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K 379MONTE CARLO CALCULATION OFTechnical Report ........ ...............I .............. ........................................................................... ...
........... NEUTRON STREAMING THROUGH.. ................................................................................................................................... ......... TWO-LEGGED-DUCT ENTRANCEWAYS........................................................................................................................................................................................................................................... ..................................................................................................................................... ....................................... ............................ .............................................................................................. - -..................................................................................... June 1965...................................................................................................................................................................................................................................................................................................................................
...............................................................................................................................................
BEST AVAILABLE COPY'.................................................................X.,.......... ..................... ................X.:
U. S. NAVAL CIVIL ENGINEERING LABORATORY
Port Hueneme, California
VIM?
MONTE CARLO CALCULATION OF NEUTRON STREAMING 'THROUGHTWO-LEGGED-DUCT ENTRANCEWAYS
Y-F008-08-05-201, DA'A-11.026
Type C
by
"Leonard B. Gardner and Alan J. Mettler
ABSTRACT
Several techniques for calculating dose rates in the study of shelter entiancewayi Iare reported herein. Calculations have been verified by ,xperiments. These calz.uln-tions also determine neutron energy spectra, a parameter that ii difficitit to measureand which is very useful in gaining insight into the design of protectivs str,,turtsi.Roth the neutron flux spectra and dose rates are calculated for various positions alongtlhir r.enterl;ne of a two-legged duct. Calculations were performed utili7int,, theAI)ONIS computer code which solves the Neumann approximation to the transporte•quation by Monte Carlo techniques. These Monte Carlo catculat;ons weiie comparedto ,tcond-leg calculations utilizing a semiempirical albedo fnrmula, aild were alsocompared to experimental measurements made with a tissue equi,.alent dosimeter.Included is a discussion of UNIGEOM, a generalized computer program for ADONISq.ometry, designed to be run on the IBM 7094.
Oualifisod requlsterit may obtain copies of tf•is report from DOC.PIolvos to rho Cleoringhouse is -3vthrirod.
The Lqborotory invites comment on thfis report, particularly on theresults obtoinad by tkose who have applied the information.
This work sponsored by the Defense Aonm*c Skpport Agant-y.
I A
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TSL-121-2/65 DATE PROCESSED: . -'•" o i,',- s
PROCESSOR: . st1L
r
INTRODUCTION
The U. S. Naval Civil Engineering Laboratory has for some time experimentedwith the streaming of nuclear radiation through the ducted entranceways of scale-model shelters, using 14.5-Mev neutrons as source particles. This energy approximatesthat of the prompt neutrons released in a fusion-type detonation.
There are many techniques for calculating the dose rate of streaming neutrons,and this report compares results of the ADONIS Monte Carlo calculations with albedocalculations. All of the calculations shown have been verified by experiment. Thegreat advantage in employing calculations is that costly and time-consuming experi-ments are minimized.
The work reported herein is for the case of neutrons streaming through 3x 3-foot-square and 11 x 1 1-inczh-square two-legged concrete ducts. The 14.5-Mev neutronsource was placed just inside the duct entrance.
ADONIS COMPUTER PROGRAM
ADONIS1 is a Monte Carlo computer program for solving the Neumannapproximation to the transport equation governing neutron and gamma-ray streaming.It is written in FORTRAN 11, version 2, for the IBM 7090, and ten tapes are required.ADONIS treats a problem having up to a maximum of 80 regions which, when com-bined, must cover all XYZ space where each region is a parallelepiped. It isimportant to note that the geometry diagram I in Appendix C of the ADONIS manualcontains an error in the designation of tWe coordinate system. Also, it is necessarythat the exit from the duct be in the positive Y direction and into the highest num-bered region.
The particle flux is divided into energy groups called bins, of which a maximumof 10 is permitted. For a neutron problem, approximately seven nuclides may be used;however, for a gamma-ray problem more nuclides are possible. These nuclides mustcompletely describe the material composition of each prrallelepiped. The compositionof each region may differ, but the composition within a particular region is limited toa combination of, at most, five elements.
The geometric input required for ADONIS is time-consuming and complicatedto prepare, even with the aid of various computer programs designed to simplify thistask. In geneial, the geometry must be recomputed for each change in duct configu-ration. In many cases all that will be changed are dimensions such as length and
width of the legs, height of the duct, and the amount of material surrounding theduct. In order to facilitate the use of ADONIS in investigating the effects of suchchanges in duct parameters, a computer program was written which will accept thephysical characteristics of the duct and as output will yield punched cards ready foran ADONIS run. These cords consist of the bounding plane cards (BPO), adjacentregion cards (IRX), complex plane cards (CMX), and horizontal and vertical planecards (H and V). They define the geometry of ADONIS. The BPO cards give thecoordinates of the mnximum and minimum extent of the regions along the axes. TheIRX cards define which of the regions are back to back. The CMX cards defhc..cwhich of the regions back to more t~aio ono rcgion.
Although subroutines called EASYGEOM and TEST G are available tofacilitate preparing the input cards to ADONIS, mistakes are easily made in geome-tries as complex as those associated with duct problems. To remedy this situation, acomputer program, UNIGEOM, was written at NCEL. The tource deck of this programis listed in Table I. This program incorporates a modified EASYGEOM program asthe main routine and TEST G and its subroutines as a subroutine. The bounding planecards required as input to EASYGEOM are calculated from the physical parametersof the duct by means of a subroutine. The UNIGEOM program all. ws three suchsubroutines. The subroutines included in this report are for a two-' !gged duct andthree-legged coplanar and non-coplanar ducts. Other configurations moy be incor-porated by substituting "duct" subroutines and appropriately changing the callingsequence in the main program.
ADONIS considers the following neutron interactions: isotropic and anisotropicelastic scattering, discrete and continuous inelastic scattering, scattering by hydrogen,and the (n, 2n) reaction in beryllium absorption. The gamma portion of the ADONISprogram considers the Compton scattering of photons where the photoelectric effectand pair production are regarded as absorption. Particle histories in ADONIS areterminated either when an absorption occurs, the particle is degraded below anarbitrary cut-off energy, a kill occurs due to splitting, or the particle escapes. Cross-section data used in ADONIS are called from an organ;zed-element-Jata tape. Asource-data tape containing the position coordinates, direction cosines, and theinitial energy of the neutron or gamma-ray source is required in addition to theorganized-element-data tape and the geometry-input data.
The source-data taFe is generated for the case of either the point sourceincident radiation of neutrons or gamma rays by PSGEN, a program modifed to beanisotropic; in the case of gamma rays produced by neutron interaction, the source-data tape is generated by the GASP'program. The input to PSGEN, which is modifiedto be a 2i source, describes the source as the probability that part'cles exist below aparticular energy. The energy is evaluated for probabilities in 0.1 increments ofprobability from 0 to 1.0. ADONIS is called in through the IBM 7090 monitor system.ADONIS contains dump and edit procedures, selected by turning sense switch 1 "on"at the time these procedures are to be initicted. After dumping, ADONIS may berestarted. Turning sense switch 2 "on" prints on-line the particle history numbers;turning sense switches 3 and 4 "on" writes an off-line trace of each particle path ontape A3.
2
1'
Particle splitting is employed to improve the efficiency of the calculation byassigning importance weights to each of the regions. Regardless of the importanceselected for each reg;on, if the ADONIS program is allowed to run for a sufficientlylong time, the answers furnished by it will be appro-xmately the same. However, inmaking many calcul"-tions it has been determined that the proper selection of weightingfunctions can significantly decrease the amount of running time required. The optimumy'.nlut' m, ;",nrw,-v,'ce for each region may best be selected by a semiempirical approach.First, the geometry is studied and a weight, inversely proportional to importcnce, isassigned to each region based upon the best knowledge of neutron or gamma-raystreaming available to the investigator. Using these values, the program is run fora short period of time, after which the calculated flux in each region is reviewed.The weight of the region is then adjusted in a way which will enhance the probabilityof neutrons going in the desired direction while reducing the probability of neutronsgoing in undesire directions.
It has been experienced that approximately five tries are necessary to optimizethe weight for each region in a duct with two legs and approximately 10 tries forsimilar optimization in a duct with fhree non-coplanar legs. It should oe emphasizedthat a proper selection of weight allows a greater percentage of computer time to bedevoted to following particles of interest; thus, running time for statistically sign;fi-cant determinations of flux may be considerably reduced. A proper selection ofimportance fjnctions and an adequate running time may be judged by comparing thestandard deviation of particle flux to the flux for each energy bin and du:t legion.ADONIS calculates the flux and particle dose in each region. The :atter is accom-plished through either a fine or coarse response function. These two functions differonly in that for the fine function, the response is evaluated at the same energies usedfor cross sections on the element-data tape, and for the coarse function, the responseis averaged over ecch energy bin. Also, the standard deviation of dose is evaluatedonly where fine response functions are used. The response function is simply a functionthat converts particle flux into dose such as relative biological effectiveness (RBE)for the case of neutrons.
ADONIS also provides, as output data for each region, the number of absorptions,births, degradations, and deaths; flux per energy bin; deviation of flux per energy bin;total number of reflected and transmitted particles; particle balance; absorption byelement and region; and coarse dose per energy region. The neu-on fl.x is reportedas the track length per source particle per unit energy in energy interval j per unitvolume for finite regions. In the case of regions infinitely bounded, the total flux isgiven.
3
Analysis of ADONIS Results
When ADONIS is restarted, each run prints only the flux and dose associated
with that run, rather than the best estimate based upon total running time. It was,therefore, necessary to calculate these parameters as follows:
nI Ni
n
n t21;=S = •/;!1(Ni•)
nIN.
nI N;Dii=1D nn
I NiHi
1 2 1 \ 2 n 217 FN-Er a..#NI1(N
In the case of only one run,
SI C "Bl (Ej),Ej 2 j 2
4
where D = best estimate of dose based upon n runs
AEE. = energy increment ofJth binJ
N. = number of histories of ith run
n = number of runs
m = number of energy bins
RBE.(E) = relative ,ologicol effectiveness averaged over the eneigyJ range of the j in bin
S= standard deviation of dose for nth run
a D = best estimate of standard deviation of dose based upon n runs
a.(4') = standard deviation of flux for jth binJ
0 = best estimate of flux based upon n runs
where DO is the incident dose due to the total number of particles emitted by theanalytically simulated neutron source. Since the analytical treatment considersthese to be emitted in one hemisphere, the value of incident dose is divided by 2 IT,
the number of stefidiams in a hemisphere. In actual practice, ADONIS calculatesthe dose per incident source particle, and thus the associated value of incident doseis one source particle multiplied by the RBE of the source particle. This is numericallyequal to the RBE of the source particle energy.
DESCRIPTION OF EXPERIMENTS
In experiments at NCEL, 14.5 Mev neutrons approximated the energy of neutronsreleased in a fusion-type detonation. Neutrons of this energy were available from aneutron generator utilizing the T(d,n)He 4 reaction. A two-legged duct x x3 feet anda three-legged duct 11 x II inches were constructed for the experimental phases ofthis work. The latter was constructed in such a way that the orientation of the thirdleg could be altered to form either the coplanar or non-coplanar case. Plan andelevation drawings of these ducts, including dimensions, will be found in Figures 1,2, and 3. The neutron source was approximated as a point source for the purpose of
5
calculations. In actuality, the active area of the target was a circle approximately
7/8 inch in diameter. Although this target radiated more or less isotropically, atten-tion was taken to orient the geometry in such a way that the plane of the target waslocated concentric to the centerline of symmetry and perpendicular to the ductapproximately one centimeter from the end of the first leg and inside the duct. Thesame locat;on was used for theoretical calculations. These calculc tions were madefor both the 3-foot and the 1 1-inch duct. However, experimental neasurementswere made only with the 3-foot duct, since the physical size of the dosimetersignificantly perturbed the flux and in certain cases simply would not fit.
There is some present concern for the statistcal variation of the experimentallymeasured dose rates, the calibration of the instrumentation utilized, and the determi-nation of tme lncident dose, Do. Nonetheless, it is believed that these results arecertainly accurate to within an order of magnitude. Although plans exist forrepeating these measurements with more care and augmenting them with measurementsperfoaied with heliurm and argon-methane detectors and foil activation techniques,this will not be done for some time. Such work reualy has little bearing upon thecomparison of ADONIS calculations reported herein, since it will, in all likelihocd,simply add more significance to the determinations.
While reviewing the results of Doty's 2 experiments, Song 3 observed that asemlempirical albedo formula could be utilized to fit the duta. He utilizea MonteCarlo results reported by Ballistic Research Laboratory 4 in order to determine theconstants of his formula. He then calculated the dose in the second leg of the
3-foot duct and found it to be in good agreement with Doty's experimentallymeasured values. While it is hrue that many different functions could undoubtedlyfit Doty's data, a physical explanation of neutron streaming can be easily madeutilizing albedo concepts. This was the motivating reason behind the albedo devel-opment for neutron streaming through ducts. For additional validity, Song calculatedthe dose in the second leg of the 11-inch duct, and the ADONIS program wasutilized to determine the dose in both ducts by Monte Carlo calculItions of theNeumann approximation to the transport equation.
MONTE CARLO CALCULATIONS
The program UNIGEOM (Table I), was written to calculate ADONIS inputgeometry from the physical parameters of the three duct configurations shown inFigures 1, 2, and 3. Since TEST G is incorporated in this program, the physicaldimensions of the duct are checked for consistency, and the samu diagnostics arewritten on the output tape as would be had EASYGEOM and TEST G been run asthey were originally intended and not incorporated in the present program.
6
- center of
ý42)
ITA /-3)TB./
,' I
S TS21
r(-A01
2Q) [2 '34
TS11. 5•- T 32 -
. - All center eleme.nt of *h--4 .trscee ae 1 , 1 r 1 cm
center of- ---.- - ceo----------
26', H,
A . .... .I i
A3)1 1 j 27 H.
Figure 1. Two-legged duct with regions and physical parameers.
7
I x-i!LI y
t *•" / center of
CoordinaqeS
"__ __ __ __ __ __ __ __ __ __ __ __ _
I "V 2IIl(D:
2 I
7") 1 , j ~
All center elements of the2r .. m trices ore 1 1 I 1 cm.
S"•"•Center of------------.. Coordinates
F;gure 2. Three-legged coplanar duct with regons and physical parameters.
8
EL
T T -,
I 4.
I ItoLI - , c
I T c
U-w
The appropriate geometry subroutine is indicated by a value on the first inputcard. Input data are read by the main program from tape A2 and are communicatedto the proper routine through Common. Input data in the format F 10.5 are read insequence XL1, XL2, XL3, W1, W2, W3, TSI1, TS12, TS21, TS22, TS31, TS32, TT, DI,D2, D3, DA, DB, DC, DAI, DA2, DA3, TA, TB, TC, TD, HH, Hi, H2, XX. Table IIlists the values of these parameters for each of the three duct configurations. Insome cases these values are zero, but for proper sequencing must be provided. Alldimensions are given in centimeters to be consistent with ADONIS. The variousregions in the duct are also identified in Figures 1, 2, and 3. It will be noted thata matrix of nine regions cuts each important leg in the duct. The center region ofthis matrix is an area 1 centimeter square and may be utilized as a detector regionuseful for comparing calculations to experimental dosimetry at a point. The geometrycoordinates of the subroutine calculations are written as X(A, B), where A has thevalue given in the following table.
Coordinate Coordinate Number
-X I+X 2-Y 3+Y 4-Z 5+Z 6
Coordinates are indicated by X(A, B), where A is thecoordinate indicator and B is the region number.
This table also compares with values in ADONIS notation. The region numberis given by B. The output of UNIGEOM is written on tapes A3 and B5, the latter ofwhich is punched as geometry cards required for ADONIS input. First the BPO cardsare punched, as identified in the preceding table, one card for each region. Thesecoordinates are punched in E 14.5; next, the cards for the coordinates of each com-plex plane for both horizontal (H cards) and vertical (V cards) are punched. Acomplex bounding plane is created for the surface of one region if it is adjacent tothe surfaces of mote than one other region. One or more cards is devoted to thecoordinates of the horizontal and vertical fields of each complex bounding plane.The adjacent region (IRX) cards and the complex plane (CMX) cards needed forADONIS input are also provided by the program. Should there be an error ingeometry or physical dimension that prevents the calculation of geometry, variousdiagnostics are provided. ADONIS input cards calculated by UNIGEOM for theparameters of Table II are listed in Table Ill. This information is provided assample problems.
10
COMPARISON OF THEORY TO EXPERIMENT
Figure 4 shows the neutron energy flux calculated by ADONIS in severalregions associated with the 1 1-inch two-legged duc,, normalized by Do/2tr. Theseregions may be identified by referring to Figure 1. In Figure 4 it is seen that theflux, due to source neutrons, steadily decreases with distance along the first leg.A few source neutrons are also found in region 14, the region in the second legadjacent to the comer. These neutrons must have arrived by direct penetration,grazing the inside comer of the duct. Had it been otherwise, their energy wouldhave been degraded because of interaction. No source neutrons are found at otherregions in the second leg.
It should be noted that the flux approximates a straight line on log-log graphpaper for energies lower than -1 Mev. In order to produce the results shown inFigure 4, it was necessary to loperate the 7090 computer for approxim.•ately 23 hours.Because of this long operating 'time and the straight-line relationship noted, it wasdecided that in the future ADONIS-runs the energy of the low-energy cut-off pointwould be raised. This should resul. in approximately the some statistical deviationwith a much shorter running time.
The dose, corresponding to the flux shown in Figure 4, is shown in Figure 5for the some energy regions. Here, the dose has been normalized as previouslydescribed, by dividing with D0 /21r. It should be noted that the dose in the first legfalls off as an inverse square function of distance, and in the second leg the dosefalls off at a much steeper rate. This corresponds to similar results obtained duringgamma streaming experiments. In Figure 5 are shown the values of dose calculatedutilizing Song's semiempirical albedo formula. It is seen that the agreement is good.
Also shown in Figure 5 are the Monte Carlo/Albedo calculations at two lowersource-particle energies, utilizing the Oak Ridge National Laboratory code. It isseen that the ORNL results do not agree too well and are consistently high. It shouldbe noted that the assumptions of comer lip secondary source preclude utilizing theolbedo formula for the corner region and makes the results of the region adjacent tothe corner somewhat questionable. In Figure 6, the value of D/Do has been correctedto remove the effects of distance. This has been done by multiplying the normalizeddose values shown in Figure 5 by the factor ,n where t is the length 4 the duct leg,and the exponent, n, is determined from the linear slope of the dos,. I;nes shown inFigure 5. If the duct were ideal and long, the figure resulting from this new calcula-tion would ideally be a step discontinuity occurring at the corner regior. Becauseof the small length for the duc! (-140 centimeters), this idealized shape is not realizedand the resultant S-shape is obtained.
In the preceding figures are seen the first collision, multiple collision, and rodtissue eqLuivalence dose rates. In Figure 7, the flux spectrum resulting from ADONIScalculations is shown for the 3-foot duct where the leg length is longer than that forthe 11-inch duct. Because of ;ncrt ised computer running time required for the larger
I1
duct, the low-energy cut-off limit was increased to I kev and the computer runningtime was considerably decreased. This resulted in an increase in the stardard devia-tion of the flux, as shown by the bounds of each of the bars comprising the histogram.This flux is very similar to that shown for the small 1 1-inch duct, and the slopes ofthe spectrum lines below 100 kev approximate those shown in Figure 4 between100 key and 1 Mev. There is considerable difference between the spectra shown forthe large duct in Figure 7 and those shown for the small duct in Figure 4. It is feltthat this could be explained by the fact that the increased length of the large ductaffords a greater opportunity for neutron interaction and, thereby, degradation ofenergy spectra. Results from the two ducts are, however, similar.
In Figure 8 is shown the dose of the large duct, normalized as before, the dosecalculations utilizing the semiempirical albedo formula of Song, the ORNL dose cal-culations, and the experimentally measured dose obtained by Doty. It is seen thatSong's and Doty's work are in good agreement; yet their dose measurements aregreater than those calculated by the ADONIS code and less than those calculatedby the 05R ORNL code. It should be noted that up to this point the importancefunctions of the regions oF the two-legged-duct problem were selected to eliminatemost corner-lip diffusion.
Another Monte Carlo ADONIS ralculation was performed, keeping allconditions similar to those in the previous calculation of the large duct, with theexception that the importance of the rectangular region between the two legs wasnow selected to allow diffusion over the entire rectangular region. The results ofthese calculations are shown in Figure 8 by the dashed lines. It is seen that theseresults lie somewhat above the results of Song and Doty and agree very well withORNL calculations.
In Figure 9 is shown the dose corrected for fall-off berause of length. This isdone by multiplying the dose of Figure 9 by tn as before. Here, the effect of thecorner is more prominent, and the resulting curves more closely approximate the idealstep function. It thus appears that it is necessary to carefully consider the size of thecomer lip secondary source for albedo calculations and, indeed, possibly include somediffision effects. A great deal of caution should be exercised in fitting formulas,because when tue standard deviations of the data are large -as found both experi-mentally and theoretically- it is usually possible to obtain what appears to be agood least-squares fit with almost any curve. On the other hand, it also appears thatit is incorrect to assume maximum diffusion through the rectangular region; rather, itis believed that a morm involved type of interaction is occurring between the twoeffects and that su'h interaction could be approximated by selecting the appropriateimportance functiool for the rectangular region adjacent to both legs. Again, calcu-lations which would eriY •ihs conclusion were not within the scope of the presentwork.
12
10-1
10.113_ _ _ _ _ _ _ _ _
10,14
Regi.on Numbers
2-
14
25
10107o o
10 12 10 104Energy (e
Figure 4. 11ix I I-inch duct
\ -..
* lea* ** 0 * ** 6* a * ** a * *a * Sa .* 0* S
_____________ _______________ _______ I _____ _ ii________________
I _a _a
- Ijif _______
* - - - ---
* � -
-� ���r-- - - -- - -
S
__________________________ ____________ _________ - i�I _____________________* @IaaaaI
10�En.tgy joy)
x 11-inch duct, neutron flux spectrum.
13
Region Numbers
1013
00
107
Aaid aclto o 4Mvnurn
10 '
0z08 0 2 6 0 4 8Di10an7 _ln _ut(m
Fiur 5.11xN I-ichdutnmil z. nutondoe
___________________14
0hC4
___________ U.
wt
In
____ ____ __ ____ __
0 _ _ 15
S.............. .......... . .J......• ..-- .-- ..-...---..• , .., ... •.... ..... .• .... ...... .
.. -,........................ • . ... • .. .... ,....... #............ :,.,•r. ........... ,. .........yr00
, 000_0.
,IU,
.. . .: . ..% I . . . -
S.._.:ii.I I -
I • I
%n x
//V',#
LL.
C4 C4
i i ip o0 d 0 2 A A O o ,/ A * / w * / u ' x f l _ _
u o io N
16
Region Numbers
2 12 13 14 24 2510 -2 -- " -- •-" - -- -'
*... .
S. . . _ - .
103 .. •
COther data combined
0 ote o toeobnv
* A
104 S . .
____i_.... -___ ____ __ _ __ _ A.-
•< 0 ifuis
Al*; caclair fo •vnurn
"*ee vi l i A
: 1N .1 3
* A
, 0* other data first coliio .f Is
• * . .
!E dae ro deN E ,e* fis :~lso rNC L edae, multidpte con*
Wid~~ .1A
"""tigured S. 3dot'ro ddata€oseoie.d
101
10. . i ncludes all dataa .th• : ......... ...
""~ : :nldsaldt ' : " pp c" bl: : : A
%1 Experimentall, observed multiple collision rem egligible
"NCOEL data, 6.r8 coevio rem negoligebe•
- - RNCL data, 1e do..Ma10.9-------_.-- • NCEL data, lirst cetlision rem nepprigoble
- -€ NEL data, mult.ipl, colli.io, rem, ea€rner.: .-
- - - - NCEL data, rod dase diffusion I
__- N• L JtsDfi sta€l~inc rAlogDct m
NFE~dae,8 3rod d dust Ied neutron dose
17 •
w
00
I;UC
'C *-
-oI �
- U)
C
___ ___ ___ ___ itIowa,
Li �___ ___ ___ __ ___ ___ ___ 0i'�
SK£
U�V
gU-
0- - ___-- __- - 0
IC.
2U -
2a0
*0-___ ___- - �EU
@0 -
Liz
Do
0
I.s �id)iO]
18
CONCLUSION AND RECOMMENDATIONS
The Monte Carlo calculations of neutron streaming through model ductedentranceways, performed utilizing the ADONIS code, and the Monte Carlo/Albedocalculations utilizing the ORNL code are in good agreement. Protection factorswere found to be proportional to the duct cross-sectional area. It was found thatalbedo calculations of dose must be based upon a much greater corner penetrationthan previously assumed. This coulJ decrease previously reported neutron protectionfactors by approximately a factor of 10. It remains, however, for these conclusionsto be verified by carefully controlled experiments. By performing analytical calcu-lations, as described, protection factors of structures may be readily determined witha fraction of the effort required by experimental methods. It is, however, necessarythat all analytical techniques be verified by careful experiments. Once verified,the techniques may be freely applied in general extensions to the experiments.
It is recommended that the physics of neutron penetration between the firstand second legs by methods other than streaming through the duct be more intensivelyinvestigated in order to establish the validity of albedo representations. It is alsorecommended that the ADONIS and ORNL codes be accepted as preferred analyticaltechniques for determining neutron streaming through ducted entranceways. TheADONIS code is applicable to most problems. The ORNL code, while requiring lessrunning time, is applicable only to the case of a duct through a dense, infinitelybounded media, and thus it has limited practical applications.
ACKNOWLEDGMENTS
The authors would like to express their appreciation to Drs. R. L. Moerker andC. E. Clifford of ORNL for their discussion and assistance. Dr. Maerker was so kindas to calculate neutron dose in the 3-foot and 11-inch ducts, making these resultsavailable for comparison. They would also like to thank Mr. Y. T. Song, NCELPhysicist, who provided the results of his albedo calculations, Mr. J. Grant, NCELPhysicist, who reduced and analyzed the data reported herein, and Mr. F. S. Moore,formerly of this Laboratory, who originally suggested the idea of writing a computerprogram to calculate ADONIS input geometry. Fortunately, before this idea couldbe implemented, the program EASYGEOM was available and both Mr. K. Pennyand Mrs. Betty Maskewitz, Radiation Shielding Information Center, ORNL, are tobe thanked for making this program available to the authors. It is understood thatEASY'GEOM was originally programmed by Los Alamos Scientific Laboratory.Mr. Penny and Mrs. Moskewitz both provided invaluable and unlimited assistanceand instructed the authors in the use of the ADONIS code. Mr. B. Eisenman ofUnited Nuclear Corporation is also to be thanked for providing to NCEL the ADONIScode. The authors would also like to thank Mr. W. L. Wilcoxson, and the staff of the
19
NCEL Computer Laboratory, and the Point Mugu Computer Laboratory for theirhelpful assistance and cooperation in making the program runs described in thereport. The latter are to be especially thanked since ADONIS requires runningunder FORTRAN II, version 2, necessitating a change in the machine room practiceat Point Mugu.
REFERENCES
1. United Nuclear Corporation, Development Division-NDA. Report no.UNUCOR0635: Adonis, an IBM-7090 Monte Carlo shielding code which solvesfor the transport of neutrons or gamma rays in three-dimensional rectangular geom-etry, v. 5, Advanced shield calculational techniques, by B. Eisenman and E. Hennessy.White Plains, N. Y., Mar. 1963.
2. U. S. Naval Civil Engineering Laboratory. Technical Report R-282: Dosemeasurements for neutron streaming in ducts, by D. R. Doty. Port Hueneme, Calif.,Mar. 1964.
3. U. S. Naval Civil Engineering Laboratory. Technical Report R-354: Fastneutron streaming through concrete ducts, by Y. T. Song. Port Hueneme, Calif.,Feb. 1965.
4. U. S. Army Ballistic Research Laboratories. Report 1189: Neutron reflection andflux versus depth for concrete, by F. J. Allen, A. Futterer, and W. Wright. AberdeenProving Ground, Md., Jan. 1963.
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Table II. Physical Parameters of Ducts
SubroutinePwa nne te•s -L2 L3Z L3NCP
(Two-Legged) (Three-Legged Coplanar) i rhiee-Legged Non-Coplanor)
First CardColum,,s 9 & 10]/ 43 47 64Column 202/ 1 2 3
XLI 200 cm%/ 167 cml/ 150 CnI/XL2 190 151 210XL3 0 141 200W1I 92 72.39 100W2 100 80.01 61W3 0 72.39 62TS1 1 29 16.51 35TS12 35.6 27.94 36TS21 35.6 16.51 16TS22 35.6 35.56 17TS31 0 27.94 16IS32 0 16.51 17TT 1 0 1DI 41.0 10 38D2 41.0 9 84D3 0 0 51DA 1.0 0 0DB 1.0 0 0DC 1.0 0 0DAI 0 1.0 1.0DA2 0 1.0 1.0DA3 0 0 1.0TA 61 61 60TB 61 61 61TC 61 61 59TD 61 61 60HH 60.9 60.96 73H 1 lu.5 16.51 28H2 16.5 16.51 17XX 0 0 0
]/ Total number of egyions
21 Subroattine tworyl,es
•/ Duct dime.iiions
68
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