l re la t ion based on previous BORAX core calculat ions:

= 0.0661 T+ 4.73 - 5.3 x 10"^ (450 - T)^

where T is the t empera tu re (°F) and T i s the core age (cm^). The ref lector savings of the top ref lector poisoned by the control blades was taken as 0.55 in. (i .e. , the dis tance between the top of the fuel and the blade tips in the full "out" posit ion).

Table V l i s t s the effective mult ipl icat ion constant calculated for co re s consist ing of 28, 30, and 59 fuel a s sembl i e s under a var ie ty of conditions.

Table V

REACTIVITY CALCULATIONS

(Control Blades Out)

Temp. , °F

68

207

207

421

421

Uniform Voids

%

0 0

0 0

10 0

0 0

10 0

Boron Rods

0 0

0 0

0 0

0 16

0 16

Fuel Assembl ies

28 30

28 30

28 30

59 59

59 59

Geometr ic Buckling

(Bg X 10* cm-2)

61.87 59.30

59.82 57.43

58.10 55.81

40.16 40.16

39.02 39.02

koo

1.3742 1.3742

1.3739 1.3739

1.3908 I.39O8

1.4140 1.3740

1.4303 1.3895

keff

1.000 1.013

0.9828 0.9954

0.9502 0.9642

1.0775 1.0477

1.0486 1.0194

The effective neutron lifetime for the BORAX-IV core was 5.6 x 10"^

sec .

The t h e o r e t i c a l t e m p e r a t u r e and void coe f f i c i en t s of r e a c t i v i t y for u n i f o r m ef fec ts in the c o r e a r e g iven in Tab le VI .

T a b l e VI

T H E O R E T I C A L T E M P E R A T U R E AND VOID C O E F F I C I E N T S O F R E A C T I V I T Y

No. F u e l Coeff ic ien t A s s e m b l i e s R a n g e V a l u e

T e m p e r a t u r e 30 68 - 207°F - 1 . 2 6 x 10"* ( A k / k ) / ° F

Void 30 0 - 10% (207°F) - 0 . 3 2 % ( A k / k ) / % Void

Void 59 0 - 10% (421°F) - 0 . 2 8 % ( A k / k ) / % Void

The D o p p l e r coef f ic ien t of r e a c t i v i t y for a loniform fuel t e m p e r a t u r e r a n g e f r o m 68 to 207°F w a s c a l c u l a t e d to be - 3 x 10"^ ( A k / k ) / ° F . T h i s r e s u l t w a s b a s e d on the t e m p e r a t u r e coef f ic ien t of the v o l u m e t e r m in the r e s o n a n c e i n t e g r a l e q u a t i o n r e p o r t e d for t h o r i u m m e t a l :

f|A=.3.8.10-V"C.

T h e o r y v s E x p e r i m e n t

The t h e o r e t i c a l kgff of un i ty for the 2 8 - a s s e m b l y c o r e a t r o o m t e m p e r a t u r e (Tab le V) i s in good a g r e e m e n t wi th the e x p e r i m e n t a l v a l u e o b t a i n e d wi th t h i s c o r e on an a s y m p t o t i c p e r i o d of 18 m i n . The a g r e e m e n t , h o w e v e r , m a y be f o r t u i t o u s . The a v e r a g e w o r t h of a n a s s e m b l y added to the p e r i p h e r y of the c o r e ( a v e r a g e of 3 a s s e m b l i e s ) w a s abou t +0.64% A k / k by e x p e r i m e n t , a s c o m p a r e d to +0.65% Ak/k by t h e o r y . Th i s t e n d s to c o n f i r m the t h e o r e t i ca l v a l u e of M^. The a v e r a g e d m e a s u r e d t e m p e r a t u r e coef f ic ien t of r e a c t i v i t y for the t e m p e r a t u r e r a n g e f r o m 68 to 2 0 7 ° F ( s e e F i g . 21) w a s -2 .47 x 10"^ ( A k / k ) / ° F ; t h e o r y (Tab le VI) gave a v a l u e of - 1 . 2 6 x 10-* ( A k / k ) / ° F .

The t h e o r e t i c a l e x c e s s r e a c t i v i t y for a 5 9 - a s s e m b l y c o r e ( con ta in ing 16 b o r o n - s t e e l r o d s ) a t 300 p s i g (420°F) w a s +4.55% A k / k . The e x p e r i m e n t a l v a l u e , d e t e r m i n e d f r o m s h i m b l a d e s c a l i b r a t i o n and c r i t i c a l p o s i t i o n , w a s +5.6% A k / k . The t e m p e r a t u r e coef f ic ien t of r e a c t i v i t y a t 420°F w a s abou t - 1 . 3 5 X 10""* ( A k / k ) / ° F by e x p e r i m e n t ( s e e F i g . 21) , c o m p a r e d to abou t - 2 . 5 X 10-* ( A k / k ) / ° F p r e d i c t e d by t h e o r y .

64

APPENDIX B

TRANSFER FUNCTION ANALYSIS

In order to obtain a bet ter understanding of the response of a r e actor to an osci l la tor , as well as of the tendency to osci l la te , it is des i rab le to at tempt the separat ion of the measured t ransfe r function into s impler components . The model assumed here (Fig. 66) is that of a single (power-dependent) feedback loop, whose cha rac te r i s t i c s a r e then determined from the data. It is fairly general since the power-to-void t ransfer function can be the composite of many loops. Factor ing the feedback loop does r e p r e sent a slight loss of generali ty; however, the analysis below can also be pursued without this factorization. The differential equations represent ing the sys tem a re as follows:

No ~ I N dk (1) Z P

k = kin + k

±i/X^ Vc dn/No/ ^

dk

dv

(2)

(3)

VOID COEFFICIENT x VOIDS,

V dk

v/V , POWER TO VOID TRANSFER FUNCTION,

dn/NT

F I G . 66 SINGLE FEEDBACK REPRESENTATION OF A REACTOR

Equation (l) is mere ly a simplified representa t ion of the l inear ized reac tor kinetics equation,

d n No / , „ X 1 V ^ ^ ^ n - = - g ^ ( l - ^ ) k + ^ X i C i - —

i

dCi _ /3ik Bin

N = No + n

where n and Ci a r e smal l deviations of total neutrons and delayed neutrons, respect ively, from their mean va lues . Sinailarly in Eq. (3), v is the deviation of the s team voids from its mean value, VQ.

The solution of Eqs . (1) to (3) for the t ransfer function of the ent i re sys tem is , by elimination of k and k. -,

( 1 dN\ n/N U dk Jzp kin ~ M d N N / dv/Vo \ dk ^ '

\N dk y^pVdn/No / ° d v

Also, the solution for the feedback t ransfer function is

dv/Vo (y dk dn/No \ ° dv

± d N \ - ^ / n/Np N dk / „ „ " \ ki

Z P ^m (5)

Equation (5) is useful for the evaluation of the unknown t ransfer function, (dv/Vo)/(dn/No), from the measured (n/No)/kij^ and the theoret ical or

/ 1 d N \ measured I — —— It should be borne in mind that all quantities in

\ N dk y ^ p . ^ these equations a r e complex and dependent upon frequency. This t r e a t ment is seen to be analogous to that given to electronic amplif iers with frequency-dependent feedback.

Figure 56 (F) shows the zero-power t ransfer function computed for jS = 0.00845. All experimental points fall within ± 20% of this curve . Any discrepancy between theory and exper iment must be ascr ibed to inherent exper imental inaccurac ies . The zero-power , non-feedback theory has been proven out by many exper iments on other r eac to r s .'^^) The phase e r r o r between theory and exper iment in F ig . 56 ( F ) was used to co r rec t the measured phases of other t ransfer functions shown in F ig . 56 ( G - J ) and Fig . 57 (F - J ) .

67

To obtain the feedback t ransfer function from Eq. (5) the amplitude and phase of (n/Np) / kin were obtained from F i g s . 56 and 57. In addition to cor rec t ing the phases as descr ibed, the uncor rec ted measu red ampli tudes shown were renormal ized upon substitution into Eq. (5). The r e n o r m a l i -zation factor, applied at all frequencies of a given run, was whatever factor was needed at high frequencies to make the measu red t ransfe r function using |3 = 0.00704 from leakage-cor rec ted Keepin data. (The exper imenta l points indicated a ^ of 0.00845 ± 20%,) Without this cor rec t ion the feedback would not approach zero at high f requencies . The need for this cor rec t ion probably a r i s e s from: a) the increased react ivi ty worth of the osci l la t ing rod at high powers over i ts zero-power worth used in plotting the data; and b) whatever exper imental inadequacy caused the phase e r r o r .

F igure 67 shows the amplitudes and the phases of the feedback t ransfer functions as a function of frequency. Relatively li t t le prec is ion may be attached to values of the amplitude because of sensi t ivi ty to ex-perinnental e r r o r s and of the cor rec t ions applied; values for phase a re somewhat more re l iab le . The s imples t function that one might a s sume to co r re l a t e the data is

d v / v dn/Np (1 + 1 2 7TfT)3

-ito

-160

_

.78 M.

.81 Nw

.87 Mw

1.77 Mw

. /

-

-

/ /

2.5M

/ /

N " - > ^

t/ '' /

3.tO

^

1

r

^

Mw-»

\f 1 i

"y / .29

/'

*», -

[ \

V ^ . 8 1 Mw

V

V

-

\ . ^ 1 . 7 7 Nw

^ .87 M » ^

ii^

^

f^ / ,

^ N \

\

^ ^ M w " ~ ^ \ ^ ^

29 M>

^ \

^ ^

y

^ 3

^

to

\ /V

Hw

FREQUENCy, cps

AMPL1TUDE AT VARIOUS

AND PHASE OF

POWER LEVELS

F I G .

FEEDBACK

67 TRANSFER FUNCTIONS VS FREQUENCY

68

The value of kp, which is ra ther imprec i se ly de termined, i s neve r the le s s about -0.02 at the lower powers , and about -0.03 at the highest power . On the other hand, r , the effective average of all the t ime constants of the sys t em is somewhat be t te r known (see Table VII).

Table VII

POWER DEPENDENCE OF THE FEEDBACK

T , sec

0.93 0 0 0

.60

.44

.40

TIME CONSTANT

Power , Mw

0.78 to 0.87 1.48 to 1.77 2.54 3.29 to 3.40

The magnitude and t rends found in both kp and r a r e in ag reemen t with the theore t ica l expectat ions:(15, l6) kp is of the o rde r of the reac t iv i ty in voids and is m o r e negative at higher powers ; T is some average of fuel and s t eam t r a n s p o r t t ime constants and is s m a l l e r a t higher powers having higher flows. The commonly observed inc reas ing resonant frequency (of t r ans fe r functions or spontaneous osci l lat ions) with inc reas ing power is thus a t t r ibuted to the s m a l l e r t ime constants shifting the 180° phase value of feedback to higher f requenc ies .

APPENDIX C

ANALYSIS OF INHERENT MECHANISMS OF REACTIVITY COMPENSATION DURING EXCURSIONS

A number of sa tura t ion and subcooled excurs ions from low power levels (100 watts) at a tmospher ic p r e s s u r e were analyzed in an at tempt to a sce r t a in the mechan i sms that contribute to react ivi ty compensation in BORAX-IV. To facili tate theore t ica l in terpre ta t ion, it was found advantageous to f i rs t compute two coefficients of react ivi ty afforded by the tes t data: the dynamic t empera tu re coefficient, and the dynamic energy coefficient.

Dynamic Tempera tu re Coefficient

The average r i s e of water t empera tu re during a subcooled excurs ion was calculated f rom a heat balance based on the measu red t e m p e r a t u r e r i s e in the fuel and aluminum clad, and the theore t ica l heat capaci t ies of the fuel e lement . It was assumed that no water was expelled from the core during the excurs ion.

F igure 68 shows the excess react iv i ty compensated as a function of water t empera tu re r i s e during subcooled excurs ions . F r o m the initial slope of this curve , the dynamic t empera tu re coefficient of react iv i ty was -2.6 X 10"* (Ak/k) /°F, approximately ten t imes the average stat ic t e m pera tu re coefficient m e a s u r e d over the range from 68°F to 207°F, and two t imes the theore t ica l s tat ic t empe ra tu r e coefficient. However, ca lculations of the sources of e r r o r s in the use of thermocouples for m e a s u r e ments of fuel t e m p e r a t u r e s showed that the indicated t empera tu re r i s e nnay have been lower by a factor of 5 than the t rue t empera tu re r i s e for the shor t e r pe r iods . Use of the t rue t empera tu re r i s e would lead to a s t ronger negative value for the dynamic t empera tu re coefficient.

Dynamic Energy Coefficient

Osci l lograph r eco rds that gave the neutron flux as a function of t ime were analyzed for the instantaneous excess react ivi ty and the co r responding total energy r e l ea se at var ious t imes during the excurs ions . The resu l t s (Fig. 69) showed that, for a given init ial uniform core t e m p e r a tu re , the dynamic energy coefficient of react iv i ty was essent ia l ly independent of the init ial period, and of the t ime after the power begins to deviate from an exponential .

Theoret ica l Interpreta t ion of Dynamic Energy Coefficient

Es t ima tes were made of the react iv i ty compensated by the effects of radiolytic production of gas , fuel heating, and water heating for

* .10

4 6 8 10 WATER TEMPERATURE RISE, °F

FIG. 68 REACTIVITY COMPENSATED AS A FUNCTION OF CALCULATED WATER TEMPERATURE RISE DURING SUBCOOLED EXCURSIONS (laCF) AT ATMOSPHERIC PRESSURE.

o

; ^

/

SIIBCOOI ED n2n°F>

aATA INITIAL PERIOD, sec

• 1.03

• 0.54 A 0.22

ARROWS INDICATE VALUES

AT PEAK POWER

- f i r/

~7

f t

X

/ /

. / • /

•

/

/

/ • • /

SATURATION f207°F)

• ^

DATA INITIAL PERIOD, sec

O 0.93 A 0.46 n 0.128

3 4 5 ENERGY, Mw-sec

FIG. 69 REACTIVITY COMPENSATED AS A FUNCTION OF TOTAL ENERGY RELEASE DURING SATURATION AND SUBCOOLED EXCURSIONS AT ATMOSPHERIC PRESSURE

71

compar ison with the exper imenta l dynamic coefficient of reac t iv i ty . In the absence of exper imenta l data on radiolytic production of gases under t rans ien t conditions, it was assumed that:

(1) the formation of one hydrogen molecule requi red 100 ev of energy;

(2) no recombinat ion occur red under t r ans ien t conditions;

(3) the formation of gas bubbles was instantaneous; and

(4) th ree per cent of the total energy r e l e a s e was avai lable for the radiolytic production of gas .

In view of the inaccurac ies assoc ia ted with the method of t e m p e r a tu r e m e a s u r e m e n t s , the react iv i ty effects due to fuel and water heating were calculated for possible maximum and min imum l i m i t s . Three methods of calculation were employed. In Method A for the max imum fuel t empe ra tu r e r i s e (i .e. , the min imum water t empe ra tu r e r i se ) , it was assumed that the re was no t ransfe r of energy from the fuel during the excurs ion. In Method B for the min imum fuel t e m p e r a t u r e r i s e ( i .e. , max imum water t empe ra tu r e r i se ) , it was a s sumed that the t e m p e r a t u r e r i s e s in the fuel, s t ruc tu ra l m a t e r i a l s , and core mode ra to r were equal . Final ly, in Method C the r i s e in water t e m p e r a t u r e was calculated by assuming that the indicated fuel center t e m p e r a t u r e was equal to the t rue average fuel pel let t e m p e r a t u r e .

The Doppler, t e m p e r a t u r e , and void coefficients used in these calculat ions (Table VIII) were , respect ive ly 1.3, 1.8, and 1.08 t imes the values for uniform effects in the core to account for the nonuniform t e m p e r a t u r e r i s e and void formation under t r ans i en t condit ions.

Table VIII

COEFFICIENTS OF REACTIVITY USED IN CALCULATION FOR NON-UNIFORM E F F E C T S

Source of Coefficient Data Value

Doppler Theore t ica l -0.388 x 10"^ (Ak/k) /°F

T e m p e r a t u r e Measured -2.68 x 10"^ (Ak/k) /°F (68-207°F)

Void Inferred from -0.0965% (Ak/k)/7o voids m e a s u r e d temp, coefficient

72

The resu l t s of these calculations (Table IX) showed that the var ious mechan i sms investigated accounted for 45 to 75% of the exper imenta l r e activity compensat ion. The major uncer ta in t ies which may reflect e r r o r s in the values l isted a r e :

(1) the void coefficient as deduced from the m e a s u r e d t e m p e r a t u r e coefficient may be too low; theory gives a void coefficient of -0.32% (Ak/k)/% voids at sa tura t ion t empe ra tu r e (207°F);

(2) the theore t ica l Doppler coefficient of react iv i ty may lack precis ion;

(3) absence of exper imenta l data on production of radiolyt ic gas under t r ans ien t conditions; and

(4) lack of sufficient and accura t e t empe ra tu r e indications for the var ious lat t ice coinponents.

Table IX

EXPERIMENTAL AND CALCULATED DYNAMIC ENERGY COEFFICIENT OF REACTIVITY

(in %Ak/Mw - sec)

Calculated

Mechanism

Radiolytic Gas Fuel Tempera tu re Water Tempera tu re

Total

Radiolytic Gas Fuel Tempera tu re

Total

Exper imenta l Method A Method B Method C

Subcooled Excurs ions (120°F)

0.0059 0.0059 0.0059 0.0154 0.00087 0.0067 ± 0.0007

0.00668 0.0032

0.030 ±0 .001 0.0213 0.01345 0.0158 ± 0.0007

Saturated Excurs ions (207°F)

0.028 ± 0.001

0.0069 0.0154

0.0223

(No fuel t e m p e r a t u r e measu remen t )

Although the exper imenta l react iv i ty compensat ion has not been ent i re ly accounted for, it is evident that the mechan i sms cited may all play an impor tant role in the self - l imit ing c h a r a c t e r i s t i c s of BORAX-IV t r a n s i e n t s .

73

APPENDIX D

CORE HYDRAULICS J . M a r c h a t e r r e

The hydrodynamic per formance of boiling r e a c t o r s at s t eady-s ta te conditions is readi ly calculated by the IBM-650 computer p r o g r a m identified as CHOP. The re su l t s for BORAX-IV a r e l is ted in Table X. The values at the higher p r e s s u r e s a r e m o r e re l iable than those at a tmospher ic p r e s s u r e , where the sl ip ra t io is uncer ta in .

Avg. Power per Assembly,

kw

124 132,1

10.54 30.48 57.4 90.7

176 291.6

12.59 36,04 67.7

106.9 207.8 342.8

P;

P :

P :

P ]

Table X

BORAX-IV HYDRAULICS

Boiling Length Total Len,

r e s s u r e : 0

0.778 0.811

r e s s u r e : 250

0.652 0.652 0.652 0.652 0.652 0.652

r e s s u r e : 300

0.642 0.642 0,642 0.642 0.642 0.642

r e s su re : 300

gth

psig.

psig;

psig;

psig;

Inlet Coolant

Velocity, fps

Feedwate r

1.82 1.81

Feedwate r

2.04 2.88 3.32 3.68 4.08 4.16

Feedwate r

1.95 2.82 3.32 3.68 4.02 4.12

Feedwate r

Slip Ratio

Temp.:

2.76 2.78

Temp.:

1.50 1.54 1.58 1.62 1.74 1.92

Temp.:

1.54 1.58 1.60 1.64 1.74 1.90

Temp.: '

Avg. Core

Voids

75°F

0.623 0.645

109°F

0.0228 0.0522 0.075 0.099 0.147 0.192

109°F

0.0225 0.0514 0.077 0.0995 0.145 0.194

75°F

Avg. Exit

Voids

0.91 0.92

0.07 0.145 0.21 0.27 0.385 0.48

0.07 0,145 0.215 0.280 0,385 0,49

124 0,627 3.78 1,66 0.107 0.30

74

A P P E N D I X E

S T E A D Y - S T A T E R E A C T I V I T Y IN VOIDS

The s t e a d y - s t a t e r e a c t i v i t y in vo id s w a s a p p r o x i m a t e d by s i m p l e m u l t i p l i c a t i o n of the void coe f f i c i en t s and the a v e r a g e v o i d s c o m p u t e d in A p p e n d i c e s A and D, r e s p e c t i v e l y . F o r the u t m o s t in r i g o r , a t h r e e -d i m e n s i o n a l i n t e g r a t i o n of the s p a t i a l l y v a r y i n g void coef f ic ien t and void d i s t r i b u t i o n should be d o n e .

As e v i d e n c e d by Tab le XI the m e t h o d of c a l c u l a t i o n p r o v i d e d i n f o r m a t i o n tha t w a s in e x c e l l e n t a g r e e m e n t wi th e x p e r i m e n t a l d a t a o b t a ined a t 300 p s i g , but d i f f e red c o n s i d e r a b l y f r o m v a l u e s ob ta ined a t a t m o s p h e r i c p r e s s u r e . Al though the d i s c r e p a n c y m a y be a t t r i b u t e d , in p a r t , to the t h e o r e t i c a l void coef f ic ien t ( d k / d a ) , t he m a j o r u n c e r t a i n t y l i e s in the h y d r a u l i c c a l c u l a t i o n , in p a r t i c u l a r , in the s l i p r a t i o .

T a b l e XI

S T E A D Y - S T A T E R E A C T I V I T Y IN VOIDS

C a l c u l a t e d

Void A v g . E x p e r i m e n t a l P r e s s u r e , No . of P o w e r , Coeff. Vo ids dk R e a c t i v i t y in

p s i g A s s e m b l i e s Mw dk/dc t a d a Voids

0 31 3.85 -0 .32 0 .623 0.199 0.0135 300 59 6,3 - 0 . 2 8 0.0995 0.0279 0.030 300 59 12.5 - 0 . 2 8 0 .145 0 .0406 0 .0505

76

ACKNOWLEDGEMENTS

The authors a r e indebted to J. R. Dietr ich, C. N. Kelber , R. C. Howard, C. K, Soppet, S. A. Bernsen of the Reactor Engineering Division, and R. A. Noland, J . H. Handwerk of the Metal lurgy Division for thei r active par t ic ipat ion in the design of BORAX-IV; to N. Kr i sbe rg and R. Roberge of the Idaho Division who ass i s t ed in the operat ion of the r eac to r ; and to J . E. Gustafson, L. Seren, J . M. Ramuta, and J . A, Koerner who performed the computations in connection with the t rans fe r function ana lys i s .

REFERENCES

1. W. H. Zinn, et al, "Trans ien t and Steady-State Cha rac t e r i s t i c s of a Boiling R e a c t o r s , " ANL-5211 (February , 1954).

2. A. J, Ulrich, "Results of Recent Analysis of BORAX-II Trans ien t Expe r imen t s , " ANL-5532 (April, 1956).

3. J , R, Dietr ich, H. V. Lichtenberger , and W. H. Zinn, "Design and Operat ing Exper ience of a Prototype Boiling Water Power Reactor,^" Proceedings of the Internat ional Conference on the Peaceful Uses of Atomic Energy, (New York: United Nations, 1956), Vol. 3, p . 56.

4. W. H. Zinn, et . a l . , "Operat ional Exper ience with the BORAX Power Plant ," Nuc. Sci. Eng. 1. (No. 5) 420 (1956).

5. O. A. Schulze, "BORAX-IV: P r e l i m i n a r y Repor t on the P r e s e n t Ser ies of Exper iments with Oxide F u e l s , " Pape r p resen ted at the Technical Briefing Session held at Argonne National Labora tory , May 27-28, 1957, TID-7535, p . 114.

6. J . H. Handwerk, C, L, Hoenig, and R, C. Lied, "Manufacture of the ThOz - UO2 Ceramic Fuel Pe l le t s for BORAX-IV," ANL-5678 (August, 1957).

7. J . H. Handwerk and R. A. Noland, "Oxide Fuel E lements for BORAX-IV," TID-7535, p . 140.

8. F . Schroeder , et . a l . , "Exper imenta l Study of Trans ien t Behavior in Subcooled Water -Modera ted Reac to r , " Nuc. Sci . Eng. _2, 96 (1957).

9. S. G. F o r b e s , F . Schroeder , and W. E . Nyer, " F i r s t Repor t s on Instabil i ty in S P E R T - I , " Nucleonics L5 (No. 1) 41 (1957).

10. J . A. Thie, "EBWR Phys ics E x p e r i m e n t s , " TID-7535, p . 40.

78

11. H. A. Bethe, "Reactor Safety and Osci l la tor T e s t s , " APDA-117 (October 15, 1956).

12. M. N. Moore, "The Determinat ion of Reactor Trans fe r Functions from Measuremen t s at Steady Operat ion," NAA-SR-1972 (August 15, 1957).

13. R. Macklin and H. Pomerance , "Resonance Capture In t eg ra l s , " Proceedings of the International Conference on the Peaceful Uses of Atomic Energy, (New York: United Nations, 1956) Vol 5, p . 96.

14. J . M. H a r r e r , et . al . , "Nuclear Reactor Control ," Nucleonics, 10, (No. 8) 32 (1952).

15. J . A. Thie, "Stability of Bubbling R e a c t o r s , " Reac tor Engineer ing Division Quar te r ly Repor t - Section II, ANL-5601, (December, 1956) p . 31 .

16. J . A. Thie, "Boiling Water Reactor Instabil i ty," Nucleonics, lb, (No. 3) 102 (1958).

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