DEVELOPMENT OF A CODE SYSTEM FOR DETERMINING …

o • » « . • ! T i l t JL e. A VKlik-im-^wu^

DEVELOPMENT OF A CODE SYSTEM FOR DETERMINING RADIATION PROTECTION OF

ARMORED VEHICLES (THE VCS CODE)

Reported By

W . A . Rhoades

MASTER

A V J' i ^ •' l U s P -l-X-V...!

• • • \ •

OAK- RIDGE NATIONAL LABORATORY OPERATED BY U N I O N CARBIDE CORPORATION •• FOR T H E U S'. A T O M I C ENERGY C O M M I S S I O N

Contract No. W-7405-eng-26

Neutron Physics Division

DEVELOPMENT OF A CODE SYSTEM FOR DETERMINING RADIATION PROTECTION OF ARMORED VEHICLES

(THE VCS CODE)

Work Performed By

w. A. Rhoades G. W. Morrison*** A. R. Buhl* J. V. Pace*** M. B. Emmett*** L. M. Petrie*** G. C. Haynes** L. R. Williams R. J. Hinton*** T. J. Hoffman****

Reported By

17. A. Rhoades

U. S. Atomic Energy Commission, Division of Reactor Research and Development, Washington, DC 20545.

* * On contract from the University of Tennessee, Knoxville, TN.

* * * Computer Sciences Division.

Consultant, University of Tennessee, Knoxville, TN

OCTOBER 1974

Work Supported by Ballistics Research Laboratories Aberdeen, Maryland

This r e p 0 r i w a 5 p , e p a r c l | „ » c c o o n , o f w o r k sponsored by ,he United S u i t s N«Uher

Co J i ? - " ^ S , " e S " ° r , h e U n i t e d States Atomic Energy ^ °f employees, nor any at

contractors, bubcontractors, or their employees ^ t e s a n y warranty, express or itipH J " " a 3 e s olefin « / « P o n s i b U i , y for the accuracy, corrT-* o d u ' f u s e f u , n S s s ° f »»y information, ap&ra?,S

I C l d ' <"«!<«<>. or represents that Its use | would not infringe privately owned rights.

NOTICE This document contains information of a preliminary nature and was prepared primarily for internal use at the Oak Ridge National Laboratory. I t is subiect to revision or correction and therefore does not represent a final report.

OAK RIDGE NATIONAL LABORATORY Oak Ridge, Tennessee 37830

operated by UNION CARBIDE CORPORATION

for the U. S. ATOMIC ENERGY COMMISSION

MASTER 8rSTRISUTI0N-0F. THIS DOCUMENT IS UNU

iii

TABLE OF CONTENTS

Page

Abstract ix

Acknowledgment xi

1.0. Introduction 1

1.1. Scope and Purpose of the VCS 1

1..2. Structure of the VCS 3

1.3. Validation of the Method 6

2.0. Reactor Data Comparisons 8

2.1. Reactor Model 8

2.2. Reactor Environment Experiments 11

2.3. Check of Method: Discrete Ordinates vs Monte Carlo . . . 14

2.4. Check of Method: Experiment vs Monte Carlo 17

3.0. Tactical Weapon Problem 34

3.1. Demonstration Problem 34

3.2. Cross-Section Data 34

3.3. Results 38

4.0. Conclusions 47

5.0. References 48

6.0. Appendices 49

6.1. Appendix A - Reactor Model. 49

6.2. Appendix B - Reactor Results 80

6.3. Appendix C - Revised Definition of Protection Factor. . . 84

V

LIST OF FIGURES

Figure Page

1.1. Reference Problem and Folding Surface. . 2

1.2. Vehicle Code System 4

1.3. VCS Data Flow Diagram 5

2.1. ARMY Pulse Radiation Facility Reactor 9

2.2. Experiment - Reactor Source 12

2.3. Experiment - Equivalent Point Source . . 13

2.4. "Toroidal Box" Model 15

2.5. Dimensions of Box Model 16

2.6. Neutron Spectra Due to Reactor Source - Box Geometry . . . 20

2.7. Photon Spectra Due to Reactor Source - Box Geometry. . . . 21

2.8. Neutron Spectra Due to Reactor Source - Vehicle Geometry . 32

2.9. Photon Spectra Due to Reactor Source - Vehicle Geometry. . 33

3.1. Neutron Spectra Due to Weapon Source 43

3.2. Photon Spectra Due to Weapon Source. . . . 44

3.3. Photon Spectra Due to Weapon Source - Without (n,y) . 45 Contribution . .

6.1. APRFR Core IIIC 55

6.2. APRFR Core IIID 56

6.3. Angular Distribution of Reactor Source in the Vertical Plane 75

6.4. APRFR Reactor Source (Neutrons) (DOT Calculation). . . . . 78

6.5. APRFR Reactor Source (Photons) (DOT Calculations). . . . . 79

6.6. Cumulative Flux Distribution at Reactor Surface 81

viii

LIST OF TABLES

Table Page

2.1. Dose Response Data . : 18

2.2. "Box" Model Comparison 19

2.3. PT-76 Experimental Neutron Dose 23

2.4. PT-76 Experimental Photon Dose 24

2.5. Reactor Source Protection Factors 25

2.6. Agreement of Experimental and Calculated Protection

Factors 26

2.7. Neutron Dose with Actual Vehicle Model 27

2.8. Photon Dose with Actual Vehicle Model 28

2.9. Renormalization of Dose Rates . . . . . . . . . ! 30

3.1. Tactical Weapon Problem Data 35

3.2. Unclassified Tactical Weapon Source Spectrum 35

3.3. Ground Composition (Nevada Test Site) . . . . . . . . . . . 36

3.4. Air Composition - 36

3.5. "Standard Man" Composition 37

3.6. Doses for a Fission Source in 3000 M Air 37

3.7. Neutron Doses and Protection Factors 39

3.8. Photon Doses and Protection Factors 40

3.9. Doses Due to Neutron Sources and Protection Factors . . . . 41

3.10. Doses Due to Photon Sources and Protection Factors 42

6.1. Engineering Drawing List 50

6.2. Materials of Manufacture 51

6.3. Fuel Composition 51

6.4. Decoupling Shield Cover Specifications 52

viii

LIST OF TABLES (CONT'D)

Table Page

6.5. Fuel Pieces. 53

6.6. Material Atomic Densities 54

6.7. IIIC Configuration — Interval Boundaries 57

6.8. HID Configuration — Interval Boundaries 58

6.9. IIIC Configuration Volume Fractions 60

6.10. HID Configuration Volume Fractions 62

6.11. 21-18 Coupled Library 64

6.12. Maximum Multiplication Factor, Rods in 65

6.13. Directions for Point Source Data 65

6.14. APRFR IIIC Leakage 67

6.15. APRFR HID Leakage 69

6.16. Flux Ratios 82

6.17. Fluence per Fission at Energy E>3 MeV at 1 Meter 83

i x

ABSTRACT

A s y s t e m o f c o u p l e d c o m p u t e r codes i s d e v e l o p e d f o r t h e c a l c u l a t i o n

o f t h e p r o t e c t i o n f r o m n u c l e a r r a d i a t i o n p r o v i d e d by an a r m o r e d v e h i c l e .

The code s y s t e m u s e s a d i s c r e t e - o r d i n a t e s a i r - t r a n s p o r t c a l c u l a t i o n

c o u p l e d t o a n a d j o i n t M o n t e C a r l o c a l c u l a t i o n . T h e v e h i c l e d e s c r i p t i o n

i s s u p p l i e d i n c o m b i n a t o r i a l g e o m e t r y f o r m . E l e m e n t s o f t h e m e t h o d w e r e

t e s t e d a g a i n s t e x p e r i m e n t a l d a t a . A r e a l i s t i c t a c t i c a l n u c l e a r weapon

p r o b l e m i s d e m o n s t r a t e d .

xi

ACKNOWLEDGMENT

I t i s a p p r o p r i a t e t o a c k n o w l e d g e t h e g u i d a n c e and s u p p o r t o f t h i s

e f f o r t b y C. E . C l i f f o r d and G. E . W h i t e s i d e s a t ORNL; and b y D . L .

R i g o t t i , N . B a n k s , J . E . L a c e t e r a , and R. R e x r o a d a t BRL. T h e method

o f c o u p l i n g was s u g g e s t e d by F . R. M y n a t t o f ORNL. We a l s o a c k n o w l e d g e

t h e t e c h n i c a l s u p p o r t o f R . L . C h i l d s , N . M. G r e e n e , and J . R. K n i g h t

o f ORNL.

1

1.0. INTRODUCTION

1.1. Scope and Purpose of the VCS

An armored vehicle can provide important protection against the

effects of a nuclear weapon. In the case of a tacticsil weapon, prompt

radiation may be the dominant effect over a considerable area surrounding

the detonation.1 It is the purpose of the Vehicle Code System (VCS) to

facilitate the calculation of radiation protection factors for a given

vehicle; i.e., the ratio by which the free-field radiation is reduced

due to the presence of the vehicle.

VCS was constructed by linking together a discrete-ordinates

air-transport calculation and an adjoint Monte Carlo vehicle dose-importance

calculation. The reference problem is illustrated in Fig. 1.1. A

tactical nuclear weapon of low-kiloton yield is detonated within a

kilometer of a vehicle. The air-transport calculation determines the

the neutron and photon flux as a function of energy on a coupling surface

surrounding the vehicle. The dose-importance calculation determines the

effectiveness of particles at the coupling surface in contributing to

dose at a detector position within the vehicle. A coupling code folds

the flux together with the dose importance, giving the dose response.

The coupling code can also rotate the vehicle, move it to different

distances from the source, and perturb the energy response of the detector.

The following section will outline the structure of the code system.

A user's manual giving details of the construction and operation of VCS

is available in another document.2

2

QRNL-DWG 73 - 7785

Weapon Source.

Fig. 1.1. Reference Problem and Folding Surface.

3

1.2. Structure of the Vehicle Code System

The general structure of VCS is shown in Figs. 1.2 and 1.3. The

compositions and source data for the air-transport calculation are fed

to the GRTUNCL-TDOT section. GRTUNCL calculates the uncollided flux and

first-collision source throughout the problem space, while DOT calculates

the collided flux and merges the two results. All flux information is

passed to the VISA section, where it is condensed and reordered for

convenient processing. Only a few ranges of interest are normally

processed at this step. Additional ranges may be obtained by rerunning

the VISA section at a minimal cost.

The complex three-dimensional vehicle geometry description arid

material composition are fed to MORSE. MORSE records the required

information for each particle leaving the coupling surface on a history

data set, which is fed to DRC-SAMBO. DRC folds the adjoint history data

together with the flux at the coupling surface for the selected orien-

tation and range and accounts for the response spectrum of the detector.

SAMBO provides edits and statistical measures of the results as requested

by the user.

Special advantage is taken of,the fact that the vehicle is small when

compared to the separation distance between weapon and vehicle. This

means that flux in a given direction and at a given elevation and energy

is essentially independent of the azimuthal variable about the vehicle.

This seduces the volume of data processed by DRC, minimizes the cost

of both VISA and DRC, and simplifies the construction of both codes.

Most of the cost of VCS is incurred in the DOT section. Therefore,

it is advantageous to save the VISA output fcr use with many MORSE runs.

ORNL-DWG 73-778)

VEHICLE CODE SYSTEM

Fig. 1.2. Vehicle Code System

5

f Air Composition Ground Composition Source Yield Source Spectrum Source Height

Vehicle Geometry Vehicle Composition Ground Composition Detector Position

MORSE Vehicle Shielding

Calculation

Orientation Range Detector Respons*

PRC Detector Response)

Calculation

I Coupling Surface Vlux Preparatioi

Detector Response

as ; a Function of Energy'

Fig. 1.3. VCS Data Flow Diagram.

6

It is also practical to use a single history data set to examine a

number of vehicle orientations, ranges, and response spectra.

The protection factor, itself, can be obtained by dividing the free-

field dose, available from DOT, by the dose response given by DRC-SAMBO.

1.3.. Validation of the Method

The ideal experiment for comparison with VCS results would clearly

be a tactical nuclear weapon test, with a well-instrumented armored vehicle

as a target, and with comparable instruments placed near the vehicle for

free-field observations. We do not have exactly this type of data avail-

able, but other checks are available which test the code in a piecewise

fashion.

The air-transport method has been studied extensively by ORNL and

others for the Defense Nuclear Agency.3 Sets of multigroup cross sections

have been developed for use in the DOT discrete-ordinates code, and com-

parisons with experiments have been made.4* The data used herein are

compared with those data in Section 3. The reliability of the neutron

data appear to be such that free-field doses within 1500 meters are

uncertain to about 30%, while the photon doses are uncertain within

roughly a factor of 2. It is possible that newer data are less uncertain.

A comprehensive investigation in this area is beyond the scope of this

study.

A series of experiments were performed by the Army's Ballistics

Research Laboratories (BRL) on the PT—76 vehicle, a lightly armored

amphibious tank.5 The Army Pulse Radiation Facility Reactor (APRFR) was

suspended near the vehicle, and protection factors were measured. Data

calculated using the techniques required for VCS will be compared with

the PT-76 data in Section 2.

7

The coupling method was checked directly in various ways. Among

these, it was required to reproduce free-field flux exactly and was

required to be invariant to 360° rotation.

A realistic demqnstration problem was solved with VCS, and the

results are reported in Section 3. While we do not have experimental

data corresponding to this calculation, the results appear credible;

8

2.0. REACTOR DATA COMPARISONS

2.1. Reactor Model

The reactor experiments used to check VCS were conducted using the

Army Pulse Radiation Facility Reactor (APRFR) as a source. A brochure

obtained from the Ballistic Research Laboratories describes the general

features of the reactor and the facility.6 Detailed models of two

configurations of the reactor were prepared from drawings and information

supplied by J. Watson of BRL7 and by M. I. Lundin of ORNL.8

The IIID configuration, illustrated in a full cross-section view in

Fig. 2.1., consisted of a stack of nested U-Mo alloy plates held together

with 9 U-Mo bolts. Three control rods penetrated the core, providing

shim, regulation, and pulsing functions. A large safety block of U-Mo

suspended on a steel hanger rod was raised into a large central hole in

the plates during operation. During shutdown, the safety block was lowered

by its hanger into the safety tube below the core. The control rods were

lowered from the core by steel followers. An environment shroud covered

the active core, the safety block, and the control rods when they were

removed from the core. The safety block had a cup-shaped centering

spring attached to its lower end, which nested into a steel plate-and-collar

device bolted to the bottom of the core.

A glory hole liner running inside the safety block hanger allowed

space for the insertion of experiments into the center of thf core. The

core was protected from the effects of nearby thermalizing material by

a layer of Dow Sylgard 184 bearing Bi C enriched in B-10. The Sylgard

was wrapped around a thin steel shell covering the portion ef the environ-

ment shroud adjacent to the core.

9

COfiE SUPPORT ROD

SAFETY TUBE-

SAFETY BLOCK HANGER

O M I L - D « r t - I M U N

SECTION WITH CONTROL R005 ROTATED INTO VIEW IISC OR IOD CONFIGURATION)

MASS ADJUSTMENT RODv

REGULATING OR PULSE R

IIIC CONFIGURATION •-SAFETY BLOCK KEY

-CENTERING SPRING

ARMY PULSE RADIATION FACILITY REACTOR (APRFRI

I ' 1 CENTIMETERS

5 to

i—i T 2 3 4 S

INCHES

-GLORY HOLE LINER

1110 CONFIGURATION

Fig. 2.1. Army Pulse Radiation Facility Reactor.

3.0

The IIIC version of the reactor differed in that it did not have

the steel plate at the bottom of the core, and it had no centering spring.

Also, the washer arrangement at the bottom of the core was slightly

different, as illustrated in the figure, and a very slight different

glory hole liner was used.

A third version, IIIB, differed from IIIC only in that it used the

glory hole liner that HID used. The reactivity difference due to liner

changes was measured to be only 1 0 c , and so the IIIC model was applicable

to IIIB experiments as well.

The details of the two-dimensional nuclear model are given in

Appendix A. The model was used with the DOT code to calculate fluxes

everywhere in the reactor. A special technique was used to convert this

flux information to an equivalent point source. The results are described

and compared with experiment data in Appendix B.

11

2.2. Reactor Experiment Environments

In the PT-76 experiments, the reactor was operated in the steady-state

mode at various positions near the vehicle, while both neutron and photon

dose measurements were taken. Measurements were taken in equivalent

positions with the vehicle removed, and the ratio of dose reduction by

the vehicle was defined to be the "protection factor." Measurements were

made at the mid-chest positions of water-filled mannikins representing

the three crew members - commander, loader, and driver. Neutron dose

was observed using Radsan dosimeters9'10 while photon dose was observed

using thermoluminescent dosimeters (TLD).11»12

The reactor was located at a constant distance of 18* from the

vehicle center (Fig. 2.2). This close distance made the normal VCS

coupling method inapplicable, since that method assumes a distant source.

The reactor is quite small in comparison to the separation distance, and

therefore the reactor was treated as a point source using the equivalent

source data tabulated in Appendix B. This is equivalent to choosing a

coupling surface about the reactor as illustrated in Fig. 2.3. Three

checks of the coupled discrete-ordinates Monte Carlo method were made

in this environment:

1. A code-to-code check between direct discrete ordinates and

the VCS Monte Carlo treatment was made.

2. Protection factors were checked against the experimental values.

3. Dose rates at the vehicle position were compared with experimental

values.

12

O R N L - D W G 7 3 - 7 7 8 3

Fig. 2.2. Experiment - Reactor Source.

13

O R N L - D W G 7 3 - 7 7 8 4

14

2.3. Check of Method: Discrete Ordlnates vs Monte Carlo

Prior to Monte Carlo simulation of the actual vehicle, the coupled

Monte Carlo treatment was checked against a direct discrete ordinates

calculation. It was recessary to choose a simple geometry which could be

simulated in both types of codes. A rectangular toroid large enough to

enclose the vehicle (except for the tip of the cannon) was chosen, with the

reactor positioned at a 45° angle and 18' distance from the center of the

vehicle. The toroid was given shell thickness and interior density roughly

representative of the vehicle. The toroid is illustrated in Fig. 2.4., and

details are given in Fig. 2.5. It can be noted that the vehicle stood on

5/8" of plywood covering 12" of borated concrete. Also, the vehicle center

is somewhat closer to the centerline than the centroid of the toroid section,

required if the curved surface is to just enclose the rectangular vehicle.

The compositions of iron, plywood, air, and concrete were as given in Table

6.6.

In the discrete ordinates calculation, the point source was used in a

forward fixed-source calculation using the GRTUNCL-DOT section of VCS. This

calculation gave energy-dependent fluences and doses at all positions.

The 39-group cross-section library described in Appendix A was used, with

a 70-direction half-symmetric quadrature set. The analytical first-collision

source option was used to mitigate ray-streaming effects.

In the Monte Carlo calculation, an adjoint calculation was performed

with the detector at the vehicle center. The MORSE section of VCS was

modified to score against the point-source data directly, rather than to

write a history data set. The 39-group cross section set was used once

15

ORNL-DWG 73 -7782

ORNL-DWG 74-8240

Fig. 2.5. Dimensions of Box Model.

17

again. Both fluences and doses at the detector position were obtained

as a function of energy.

In both calculations, dose response data labelled #1 and #4 in Table

2.1 were used. These are the standard responses supplied with the cross

section library. Several calculations were made with selected materials

present, as shown in Table 2.2.

The comparison between adjoint MORSE and direct DOT showed excellent

agreement without concrete present. With both concrete and vehicle present

agreement was only fair, with MORSE giving 25% less photon dose than DOT.

A later comparison will show that the experiment indicated ewan more

photon dose than DOT. Thus, DOT appears to be the more accurate of

the calculated results, in this instance. Spectral comparisons, shown

in Figs. 2.6 and 2.7 show spectra softened somewhat as compared to the

reactor leakage spectra (Figs. 6.4 and 6.5). The Monte Carl® and discrete

ordinates plots differ principally in low-energy neutrons, and very

high-energy photons where the variance of the Monte Carlo results were

poor due to the low magnitude of the fluence. Otherwise, spectral agree-

ment appeared satisfactory.

2.4. Check of Method: Experiment vs Monte Carlo

In the next step, the geometry of the PT-76 vehicle was described in

a combinatorial geometry model which included representation of the vehicle

hull, turret, cannon barrel, engine, battery, wheels, and mannikin crew

members. Fuel and ammunition were not simulated, since the experimental

vehicle did not have those aboard. The vehicle model sat on plywood and ,

concrete as described in the previous section. Doses in free-field and'

inside the vehicle were calculated as in the Monte Carlo portion of the

18

Table 2.1. Dose Response Data

#1 #2 #3 #4 #5

Energy Group

21-18 Standard Neutron Dose

Snyder-Neufeld Neutron Dose

Hurst Neutron Dosimeter Response

21-18 Standard Photon Dose

Henderson Photon Dose

mrem/hr n/cm^Sec

mrad/hr n/cmzSec

mrad/hr n/cm*Sec

mrad/hr y/cm^Sec

mrad/hr y/cmzSec

1 .150 .0252 .0187 .0098 .00889 2 .150 .0250 .0170 .0085 .00750 3 .137 .0213 .0158 .0076 .00671 4 .132 .0177 .0147 .0067 .00598 5 .131 .0158 .0118 .0058 .00519

6 .125 .0146 .0102 .0050 .00455 7 .116 .0138 .00876 .0045 .00407 8 .106 .0116 .00680 .0040 .00364 9 .0757 .00805 .00542 .0035 .00313 10 .0551 .00615 .00393 .0030 .00266

11 .0401.. .00488 .00314 .0024 .00222 12 .0245 .00349 .00184 .0020 .00176 13 .0085 .00215 .000621 .0015 .00133 14 .0050 .00200 .0000586 .00105 , .000923 15 .0050 .00217 0 .00060 " .000556

16 .0050 .00238 0 .00028 .000277 17 .0050 .00216 0 .00014 .000147 18 .0050 .00141 0 .00040 .000466 19 .0050 .00121 0, 20 .0050 .00117 0

21 .00375 .00115 0

Table 2.2. "Box" Model Comparison

Neutron Dose —8 (xlO mrem/hr) Photon Dose (xlO"10 mrad/hr)

DOT MORSE DOT MORSE

[Jncollided 2.8 2.6

Air Only 3.1 3.0 ± 1% 2.6 2.5 + 1%

Air and Vehicle 3.6 3.6 ± 2% 2.0 2.0 ± 3%

Air and Concrete 4.4 . 4.1 ± 1% 3.1 2.8 ± 1%

Air, Concrete, and Vehicle 4.3 4.5 ± 2% 2.7 2.1 ± 3%

ORNL-DWG 7 4 - 8 4 5 7

COUPLED DOT-HORSE CALCULATION -J—I 1—4—1 J—I—I 1—1—I L COUPLED DOT-DOT CALCULATION

J

10 F3T 1 0 " ' W 10' 10 rt 10* ENERGY

ID3* 1EV1

10' Fa To5* 10' Fi 10 rr 10°

Fig. 2.6. Neutron Spectra Due to Reactor Source - Box Geometry. (Inside Box)

ORNL-DWG 7 4 - 8 4 5 7

COUPLED DOT-MORSE CALCULATION COUPLED DOT-DOT CALCULATION

w w iW 1 ENERCT (EV)

10'

Fig. 2.7. Photon Spectra iiue to Reactor Source - Box Geometry (Inside Box)

22

box-model comparison, except that dosimeter response functions 93 and

#5, as shown in Table 2.1 were used.

The doses and protection factors for the experiment are listed in

Tables 2.3 and 2.4. These were supplied by R. Rexroad of BRL.1

Eight combinations of detector position and vehicle orientation were

considered in the calculation. The comparison between calculated and

measured results is shown in Table 2.5. An error estimate on the DOT-MORSE

result was taken to be the linear sum of the variances in the free-field

and ii vehicle data (this is the most pessimistic option). It is evident

that the agreement ranges from good to poor. To quantify this, we have

compiled an "agreement table" in Table 2.6. Part A of this table shows

that the errors are reasonably well fit by a normal distribution with

a = 39%.

The general trend was toward excessively low protection factors for

neutrons and high for photons. This suggests a lack of capture and (n,y)

production. We can look deeper into this by examining the raw dose rate

comparison, as presented in Tables 2.7 and 2.8. These data show a trend

toward high neutron and low photon dose rates. Examining the neutron

data in detail, the in-vehicle data for "Front 45°" and "Left Flank 45°"

follow the general trend. Both "Right Flank 4°" experimental values

are strangely low in comparison to the other data. The commander could

be affected by shadowing from the loader, who sits with his back to the

right flank, but this argument would not apply to the driver. The

calculated data appear more consistent with our understanding of the

radiation environment. The "Rear 4°" position involves doses made up

largely by scattered particles, and any inaccuracy in geometric treatment

would be most evident in that case.

23

Table 2.3. PT-76 Experimental Neutron Dose

Crew Reactor Vehicle In Dose Vehicle

Free Field Dose Protection

Member Angle Orientation xlO* .IO rad in_i? rad Factor xlO* n/cm2 xiu • v n/cm^

Commander 4° Front On Rear On Left Flank On Right Flank On

3.2 1.0 5.7 1.7

10.2 7.9

10.7 7.6

3.2 7.9 1.9 4.5

45° Front On Rear On Left Flank On Right Flank On

7.2 2.2 8.2 5.5

8.7 7.1 9.1 7.1

1.2 3.2 1.1 1.3

90° 4.7 5.0 1.1

Loader 4° Front On Rear On Left Flank On Right Flank On

2.2 1.3 1.9 2.2

10.3 7.8 7.6 10.7

4.7 6.0 4.0 4.9


6.8 5.2 4.6 2.5

8.7 7.1 7.1 9.5

1.3 1.4 1.5 3.8

90° 4.2 5.0 1.2

Driver 4° Front On Rear On Left Flank On Right Flank On

10.4 0.35 4.7 2.9

19.8 4.8 9.1 9.1

1.9 13.7 1.9 3.1


4.9 0.91 4.9 4.8

9.8 5.0 8.0 8.0

2.0 5.5 1.6 1.7

90° 2.1 4.8 2.3

Note: Units refer to rad at a detector adjacent to the tnannikin indicated per neutron of energy > 3 MeV passing through a sulfur pellet on the decoupling shield of the reactor.

24

Table 2.4. PT-76 Experimental Photon Dose

Crew Reactor Vehicle In Dose Vehicle

Free Field Dose Protection

Member Angle Orientation xlO" -12 rad

n/cm* xiO-12-J^ n/cmz Factor

Commander 4° Front On 1.2 1.3 1.1 Rear On 0.55 1.0 1.8 Left Flank On 1.9 1.4 0.74 Right Flank On 1.0 1.0 1.0

45° Front On 2.4 1.3 0.54 Rear On 1.1 1.1 1.0 Left Flank On 2.4 1.4 0.58 Right Flank On 2.1 1.1 0.52

90° 1.2 0.67 0.56

Loader 4° Front On 1.1 1.4 1.3 Rear On 0.72 1.0 1.4 Left Flank On 1.2 1.0 0.83 Right Flank On 2.0 1.4 0.70


90° 0.98 0.67 0.68

Driver 4° Front On 4.6 3.3 0.72 Rear On 0.25 0.70 2.8 Left Flank On 1.6 1.2. 0.75 Right Flank On 1.2 1.2 1.0


90° 0.66 0.86 1.3

Note: Units as described in the previous table.

25

Table 2.5. Reactor Source Protection Factors

Neutron Photon

Calc E X R Calc

Commander

Rear, 4° 7.9 5.9 + 9% i.e 2.3 ± 11%

Right Flank, 4° 4.5 1.3 + 8% 1.0 1.2 ± 18%

Front, 45° 1.2 1.2 + 9% 0.54 0.62 ± 46%

Left Flank, 45° 1.1 1.0 + 8% 0.58 1.1 ± 12%

Driver

Rear, 4° 13.7 7.0 + 18% 2.8 3.4 ± 17%

Right Flank, 4° 3.1 1.4 + 7% 1.0 1.2 ± 9%

Front, 45° 2.0 1.2 + 6% 0.82 0.93 ± 10%

Left Flank, 45° 1.6 1.6 + 6% 0.86 1.4 ± 8%

26

Table 2.6. Agreement of Experimental and Calculated Protection factors

(A. Before Normalization)

Error Band Number Within Normal Distribution a = 39%

± 10% 3 3.3

+ 20% 5 6.3

± 30% 10 9.0

± 50% 13 12.9

± 100% 16 15.8

± 200% 16 16.0

(B. After Normalization)

Error Band (6) Number Within Normal Distribution a = 32%

± 10% 2 3.9

± 20% 9 7.5

± 30% 10 10.5

± 50% 15 14.1

± 100% 16 16.0

± 200% 16 16.0

27

Table 2.7. Neutron Dose with Actual Vehicle Model

Free Field Dose

In Vehicle Dose

m-12 rad xlO —j—5-n/cm^ xlO -12 rad n/cmz

Exp DOT-MORSE Exp DOT-MORSE

Commander

Rear, 4° 7.9 12.4 1.0 2.1

Right Flank, 4° 7.6 11.7 1.7 9.0

Front, 45° 8.7 12.0 7.2 9.6

Left Flank, 45° 9.1 11.6 8.2 11.1

Driver

Rear, 4° 4.8 6.4 0.35 0.92

Right Flank, 4° 9.1 11.7 2.9 8.3

Front, 45° 9.8 13.4 4.9 10.9

Left Flank, 45* 8.0 11.6 4.9 7.2

Note: Units as described in Table 2.3.

28

Table 2.8. Photon Dose with Actual Vehicle Model

Free Field Dose

In Vehicle Dose

xlO" -12 rad n/cm* xlO - 12 rad

n/cm*

Exp DOT-MORSE Exp DOT-MORSE

Commander

Rear, 4° 1.0 1.0 0.55 0.43

Right Flank, 4 6 1.0 1.0 1.0 0.82

Front, 45° 1.3 1.0 2.4 1.6

Left Flank, 45° 1.4 1.0 2.4 0.88

Driver

Rear, 4° 0.70 0.54 0.25 0.16

Right Flank, 4° 1.2 1.0 1.2 0.83

Front, 45° 1.4 0.93 1.7 1.0

Left Flank, 45° 1.2 1.0 1.4 0.71

Note: Units as described in Table 2.3.

29

The photon data follow the trend with the "Left Flank 45° being

somewhat worse than the others.

One might wonder whether removing the consistent biases would improve

the fit. The neutron and photon data, free field and in-vehicle, were each

normalized as a set by finding' F to minimize the standard deviation defined

as:

This treatment nearly eliminated free-field error, and reduced error in the

in-vehicle data by factors on the order of 2 (Table 2.9). The distribution

of errors in the protection factors was moved more toward the 10-20 per-

centile bracket, and the variance of the best normal fit was decreased

to 32%. Thus, the removal of the consistent bias was reflected bjf some

improvement in the protection factors.

This is a significant point in identifying the source of error. If

the trouble were errors in the cross sections or in the reactor leakage,

one would suspect it to be a more-or-less consistent trend, and thus largely

removable by normalization. Instead, 10 of the 16 results fell within

a ± 30% spread before normalization, and this statistic was not helped

by normalization, even though the variance of a best-fit normal curve

S N-l

where: F = calibration parameter

Cp = calculated dose at position p

Mp = measured dose at position p

N = number of positions (8)

30

Table 2.9. Renormalization of Dose Rates

Type Condition S Before Normalization

S After Normalization

Factor of Normalization

Neutron

Neutron

Photon

Photon

Free Field

In Vehicle

Free Field

In Vehicle

44%

199%

23%

42%

7.9%

74%

15%

26%

0.72

0.53

1.23

1.70

31

was reduced. This would indicate that tl.e major errors are local effects

in the modeling of the vehicle, in its treatment by the code, or in the

measurements, themselves. This is far from a certain conclusion, however.

Spectral plots, shown in Figs. 2.8 and 2.9, show significantly softened

neutron and photon spectra inside the vehicle, evidently due to moderation

by the vehicle material, and a prominent ( n l i n e above 5 MeV in the

photon spectrum.

lCf3*

ORNL-DWG 7 4 - 8 4 5 7

FREE FIELD H H H 1-IN VEHICLE

i W ' To5* IO1 rt W To3® ENERGY (EV)

IF* lcFir 10' 72

u> N i

108

Fig. 2.8. Neutron Spectra Due to Reactor Source - Vehicle Geometry. (Coupled DOT-MORSE Calculation)

ir

ORNL-DWG 7 4 - 8 4 5 7

FREE FIELD

IN VEHICLE

IF" 2 ENERGT (EV I

I T

^ t i bo U>

10'

Fig. 2.9. Photon Spectra Due to Reactor Source - Vehicle Geometry (Coupled DOT-MORSE Calculation)

34

3.0. TACTICAL WEAPON PROBLEM

3.1. Demonstration Problem

The VCS code was used to solve a demonstration problem in which the

PT-76 tank was exposed to nuclear radiation from an unclassified tactical

weapon source supplied by BRL. The geometric model of the vehicle used in

the analysis of the experiments was changed in the following ways:

1. Fuel was added.

2. Ammunition was included.

3. The crew were represented by "standard men."

4. The vehicle sat on the ground, rather than plywood.

The source specification, air and group composition, and the

composition of the 4-element standard man are listed in Tables 3.1.

through 3.5. A new definition of protection factor was used as discussed

in Appendix C. (Data are summarized both ways in the tables.)

3.2. Cross-Section Data

The cross sections used were the 39-group set as used in the reactor

study of Appendix A, except that special air cross sections were obtained

from ENDF/B Version III data. The new air data were compared with a well-

accepted 40-group set also derived from the ENDF/B source (Table 3.6), and

with older data by Straker. The ENDF/B sets are derived from an evaluation

by Young and Foster. Young and Foster's data are compared with Straker's

and with two experiments, in Reference 4. Both sets of data were found to

be reliable at ranges of 1500m or less to within 30% with respect to neutron

dose, and to within a factor of 2 with respect to photon dose. Neither is

clearly indicated as better, although the Young and Foster evaluation is

35

Table 3.1. Tactical Weapon Problem Data

Slant Range = 692 m Height = 127 m Yield = 9.4 kt

Table 3.2. Unclassified Tactical Weapon Source Spectrum

Energy Interval (MeV)

Neutrons/KT (X 1022)

12.0 - 14.1 0.964 8.3 - 12.0 0.482 5.3 - 8.3 1.14 3.0 - 5.3 2.35 1.3 - 3.0 7.11 0.75 - 1.3 3.79 0.33 - 0.75 4.22 0.083 - 0.33 4.28 0.021 - 0.083 2.17 0.005 - 0.021 1.51 0.0013 - 0.005 1.02 10.0013 1.99

Total 31.0

36

Table 3.3. Ground Composition (Nevada Test Site)

Atomic Density Element (Atoms/A*)

Oxygen a3.573-2 Silicon 1.164-2 Hydrogen 9.613-3 Potassium 5.481-4 Aluminum 4.508-4 Magnesium 4.901-4 Sodium 4.552-4 Iron 3.427-4

Mass Density % 1.63 gm/co3

Table 3.4. Air Composition

„, . Atomic Density Element ( a t o n s/A 3)

'Nitrogen Oxygen

3.7368"5

8.6960"6

Mass Density = 1.1 3 gm/cm3

aRead as 3.573 x 10~2.

37

Table 3.5. "Standard Man" Composition

Atomic Density Element (atoms/P)

C 0.0094 0 0.0225 H 0.0626 N 0.00134

Table 3.6. Doses for a Fission Source in 3000 M Air

Neutron Dose Photon Dose Distance /mrem / n \ fmrad / n \

I hr / secJ V hr / sec/

39G 40G Straker 39G 40G Straker

1000 m 3.4-10 3.6-10 3.6-10 0.24-10 0.27-10 0.32-10

1500 m 3.5-11 3.8-11 3.9-11 0.67-11 0.78-11 0.94-11

2000 m 3.2-12 3.5-12 3.6-12 1.7-12 2.0-12 2.5-12

2500 m 2.9-13 3.1-13 3.2-13 4.6-13 5.4-13 6.8-13

38

newer. The table shows that the 39-group data agree well with the 40-group

evaluation within 1500m, and so the difference in group structure does not

significantly degrade or reduce the overall reliability in that range.

The dose response data labelled #2 and #5 in Table 2.1 were used in

the tactical calculations. Detectors were placed at the chests of the

mannikins as in the reactor experiment.

3.3. Results

The doses at the vehicle position without the vehicle present were

obtained from the DOT code and are shown in Tables 3.7 and 3.8. The

in-vehicle doses obtained with VCS and the resulting protection factors

are also shown. The weapon position corresponds to a source angle of

10.6°, and so none of the reactor data apply directly. Tables 3.9 and

3.10 show doses and protection factors calculated as indicated in

Appendix C. It is evident that secondary photons more than replace those

captured in penetrating the vehicle. In the absence of neutrons, the

vehicle would afford significant protection against gamma source.

The increased protection from the rear for the commander and the

driver and from the right flank for the loader is evident. This is

probably due to the effect of each crew member's body on the detector

located on his chest.

The neutron and photon spectra are shown in Figs. 3.1 and 3.2. The

incident spectra have been greatly softened and structured by the air

penetration, and they do not resemble the reactor spectrum at all. This

further discourages direct comparison. Both spectra are restructured

somewhat by penetration into the vehicle. A prominent (n,y) line is

apparent above 5 MeV in the photon spectrum. Figure 3.3 shows this

spectrum with the (n,y) contribution removed.

39

Table 3.7. Neutron Doses and Protection Factors

In-Vehicle Dose (xlO3 rad)

Free-Field Dose (xlO3 rad)

Protection Factor

Commander

Front 34 49 1.4

Rear 26 49 1.9

Left Flank 35 49 1.4

Right Flank 31 49 1.6

Driver

Front 39 49 1.3

Rear 25 49 2.0



Loader

Front 36 49 1.4

Rear 37 49 1.3



40

Table 3.8. Photon Doses and Protection Factors



Protection Factor

Commander

Front 4.9 4.1 .84

Rear 4.6 4.1 .89

Left Flank 5.1 4.1 .80

Right Flank 4.9 4.1 .84

Driver

Front 5.4 4.1 .76

Rear 4.5 4.1 .91



Loader

Front 6.0 4.1 .68

Rear 6.0 4.1 .68



41

Table 3.9. Doses Due to Neutron Sources and Protection Factors

In-Vehicle Dose Free-Field Dose Protection (xlO3 rad) (xlO3 rad) Factor

Commander

Front 37 49 1.3

Rear 29 49 1.7



Driver

Front 43 49 1.1

Rear 28 49 1.8



Loader

Front 41 49 1.2

Rear 41 49 1.2



42

Table 3.10. Doses Due to Photon Sources and Protection Factors



Protection Factor

Commander

Front 1.7 4.1 2.4

Rear 1.4 4.1 2.9

Left Flank 1.7 4.1 2.4

Right Flank 1.7 4.1 2.4

Driver

Front 1.7 4.1 2.4

Rear 1.3 4.1 3.2



Loader

Front 1.5 4.1 2.7

Rear 1.5 4.1 2.7



ORNL-DWG 7 4 - 8 4 6 1

FREE FIELD-DOT CALCULATION I I I i l l I I I II IN VEHICLE - COUPLED DOT-HORSE CALCULATION

J t r 1. f 1 = :

Cf

TtfTs 107 * *1CP ,«=J2 HJ-82 5 p itf 10' 10® 10® * 10f W ' ENERGY (EV)

Fig. 3.1. Neutron Spectra Due to Weapon Source.

ORNL-DWG 7 4 - 8 4 6 1

F ilE FIELD-DOT CALCULATION i i IN VEHICLE-COUPLED DOT-MORSE CALCULATION

t = T

r u j E

JO-'L i r £N£flGr (EV) T T 10'

Fig. 3.2. Photon Spectra Due to Weapon Source.

ORNL-DWG 7 4 . 0 4 6 3

J

iW ir I T ENERGY

s (EV)

.10'

Fig. 3.3. Photon Spectra Due to Weapon Source - Without (n,y) Contribution.

46

Without direct experimental comparison, little else can be said

about the results except that they appear generally credible.

47

4.0. CONCLUSIONS

VCS was successful in solving the type of problem for which it was

designed. The computing time was reasonable for this type of calculation -

about 11/2 hours on the IBM System/360 Model 91. Most, of the computing

time was due to the air-transport calculation. Additional vehicle descriptions

and detector positions can be obtained by repeating the Monte Carlo calcu-

lation which requires approximately 1/4 hour computation for 20,000 histories.

Additional orientations, ranges, and perturbations to the response spectrum

can be obtained in much less than a minute of computer time.

The reactor source spectrum and magnitude checked very well against

measured data. The comparison of protection factors calculated with this

source, however, showed mixed results - some protection factors were calcu-

lated fairly accurately, e.g., 2.3 vs 1.8 and 3.4 vs 2.8. Others were so

much in error, e.g., 1.3 vs 4.5 that only local effects in the experiment,

inadequacy in the geometric model, or inadequacy in the Monte Carlo treat-

ment of the model would seem to explain then. There was a consistent trend

toward too many neutrons and too few photons, probably due to cross section

error, but removing these trends by normalization made only slight

improvement in the protection factors.

The protection factors and doses calculated for a weapon source

problem appeared credible, although we have no applicable experimental

data for that case.

48

5.0. REFERENCES

1. R. Rexroad, Ballistics Research Laboratories, Aberdeen, MD, (Personal Communication).

2. W. A. Rhoades, et al, "Vehicle Code System (VCS) User's Manual," 0RNL-TM-4648.

3. L. S. Abbott., "Shielding Against Initial Radiations from Nuclear Weapons," ORNL-1RSIC-36 (July 1973),. (Contains a summary of numerous other works.)

4. E. A. Straker, "Investigation of the Adequacy of Nitrogen Cross-Section Sets: Comparison of Neutron and Secondary Gamma-Ray Transport Calculations with Integral Experiments," ORNL-TM-3768 (August 1972).

5. "Prompt Radiation Shielding Experiments, Soviet PT-76 Tank, MCN-23418," FSTC-CR-20-22-73 (February 1973).

6. "Army Pulse Radiation Facility," U. S. Army Ballistics Research Laboratories, AMXRD-BTD, Aberdeen Proving Ground, MD 21005 (Brochure).

7. J. Watson, "U. S. Army Ballistics Research Laboratories, Aberdeen Proving Ground, MD -21005, (Personal Communication).

8. M. I. Lundin, Oak Ridge National Laboratory, Oak Ridge, TN 37830, (Personal Communication).

9. G. S. Hurst and E. B. Wagner, Review of Scientific Instruments3 Vol. 29, No. 2, 153 (February 1958).

10. G. S. 'Hurst, Brit. J. Radiologya 27, 353 (1954).

11. J. R. Cameron, N. Sontharalingam, and G. N. Kenney, Thermoluminescent Dosimetry3 University of Wisconsin Press (1968).

12. N. N. Gibson, et al, "Thermoluminescent Dosimetry and It's Uses at the U. S. Army Nuclear Defense Laboratory," NDL-TM-49 (November 1968).

13. J. Jacobson, U. S. Army Ballistics Research Laboratories, Aberdeen Proving Ground, MD 21005 (Personal Communication).

14. A. H. Kazi and D. 0. Williams, "Intercomparison of Sulfur and Total Neutron Fluence Measurements at APRFR and HPRR," Unpublished Memorandum (January 3, 1973).

15. A. H. Kazi, U. S. Army Ballistics Research Laboratories, Aberdeen Proving Ground, MD 21005, (Personal Communication).

49

6.0. APPENDICES

6.1. Appendix A - Reactor Model

The actual engineering drawings used in the models are listed in

Table 6.1. The materials are specified in Tables 6.2 through 6.4.

Elastuff was taken to be equivalent to SS304. The aluminum was taken

to be pure A1 of density 2.70. Table 6.5 shows the specification of the

fuel pieces. Table 6.6 shows the atomic density of the pertinent materials.

The concrete, air, and iron were used in the "Box Model*1 calculation.

The two-dimensional cylindrical models are represented by the

material maps (not to scale) shown in Figs, 6.1 and 6.2. The radial and

axial boundary positions corresponding to each interval are shown in

Tables 6.7 and 6.8. It may be noted immediately that the reactors are

pictured upside down! This gave important flexibility in changing from

one model to the other. In addition, it was possible to use the portion

above the safety ring in a neutron criticality calculation, and then to

add the substructure for a fixed-source neutron-photon calculation.

The only major difficult in the modeling was the bolts, the treatment

of the control rods, and their associated hardware. These were treated by

using a number of radial zones into which the corresponding fraction of

each item was placed. This treatment was also used for the thermocouple

penetrations into the side of the center-fuel plate. The three core

support rods and corresponding bulges in the environment shroud were

ignored. In a few cases, small errors were allowed in the representation

of a structural piece to hold the number of intervals to an acceptable

limit. No such approximations were made with fuel pieces.

50

Table 6.1. Engineering Drawing List

Drawing Number Issue or Revision Date

1. 2.

3.

4.

5.

6.

7.

8. 9. 10.

11.

Environment Shroud & Safety Ring Decoupling Shield (covered with Sylgard - B^C Layer) Safety Tube m u -i i IIIB & HID Glory Hole Liner | iIIC } Safety Block Center (IIID Only) Safety Block Hanger c c - TJ1 i v /IIIB & IIIC\ Safety Block Key < 1 I I D f

Centering Spring (IIID Only) Safety Block

\ Core Plates Core Bolts Control Rods Liners Mounting Bracket Coolant Baffle Washer

12. Core Support Rod

BRL—RB-094—70

BRL-RB-098—70 BRL-RB-091—70 BRL-RB-97-70 BRL-R3-138-71

BItL-RB-140-71 UNC 18425 UNC 18425 BRL-RB-141-71 BRL-RB-125-71 UNC 18436

ORNL 49090E2

UNC 15867

UNC 15924

Rev 1-2-70

1-2-70 Rev 3-16-70

12-3-69 2-12-71

3-10-71 5-5-69 5-5-69 3-26-71 10-30-70

Rev 5-9-69

Rev 10-16-69

Rev 3-2-66

Rev 8-4-66

BRL: U. S. Army Ballistics Research Laboratories UNC: United Nuclear Corporation ORNL: Oak Ridge National Laboratories

51

Table 6.2. Materials of Manufacture

Iron Material

Core Plates U-Mo Alloy Fuel Safety Block U-Mo Alloy Fuel Core Bolts U-Mo Alloy Fuel Control Rods U-Mo Alloy Fuel Core Nuts Inconel X750 Safety Block Centering Plate Armco 17-4 PH Steel Centering Spring Elastuff Tool-Type Steel Coolant Baffle Type 2024 Aluminum Decoupling Shield Cover Dow Sylgard 184 + B^C

All other pieces Stainless Steel, Type 304 or Equivalent

Table 6.3. Fuel Composition

Analysis of Fuel By Element Mo 10.0 w/o U 90.0 w/o

Analysis of Uranium by Isotope U-235 93.2 a/o U-238 6.8 a/o

52

Table 6.4. Decoupling Shield Cover Specifications

Composition: 478.7 gm B^C 332.3 gm Dow Sylgard 184 33.2 gm Catalyst

Casting: 10" x 31" mold, 1/10" thickness

Isotopic Analysis of Boron:

Analysis of Sylgard + Catalyst by Element:

?.-10 91.24 w/o I _B-11 8.76 w/oj

C 27.8 w/o H 8.0 w/o Si 37.9 w/o 0 26.0 w/o Other 0.3 w/o

53

Table 6.5. Fuel Pieces Core Plates:

Serial No. Core IIIC Core HID

Thickness Fuel Mass Thickness Fuel Mass

Top Plate 7880--24--0010 0. 813 cm. 3.626 kg Regular Plate 7880--51--0341 0. 641 2.742 Regular Plate 7880--21--0105 3. 346 14.666 Regular Plate 7880--23--0111 3. 347 14.677 Center Plate 7880--19--0103 3. 419 14.682 Regular plate 7880--20--0104 3. 346 14.687 Regular Plate 7880--22--0106 3. 343 14.639 Bottom Fuel Plate * 1. 124 . 4.978 Steel Plate * — —

19. 379 cm 84.697 kg

Same as IIIC

0.493 0.635

2.104

Core IIIC had plate 7880-25-0112. Core HID had plate 7880-51-0344 followed by the safety block centering plate.

Other Fuel Pieces: Serial No. OD Length • Mass

Safety Block 338 Mass Adjustment Rod 360 Regulating Rod 121 Pulse Rod 113 9 Bolts

10.158 cm 21.7415 cm 15.734 kg 2.565 25.400 . 2.202 2.149 25.404 1.533 2.149 25.380 1.529 2.266 28.260 16.708

Total Fuel Mass:

Configuration IIIC: 122.02 kg Configuration IIID: 119.53 kg

ORNL-DWG 74-9626

Table 6.6, Material Atomic Densities

Fuel SS Type 304 Armco 17-4 PH Tool Steel Inconel Aluminum Decoupling

•Wrapper Concrete Air Iron Plyuooi

1 Hydrogen - - - - ,0335 .00702 - - .02184 2 Boron - - - - - .003912 .01458 3 Boron-10 - - - - .03671 - - - -

4 Carbon - - - - .0238 - - - .01311 5 Nitrogen - - - - - - - .00004023 ** —

6 Oxygen - - - - - .006853 .05908 .0000X0695 - .01092 7 Sodium - - - - - - - - ** •

8 Magnesium - - - - - - .001659 -

9 Aluminum - - - - .0603 - .004656 —

10 Silicon - — .001675 — — .005690 .010799 ** • —

11 Potassium - - - - - - - - - -

12 Calcium - - - - - - .003486 -

13 Titanium - - - - - - - — —

14 Chromium - .01662 .01492 .0166 - - - - •

IS Manganese (SS) - .0012 .0008562 .0009 — - — •

16 Iron (SS) - .05775 .06159 .0073 - - .001431 - .08444 -

17 Nickel .00752 .003205 .0624 - - - - -

18 Copper ' - - .00296 - - - —

19 Zirconium - - - - - - .0007667 **

20 Niobium - - — — - .0006709 •

21 Molybdenum (SS) .010358 .00011 - - - - - - - -

22 Tantalum - - - — —

** •

23 Tungsten - — - — — —

24 Uranium-235 .03544 — —

25 Uranium-238 .002585 —

- — -— —

55

ORNL-DWG 74-9702

iUHt "I -t1

ftj

t c c •u. If* rj •

u rx. D — H 'C 3 —t

r- > ••C t: I" !>

ro .v

-J x o uj x is s IX I t * * =» •i" z

4 o i*>

• c m

k <n c at w > —« m'

v/i I -vj ft. >r

A IT

o 4 t\. v !•> rvi r rvj fti

liilinilit'skf.c.eti-'

Fig. 6.1.' APRFR Core IIIC.

56

ORNL-DWG 74-9703 ZONE

• - - - ->• • •*Ti«T»•»»•« .

<»»*«.»••«•* i * *'**»'* i' t *********** t> I»••••»••••«k I ***********

•VV*"»*VWTi V ******

j ***********

1*5444 »5544» i U W «44444« 444440 444444 »4444« 4»444« »V4"4'*5 * 4*444* •44444 44444K J44444 4 Hiia 4444*1* HUM 1.444* * Ntf* 14-14'. HU«4444<. 4444" au«i444t t'iWi rftf* 4444* NrfN >444"

UOTT iJQTT OuwgiT

• •

ixuflA4Rtu 11117667111 11117667*11 frnrevrrn 11117667111 11117667111 11117667111 11117667111 1112988033 1TT29B&9733 • 11117667111 llll7667ili 11117667111 11117667)li 1111766711* nTIHXX&TVi 11UUXXR111 llltUXBl HSUCCDb|TTT|ZZZ7 -soccnstrJiTTnlz

M»«

n

*******

V T m -) »

*

a 1 « • r a <=> « c >c * o> m U. IT • «

ii » a r> u M a <*i « o ! * r> » » l a w

| m 1 3 S 1 "I -O : CU

tnifl i in a • 1X1 •e r

! <*•' ! c* ! N w <VI * « ! a in ! W

- - r-* j O •* -i rr O UJ S (C 11 V 3 V) z

Z <•) CM X <v PU -J M ni

l£34Sh7890lt'345676>01234567ft9 1J111111

Fig. 6.2. APRFR Core IIID.

Table 6.7. IIIC Configuration — Interval Boundaries

Interval Radius Height Interval Radius Height

1 1.9840E-00 7.5400E-01 2 2.1430E-00 1.5080E-00 3 2.7790E-00 1.9050E-00 4 3.0960E-00 2.7385E-00 5 3.4140E-00 3.5720E-00 6 3.6510E-00 3.8100E-00 7 3.8890E-00 4.9740E-00 8 4.1280E-00 6.1380E-00 9 4.6040E-00 7.3020E-00 10 5.0800E-00 8.3722E-00 11 5.3090E-00 9.4424E-00 12 5.8740E-00 1.0513E-01 13 6.3500E-00 1.1583E-01 14 6.5090E-00 1.2653E-01 15 7.1960E-00 1.3667E-01 16 7.6960E-00 1.4681E-01 17 8.5725E-00 1.5763E-01 ,18 9.4490E-00 1.6845E-01 19 9.9490E-00 1.7927E-01 20 1.0636E-01 1.9009E-01 21 1.0947E-01 2.0091E-01 22 1.1303E-01 2.0999E-01 23 1.1989E-01 2.1908E-01 24 1.2148E-01 2.2548E-01 25 1.2227E-01 2.3189E-01 26 1.2481E-01 2.3807E-01 27 1.4135E-01 2.4142E-01 28 1.4532E-01 2.5094E-01 29 2.5552E-01

30 2.6187E-01 31 2.6999E-01 32 2.7457E-01 33 2.7952E-01 34 2.8258E-01 35 2.9210E-01 36 3.1434E-01 37 3.3784E-01 38 3.6135E-01 39 3.8485E-01 40 4.0836E-01 41 4.3186E-01 42 4.5537E-01 43 4.7887E-01 44 5.0238E-01 45 5.2588E-01 46 5.4939E-01 47 5.6594E-01 48 5.7071E-01 49 5.9543E-01 50 5.9611E-01 51 6.0019E-01 52 6.0654E-01 53 6.2876E-01 54 6.5099E-01 55 6.5734E-01 56 6.7004E-01 57 6.7639E-01

Table 6.8. 1IID Configuration — Interval Boundaries

Interval Radius Height Interval Radius Height

1 1.9840E-00 7.5400E-01 2 2.1430E-00 1.5080E-00 3 2.7790E-00 1.9050E-00 4 3.0960E-00 2.7385E-00 5 3.4140E-00 3.5720E-00 6 3.6510E-00 3..8100E-00 7 3.8890E-00 4.9740E-00 8 4.1280E-00 6.1380E-00 9 4.6040E-00 7.3020E-00 10 4.9150E-00 8.3722E-00 11 5.0800E-00 9.4424E-00 12 5.3090E-00 1.0513E-01 13 5.8740E-00 1.1583E-01 14 6.3500E-00 1.2653E-01 15 6.5090E-00 1.3667E-01 16 7.1960E-00 1.4681E-01 17 7.6960E-00 1.5763E-01 18 8.5725E-00 1.6845E-01 19 9.4490E-00 1.7927E-01 20 9.9490E-00 1.9009E-01 21 1.0636E-01 2.0091E-01 22 1.0922E-01 2.0999E-01 23 1.1303E-01 2.1908E-01 24 1.1989E-01 2.2400E-01 25 1.2148E-01 2.2568E-01 26 1.2227E-01 2.3193E-01 27 1.2481E-01 2.3807E-01 28 1.4135E-01 2.4452E-01 29 1.4532E-01 2.5098E-01 30 2.5552E-01

31 2.6050E-01 32 2.7003E-01 33 2.7956E-01 34 2.8258E-01 35 2.9210E-01 36 2.9972E-01 37 3.1437E-01 38 3.3953E-01 39 3.6468E-01 40 3.8984E-01 41 4.1500E-01 42 4.4015E-01 43 4.6531E-01 44 4.9047E-01 45 5.1563E-01 46 5.4078E-01 47 5.6594E-01 48 5.6848E-01 49 5.7071E-01 50 5.9611E-01 51 6.1452E-01 52 6.1928E-01 53 6.2563E-01 54 6.5103E-01 55 6.7643E-01 56 6.8278E-01 57 6.9548E-01 58 7.0183E-01 59

59

The volume fraction of each material in each zone is specified in

Tables 6.9 and 6.10. A special method was used to insure accurate fuel

mass. The atomic densities for fuel were calculated using a nominal mass

density of 16.5 gm/cm3. Then the mass was calculated from the model

volumes, volume fractions, and atomic densities. An adjustment factor of

1.0286, applied to the atomic densities for the fuel material, was found

to bring the calculated mass into agreement with the measured mass for

both the IIIC and IIID cores.

The cross-section set vised was the 39-group set developed at ORNL

for space systems studies. The 21 groups of neutron data are based on

the GAM-II 99-group library, while the 18 groups of photon data are of

ORNL manufacture. The group structure is given in Table 6.11.

The models for both configurations were used as input to the DOT

section of VCS in a criticality calculation using a half symmetric

quadrature set having 30 angles. Only the portion of the reactor above

the bottom of the safety ring was used in this calculation, and only

the neutron portion of the cross-section library was used. The calcu-

lation gave values for the multiplication factor shown in Table 6.12.

A comparison with experiment shows agreement within a fraction of a

percent, which is quite satisfactory.

The fission density results were then used as a fixed source in

a DOT calculation using the entire model, including the substructure,

and using the full coupled neutron-photon cross-section library. The

result was a table of neutron and photon fluxesieverywhere in the reactor.

The FALSTF code was then used to convert the reactor to an equivalent

point source by calculating the flux at great distance in a given

ORNL-DWG 74-9627

Table 6.9. IIIC Configuration Volume Fractions

Zone Fuel SS Type 304 pjJ'rSo^Steel l n C O n e l A l u D l n u m ""rawer® C o n c r e t e A l r

1 Fuel Plates 1 2 Fuel Plates + T.C. (Inner) .9887 .0113 - -3 Fuel Plates + T.C. (Outer) .9050 .0950 - -4 Safety Block 1 - - -5 Safety Block + Key Notch .9758 .0318 - - - - - -

6 Fuel + So Bolts + CR (Center) .9136 .0200 _ .0664 7 Fuel + Sm Bolts + CR (Outer) .8902 .0349 - .0749 8 Fuel + Sa Bolts + T.C. + CR (Center) .8751 .0585 - .0664 9 Fuel + So Bolts + T.C. + CR (Otter) .8483 .0768 - .0749 10 Fuel + Th Bolts + CR (Center) .9328 .0200 - .0472

11 Fuel + Ig Bolts + CR (Outer) .9382 .0350 - - .0268 12 Bolts + 6 Hashers + 3 Brackets + CRF (Center) .4164 .3495 - .2341 13 Bolts + 6 Washers + 3 Brackets + CRF (Outer) .0759 .5349 _ - . 3B92 14 Bolt Heads + CRF (Center) .5803 .0289 - . 3908 IS Bolt Heads + CRP (Outer) .4674 .0258 - ,5068

16 Bolt Heads (Outermost) .1706 - - - _ .8294 17 Bolts + 9 Nuts + CR (Center) .4163 - .2568 . 3269 18 Bolts + 9 Nuts + CR (Outer) .0759 - .3981 .5260 19 Bolts + 6 Hashers + 3 Tabs + CR (Center) .5298 .3206 - .1496 20 Bolts + 6 Washers + 3 Tabs + CR (Outer) .1075 .5091 - .3834

21 Threads .4178 .4600 _ .1222 22 6 Washers + 3 Tabs (Partial) - .2459 - ,7541 23 Bolts + 9 Washers + CR (Center) .4163 .3297 - .2539 24 Bolts + 9 Washers + CR (Outer) .0759 .4863 - ,4378 25 Bolt lips + CR .2927 - - . 7073

ORNL-DWG 74-9628

Table 6.9. Confi.

Zone Fuel CO _„„„ , n / Arnco 17-4 SS Type 304 p H T o o l S t e e l Inconel Aluminum Decoupling C o n c r e t e Wrapper Air

26 Baffle _ .8162 .1838 27 Control Rod Tips .0836 - - - - .9164 28 Bolts + 6 Hashers + 3 Brackets + CRF (Outermost) - .4503 - _ - .5497 29 3 Brackets + Support Ring - .2127 - - - .7873 30 Bolts + 9 Nuts + CR (Outermost) - - .1332 - - .8668

31 Bolts + 9 Hashers + CR (Outermost) .3544 _ - .9556 32 Safety Block Hanger - 1 - - - -

33 Fuel + Lg Bole + CR + CRF (Center) .9491 .0384 - - - .0125 34 Safety Tube - 1

1 _ _ — — —

35 Sylgard + B.C Wrapper _ _ _ _ „ 1 36 Glory Hold Liner - 1 - - - -

37 Air - - - - - 1 38 Substructure - 0.8411 - - - -

Notes: CR - control rods; CRF • control rod followers; T.C. - thermocouple

ORNL-DWG 74-9629

Table 6.10. HID Configuration Volume Fractions

Zone Fuel SS Type 304 Arraco 17-4 FH Tool Steel Inconel Aluminum Decoupling

Wrapper Concrete Air

1 Fuel Plates 2 Fuel Plates + T.C. (Inner) 3 Fuel Plates + T.C. (Outer) 4 Safety Block 5 Safety Block + Key Notch

6 Fuel + Sm Bolts + CR (Center) 7 Fuel + Sm Bolts + CR (Outer) 8 Fuel + Sm Bolts + T.C. + CR (Center) 9 Fuel + So Bolts + T.C. + CR (Outer)

10 Fuel + Th Bolts + CR (Center)

11 Fuel + Lg Bolts + CR (Outer) 12 Bolts + 6 Washers + 3 Brackets + CRF (Center) 13 Bolts + 6 Washers + 3 Brackets + CRF (Outer) 14 Bolt Heads + CRF (Center) 15 Bolt Heads + CRF (Outer)

16 Bolt Heads (Outermost) 17 Solts + 3 Huts + CR (Center) 18 Bolts + 3 Nuts + CR (Outer) 19 Bolts + 6 Nuts + 3 Tabs + CR (Center) 20 Bolts + 6 Nuts + 3 Tabs + CR (Outer)

21 Threads 22 Bolts + 6 Nuts + 3 Tabs + CR (Outermost)

+ 9 Washers + CR 23 Bolts + 6 Nuts + 3 Washers + CR

+ 9 Washers + CR 24 Bolts + 6 Nuts + 3 Washers + CR 25 Control Rod Tips

(Center)

(Outer)

1 .9887 .9050 1

.9758

.9136

.6902

.8751

.8483 .9328

.9382

.4164

.0759

.5803 .4674

.1706 .4163 .0759 .5296 .1075

. 4178

.4153

.0759

.0836

.OU3

.0950

.0296

.0200

.0349

.0585

.0768

.0200

.0350

.3495

.5349

.0289 .0258

.1006

.1849

.4600

.3133

.2564

.3782

.0856 .1328 .1712 .2653

.1712

.2653

.0664

.0749

.0664 .0749 .0472

.0268

.2341

.3892

.3908

.5068

.8294

.4931 .7913 .1986 .4426

.1222

.6867

.1570

.2805

. 9 1 6 4

ORNL-DWG 74-9630

Table 6.10. Contd.

Zone Fuel SS Type 304 Araco 17-4 PH Tool S tee l Inconel Aluminum Decoupling

Wrapper Concrete Air

26 27 28 29 30

Baf f l e Key Ring + Spring Bottom Bolts + 6 Washers + 3 Brackets + CRF (Outermost) 3 Brackets + Support Ring Bol ts + 3 Nuts + CR (Outermost)

31 Bolts + 32 33 34 35

9 Washers + CR 6 Nuts + 3 Washers + CR

Safety Block Hanger Fuel + Lg Bolt + CR +• CHF (Center) Safe ty Tube Environment Shroud & Decoupling Shield

36 Sylgard + B,C Wrapper 37 Glory Hold Liner 38 Air 39 Subst ructure 40 Centering Spring

Al Bol ts + CR + P l a t e (Outer) 42 P l a t e 43 Bolts + CR + P l a t e (Center) 44 Bol ts + CR

(Outermost)

. 9 4 9 1

.0759

.4163

.2927

.8647

.4503

.2127

.2757 1

. 0384 1 1

0.8411 1 .0349

.0200

.8162

.0445

.0888

.8322 1

.5164

.1838

.5497

.7873

.9555

.6355

.0125 o> Ul

.0570

.0472

.7073

64

Table 6.11. 21-18 Coupled Library

r Neutron Photon Fission Neutron Photon U p E Lower E Lower Yield AE AE

0 a14.91825+6 10.0+6 1 10.00000+6 8.0+6 0.0010407 4.92+6 2.0+6 2 6.70320+6 7.0+6 0.0132450 3.30+6 1.0+6 3 4.49329+6 6.0+6 0.0597334 2.21+6 1.0+6 4 3.01194+6 5.0+6 0.1327007 1.48+6 1.0+6 5 2.01897+6 4.0+6 0.1829218 .993+6 1.0+6

6 1.35335+6 3.5+6 0.1836936 .666+6 0.5+6 7 9.07180+5 3.0+6 0.1498390 .446+6 0.5+6 8 5.50232+5 2.5+6 0.1271828 .357+6 0.5+6 9 3.33733+5 2.0+6 0.0731519 .216+6 0.5+6 10 2.02419+5 1.6+6 0.0388772 .131+7 0.4+6

11 1.22773+5 1.2+6 0.0197126 79.6+3 0.4+6 12 4.08677+4 0.90+6 0.0150226 81.9+3 0.3+6 13 1.17088+4 0.60+6 0.0028787 29.2+3 0.3+6 14 3.35463+3 0.40+6 0 8.35+3 0.2+6 15 7.48519+2 0.21+6 0 2.61+3 0.19+6

16 1.67017+2 0.12+6 0 0.582+3 0.09+6 17 3.72665+1 0.07+6 0 0.130+3 0.05+6 18 8.31529 0.01+6 0 29.0 0.06+6 19 1.85539 0 6.46 20 4.13994-1 0 1.44

21 0.001 0 0.413

a means 14.9182.5xl0+6

65

Table 6.12. Maximum Multiplication Factor, Rods In

Configuration IIIC: 1.016 (Calculated)

Configuration IIIC: ^ 1.012 (Experimental)

Configuration IIID: 1.017 (Calculated)

* Assumes 3 = 0.0068

Table 6.13. Directions for Point Source Data

1 (Down) -90° 2 - 8 0 ° 3 -70° 4 -60° 5 -45° 6 -25° 7 -4° 8 25° 9 45°

10 60° 11 80° 12 (Up) 90°

66

direction. FALSTF does this by calculating the adjoint due to the distant

point detector at each position in the core, and then folding this to-

gether with the number of particles being scattered toward the source at

that position.

The latitudinal angles to the positions used are shown in Table 6.13,

and the equivalent point source data are tabulated in Tables 6.14 and

6.15. The effect of the substructure can be seen in the downward angles.

By comparing the two sets of data, the effect of the added steel below

the core in IIID is evident.

The data are normalized such that the fluence at distance R in direction

r| at group g due to one fission neutron is S /'4irR2, where S is the source 1 »6

tabulated. Polar plots of the flux in each energy group for IIIC are

shown in Fig. 6,3. Isotropic flux would appear as a semicircle in these

plots. The reduction of flux toward the vertical is evident, as is the

distortion of low-energy neutron flux near the horizontal due to the

decoupling shield.

Spectral plots are shown in Figs. 6.4 and 6.5. In the -90° direction,

the neutron spectrum is hardened by the substructure below 200 keV, and

the photon spectrum is generally hardened over the entire range.

Table 6.14. APRFR IIIC Leakage.

ORNL-DWG 74-9633

ARRAY ROWS ARRAY COLUMNS » » * INVERT IN = 12 INPUT JN = 39 INPUT 10 = 12 OUTPUT ARRAY ROWS JO = 39 OUTPUT ARRAY COLUMNS NEO » 0 0/1 EDIT/ Nfl 60IT NOU = 6 OUTPUT LOGICAL UNIT NEUTRON • IR. 1

2 3 4 5 6 7 8 9 10 11 12

GRP. 1 1.92790F-04 2m 01930E—0A 2.63130E—04 3. 13440F-04 3.49500E-04 3.69340E—04 3.75780F-C4 3. 607206—04 3.44030E-04 3.254006— 04 -2.90420E-04 2.66510E—04

DIR. 1 2 3 4 5 6 1 8 9 10

11 12 DIR. 1

2 \ 3 4 5 6 7 8 1

10 11 12

GRP. 9 3. 7731 OE-02 4. 29190F-02 5.63430E-02 6. 739196—02 7.68339E-02 S.29629E-02 8.46709F-02 8. 26119E—02 7.90229F-02 7.43489F-02 6.39399E-02 5.380706-02 GRP.: 17 1. 024406—06 I. 695706—06 4.79090F—06 7.90610E-06 1.I5910E—05 1.44930F-05 1. 54090E-05 1.40 450E-05 1.naicf-os 7. 72630E-06 2. 14030E-06 1.1737CE-06

GRP. 2 2.21020E-0S 2.29820E-03 3. 083805-03 3.7482CE—03 4.25190C-03 4.54229E-03 4.641O0E—03 , 4.4I930C-03 4.1867CE-03 3.9505CF-03 3.55520E—03 3.265906-03 GRP. 10 2,133306-02 2.48730E-0Z 3.31590E-02 3.9926 OE-02 4. 5 792 OE-02 4.9618OE-02 5.066606-02 4.953306-02 4.7363 CE—02 4.4461 CE-02 3.7776 06-02 3.1083DE-02 GRP. 18 1.56330E-07 1.7 54206 -07 4.302706-07 8.315206-07 1.440506—06 2.019106-06 2.23750E-06 1.958706-06 1.409606-06 8.5 8050E-07 2.869T0E-07 1.82050E-07

GRP. 3 9.19940E—03 9.55610E-03 1.30410E-02 1.605406-02 1.B45BQE-02 1.99130E-02 2.03950F-02 1.93420E-02 1.82280E—02 1.713ZOf-02 1.53850F-02 1.40520E-02 GRP. II 9.B5660E-03 1.19040E—02 1.63490E—02 1.997C0E-02 2.317206-02 2.52590E-02 2.58200E-02 2.52350E-02 2.40030E-02 2.23830E-02 1.86120E-02 1.49060E—02 GRP. 19 2.70240E-08 2.90050E—08 4.02110E-08 6.34050E—08 I.176806-07 1.84000E-07 2.10660E-07 1.78400E-07 1.21000E-07 7. 87489F—08 5. 38640E- C8 3.555SOF-08

GRP. 4 1.95220E-02 2.03900E-02 2.78270E-02 3.43270E—02 ' 3.96830E-02 4.30580E-02 4.41360E-02 4.19710E-02 3.95170E-02" 3.69960E-02 3.28020E-02 2-95520E—02 GRP. 12 5.71420E-03 7.47520E-03 IV08770E-02 I.36440E-02 1.62050E-02 1.79270E-02 1.84030E-02 I.79010E—02 1.683B0E-02 I.54860E-02 1.23040 E-02 9.35210E—03 GRP. 20 * 3.967108—09 4.41360E-09 S.599005-09 6.48840E—09 8.253706—09 1.07410E-08 1.13820E-08 1.05100E—08 9.63740E—09 9.44799E-09 8 .518 20E—09 S.43360E—09

GRP. 5 2.880106-02 3.07380E-02 4.14480E-02 5.07140E-02 " 5.83640E-02 6.31979E-02 6.46119E-02 6.18240E-02 5.84I70E-O2 5.47320E-02 4.61T80E-02 4.263506-02 GRP. 13 9.33B60E-04 1.67510E-03 2.60220E-03 3.25690E—03 3.85740E-03 4.25150E-03 4.36070E-03 4.25470E-03 3.96560E-03 3. 55 94 OE—03 2.43530E-03 1.58190E-03 GBP..21 ' 1.46340E—10 1.46540E-10 1.77150E-10 1.95830E-10 2.21190E-10 2.2T5IOE-tO 1.903006—10 . 2.17380E-10 2.770106-10 3.06850E-10 2.72800E-10 1.66600E—10

GRP. 6 3.65570E-02 3.99270E-02 5.242606-02 6.29809E-02 7.15449E-02 7.69209E-02 7.84130E-02 7.56359F-02 7.19879E-02 6.77869E-02 "5.958406-02 S.20350E-02 GRP. 14 1.038606—04 2.96170E-04 5.496606-04" 7.19890E—04 8.8O720F-O4 9.85920E-04 1.00920E-03 9.630106-04 8.58120E-04 7.07830E-04 3.230606-04 1.60920F-04

GRP. 7 4.19500E-02 4.63900E—02 5.96020E—02 7.05369E-02 "7.93799E-02 8.49549E-02 8. 648596-02 8. 3943 96—02 8.03120E-02 7.58389E-02 ~6.-64me-02 5.75820E-02 GRP. 15 2.78070E-05 8.39990E-05 "1.70970E-04 2.312306-04 2.88590E-04 3.264406-04 3.35140E-04 3.17130E-04 2.77860E-04 2.21710E-04 8.276606-05 3.55620E-05

GRP. 8 5.49010E-O2 6.17370E-02 7.9I719E-02 9.34199 E-02 i;05tlflE-0l 1.124506-01 1.14100 E-01 1.11220E-01 1.06570E-01 1.007C0E-01 8:773«E-02 7.525 89E-02 GRP. 16 5.60B20E-06 1.38990E-05 3.33860E-05 4.89350E-05 6.480 IQE-05 7.588506-05 7.876106-05 7.34370E-05 6.21080E-05 4.66100E-05 1.4083OF-0S 6.56610E-06

Table 6.14 (continued)

O R N L - D W G 7 4 - 9 6 3 4

OIR. GRP. L GRP. 2" GRP. 3 GPP. 4 GRP. 5 GRP. 6 GRP. 7 GRP. 6 1 1.972505-05 3.15320E-05 8.30120E-05 3.15780F-04 1.16690E-03 1.40290E-03 2.12680E-03 3.03910E-03 2 3.55750E-05 4.44050E-05 I.00660E-04 3.568706-0* 1.2S850F-03 1.54090E-03 2.29240E-03 4.23320E-03 3 10130E-05 5. 76270E-05 "" I T S T O D F ^ 5'.LIB20E-0«—OTVT:TOE^r~Z.15J60e-03 -3:388«F-W6.W869e-(53-4 4.40320E-05 6.794S0E-05 1.71190E-04 6.44500E-04 2.35040E-03 2.87760E-03 4.35850E-03 B.14680E-03 5 4.64150E-05 7.65560E-05 1.98390E-04 7.58230E-04 2.78880E-03 3.41670E-03 5.19739E-03 9.75490^-03

6 4.63760E-03 7 4.38320E-05 8 4.41130E-05 9 4.49190E-05 10 4.4537CE-05 11 4. 12000F-05 12 2.63310E-05

8. 067C0E 7,992306 7,9301 OE 7. 7566 OE' 7.29270E 6. 0675 OE' 4.5508 OE

-05 2.13350E-04 •05 Z. 13880E—04 -05 2 . 09590E-04 :o§~ 2.b0200F-c)4 -05 1.82960E-04 •05 1.44480E—04 -05 1.16400E-04

8.24040E-04 8.31760E-04" 8.11220E-04 T 67340E-0* 6.92780E-04 5.35240E-04 4.46100E—04

3.04890E-03 3.08990E-03 3.001BOE-O3 2.53010E-03 1.93750E-03 1.65380E-03

3.73620E-03 3.78750E-03 3.67750E-03 3.45743 3.I0590E-03 2.39850E-03 2.03010E-03

5.69740E-03 5.78B80E-03 5.60790E-03 5.25615F-63" 4. T0T60E—03 3.63120E-03 3.11 WOE—03

1.072 OOE-O2 1.09110E-02 1.055 20E-02

8.830 19E-03 6.835 40E-03 5.87869E-03

O I R . 1 2 3 4 5 6 7 8 9

10 11 12 DIR. 1

2 3 4

" " 5 6 7 8 9

10 "11 12

GRP. 9 6.83260E—03 7.13729E-03 1. 08370E-02 1.42180E—02 1. 7192 OP-02 1.90040E-02 1.94250E-02 1. 87150E-02 1.74100E—02 1. 54S80E-02 1. 19760E-02 1.04910E-02

GRP. 17 1. 85240E—04 2.88920E-04 4.36S20F-04 5.61210E-04 7.05300E-04 7.88390E-04 7.I6380E-04 8.26400F-04 9.01640E-04 8.89040E-04 6.58260E-04 5.06050F-04

GRP. 10 8.?5"<5J"9E-Sr 9.22060E-03 1.41010E-02 I. 8636 OE-02 2.26720E-02 2.51270E-02

2.46650E—02 2.2 8470E-02 2.02940E—02 1.5 7500E-02 1.38130E—02

GRP. il "T."5U860E-er" 1.372106-02 2.14040F—02 2.87360E—OZ 3.53900E-02 3.94460E-02

3.86260E-02 3.55710E-02 3.14650E-02 2.446TOE—02 2.1&870E-02

GRP. 12 1.16430E-02 1.26990E-02 2.00500E-02 2.7Z890E-02 3.40250E-02 3.79990E-02

3 .69750E-02 3.39340F-02 3.QOOlOE-02 2.34130E-02 2.07140E-02

GRP. 13 L.36070E-02 1.51830E-02 2.45410E-02 3.43070E—OZ 4.39820E-02 4.96840F—02

4.78360E-02 4.33460E-02 3.80 830E—02 2.95950E-02 2.61470E—02

GRP. 14 T . 7BL49G-03 1.27800E-0Z 1.95950P-02 Z.7Z470E-0Z 3.55880E-02 4.05320E-02

3I86590F-02 3.47440P-02 3.05560E-02 2.36240E-02 1.93120E-02

GRP. 15 ~K<UlO<JE-05~ 8.81319E-.03 1.24070E-02 I.S9I20E-0Z 2.00270E-02 2.21670E-02 2.2046OE-OZ 2.16970E—02 2.01930E—OZ 1.573706-02 9.40739E-03

GRP. 18 3. 18460E-07 2.54340E—06 4.53430E—06 5.44760E-06_ 5. 9 809 0£-"06 " 6.19570E-06 6.29380E—06 5.90710E-06 6.3095OE-06 5. 973 5 OE-06 3.O30r0F-05~ 2.29760E—06

GRP. 16 T."«2TJ5C=5r~ Z.62230E-03 3.69010E-03 4.47830E—03 5.31569E—03 5.60170E-03 Si l9549E=ar -5.90333E-03 6.S6890E—03 6.512 19E-03 4.81980E-03 2.68120E-03

ON 00

Table 6.15. APRFR IIID Leakage. ORNL-OWG 74-9631

• * » INVERT I N * 12 INPUT ARRAY ROWS JN = 39 INPUT ARPAY COILMNS JO » 1Z UUTPUT ARPAY ROWS JO * 39 OUTPUT ARRAY CULUHNS NED « 0 0 / 1 EDIT / NO EDIT NOU > 6 OUTPUT LOGICAL UNIT

NEUTRON

D IR . 1 2 3 4 5 6 7 B 9 10 11 IZ

GRP. I 1 .60990E-04 1 .792406 -0 4 2 . 3 81506-C4 2 .87940E-04 3 .30140E-04 3.61 Taoe-m 3. 748506-04'• 3 . 6 1 2 8 0 6 - 0 4 3 . 465306- 04 3 . 2 9 7 0 0 6 - 0 4 2 .97 3006-04 2 .735006 -04

GRP. 2 1 .789506-03 1. 999606-03 2 . 7575 OE-03 3.4028OE-O3 3 . 9 9 6 8 06-03 4 . 4 3 6 8 0 6 - 0 3 .4 .6 27006-03 4 .426406 -03 4 .2166 06-03 4 . 002906-03 3 .640206-03 3 .352106 -03

GRP. 1 7 . 3 2 1 1 0 6 - 0 3 8 .234506 -03 1 .158006-02 1 .449506-02 1 .72550E-02 1 . 9 * 3 3 0 6 - 0 2 2 . 0 3 3 6 9 6 - 0 2 I . 9 3 8 9 0 6 - 0 2 1 .837306 -02 1 .737606-02 US7730E-02 1 .444206-02

GRP. 4 1 .554906-02 1 .762506 -02 2 . 4 7 *706-02 3 . 1 0 2 7 0 6 - 0 2 3 .714006 -02 4 . 2 0 4 1 0 6 - 0 2 4 . 4 0 4 2 0 6 - 0 2 4 .21230E-02 3 . 9 6 8 2 0 6 - 0 2 3 . 7 5 6 7 0 6 - 0 2 3 .367006 -02 3 . 0 4 1 6 0 6 - 0 2

GRP. 5 2 .362206-0? 2 .713906-02 3 .745706-02 4 .646606 -02 5 . S U 7 0 E - 0 2 6.212106-02 6 .475096 -02 6.226606-02 5 .909906 -02 $ .566206-02 4 .946606 -02 4 . 3 9 1 9 0 6 - 0 2

GRP. 6 3 .115106 -02 3 .61580F-02 4 .833106 -02 5 .872206 -02 6 .654996- 02 7 .62309E-02 7 .901296 -02 7 .647196-02 7 . 3 0 0 6 9 6 - 0 2 6 .90230F-02 6 . 1 1 8 9 0 6 - 0 2 5 .358306 -02

GRP. 7 3 .662606-02 4 .270006 -02 5 .564106 -02 6 . 6 4 9 2 9 6 - 0 2 7 .669196-02 8 . 463596-02 8 .745396 -02 8 .506196-02 8 .196296 -02 7 .727496-02 6 .819496 -02 5 .926506 -02

GRP. 8 4 .900606-02 5.776106—02 7 .490306-02 8 .908196 -02 1 .025006-01 1 .129006 -01 1 .161406 -01 1 .13O00E-0 I 1 .083906-01 I.C2680E-01 9 .007896 -02 7 . 7 4 1 9 9 6 - 0 2

D I R . 1 2 3 4 5 6 7 8 9

10 U 12

GRP. 9 3 . 349606-02 4 .016806 -02 5 .33220E-02 6 .422696 -02 7.495496—02 8 .33399E-02 8 .613096 -02 8.398096—02 8.040296—02 7 .584796 -02 6 .56 9096-02 5.5377CE-02

GRP. 10 1 .922906-02 2 .359206 -02 3. 1746 06-02 3 . 841906-62 4 .5039C6-02 5 .014906 -02 5 .176706 -02 5 .049906-02 4 .827906 -02 " 4 . 5 4 1 1 0 6 - 0 2 3 . 8 84 1 06 - 0 2 3 . 20070H-02

GRP. 11 9 . 0 1 0 8 0 6 - 0 3 1 .144606-02 1 .584606-02 1 ,940906-02 2 . 2 9 6 6 0 6 - 0 2 2 . 5 6 6 2 0 6 - 0 2 2 .646806 -02 2 . 5 7 8 2 0 6 - 0 2 2.4SO<T06-02 2 .288406 -02 1 .915306-02 1 .536206-02

GRP. 12 5.227106—03 7 . 2 4 2 2 0 6 - 0 3 I .O6360E-02 1 .336006-02 1 . 6 I 4 8 0 6 - 0 2 1 .824806-02 1.086106-02 1 .829806-02 1.71990E-02" 1 .584506 -02 1 .267306-02 9 . 6 5 4 6 0 6 - 0 3

GRP. 1 ) 9 .240506-04 1 .685406-03 2 .629806-03 3 .291606-03 3 .931006-03 4 .367106 -03 4 .48260E-03 4 .358706-03 4 .059f i0£-03 3 .646106-03 2 .508306 -03 1 .635506-03

GRP. 14 1 .168306-04 3 .089206 -04 S .720706-04 7 . 4 9 3 5 0 6 - 0 4 9 . 1 6 0 8 0 6 - 0 4 1 .021506-03 1 .042206-03 9 . 9 1 7 3 0 6 - 0 4 8 .81620E-04 7 .264206 -04 3 .32410E-04 1 .684406-04

GRP. 15 3 . 2 5 7 8 0 6 - 0 5 B.826506-05 1 .787206-04 2 . 4 1 8 5 0 6 - 0 4 3 . 0 ! 1606-04 3 .388806-04 3 . 4 6 4 8 0 6 - 0 4 3 . 2 6 9 2 0 6 - 0 2 . 8 5 7 2 0 6 - 0 4 2 .277306 -n4 8 .515806 -05 3. 760206-05

GRP. 16 6 .454606 -06 1 .458306-05 3 .484206-05 5 .110806 -05 6 . 7 5 1 0 0 6 - 0 5 7 .870306-05 8 .135906-05 7 .565806-05 6 .383206 -05 4 .787706 -05 1 .449406-05 7 . 0 2 6 1 0 6 - 0 6

D I R . 1 2 3 4 5 6 7 8 9

1 0 11 12

GRP. 17 1 .248106- 06 I . 844206—06 5 .092706 -06 8. 368206-06 1 .216006-05 I . 508306-05 1.592 706-05 I . 446006-05 1. 149006-05 7 .93 820E-06 2.206006-06 J .262306 -06

GRP. 18 1.9757C6-07" 2 . 0 0 0 3 0 8 - 0 7 4 . 7 6 1 0 0 6 - 0 7 9 . 0 2 4 9 0 6 - 0 7 1.52780E—06 2 . 1 1 0 4 0 6 - 0 6 2 .313306-06 '" 2 .014006 -06 1 .446206 -06 8.82I40E—07 2 .962006 -07 1 .97940E-0?

GRP. 19 3 .562106 -08" 3 . 3 9 0 6 0 6 - 0 8 4 . 8 4 1 5 0 6 - 0 8 7.4A0C96-08 1 .30470E-07 1 .956006-07 2 : i 8 7 1 0 r - 0 7 " 1 .831106 -07 1 .23880E-07 8 . 1 0 6 7 0 6 - 0 8 5 . 5 6 5 6 0 6 - 0 8 3.8646OE—08

GRP. 20 5 . 4 4 4 2 0 6 - 0 9 5 .17630E-09 6 . 8 7 4 2 0 6 - 0 9 8 . 2 4 1 6 0 6 - 0 9 1 .007306 -08 1.216806-08 1 .208J0E-08 t . 0 7 5 9 0 6 - 0 9 9 .83090E-09 9 . 7 1 6 9 0 6 - 0 9 8 .803406 -09 5 . 9 1 9 6 0 6 - 0 9

GRP. 21 1 .903406-10 1 .709706-10 2 .21250E-10 2 . 6 1 4 5 0 6 - 1 0 2 .942106-10 2.9248OE-10 2 .2S490E-10 2.314406—10 2.87T60E-10 3 .184306 -10 2 .838606 -10 1 .875306-10

Table 6.14 (continued)

PHOTON ORNL-DWP 74-9632

D I R . 1 2 3 4 s

G R P . 1 2 . 8 4 6 8 0 E - 0 5 4 . 1 1 7 1 0 E - 0 5 4 . 7 0 6 6 0 6 - 0 5 5 . 0 7 9 B 0 E - 0 5 5 . 3 2 9 3 0 E - 0 5

GRP. 2 3 . 4 B 5 3 0 E - 0 5 4 . 6 5 7 4 0 E - 0 5 6 . 0 1 7 8 0 6 - 0 5 T . 0 5 7 2 0 E - 0 5 7 . 9 5 9 4 0 E - 0 5

GAP. 3 7 . 5 7 6 7 0 6 - 0 5 9 . 5 8 5 4 0 E - 0 5 I : 3 3 M O F = « 1 .64S60E—04 1 . 9 5 6 1 0 E - 0 4

GRP. 4 2 . 6 4 5 9 0 E - 0 4 3 . 2 3 5 5 0 6 - 0 4 *;745T0r-«" 6.000506-04 7.21«30E-M

GRP. 9 9 . 3 6 4 1 0 E - 0 4 1 . 1 1 2 3 0 6 - 0 3 U6T750E-01 2 . 1 5 5 3 0 6 - 0 3 2 * 6 2 6 5 0 6 - 0 3

GRP. 6 1 . 1 3 2 5 3 6 - 0 3 1 . 3 6 5 9 0 6 — 0 3 J . 0 5 6 6 0 E - 0 3 2 . 6 4 3 0 0 6 - 0 3 1 . 2 2 1 8 0 E - 0 3

GRP. 7 1 . 6 8 9 3 0 E - 0 3 2 . 0 1 1 3 0 6 - 0 3 3 . 0 7 1 2 0 E - 0 3 3 . 9 7 9 8 0 E - 0 3 4 , 8 8 1 3 0 5 - 0 3

GRP. 8 3 . 1 0 3 6 0 E - 0 3 3 . 6 9 7 4 0 6 - 0 3 5 . 6 9 2 7 9 E - 0 3 7 . 4 2 0 0 0 E - 0 3 9 . 1 4 5 8 9 6 — 0 3

6 5 . 2 i a \ 0 f - 0 5 7 4 . 8 7 U S 0 E - 0 5 8 4 . 7 0 3 6 0 6 - 0 5 9 4 . 6 7 4 0 0 E - 0 5

10 4 . 5 8 6 5 0 E - 0 5 11 4 . 2 1 4 0 0 F - 0 5 1 2 2 . 7 2 0 8 0 6 - 0 5

D I R . GRP. 9 1 5 . 2 2 8 6 9 6 - 0 3 2 6.1262 OF-03 3 9 . 6 8 9 7 0 6 - 0 3 4 1 . 2 B 3 1 0 E - 0 2 5 1 . 6 0 1 7 0 F - 0 2 6 1 . 8 5 0 6 0 6 - 0 2 7 1 . 9 3 6 8 0 6 - 0 2 8 1 . 8 7 5 8 0 F - 0 2 9 1 . 7 5 5 5 0 E - 0 J

10 1 . 5 7 2 1 0 E - 0 2 11 1 . 2 3 3 8 0 E - 0 2 12 1 . 0 8 2 0 0 E - 0 2

D I R . t 2 3 4 5 6 7 8 9

10 1 1 1 2

GRP. 17 1 . 8 6 0 5 0 E — 0 4 2 . 8 2 5 4 0 E - 0 4 4 . 2 B 9 8 0 E - 0 4 5 . 5 6 2 8 0 6 - 0 4 7 . O 3 0 S 0 E - 0 4 " 7 . 8 5 7 3 0 E - 0 4 7 . 7 4 1 8 0 6 - 0 4 8 . 3 5 4 6 0 E - 0 4 9 . 1 6 9 1 0 6 - 0 4 9 . 0 6 1 1 0 6 - 0 4 6 . 7 6 9 2 0 6 - 0 4 5 . 3 7 7 8 0 6 - 0 4

8 . 4 3 4 9 0 6 - 0 5 8 . 3 7 4 9 0 6 - 0 5 8 . 1 4 7 1 0 1 : - O S 7 . 9 2 0 9 0 6 - 0 5 7 . 4 4 2 8 0 E - 0 5 6 . 2 2 9 8 0 6 - 0 5 4 . 6 9 4 7 0 F - 0 5

GRP. 10 6 . 7 2 4 5 0 6 - 0 3 7 . 9 2 9 4 0 E - 0 3 1 . 2 6 3 4 OE-02 1 . 6 8 3 7 0 E — 0 2 2 . 1 1 3 8 0 6 - 0 2 2 . 4 4 8 5 0 6 - 0 2 2 . 4 6 4 5 * 0 6 - 0 2 " 2 . 4 7 2 4 0 6 - 0 2 2 . 3 0 3 7 0 6 - 0 2 2 . 0 5 8 5 0 6 - 0 2 1 . 6 2 2 7 0 6 - 0 2 1 . 4 2 4 6 0 6 - 0 2

2 . 1 3 3 8 0 6 — 0 4 2 . 1 7 0 8 0 6 - 0 4 2 . 1 2 0 6 0 F - 0 4 2 . O 2 3 5 0 F - 0 4 " 1 . U 5 9 4 0 E - 0 4 1 . 4 8 4 1 0 E - 0 4 1 . 2 0 0 3 0 E - 0 4

GRP. U 9.9SS*0p:0T 1 . 1 7 1 2 0 E - 0 2 1 . 9 1 2 7 0 E - 0 2 2 . 5 8 9 1 0 6 - 0 2 3 . 2 9 2 1 0 E - 0 2 3 . 8 4 0 2 0 6 - 0 2

3 . 8 7 0 8 0 6 - 0 2 3 . 5 8 6 1 0 E - 0 2 3 . 1 9 2 1 0 6 - 0 2 2 . 5 2 2 8 0 E - 0 2 2 . 2 3 7 0 0 E - 0 2

8 . 1 1 2 8 0 6 - 0 4 8 . 3 4 9 9 0 6 — 0 4 8 . 1 5 9 5 0 E - 0 4 7.7ri?/X-04-7 . 0 3 1 1 0 E - 0 4 5 . 5 0 3 6 0 E - 0 4 4 . 6 0 1 2 0 6 — 0 4

GRP. 12 " * 7 1 2 2 1 0 E - 0 J •

1 . 0 9 3 9 0 6 - 0 2 1 . 8 1 0 7 0 E - 0 2 2 . 4 7 9 0 0 E - 0 2 3 . 1 7 8 9 0 E - 0 2 3 . 7 0 8 2 0 6 - 0 2

2 . 9 8 3 0 0 6 - 0 3 3 . 0 9 9 4 0 6 - 0 3 3 . 0 1 3 4 0 6 - 0 1

2 . 5 6 7 1 0 6 - 0 3 1 . 9 9 3 8 0 E - 0 3 1 . 7 0 5 7 0 E - 0 3

GRP. 13 -r:usB70F=0r" 1 . 3 2 1 2 0 6 - 0 2 2 . 2 4 4 8 0 E - 0 2 3 . 1 4 7 2 0 6 - 0 2 4 . 1 2 9 1 0 E - 0 2 4 . 8 5 5 4 0 E - 0 2

3 . 7 0 5 1 0 6 - 0 2 4 . T 8 9 2 0 E - 0 2 3 . 4 2 0 6 0 6 - 0 2 3 . 0 4 3 1 0 6 - 0 2 2 . 4 1 4 7 0 E - 0 2 2 . 1 3 6 7 0 E - O 2

4 . 3 6 6 4 0 E — 0 2 3 . 8 6 2 6 0 E - 0 2 3 . 0 5 3 9 0 E - 0 2 2 . 6 9 8 3 0 E - 0 2

3 . 6 5 8 7 0 E - 0 3 3 . 7 8 8 4 0 6 - 0 3 3 . 6 9 1 8 0 F - 0 3 3 . 4 8 9 0 0 6 - 0 3 3.150806-03 2 . 4 6 7 3 0 F - 0 3 2 . 0 9 3 8 0 E - 0 3

GRP. 14 1 . 1 8 3 1 0 F - 0 2 1 . 8 7 1 0 0 E - 0 2 2 . 5 8 5 9 0 6 - 0 2 3 .406OOF—02 3 . 9 8 6 0 0 E - 0 2

~ 4 V 0 « 3 J W - 0 2 " 3 . 8 5 9 6 0 6 - 0 2 3 . 4 9 1 7 0 E - 0 2 3 . 0 9 5 5 0 E - 0 2 2 . 4 3 1 9 0 6 - 0 2 1 . 9 9 3 3 0 E — 0 2

3 . S 6 8 6 0 E - 0 3 5 . 7 8 4 0 9 6 - 0 3 5 . 6 2 7 1 0 E - 0 3 5 . 3 0 3 3 0 E - 0 3 4 . 7 7 5 8 0 6 - 0 3 3 . 7373 0 6 - C 3 3 . 2 1 1 7 0 E - 0 3

GRP. I S S.4822dr-01 8.96699E-03 1 . 2 R 3 6 0 E - 0 2 1 . 6 3 5 7 0 6 — 0 2 2.023106-02 2 . 2 2 2 4 0 E - 0 2 2.141306-02 2.186206-02 2 . 1 7 I 8 0 E - 0 2 2 . 0 4 0 7 0 E - 0 2 1 . 6 0 3 7 0 F — 9 . 7 9 1 4 0 6 - 0 3

1 . 0 4 7 0 0 E - 0 2 1 , 0 8 9 6 0 6 - 0 2 1 . 0 5 8 4 0 6 - 0 2 9 . 9 5 $ < # E - 4 ) 3 8 . 9 5 6 9 9 6 - 0 3 7 . 0 3 * 3 0 E - 0 3 6 , 0 6 2 7 0 E - 0 3

GRP. 1 6 1 . 9 4 2 2 0 F - C 3 2 . 6 6 0 5 0 6 - 0 3 3 . 7 9 4 3 0 6 - 0 3 4 . 6 6 2 5 0 F - 0 3 5 . 5 0 1 2 0 6 - 0 3 5 . 7 3 6 1 9 6 - 0 3 5 . 2 4 2 7 4 F - 0 3 5 . 9 6 5 5 0 6 - 0 3 6 . 6 6 1 8 0 E - 0 3 6 . 6 1 6 2 0 E - 0 3 4 . 9 0 J 5 0 E - 0 3 2 . 8 6 4 5 0 6 - 0 3

GRP. 18 3 . 1 9 0 0 0 6 - 0 7 2 . 5 B 5 1 0 E - 0 6 4 . 6 1 0 8 0 E - 0 6 5 . 5 3 9 2 0 E - 0 6 6 . < 3 f l 0 5 < S - W 6 . 2 9 7 7 0 6 - 0 6 6 . 3 9 7 7 0 6 — 0 6 6 . 0 9 5 2 0 6 - 0 6 6 . 4 4 3 0 0 5 — 0 6 6.1000 06-06 3 . 1 4 9 9 0 6 - 0 6 " 2 . 3 7 0 7 0 E - 0 6

O

71

«u>r S.0 -

WAFCUTFLM L&KPGE C W

».o .

30.0 .

tt.0 .

10.0 .

106 .

&.tno .

•vtn _

Z

-JS.0 .

>a.o .

•0.9 .

•30.0 .

OPWR JCUTFON i&*fcz omn-ovc 74-BU PPFLFR NCUTKN LERKPCE CPOUP a

5 «o.o

/ \ \ "V

\ I

) I

1 /

/

-so.o

i

/ X —' lN

V 1 \ 2.00 2.00

yi / / /I

y -14.0 -lt.0 -1L0 -lt.0 -1L0

i •K.0 RpRfR tcwnoN UMAGE BWTFT RCUTRON ICFKFLCE C R U , 6

30.0 -2V0 -30.0 -i*.o -10.0 -V00 -

0.001 — . -S.00 -

->».o --20.0 -•RO -•30.0 --3S.0 . •*XQ -

•S0.FI -•8.0 -

I * IC-0 _

S0.0 .

«.o _ AO ->0.0 _

10.0 . f.OOl _

49.0 .

-30.0 .

-"0.0 -

•SO.O _

"A"

; i ' f t

•n

Fig. 6.3. Angular Distribution of Reactor Source in the Vertical Plane.

72

flAara i d i t M u • c i m v c a «

<40.0

flpffft tgUlfOM LEPKBCE CBSff 10 -nn ««-t> ««-t>

\ \ lft.0

<0.0

9. CO

\ lft.0

<0.0

9. CO

\ lft.0

<0.0

9. CO \

lft.0

<0.0

9. CO

-s.co -s.co 1 -IS.0 I -IS.0 { /

/

S

•10 0 •10 0

-40.0

Fig; 6.3 (continued)

73

Fig. 6.3 (continued)

fiPRFR NEUTRON LEAKAGE GROUP 19

\ \

y \

; / » ! 1 /

V /

<

j

12.0 n 11.0 1 10.0 I 9.00 4 8.00 7.00 6.00 S.OO 4.00 3.00 2.00 I.OO n.oos -MM

-..00 -3.00 -4.00 -S.OO -6.00 -7.00 -8.00 -9.00

flPRFR NEUTRON LEAKAGE GROUP 20

-11.0 •12.0 -O.O -14.0 -IS.0 -16.0 -17.0 -IS.0 -19.0 -20.0

V \

r t

•4 V "7*

fS

-A V-


ORNl-DWS 74-0534 flPBFR NEUTRON LEAKAGE GROUP 21

[ 24.0 1 22.0 (

20.0

18.0 IS.O 14.0 12.0 10.0 s.oo 6.00

4.00 2.00

0.000 -2.00 -4.00 -6.00 -0.00 MM" -12.0 -14.0 -16.0 -ID.0 -20.0 -22.0

-26.0

-26.0

-90.0

"S s. \ V 1 1 1

\ \ / \ / \

Sr /

VI

75



77

Fig; 6.3 (continued)

ORNL-DWG 74-7510 s 1 1 II 1 II 1 ... J | 2 .SOURCE AT -4° "1 -1 5 OURCE AT -45°

DURCE AT -90° (DOWN)

-1 5 p OURCE AT -45°

DURCE AT -90° (DOWN)

J I

TS

7 OURCE AT -45°

DURCE AT -90° (DOWN) •2 OURCE AT -45°

DURCE AT -90° (DOWN) •2 OURCE AT -45°

DURCE AT -90° (DOWN) 1

3 S 3 S 1 j r-. . . J

*

s * «

*

s 2

«T

i I

2

«T 2

«T i J

i 4

s i 4

s I

? 7 s

—J 7 s f 8 8

; S «! S «! J if » A » A -1-3? s -,-1 ? a: S s -5 nS "2 1 r,7 tr

ENERGY (EV)

Fig. 6.4. APRFR Reactor Source (Neutrons) (DOT Calculation).

10

10"

ORNL-DWC 74-6465

SOURCE AT -4°

SOURCE AT -45°

SOURCE AT -90° (DOWN) . J

• 5 10 £ I- -2 Q 10 U i

K H-

I -S 10"

£ 10 —i i- 4

£ Ui M 3 EL

JO

10

10 ,-7 icT IT ENERCr (EV) 10'

Fig. 6.5. APRFR Reactor Source (Photons) (DOT Calculations).

80

6.2. Appendix B - Reactor Data vs Experiment

The reactor leakage data can be compared with experiments performed

by Kazi and Williams.1£f The fraction of flux above energy E at the radial

reactor surface is shown in Fig. 6.6 for the IIIC and HID configurations.

The two results are almost identical. These data can be compared with

integral spectrum measurements made by activating foils of materials

having a more-or-less distinct energy threshold for neutron interaction.

Table 6.16 shows the foils, the thresholds, and certain ratios which can

be formed between them. Tlie experimental data involving Pu have been

revised to reflect a Pu/S ratio of 8.0, as indicated by Kazi in August,

1973.15

The calculated ratios agree with the experiment within an RMS error

of 8%, which indicates an accurate leakage spectrum. The total neutron

fluence of energy E > 3 MeV is also available for comparison, but the

experimental data are ambiguous here. The value quoted for APRFR (Table

6.17) does not agree very well with comparable measurements on the nearly

identical Health Physics Research Reactor (HPRR) at Oak Ridge. The

resolution of the discrepancy was not known at this writing. A measure-

ment on a similar reactor, WSMR-FBR at White Sands, agrees better with

the APRFR value.

The calculation lies between the APRFR value and the WSMR-FBR value.

Thus, we can conclude that our results agree with these two of the three

experiments.

8 1

ORNL-DWG 74-9743

RPRFR RRDIRt SURFACE FLUX

10- * s 1(F 2 T JQO 2 5 10' ENERGY.E CEVI

Fig. 6.6. Cumulative Flux Distribution at Reactor Surface.

Table 6.16. Flux Ratios

Foil i. Min Flux E>E Min

S3 3 MeV 0.112 S2.5 2.5 MeV 0.155 U 1.5 MeV 0.310 Np 0.75 MeV 0.570 Pu 1 KeV 1.000

Meas Calc Error

Pu/S3 8 . 0 8 . 7 9%

Pu/S2>5 6 . 0 , 6 . 4 7% .

N P / S 2 . 5 3 . 9 3 . 7 -5%

U / S 2 . 5 1 . 9 2 . 0 5 %

Pu/U 3 . 2 3 . 2 0

Np/U 2 . 1 1 . 8 -14%

Pu/Np 1 . 6 1 . 8 13%

RMS Error In Ratios 8%

83

Table 6-17. Fluence per Fission at Energy E>3 MeV at 1 Meter

A ft J Calculated at -4° 1.3x10 n/cm /fission Measured (APRFR) 1.17xl0-6 Measured (WSMR-FBR) 1.37xl0_6 Measured (HPRR) 1.92xl0-6

Based on 2.66 neutrons per fission

84

6.3. Appendix C - Revised Definition of Protection Factor

For the reactor-source experiments, the protection factors were defined in terms of directly observable quantities:

Neutron Dose with Vehicle Absent Neutron Dose with Vehicle Present

Gamma Dose with Vehicle Absent Gamma Dose with Vehicle Present

This has the advantage that it can be compared directly with dosimeter

data.

For the weapon-source, a revised definition was also used:

„„ Neutron Dose with Vehicle Absent n PF — Dose Due to Neutron Sources with Vehicle Present

pp _ Y Dose with Vehicle Absent ^ ~ Dose Due to Photon Sources with Vehicle Present

The difference is that capture Y'S produced in the vehicle are included

in the n protection factor determination.

The advantage of the new definitions is that the protection factors

so derived are relatively independent of the ratio of free-field neutron

dose to free-field Y dose. The disadvantage is that these factors could

not be measured directly with instruments.

The effect on the neutron protection factor in the problem studied

is negligible, but the effect on the y factor is to increase it considerably.

Capture Y'S dominated direct penetration by roughly a factor of 2, partly

due to the fact that the external dose is more than 90% neutrons. Thus,

85

the Y dose due to external Y'S only, is only a small portion of the

total Y dose, and the protection factor is increased by roughly a factor

of 3.

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