AN ABSTRACT OF THE THESIS OF
Shahab A. Abdul-hamid for the degree of Master of Science in Nuclear Engineering
presented on September 30,1993.
Title:
Monte Carlo Bumup Analysis Code Development and Application to an Incore
Thermionic Space Nuclear Power System.
Abstract Approved:
Redacted for privacy
Andrew C. Klein
Lattice bum-up calculations in thermal reactors are complicated by the necessity
for use of transport theory to represent fuel rods, control rods, and burnable absorbers,
by many time-dependent variables which must be considered in the analysis, and by
geometric complexity which introduces time-dependent, spatial-spectral variations.
Representation of lattice structure in a core is further complicated by fuel materials and
loading patterns which can be non-symmetric, and by the type of material used as the
moderator.
The incore thermionic reactor system developed under the Advanced Thermionic
Initiative (ATI) is an example of such a reactor. In this design, the fuel is highly enriched
uranium dioxide and the moderating medium is zirconium hydride. The traditional bum-up
and fuel depletion analysis codes have been found to be inadequate for these
calculations, largely for the reasons mentioned above and because the neutron spectra
assumed for the codes such as LEOPARD and ORIGEN do not even closely fit that for
a small, thermal reactor using ZrH as moderator. A more sophisticated codes such as the
transport lattice type code WIMS is suitable for the terrestrial commercial reactors.
However it lacks some materials, such as ZrH, needed in special applications and it is not
capable of performing calculations with highly enriched fuel. Thus a new method which
could accurately calculate the neutron spectrum and the appropriate reaction rates within
the Thermionic Fuel Elements (TFE) is needed to be developed. The method developed
utilizes and interconnects the accuracy of the Monte Carlo Neutron/Photon (MCNP)
method to calculate reaction rates for the important isotopes, and a time dependent
depletion routine to calculate the temporal effects on isotope concentrations within the
TFEs. This required the modification of the MCNP itself to perform the additional task of
accomplishing burn-up calculations. The modified version called, MCNPBURN, evolved
to be a general dual purpose code which can be used for standard calculations as well
as for burn-up. The of burnable absorber Gadolinium which adds complications both in
the physical model and the numerical analysis requires frequent spatial and spectral re-
evaluations as a function of burn-up. This difficulty is overcome by the application of
MCNPBURN by assuming that the burnable poison is uniformly mixed in the fuel.
MCNPBURN was benchmarked using a standard Pressurized Water Reactor fuel
element against the LEOPARD and WIMS computer codes.
The results from
MCNPBURN show good agreement with LEOPARD and WIMS. The maximum difference
between MCNPBURN and either of the two codes was approximately 9%.
The
differences can be accounted for by the appropriate treatment of the accumulated fission
product.
Application of the MCNPBURN for the ATI reactor core, which consists of 165
TFEs and operates at 375 kW of thermal power, showed a system lifetime greater than
the projected lifetime of 7 years at full power. The average efficiency is about 5.86% and
the change in the overall efficiency over the life time is 0.2%. The percentage of fuel
mass burned is estimated to be about 3.6% of the initial mass.
Another calculation
includes the influence of burnable poisons mixed in the peak pins to flatten the overall
core radial power distribution was performed.
The efficacy of this change is quite
apparent in reducing the power effectively in the peak pins though it may give rise in
power elsewhere in the core.
Monte Carlo Burnup Analysis Code Development and Application to an Incore
Thermionic Space Nuclear Power System.
by
Shahab A. Abdul-hamid
A THESIS
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Master of Science
September 30, 1993
Commencement June 1994
APPROVED:
Redacted for privacy
Associate Professor of Nuclear Engineering in charge of major
Redacted for privacy
Head of Department of Nuclear Engineering
Redacted for privacy
Dean of Gra
School
Date thesis is presented
Typed by:
September, 30 1993
Shahab A. Abdul-hamid
ACKNOWLEDGMENT
I
wish to thank Dr. Andrew C. Klein, my major professor and advisor, who
contributed significantly to the development of the code detailed in this thesis. The idea
to use MCNP to perform burnup was originally conceived by him. My thanks extend to Dr.
Alan H. Robinson, chairman of the Nuclear Engineering Department, fOr his input as well
as to Mr. Hsing H. Lee, graduate student and friend, for his contribution of various aspect
of the thesis.
This work was supported partially by the Advanced Thermionic Initiatives of the
Wright Research and Development Center, Wright-Patterson Air Force Base, Ohio; T.
Lamp, Program Director.
Table of Contents
Page
1.
INTRODUCTION AND LITERATURE REVIEW
1.1.
2.
Neutronics and Burnup
MONTE CARLO NEUTRON PHOTON BURNUP CODE
2
6
2.1
Burnup Solution Method
6
2.2.
Defined Parameters
7
2.2.1.
Lattice Equivalency
7
2.2.2. Fuel Loading
8
Fission Rate
8
2.2.3.
2.2.4. Power
9
2.2.5. Neutron Source Rate
11
2.2.6. Neutron Flux
11
2.2.7. Reaction Rates
12
2.2.8.
3.
1
Nuclide Chain Equations
13
2.3.
Balance Equations
28
2.4.
Computer Implementation
29
2.5.
Verification of MCNPBURN code
29
2.6.
Error Estimate in Burnup
42
APPLICATION OF MCNPBURN TO THE ATI REACTOR
52
3.1.
Reactor Model
52
3.2.
ATI Bumup Results
54
3.2.1. Power Distribution
56
3.2.2. Effects of Irradiation on Fuel
59
3.2.3. Reactivity and Criticality
72
3.2.4. Power Shaping
72
4.
CONCLUSION AND RECOMMENDATIONS
78
5.
LITERATURE CITED
80
APPENDICES
APPENDIX I: MCNPBURN
83
A.
Code
84
B.
Benchmark
106
APPENDIX II: ATI MCNPBURN'S OUTPUTS
121
A.
ATI
121
B.
Burnable Poison in Some TFEs
135
APPENDIX III: MATRIX OPERATOR MATHEMATICS
138
List of Figures
Page
Figure
1.
Isotope chains for burnup analysis.
30
2.
MCNPBURN main program flow diagram.
31
3.
Unit cell representation used in LEOPARD, WIMS, and MCNPBURN.
33
4.
Unit cell koo for two years burnup (logarithmic time axis).
34
5.
Unit cell lc for two years bumup (normal time axis).
35
6.
Unit cell koo for 30 days burnup.
36
7.
Differences in MCNPBURN from LEOPARD or WIMS in lc.
37
8.
Unit cell flux for two years burnup (logarithmic time axis).
38
9.
Unit cell flux for two years burnup (normal time axis).
39
10.
Differences in MCNPBURN from LEOPARD or WIMS in flux.
40
11.
235U depletion for the unit cell two years burnup.
41
12.
236U buildup for the unit cell two years bumup.
43
13.
238U depletion for the unit cell two years burnup.
44
14.
239PU
buildup for the unit cell two years bumup.
45
15.
240Pu buildup for the unit cell two years burnup.
46
16.
241Pu buildup for the unit cell two years burnup.
47
17.
135Xe concentration under constant power level for the unit cell.
48
18.
135Sm concentration under constant power level for the unit cell.
49
19.
Non-saturated pseudo-fission product buildup for the unit cell.
50
20.
Cross sectional view of Thermionic Fuel Element.
53
21.
ATI quarter core TFEs relative power at BOC.
57
22.
ATI quarter core TFEs relative power at EOC.
58
23.
ATI full core TFEs power profile at BOC.
60
24.
ATI full core TFEs power profile after 1 day of burnup.
61
25.
ATI full core TFEs power profile after 2 weeks of burnup.
62
26.
ATI full core TFEs power profile after 1 month of burnup.
63
27.
ATI full core TFEs power profile after 3 months of burnup.
64
28.
ATI full core TFEs power profile after 1/2 year of bumup.
65
29.
ATI full core TFEs power profile after 1 year of burnup.
66
30.
ATI full core TFEs power profile after 2 years of burnup.
67
31.
ATI full core TFEs power profile after 4 years of burnup.
68
32.
ATI full core TFEs power profile after 7 years of burnup.
69
33.
Normalized 235U and 238U depletion over the ATI center of core lifetime.
70
34.
236U, 'Pu, and 240Pu buildup over the ATI center of core lifetime.
71
35.
135Xe and 149Sm concentration over the ATI center of core lifetime.
73
36.
ATI lifetime criticality within statistical error of ± 0.0018.
74
37.
ATI BOC TFEs power as compared when using burnable poison.
76
38.
ATI EOC TFEs power as compared when using burnable poison.
77
List of Tables
Page
Table
1.
MCNP reaction numbers and types used in MCNPBURN.
12
2.
Data used in the bumup computation of the MCNPBURN.
14
3.
ATI total core burnup parameters.
55
4.
Peak-to-average core power ratio over 7 years life.
56
Monte Carlo Burnup Analysis Code Development and Application to an Incore
Thermionic Space Nuclear Power System.
1.
INTRODUCTION AND LITERATURE REVIEW
Nuclear technology is being implemented to respond to a variety of civilian and
military space mission requirements (Klein et al., 1992). Such missions require a reliable
electrical energy supply to power equipment. As the distance from the sun increases, it
is not practical to deploy solar cell arrays large enough to produce sufficient electrical
power for the mission. The continuous increase of power consumption by spacecraft can
be provided only by nuclear power sources.
The former Soviet Union performed extensive research including space based
testing on space reactors. Its most recent systems, such as the TOPAZ (Nickitin et al.,
1991) reactor, produces 5 to 10 kW of electricity using single cell in-core thermionic fuel
elements.
The Thermionic Fuel Element Verification Program conducted by the U.S.
(Lamp et al, 1991) has been highly successful in developing a feasible system for use in
high power space applications using a multi-cell arrangement. Close cooperation between
the former Soviet Union and U.S. in this area is currently proceeding.
The effect of irradiation is to produce changes in the isotopic composition of the
fuel and other materials present in a reactor core. These, in turn, lead to local changes
in reactivity, heat generation, kinetic characteristics, control and poison worth, etc. A
quantitative knowledge and understanding of all these effects is necessary for reactor
design and operation purposes.
For over two decades there has been significant progress in the development of
improved theoretical models for the calculation of the reactor-physics parameters during
burn-up of complex power-reactor lattices. Integral transport theory and full-spectrum
Monte Carlo methods have been developed which are practical for analysis of a limited
range of reactor conditions. Full-spectrum Monte Carlo techniques have been utilized in
burnup problems for the purposes of testing the validity of the physical approximations and
to compute special effects (Crowther, 1973). This was done in conjunction with spectrum
analysis codes such as the alternate 2-D Sn (discrete ordinates method) and 2-D integral-
2
transport-theory calculations with lattice geometry. Others merely applied the Monte Carlo
code MCNP (Briesmeister, 1986) for the sole purpose of obtaining reaction rates to be
used in their own developed burnup codes (Jordheim, 1991).
Several burnup codes (Barry, 1973, Croft 1980, Askew et al., 1966, England,
1962, Shanstrom et al., 1961, Fowler et al, 1971, Breen et al., 1965, Stamm ler et al.,
1983) have been developed and are widely implemented. However, each one of these
codes has a constraint limiting accuracy or generality of use. Simpler methods have been
developed through comparison with the more accurate methods and with better and more
comprehensive power-reactor experiments.
Advances in computational speed have
extended the practical capabilities of reactor-physics calculations.
1.1.
Neutronics and Bumup
One of the main aspects of reactor dynamics is concerned with the long-term
changes in the isotopic composition of the fuel caused by exposure to the neutron flux
under various conditions of reactor operation. These changes, in both time and space,
have an important bearing on the operational life time of a reactor core. In addition, they
can affect the stability and control of the reactor. Consequently, such changes must be
taken into consideration in the design of the reactor system.
During operation of the reactor, the fissile nuclides are consumed by fission and
about two hundred fission products are formed, some directly and others by radioactive
decay. A number of these fission products have high or moderately high cross sections
for neutron capture, and they consequently have a significant influence on the neutron
economy (and reactivity) of the system. Furthermore, the conversion of fertile to fissile
nuclides has, of course, an important effect on reactor lifetime and control.
In addition, radiative capture of neutrons by both fissile and fertile species leads
to the formation of such nuclides as 236U,
240r,
2330,
and so on. These can also capture
neutrons or suffer decay (or both) so that many new heavy isotopes (or heavy nuclides),
i.e., isotopes of uranium, neptunium, plutonium, etc., are present in the fuel after a period
of reactor operation.
3
A complete treatment of fuel bumup requires a knowledge of the cross sections
of all the fission products and the heavy isotopes. In order to reduce the number of
nuclides that need to be included specifically in a burnup calculation, one general principle
is helpful.
The only fission products treated explicitly are those with particularly large
capture cross sections. In practice, this means that the great majority of fission products
are lumped into one class, to which is described an average cross section. 135Xe and
149Sm are always considered individually. Another dozen or so other heavy nuclides, with
fairly large cross sections, may also be included in this manner in an accurate bumup
study. These heavy nuclides are those which are important in determining the neutron
economy of the reactor.
The short thermal-neutron mean free path in thermal-reactor lattices and the
resultant sensitivity to geometry introduce complexity to lattice bum-up calculations.
Transport theory is essential to accurately predict the nuclear reaction rates in the fuel
rods, control rods, and burnable absorbers.
Both the thermal and epithermal neutron
spectra are space-and-time-dependent. Isotopic production and destruction are spatially
non-uniform between fuel rods and within fuel rods.
For most thermal reactor systems, three-dimensional core calculations are required
for realistic analysis to determine power distributions, isotopic production and destruction,
reactivity coefficients, spatial stability, fuel loading and control rod patterns, and operating
strategy. Multigroup calculations are required to describe the neutron spectra, isotopic-
dependent resonance capture and the interaction between fuel pins. For most burnup
codes, it is impractical to carry out the multigroup calculations in three dimensions.
Separability assumptions are thus essential.
Commonly, two methods are utilized to represent complex reactor lattices in
thermal reactor fuel burn-up calculations (Crowther, 1973):
1.
Parametric cell multigroup burnup calculations are carried out for cells consisting
of one or more fuel assemblies as a function of moderator density, cell geometry,
control-rod position, fuel temperature, etc. The generated few-group macroscopic
cross-sections and isotopic compositions are utilized
in
three dimensional
calculations in which the isotopic depletions are not solved.
frequently applied to the analysis of boiling water reactors (BWR).
This method is
4
2.
Parametric cell multigroup calculations are carried out at a few bum-up levels to
develop microscopic few-group cross sections. Calculations are performed with
a relatively fine mesh, for example, with every fuel rod described discretely. The
fuel isotopic depletion equations are solved using the fine-mesh global core
calculations results. This method is frequently applied in pressurized water reactor
(PWR) analysis.
Although both of the preceding methods have been successful in providing
analyses which are accurate enough for reliable design of thermal reactors, they are
limited to these specific designs. A general approach to the neutronics analysis and
hence burn-up is the application of the Monte Carlo methods which are very different from
deterministic transport methods. Deterministic methods, the most common of which is the
discrete ordinates method, solve the transport equation for the average particle behavior.
By contrast, Monte Carlo does not solve an explicit equation, but rather obtains answers
by simulating individual particles and recording some aspects (tallies) of their average
behavior. The average behavior of particles in the physical system is then inferred (using
the central limit theorem) from the average behavior of simulated particles (Briesmeister,
1986).
Monte Carlo methods can be used to theoretically duplicate a statistical process
(such as the interaction of nuclear particles with material) and are particularly useful for
complex problems that cannot be modeled by computer codes of deterministic methods.
The individual probabilistic events that comprise a process are simulated sequentially, and
the probability distributions governing these events are statistically sampled to describe
the total phenomenon. The statistical sampling process is based on the selection of
random numbers.
In particle transport, it consists of actually following each of many
particles from a source throughout its life to its death in some terminal category
(absorption, escape, etc.). If enough source particles are introduced into the model, the
tallies will describe the average behavior one can expect of the real life situation with
equivalent source particles in a three dimensional environment.
5
The non-uniform Dancoff resonance' interaction between fuel pins causes the
plutonium production rates from resonance capture in 238U to vary among fuel pins. It also
causes azimuthal variations in surface 238U capture around the fuel pins which creates
scallops in the 239PU surface production rates for the fuel pins in the central regions of the
fuel assemblies in a core, located in a close to azimuthal symmetric thermal neutron flux.
The production of 239PU by resonance capture in 238U is fuel-temperature-dependent
because of the important effects of Doppler broadening on 238U resonance capture. It also
varies globally in the core because of the space variable moderator density. On the other
hand, the build-up of 240Pu with its large 1 eV resonance introduces additional
complications. For a thermal reactor lattices with ZrH moderator, chemical binding and
up scattering cannot be ignored at 1 eV.
Thus, 240Pu effects should be analyzed with
realistic moderator scattering kernels. The Doppler broadening effect of 240Pu on the fuel
temperature dependence of reactivity is sensitive to the self-shielding of the
1 eV
resonance and, thus, the Doppler effect varies spatially with both 240Pu isotopic content
and fuel temperature within fuel pins, from pin-to-pin, and globally within the core. The
Dancoff correction factor for 240Pu is a function of not only geometry but also the spacedependent concentration of 240Pu. Hence, in comparison with 238U, an added complication
is introduced in the analysis of the effects of 240Pu. The 240Pu spatial isotopic production
is a function of the non-uniform 239PU production rate from 238U captures and, because of
the large 239PU resonance at 0.3 eV, also varies with the space-dependent thermal neutron
spectrum.
In view of the preceding complications, such as determining the Dancoff correction
factor in the lattice type calculations, and the capabilities of existing high speed
computers, the modified Monte Carlo Neutron and Photon transport code for bumup
(MCNPBURN) developed here provides the availability of a very accurate method within
the statistical bound.
If the fuel rods in a lattice are in fact separated by a moderator that is not many
free paths thick, it is possible for neutrons with energies in the resonance
region to pass from one fuel lump to another.
6
2.
MONTE CARLO NEUTRON PHOTON BURNUP CODE
MCNPBURN is a general-purpose, continuous-energy, generalized geometry, time-
dependent, coupled neutron-photon Monte Carlo transport code system modified to
perform an additional task of burnup.
MCNPBURN computes the isotopic production and decay of radioactive materials
in designated cells for burnup by considering the production and decay rate equations as
coupled linear system of equations and solves them by a matrix operator technique (the
Volterra method of the multiplicative integral) (Lee et al., 1976). The method allows a
rapid and accurate calculation of the change in isotopic density, independent of the
magnitude of the time constant, production or decay rate, or flux levels. The calculations
can also follow the irradiation history through a number of step changes of unrestricted
power levels.
2.1. Burnup Solution Method
The atom densities of all the nuclides included in the calculations will affect the
neutron flux in a complicated manner.
Suppose, however, that the neutron flux is
computed at time t, and suppose, furthermore, that the flux can be assumed to remain
constant for a substantial time period, At, after time t. The coefficients in the differential
equations for all the nuclide concentrations could be calculated and assumed to remain
constant from t to t + M. The resulting system of burnup (or depletion) equations can be
solved by a matrix operator technique.
The method allows a rapid and accurate
calculation of the change in isotopic density, independent of the magnitude of the time
constant, production or decay rate, or flux levels. With the atom densities known at time
t + At, the calculation could be advanced to time t + At by recomputing the flux at this
time, and so on. Thus the values of the atom densities are advanced in a series of time
intervals At during each of which the neutron flux is assumed to remain constant. The
procedure is repeated until it has been carried far enough in time. In long-range burnup
calculation, the intervals are chosen to be of the order of weeks, months, or even a year,
provided it is not desired to follow transients involving nuclides of short half-life, in
7
particular xenon-135 and iodine-135.
The burnup calculations are required to follow
changes with time of such parameters as the concentration of fissile nuclides, heavyisotope production, specific power, etc., in individual bumup cells. Each of these isotopes
have five flux averaged reaction rates namely absorption, fission, capture, (n,2n), and
(n,3n).
Numerous approximate techniques have been developed to solve the problem of
an accurate calculation of isotope production and depletion in linear systems. The matrix
operator method chosen is unique since the method allows a rapid accurate calculation
of the change in isotopic density independent of the magnitude of time steps, production
or decay rates, or flux levels.
2.2.
Defined Parameters
Defining a set of equations whereby their parameters are the tallies values
computed by the MCNP and thus preparing the necessary parameters for the bumup
routines. For output results, the lattice2 equivalent volume of each fuel pin is computed
and used to determine the fuel loading. Other output parameters computed includes the
power density, the specific power and irradiation magnitude.
In order to determine the absolute neutron flux from the MCNP fluence tally and
the reaction rates, one need to scale these parameters to the reactor input thermal power.
This requires computations of the fission rate along with the actual power produced by the
various fuel rods.
An indepth look at these various parameters is presented in the
following sections.
2.2.1. Lattice Equivalence
In some instances, modeling a reactor core in the MCNP requires defining the fuel
rods with its cladding only. These fuel rods then are immersed in a moderating medium.
2
Lattice includes a single fuel rod with an equivalent moderator radius of 1/2 pitch.
8
To calculate the fuel loading per lattice (fuel, clad, and moderator) necessitate the
inclusion of the moderator. Thus, to obtain the volume of the individual fuel rods including
a moderator volume, an equivalent lattice volume must be determined.
The lattice
volume, constitute the fuel, cladding, and moderator volumes, can be determined from
the following simple equation
VLTC.
CVOL.
CTV
VFUEL
(1)
where, VLTC is the volume of the lattice equivalent of fuel rod i and has a unit of cm3.
CVOL is the fuel volume per cell i and CTV is the total core volume in cm3. VFUEL is the
sum of all the fuel rods volumes in the core.
2.2.2. Fuel Loading
The fuel loading is given in terms of the initial heavy material mass (i.e. U and or
Pu) (Robinson, 1984). The fuel loading FLOAD is averaged over the lattice cell as
FLOAD = SUMF
VLTC,
where, SUMF =
XINIT,) CAW)
.
CVOL,
(2)
AVGDN
FLOAD is the fuel load in g/cm3, XINIT is the initial
atomic density (atom/b-cm) for the heavy elements j
in
fuel rod i, CAW is the
corresponding atomic weight of element j (g/mole), and AVGDN is Avogadro number
(atom/b-mole).
The core total metric ton of initial heavy material TIHM is equal to Ei FLOAD, VLTC,
and the core average loading (g/cm3) is then the TIHM/CTV.
2.2.3. Fission Rate
Given an average operating thermal power POWERT (Watts) for each bumup step,
ISTEP (constant over the period, At), and the cell averaged total prompt energy release
9
per fission, the cell averaged fission rate (Fission/s) is determined by the following
equation,
FRAT E=
POWERTISTEP x PCONV
CQ,
(3)
where PCONV is equal to 6.25 x 10'2 MeV/w-s and the cell averaged energy per fission,
CQ, (MeV/Fission) is the Q-fission and can be obtained via the MCNP reaction tallies as
follows
=
REACTION (-6 -8)
REACTION (-6)
(4)
which is in reactor physics has the form
Q;
E I dE
E icro); dE
(5)
2.2.4. Power
The core average core power density (W/cm3) can be computed as follow
PD =
POWE RTis-rEp
(6)
CTV
the specific power per fuel rod is computed from
PS; =
PD
FLOAD;
(7)
and the irradiation (or burnup, MWD/MT) is
BURNTISTEP
=E
!STEP
where A is the time step length in seconds.
PSI x AISTEP
(8)
10
To compute the power, the heating tally of the MCNP is used. The track-length
estimate of energy deposition due to fission in cell i, including photon energy from fission
(MeV/g) is
t,
1
En
F7, =C I I ICE,t,p)H(E)dEdtdp
-1
t
(9)
.
E,
Where C is the atom/g of cell material and H = af(E) Qfission
af(E) is the material
microscopic fission cross section (cm2) and Qfission is the fission Q (MeV/fission).
The fuel rod i power (PWR) in watts is then given by
PWR, =
F7, x CMASS, x FRATE, x CNU,
(10)
PCONV
where CMASS (g)= CVOL, X CDEN,. CDEN,(g/cm3) is the fuel material density of cell i.
CNU, is the v fission and it is determined in a similar fashion as of the
CNU =
ass
REACTION (-6: -7)
REACTION (-6)
In reactor physics the cell averaged u (n/fission) is given by
E v; lac cp, dE
v, =
E fafT, dE
(12)
Calculating the power normalization (necessary to scale individual fuel rods to average
core power) is thus
PNORM =
POWERTIsTEp
E
(13)
PWR,
The fuel rod normalized power is then,
POWER, = PWR, X PNORM
.
11
2.2.5. Neutron Source Rate
In all the MCNP tallies the source has units of neutrons, thus these tallies
represents a fluence tallies. On the other hand, if the source has units of neutrons per
unit time, the tally is also neutrons per unit time.
The parameter tally scaling factor (TSF) of cell i can be defined to be the neutron
source rate scaled to the average reactor power which yields
TSF,(n/s)=FRATE, x CNU x PNORM
.
(14)
2.2.6. Neutron Flux
The neutron flux tally is an estimate of
F4, = IIT(r,E,t) dE dt
(15)
.
tE
where tp(E) is the energy-dependent fluence (neutrons/cm2). Thus the thermal, fast and
total flux respectively are
625 eV
TFLUX =I I (p(r,E,t)dEdt
t
(16)
,
0
20MeV
FFLUX, = I
t
I p(r,E,t)dEdt
,
20 MeV
FLUX, = I
(17)
625 eV
I
w(r,E,OdEdt
.
(18)
t
The units of the flux tally are the units of the source. Since the source in the criticality
computation is neutrons, this tally actually represents a fluence tally. Therefore, to obtain
the absolute flux, one may multiply the fluence tally by the neutron source rate as follow
= F4 x TSF; .
The fluence (F4) units are 1/cm2 and the flux has the units of n/cm2-s.
(19)
12
2.2.7. Reaction Rates
The FMn card is used to calculate any quantity of the form
RRX,jk = TSF, x BARN fq)(E)1:2,(E)dE
where the conversion factor BARN is equal to 1 X 1044 cm2/b
(20)
,
.
R(E) is an operator of
additive and/or multiplicative response functions from the MCNP cross-section libraries or
specially designated quantities for reaction type k (see Table (1)) of nuclide of material j
and it is averaged over cell i. The reaction cross sections are microscopic (with units of
barns). For the absorption, fission, capture, (n,2n), and (n,3n) reactions, the units are then
(n-b/cm2-s), thus when multiplied by material m nuclide atomic density (with units of
atoms/b-cm) the appropriate unit of the reaction rate is obtained as (n-atom/cm3-s) or
(reactions/cm3-s). The reactions are components of the reaction rate since they must be
multiplied by the atomic density to yield a reaction rate.
Hence, they are called here
reaction coefficients. Table (1) is a list of special reactions present in the MCNP crosssection libraries which are used in the computations.
Table 1. MCNP reaction numbers and types used in MCNPBURN.
3
Index K
Reaction number
Reaction Type
1
(-2:-6)3
a (absorption)
2
(-6)
f (fission)
3
(102)
n,y (capture)
4
(16)
n,2n
5
(17)
n,3n
Reaction number (-2) is defined in the MCNP manual as the total absorption cross
section, however, in actuality it is the total capture (n,2n, n,3n,.. etc) cross section
only.
13
2.2.8. Nuclide Chain Equations
The rate at which the number of nuclei per unit volume changes with time may be
written as
dt
= [ Formation Rate ]
[ Destruction Rate + Decay Rate ].
The decay rate term is simply the decay constant
in cell
i
(kiX,i) during time period dt.
(21)
of nuclide j times its concentration X
The decay constants have units of s-1 and the
concentration X has units of atom/b-cm. The destruction term can be due to neutron
capture by this nuclide which forms a different nuclide or/and due to fission if it is a fissile
nuclide.
For example, in cell
i
(fuel pin), the destruction rate is well represented by
capture reaction rate (-cry*Xu), where
is is the capture microscopic cross section, in
barns, for nuclide j and (I) is the neutron flux with units of neutron per cm2 per second.
Loss due to fission is (-01),X,) where of is the microscopic fission cross section with units
of barns.
Daughter formation is by virtue of parent m nuclide decay (X,Xim).
Upon
capture of a neutron by nuclide j-1, nuclide j is accumulated by the reaction rate
(c57'14),X0).
Finally, let Xik be the concentration of fissile and fissionable nuclides, and let
YKJ be the probability that a type K nuclide will be formed as a fission product by
absorption of a neutron by a nuclide of type j. Thus the Y term represents the fission yield
of isotope K from the fission of isotope j. If the nuclide of type K is not a fission product
then the YK is zero. With the foregoing conditions the reaction rate RR,J will be
RFR4
= E Ykjat 4)Xik
(22)
k
All reaction rates thus have units of reactions per cm3 per second. Table (2) include a list
of the 25 nuclides along with their corresponding decay rate constants and fission yields
(Robinson, 1984 & Bennett, 1966). For example the fission of 235U yields about .24%
135Xe as defined by the variable YXe. Each of the 25 burnup designated nuclides will
undergo one, several, or all types of the designated reactions. The concentration of the
jth nuclide for each cell
i
in a linear chain is determined by the coupled differential
equations along with an illustration that shows the nuclear reaction and radioactive decay
pathways for each of the isotopes considered. Here RRX(i,j,k) stands for the reaction rate
14
Table 2. Data used in the burnup computation of the MCNPBURN.
No.
Isotope
1,a(e)
1,0 (e)
YXe
YI
YPm
YFP
233u
1.4E-13
0
.01388
.0562
.00769
1.119
2
234u
8.9E-14
0
.0020
0
.0100
0
3
235u
3.1E-17
0
.0024
.0617
.0113
1.26
4
236u
9.4E-16
0
.0020
.0620
.0113
0
2370
0
1.19E-6
.0020
.0600
.0200
0
6
238u
4.9E-18
0
.0022
.0578
.0210
1.426
7
239u
0
4.92E-4
.0020
.0600
.0200
0
8
240U
0
1.37E-5
.0020
.0600
.0200
0
9
237Np
1.0E-14
0
.0022
.0666
.0113
0
10
238Np
0
3.79E-6
.0020
.0600
.0200
0
11
239Np
0
3.40E-6
.0020
.0600
.0200
0
12
240Np
0
1.87E-4
.0020
.0600
.0200
0
13
238 PU
2.5E-10
0
.0020
.0630
.0113
0
14
239PU
9.0E-13
0
.0027
.0693
.0130
1.456
15
240Pu
3.4E-12
0
.0022
.0578
.0210
0
16
241Pu
3.4E-14
1.46E-9
.0024
.0626
.0120
1.456
17
242PU
5.7E-14
0
.0020
.0630
.0200
0
18
241Am
5.1E-11
0
.0020
.0630
.0152
0
19
F.P
0
0
0
0
0
0
1
5
20
1351
0
2.93E-5
0
0
0
0
21
135Xe
0
2.10E-5
0
0
0
0
22
149Pm
0
3.63E-6
0
0
0
0
23
149SM
0
0
0
0
0
0
24
Gd
0
0
0
0
0
0
25
160
0
0
0
0
0
0
15
of type k and nuclide j taken place in burnup cell i. ALAM and BLAM are the alpha and
beta decay constants, respectively. The three dimensional array A(i x j x k) is the matrix
array containing all of the reaction rate coefficients to be solved for the concentration Xg.
The fission products (other than 1351, 135 Xe, 149Pm, and 149Sm) are lumped into a
single pseudo-fission product (nuclide No. 19). This non-saturated, pseudo fission product
is accumulated at one atom per fission (Bennett, 1966). The MCNP cross section library
includes a crude-pseudo fission product cross section (represented by ZAID number
50999). Unfortunately, this fission product has an exceedingly high capture cross section
below 1 keV (Seamon, 1990 & 1992). Therefore it is to be accumulated only, and it is
prevented from being an effective contributor.
The following is a list of all the nuclides involved in the burnup calculation. This
includes the appropriate rate equations, a pictorial representation of each reaction, and
the corresponding matrix formulation. Xj is the atom density of nuclide j as indexed in the
MCNPBURN code.
ISOTOPE 1 - 233U
d X1
dt
in a matrix form yield,
A(i,1,1)=-(RRX(i,1,1)+ALAM(1))
A(i,1,2)= RRX(i,2,4)
A(i,1,3)= RRX(i,3,5)
4.0.(3n,304)
-[
(23)
16
ISOTOPE 2 - 234U
dX2
+a(3n,2n)
(24)
+a(4n,3n)4)
dt
in a matrix form yield,
0( (Pu 238)
A(i,2,1)= RRX(i,1,3)
n, 2n (U 235)
A(i,2,2)=-(RRX(i,2,1)+ALAM(2))
n,
(U 233)
A(i,2,3)= RRX(i,3,4)
n, 3n (U 236)
A(i,2,4)= RRX(i,4,5)
A(i,2,13)= ALAM(13)
ISOTOPE 3 - 235U
dX3
4.a(4n,2n)(1)
[a:4)
+a(5n,3n)(1)
(25)
dt
in a matrix form yield,
°E (Pu 239)
a
A(i,3,3)=-(RRX(i,3,1)+ALAM(3))
A(i,3,4)= RRX(i,4,4)
n, 2n (U 236)
n,
A(i,3,5)= RRX(i,5,5)
A(i,3,14)= ALAM(14)
(U 234)
235
U
92
0(
n, 3n (U 237)
17
ISOTOPE 4 - 236U
dX4
dt
=
X3 +65n'2n)4 ) X5 +a(6n'3n)+X6 +X.,5X15]
(26)
jaa4+ +kci) X4
in a matrix form yield,
oc (Pu 240)
A(i,4,3)= RRX(i,3,3)
A(i,4,4)=-(RRX(i,4,1)+ALAM(4))
A(i,4,5)= RRX(i,5,4)
n, 2n (U 237)
n,
(U 235)
n, 3n (U 238)
A(i,4,6)= RRX(i,6,5)
A(i,4,15)= ALAM(15)
ISOTOPE 5 - 232U
dX5
dt
=[
cr74+ X4 +a:1'2")(1) X6 +a?''3n)(1) X7 +Xat6 X161
(a:41 +Xp, X5
in a matrix form yield,
04.(Pu 241)
A(i,5,4)= RRX(i,4,3)
A(i,5,5)=-(RRX(i,5,1)+BLAM(5))
A(i,5,6)= RRX(i,6,4)
A(i,5,7)= RRX(i,7,5)
A(i,5,16)= ALAM(16)
(27)
18
ISOTOPE 6 - 238U
dX6
dt
X5
+a7n,2n)4
((8n,3n)
[c7:0
in a matrix form yield,
cX
(28)
(Pu 242)
A(i,6,5)= RRX(i,5,3)
A(i,6,6)=-(RRX(i,6,1)+ALAM(6))
A(i,6,7)= RRX(i,7,4)
A(i,6,8)= RRX(i,8,5)
A(i,6,17)= ALAM(17)
ISOTOPE 7 - 239U
dX7
dt
=[c44) X6 +0-(8n'2")(1) X8] -[(7,0 +X.07];
in a matrix form yield,
A(i,7,6)= RRX(i,6,3)
A(i,7,7)=-(RRX(i,7,1)+BLAM(7))
A(i,7,8)= RRX(i,8,4)
(29)
19
ISOTOPE 8 - 24°U
X8
=jcir74) X7] ION) +kpa] X8
(30)
in a matrix form yield,
A(i,8,7)= RRX(i,7,3)
A(i,8,8)=-(RRX(i,8,1)+BLAM(8))
ISOTOPE 9 - 237NP
dX
dt
in a matrix form yield,
A(i,9,5)= BLAM(5)
A(i,9,9)=-(RRX(i,9,1)+ALAM(9))
A(i,9,18)= ALAM(18)
+ka, X
9 =[
06X 5
-
[a:4 ) +ko.9] X8
18]
(31)
20
ISOTOPE 10 - 238Np
dX,
dt
(32)
° =cs9 (I) X0 -k01° X10
in a matrix form yield,
A(i,10,9)= RRX(i,9,3)
A(i,10,10)=-BLAM(10)
n, )/ (Np 237)
238
Np
93
ISOTOPE 11 -239NP
dXli
dt
(33)
=XpiX7 -2,13,X11
in a matrix form yield,
P (U 239)
A(i,11,7)= BLAM(7)
A(i,11,11)=-BLAM(11)
239
Np
93
1
13
21
ISOTOPE 12 - 240Np
dX12
(34)
X8 --"A.R X12
Ir-X
d
r8
"2
in a matrix form yield,
r(U 240)
A(i,12,8)= BLAM(8)
A(i,12,12)=-BLAM(12)
240
Np
93
ISOTOPE 13 -238PU
dX13
dt
= [a(1n42n) 4) Xi4
+a(153n)(1:1
X15 +1,1310X10]
(35)
[a134) +2,,,.13] x13
in a matrix form yield,
13(Np 238)
A(i,13,10)= BLAM(10)
n, 2n
A(i,13,11)=-(RRX(i,13,1)+ALAM(13))
A(i,13,14)= RRX(i,14,4)
A(i,13,15)= RRX(i,15,5)
(Pu 239)
238
94
Pu
n, 3n
(Pu 240)
22
ISOTOPE 14 - 239PU
(36)
dX74
= [0130 X13 +a1nen)4 X15 +a1nen)0 X16
dt
+kpX11]
in a matrix form yield,
[c574 + cjX14
P (Np 239)
A(i,14,11)= BLAM(11)
A(i,14,13)= RRX(i,13,3)
A(i,14,14)=-(RRX(i,14,1)+ALAM(14))
A(i,14,15)= RRX(i,15,4)
A(i,14,16)= RRX(i,16,5)
ISOTOPE 15 - 240Pu
(37)
dX15
dt
= [175140 X14
l'a(nen)0 X16 4-a(1n7 3n)0
X17
+kp,,X12)
[C5150 .f)cc,)X15
in a matrix form yield,
P(Np 240)
A(i,15,12)= BLAM(12)
A(i,15,14)= RRX(i,14,3)
A(i,15,15)=-(RRX(i,15,1)+ALAM(15))
A(i,15,16)= RRX(i,16,4)
A(i,15,17)= RRX(i,17,5)
23
ISOTOPE 16 -2"Pu
dX16
dt
=[(7154) X15 -fa(In72n)4 X17] -10'16+ +k.-4.0) X16
(38)
in a matrix form yield,
A(i,16,15)= RRX(i,15,3)
A( 1,16,16)=-(RRX(i,16,1)+ALAM(16)
+BLAM(16))
A(i,16,17)= RRX(i,17,4)
ISOTOPE 17 - 242PU
dX17
dt
(39)
-x164 Xl6 -[a174 +ka.,,l X17
in a matrix form yield,
A(i,17,16)= RRX(i,16,3)
A(i,17,17)=-(RRX(i,17,1)+ALAM(17))
n,
(Pu 241)
242
94
Pu
24
ISOTOPE 18 -241Am
dX18
dt
=kpi8 X16 '46480
(40)
X18
in a matrix form yield,
(Pu 241)
A(i,18,16)= BLAM(16)
a
A(i,18,18)=-(RRX(i,18,1)+ALAM(18))
241
95
Am
ISOTOPE 19 - Bulk fission products
dX19_Va
dt
in a matrix form yield,
A(i,19, k)= RRX(i,k,2),
k=1,N
Yfpj
(41)
25
ISOTOPE 20 -'351
c1X20
N
=rs-,
dt
of
(42)
XI] -X1320 X20
in a matrix form yield,
A(i,20, k)= RRX(i,k,2)YI(k),
k=1,N
A(i,20,20)=-BLAM(20)
ISOTOPE 21 - 135Xe
dX2
dt1 =
N
(E Yx. af4) Xj] -0,13,0 X20
[ AS/32,
(43)
+a:11:1)] X21
1.1
in a matrix form yield,
(I 135)
A(i,21, k)=RRX(i,k,2)YXE(k),
k=1,N
A(i,21,20)= BLAM(20)
A(i ,21,21)=-(RRX(i,21,1)+BLAM(21))
a
26
ISOTOPE 22 - 149Pm
clX22
dt
N
=[
(44)
Yp, of(l) Xj -k X
X22
t1 22
in a matrix form yield,
Y Pm
A(i,22, k)=RRX(i,k,2)YPM(k),
k=1,N
A(i,22,22)=-BLAM(22)
149
61
Pm
ISOTOPE 23 - 149Sm
23
=kp X22
"
(45)
CS:3 4/ X23
in a matrix form yield,
15 (Pm 149)
A(i,23,22)= BLAM(22)
a
A(i,23,23)=-RRX(i,23,1)
149
62SM
27
ISOTOPE 24 - 160
dX24
(46)
X24 X24
dt
in a matrix form yield,
a
A(i,24,24)=-RRX(i,24,1)
N
16
8
0
ISOTOPE 25 - 157Gd
dX2
dt
5
(47)
= -a25 4) X25
in a matrix form yield,
A(i,25,25)=-RRX(i,25,1)
a
157
Gd
64
28
2.3. Balance Equations
Let Xj(r,t) be the nuclear density of the jth isotope in a general transmutation chain
at position r and time t in a system with neutron flux 4)(r,E,t) having energy between E and
E+dE. No processes involving neutrons as initial or final products need to be excluded,
although their effects must be approximated in order to achieve a linear system of
equations. The general balance equation, including production and decay, is then given
by Bell & Glasstone (1970) as
8X,(0)
+ E ,k(r) Xk (r,t) +
dt
(48)
k
co
Id E [-a7(r,E,t)Xj(r,t) +E ajk(r,E,t)Xk(r,t)]4)(r,E,t),
0
where kj is the decay constant of the jth isotope, kik is the decay of isotope k to j,
is the
absorption cross section for conversion of isotope k to j, for example, by (2,2n), (n,3n),
etc. and 4 is the neutron flux.
Equation (48) may be written simply in terms of reaction rates as
dxu
dt
E
(49)
ij,k
where R = f(a,k,4)) is desired.
Equation (50) may be written in matrix form by letting X4 be elements of a column
vector. Matrix A includes the coefficients of the reaction rates and decay constants. The
solution to equation (50) using the matrix operator mathematics is well documented in
Appendix Ill.
29
2.4. Computer Implementation
The MCNP cross section library contains only 20 nuclides out of the 25, shown in
Figure 1, needed in the bumup routine. The five nuclides, namely 238Np, 239Np, 240Np, 1351
and 149Pm, not included in the MCNP data libraries are therefore treated separately. A
brief description of the program flow is shown in Figure 2. It includes the main routine,
called MCNPBURN, which calls upon subroutine MCNP (previously, the main routine in
MCNP version 3B) which has been modified such that it will read the additional input
cards that are burnup specific. If the burnup cards are present, then this signals the
program for the burnup procedures; otherwise it proceeds with its normal function. The
Subroutine MCNP calls on three major routines in the following order; first it calls IMCN
for input manipulation, then it calls XACT to read cross sections and finally subroutine
MCRUN is called to perform the actual neutron histories and transport computations. If
burnup was requested, the program bypasses subroutines IMCN and XACT after the
completion of the first burnup step since these subroutines need to be done only once.
Modifications were made to several MCNP routines. Especially the subroutines TALLYP
and KCALC which include variables which are transferred through the modified STATIC
common block to the burnup routines. These variables are the thermal, fast, and total
fluxes, the heating tallies to calculate the actual power, the reaction rate coefficients for
the five important reactions, namely the absorption, fission, capture, n,2n, and n,3n, the
Q-fission and v-fission, and the criticality eigenvalues. The burnup routines perform matrix
set up for 25 nuclides for each cell that may undergo burnup calculations and then solves
this matrix by the Volterra multiplicitve method. Burnup subroutines that follow print the
results to the output file and then clear some of the KCALC and TALLYP variables prior
to the start of the next time step.
2.5.
Verification of MCNPBURN code
Experiments are required to confirm the validity of the theoretical methods above.
However, such experiments are not readily available and one needs to resort to standard
bumup codes known to have been benchmarked in experimental or commercial studies.
2
U-234
1
U-233
--?
4
3
--0
U-235
U-236
Pm
Yield
22
Pm 149
Yield
9
10
Yield
19
FISS.
7
U-239
11
8
U-240
12
Np238
N p239
N p240
13
14
15
Pu238 --0 Pu239
23
Sm 149
F.P.
25
Gd 157
4
Np237
Yield
Xe
U-237
6
U-238
5
24
0-16
16
Pu241
Pu240
17
Pu242
18
Am241
PROD.
Figure 1. Isotope chains for bumup analysis.
ow
BXPREP2
MCRUN
BXSCALE
BXOUT
BXBURN
Figure 2. MCNPBURN main program flow diagram.
32
The lattice code WIMS (Askew et al., 1966) and zero dimensional multigroup LEOPARD
(Barry, 1973) code have been found to be reliable in the nuclear industry and hence
adequate for such a comparison in this work.
A Westinghouse Pressurized Water Reactor (Duderstadt et al., 1976) was chosen
for the study. The lattice for such a reactor is a unit cell comprised of fuel enriched to 3%
UO2 with a density of 10.4 g/cm3. The fuel rod radius is 0.4095 cm and the cladding is
zirconium with an outer radius of 0.47 cm. The gap between the cladding and the fuel is
about 0.0019 cm and the moderating medium is light water. The pitch in this model is
1.25 cm and the operating conditions are at STP. Since the model consists of a unit cell,
it was important to maintain the cell volume fractions in the three codes. These are
0.3371 cm3 for the fuel, 0.1069 cm3 for cladding, and 0.5559 cm3 for the water moderator.
Also the equivalent moderator outside radius is 0.7053 cm which represents a pitch of
1.25.
The model input files of LEOPARD, WIMS, and MCNPBURN can be seen in
Appendix I. A pictorial representation of the cell model is shown in Figure 3.
Results of the MCNPBURN versus LEOPARD and WIMS can be presented in
graphical form to include their prespective curves in such manner that is made simple for
a rational comparison. Figure 4 shows a plot of the infinite criticality eigenvalue for the
three codes in a logarithmic time scale. k. in WIMS compared higher than LEOPARD,
and MCNPBURN in turn is higher than WIMS. This can be attributed mainly to the
method of bulk fission products treatment. Figure 5 represents a normal time scale and
magnifies the difference in the infinite neutron multiplication factor. Although koo of WIMS
and MCNPBURN were higher than LEOPARD for most of the time, they were in fact lower
at beginning of core life (BOC) as can be seen in Figure 6 which shows the infinite
criticality eigenvalue for the first 30 days.
Figure 7 details the difference between
MCNPBURN and the other two codes in criticality. This difference as discussed earlier
is characteristic of modeling the lumped fission products. Figure 8 and Figure 9 represent
the absolute total flux in a similar fashion to Figure 4 and Figure 5. The difference in the
flux and the other codes can be seen in Figure 10. Unlike the criticality eigenvalue, the
flux is more sensitive to the Q-fission value used. The 235U depletion is shown in Figure
11. It depletes more significantly in MCNPBURN than the other codes. This is as a result
of not employing the bulk fission products as an effective absorber in the fuel in
MCNPBURN.
0.625 cm
0.625 cm
Figure 3. Unit cell representation used in LEOPARD, WIMS, and MCNPBURN.
.....
.......
ockek1/462
06'1
`1,0)
<0(\
ee 340.
0
10
15
Time (days)
Figure 6. Unit cell koo for 30 days bumup.
30
10%
MCNPBURN
9%-
error from:
LEOPARD
8%-
WIMS
7%6%5%-
4%3%2%1%0%
I
0
I
1
I
I
I
7
30
60
1
1
120
210
365
730
Time (days)
Figure 7. Differences in MCNPBURN from LEOPARD or WIMS in ko.
2.90
2.80-
1 WIMS
2 LEOPARD
3 MCNPBURN
2.702.60-
2.502.40-
3
2.202.102.00
1.90
0.001
1
1
1
I II
0.I01
I
1
1
1
1
1
1
1
1
0.1
I
1
1
1
1
1
1 11
I
1
1
1
I
1
1111
10
I
1
1
1
11
100
Time (days)
Figure 8. Unit cell flux for two years bumup (logarithmic time axis).
1
1
I 1 11
1000
2.90
2.802.702.602.502.402.302.20-
2.102.00.,
1.90
0
100
200
300
400
500
600
Time (days)
Figure 9. Unit cell flux for two years bumup (normal time axis).
700
800
10%
9%8%7%6%MCNPBURN
error frorn:
5%-,
WIMS
LEOPARD
4 %3%-1
2%1%0%
0
1
7
30
60
120
Time (days)
210
365
730
Figure 10. Differences in MCNPBURN from LEOPARD or WIMS in flux.
8.00E-04
7.00E-04
1 WIMS
2 LEOPARD
3 MCNPBURN
6.00E-04-
5.00E-04-
4.00E-04-
3.00E-041
2.00E-04
2
3
0
100
200
300
400
500
Time (days)
600
Figure 11. 235U depletion for the unit cell two years bumup.
700
800
42
236U buildup is slightly higher in MCNPBURN during the first year, then decreases below
WIMS or LEOPARD for the second year as in Figure 12. The contribution to fission from
239Pu becomes significant in about a year of bumup. thus the yield of 236U from the
fissioning of 235U decreases. Another factor affecting the lower rate of accumulating 236U
as well is the faster rate of 235U depletion.
238U depletion is plotted in Figure 13 and
shows a good agreement between the three codes. The negligible difference in 238U
between the three codes can be reasoned to the fact that 238U is not a thermally fissioned
isotope and thus depletes very slowly. The higher conversion in MCNPBURN to 239PU,
24°Pu, and 241Pu is due to the greater rate of 235U depletion. These plutonium isotopes
buildup can be seen in Figures 14 through 16. The 135Xe and 149Sm concentration during
the two years is presented in Figures 17 and 18, where the absence of the pseudo-fission
product affects the rate at which these isotopes absorbs neutrons.
saturating, pseudo-fission product is shown in Figure 19.
Finally, the non-
The MCNPBURN uses
somewhat better data in the yield of the pseudo-fission product from the fissionable
isotopes, whereas LEOPARD uses a yield value of unity and even a lower value by WIMS
which treat significantly many fission products as well.
From observation of these figures one may conclude that the errors are reasonably
small, bearing in mind that the MCNP cross section library is a much more detailed one
than the other codes. The difference in the total flux could be attributed largely to the fact
that it is sensitive to the Q-fission value used. The average Q-fission in LEOPARD is
about 210 MeV/fission, while WIMS uses 197.7 MeV/fission and the MCNP value is about
180.9 MeV/fission. This difference is significant since the Q-fission value used in MCNP
represent the prompt values and does not take into account the fission products or
radiation capture contributions. The difference in the criticality calculation may be due to
the effects of the pseudo-fission product. MCNPBURN simply accumulates the pseudofission product and does not allow its contribution in the fuel during bumup.
2.6.
Error Estimate in Burnup
All standard MCNP tallies are normalized to be per starting particle and are printed
in the output of MCNPBURN for the criticality with a second number, which is the
8.00E-05
7.00E-056. 00E-05
5.00E-054. 00E-05
3.00E-052.00E-05
1.00E-05-
0.00E+00
0
100
200
300
400
500
600
Time (days)
Figure 12. 2 3611 buildup for the unit cell two years bumup.
700
800
2.25E-02-
2.24E-02E
0
2.24E-02'43
ap 2.23E-02
a)
0
co
2.23E-02-
3
0
100
200
300
400
500
600
Time (days)
Figure 13. 238U depletion for the unit cell two years bumup.
700
800
1.00E-04-
8.00E-05rts
ri
3-
O
6.00E-05-
U_
E
:2
<
4.00E-05-
o)
co
cv
o_
100
200
300
400
500
600
Time (days)
Figure 14. 239PU buildup for the unit cell two years bumup.
700
800
3.50E-05
3.00E-05-
2.50E-05-
2.00E-05-
1.50E-05-
1.00E-05
5.00E-06-
0.00E+00
1
0
100
1
I
I
I
200
300
400
500
1
600
Time (days)
Figure 15. 240Pu buildup for the unit cell two years burnup.
1
700
800
2.00E-05
1.80E-051.60E-051.40E-051.20E-05-
1.00E-05-
8.00E-066.00E-064.00E-062.00E-06O. 00E + 00
0
100
200
300
400
500
600
Time (days)
Figure 16. 241Pu buildup for the unit cell two years bumup.
700
800
1.00E-08
ft.,
3
........... . ...........
2
1 WIMS
2 LEOPARD
3 MCNPBURN
1.00E-09
0
100
200
300
400
500
600
Time (days)
Figure 17. 135Xe concentration under constant power level for the unit cell.
700
800
1.00E-07
1
1 WIMS
2 LEOPARD
3 MCNPBURN
1.00E-08
0
100
200
300
400
500
600
Time (days)
Figure 18. 135Sm concentration under constant power level for the unit cell.
700
800
1.00E-07
0
100
200
300
400
500
600
Time (days)
Figure 19. Non-saturated pseudo-fission product buildup for the unit cell.
700
800
51
estimated relative error defined as
R
a Syd FC
(50)
The Monte Carlo mean x is the average value of the score x, (for example,
x,=energy deposited by
random walk) for all the histories calculated in the problem. The
quantity S is the estimated standard deviation of the population of x based on the values
of x, that were actually sampled. Relative error is a convenient parameter used by MCNP
because it represents statistical precision as a fractional result.
However, it is very
complicated to be computed for the various parameters used in the burnup routines.
Rather, the tally relative errors are shown at the end of each burnup step as a tally
fluctuation chart. MCNPBURN prints in addition to the relative error a FOM number which
is a very important statistic about a tally bin and provides significant information. FOM of
a tally is defined to be
FOM= 1/R2T.
Where T is the computer time and R2 is the estimated relative error squared which is
proportional to 1/N (N is the number of histories calculated in the problem). FOM is a tally
reliability indicator in the sense that if the tally is well behaved, the FOM should be
approximately a constant.
52
3.
APPLICATION OF MCNPBURN TO THE ATI REACTOR
Thermionic conversion of heat energy into electrical energy makes use of the fact
that electrons are emitted from a heated surface (Klein et al., 1992). The thermionic
conversion system does not require either an intermediate form of energy or a working
fluid. The principal device in a thermionic conversion system is the thermionic converter.
Basically it consists of a metal surface connected to the heat source and a secondary
surface acting as electron collector. In the Advanced Thermionic Initiative (ATI) reactor
the thermionic conversion occurs inside the thermionic fuel elements (TFE), converting
heat from fission into electrical power.
3.1.
Reactor Model
The ATI is classified as a single-cell type configuration (Klein et al., 1992) where
the thermionic converter is a part of the TFE and extends the entire length of the TFE.
The overall dimension for a single cell TFE is therefore the same as the core height.
The TFE shown in Figure 20 consists of:
1.
a central void to remove gaseous fission products,
2.
uranium oxide fuel to generate heat,
3.
emitter material made of tungsten which emits electrons,
4.
emitter/collector gap filled with cesium vapor for electron transport,
5.
collector material made of molybdenum or tungsten to collect the electrons,
6.
insulator sheath made of diamond or A1203 to electrically insulate the collector,
7.
cladding,
8.
coolant channel with NaK coolant, and
9.
a liner made of stainless steel that contains the TFE's coolant channel within the
overall core material.
53
Collector
Sheath
Cladding
Central
void
Liner
Emitter
Coolant
Fuel
Pellet
Emitter
collector
gap
Figure 20. Cross sectional view of Thermionic Fuel Element.
There are two types of thermionic reactors: ex-core reactor and incore reactor. In
ex-core reactors the converters are mounted external to the reactor core and are coupled
to the core by means of conductive or convective heat transfer paths. In the ATI, which
is an incore type of reactor, the converters are integral parts of the nuclear fuel elements
and are dispersed throughout the core.
Considering the low power levels for which the reactor will be designed, another
important variable is the potential addition of driver fuel elements. Driver fuel elements
are small rods without the thermionic capabilities and hence without the extra nonfissionable material. The use of driver fuel elements can enable smaller reactor designs
to be critical where, if the reactor was only made of TFEs designed to run at full power,
it would not attain criticality (Klein et al., 1992). This, of course, leaves the option of using
enough TFEs to obtain criticality and then down rating the required electrical power from
54
each TFE to obtain the desired total core power. The ATI design is a driverless core
which does not require the driver rods. For this design it is necessary to increase the
number of TFEs to achieve criticality (Klein et al., 1992). In this configuration, all of the
TFEs convert heat energy into electrical power. It is expected that the total electrical
power will be higher for the driverless core than for the driven core, for the same total
input thermal power, since 100% of the heat energy can be converted into electricity. The
main disadvantage of the driverless core is the necessity of enriching the tungsten-184
in large quantities (Klein et al., 1992). Tungsten enriched in tungsten-184 which has a
reasonable low thermal neutron absorption cross section is used as the optimal
emitter/collector material. A fast spectrum reactor hence will be less effected by the
strong thermal neutron absorption of natural tungsten than a more thermalized reactor
configuration. The ATI configuration however cannot produce a low power reactor (less
than about 15 kWe) without degrading the reactor performance. The reactor uses a block
made of zirconium hydride which acts as neutron moderator. Holes are drilled in the block
where the 165 fuel elements are placed in hexagonal array for the pitch to diameter ratio
of 1.3, core of 24 cm radius, and 8 cm thick BeO reflector.
3.2.
ATI Burnup Results
The input to MCNPBURN is a heterogeneous core that is a spatially complete
description of the core (Lewis et al., 1991). This 3-D heterogeneous model uses a
reflector' midplane, vertical plane and horizontal plane. This is a technique used in MCNP
to have a partial model simulating the results of a full model. For the ATI, 1/8th of the
core is modeled using a reflector plane by symmetry (i.e. the 1/8 section is the same as
the other 7/8 sections). A sample of a typical input/output deck is included in Appendix
I.
The bumup parameters for the full core ATI computed by the MCNPBURN are
tabulated in Table (3).
4
The use of reflector planes in MCNP is intended for geometry simplification where any
particle hitting a reflector plane is speculary (mirror) reflected. Thus, It should not be
confused with the reactor reflector (BeO).
55
Table 3. ATI total core burnup parameters.
Volume
70652 cm3
Powerth
375 kW
Fuel Mass
0.0382556 MTIHM
Power Density
5.3077 W/cm3
Loading
0.541462 g/cm3
Specific Power
9.8 W/g
BURNUP
25045 MWD/TE
Oth
3.4 X 1011 n/cm2-s
Burnup
7 Years
Of
1.8 X 1013 n/cm2-s
Fission Rate
1.62 X 1015 Fission/s
4T
1.8 X 1013 n/cm2-s
It is a requirement of fuel management in this reactor that the power of every TFE
relative to the core average be kept below approximately 1.98 to prevent fuel melting.
The fuel melting was chosen rather than the NaK coolant boiling point at atmospheric
pressure (Faust, 1972) because the fuel melting temperature is approximately 3053 K
which corresponds to a TFE power of about 4.6 KW (Pawlowski et al, 1992). Although
the NaK boiling temperature 1057 K is lower than the fuel melting temperature, the
corresponding TFE thermal power exceeds 19 KW as per
q" = m Cp
Tpoil
Time )
(51)
Where Tbod = 1057 K
Cp = 997 j/kg-K
Tom= 895 K
=0.12 kg /s
The average TFE power is about 2320 W and thus the relative power limit value (RPLV)
can be determined as follow
RPLV = 4600 / 2320
= 1.98.
56
3.2.1.
Power Distribution
An important objective of fuel management in this reactor is to follow the shifts in
flux and power density distributions that take place in the reactor as a result of spatially
nonuniform changes in fuel composition. Ten bumup steps where used in coarse time
steps. Table (4) shows that the configuration leads to an acceptably low peak-to-average
core power ratio of 1.247 at bumup of 872 MWD/MT (in the center of core TFE ). Notice
that these relative powers are well below the 1.8 limit discussed above. The relative
power throughout the 7 year operation period are almost identical, hence, this is evidence
that a steady state condition has been reached.
Figure 21 and Figure 22 show the
relative power distribution at beginning of core (BOC) and at end of core (EOL) for the ATI
configuration.
Table 4. Peak-to-average core power ratio over 7 years life.
Burnup (MWD/MT)
TFE Relative Power
Peak Power TFE
9.8
1.211
8
137
1.224
8
284
1.220
1
872
1.247
1
1755
1.217
2
3568
1.216
8
7146
1.209
2
14302
1.200
8
25036
1.234
4
25045
1.218
1
The power conversion efficiency is determined by using TFEHX (Pawlowski et al.,
1992) which is a coupled thermionic/thermal hydraulics computer code to calculate the
Figure 21. ATI quarter core TFEs relative power at BOC.
Figure 22. ATI quarter core TFEs relative power at EOC.
59
output electrical power of a single thermionic fuel element for a input thermal power.
TFEHX is used for each of the 46 TFEs in a quarter core. By summing the electrical
power of each of the TFEs, the power conversion is calculated for a certain reactor
thermal power. The core total electrical power efficiency was found to be 5.863% at the
beginning of life and increases ever slightly to 5.865% at end of life.
Thus the overall
change in electrical power efficiency is negligible. The 3-D effects over time are especially
important and these effects are represented through Figures 23 through 32. These figures
show the power profile (SURFER, Ver. 4) of the ATI reactor core for each of the bumup
steps.
3.2.2. Effects of Irradiation on Fuel
The changes in fuel composition for the ATI over the core lifetime take place over
a much longer time than the buildup of 135Xe and 149Sm to steady state concentrations,
because the cross sections of the nuclides involved are much smaller, being less than
2200 b. The changes in composition of all the nuclides except 135Xe and 149Sm take place
over a long period of time. These changes continue to take place during the entire
lifetime of the fuel. One of the principal objectives of fuel lifetime analysis is to follow
quantitatively the changes in concentrations of the fissile and fertile nuclides and fission
products during neutron irradiation.
The fuel charged to the ATI reactor originally contains 95 w/o enriched uranium
and depletes at the end of life time to about 90 w/o in the center of core TFE as shown
in Figure 33. As these figures show, the 235U concentration decreases almost linearly with
burnup.
In Figure 34 236U, a neutron-absorbing isotope of uranium, builds up to a
concentration of around 0.94 w/o of the total fuel while 239PU, a fissionable isotope builds
up to a concentration of around 0.04 w/o and 240Pu builds up more slowly to around 0.001
w/o. When 240Pu absorbs a neutron, 241Pu, another fissionable isotope, is formed. When
this absorbs still another neutron,
242Pu,
a neutron absorber, results. The net effect is
that 239PU and 241Pu are desirable isotopes, which increases the reactivity of the fuel, and
240Th
is not detrimental because it makes a fissionable isotope. 242-u, however like 236U,
is a deleterious, neutron-absorbing end product along with all the fission product
:
_
I
.
_
111
II
I
Ii
I
II
6
908 MWD/NTU
Figure 24. ATI full core TFEs power profile after 1 day of bumup.
137 MWD/MTU
L
Z
3
C)
Q.
Figure 25. ATI full core TFEs power profile after 2 weeks of bumup.
I
;00141,thil..11,;;
Is\
'-e.t
.
0440
0 ii06101$104*Vi
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I
..00
It
:tii44:;4;9
it
04 41
S0
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10101110710101014
11 11111111110/ 10110 11\\1041
it '1111 0010 \litii41\\10iS
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h 'i$t!
itt
01$N1),O_
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ft.b..04t4W
41i
,
..:...,-
1
872 MWD/MTU
Figure 27. ATI full core TFEs power profile after 3 months of bumup.
1755 MWD/MTU
Figure 28. ATI full core TFEs power profile after 1/2 year of bumup.
3568 MWD/MTU
Figure 29. ATI full core TFEs power profile after 1 year of bumup.
19 .1
Al
Nr2.
.9
26,
00,6
PoyeOp
:1
-"s0t
ofize
Or
Ji
14302 MND /MTU
Figure 31. ATI full core TFEs power profile after 4 years of bumup.
25036 MWD/MTU
Figure 32. ATI full core TFEs power profile after 7 years of bumup.
1.00U-238
0.99-
0.99-
0.98-
0.98-
0.97-
g Time 0
U-235=95 w/o
U-238= 5 w/o
0.97-
0.98-
0.96U-235
1000
1500
2500
Time (days)
Figure 33. Normalized 235U and 235U depletion over the ATI center of core lifetime.
1.00-
U-236
0.10:
Pu-240
Maximum w/o
U-236 = .942
Pu-239= .041
Pu-240= .001
0.01:
0.00
0
500
1000
1500
2600
Time (days)
Figure 34. 236U, 236PU, and 240Pu buildup over the ATI center of core lifetime.
72
accumulated. The fission products 135Xe and 149Sm concentration is shown in Figure 35.
3.2.3. Reactivity and Criticality
The changes in the fuel composition cause the reactivity of the fuel to decrease
with increasing burnup.
These reactivity changes take place as fissile nuclides are
depleted or formed from fertile nuclides, and as neutron poisons are formed through the
buildup of fission products.
Factors which also affect the reactivity include neutron
leakage and fuel non-uniformity. As each TFE in the reactor is irradiated, its composition
changes, as well as its contribution to the overall reactivity.
The ATI core average
conversion factor at EOC is about .03%. The C conversion ratio was calculated by taken
the percent ratio of production to consumption. The production is the sum of the fissile
material produced from the fission, basically these are the atom densities of 233U, 239PU,
and 241Pu. While the consumption is the 235U atom density. The conversion factor (C) is
a measure of burnup, thus if C is 100%, then each fuel nuclide that is burned is exactly
replaced by a new one. Hence, for the ATI, the low rate of isotopes buildup leads to a
negligible change in the overall reactivity. The criticality represented by keffective as a
function of time can be seen in Figure 36. Note that the reactor has sufficient reactivity
to last for the entire 7 year projected lifetime for the ATI reactor. Although the figure
shows the criticality eigenvalue to be chaotic somewhat, however, it declines within the
limit of the statistical relative error. The overall change in criticality eigenvalue over the
lifetime is in the order of .002 which is rather small. The reason that keffective does not
change much is because the fuel is highly enriched in uranium.
3.2.4. Power Shaping
Use of MCNPBURN as a tool for fuel management is possible to carry out survey
studies for fuel lifetime economy. To increase fuel burnup it is necessary to flatten the
core radial power profile, thus lowering the peak power pins to the average power TFEs
and hence make it possible to increase the overall core power which in turn means higher
Xe 135
Sm 149
2000
2500
Figure 35. 135Xe and '49Sm concentration over the ATI center of core TFE lifetime.
1.108
1.107-
1.106-
r
1.105-
1.102-
1.101-
1.099
0.01
1
1
1
1
1
1
11131
I
1
1
1
1
1
1
1
11
I
1
1
11111
10
1
1
1
00
111111
I
1
1
11111
1000
Time (days)
Figure 36. ATI lifetime criticality within statistical error of ± 0.0018.
1
1
111111
75
consumption rate and higher electrical efficiency.
A preliminary attempt was made to flatten the core power distribution by
introducing Gadolinium burnable absorber into selected peak TFEs. 0.3343 w/o (.0978
g) of natural Gd was loaded in TFEs No.1, 2, 3, 8, 9, 15, and 46. The Gd was depleted
linearly to the amount 0.2 w/o at EOC. This trial produced a somewhat better results in
the power profile shown in Figure 37 for beginning of core and Figure 38 at end of core.
Further work in this area which is not in the scope of this study is left for future study.
The MCNPBURN ATI input for this purpose is listed per Appendix II.
Burnable poison thus possesses a number of advantages (Duderstadt et al., 1976).
They increase core lifetime without any decrease in control safety, and if distributed in a
proper fashion, can also improve core power distributions, for example, by suppressing
reactivity in high flux regions. From this discussion, several desirable characteristics of
gadolinium burnable poison are apparent.
Obviously they should be characterized by
absorption cross sections somewhat higher than those of the fuel, since then they will
bum out more rapidly than the fuel, leaving minimal poison residue at the EOC.
.
.
411.
O.
"ME
IMO
.4e
SI
-
S
.
78
4.
CONCLUSIONS AND RECOMMENDATIONS
The LEOPARD and WIMS codes were used to make estimates of the neutron
multiplication and fuel composition in a unit cell burnup computation.
Geometric
description of the fuel rod unit cell, appropriate temperatures, that fraction of the cell void
of fuel and the degree of enrichment of fissile material to represent a standard pressurized
water reactor were employed. With such information, these codes compute the nuclide
burnup equations which are solved with the assumption that neutron fluxes and energy
spectra are constant during a time step. At the end of each time step, new fluxes and
energy spectra are computed and additional depletion calculations are performed using
these data. These calculations were run to a total of 2 years at 23.7 MWD/TE. For the
same unit cell model, the MCNPBURN was employed to make comparison against these
two codes as a mean of benchmarking since LEOPARD and WIMS are known to be
benchmarked to measured commercial or experimental data.
It was found that
MCNPBURN calculations indicate that most of its parameters represents a maximum
difference of 9% higher than the LEOPARD or WIMS.
A detailed burnup analysis was conducted to assess the reactor lifetime relevance
of the technology developed
under the Advanced Thermionic Initiative (ATI).
This
analysis included the development of a model for the assessment of the use of single cell
thermionic fuel elements (TFEs) in a low power nuclear reactor core. The power level for
these driverless reactors is to be about 38.75 kW of electrical power.
The code
developed, called MCNPBURN, is an improvement to MCNP, and it includes a module
for the calculation of the effects of the burnup and conversion of the nuclear fuel over the
lifetime of the system. The ATI reactor shows to have a full power operation lifetime
greater than 7 years. The reactor core was designed to be critical, or self-sustained, for
a given core dimension. The core calculation is done by using the MCNPBURN code to
perform the burnup analysis. The calculations for the electrical power were based on the
true axial power distribution where there is a considerable amount of neutron leakage out
of the top and bottom of the reactor. The MCNPBURN analysis reveals that charging
peak power TFEs with Gadolinium burnable poison does indeed reduce their power and
improve the overall core radial power profile.
79
A few distinct conclusions can be drawn from this analysis. They include:
1.
A method for analyzing burnup of single cell thermionic fuel element based nuclear
reactor systems has been developed during the course of this effort. A method
to accurately model complex neutronics, composition, conversion, and power
production using MCNPBURN has been completed and benchmarked. This model
allows the performance of all of the TFEs within a reactor core to be individually
assessed and determined. It also allows the complete and accurate assessment
of the three dimensional effects that the real thermal power distribution imposes
on the reactor.
2.
Three dimensional analysis of incore thermionic reactor cores is necessary to
account for all of the important nuances of their operation. This is needed to
account for both neutronics and burnup performance effects.
3.
The application of MCNPBURN made it possible to explore flattening the radial
power distribution using burnable poison for single cell thermionic space reactor
systems.
Recommendations for future efforts include:
1-
Other benchmarking of MCNPBURN to include the effect of the lumped
fission product on the criticality eigenvalue versus a well documented
measured burnup data is needed.
2
Expanding the number of nuclides or chains involved in the bumup to
include the thorium chain as well as material such as europium.
3
Additional simplification of the material card in the input deck relevant to
cells undergoing burnup (where the minimum 20 nuclides must appear in
the material card in the present input deck) to the same input as for the
standard MCNP.
4
Further study of the ATI to include the axial power profile is necessary
since the MCNPBURN has the capabilities to do such task.
80
5.
LITERATURE CITED
1.
Askew, J.R., Fayers, F.J., and Kemshell, P.B. (1966) "A General Description of
the Lattice Code WIMS," J. Br. Nucl. Enemy Soc., Vol. 5.
2.
Barry, R.F. (1973) "LEOPARD - A Spectrum-Dependent Non-Spatial Depletion
Code," WCAP-3269-26, Westinghouse Electric Corp., Pittsburgh, PA.
3.
Bennett, L.L. (1966) "Recommended Fission Product Chain for Use in Reactor
Evaluation Studies," ORNL-TM-1658, Oak Ridge National Laboratory, Oak Ridge,
TN.
4.
Bell, G.I. and Glasstone, S. (1970) Nuclear Reactor Theory, Van Norstrand, New
York.
5.
Breen, R.J., Marlow, OA and
Pfeifw, C.J. (1965) "HARMONY: A System for
Nuclear Reactor Depletion Computation," WAPD-TM-478, Westinghouse Electric
Corp., Pittsburgh, PA.
6.
Briesmeister, J.F. ed. (1986) "MCNP-A General Monte Carlo Code for Neutron
and Photon Transport," LA-7396-M, Rev.2, Los Alamos National Laboratory, Los
Alamos.
7.
Croff, A.G. (1980) "A User's Manual for the ORIGEN2 Computer Code,"
ORNUTM-7175, Oak Ridge National Laboratory, Oak Ridge, TN.
8.
Crowther, R.L. (1973) "Lattice Burn-up Calculations for Thermal Reactors,"
Reactor Burn-up Physics, Proceedings of a Panel, IAEA, Vienna, Austria.
9.
Duderstadt, J.J. and Hamilton, L.J. (1976) "Nuclear Reactor Analysis," John Wiley
and Sons, New York, NY.
10.
England, T.R. (1962) "CINDER, A One-Point Depletion and Fission Product
Program," WAPD-TM-34, Westinghouse Electric Corp., Pittsburgh, PA.
81
11.
Faust, 0. ed. (1972) Sodium-NaK Engineering Handbook, Vol. 1, Gordon and
Breach, New York, NY.
12.
Fowler, T.B. and Vondy, D.R. (1971) "Nuclear Reactor Core Analysis Code:
CITATION," ORNL-TM-2496, Rev.2, Oak Ridge National Laboratory, Oak Ridge,
TN.
13.
Jordheim, D.P. (1991) "Chain.238 DJ: A computer code for calculating Pu-238
production, quality, and impurity levels in the Np-237 transmutation chain," Thesis,
Oregon State University, Corvallis, OR.
14.
Klein, A.C., Lee H.H., Lewis, B.R., Pawlowski, R.A., AND Abdul-hamid, S.A. (1992)
"Advanced Single Cell Thermionic Reactor System Design Studies", Final report
for the Wright-Patterson Air Force, Wright Research and Development Center,
OSU Annual report, OSU-NE-9209, Department of Nuclear Engineering, Oregon
State University, Corvallis, OR.
15.
Lamp T. and Donovan, B. (1991) "The Advanced Thermionic Initiative Program,
"Proceeding 26th Intersociety Energy Conversion Engineering Conference, Boston,
MA.
16.
Lee, C.E., Apperson Jr., C.E., and Foley, J.E. (1976) "LEAF: A Computer program
TO calculate fission product release rates from a reactor containment building for
arbitrary radioactive decay chains," LA-NUREG-6750-MS, Los Alamos Scientific
Laboratory.
17.
Lewis, B.R., Pawlowski, R.A., Greek, K.J., and Klein, A.G. (1991) "Advanced
Thermionic Reactor System Design Code, "8th Symposium on Space Nuclear
Power Systems Proceedings, CONF-910116, Albuquerque, NM.
18.
Nickitin, V.P., Oglob lin, B.G., Luppov, A.N., Pomomarev-Stepnoi, N.N., Usov,
V.A., Nicolaev, Y.V., and Wetch, J.R. (1991) "TOPAZ-2 Thermionic Space Nuclear
Power System and Perspectives of its Development," 8th Symposium on Space
Nuclear Power Systems Proceedings, CONF-910116, Albuquerque, NM.
19.
Pawlowski, R.A. and Klein, A.C. (1992) "Modeling the energy Transport through
a Thermionic Fuel Element, "9th Symposium on Space Nuclear Power Systems
Proceedings, CONF-920104, Albuquerque, NM.
82
20.
Robinson, A.H. (1984) "BURN-Two group Multi region Burnup Code", Nuclear
Engineering Department, Oregon State University, Corvallis, OR.
21.
Seamon, R.E. (1990) Los Alamos National Laboratory letter X-6: Res-90-305 to
L.L. Carter.
22.
Seamon, R.E. (1992) Los Alamos National Laboratory letter X-6: Res-92-516 to
S.A. Abdul hamid.
23.
Shanstrom, R.T. and Benedict, M. (1961) Nuclear Since and Engineering, 11,377.
24.
Stamm ler, R.J.J. and Abbate, M.J. (1983) "Methods of Steady-State Reactor
Physics in Nuclear Design," Academic Press.
25.
"SURFER Reference Manual," Ver. 4, Golden Software, Inc., Golden, CO.
APPENDICES
83
APPENDIX I:
MCNPBURN
FORWARD
This Appendix serves as a manual and hence it is a practical guide for the use of the
general-purpose Monte Carlo and Burnup code MCNPBURN. This manual was prepared
based and an extension to the regular MCNP manual and thereby will discuss only the
bumup related material.
The idea to make the MCNP do burnup was born of the
necessity to obtain more reliable results for a model that can be very difficult to model
using any other available code. As an example of some of these difficulties is having a
zirconium hydride for a moderator in a small thermal reactor with a multilayer of different
type of cladding materials. Thus, upon a suggestion from Dr. A. C. Klein, at Oregon State
University, this code was developed to obtain reaction rates from MCNP and apply them
in a simple burnup routine.
S. A. Abdul-hamid
Modification editor
84
A.
Code
Code Package
1.
Name and Title
MCNPBURN: Monte Carlo Neutron Photon and Burnup Transport Code
System.
AUXILIARY FILES
GENERAL.CMN, STATIC.CMN, IBLDATA.CMN, RBLDATA.CMN, and
DYNAMIC.CMN:
External common blocks included in the program and must
be present upon compilation.
DATA LIBRARIES:
ENDL852, BMCCS2, D92, MCPLIB2, 531DOS2, 532DOS2, LLLDOS2,
TMCCS2, OSUXS2, AH1(Xe-135 & Sm-149) and XSDIR (Nuclear data
directory file)
2.
Contributors
Oregon State University, Nuclear Engineering Department, Corvallis, OR.
3.
Coding and Language and Computers
FORTRAN 77; PC 486.
85
4.
Typical Running Time
The running time varies considerably and it is problem dependent.
For
example using a 486 33MHz P.0 for unit cell modeling (reflected surfaces around
the cell boundaries), it takes about 1 day per burnup time step with a 1000
nominal source, 250 cycles and 5 cycles to skip. The 250 cycles are needed to
obtain a stable FOM while the 1000 nominal source to have a relative error less
than 0.01. For the same nominal source and cycles, the ATI, ( 1/8 full core, see
Appendix II) typically takes about 9 hours per burnup step. However, the relative
error is larger by a factor of 10.
5.
COMPUTER HARDWARE REQUIREMENTS
MCNPBURN requires a minimum of about 40 megabytes of hard disk
space.
Executable files for the PC version are provided for running on 8MB
memory under DOS5.0 on a PC486.
6.
Computer Software Requirements
A FORTRAN 77 compiler such as the Lahey Fortran compiler F77I-EM/32,
Version 5.00.
7.
Restriction or Limitations
The following restrictions apply only for bumup problems.
The fuel
materials are limited to 20 nuclides and these nuclides must appears in special
order and have a minimum trace element value greater than zero (i.e. the material
card for a nuclide may have an atom fraction or density as small as 1.0D-300).
Thus for each fuel cell, (if there are different compositions) undergoing burnup, a
corresponding material card that includes all of the 20 elements must be present.
These nuclide and their order can be seen in any of the input or output samples
in Appendices I and II. The code can handl up to 100 time steps, additional steps
86
require updating the parameter "MXSTP" found in the file common block
"GENERAL.CMN".
8.
Description of MCNPBURN Input
User input to the standard MCNP for non burnup cases can be used in
MCNPBURN as well. The input file name is common as inp and this file includes
set up of a problem (describe geometry, material, tallies, burn-ups, etc.). The file
has the following form:
Message Block
Blank Line Delimiter
Title Card
Cell Cards
Optional
Blank Line Delimiter
Surface Cards
Blank Line Delimiter
Data Cards
Blank Line Delimiter
Anything else
Optional
Blank Line Delimiter
Burn-up Cards
Required
If burn-up is desired
Except for the burn-up cards details of the input cards are well presented in the MCNP
manual.
requested.
However, the following is a description of the burn-up cards if bumup is
87
BURN-UP FLAG CARD
Form: BURN X1
Xl= Total core volume (cm3).
Use:
BURN card is required to signal burn-up procedures.
First BURN card include total core volume defined as every thing interior to the
reflector. The application of symmetry i.e. modeling a core by 1/8 require an equivalent
1/8 of the total core volume.
BURNUP TIME STEPS AND POWER
Form: DEL
X1 X2
X1 = DELTA (Days)
X2 = POWERT (Watts)
Use:
DEL cards include the step time width in days and the thermal power for that step.
This card can be repeated for up to 100 steps. Note that these cards must be sequential,
that is, the first DEL card signifies the first burnup step and so on. The POWERT card
is the total core thermal power in Watts (equivalent power in symmetric models).
88
Program Listing.
The following is a partial listing of the modified MCNP version 3B routines.
Replaced original MCNP 3B statement(s) was commented out and labeled "C/O", added
fortran statement have the label "BURNX" and the truncated portion of the program was
labeled by "I" on column 1. The titles hold the extension .CMN refers to the external
common statements while the extension .FOR is the Fortran source file.
9.
GENERAL.CMN
C
CODE NAME AND VERSION NUMBER.
CHARACTER KOD*B,VER*5
PARAMETER (KOD='MCNP',VERm'3133')
C
INITIALIZE GENERAL COMMON.
IMPLICIT DOUBLE PRECISION (A-H2O-Z)
C
C
C
C
C
C
C
C
C
C
C
PROCESSOR-DEPENDENT NAMED CONSTANTS.
MDAS IS THE INITIAL SIZE OF DYNAMICALLY ALLOCATED COMMON /DAC/.
ON SYSTEMS WHERE MEMORY ADJUSTMENT IS NOT AVAILABLE, SET MDAS
LARGE ENOUGH FOR YOUR BIGGEST PROBLEM.
PARAMETER (ADAS=1000000)
PARAMETER (NDP2=2,HUGE=1D37)
PARAMETER (FTLS=.2,DFTINT=100.)
ARRAY DIMENSIONS. I/O UNIT NUMBERS. GENERAL CONSTANTS.
PARAMETER (MAXE=50,MAXF=16,MAXV=18,MAXW=2,MEMAX=150,MINK=200,
PARAMETER (MAXE=100,MAXF=16,MAXV=18,MAXW=2,MEMAX=1500,MINX=200,
1 MIPT=2,MJSF=9,MKFT=7,MKTC=22,MSEB=301,MXC=180,MXDT=20,MXDX=5,
2 MXLV=10,MEMTX=150,NBMX=100,NDEF=14,NOVR=5,IUI=31,IU032,IURF33,
2 MXLV=10,MXMTX=1500,NBMX=100,NDEF=14,NOVR=5,IUI=31,IU0=32,IUR=33,
3 IUX=34,IUD=35,IUB=36,1UP=37,1US=38,IU1=39,IU2=40,IUSW=41,
4 IUSRR42,IUSC=43,IUC=44,IUT=45,IUZ=46,IUK=47,JTTY=6,
5 ZER0=0.,ONE=1.,PIE=3.1415926535898D0 ,FIVE19=(ZER0+5.)**19,
6 ANGDN=.59703109DO,GELEC=.511008,GNEUT=939.58,SLITE=299.7925)
6 AVGDN=.59703109DO,GELEC=.511008,GNEUT=939.58,SLITE=299.7925,
7 MXCL=50,NIS0=25,NRRX=5,IXT=96,IX0=99,MXDL=100)
C\O
BURNX
C\O
BURNX
C\O
BURNX
BURNX
89
10.
STATIC.CMN
STATIC COMMON
C
FIXED COMMON -- CONSTANT AFTER THE PROBLEM IS INITIATED.
COMMON /FIXCOM/ ATET(MEMAX),BCW(2,3),DDG(MIPT,MXDT),DXW(MIPT,3),
1 DXX(MIPT,5,MXDX),ECF(MIPT),EMCF(MIPT),EMX,ERGSAB(0:MAXE),
/
C
COMMON /BACKUP/ GVBU(NVARCM)0NBU(LVARCI)
C
C
11.
C
BURNUP ROUTINE, BURNX, COMMON STATEMENTS
BURNX
COMMON /BXBURN1/ RRWMAXE*NISO*NRRX),RRX(MAXE,NISO,NRRX),ANX(MAXE)BURNX
1 ,RONU(3*MAXE),F4(3*MAXE),F7(MAXE),CQ(IAXE),CNU(MAXE),CVOL(MAXE), BURNX
2 CDEN(MAXE),CRHO(MAXE),ICELL(MAXE),FRCN(MAXE,NISO),CAW(MAXE),
BURNX
3 XINIT(MAXE,NISO),XATOM( MAXE,NISO),FLOAD(MAXE),POWERT(0:MXDL),
BURNX
4 DELTA(0:MXDL),BURNT(MAXE),TFLX(MAXE),FFLX(MAXE),FLUX(MAXE),
BURNX
5 POWER(vD{DL),FRATE(MAXE),TSF(MAXE),WTOT(MAXE),XTOT(MAXE),CZH(3),
BURNX
6 VITC(MAXE),C22(3),CLA(3),CEA(3),CEH(3),CZG(3),CEG(3),CZC(3)
BURNX
COMMON /BXBURN2/ DELT,NSTEP,ISTEP,NCELL
BURNX
COMMON /BXBURN3/ CKCY,CMC,PNORM,CTV,PD,VTUEL
BURNX
COMMON /BXBURN4/ BURN
BURNX
LOGICAL BURN
BURNX
IBLDAT.CMN
BLOCK DATA IBLDAT
PARAMETER (NKCD=83,NTALMX=100)
C
COMMON /IMCCOM/ AJSH,BBB(4,4),FES(33),RF114,SWTM,SETX,
1 ICA,ICN,ICX,IFIP(MIPT),IITM,IME(2,MEMAX),IOID,IPL,IRC,IRS,
C
C
12.
C
C
C
C
C
C
C
C
CHARACTER COMMON
CHARACTER CNM(NKCD)*5,HDR(MAXE)*10,HITM*80,HLIN*80,ICH*5
1 ,BXLIN*80,BLIN(100)*80
COMMON /JMCCOM/ CNM,HDR,HITM,HLIN,ICH,BLIN,BXLIN
COMMON /3MCCOM/ CNM,HDR,HITM,HLIN,ICH
BURNX
BURNX
C/O
MCNPBURN.FOR
PROGRAM MCNPBURN
BURNX
This program modified to perform burnup analysis.
Shahab A. Abdul-hamid
Department of Nuclear Engineering
Oregon State University
Corvallis, OR 97331
May 16, 1993.
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
INCLUDE 'DYNAMIC.CMN'
C
CALL MCNP
IF(BURN)TEEN
C
C
CHANGE FILES STATUS
BURNX
BURNX
BURNX
BURNX
90
CLOSE (ITTY)
C
CLOSE(JTTY)
CLOSE(IU0)
OPEN(ITTY,FILE='INPUT',STATUS='SCRATCH')
OPEN(JTTY,FILE='OUTPUT',STATUS='SCRATCH')
OPEN(IUO,FILE=OUTP,STATUS='SCRATCH')
BURNUP LOOP
ISTEP=0
CALL BXPREP1
ISTEP=1
GOTO 20
10 CALL BXPREP2
CALL MCRUN
20 CALL BXSCALE
CALL BXOUT
CALL BXBURN
ISTEP=ISTEP+1
IF(ISTEP.LE.NSTEP)GOTO 10
ENDIF
STOP
END
PROGRAM MCNP
SUBROUTINE MCNP
GENERAL MONTE CARLO NEUTRON AND PHOTON TRANSPORT CODE.
MAIN OVERLAY.
RETURN
STOP
END
SUBROUTINE TPEFIL(MPO
DO ALL I/O ON RUNTPE, THE FILE OF RESTART DUMPS.
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
C/O
BURNX
BURNX
C/O
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
INCLUDE 'DYNAMIC.CMN'
CHARACTER HK*S,HV*5,HL*S,HI*19,HC*10,HP*19
IF(ISTEP.GT.0)RETURN
GO TO(10,20,40,60,90,205,90,210)MM
BURNX
>>>>> MM*1 -- CREATE RUNTPE WITH A UNIQUE NAME. WRITE FIRST RECORD.
10 CALL UNIQUE(RUNTPE,JTTY)
IF(.NOT.BURN)THEN
BURNX
OPEN(IUR,FILE=RUNTPE,FORM='UNFORMATTED',STATUS='NEW')
ELSE
BURNX
OPEN(IUR,FILE=RUNTPE,FORM='UNFORMATTED',STATUS='SCRATCH')
BURNX
ENDIF
BURNX
RETURN
END
SUBROUTINE KSRCTP(MM)
DO ALL I/O ON SRCTP, THE KCODE SOURCE FILE.
INCLUDE 'GENERAL.CHN'
INCLUDE 'STATIC.CMN'
INCLUDE 'DYNAMIC.CMN'
GO TO(10,20,30,40)!+1
C
/
/
C
C >>>>> MM*3 -- CREATE THE SRCTP FILE WITH A UNIQUE NAME.
30 CALL UNIQUE(SRCTP,JTTY)
IF(.NOT.BURN)THEN
OPEN(IUS,FILE=SRCTP,FORW'UNFORMATTED',STATUS='NEW)
ELSE
OPEN(IUS,FILE=SRCTP,FORM='UNFORMATTED',STATUS='SCRATCH')
ENDIF
RETURN
RETURN
BURNX
BURNX
BURNX
BURNX
91
C
C
END
SUBROUTINE IMCN
MAIN CODE OF OVERLAY IMCN.
INITIATION CODE FOR MONTE CARLO TRANSPORT.
C
C
INCLUDE
INCLUDE
INCLUDE
INCLUDE
'GENERAL.CMN'
'STATIC.CMN'
'DYNAMIC.CMN'
'IBLDATA.CMN'
C
CHARACTER*6 BXCH
BURNX
C
C
C
C
REREAD THE REST OF THE INP FILE AND SET UP THE PROBLEM.
140 CALL RDPROB
READ THE BURNUP DATA
IF(BURN)THEN
OPEN(IXO,'MCNPBURN.OUT')
OPEN(IXT,STATUS='SCRATCH')
READ(IUI,*)BXCH,CTV
IF(CTV.EQ.0) CALL ERPRNT(1,1,0,0,0,0,0,0,
1
'52HTHE CORE TOTAL VOLUME IS ZERO OR CTV CARD IS MISSING')
JJ=1
142 READ(IUI,*,END=143)BXCH,DELTA(JJ),POWERT(jj)
JJ=JJ+1
GOTO 142
143 NSTEP=JJ -1
ENDIF
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
C
/
/
C
C
C
C
C
RETURN
END
SUBROUTINE PASS1
MAIN CODE OF OVERLAY PASS1.
READ THE INP FILE THE FIRST TIME, IN ORDER TO GET THE
DIMENSIONS FOR DYNAMICALLY ALLOCATED STORAGE.
INCLUDE
INCLUDE
INCLUDE
INCLUDE
'GENERAL.CMN'
'STATIC.CMN'
'DYNAMIC.CMN'
'IBLDATA.CMN'
C
C
EXTERNAL NXTIT1
INQUIRE INP FOR BURNUP
II=0
BURN=. FALSE.
REWIND IUI
5 READ(IUI,'(A60)',END=6)HLIN
IF(HLIN(1:2).EQ.'BU')BURN=.TRUE
IF(BURN)GOTO 6
II=II+1
GOTO 5
6
LL=1
MM=0
NFG1=0
NFG2=0
NFLAG=0
REWIND IUI
C
C
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
PROCESS 3 DATA BLOCKS, WHICH ARE SEPARATED BY BLANK LINES.
HOVR='PASS1'
REWIND IU1
DO 50 IB=1,3
IF(IB.EQ.3.AND.NCPARF.NE.0)CALL CPRINP
ICS=0
IF(IB.EQ.1)INCL=1
IF(IB.EQ.2)LNSF=LNCL+MXA
IF(IB.EQ.3)GO TO 20
C
C
C
READ AND PROCESS LINES OF DATA UNTIL A BLANK OR EOF IS FOUND.
10 JUI=IUI
20 KL=0
READ(JUI,'(A80)',END=30)HLIN
C/O
92
C
C
C
C
READ MATERIALS NEEDED FOR FM
IF(BURN.AND.IB.EQ.3.AND.LL.LE.20)THEN
CALL BXM(LL)
LL=LL+1
GOTO 25
ENDIF
READ CELLS UNDERGOING BURNUP LISTED IN F7 AND ASSIGNED TO FM
IF(BURN.AND.NFLAG.EQ.2)GOTO 22
21 READ(JUI,'(A20)',END=30)HLIN
IF(BURN.AND.NFLAG.EQ.3)GOTO 25
IF(BURN.AND.IB.EQ.3)THEN
IF(HLIN(1:2).EQ.'F7')THEN
NFG=1
NFLAG=1
BLIN(1)=HLIN
ELSEIF(NFLAG.EQ 1.AND.HLIN(1:2).EQ.".AND.HLIN.NE.")THEN
NFG=NFG+1
BL/N(NFG)=HLIN
ELSEIF(NFLAG.EQ.1)THEN
BACKSPACE(JUI)
NFLAG=2
ENDIF
ENDIF
IF(BURN.AND.NFLAG.EQ.0.0R.NFLAG.EQ.1)GOTO 25
22 IF(BURN.AND.IB.EQ.3)THEN
IF(NFG1.LT.NFG)THEN
NFG1=NFG1+1
CALL BXF1(NFG1,1)
ELSEIF(NFG2.LT.NFG)THEN
NFG2=NFG2+1
CALL BXF1(NFG2,2)
ELSEIF(MM.LE.21)THEN
MM=MM+1
CALL BXF2(MM)
ELSE
NFLAG=3
GOTO 21
ENDIF
ENDIF
25 CONTINUE
CALL CKCHAR(HLIN,JTTY,IUOU)
KL=4
C
C
C
C
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
RETURN
END
SUBROUTINE RDPROB
MAIN CODE OF OVERLAY RDPROB.
READ IN THE PROBLEM OR CONTINUE-RUN SPECS FROM THE INP FILE.
INCLUDE
INCLUDE
INCLUDE
INCLUDE
'GENERAL.CMN'
'STATIC.CMN'
'DYNAMIC.CMN'
'IBLMATA.CMN'
C
C
EXTERNAL NEXTIT
C
LL=1
MH=O
NFG1=0
NFG2=0
NFLAG=0
BURNX
BURNX
BURNX
BURNX
BURNX
C
/
C
C
C
C
READ AND STORE LINES OF DATA UNTIL A BLANK OR EOF IS FOUND.
30 JUI=IUI
40 KL=0
READ(JUI,'(A130)',END=50)HLIN
READ MATERIALS NEEDED FOR FM
IF(BURN.AND.IB.EQ.3.AND.LL.LE.20)THEN
CALL BXM(LL)
LL=LL+1
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
93
GOTO 25
ENDIF
C
C
READ CELLS UNDERGOING BURNUP LISTED IN F7 AND ASSIGNED TO FM
IF(BURN.AND.NFLAG.EQ.2)GOTO 22
21 READ(JUI,'(A20)',END=50)HLIN
IF(.NOT.BURN)GOTO 25
IF(BURN.AND.NFLAG.EQ.3)GOTO 25
IF(BURN.AND.IB.EQ3)THEN
IF(HLIN(1:2).EQ.'F7')THEN
NFG=1
NFLAG=1
BLIN(1)=HLIN
ELSEIF(NFLAG.EQ.1.AND.HLIN(1:2).EQ.".AND.HLIN.NE.")THEN
NFG=NFG+1
BLIN(NFG)=HLIN
ELSEIF(NFLAG.EQ.1)THEN
BACKSPACE(JUI)
NFLAG=2
ENDIF
ENDIF
IF(BURN.AND.NFLAG.EQ.0.0R.NFLAG.EQ.1)GOTO 25
22 IF(BURN.AND.IB.EQ.3)THEN
IF(NFG1.LT.NFG)THEN
NFG1=NFG1+1
CALL BXF1(NFG1,1)
ELSEIF(NFG2.LT.NFG)THEN
NFG2=NFG2+1
CALL BXF1(NFG2,2)
ELSEIF(MM.LE.21)THEN
MM*MM+1
CALL BXF2(MM)
ELSE
NFLAG=3
GOTO 21
ENDIF
ENDIF
25 CONTINUE
KL=4
50 IF(KL.EQ.O.AND.JUI.NE.IUI)G0 TO 30
IF(KL.EQ.0)HLIN='
EOF'
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
C
C
C
RETURN
END
SUBROUTINE NEWCRD(IB)
SET UP AND CHECK A NEW INPUT CARD FOR PROCESSING.
/
/
RETURN
C 270 DO 280 1=1,8
270 IF(BURN)RETURN
DO 280 1=1,8
C/O
BURNX
BURNX
/
C
340 IME(1,I)=-ABS(IME(1,I))
IF(IME(2,I).EQ.0)CALL ERPRNT(2,2,1,ICN,0,0,0,0,
IF(.NOT.BURN.AND.IME(2,I).EQ.0)CALL ERPRNT(2,2,1,ICN,0,0,0,0,
1 '8HMATERIAL,I4,27H IS USED ONLY FOR TALLYING.')
C/O
BURNX
/
/
C
C
RETURN
END
SUBROUTINE ITALLY
MAIN CODE OF OVERLAY ITALLY.
PROCESS THE TALLY SPECIFICATIONS.
/
/
IF(NP.EQ.3)A,...FIM(LFIM+1,K)*FIM(LFIM+2,K)
C
C
ASSIGN CELLS WHICH UNDERGOES BURNUP
IF(BURN.AND.ISTEP.EQ.O.AND.KL.EQ.7)THEN
ICELL(I)=NCL(LNCL+K)
NCELL=I
ENDIF
IF(IY.GE.4.AND.A.EQ.0.)CALL ERPRNT(1,2,2,NCL(LNCL+K),KL,0,0,0,
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
94
1 '4HCELL,I5,9H OF TALLY,I4,21H HAS ZERO IMPORTANCE.')
LI=LI+1
C
RETURN
END
SUBROUTINE KCALC
CALCULATE AND PRINT K AND PREPARE FOR THE NEXT CYCLE.
C
C
INCLUDE 'GENERAL.CMN'
/
130 WRITE( JTTY,140)KCY,ZZ(1),MC,LA(1),CTS/60.
140 FORMAT(7H CYCLE=,I6,3X,2HK=,F7.5,3X,6HAVE OF,I6,8H CYCLES=,
1 F7.5,3X,4HCI24m,F8.2)
IF(BURN.AND.KCY.EQ.KCT)THEN
CKCY=KCY
CMC=MC
DO 145 1=1,3
CZZ(I)=ZZ(I)
CZA(I)=ZA(I)
CZA(I)=EA(I)
CZG(I)=ZG(I)
CEG(I)=EG(I)
CZH(I)=ZH(I)
CEH(I)=EH(I)
145 CZC(I)=ZC(I)
ENDIF
WRITE(IU0,150)KCY,MC,(ZZ(I),ZA(I),EA(I),ZG(I),EG(I),
1 ZH(I),EH(I),ZC(I),I=1,3)
BURNX
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BURNX
BURNX
BURNX
BURNX
BURNX
/
C
C
C
RETURN
END
SUBROUTINE TALLYP
PRINT THE TALLIES.
INCLUDE 'GENERAL.CMN'
/
IF(T.LT..5)RETURN
IF(KNRM.NE.0)T=NPS-NSKK
10 FPI=1./T
C
C
IT1=0
IT2=0
IT3=0
IT4=0
IF(BURN.AND.NTAL.NE.4) CALL ERPRNT(0,1,0,0,0,0,0,0,
1 '29HF4 AND/OR F7 CARD IS MISSING.')
DO ALL OF THE TALLIES IN THE PROBLEM.
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BURNX
DO 140 ITAL=1,NTAL
MK=IPTAL(LIPT+IP(8),3,ITAL)
DO 90 IK=1,MK,5
N=MIN(5,MK-IK+1)
C
C
IF(BURN.AND.N.GT.1) CALL ERPRNT(0,1,0,0,0,0,0,0,
1 '46HFQn CARDS ARE NOT PERMITTED IN BURNUP PROBLEMS')
PRINT THE COLUMN HEADING.
BURNX
BURNX
/
/
IF(IPTAL(LIPT+4,2,ITAL).NE.0)T=T/TDS(IPTAL(LIPT+4,2,ITAL)+
1 IPTAL(LIPT+4,3,ITAL)*(IV(1)-1)+IV(4))
IF(IY.GE.6.AND.JPTAL(LJPT+4,ITAL).NE.0)T=T*1.60219E-22
C
80 TPP(I) =T *FPI
TPP(I) =T *FPI
IF(.NOT.BURN)GOTO 80
IF(ITAL.EQ.1)THEN
IT1=IT1+1
F4(IT1) =TPP(I)
ELSEIF(ITAL.EQ.2) THEN
IT2=1T2+1
F7(IT2) =TPP(I)
ELSEIF(ITAL.EQ.3)THEN
C/O
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95
IT3=IT3+1
RRM(IT3)=TPP(I)
ELSE
IT4=IT4+1
RQNU(IT4)=TPP(I)
ENDIF
80 CONTINUE
C
C
C
C
C
BURNX
BURNX
BURNX
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BURNX
BURNX
BURNX
PRINT THE TALLY TABLE LINE.
90 WRITE(IUO,100)HT(1: 11),(TPP(I),TPP(5+I),I=1,N)
RETURN
END
SUBROUTINE PTFC
PRINT THE TALLY FLUCTUATION CHARTS.
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
/
LA=MIN(JT+2,NTAL)
IF(MOD(JT/3,60/(NN+5)).E0.0)WRITE(IU0,30)
IF(BURN.AND.MOD(JT/3,60/(NN+5)).EQ.0)WRITE(IXT,30)
30 FORMAT(25H1TALLY FLUCTUATION CHARTS)
IF(MOD(JT/3,60/(NN+5)).NE.0)WRITE(IUO,'(1H )')
IF(BURN.AND.MOD(JT/3,60/(NN+5)).NE.0)WRITE(IXT,'(1H )')
WRITE(IU0,40)(ITALLY',JPTAL(LJPT+1,I),I=JT,LA)
IF(BURN)WRITE(IXT,40)('TALLY',JPTAL(LJPT+1,I),I=JT,LA)
BURNX
BURNX
BURNX
40 FORMAT ( /15X , 3 (A5 , I4,25X) )
WRITE(IU0,50) ('MEAN' , 'ERROR' , 'FOM' ,I=JT,LA)
IF(BURN)WRITE(IXT,50)('MEAN','ERROR','FOM',I JT,LA)
50 FORMAT(7X,3HNPS,5X,3(3X,A4,6X,A5,5X,A3,8X))
C
C
PRINT THE NPC, TFC TABLE.
DO 70 L=1,NN
DO 60 I=JT,LA
T=TFC(LTFC+3,L,I)
IF(T.LE.9999999..AND.T.GE.9.95)WRITE(HA(I-JT+1),'(I8)')INT(T+.5)
60 IF(T.GT.9999999..OR.T.LT.9.95)WRITE(HA(I-JT+1),'(1PE8.1)')T
IF(BURN)WRITE(IXT,80)NPC(L),((TFC(LTFC+J,L,I),J=1,2),HA(I-JT+1),
1 I=JT,LA)
70 WRITE(IU0,80)NPC(L),((TFC(LTFC+J,L,I),J=1,2),HA(I-JT+1),I=JT,LA)
80 FORMAT( 1X,I10,3(1PE15.5,OPF7.4,A8,4X))
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C
C
C
DELETE THE LINE FOR NPS IF IT WAS ADDED HERE.
IF(LL.NE.0)NPC(NN)=0
RETURN
END
SUBROUTINE BXBURN
MAIN BURNUP ROUTINE.
C
BURNX
BURNX
BURNX
C
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
DIMENSION AR(NISO,NISO)
C
C
C
C
C
SET MATRIX IN CHAIN, SOLVE FOR NEW ATOM DENSITY AND PRINT OUTPUTBURNX
FOR EACH CELL UNDERGOING BURNUP.
BURNX
DO 10 I=1,NCELL
BURNX
CALL CHAIN(I,AR)
BURNX
10 CALL SOLVER(I,AR,XATOM,DELT)
BURNX
END
BURNX
SUBROUTINE BXPREP1
BURNX
PREPARE CONDITION AND STATIC VARIABLES AND NUCLIDES REORDERING. BURNX
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
INCLUDE 'DYNAMIC.CMN'
INCLUDE 'IBLDATA.CMN'
CHARACTER HP*119
BURNX
C
C
C
C
INITIALIZE
ASSIGN CELLS WHERE BURNUP IS DESIRED(CELLS CONTAIN THE 20
BASIC NUCLIDES)
IC=0
DO 30 I=1,1vDCA
ICOUNT=0
DO 10 M*MLL(IMIL+1,I),MILL(LMIL+2,I)
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96
10 ICOUNT=ICOUNT+1
IF(ICOUNT.EQ.20)THEN
IC=IC+1
NCTR=1
DO 20 1.-MLL(LMIL+1,I),MLL(LMLL+2,I)
IF(MODE.NE.2)AWX(NCTR)=ABSCATWT(LME(1,M)))
IF(MODE.EQ.2)AWX(NCTR)=ABS(AFWIT.Q)
FRCN (IC, NCTR) =FME (M)
C
C
20 NCTRpNCTR+1
CRHO(IC)=RHO(LRHO+I)
CDEN(IC)=DEN(LDEN+I)
CVOL(IC)=VOL(LVOL+I)
ENDIF
30 NCELL=IC
RE-ORDER ATOMIC WEIGHTS
DO 50 J=1,9
50 CAW(J)=AWX(J)
CAW(10)=236.0044
CAW(11)=236.9977
CAW(12)=237.9915
DO 60 J=13,19
60 CAW(J)=AWX(J-3)
CAW(20)= 133.8105
CAW(21)=AWX(17)
CAW(22)=147.6382
DO 70 J=23,NISO
70 CAWMPAWX(J-5)
C
C
RE -ORDER & ATOM FRACTIONS
80
90
100
110
C
C
C
DO 110 I=1,NCELL
DO 80 J=1,9
XINIT(I,J)=FRCN(I,J)
DO 90 J=13,19
XINIT(I,J)=FRCN(I,J-3)
XINIT(I,21)=FRCN(I,17)
DO 100 J=23,NISO
XINIT(I,J)=FRCN(I,J-5)
CONTINUE
COMPUTE ATOMIC DENSITIES
DO 160 I=1,NCELL
DO 160 J=1,NISO
IF(XINIT(I,J).LT.1.D-100) XINIT(I,J)=0.0D0
XINIT(I,J)=XINIT(I,J)*CRHO(I)
160 XATOM(I,J)=XINIT(I,J)
C
TOTAL WEIGHT
C
VFUEL=O.
DO 165 I=1,NCELL
VFUEL=VFUEL+CVOL(I)
WTOT(I)=0.
XTOT(I)=0.
DO 165 J=1,15
WTX=XINIT(I,J)*CAW(J)
XTOT(I)=XTOT(I)+XINIT(I,J)
165 WTOT(I)=WTOT(I)+WTX
C
COMPUTE FULE LOADING FOR EACH CELL LATTICE.
C
TIHM=O.
DO 190 I=1,NCELL
VITC(I)=CVOL(/)*CTV/VFUEL
SUMF=0.
DO 170 J=1,9
170 SUMF=SUMF+XINIT(I,J)*CAW(J)
DO 180 J=13,18
180 SUMF=SUMF+XINIT(I,J)*CAW(J)
FLOAD(I)=SUMF/AVGDN*CVOL(I)/VITC(I)
190 TIEMPTIHM+FLOAD(I)*VLTC(I)
C
C
REREAD AND PRINT THE INP MESSAGE BLOCK AND TITLE LINE.
WRITE(IX0,195)KOD,VER,LODDAT,IDTM
195 FORMAT(//1X,A8,17H/BURNUP/ VERSION ,A5,3X,A8,9X,A/1X,73(1H-)//)
REWIND IUI
ILN=0
197 READ(IUI,'(A80)',END=200)AID
ILN=ILN+1
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97
WRITE(IXO,'(I5,1H-,7X,A80)')ILN,AID
GOTO 197
200 CONTINUE
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C
BURNX
C
PRINT THE PRINCIPAL CELL PARAMETERS.
BURNX
HP='
BURNX
HP (24: 27)= 'ATOM'
BURNX
HP (37: 40)=' GRAM'
BURNX
WRITE(IXO,'(/A119)')HP
BURNX
HP='
CELL MAT
DENSITY
DENSITY
VOLUME' //
BURNX
1
MASS'
BURNX
CC
1=71
BURNX
WRITE(IXO,'(A119/)')HP
BURNX
TV=0.
BURNX
TH=0.
BURNX
DO 310 IC=1,MXA
BURNX
HP='
BURNX
WRITE(HP,250)IC,NCL(LNCL+IC),MAT(LMAT+1C),RHO(LRH0+1C),
BURNX
1 DEN(LDEN+IC),VOL(LVOL+IC),DEN(LDEN+IC)*VOL(LVOL+IC)
BURNX
250 FORMAT(216,I5,1PE14.5,3E13.5)
BURNX
TV=TV+VOL(LVOL+IC)
BURNX
TM=TM+DEN(LDEN+IC)*VOL(LVOL+IC)
BURNX
310 WRITE(IXO,'(A119)')HP
BURNX
WRITE(IX0,320)TV,TM
BURNX
320 FORMAT(/68 TOTAL,1PE51.5,E13.5)
BURNX
WRITE(IX0,330)NSTEP,CTV,VFUEL/CTV,TIHM/1.0E6,TIHM/CTV
BURNX
330 FORMAT(//30H NUMBER OF BURNUP STEPS
BURNX
Ill/
1
30H CORE TOTAL VOLUME (CC)
1PE11.5/
BURNX
2
30H CORE FUEL REGION FRACTION
1PE11.5/
BURNX
3
30H CORE TOTAL MTIHM
1PE11.5/
BURNX
4
30H AVERAGE CORE LOADING (G/CC)
1PE11.5//)
BURNX
C
BURNX
WRITE(IX0,340)
BURNX
340 FORMAT(/80 LATTICE,3X,11H VOLUME
,3X,11H LOADING
,3X,
BURNX
1 11H
MASS
/8X,3X,11H
CC
,3X,11H
G/CC
,3X,
BURNX
3 11H
GRAM
/)
BURNX
DO 350 I=1,NCELL
BURNX
GIHM=FLOAD(I)*VLTC(I)
BURNX
350 WRITE(IX0,360)ICELL(I),VLTC(I), FLOAD(I),GIHM
BURNX
360 FORMAT(I4,4X,3(3X,1PE11.4))
BURNX
END
BURNX
SUBROUTINE BXPREP2
BURNX
C
PREPARE CONDITION AND STATIC VARIABLES AND NUCLIDES REORDERING. BURNX
C
INCLUDE 'GENERAL.CN'
INCLUDE 'STATIC.QIN'
'
INCLUDE 'DYNANEIC.CMN'
INCLUDE 'IBLDATA.CMN'
INCLUDE 'RBLOAMA.CMN'
DIMENSION WF (MEMAX)
BURNX
C
DO 290 I=1,NCELL
DO 250 J=1,9
250 FRCN(I,J)=XATOM(I,J)
DO 270 J=13,18
270 FRCN(I,J-3)=XATOM(I,J)
FRCN(I,17)=XATOM(I,21)
DO 280 J=23,NISO
280 FRCN(I,J- 5)= XATOM(I,J)
C
C
290 CONTINUE
CELL MATERIAL FRACTION FOR THE BURNABLE NUCLIDES IN MCNP.
DO 340 IC=1,NCELL
ICOUNT=0
DO 340 I=1,MXA
DO 300 I.@MLL(LMLL+1,I),MLL(LMLL+2,I)
300 ICOUNT=ICOUNT+1
IF(ICOUNT.EQ.20)THEN
NCTR=1
DO 310 M=MLL(LMLL+1,I),MLL(LMLL+2,I)
FME(M)=FRCN(IC,NCTR)
310 NCTR=NCTR+1
C
C
CONVERT MASS FRACTIONS TO ATOM FRACTIONS.
SF=0.
SW=0.
DO 320 M=MLL(LMLL+1,I),MLL(LMLL+2,I)
IF(MODE.NE.2)A=ABS(ATWT(LME(1,M)))
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98
IF(MODE.EQ.2)A=ABS(ATWT(M))
WP(M)=FME(M)*A
SF=SF+FME(M)
320 SW=SW+WF(M)
C
C
NORMALIZE THE ATOM FRACTIONS AND MASS FRACTIONS.
DO 330 M=BE L(LMLL+1,I),MLL(LMLL+2,I)
FME(M)=FME(M) /SF
330 WF(M)=WF(M) /SW
C
ENDIF
340 CONTINUE
C
CLEAR VARIABLES. AFTER BURNUP FOR NEXT STEP.
CLEAR KCALC
NST=0
KCY=1
DO 350 1=1,3
OSUM(I)=0
DO 350 J=1,3
350 OSUM2(I,J)=0
DO 360 1=1,2
RSUM(I)=ZERO
DO 360 J=1,2
360 RSUM2(I,J) =ZERO
CLEAR TALLIES AND ERRORS.
NPS=0
JSU=0
DO 370 1=1,3
370 SMUL(I) =ZERO
DO 380 I=1,MXFO
TAL(LTAL+MXF+I)=ZERO
380 TAL(LTAL+MXF2+I)=ZERO
END
SUBROUTINE BXRR
C
DO ALL REACTION RATE COMPONENTS, FLUXES, NU AND Q VALUES,
C
ALONG WITH THEIR CORRESPONDING STANDARD ERROR, CELLS AND
C
20 TO 25 NUCLIDES REORDERING.
C
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INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
C
C
CLEAR ALL REACTION RATE AND ITS ERRORS.
C
C
C
DO 5 I=1,NCELL
DO 5 J=1,NISO
DO 5 K=1,NRRX
5 RRX(I,J,K)=0.0D0
SORT ALL REACTION RATE AND ITS ERRORS.
10
12
14
16
20
C
C
C
C
M=0
DO 20 I=1,NCELL
DO 10 J=1,9
DO 10 K=1,NRRX
M=M+1
RRX(I,J,K)=RRM(M)
DO 12 J=13,19
DO 12 K=1,NRRX
MON+1
RRX(I,J,K)=RRM(M)
J=21
DO 14 K=1,NRRX
M=M+1
RRX(I,J,K)=RRM(M)
DO 16 J=23,NISO
DO 16 K=1,NRRX
M=M+1
RRX(I,J,K)=RRM(M)
CONTINUE
SORT ALL FLUXES AND HEATING TALLIES.
M=1
DO 30 I=1,NCELL
TFLX(I)=F4(M)
FFLX(I)=F4(M+1)
FLUX(I)=F4(M+2)
30 M=M+3
SORT NU, Q-FISSION.
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99
M*1
DO 40 I=1,NCELL
IF(RaMMO.EQ.0.)TBEN
CNU(I)=0.
CQ(I)=0.
ELSE
CNU ( I ) =RQNU (M+1) /RQNU (M)
C
C
CQ(I)=RQNU(M+2)/RQNU(N)
ENDIF
40 M=M+3
END
SUBROUTINE BXOUT
PRINT RESULTS
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INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
INCLUDE 'DYNAMIC.CMN'
CHARACTER BHA*80, CLIST(NISO)*5
BURNX
DATA CLIST/'92233','92234','92235','92236','92237','92238','92239'BURNX
1
,'92240','93237','93238','93239','93240','94238','94239'BURNX
2
,'94240','94241','94242','95241','50999','53135','54135'BURNX
3
,'61149','62149',' 8016','64000'/
BURNX
C
WRITE(*,5)KOD,VER,LODDAT,IDTM
WRITE(IX0,5)KOD,VER,LODDAT,IDTM
5 FORMAT( / /1X,A8,17H /BURNUP/ VERSION ,A5,3X,A8,9X,A/1X,73(1H -))
C
START=END
END=START+DELTA(ISTEP)
C
WRITE(*,10)ISTEP,START,END
WRITE(IX0,10)ISTEP,START,END
10 FORMAT(/12H BURNUP STEP,/3,11H STARTS AT ,G10.3,5H DAYS/
1
15X,11H
ENDS AT ,G10.3,5H DAYS/)
WRITE(IX0,12)POWERT(ISTEP),PD,PNORM
12 FORMAT(/28HSTEP INPUT THERMAL POWER:
,1PE11.4,7H WATTS./
1
28HAVERAGE POWER DENSITY:
,1PE11.4,9H KW/LITER/
2
28HPOWER NORMALIZATION FACTOR: ,1PE11.4/)
WRITE(IX0,16)
16 FORMAT(/5H CELL,3X,11HIRRADIATION,3X,11H Q-FISSION ,3X,
1 11H NU-FISSION,3X,11HFISION RATE/8X,11H MWD /TE
,3X,
2 11HMeV /FISSION,3X,11H N/FISSION ,3X,11H FISSION/S )
DO 20 I=1,NCELL
IF (FLOAD (1 ) . NE . ZERO) PS=PD/FLOAD (1 )
BURNT(I)=BURNT(I)+PS*DELTA(ISTEP)
20 WRITE( IX0,30)/CELL(I),BURNT(I),CQ(I),CNU(I),FRATE(I)
30 FORMAT(I4,4(3X,1PE11.4))
WRITE(IX0,100)
100 FORMAT(//4HCELL,3X,12HTHERMAL FLUX,2X,11H FAST FLUX ,3X,
1 110 TOTAL FLUX,3X,11HSP. POWER ,3X,11H POWER
/7X,
2 11H N/CM/CM/S ,3X,11H N/CM/CM/S ,3X,11H N/CM/CM/S,3X,
3 11H MW/TE
,3X,11H WATTS
)
C
DO 110 I=1,NCELL
IF(FLOAD(I).NE.ZERO)PS=PD/FLOAD(I)
110 WRITE( IX0,120)ICELL(I),TFLX(I),FFLX(I),FLUX(I),PS,POWER(I)
120 FORMAT(/4,5(3X,1PE11.4))
WRITE(IX0,130)CKCY,CMC,(CZZ(I),CLA(I),CEA(I),I=1,3)
130 FORMAT(//13H CRITICALITY:,//11H ESTIMATOR,5X,5HCYCLE,I6,3X,
1 6HAVE OF,I6,7H CYCLES/
2 14H K(COLLISION) ,F13.6,F15.6,F7.4/
2 140 K(ABSORPTION),F13.6,F15.6,F7.4/
3 14H K(TRK LENGTH),F13.6,F15.6,F7.4/)
WRITE(IX0,140)(CZG(I),CEG(I),CZH(I),CEH(I),CZC(I),I=1,3)
140 FORMAT(/120 COMBINATION,9X,14HSIMPLE AVERAGE,4X,
1 16HCOMBINED AVERAGE,5X,4HCORR/
2 17H K(COL/ABS)
,F12.6,F7.4,F13.6,F7.4,F9.4/
3 17H K(ABS/TK LN)
,F12.6,F7.4,F13.6,F7.4,F9.4/
4 17H K(TK LN/COL)
,F12.6,F7.4,F13.6,F7.4,F9.4)
C
C
WRITES BURNUP RESULTS TO FILE IXO, MCNPBURN.OUT
DO 220 I=1,NCELL
SUM1=0.
SUM2=0.
SUM3=0.
SUM4=0.
WRITE(IX0,180)ICELL(I)
180 FORMATU5X,6HCELL: ,I8//6X,7HISOTOPE,3X,11HATOM DENS. ,2X,
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100
1 11H CURRENT ,4X,8HWEIGHT %,4X,8H% CHANGE/15X,11H(atom/b.cm),
2 5X,8HLOAD(GM),7X,3HIHM,7X,8HFROM IBM)
DO 190 J=1,NISO
WTX=XATOM(I,J)*CAW(J)
WF=WTX/WTOT(I)*100.
IF(J.EQ.24)WF=0.
GRAM=WTX/AVGDN*CVOL(I)
CHNG=(XATOM(I,J)-X/NIT(I,J))/XTOT(I)*100.
SUM2=SUM2+GRAM
SUMIO=SUM3+WF
SUM4=SUM4+CHNG
SUM1=SUM1+XATOM(I,J)
190 WRITE(IX0,200)J,CLIST(J),XATOM(I,J),GRAM,WF,CHNG
200 FORMAT(I3,4X,A5,2X,1PE13.6,3(2X,1PE11.4))
WR/TE(IX0,210)SUM1,SUM2,SUM3,SUM4
210 FORMAT(6HTOTAL:6X,2X,1PE13.6,3(2X,1PE11.4))
C
C
220
225
C
230
240
C
C
COMPUTE CONVERSION FACTOR
PRODUC=XATOM(I,1)+XATOM(I,14)+XATOM(I,16)
CONSUM*XATOM(I,3)
CR=PRODUC/CONSUM*100.
WRITE(IX0,225)CR
FORMAT(/26H BURNUP CONVERSION FACTOR ,F10.4,2H %//)
PRINT 3 TALLIES ACROSS, WITH PAGE EJECTS WHERE NEEDED.
REWIND IXT
K=1
READ(IXT,'(A80)',END=240)BHA
WRITE(IXO,'(A80)')BHA
K=K+1
GOTO 230
REWIND IXT
END
SUBROUTINE CHAIN(I,AR)
PUTS COEFFICIENTS OF dX /dT= SUM(RRXij *Xij) IN MATRIX FORM.
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
DIMENSION ALAM(NISO),BLAM(NISO),YI(NISO),YXE(NISO),YPM(NISO)
DIMENSION AR(NISO,NISO),YFP(NISO)
DATA ALAM/1.38E-13,
8.93E-14, 3.08E-17,
0.000000,
9.39E-16,
2
4.91E-18,
0.000000, 0.000000,
0.000000,
1.03E-14,
3
0.000000,
0.000000, 2.50E-10,
9.01E-13,
3.36E-12,
4
3.37E-14,
5.68E-14, 5.07E-11,
0.000000,
0.000000,
5
0.000000,
0.000000, 0.000000,
0.000000/
0.000000,
DATA BLAM/0.000000,
0.000000, 0.000000,
0.000000,
1.189E-6,
2
0.000000,
4.916E-4,
1.366E-5, 0.000000,
3.790E-6,
3
3.400E-6,
1.866E-4, 0.000000,
0.000000,
0.000000,
4
1.464E-9,
0.000000, 0.000000,
0.000000,
2.875E-5,
5
2.092E-5,
3.556E-6,
0.000000,
0.000000,
0.000000/
DATA YI /0.056200,
0.000000, 0.061700,
0.000000,
0.000000,
2
0.057800,
0.000000, 0.000000,
0.000000,
0.000000,
3
0.000000,
0.000000,
0.000000,
0.069300,
0.000000,
4
0.062600,
0.000000,
0.000000,
0.000000,
0.000000,
5
0.000000,
0.000000, 0.000000,
0.000000,
0.000000/
DATA YXE /0.013880,
0.002000, 0.005580,
0.002000,
0.002000,
2
0.000330,
0.002000, 0.002000,
0.002200,
0.002000,
3
0.002000,
0.000000, 0.002000,
0.012520,
0.005620,
4
0.002830,
0.002000, 0.002000,
0.000000,
0.000000,
5
0.000000,
0.000000, 0.000000,
0.000000,
0.000000/
DATA YPM /0.007690,
0.010000, 0.010800,
0.011300,
0.010000,
2
0.016700,
0.010000, 0.010000,
0.011300,
0.010000,
3
0.010000,
0.000000, 0.011300,
0.015100,
0.014600,
4
0.012000,
0.020000,
0.015200,
0.000000,
0.000000,
5
0.000000,
0.000000,
0.000000,
0.000000,
0.000000/
DATA YFP /1.119000,
0.000000, 1.260000,
0.000000,
0.000000,
2
1.426000,
0.000000, 0.000000,
0.000000,
0.000000,
3
0.000000,
0.000000, 0.000000,
1.456000,
0.000000,
4
1.456000,
0.000000, 0.000000,
0.000000,
0.000000,
5
0.000000,
0.000000, 0.000000,
0.000000,
0.000000/
C
C
C
C
C
C
C
C
C
ISOTOPE INDEX:
1. U-233
2.
6. U-238
7.
11. NP239
12.
16. PU241
17.
21. XE135
22.
ISOTOPES NO. 10,11 ,12,20
,
,
,
,
,
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BORNE
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BORNE
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BURNX
BORNE
BORNE
BORNE
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& 22 N/A IN MCNP XS LIBRARY (RADIOACTIVE)BURNX
BURNX
U-234,
3. U-235,
4.
U-239,
8. U-240,
9.
NP240, 13. PU238, 14.
PU242, 18. AM241, 19.
PM149, 23. SM149, 24.
U-236,
NP237,
PU239,
F.P.
0- 16,
,
5.
10.
15.
20.
25.
U-237,
NP238,
PU240,
1-135,
GDNAT,
mane
oa ot =rosni't
oa ot osim't=m
ot
3
3
mulls
o=(x'r)uv
=mu matotaamoo
moixorau=cm'r't)muu
uoa
Tao
'I
mamma
mot,tovau IdAZ 'm saii=t)s't'Esz't=m 'sta=z 'alto=E 'mz'a=t
rev
=(t ((t)trero(tst'Dxrnn=0 (t'z'Dxutt
=(£
(s'Elt)xuu
)uv 'z =(t
(Eit'Moau
)uv 'z =(Z ((Z)14vTa+(t'z't)x2ia)'t
Ytra 't
)1ra 'I
)Iry
)'iv
)tre
)lay
)'az
'z
'z
=0
=(17
=(Et'z
'E =(Z
'E
=0
)uv 'E =(17
>we 'E =0
)1ra =(tt'E
)1r5r ''
=(£
)ukr 't =(17
)1aNt `t =(g
)try 't =(9
)'av --(st't
)1ty 's =(17
)uit 's =(s
>uv 's =(9
)uNr 's =(c.
(t'E'Dxuu
(s't'thom
(Et)New
(E'z'Mm
((E)tavtv+(t`E'Dxutt)(t't't)xuu
(s's'Dxutt
(tt)Hirra
(E'E'Dxuu
((t)trera+(t't'i)xuu)(t's'x)xlm
(s's'x)xuu
r amv
mune
mune
xmuna(m'a=s
mina
xauna
moms
xmuna
mane
mane
mune
name
xauna
mune
mune
mans
mune
mina
mane
mune
mina
(st)kprrir
xmuna
(E't'x)xuu
mina
mune
mune
mune
((s)kreta+(t'sDxutn(t's'i)xuu
(s'L'Mom
)uv =(st's
(st)kretv
)uv '9 =(g
(E's't)xuu
)uy '9 =(9 ((9)www+(t'9'i)xtoo)uv '9 =(L
(t'L'I)xuu
)ty '9 =(8
(s'et)xuu
))1'd =(Li'9
(LI)KV1V
)1111 'L =(9
(E's'i)xlma
)try 'L =(L ((L)mrta+(i'L'i)xiu)Yuy 'L =(8
(4'6'1)3(1:111
xmuna
))8v
xmuna
'8
=(L.
)1Dt '8 =(8
)uv '6 =(g
>uy '6
)tre =(8t'6
=0
(E'L'thotre
((8)serta+(t'et)xutn(s)iarta
mune
xmuna
mum
mane
XNWAt
muse
mina
mune
mune
mum
((6)14Ti+(t'6'i)x2iu)(6t)mrtv
'ot)uv =(6
(E'6'i)x2u
=(ot'othav (ot)Nrie'11)W =(L
(L)NYIEE
=(tt'tauv (tt)mrta'zt)uv =(8
(8)WY'Ig
};Nuns
=(ztlzt)uv
(zt)Prets-
mune
=(ot'Et)ukr
(ot)wvia
=(Et'et)lay ((£t)mrra+(t'Et'thon3)-
xmuna
xmuna
-(tt'Et)uv
=(st'Et)uv
=(tt'tt)uv
mune
xmuna
xmuna
xmuns
(t'tt'Dmuu
mans
(s'st'i)xiR
(tt)mrta
xmuna
xmuna
xuuna
(E'Et't)xuu
=(ttitt)uy ((6t)wv7v+(t'tt't)x2n0=(st'tt)uv
(t'st'Dmutt
=(st'tthav
(s'st't)muu
=(zt'sthra
(zt)wvia
=(tt'st)uv
(Eittat)xuu
--(st'st)lav ((st)mutv+(t'st'i)xuu)--(st'st)uv
(t'st'I)xuu
=(Lt'st)2rt
x)xuu Li (s
=(st'st)uv
(E'st'Dxuu
=(st'st)uv ((sworta+(st)mwm+(t'st't)muu)=(at'sthav
(''Lt'I)xN
=(st'Lt)ukr
(E'st't)xuu
=(Lt'Lt)uv ((Lt)Hviv+(t'Lt't)muu)=(st'st)uv
(9t)koria
=(st'Est)uv ((8t)katv+(t'8t'i)xuu)oa oz =)IOSIN't
oz 16t)2lv =(m
()I)a3a.4(z')I'i)x2Ri
oa oE ostu't=m
oE 'oz)uv =(I
onta.*(z')I'i)xuu
=(EtItt)uir
'
=(oz'oz)uit
xmuna
xauna
'
lozpreia-
oa OP ostm't=m
ot 'tz)lra =(I
Mau
(z')I' mu.* (In
=(ozitz)utr
(oz)Wna
=(tz'tz)utr ((Iz)mrta+(t'tz't)xuu)oa os ostret=m
mina
xuuna
xmuna
ina X
mane
mum(
mune(
um' X
mune
mum
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mune
xmuna
mune
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mans
mune
xmuna
xmuna
xuuna
xmuna
xmuna
mum
xxung
mune
102
50 AR(22, K)=
AR(22,22)=
AR(23,22)=
AR(23,23)=
AR(24,24)=
AR(25,25)=
END
RRX(I,K,2) *YPM(K)
-BLAM(22)
BLAM(22)
-RRX(I,23,1)
-RRX(I,24,1)
-RRX(I,25,1)
SUBROUTINE SOLVER (IC , A, XATOM, DELT)
C
C
SOLVES THE COUPLED DIFFERENTIAL EQUATIONS FOR Xij.
INCLUDE 'GENERAL.CMN'
PARAMETER(H=30,N=NISO)
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LEAF
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C
C
C
C
SOLVER EVALUATES D(A) & I+A*D(A)
DIMENSION A(N,N),B(N,N),C(N,N),D(N,N),E(N,N),F(N,N),X1(N),X2(N),
1 XATOM(MAXE,N)
SUM*0.0D0
DO 20 J=1,N
C
DO 20 JJ=1,N
20 SUM=SUM+A(J,JJ)*A(J,JJ)
IF(DELT.EQ.0)GOTO 30
P=(DLOG(SUM)+2.0D0*DLOG(DELT))/(2.0DO*DLOG(2.0D0))
IF(P)30,30,40
30 NP=1
GO TO 50
40 NP=P+1.0D0
50 T=DELT/(2.0D0**NP)
CALL SCALAR(A,T,C,N)
DO 70 J =1,N
DO 60 JJ=1,N
60 B(J,JJ) =0.0D0
70 B(J,J ) =1.0D0
CALCULATE D(H)
C
80
90
100
120
C
C
DO 90 J=1,M
FM=1.0D0/(M+2.0DO-J)
CALL SCALAR(B,FM,D,N)
CALL MULTI(C,D,E,N)
DO 80 JJ=1,N
E(JJ,JJ)=E(JJ,JJ)+1.0D0
CALL EQUAL(E,B,N)
S=1.0D0
DO 120 J=1,NP
Q=S/2.0D0
S=S*2.0D0
CALL SCALAR(C,Q,F,N)
CALL MULTI(F,B,E,N)
DO 100 JJ=1,N
E(JJ,JJ)=E(JJ,JJ)+1.0D0
CALL MULTI(B,E,F,N)
CALL EQUAL(F,B,N)
B=D (A)
CALL SCALAR(A,DELT,F,N)
CALL MULTI(F,B,E,N)
DO 130 JJ=1,N
130 E(JJ,JJ)=E(JJ,JJ)+1.0D0
C
C
E=I+A*D (A)
NOW DETERMINE THE INVENTORIES X2
C
DO 140 J=1,N
140 X1(J)=XATOM(IC,J)
CALL MVMUL(E,X1,X2,N)
DO 150 J=1,N
150 XATOM(IC,J)=X2(J)
END
SUBROUTINE SCALAR(A,S,B,N)
C
SCALAR MULTIPLIES A SCALAR TIMES A MATRIX IN DOUBLE
C
C
IMPLICIT DOUBLE PRECISION(A-H2O-Z)
DIMENSION A(N,N) ,B(N,N)
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LEAF
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C
DO 10 I=1,N
DO 10 J=1,N
10 B(I,J)=StA(I,J)
LEAF
LEAF
LEAF
103
C
C
C
END
SUBROUTINE MULTI(A,B,C,N)
MULTI MULTIPLIES TWO MATRICES IN DOUBLE
LEAF
LEAF
LEAF
LEAF
IMPLICIT DOUBLE PRECISION(A-H2O-Z)
DIMENSION A(N,N),B(N,N),C(N,N)
LEAF
LEAF
C
C
C
C
DO 20 I=1,N
DO 20 J=1,N
AM=0.0
DO 10 K=1,N
10 AM=AM+A(I,K)*B(K,J)
20 C(I,J)=AM
END
SUBROUTINE EQUAL(A,B,N)
EQUAL SETS A MATRIX EQUAL TO A MATRIX IN DOUBLE
IMPLICIT DOUBLE PRECISION(A-H2O-Z)
DIMENSION A(4,N),B(N,N)
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
C
C
C
DO 10 J=1,N
DO 10 K=1,N
10 B(J,K)=A(J,K)
END
SUBROUTINE MVMUL(A,B,C,N)
MVMUL DOES PRODUCT OF MATRIX AND VECTOR
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
C
IMPLICIT DOUBLE PRECISION(A-H2O-Z)
DIMENSION A(N,N),B(N),C(N)
LEAF
LEAF
C
C
C
C
C
C
C
C
C
C
DO 20 I=1,N
AM=0.0
DO 10 J=1,N
10 AM=AM+A(I,J)*B(J)
20 C(I)=AM
END
SUBROUTINE BXSCALE
SCALE TALLIES AND REACTIONS TO POWER USING PNORM
LEAF
LEAF
LEAF
LEAF
LEAF
LEAF
BURNX
BURNX
INCLUDE 'GENERAL.CMN'
INCLUDE 'STATIC.CMN'
DATA PCONV,SEC,BARN /6.24146E +12,86400,1.OD -024/
BURNX
GET THE REACTION RATE COMPONENTS
CALL BXRR
COMPUTE DELT, STEP WIDTH IN SECONDS.
DELT=DELTA(ISTEP)*SEC
HEATING TALLY IS USED TO COMPUTE THE POWER
PD=POWERT(ISTEP)/CTV
PSUM=0.
DO 10 I=1,NCELL
IF(CQ(I).EQ.0.)CQ(I)=180.88
FRATE(I)=POWERT(ISTEP)*PCONV/CO(I)
CMASS=CVOL(I)*CDEN(I)
10 PSUM=PSUM+(F7(I)*CMASS*CNU(I)/CQ(I))
PNORM=1./PSUM
C
DO 20 I=1,NCELL
C
C
NORMALIZE POWER.
CMASS=CVOL(I)*CDEN(I)
POWER(I)=F7(I)*CMASS*FRATE(I)*CNU(I)*PNORM/PCONV
C
C
C
C
C
TSF(/)=FRATE(I)*CNU(I)*PNORM
COMPUTE AND SCALE FLUXES
FLUX(I)=FLUX(I)*TSF(I)
TFLX(I)=TFLX(I)*TSF(I)
FFLX(I)=FFLX(I)*TSF(I)
SCALE REACTION RATE COMPONENTS.
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104
RSF=TSF(I)*BARN
DO 20 J=1,NISO
DO 20 K=1,NRRX
20 RRX(I,J,K)=RRX(I,J,K)*RSF
END
SUBROUTINE BXM(LL)
INCLUDE
INCLUDE
INCLUDE
INCLUDE
'GENERAL.CMN'
'STATIC.CMN'
'DYNAMIC.CMN'
'IBLDATA.CMN'
GOTO(101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,
1 116,117,118,119,120)LL
101 HLIN=q42233 92233
1'
RETURN
102 HLIN='M2234 92234
1'
RETURN
103 HLIN='N2235 92235
1'
RETURN
104 HLIN= 'M2236 92236
1'
RETURN
105 HLIN='M2237 92237
1'
RETURN
106 HLIN='M2238 92238
1'
RETURN
107 HLIN='M2239 92239
1'
RETURN
108 HLIN ='M2240
109
110
111
112
113
114
115
116
117
RETURN
HLIN='M3237
RETURN
HLIN='M4238
RETURN
HLIN='M4239
RETURN
HLIN='M4240
RETURN
HLIN='M4241
RETURN
HLIN='M4242
RETURN
HLIN='M5241
RETURN
HLIN='M0999
RETURN
HLIN='M4135
RETURN
92240
1'
93237
1'
94238
1'
94239
1'
94240
1'
94241
1'
94242
1'
95241
1'
50999
1'
54135
1'
118 HLIN= 'M2149
62149
1'
RETURN
119 HLIN='M8016
8016
1'
RETURN
120 HLIN='M6400
64000
1'
RETURN
END
SUBROUTINE BXF1(NFGN,NSH)
INCLUDE
INCLUDE
INCLUDE
INCLUDE
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
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BURNX
BURNX
BURNX
BURNX
BURNX
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'GENERAL.CMN'
'STATIC.CMN'
'DYNAMIC.CMN'
'IBLDATA.CMN'
IF(NFGN.EQ.1)THEN
IF(NSH.EQ.1)BXLIN(1:5)='F14:N'
IF(NSH.EQ.2)BXLIN(1:5)='F24:N'
BXLIN(6:80)=BLIN(1)(6:80)
HLIN=BXLIN
ELSE
HLIN=BLIN(NFGN)
ENDIF
RETURN
END
SUBROUTINE BXF2(MM)
INCLUDE
INCLUDE
INCLUDE
INCLUDE
BURNX
BURNX
BURNX
BURNX
BURNX
BURNX
'GENERAL.CMN'
'STATIC.CHN'
'DYNAMIC.CMN'
'IBLDATA.CMN'
BURNX
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BURNX
BURNX
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mans
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MOM
mans
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MEM
:
:
KIIIILZ8
mans
mune
Xlitifla
XM21119
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NUMMI
6IZ
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1) Z4Z4
(ZOI)
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mane
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mitina
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mins
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106
B.
Benchmark
As a mean of benchmarking MCNPBURN, a model must be designed to fit other
codes in which a comparison can be made. The objective is to compare the closely
related spatial and energy dependent transport based WIMS code to MCNPBURN. These
codes were tested to compare their results for a simple PWR pin model. The simple
Pressurized Water Reactor fuel pin chosen for the comparison.
The results indicate
some but relatively small variations which can be attributed to the statistical error of the
MCNP and or the different approximations or method employed in the transport
calculation.
However, a conclusion that may be drawn is that MCNPBURN appear to
compares fairly well to WIMS.
1.
Unit Cell Output
MOW
/BURNUP/ VERSION 3E3
123456789-
1011121314151617181920212223242526272829303132-
09/02/93
16:00:08.16
PWR SAMPLE INPUT FOR MOM- 3 W/O WESTINGHOUSE / LATTICE UNIT CELL MODEL /
10
1 6.957990E-02 -1
8 -9 IMP:N=1
20
0
1 -2
8 -9 IMP:N=1
30
2 4.195717E-02 2 -3
8 -9 IMP:N=1
40
3 9.996049E-02 3 4 -5 6 -7 8 -9 IMP:N=1 VOL=0.869022222822
50
0
-4:5:-6:7:-8:9 IMP:N=0
$ 0/S WORLD
1
2
3
*4
*5
*6
*7
*8
*9
Ma
CY 0.4095
CY 0.411444458
CY 0.47
PX -0.6251
PX 0.6251
PZ -0.6251
$
$
$
$
$
UO2 FUEL RADIUS
GAP
ZR CLAD RADIUS
H2O MODERATOR IN A SQUARE CELL WITH A
PITCH=1.2502
PZ
0.6251
PY -0.5
PY 0.5
92233
92234
92235
92236
92237
92238
92239
92240
93237
$ NON
$ NON
$ NON
94238
94239
94240
$ AND UNIT LENGTH
1.000000D-300
1.000000D-300
7.044083D-004
1.000000D-300
1.000000D-300
2.248889D-002
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
1.000000D-300
$
$
$
$
$
$
$
$
$
$
$
$
$
$
$
U-233
U-234
U-235
U-236
U-237
U-238
U-239
U-240
NP237
NP238
NP239
NP240
PU238
PU239
PU240
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
ISOTOPE
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
NO.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
107
333435363738394041424344454647484950515253545556575859-
94241
94242
95241
50999
$ NON
54135
$ NON
62149
8016
64000
40000
1001
M2
M3
F7:N
F4:N
KCODE
KSRC
MAT
10
20
30
40
50
1
0
1
2
3
4
5
0
1.563
1
6
23
30
60
90
155
365
1
156.3
156.3
156.3
156.3
156.3
156.3
156.3
156.3
156.3
ATOM
DENSITY
GRAM
DENSITY
1.03969E+01
0.00000E+00
6.35579E+00
9.96558E-01
0.00000E+00
TOTAL
NUMBER OF BURNUP STEPS
CORE TOTAL VOLUME (CC)
CORE FUEL REGION FRACTION
CORE TOTAL MTIHM
AVERAGE CORE LOADING (G/CC)
LATTICE
VOLUME
CC
1.5630E+00
10
MCNP
CELL
10
5.26814E-01
5.01490E-03
1.62148E-01
8.69022E-01
0.00000E+00
5.47722E+00
0.00000E+00
1.03058E+00
8.66031E-01
0.00000E+00
1.56300E+00
7.37384E+00
9
G /CC
3.0890E+00
1 STARTS AT
ENDS AT
IRRADIATION
MWD /TE
10
MASS
1.56300E+00
3.37053E-01
4.82814E-06
3.08902E+00
LOADING
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
VOLUME
MASS
GRAM
4.8281E+00
/BURNUP/ VERSION 3B3
BURNUP STEP
3.2373E+01
THERMAL FLUX
w/cm/cm/s
3.5799E+13
09/02/93
0.000
1.00
ESTIMATOR
1.5630E+02 WATTS.
1.0000E+02 KW /LITER
7.2530E-01
Q-FISSION
HIV/FISSION
1.8090E+02
NU-FISSION
N/FISSION
2.4393E+00
FAST FLUX
N/CM/CM/S
1.8019E+14
TOTAL FLUX
N/CM/CM/S,
2.1599E+14
CYCLE
250
1.429408
1.385817
1.438960
16:00:08.16
DAYS
DAYS
CRITICALITY:
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
H2O.
50 1.383 5 100
0 2R
6.95799E-02
0.00000E+00
4.19572E-02
9.99605E-02
0.00000E+00
2
3
16
17
18
19
20
21
22
23
24
25
10
(10 20 30 40)
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
CELL
1.000000D-300
$ PU241 ISOTOPE NO.
$ PU242 ISOTOPE NO.
1.000000D-300
1.000000D-300
$ AM241 ISOTOPE NO.
ISOTOPE NO.
$ F.P
1.000000D-300
1.000000D-300
$ I-135 ISOTOPE NO.
1.000000D-300
$ XE135 ISOTOPE NO.
$ PM149 ISOTOPE NO.
1.000000D-300
1.000000D-300
$ SM149 ISOTOPE NO.
4.638660D-002
$ OXYG ISOTOPE NO.
1.000000D-300
$ GdNAT ISOTOPE NO.
4.195717E-02
$ CLAD, Zr.
6.664032E-02 8016 3.332016E-02 $ MODERATOR,
AVE OF
245
1.377528
1.373055
1.378747
CYCLES
0.0013
0.0009
0.0017
FISION RATE
FISSION /S
5.3927E+12
SP. POWER
MW/TE
3.2373E+01
POWER
WATTS
1.5630E+02
108
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
SIMPLE AVERAGE
1.375292 0.0008
1.375901 0.0010
1.378138 0.0013
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
CORR
0.1727
0.1077
0.6408
10
CURRENT
LOAD(GM)
0.0000E+00
0.0000E+00
1.4484E-01
0.0000E+00
0.0000E+00
4.6833E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
6.4909E-01
0.0000E+00
5.4772E+00
ATOM DENS.
(atom/b.cm)
1
COMBINED AVERAGE
1.374352 0.0008
1.374064 0.0008
1.377668 0.0012
0.000000E+00
0.000000E+00
7.044083E-04
0.000000E+00
0.000000E+00
2.248889E-02
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
4.638660E-02
0.000000E+00
6.957990E-02
BURNUP CONVERSION FACTOR
WEIGHT %
IHM
0.0000E+00
0.0000E+00
2.9999E+00
0.0000E+00
0.0000E+00
9.7000E+01
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
1.0000E+02
% CHANGE
FROM IBM
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000 %
1TALLY FLUCTUATION CHARTS
NPS
16000
32000
48000
64000
80000
96000
112000
128000
144000
160000
176000
192000
208000
224000
240000
250207
NPS
16000
32000
48000
64000
80000
96000
112000
128000
144000
160000
176000
192000
208000
224000
240000
TALLY
4
MEAN
2.25973E+01
2.26272E+01
2.26188E+01
2.26132E+01
2.26321E+01
2.26345E+01
2.26271E+01
2.26222E+01
2.26273E+01
2.26313E+01
2.26429E+01
2.26452E+01
2.26495E+01
2.26471E+01
2.26467E+01
2.26383E+01
TALLY 24
MEAN
1.55035E+01
1.55345E+01
1.54627E+01
1.54336E+01
1.54231E+01
1.54380E+01
1.54246E+01
1.54047E+01
1.54183E+01
1.54131E+01
1.54268E+01
1.54279E+01
1.54333E+01
1.54320E+01
1.54213E+01
ERROR
0.0039
0.0025
0.0020
0.0017
0.0015
0.0013
0.0012
0.0011
0.0011
0.0010
0.0010
0.0009
0.0009
0.0009
0.0008
0.0008
ERROR
0.0086
0.0056
0.0044
0.0038
0.0033
0.0030
0.0028
0.0026
0.0025
0.0023
0.0022
0.0021
0.0020
0.0020
0.0019
FOM
902
912
932
939
936
940
941
941
950
948
946
943
948
947
941
938
FOM
187
182
181
181
182
182
182
182
182
182
182
181
181
181
181
7
TALLY
MEAN
1.87694E+01
1.88068E+01
1.87200E+01
1.86847E+01
1.86721E+01
1.86901E+01
1.86739E+01
1.86498E+01
1.86663E+01
1.86599E+01
1.86766E+01
1.86779E+01
1.86844E+01
1.86828E+01
1.86699E+01
1.86680E+01
ERROR
TOM
0.0086
0.0056
0.0044
0.0038
0.0033
0.0030
0.0028
0.0026
0.0025
0.0023
0.0022
0.0021
0.0020
0.0020
0.0019
0.0019
187
182
181
181
182
182
182
182
182
182
182
181
182
181
181
181
109
250207
MCNP
1.54198E+01 0.0019
181
/BURNUP/ VERSION 383
BURNUP STEP
2 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
10
CELL
IRRADIATION
MWD/TE
2.2661E+02
THERMAL FLUX
N/CM/CM/S
3.6020E+13
10
09/03/93
19:10:15.09
DAYS
DAYS
1.00
7.00
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.3809E-01
Q-FISSION
MeV/FISSION
1.8090E+02
NU-FISSION
N/FISSION
2.4400E+00
FAST FLUX
TOTAL FLUX
N/CM/CM/S,
2.2286E+14
N /CM /CM /S
1.8684E+14
FISION RATE
FISSION/S
5.3926E+12
POWER
WATTS
1.5630E+02
SP. POWER
MW /TE
3.2373E+01
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.345126
1.323257
1.321062
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
SIMPLE AVERAGE
1.330748 0.0009
1.328865 0.0011
1.329357 0.0015
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
CYCLES
0.0014
0.0009
0.0018
COMBINED AVERAGE
1.330528 0.0008
1.329764 0.0009
1.330645 0.0014
CORR
0.1200
0.1384
0.6872
10
ATOM DENS.
(atom/b.cm)
1
AVE OF
245
1.331240
1.330256
1.327473
4.920386E-14
3.776018E-11
7.033935E-04
1.727513E-07
2.515695E-09
2.248844E-02
9.534184E-09
4.235877E-13
1.308345E-10
2.750160E-14
3.437440E-07
2.987716E-14
2.687772E-15
5.162487E-08
1.966542E-11
2.163249E-14
4.381166E-18
5.427126E-19
1.120599E-06
2.005837E-08
6.947735E-09
8.430574E-09
1.296717E-09
4.638660E-02
0.000000E+00
6.958017E-02
BURNUP CONVERSION FACTOR
CURRENT
LOAD(GM)
1.0031E-11
7.7311E-09
1.4463E-01
3.5672E-05
5.2185E-07
4.6832E+00
1.9945E-06
8.8983E-11
2.7131E-08
5.7272E-12
7.1885E-05
6.2742E-12
5.5972E-13
1.0796E-05
4.1298E-09
4.5633E-12
9.2774E-16
1.1445E-16
1.1470E-04
2.3684E-06
8.1996E-07
1.0983E-06
1.6893E-07
6.4909E-01
0.0000E+00
5.4772E+00
WEIGHT %
IHM
2.0776E-10
1.6013E-07
2.9956E+00
7.3884E-04
1.0808E-05
9.6998E+01
4.1310E-05
1.8430E-09
5.6194E-07
1.1862E-10
1.4889E-03
1.2995E-10
1.1593E-11
2.2361E-04
8.5536E-08
9.4514E-11
1.9215E-14
2.3704E-15
2.3756E-03
4.9053E-05
1.6983E-05
2.2748E-05
3.4988E-06
0.0000E+00
0.0000E+00
9.9999E+01
% CHANGE
FROM IHM
2.1215E-10
1.6281E-07
-4.3755E-03
7.4483E-04
1.0847E-05
-1.9260E-03
4.1107E-05
1.8263E-09
5.6410E-07
1.1858E-10
1.4821E-03
1.2882E-10
1.1589E-11
2.2259E-04
8.4789E-08
9.3270E-11
1.8890E-14
2.3400E-15
4.8316E-03
8.6483E-05
2.9956E-05
3.6349E-05
5.5909E-06
-1.0808E-05
0.0000E+00
1.1798E-03
0.0073 %
1TALLY FLUCTUATION CHARTS
NPS
32000
64000
TALLY
4
MEAN
ERROR
2.26272E+01 0.0025
2.26132E+01 0.0017
FOM
912
939
7
TALLY
ERROR
MEAN
1.88068E+01 0.0056
1.86847E+01 0.0038
FOM
182
181
110
96000
128000
160000
192000
224000
16000
48000
80000
96000
128000
160000
192000
224000
250808
NPS
32000
64000
96000
128000
160000
192000
224000
16000
48000
80000
96000
128000
160000
192000
224000
250808
MCNP
2.26345E+01
2.26222E+01
2.26313E+01
2.26452E+01
2.26471E+01
3.28379E+01
2.51658E+01
2.39951E+01
2.37344E+01
2.34212E+01
2.32249E+01
2.31022E+01
2.30094E+01
2.29475E+01
0.0013
940
0.0011
941
0.0010
948
0.0009
943
0.0009
947
0.0000 3.9E+07
0.0009
4134
0.0011
1766
0.0010
1532
0.0010
1329
0.0009
1236
0.0008
1176
0.0008
1146
0.0007
1120
TALLY 24
MEAN
1.55345E+01
1.54336E+01
1.54380E+01
1.54047E+01
1.54131E+01
1.54279E+01
1.54320E+01
2.17393E+01
1.66489E+01
1.58690E+01
1.56788E+01
1.54680E+01
1.53362E+01
1.52620E+01
1.51918E+01
1.51481E+01
ERROR
0.0056
0.0038
0.0030
0.0026
0.0023
0.0021
0.0020
0.0048
0.0039
0.0031
0.0029
0.0025
0.0022
0.0021
0.0019
0.0018
3 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
IRRADIATION
10
CELL
10
9.7118E+02
THERMAL FLUX
N/CM/CM/S
3.6223E+13
239
212
206
200
197
195
193
193
22:17:09.39
DAYS
DAYS
Q-FISSION
1.8094E+02
FAST FLUX
N /CM /CM /S
1.8759E+14
FISION RATE
NU-FISSION
N/FISSION
2.4417E+00
TOTAL FLUX
N/CM/CM/S,
2.2382E+14
FISSION /S
5.3916E+12
POWER
WATTS
1.5630E+02
SP. POWER
MW/TE
3.2373E+01
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.330791
1.336964
1.342173
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
1
2
3
92233
92234
92235
AVE OF
245
1.321199
1.317682
1.322960
SIMPLE AVERAGE
1.319441 0.0009
1.320321 0.0011
1.322080 0.0015
CYCLES
0.0013
0.0009
0.0019
COMBINED AVERAGE
1.318810 0.0008
1.318634 0.0009
1.321260 0.0013
CORR
0.1293
0.0786
0.6659
10
ATOM DENS.
(atom /b. cm)
2.507288E-13
2.695554E-10
6.973293E-04
197
195
193
193
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.4060E-01
mev/ETssim
MWD /TE
239
212
206
200
182
181
182
182
182
181
181
608
09/04/93
7.00
30.0
182
182
182
181
181
609
FOM
/BURNUP/ VERSION 3B3
BURNUP STEP
0.0030
0.0026
0.0023
0.0021
0.0020
0.0048
0.0039
0.0031
0.0029
0.0025
0.0022
0.0021
0.0019
0.0018
1.86901E+01
1.86498E+01
1.86599E+01
1.86779E+01
1.86828E+01
2.63190E+01
2.01562E+01
1.92121E+01
1.89817E+01
1.87266E+01
1.85670E+01
1.84772E+01
1.83922E+01
1.83393E+01
CURRENT
LOAD(GM)
5.1115E-11
5.5189E-08
1.4338E-01
WEIGHT %
IHM
1.0587E-09
1.1431E-06
2.9698E+00
% CHANGE
FROM IHM
1.0810E-09
1.1622E-06
-3.0522E-02
111
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
1.209670E-06
1.471714E-08
2.248569E-02
9.793267E-09
6.452669E-13
5.690352E-09
5.775563E-12
1.231995E-06
4.723556E-14
3.812542E-12
1.644189E-06
4.967950E-09
4.381575E-11
6.635616E-14
8.161227E-15
7.835539E-06
2.182378E-08
7.864248E-09
2.814668E-08
2.825827E-08
4.638658E-02
0.000000E+00
6.958164E-02
2.4979E-04
3.0529E-06
4.6826E+00
2.0487E-06
1.3555E-10
1.1800E-06
1.2027E-09
2.5764E-04
9.9195E-12
7.9395E-10
3.4384E-04
1.0433E-06
9.2427E-09
1.4051E-11
1.7210E-12
8.0199E-04
2.5768E-06
9.2812E-07
3.6668E-06
3.6813E-06
6.4908E-01
0.0000E+00
5.4768E+00
BURNUP CONVERSION FACTOR
5.1736E-03
6.3231E-05
9.6986E+01
4.2432E-05
2.8075E-09
2.4440E-05
2.4911E-08
5.3362E-03
2.0545E-10
1.6444E-08
7.1216E-03
2.1608E-05
1.9143E-07
2.9103E-10
3.5646E-11
1.6611E-02
5.3371E-05
1.9223E-05
7.5946E-05
7.6247E-05
0.0000E+00
0.0000E+00
9.9991E+01
5.2156E-03
6.3454E-05
-1.3801E-02
4.2225E-05
2.7821E-09
2.4534E-05
2.4902E-08
5.3119E-03
2.0366E-10
1.6438E-08
7.0891E-03
2.1420E-05
1.8892E-07
2.8610E-10
3.5188E-11
3.3784E-02
9.4095E-05
3.3907E-05
1.2136E-04
1.2184E-04
-7.8325E-05
0.0000E+00
7.5236E-03
0.2358 %
1TALLY FLUCTUATION CHARTS
NPS
64000
128000
192000
16000
80000
128000
192000
32000
96000
160000
192000
250168
TALLY
4
MEAN
2.26132E+01
2.26222E+01
2.26452E+01
3.28379E+01
2.39951E+01
2.34212E+01
2.31022E+01
2.66758E+01
2.37629E+01
2.32352E+01
2.31075E+01
2.29559E+01
0.0017
939
0.0011
941
0.0009
943
0.0000 3.9E+07
0.0011
1766
0.0010
1329
0.0008
1176
0.0000 5.1E+10
0.0011
1438
0.0009
1188
0.0008
1146
0.0008
1095
NPS
64000
128000
192000
16000
80000
128000
192000
32000
96000
160000
192000
250168
TALLY 24
MEAN
1.54336E+01
1.54047E+01
1.54279E+01
2.17393E+01
1.58690E+01
1.54680E+01
1.52620E+01
1.75040E+01
1.56169E+01
1.52769E+01
1.51679E+01
1.50860E+01
ERROR
0.0038
0.0026
0.0021
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0018
MCNP
4 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
IRRADIATION
MWD /TE
10
FOM
1.9424E+03
7
TALLY
MEAN
1.86847E+01
1.86498E+01
1.86779E+01
2.63190E+01
1.92121E+01
1.87266E+01
1.84772E+01
2.11956E+01
1.89105E+01
1.84988E+01
1.83668E+01
1.82677E+01
ERROR
FOM
0.0038
0.0026
0.0021
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0018
181
182
181
609
212
200
195
273
205
DAYS
DAYS
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.4656E-01
Q-FISSION
MeV/FISSION
1.8113E+02
194
192
181
182
181
608
212
200
195
272
205
196
194
192
09/06/93
30.0
60.0
196
FOM
/BURNUP/ VERSION 383
BURNUP STEP
CELL
ERROR
NU-FISSION
N/FISSION
2.4526E+00
FISION RATE
FISSION/S
5.3857E+12
01:21:03.48
112
CELL
THERMAL FLUX
N/CM/CM/S
3.6295E+13
10
FAST FLUX
N/CM/CM/S
1.8987E+14
TOTAL FLUX
N/CM/CM/S,
2.2617E+14
POWER
WATTS
1.5630E+02
SP. POWER
MW/TE
3.2373E+01
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.310244
1.328749
1.300898
COMBINATION
K(COL/ABS)
SIMPLE AVERAGE
1.311642 0.0009
1.311906 0.0010
1.312452 0.0015
K(ABS /TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
CYCLES
0.0014
0.0010
0.0018
COMBINED AVERAGE
1.311439 0.0008
1.311449 0.0009
1.312259 0.0014
CORR
0.1162
0.0402
0.6627
10
ATOM DENS.
(atom/b.cm)
1
AVE OF
245
1.312188
1.311096
1.312716
1.097636E-12
1.122146E-09
6.744661E-04
5.097475E-06
3.838975E-08
2.247512E-02
9.811915E-09
6.501772E-13
7.145527E-08
1.279701E-10
1.418568E-06
4.759610E-14
4.263300E-10
1.056551E-05
1.593097E-07
6.710029E-09
4.816940E-11
5.851201E-12
3.357701E-05
2.179046E-08
7.841942E-09
3.197796E-08
6.616429E-08
4.638652E-02
0.000000E+00
6.958718E-02
BURNUP CONVERSION FACTOR
CURRENT
LOAD(GM)
2.2377E-10
2.2975E-07
1.3868E-01
1.0526E-03
7.9635E-06
4.6804E+00
2.0526E-06
1.3658E-10
1.4818E-05
2.6650E-08
2.9666E-04
9.9952E-12
8.8782E-08
2.2095E-03
3.3455E-05
1.4154E-06
1.0200E-08
1.2339E-09
3.4367E-03
2.5729E-06
9.2549E-07
4.1659E-06
8.6195E-06
6.4908E-01
0.0000E+00
5.4753E+00
WEIGHT %
IHM
4.6348E-09
4.7585E-06
2.8724E+00
2.1801E-02
1.6494E-04
9.6941E+01
4.2513E-05
2.8289E-09
3.0691E-04
5.5196E-07
6.1443E-03
2.0702E-10
1.8389E-06
4.5763E-02
6.9292E-04
2.9317E-05
2.1126E-07
2.5556E-08
7.1181E-02
5.3289E-05
1.9169E-05
8.6284E-05
1.7853E-04
0.0000E+00
0.0000E+00
9.9960E+01
% CHANGE
FROM IHM
4.7326E-09
4.8382E-06
-1.2910E-01
2.1978E-02
1.6552E-04
-5.9389E-02
4.2305E-05
2.8033E-09
3.0809E-04
5.5175E-07
6.1163E-03
2.0521E-10
1.8382E-06
4.5554E-02
6.8688E-04
2.8931E-05
2.0769E-07
2.5228E-08
1.4477E-01
9.3952E-05
3.3811E-05
1.3788E-04
2.8527E-04
-3.3546E-04
0.0000E+00
3.1386E-02
1.5675 %
1TALLY FLUCTUATION CHARTS
96000
160000
192000
64000
128000
192000
250073
TALLY
4
MEAN
2.26132E+01
2.26222E+01
2.26452E+01
3.28379E+01
2.39951E+01
2.34212E+01
2.31022E+01
2.66758E+01
2.37629E+01
2.32352E+01
2.31075E+01
2.43730E+01
2.34102E+01
2.30754E+01
2.29344E+01
NPS
64000
128000
192000
TALLY 24
ERROR
MEAN
1.54336E+01 0.0038
1.54047E+01 0.0026
1.54279E+01 0.0021
NPS
64000
128000
192000
16000
80000
128000
192000
32000
ERROR
FOM
0.0017
939
0.0011
941
0.0009
943
0.0000 3.9E+07
0.0011
1766
0.0010
1329
0.0008
1176
0.0000 5.1E+10
0.0011
1438
0.0009
1188
0.0008
1146
0.0011
2092
0.0010
1326
0.0008
1165
0.0008
1096
FOM
181
182
181
7
TALLY
MEAN
1.86847E+01
1.86498E+01
1.86779E+01
2.63190E+01
1.92121E+01
1.87266E+01
1.84772E+01
2.11956E+01
1.89105E+01
1.84988E+01
1.83668E+01
1.91798E+01
1.83871E+01
1.81576E+01
1.80612E+01
ERROR
FOM
0.0038
0.0026
0.0021
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0035
0.0025
0.0021
0.0018
181
182
181
609
212
200
195
273
205
196
194
219
200
194
191
113
16000
80000
128000
192000
32000
96000
160000
192000
64000
128000
192000
250073
MCNP
2.17393E+01
1.58690E+01
1.54680E+01
1.52620E+01
1.75040E+01
1.56169E+01
1.52769E+01
1.51679E+01
1.58221E+01
1.51681E+01
1.49788E+01
1.48993E+01
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0035
0.0025
0.0021
0.0018
5 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
CELL
10
09/07/93
/BURNUP/ VERSION 3B3
BURNUP STEP
10
608
212
200
195
272
205
196
194
219
200
194
191
IRRADIATION
MWD/TE
3.8847E+03
THERMAL FLUX
N/CM/CM/S
3.6486E+13
04:23:21.57
DAYS
DAYS
60.0
120.
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.5112E-01
Q-FISSION
MeV/FISSION
1.8138E+02
NU-FISSION
N/FISSION
2.4659E+00
FAST FLUX
TOTAL FLUX
N/CM/CM/S,
2.2818E+14
N /CM /CM /S
1.9170E+14
FISION RATE
FISSION/S
5.3785E+12
SP. POWER
MW/TE
3.2373E+01
POWER
WATTS
1.5630E+02
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.319920
1.297391
1.332123
COMBINATION
K(COL/ABS)
SIMPLE AVERAGE
1.303035 0.0009
1.302989 0.0010
1.304268 0.0013
K(ABS /TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
AVE OF
245
1.304314
1.301756
1.304222
CYCLES
0.0012
0.0010
0.0016
COMBINED AVERAGE
1.302696 0.0009
1.302402 0.0009
1.304297 0.0012
CORR
0.3868
0.1481
0.6051
10
ATOM DENS.
CURRENT
(atom/b.cm)
LOAD(GM)
3.9119E-10
4.5168E-07
1.3274E-01
2.0566E-03
1.2143E-05
4.6775E+00
1.918865E-12
2.206100E-09
6.455868E-04
9.959673E-06
5.853694E-08
2.246117E-02
9.911805E-09
6.616456E-13
2.188436E-07
4.304412E-10
1.433229E-06
4.843564E-14
3.021474E-09
2.153336E-05
6.587706E-07
5.804131E-08
8.758394E-10
1.050222E-10
6.719861E-05
2.176664E-08
7.831801E-09
3.221594E-08
6.820706E-08
4.638644E-02
0.000000E+00
2.0735E-06
1.3899E-10
4.5382E-05
8.9639E-08
2.9972E-04
1.0172E-11
6.2922E-07
4.5032E-03
1.3834E-04
1.2244E-05
1.8546E-07
2.2147E-08
6.8780E-03
2.5701E-06
9.2429E-07
4.1969E-06
8.8856E-06
6.4908E-01
0.0000E+00
WEIGHT %
IHM
8.1024E-09
9.3551E-06
2.7494E+00
4.2597E-02
2.5150E-04
9.6881E+01
4.2946E-05
2.8788E-09
9.3995E-04
1.8566E-06
6.2078E-03
2.1067E-10
1.3032E-05
9.3269E-02
2.8653E-03
2.5359E-04
3.8413E-06
4.5871E-07
1.4246E-01
5.3231E-05
1.9144E-05
8.6926E-05
1.8404E-04
0.0000E+00
0.0000E+00
% CHANGE
FROM IHM
8.2734E-09
9.5118E-06
-2.5361E-01
4.2942E-02
2.5239E-04
-1.1952E-01
4.2736E-05
2.8527E-09
9.4356E-04
1.8559E-06
6.1795E-03
2.0883E-10
1.3027E-05
9.2843E-02
2.8403E-03
2.5025E-04
3.7763E-06
4.5281E-07
2.8973E-01
9.3849E-05
3.3768E-05
1.3890E-04
2.9408E-04
-6.7592E-04
0.0000E+00
114
6.959447E-02
TOTAL:
5.4733E+00
BURNUP CONVERSION FACTOR
9.9919E+01
6.2801E-02
3.3445 %
1TALLY FLUCTUATION CHARTS
NPS
64000
128000
192000
16000
80000
128000
192000
32000
96000
160000
192000
64000
128000
192000
64000
128000
192000
250187
NPS
64000
128000
192000
16000
80000
128000
192000
32000
96000
160000
192000
64000
128000
192000
64000
128000
192000
250187
MCNP
TALLY
4
MEAN
2.26132E+01
2.26222E+01
2.26452E+01
3.28379E+01
2.39951E+01
2.34212E+01
2.31022E+01
2.66758E+01
2.37629E+01
2.32352E+01
2.31075E+01
2.43730E+01
2.34102E+01
2.30754E+01
2.43343E+01
2.33568E+01
2.30414E+01
2.29052E+01
0.0017
939
0.0011
941
0.0009
943
0.0000 3.9E+07
0.0011
1766
0.0010
1329
0.0008
1176
0.0000 5.1E+10
0.0011
1438
0.0009
1188
0.0008
1146
0.0011
2092
0.0010
1326
0.0008
1165
0.0011
2191
0.0010
1319
0.0008
1164
0.0008
1100
TALLY 24
MEAN
1.54336E+01
1.54047E+01
1.54279E+01
2.17393E+01
1.58690E+01
1.54680E+01
1.52620E+01
1.75040E+01
1.56169E+01
1.52769E+01
1.51679E+01
1.58221E+01
1.51681E+01
1.49788E+01
1.56536E+01
1.50224E+01
1.48393E+01
1.47288E+01
ERROR
0.0038
0.0026
0.0021
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0035
0.0025
0.0021
0.0035
0.0025
0.0021
0.0018
ERROR
6 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
IRRADIATION
MWD /TE
10
CELL
6.7983E+03
THERMAL FLUX
N /CM /CM /S
10
7
TALLY
MEAN
1.86847E+01
1.86498E+01
1.86779E+01
2.63190E+01
1.92121E+01
1.87266E+01
1.84772E+01
2.11956E+01
1.89105E+01
1.84988E+01
1.83668E+01
1.91798E+01
1.83871E+01
1.81576E+01
1.90012E+01
1.82351E+01
1.80129E+01
1.78787E+01
3.7078E+13
ESTIMATOR
181
182
181
609
212
200
195
273
205
196
194
120.
210.
219
200
194
219
198
192
190
219
200
194
219
197
192
190
09/08/93
07:27:12.97
DAYS
DAYS
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.6126E-01
Q-FISSION
MeV/FISSION
1.8182E+02
FAST FLUX
N/CM/CM/S
1.9625E+14
CYCLE
250
1.256008
1.277959
TOM
181
182
181
608
212
200
195
272
205
196
194
FISION RATE
FISSION/S
5.3653E+12
NU-FISSION
N /FISSION
2.4900E+00
TOTAL FLUX
SP. POWER
N /CM /CM /S,
MW /TE
2.3333E+14
CRITICALITY:
K(COLLISION)
K(ABSORPTION)
ERROR
0.0038
0.0026
0.0021
0.0048
0.0031
0.0025
0.0021
0.0046
0.0029
0.0023
0.0021
0.0035
0.0025
0.0021
0.0035
0.0025
0.0021
0.0018
FOM
/BURNUP/ VERSION 3B3
BURNUP STEP
CELL
FOM
AVE OF
245 CYCLES
1.288333 0.0014
1.285487 0.0010
3.2373E+01
POWER
WATTS
1.5630E+02
115
K(TRK LENGTH)
1.248110
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
1.287078 0.0017
SIMPLE AVERAGE
1.286910 0.0009
1.286282 0.0011
1.287706 0.0014
COMBINED AVERAGE
1.286440 0.0009
1.285858 0.0009
1.288127 0.0014
CORR
0.1736
0.1309
0.6808
10
ATOM DENS.
CURRENT
(atom/b.cm)
LOAD(GM)
9.2564E-10
8.7655E-07
1.2152E-01
3.9153E-03
1.9901E-05
4.6717E+00
4.540420E-12
4.281261E-09
5.909809E-04
1.896065E-05
9.593587E-08
2.243297E-02
1.002032E-08
6.744544E-13
6.816161E-07
1.410876E-09
1.448924E-06
4.937331E-14
1.968521E-08
4.062048E-05
2.408651E-06
4.217807E-07
1.348125E-08
1.570535E-09
1.342829E-04
2.155494E-08
7.726435E-09
3.236240E-08
6.791681E-08
4.638628E-02
0.000000E+00
6.960933E-02
2.0962E-06
1.4168E-10
1.4135E-04
2.9381E-07
3.0301E-04
1.0368E-11
4.0994E-06
8.4948E-03
5.0582E-04
8.8972E-05
2.8547E-06
3.3119E-07
1.3744E-02
2.5451E-06
9.1186E-07
4.2160E-06
8.8478E-06
6.4908E-01
0.0000E+00
5.4695E+00
BURNUP CONVERSION FACTOR
WEIGHT %
IHM
1.9172E-08
1.8155E-05
2.5168E+00
8.1093E-02
4.1218E-04
9.6759E+01
4.3416E-05
2.9345E-09
2.9276E-03
6.0854E-06
6.2758E-03
2.1475E-10
8.4907E-05
1.7594E-01
1.0477E-02
1.8428E-03
5.9127E-05
6.8596E-06
2.8467E-01
5.2713E-05
1.8886E-05
8.7321E-05
1.8326E-04
0.0000E+00
0.0000E+00
9.9840E+01
% CHANGE
FROM IBM
1.9576E-08
1.8459E-05
-4.8905E-01
8.1751E-02
4.1364E-04
-2.4111E-01
4.3204E-05
2.9080E-09
2.9388E-03
6.0831E-06
6.2472E-03
2.1288E-10
8.4875E-05
1.7514E-01
1.0385E-02
1.8185E-03
5.8126E-05
6.7715E-06
5.7897E-01
9.2936E-05
3.3313E-05
1.3953E-04
2.9283E-04
-1.3755E-03
0.0000E+00
1.2690E-01
6.9448 %
1TALLY FLUCTUATION CHARTS
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
192000
250141
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
192000
250141
MCNP
TALLY
4
MEAN
2.26222E+01
3.28379E+01
2.34212E+01
2.66758E+01
2.32352E+01
2.43730E+01
2.30754E+01
2.33568E+01
2.44051E+01
2.30864E+01
2.29418E+01
0.0011
941
0.0000 3.9E+07
0.0010
1329
0.0000 5.1E+10
0.0009
1188
0.0011
2092
0.0008
1165
0.0010
1319
0.0011
2144
0.0009
1139
0.0008
1085
TALLY 24
MEAN
1.54047E+01
2.17393E+01
1.54680E+01
1.75040E+01
1.52769E+01
1.58221E+01
1.49788E+01
1.50224E+01
1.52406E+01
1.44710E+01
1.43920E+01
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0018
ERROR
FOM
7 STARTS AT
210.
ERROR
FOM
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0018
182
609
200
273
196
219
194
198
215
189
186
FOM
182
608
200
272
196
219
194
197
215
188
186
/BURNUP/ VERSION 3B3
BURNUP STEP
TALLY
7
MEAN
1.86498E+01
2.63190E+01
1.87266E+01
2.11956E+01
1.84988E+01
1.91798E+01
1.81576E+01
1.82351E+01
1.85451E+01
1.76087E+01
1.75125E+01
09/09/93
DAYS
10:31:11.89
116
ENDS AT
365.
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
10
CELL
IRRADIATION
MWD/TE
1.1816E+04
THERMAL FLUX
N/CM/CM/S
3.8439E+13
10
DAYS
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
7.7783E-01
Q-FISSION
MeV/FISSION
1.8241E+02
FAST FLUX
N /CM /CM /S
2.0236E+14
FISION RATE
FISSION/S
5.3480E+12
NU-FISSION
N /FISSION
2.5223E+00
TOTAL FLUX
N/cm/cm/s,
2.4079E+14
POWER
WATTS
1.5630E+02
SP. POWER
MW/TE
3.2373E+01
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.232607
1.253409
1.247313
COMBINATION
N(coL/Ass)
SIMPLE AVERAGE
1.259243 0.0010
1.258419 0.0011
1.260849 0.0015
K(ABS /TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
50999
53135
54135
61149
62149
8016
64000
AVE OF
245
1.261673
1.256813
1.260025
CYCLES
0.0015
0.0011
0.0019
COMBINED AVERAGE
1.258330 0.0009
1.257611 0.0009
1.261415 0.0015
CORR
0.1820
-0.0045
0.6828
10
ATOM DENS.
CURRENT
(atom/b.cm)
LOAD(GM)
1.3176E-09
1.4519E-06
1.0609E-01
6.3828E-03
2.9391E-05
4.6627E+00
6.463162E-12
7.091538E-09
5.159691E-04
3.090996E-05
1.416864E-07
2.238983E-02
1.020899E-08
7.025310E-13
1.705966E-06
3.676146E-09
1.476207E-06
5.142866E-14
8.741047E-08
6.334683E-05
6.131590E-06
1.794099E-06
1.071130E-07
1.187662E-08
2.346056E-04
2.125634E-08
7.525588E-09
3.250736E-08
6.694800E-08
4.638603E-02
0.000000E+00
6.963229E-02
BURNUP CONVERSION FACTOR
2.1356E-06
1.4758E-10
3.5377E-04
7.6555E-07
3.0871E-04
1.0800E-11
1.8203E-05
1.3247E-02
1.2876E-03
3.7846E-04
2.2682E-05
2.5045E-06
2.4013E-02
2.5098E-06
8.8815E-07
4.2349E-06
8.7216E-06
6.4908E-01
0.0000E+00
5.4639E+00
WEIGHT %
IHM
2.7291E-08
3.0072E-05
2.1974E+00
1.3220E-01
6.0875E-04
9.6573E+01
4.4233E-05
3.0567E-09
7.3272E-03
1.5856E-05
6.3940E-03
2.2369E-10
3.7702E-04
2.7438E-01
2.6670E-02
7.8386E-03
4.6978E-04
5.1874E-05
4.9735E-01
5.1983E-05
1.8395E-05
8.7712E-05
1.8064E-04
0.0000E+00
0.0000E+00
9.9724E+01
% CHANGE
FROM IHM
2.7867E-08
3.0576E-05
-8.1247E-01
1.3327E-01
6.1089E-04
-4.2712E-01
4.4017E-05
3.0290E-09
7.3554E-03
1.5850E-05
6.3648E-03
2.2174E-10
3.7688E-04
2.7313E-01
2.6437E-02
7.7354E-03
4.6183E-04
5.1207E-05
1.0115E+00
9.1649E-05
3.2447E-05
1.4016E-04
2.8865E-04
-2.4608E-03
0.0000E+00
2.2590E-01
12.6250 %
1TALLY FLUCTUATION CHARTS
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
TALLY
4
MEAN
2.26222E+01
3.28379E+01
2.34212E+01
2.66758E+01
2.32352E+01
2.43730E+01
2.30754E+01
2.33568E+01
2.44051E+01
ERROR
FOM
0.0011
941
0.0000 3.9E+07
0.0010
1329
0.0000 5.1E+10
0.0009
1188
0.0011
2092
0.0008
1165
0.0010
1319
0.0011
2144
7
TALLY
MEAN
1.86498E+01
2.63190E+01
1.87266E+01
2.11956E+01
1.84988E+01
1.91798E+01
1.81576E+01
1.82351E+01
1.85451E+01
ERROR
FOM
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
182
609
200
273
196
219
194
198
215
117
192000
128000
250219
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
192000
128000
250219
MCNP
2.30864E+01 0.0009
2.34213E+01 0.0010
2.29494E+01 0.0008
TALLY 24
MEAN
1.54047E+01
2.17393E+01
1.54680E+01
1.75040E+01
1.52769E+01
1.58221E+01
1.49788E+01
1.50224E+01
1.52406E+01
1.44710E+01
1.41892E+01
1.39052E+01
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0026
0.0018
8 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
10
CELL
10
IRRADIATION
MWD/TE
2.3632E+04
THERMAL FLUX
N/CM/CM/S
4.1120E+13
219
194
197
215
188
192
185
13:42:22.37
DAYS
DAYS
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
8.0884E-01
Q-FISSION
MeV/FISSION
1.8331E+02
NU-FISSION
N/FISSION
2.5715E+00
FAST FLUX
N/CM/CM/S
2.1403E+14
TOTAL FLUX
N/CM/Cm/S,
2.5515E+14
FISION RATE
FISSION /S
5.3219E+12
POWER
WATTS
1.5630E+02
SP. POWER
MW /TE
3.2373E+01
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
CYCLE
250
1.187881
1.236128
1.202074
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
AVE OF
245
1.212630
1.213088
1.212038
SIMPLE AVERAGE
1.212859 0.0010
1.212563 0.0011
1.212334 0.0015
CYCLES
0.0014
0.0011
0.0019
COMBINED AVERAGE
1.212927 0.0009
1.212834 0.0010
1.212591 0.0014
CORR
0.1551
0.0564
0.7118
10
ATOM DENS.
CURRENT
(atom/b.cm)
LOAD(GM)
9.848143E-12
1.169666E-08
4.042282E-04
4.760917E-05
2.069452E-07
2.231293E-02
1.056292E-08
7.536326E-13
4.173748E-06
9.435300E-09
1.527389E-06
5.516954E-14
3.714027E-07
9.028748E-05
1.375449E-05
6.094046E-06
7.018171E-07
7.054006E-08
192
185
182
608
200
272
196
09/10/93
365.
730.
189
FOM
/BURNUP/ VERSION 383
BURNUP STEP
CELL
1.76087E+01 0.0021
1.73220E+01 0.0026
1.69750E+01 0.0018
1139
1271
1083
2.0077E-09
2.3948E-06
8.3117E-02
9.8311E-03
4.2928E-05
4.6467E+00
2.2097E-06
1.5832E-10
8.6552E-04
1.9649E-06
3.1941E-04
1.1586E-11
7.7344E-05
1.8881E-02
2.8885E-03
1.2855E-03
1.4861E-04
1.4875E-05
WEIGHT %
IHM
4.1584E-08
4.9601E-05
1.7215E+00
2.0362E-01
8.8912E-04
9.6241E+01
4.5767E-05
3.2790E-09
1.7927E-02
4.0696E-05
6.6157E-03
2.3996E-10
1.6019E-03
3.9107E-01
5.9826E-02
2.6625E-02
3.0781E-03
3.0810E-04
% CHANGE
FROM IHM
4.2461E-08
5.0431E-05
-1.2943E+00
2.0527E-01
8.9226E-04
-7.5869E-01
4.5543E-05
3.2494E-09
1.7995E-02
4.0681E-05
6.5855E-03
2.3787E-10
1.6013E-03
3.8928E-01
5.9304E-02
2.6275E-02
3.0259E-03
3.0414E-04
118
19
50999
20
53135
21
54135
22
61149
23
62149
24
8016
25
64000
TOTAL:
4.054745E-04
2.055586E-08
7.070735E-09
3.225780E-08
6.367465E-08
4.638558E-02
0.000000E+00
6.967316E-02
4.1501E-02
2.4271E-06
8.3447E-07
4.2024E-06
8.2952E-06
6.4907E-01
0.0000E+00
5.4547E+00
BURNUP CONVERSION FACTOR
8.5957E-01
5.0270E-05
1.7284E-05
8.7039E-05
1.7181E-04
0.0000E+00
0.0000E+00
9.9534E+01
1.7482E+00
8.8628E-05
3.0486E-05
1.3908E-04
2.7454E-04
-4.3988E-03
0.0000E+00
4.0211E-01
23.8433 %
1TALLY FLUCTUATION CHARTS
64000
192000
128000
64000
192000
128000
128000
249970
TALLY
4
MEAN
2.26222E+01
3.28379E+01
2.34212E+01
2.66758E+01
2.32352E+01
2.43730E+01
2.30754E+01
2.33568E+01
2.44051E+01
2.30864E+01
2.34213E+01
2.34961E+01
2.30503E+01
0.0011
941
0.0000 3.9E+07
0.0010
1329
0.0000 5.1E+10
0.0009
1188
0.0011
2092
0.0008
1165
0.0010
1319
0.0011
2144
0.0009
1139
0.0010
1271
0.0010
1270
0.0008
1060
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
192000
128000
128000
249970
TALLY 24
MEAN
1.54047E+01
2.17393E+01
1.54680E+01
1.75040E+01
1.52769E+01
1.58221E+01
1.49788E+01
1.50224E+01
1.52406E+01
1.44710E+01
1.41892E+01
1.33633E+01
1.31162E+01
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0026
0.0026
0.0019
NPS
128000
16000
128000
32000
160000
MCNP
9 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
IRRADIATION
MWD /TE
10
CELL
10
7
TALLY
MEAN
1.86498E+01
2.63190E+01
1.87266E+01
2.11956E+01
1.84988E+01
1.91798E+01
1.81576E+01
1.82351E+01
1.85451E+01
1.76087E+01
1.73220E+01
1.63936E+01
1.60904E+01
FOM
2.3664E+04
THERMAL FLUX
N/CM/CM/S
4.9167E+13
ESTIMATOR
219
194
198
215
189
192
187
180
194
197
215
188
192
187
180
17:28:06.72
DAYS
DAYS
1.5630E+02 WATTS.
1.0000E+02 KW/LITER
8.7870E-01
Q-FISSION
MeV/FISSION
1.8508E+02
NU-FISSION
N/FISSION
2.6704E+00
FAST FLUX
N/CM/CM/S
2.4017E+14
TOTAL FLUX
N/CM/CM/S,
2.8933E+14
CYCLE
250
1.134338
1.128284
1.151668
182
609
200
273
196
219
CRITICALITY:
K(COLLISION)
K(ABSORPTION)
K(TRK LENGTH)
FOM
182
608
200
272
196
09/11/93
730.
731.
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0026
0.0026
0.0019
FOM
/BURNUP/ VERSION 3B3
BURNUP STEP
CELL
ERROR
AVE OF
245
1.115954
1.116653
1.115542
CYCLES
0.0014
0.0013
0.0019
FISION RATE
FISSION/S
5.2709E+12
SP. POWER
MW/TE
3.2373E+01
POWER
WATTS
1.5630E+02
119
COMBINATION
K(COL/ABS)
K(ABS/TK LN)
K(TK LN/COL)
CELL:
ISOTOPE
SIMPLE AVERAGE
1.116303 0.0010
1.116098 0.0011
1.115748 0.0015
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
CORR
0.1780
-0.0659
0.6956
10
ATOM DENS.
(atom/b.cm)
1
COMBINED AVERAGE
1.116360 0.0010
1.116297 0.0010
1.115912 0.0014
1.187099E-11
2.538885E-08
2.163500E-04
7.065635E-05
3.029018E-07
2.212148E-02
1.114241E-08
8.532440E-13
1.177012E-05
2.855272E-08
1.611191E-06
6.246158E-14
2.046477E-06
1.179005E-04
2.981068E-05
1.926743E-05
5.287264E-06
4.212815E-07
7.899738E-04
1.846667E-08
5.982687E-09
3.032351E-08
5.520620E-08
4.638446E-02
0.000000E+00
6.977152E-02
BURNUP CONVERSION FACTOR
CURRENT
LOAD(GM)
2.4201E-09
5.1981E-06
4.4486E-02
1.4590E-02
6.2833E-05
4.6068E+00
2.3309E-06
1.7924E-10
2.4408E-03
5.9460E-06
3.3694E-04
1.3117E-11
4.2617E-04
2.4656E-02
6.2603E-03
4.0644E-03
1.1196E-03
8.8839E-05
8.0856E-02
2.1804E-06
7.0606E-07
3.9504E-06
7.1920E-06
6.4906E-01
0.0000E+00
5.4353E+00
WEIGHT %
IBM
5.0125E-08
1.0766E-04
9.2138E-01
3.0219E-01
1.3014E-03
9.5415E+01
4.8278E-05
3.7124E-09
5.0554E-02
1.2315E-04
6.9787E-03
2.7168E-10
8.8269E-03
5.1067E-01
1.2966E-01
8.4181E-02
2.3189E-02
1.8400E-03
1.6747E+00
4.5161E-05
1.4624E-05
8.1820E-05
1.4896E-04
0.0000E+00
0.0000E+00
9.9131E+01
% CHANGE
FROM IBM
5.1183E-08
1.0947E-04
-2.1043E+00
3.0464E-01
1.3060E-03
-1.5841E+00
4.8042E-05
3.6788E-09
5.0748E-02
1.2311E-04
6.9468E-03
2.6931E-10
8.8236E-03
5.0834E-01
1.2853E-01
8.3073E-02
2.2797E-02
1.8164E-03
3.4060E+00
7.9621E-05
2.5795E-05
1.3074E-04
2.3803E-04
-9.2344E-03
0.0000E+00
8.2617E-01
63.4010 %
1TALLY FLUCTUATION CHARTS
TALLY
64000
192000
128000
64000
192000
128000
128000
128000
250166
TALLY
4
MEAN
2.26222E+01
3.28379E+01
2.34212E+01
2.66758E+01
2.32352E+01
2.43730E+01
2.30754E+01
2.33568E+01
2.44051E+01
2.30864E+01
2.34213E+01
2.34961E+01
2.38481E+01
2.33940E+01
0.0011
941
0.0000 3.9E+07
0.0010
1329
0.0000 5.1E+10
0.0009
1188
0.0011
2092
0.0008
1165
0.0010
1319
0.0011
2144
0.0009
1139
0.0010
1271
1270
0.0010
0.0010
1202
0.0008
1036
NPS
128000
16000
128000
32000
160000
64000
192000
128000
64000
192000
128000
128000
128000
250166
TALLY 24
MEAN
1.54047E+01
2.17393E+01
1.54680E+01
1.75040E+01
1.52769E+01
1.58221E+01
1.49788E+01
1.50224E+01
1.52406E+01
1.44710E+01
1.41892E+01
1.33633E+01
1.18251E+01
1.16265E+01
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0026
0.0026
0.0026
0.0019
NPS
128000
16000
128000
32000
160000
ERROR
FOM
FOM
182
608
200
272
196
219
194
197
215
188
192
187
179
173
7
MEAN
1.86498E+01
2.63190E+01
1.87266E+01
2.11956E+01
1.84988E+01
1.91798E+01
1.81576E+01
1.82351E+01
1.85451E+01
1.76087E+01
1.73220E+01
1.63936E+01
1.46469E+01
1.44009E+01
ERROR
0.0026
0.0048
0.0025
0.0046
0.0023
0.0035
0.0021
0.0025
0.0035
0.0021
0.0026
0.0026
0.0026
0.0019
FOM
182
609
200
273
196
219
194
198
215
189
192
187
179
173
120
WIMS INPUT
2.
SIMPLE PWR TYPE PIN FOR COMPARISON (MODIFIED EXAMPLE WT70021 OF WIMSD4). 1993
CELL 6
SEQUENCE 2
NGROUP 32
NMESH 3
NREGION 3
NMAT 3 2
PREOUT
INITIATE
SUPPRESS 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 1
MATERIAL 1 -1 300 1 235.4 7.044083E-04 2238.4 2.248889E-02 $
16 4.638660E-02 3239.1 1.E-20
MATERIAL 2 -1 300 2 91 4.195717E-02
MATERIAL 3 -1 300 3 2001 6.664032E-02 16 3.332016E-02
ANNULUS 1 0.409500000 1
ANNULUS 2 0.470000000 2
ANNULUS 3 0.705349808 3
FEWGROUPS 1
2
3
4
5
7 10 13 15 17 20 23 25 27 30 33 $
35 37 40 43 45 47 50 53 55 57 60 63 65 67 68 69
MESH 1 1 1
POWERC 1 32.372
1 1
BEGINC
BEGINC
POWERC 1 32.372
6 1
BEGINC
BEGINC
POWERC 1 32.372 23 1
BEGINC
BEGINC
POWERC 1 32.372 30 1
BEGINC
BEGINC
POWERC 1 32.372
60 1
BEGINC
BEGINC
POWERC 1 32.372
90 1
BEGINC
BEGINC
POWERC 1 32.372 155 1
BEGINC
BEGINC
POWERC 1 32.372 365 1
BEGINC
BEGINC
POWERC 1 32.372 1
1
BEGINC
BEGINC
LEOPARD INPUT
3.
WPWR
SAMPLE INPUT FOR LEOPARD - SIMPLE PWR EXAMPLE (3% ENRICHMENT)
0
0
0
1
0
0
0
0
0
0
0
1
0
0 -2 0
99 1.00000000
0.00000000 0.00000000 0.00000000
3
0.00000000 0.97000000 0.00000000 0.00000000
100 0.00000000 0.00000000 1.00000000 0.00000000
777 0.00000000
0.00000000 0.00000000 0.00000000
18 -0.03000000
777 0.00000000
300.000000 300.000000 300.000000 300.000000 0.00000000 1.00000000
0.40950000 0.47000000 1.25000000 0.00000000 0.00000000 0.00000000
14.7000000 0.00000000 0.95000000 0.00000000 0.00000000 0.00000000
1.00000000 100.000000 0.00000000 0.00000000 1.00000000
1
24.0000000
2
144.000000
3
552.000000
4
720.000000
5
1440.00000
6 2160.00000
7
3720.00000
8
8760.00000
9 24.0000000
777
0.00000
0
2
121
APPENDIX II:
ATI MCNPBURN'S OUTPUTS
The MCNPBURN output listing contains reprints of the input file. Due to the length
of the document, it was found necessary to truncate major irrelevant portions.
ATI
A.
NENP
123456789-
101112131415161718192021222324252627282930313233343536373839404142434445464748495051-
525354555657585960616263646566676869707172-
/BURNUP/ VERSION 3B3
09/01/93
22:03:58.90
ati driver reactor reference startup radius=24 cm
pitch=1.3 cm
0 (-3:-4:-6:2:5) -1 I4P:N=0 IMP=6.9896795E -8 $ outside reactor Void outsi
1
2
0 (-3:-4:-6:2:5) 1 IMP:N=0 IM8 =6.9896795E-8 $ infinity Void outside react
7 -2.96 -7 8 -2 4 6 IMP:N=1 IMP=6.9896795E -8 $ top reflector Reflector
3
4
7 -2.96 7 -5 -2 3 4 6 IMP:N=1 IMP=6.9896795E-8 $ outer reflector Reflecto
5
11 -1.86 -7 9 -8 4 6 IMP:N=1 IMP-6.9896795E-8 $ top of core region Reflec
6
8 -5.6 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 $ moder
171 180 189 198 207 216 225 234 243 252 261 270 279 288 297 306
315 324 333 342 351 360 369 378 387 396 405 414 423 -9 -7 3 4 6
IMP:N=1 IMP-6.9896795E-8
7
0 -10 -9 3 4 6 IMP:N=1 IMP=1.6399443E-7 VOL=2.2218324E-1 $ void TFEI
8
1 -10.0 10 -11 -9 3 4 6 IMP:N=1 'HP=1.6399443E-7 VOL=3.3327486 $ fuel TFE
14 -18.8 11 -12 -9 3 4 6 IMP:N=1 TMP=1.4417533E-7 VOL=1.9996492 $ emitter
9
10
3 0 12 -13 -9 3 4 6 IMP:N=1 IMP=1.4400299E-7 VOL=7.6529784E-1 $ gap TFEI
11
4 -8.4286 13 -14 -9 3 4 6 /MP:N=1 TMP=1.0109033E-7 VOL=1.6787178 $ collec
12
10 -3.56 14 -15 -9 3 4 6 IMP:N=1 INW=1.0022863E-7 $ sheath TFE1
VOL=9.1342001E-1
13
$ cladding TFE1
4 -8.4286 15 -16 -9 3 4 6 IMP:N=1 IMP - 7.7565925E -8
VOL=9.6279406E-1
14
5 -0.75 16 -17 -9 3 4 6 IMP:N=1 TMP- 7.7565925E -8 VOL- 5.5545811 $ coolant
15
4 -8.4286 17 -18 -9 3 4 6 IMP:N=1 IMP=7.7565925E-8 VOL=0.1236820 $ liner
16
0 -19 -9 3 6 IMP:N=1 IMP=1.6399443E-7 v01=4.4436649E-1 $ void TFE2
1 -10.0 19 -20 -9 3 6 IMP:N=1 TM:P=1.6399443E-7 VOL=6.6654973 $ fuel TFE2
17
18
14 -18.8 20 -21 -9 3 6 IMP:N=1 IMP=1.4417533E-7 VOL=3.9992984 $ emitter T
19
3 0 21 -22 -9 3 6 IMP:N=1 V4P=1.4400299E-7 VOL=1.5305957 $ gap TET.2
4 -8.4286 22 -23 -9 3 6 IMP:N=1 IMP=1.0109033E-7 VOL=3.3574357 $ collecto
20
21
10 -3.56 23 -24 -9 3 6 IMP:N=1 IMP=1.0022863E-7 VOL=1.8268400 $ sheath TF
22
4 -8.4286 24 -25 -9 3 6 IMP:N=1 TMP- 7.7565925E -8 VOL=1.9255881 $ cladding
23
5 -0.75 25 -26 -9 3 6 IMP:N=1 IMP=7.7565925E -8 VOL=11.109162 $ coolant TF
24
4 -8.4286 26 -27 -9 3 6 IMP:N=1 IMP=7.7565925E-8 VOL=2.4736401E-1 $ liner
0 -28 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL=4.4436649E-1 $ void TFE3
25
26
1 -10.0 28 -29 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL=6.6654973 $ fuel TFE3
27
14 -18.8 29 -30 -9 3 6 IMP:N=1 IMP=1.4417533E-7 VOL=3.9992984 $ emitter T
28
3 0 30 -31 -9 3 6 IMP:N=1 IMP=1.4400299E -7 VOL=1.5305957 $ gap TFE3
29
4 -8.4286 31 -32 -9 3 6 IMP:N=1 IMP=1.0109033E-7 VOL=3.3574357 $ collecto
30
10 -3.56 32 -33 -9 3 6 IMP:N=1 IMP=1.0022863E-7 VOL=1.8268400 $ sheath IF
4 -8.4286 33 -34 -9 3 6 IMP:N=1 TMP=7.7565925E-8 VOL=1.9255881 $ cladding
31
32
5 -0.75 34 -35 -9 3 6 IMP:N=1 TMP- 7.7565925E -8 VOL=11.109162 $ coolant TF
33
4 -8.4286 35 -36 -9 3 6 IMP:N=1 TMP=7.7565925E-8 VOL=2.4736401E-1 $ liner
34
0 -37 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL=4.4436649E-1 $ void TFE4
35
1 -10.0 37 -38 -9 3 6 IMP:N=1 TMP=1.6399443E-7 VOL=6.6654973 $ fuel TFE4
36
14 -18.8 38 -39 -9 3 6 IMP:N=1 IMP=1.4417533E-7 VOL- 3.9992984 $ emitter T
37
3 0 39 -40 -9 3 6 I24P:N=1 TM:P=1.4400299E-7 VOL=1.5305957 $ gap TFE4
4 -8.4286 40 -41 -9 3 6 M4P:N=1 IMP...1.0109033E-7 VOL=3.3574357 $ collecto
38
39
10 -3.56 41 -42 -9 3 6 IMP:N=1 IMP=1.0022863E-7 VOL=1.8268400 $ sheath IF
40
4 -8.4286 42 -43 -9 3 6 IMP:N=1 IMP=7.7565925E-8 VOL=1.9255881 $ cladding
41
5 -0.75 43 -44 -9 3 6 IMP:N=1 TMP=7.7565925E-8 VOL=11.109162 $ coolant IF
42
4 -8.4286 44 -45 -9 3 6 IMP:N=1 IMP=7.7565925E-8 VOL=2.4736401E-1 $ liner
43
0 -46 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL=4.4436649E-1 $ void TFE5
44
1 -10.0 46 -47 -9 3 6 IMP:N=1 TMP=1.6399443E-7 VOL=6.6654973 $ fuel TFE5
45
14 -18.8 47 -48 -9 3 6 IMP:N=1 TMP=1.4417533E-7 VOL=3.9992984 $ emitter T
46
3 0 48 -49 -9 3 6 IMP:N=1 IMP=1.4400299E-7 VOL=1.5305957 $ gap TEES
47
4 -8.4286 49 -50 -9 3 6 IMP:N=1 TM:P=1.0109033E-7 VOL=3.3574357 $ collecto
48
10 -3.56 50 -51 -9 3 6 IMP:N=1 IMP=1.0022863E-7 VOL=1.8268400 $ sheath IF
49
4 -8.4286 51 -52 -9 3 6 IMP:N=1 TMP- 7.7565925E -8 VOL- 1.9255881 $ cladding
50
5 -0.75 52 -53 -9 3 6 IMP:N=1 THP=7.7565925E-8 VOL=11.109162 $ coolant IF
4 -8.4286 53 -54 -9 3 6 IMP:N=1 IMP=7.7565925E-8 VOL=2.4736401E-1 $ liner
51
52
0 -55 -9 3 6 II8:N=1 1'MP...1.6399443E-7 VOL=4.4436649E-1 $ void TFE6
1 -10.0 55 -56 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL...6.6654973 $ fuel TFE6
53
54
14 -18.8 56 -57 -9 3 6 IMP:N=1 TMP=1.4417533E-7 VOL...3.9992984 $ emitter T
55
3 0 57 -58 -9 3 6 IMP:N=1 IMP=1.4400299E-7 VOL=1.5305957 $ gap TFE6
56
4 -8.4286 58 -59 -9 3 6 IMP:N=1 TMP=1.0109033E-7 VOL=3.3574357 $ collecto
57
10 -3.56 59 -60 -9 3 6 IMP:N=1 TMP=1.0022863E-7 VOL=1.8268400 $ sheath IF
58
4 -8.4286 60 -61 -9 3 6 IMP:N=1 TMP- 7.7565925E -8 VOL=1.9255881 $ cladding
59
5 -0.75 61 -62 -9 3 6 IMP:N=1 IMP=7.7565925E-8 VOL=11.109162 $ coolant IF
60
4 -8.4286 62 -63 -9 3 6 IMP:N=1 INP=7.7565925E-8 VOL=2.4736401E-1 $ liner
61
0 -64 -9 3 6 IMP:N=1 IMP=1.6399443E-7 VOL=4.4436649E-1 $ void TFE7
62
1 -10.0 64 -65 -9 3 6 IMP:N=1 IMP - 1.6399443E -7 VOL=6.6654973 $ fuel TFE7
63
14 -18.8 65 -66 -9 3 6 IMP:N=1 TMP=1.4417533E-7 VOL=3.9992984 $ emitter T
64
3 0 66 -67 -9 3 6 IMP:N=1 IMp=1.4400299E-7 VOL- 1.5305957 $ gap TFE7
65
4 -8.4286 67 -68 -9 3 6 IMP:N=1 IMP-1.0109033E-7 VOL- 3.3574357 $ collecto
66
10 -3.56 68 -69 -9 3 6 IMP:N=1 IMP=1.0022863E-7 VOL=1.8268400 $ sheath IF
122
737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175-
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
4 -8.4286 69 -70 -9 3 6 IMP:N=1 TMP7.7565925E-8 VOL1.9255881 $ cladding
5 -0.75 70 -71 -9 3 6 IMP:N.1 THP7.7565925E-8 VOL11.109162 $ coolant TF
4 -8.4286 71 -72 -9 3 6 IMP:N.1 TWP7.7565925E-8 V01.2.4736401E-1 0 liner
0 -73 -9 3 I4P:N=1 TMP-1.63994431E-7 VOL=8.8873298E-1 $ void TIES
1 -10.0 73 -74 -9 3 I1 P:N1 TMP=1.6399443E-7 VOL- 13.330994 $ fuel TFE8
14 -18.8 74 -75 -9 3 IMP:N.1 TMP=1.4417533E-7 VOL- 7.9985968 $ emitter TIE
9 0 75 -76 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL- 3.0611913 $ gap TFE8
4 -8.4286 76 -77 -9 3 IMP:N.1 TMP1.0109033E-7 VOL6.7148714 $ collector
10 -3.56 77 -78 -9 3 I4:N1 TMP1.0022863E-7 VOL- 3.6536800 0 sheath TFE8
4 -8.4286 78 -79 -9 3 IMP:N.1 TMP7.7565925E-8 V01.3.8511762 $ cladding T
5 -0.75 79 -80 -9 3 IMP:N.1 TMP- 7.7565925E -8 VOL=22.218324 $ coolant TIES
4 -8.4286 80 -81 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=4.9472802E-1 $ liner T
0 -82 -9 3 MMP:Nml TMP1.6399443E-7 VOL8.8873298E-1 $ void TFE9
1 -10.0 82 -83 -9 3 IMP:N=1 TMP1.6399443E-7 V0143.330994 $ fuel TFE9
14 -18.8 83 -84 -9 9 IMP:N1 TMP=1.4417533E-7 VOL=7.9985968 $ emitter TIE
3 0 84 -85 -9 3 IMP:N=1 TMP1.4400299E-7 VOLm3.0611913 $ gap TFE9
4 -8.4286 85 -86 -9 3 IMP:N=1 TMP1.0109033E-7 VOL6.7148714 $ collector
10 -3.56 86 -87 -9 3 IMP:N1 TMP1.0022863E-7 VOL3.6536800 $ sheath TFE9
4 -8.4286 87 -88 -9 3 IMP:N =1 TMP=7.7565925E-8 VOLm3.8511762 0 cladding T
5 -0.75 88 -89 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=22.218324 $ coolant TFE9
4 -8.4286 89 -90 -9 3 1MP:N=1 THP=7.7565925E-8 VOL.4.9472802E-1 $ liner T
0 -91 -9 3 IMP:N.1 TMP1.6399443E-7 VOL=8.8873298E-1 $ void TFE10
1 -10.0 91 -92 -9 3 IMP:N.1 TMP1.6399443E-7 VOL13.330994 $ fuel TFE10
14 -18.8 92 -93 -9 3 IMP:N=1 TMP=1.4417533E-7 VOL=7.9985968 $ emitter TIE
3 0 93 -94 -9 3 IMP:N.1 IMP=1.4400299E-7 VOL=3.0611913 $ gap TFE10
4 -8.4286 94 -95 -9 3 IMP:N.I. 111Pm1.0109033E-7VOL=6.7148714 $ collector
10 -3.56 95 -96 -9 3 IMP:N =1 TMP1.0022863E-7 VOL=3.6536800 $ sheath TFE1
4 -8.4286 96 -97 -9 3 IMP:N=1 TMP7.7565925E-8 VOL3.8511762 $ cladding T
5 -0.75 97 -98 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL22.218324 $ coolant TFE1
4 -8.4286 98 -99 -9 3 IMP:N =1 TMP7.7565925E-8 VOL=4.9472802E-1 $ liner T
0 -100 -9 3 IMP:N=1 TMP1.6399443E-7 VOL=8.8873298E-1 $ void TFEll
1 -10.0 100 -101 -9 3 IMP:N1 TMP1.6399443E-7 VOL=13.330994 $ fuel TFEll
14 -18.8 101 -102 -9 3 IMP:N.1 TMP1.4417533E-7 VOL7.9985968 $ emitter T
3 0 102 -103 -9 3 IMP:N=1 IMP 1.4400299E-7 VOL3.0611913 $ gap TFEll
4 -8.4286 103 -104 -9 3 IMP:N=1 TMP1.0109033E-7 VOL6.7148714 $ collect°.
10 -3.56 104 -105 -9 3 IMP:N =1 TMP1.0022863E-7 VOL=3.6536800 $ sheath TF
4 -8.4286 105 -106 -9 3 IMP:N=1 TMP7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 106 -107 -9 3 lIMP:N1 TMP7.7565925E-8 VOL=22.218324 $ coolant TI
4 -8.4286 107 -108 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL 4.9472802E -1 $ liner
0 -109 -9 3 M4P:N=1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE12
1 -10.0 109 -110 -9 3 IMP:N.1 TM71.6399443E-7 VOL=13.330994 $ fuel TFE12
14 -18.8 110 -111 -9 3 IMP:N=1 TMP1.4417533E-7 VOL7.9985968 $ emitter T
3 0 111 -112 -9 3 IMP:N=1 TMP1.4400299E-7 V0L3.0611913 $ gap T17412
4 -8.4286 112 -119 -9 3 IMP:N=1 TMP1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 113 -114 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath TF
4 -8.4286 114 -115 -9 3 IMP:N=1 TMP7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 115 -116 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL22.218324 $ coolant TF
4 -8.4286 116 -117 -9 3 IMP:N=1 IMP=7.7565925E-8 VOL- 4.9472802E -1 $ liner
0 -118 -9 3 IMP:N=1 TMP=1.6399443E-7 V01,8.8873298E-1 $ void TFE13
1 -10.0 118 -119 -9 3 IMP:N=1 IMP=1.6399443E-7 VOL13.330994 $ fuel TFE13
14 -18.8 119 -120 -9 3 IMP:N=1 IMP1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 120 -121 -9 3 IMP:N.1 IMP=1.4400299E-7 VOL- 3.06119l3 $ gap TFE13
4 -8.4286 121 -122 -9 3 IMP:N1 IMP1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 122 -123 -9 3 IMP:N.1 TMP1.0022863E-7 VOL =3.6536800 $ sheath TI
4 -8.4286 123 -124 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL.3.8511762 $ cladding
5 -0.75 124 -125 -9 3 MMP:N-1 TMP7.7565925E-8 VOL22.218324 $ coolant TF
4 -8.4286 125 -126 -9 3 IMP:N=1 TMP7.7565925E-8 VOL4.9472802E-1 $ liner
0 -127 -9 3 IMP:N =1 TMP=1.6399443E-7 V010..8.8873298E-1 $ void TFE14
1 -10.0 127 -128 -9 3 EMP:N1 TH2.1.6399443E-7 VOL=13.330994 $ fuel TFE14
14 -18.8 128 -129 -9 3 IMP:N=1 TMP=1.4417533E-7 VOL- 7.9985968 $ emitter T
3 0 129 -130 -9 3 M4P:N1 TMP=1.4400299E-7 VOL.3.0611913 $ gap TFE14
4 -8.4286 130 -131 -9 3 IMP:N.1 TMP1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 131 -132 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL- 3.6536800 $ sheath Tr
4 -8.4286 132 -133 -9 3 IMP:N =1 IMP7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 133 -134 -9 3 IMP:N =1 TMP7.7565925E-8 VOL22.218324 $ coolant TI
4 -8.4286 134 -135 -9 3 IMP:N=1 2MP-7.7565925E-8 VOL4.9472802E-1 $ liner
0 -136 -9 3 4 IMP:N1 IMP=1.6399443E-7 VOL-4.4436649E-1 $ void TFE15
1 -10.0 136 -137 -9 3 4 IMP:N=1 Tham1.6399443E-7 VOL=6.6654973 $ fuel TFE
14 -18.8 137 -138 -9 3 4 IMP:N1 TMP=1.4417533E-7 VOL=3.9992984 0 emitter
3 0 138 -139 -9 3 4 IMP:N=1 THP=1.4400299E-7 VOL=1.5305957 $ gap TFE15
4 -8.4286 139 -140 -9 3 4 IMP:N =1 TMP1.0109033E-7 VOL3.3574357 $ collec
10 -3.56 140 -141 -9 3 4 IMP:Nml TMP1.0022863E-7 VOL1.8268400 $ sheath
4 -8.4286 141 -142 -9 3 4 IMP:N=1 THP7.7565925E-8 VOL=1.9255881 $ claddi
5 -0.75 142 -143 -9 3 4 1MP:N1 IMP=7.7565925E-8 VOL=11.109162 $ coolant
4 -8.4286 143 -144 -9 3 4 IMP:N=1 THP=7.7565925E-8 $ liner TFE15
VOL2.4736401E-1
0 -145 -9 3 IM8:N1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE16
1 -10.0 145 -146 -9 3 IMP:N=1 TMP1.6399443E-7 VOL=13.330994 $ fuel TFE16
14 -18.8 146 -147 -9 3 IMP:N=1 TMP1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 147 -148 -9 3 IMP:N1 TMP=1.4400299E-7 VOL.3.0611913 $ gap TFE16
4 -8.4286 148 -149 -9 3 IMP:N=1 TMP1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 149 -150 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL- 3.6536800 $ sheath TF
4 -8.4286 150 -151 -9 3 DIP:N1 TMP- 7.7565925E -8 VOL=3.8511762 $ cladding
5 -0.75 151 -152 -9 3 IMP:N.1 THP7.7565925E-8 VOL22.218324 $ coolant TI
4 -8.4286 152 -153 -9 3 IMP:N=1 IMP7.7565925E-8 VOL4.9472802E-1 $ liner
0 -154 -9 3 IMP:N.1 TME-i.6399443E -7 VOL=8.8873298E-1 $ void TFE17
1 -10.0 154 -155 -9 3 IMP:N=1 TMP1.6399443E-7 VOL-13.330994 $ fuel TFE17
14 -18.8 155 -156 -9 3 IMP:N1 IMP.1.4417533E-7 VOL7.9985968 $ emitter T
3 0 156 -157 -9 3 IMP:N =1 TMPm1.4400299E-7 VOL.3.0611913 $ gap TFE17
4 -8.4286 157 -158 -9 3 IMP:N1 TMPm1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 158 -159 -9 3 IMP:N =1 MP-1.0022863E-7 VOL3.6536800 $ sheath TI
4 -8.4286 159 -160 -9 3 /4P:N1 IMP7.7565925E-8 vOL3.8511762 $ cladding
5 -0.75 160 -161 -9 3 IMP:N1 TMP=7.7565925E-8 VOL=22.218324 $ coolant TF
4 -8.4286 161 -162 -9 3 IMP:N.1 IMP7.7565925E-8 VOL4.9472802E-1 $ liner
0 -163 -9 3 IMP:N1 TMP1.6399443E-7 VOL=8.8873298E-1 $ void TFEI8
1 -10.0 163 -164 -9 3 IMP:N=1 TMP=1.6999443E-7 VOL=13.330994 $ fuel TFE18
14 -18.8 164 -165 -9 3 IMP:N=1 Imp1.4417533E-7 VOL7.9985968 $ emitter T
3 0 165 -166 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE18
4 -8.4286 166 -167 -9 3 IMP:N=1 TMP1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 167 -168 -9 3 IMP:N=1 IMP1.0022863E-7 VOL.3.6536800 $ sheath TF
4 -8.4286 168 -169 -9 3 I3P:N=1 THP=7.7565925E-8 V01,3.8511762 $ cladding
5 -0.75 169 -170 -9 3 EMP:N1 TMP7.7565925E-8 V01=22.218324 $ coolant TI
4 -8.4286 170 -171 -9 3 IMP:N=1 TMP7.7565925E-8 VOL4.9472802E-1 4 liner
123
176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278-
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
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223
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225
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230
231
232
233
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235
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237
238
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241
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243
244
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246
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252
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256
257
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262
263
264
265
266
267
268
269
270
0 -172 -9 3 IMP:N=1 TMP=1.6399443E-7 VOI=8.8873298E-1 $ void TFE19
1 -10.0 172 -173 -9 3 IMP:N=1 THP=1.6399443E-7 VOL=13.330994 $ fuel TFE19
14 -18.8 173 -174 -9 3 IMP:N=1 TMP=1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 174 -175 -9 3 7249:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE19
4 -8.4286 175 -176 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 8 collecto
10 -3.56 176 -177 -9 3 1MP:N=1 THP=1.0022863E-7 VOL- 3.6536800 $ sheath IT
4 -8.4286 177 -178 -9 3 IMP:N=1 THP=7.7565925E-8 VOL- 3.8511762 $ cladding
5 -0.75 178 -179 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=22.218324 $ coolant IT
4 -8.4286 179 -180 -9 3 IMP:N =1 TMP- 7.7565925E -8 VOL=4.9472802E-1 8 liner
0 -181 -9 3 IMP:N =1 TMP=1.6399443E-7 VOL- 8.8873298E -1 $ void TFE20
1 -10.0 181 -182 -9 3 /4P:N=1 TMP=1.6399443E-7 VOL=13.330994 8 fuel TFE20
14 -18.8 182 -183 -9 3 IMP:N=1 TMP=1.4417533E-7 VOL- 7.9985968 $ emitter T
3 0 183 -184 -9 3 fl :N =1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE20
4 -8.4286 184 -185 -9 3 IMP:N=1 THP=1.0109033E-7 VOL=6.7148714 8 collecto
10 -3.56 185 -186 -9 3 IMP:N=1 THP=1.0022863E-7 VOI=3.6536800 $ sheath IF
4 -8.4286 186 -187 -9 3 IMP:N=1 TMP=7.7565925E-8 V0L=3.8511762 8 cladding
5 -0.75 187 -188 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=22.218324 $ coolant IF
4 -8.4286 188 -189 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=4.9472802E-1 $ liner
0 -190 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE21
1 -10.0 190 -191 -9 3 IMP:N=1 THP=1.6399443E-7 VOL=13.330994 $ fuel TFE21
14 -18.8 191 -192 -9 3 IMP:N =1 TMP=1.4417533E-7 VOL=7.9985968 8 emitter T
3 0 192 -193 -9 3 IM8:N=1 IMP- l.4400299E -7 VOL=3.0611913 8 gap TFE21
4 -8.4286 193 -194 -9 3 IMP:N=1 TMP=1.0109033E-7 V0L=6.7148714 8 collecto
10 -3.56 194 -195 -9 3 14P:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IT
4 -8.4286 195 -196 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=3.8511762 8 cladding
5 -0.75 196 -197 -9 3 IMP:N=1 TMP=7.7565925E-8 vOL=22.218324 8 coolant TF
4 -8.4286 197 -198 -9 3 IMP:N=1 TMP .7.7565925E -8 VOL=4.9472802E-1 8 liner
0 -199 -9 3 IMP:N=1 TMP=1.6399443E-7 V01=61.8873298E-1 8 void TFE22
1 -10.0 199 -200 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 8 fuel TFE22
14 -18.8 200 -201 -9 3 /MP:N=1 2MP=1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 201 -202 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 8 gap TFE22
4 -8.4286 202 -203 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 8 collecto
10 -3.56 203 -204 -9 3 fl :N =1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IF
4 -8.4286 204 -205 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 205 -206 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=22.218324 $ coolant TF
4 -8.4286 206 -207 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL- 4.9472802E -1 $ liner
0 -208 -9 3 IMP:N =1 THP=1.6399443E-7 V01=8.8873298E-1 0 void TFE23
1 -10.0 208 -209 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE23
14 -18.8 209 -210 -9 3 I4P:N=1 THP=1.4417533E-7 VOL- 7.9965968 8 emitter T
3 0 210 -211 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE23
4 -8.4286 211 -212 -9 3 IMP:N =1 TMP=1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 212 -213 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IF
4 -8.4286 213 -214 -9 3 IMP:N=1 THP=7.7565925E-8 V01=3.8511762 $ cladding
5 -0.75 214 -215 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=22.218324 $ coolant IT
4 -8.4286 215 -216 -9 3 IMP:N=1 TMP=7.7565925E-8 V01=4.9472802E-1 $ liner
0 -217 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE24
1 -10.0 217 -218 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE24
14 -18.8 218 -219 -9 3 IMP:N=1 TMP=1.4417533E-7 V01=7.9985968 $ emitter T
3 0 219 -220 -9 3 1MP:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE24
4 -8.4286 220 -221 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 0 collecto
10 -3.56 221 -222 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IF
4 -8.4286 222 -223 -9 3 I1P:N=1 TMP=7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 223 -224 -9 3 IMP:N =1 TMP=7.7565925E-8 VOL=22.218324 8 coolant IT
4 -8.4286 224 -225 -9 3 IMP:9T=1 TMP=7.7565925E-8 V01=4.9472802E-1 8 liner
0 -226 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=8.8873298E-1 8 void TFE25
1 -10.0 226 -227 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE25
14 -18.8 227 -228 -9 3 MMP:N=1 TMP=1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 228 -229 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 8 gap TFE25
4 -8.4286 229 -230 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 230 -231 -9 3 ImP:N=1 TMP=1.0022863E-7 VOL- 3.6536800 $ sheath TF
4 -8.4286 231 -232 -9 3 IMP:N=1 THP=7.7565925E-8 VOL- 3.8511762 $ cladding
5 -0.75 232 -233 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=22.218324 $ coolant IF
4 -8.4286 233 -234 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=4.9472802E-1 $ liner
0 -235 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL- 8.8873298E -1 8 void TFE26
1 -10.0 235 -236 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE26
14 -18.8 236 -237 -9 3 IMP:N=1 THP=1.4417533E-7 VOL- 7.9985968 $ emitter T
3 0 237 -238 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE26
4 -8.4286 238 -239 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 239 -240 -9 3 IMP:N =1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IF
4 -8.4286 240 -241 -9 3 IMP:N=1 THP=7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 241 -242 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL22.218324 $ coolant TF
4 -8.4286 242 -243 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=4.9472802E-1 $ liner
0 -244 -9 3 IMP:N=1 THP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE27
1 -10.0 244 -245 -9 3 1MP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE27
14 -18.8 245 -246 -9 3 IMP:N=1 TMP=1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 246 -247 -9 3 IMP:N=1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE27
4 -8.4286 247 -248 -9 3 IMP:N=1 TMP=1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 248 -249 -9 3 IMP:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IT
4 -8.4286 249 -250 -9 3 IMP:8=1 TMP=7.7565925E-8 V0L=3.8511762 $ cladding
5 -0.75 250 -251 -9 3 IMP:N=1 MP-7.7565925E-8 VOL=22.218324 $ coolant IF
4 -8.4286 251 -252 -9 3 IMP:N=1 TMP=7.7565925E-8 VOL=4.9472802E-1 $ liner
0 -253 -9 3 4 IMP:N=1 TMP=1.6399443E-7 VOL=4.4436649E-1 $ void TFE28
1 -10.0 253 -254 -9 3 4 IMP:N=1 TMP=1.6399443E-7 VOL=6.6654973 $ fuel TFE
14 -18.8 254 -255 -9 3 4 IMP:N=1 TMP=1.4417533E-7 VOL=3.9992984 8 emitter
3 0 255 -256 -9 3 4 IMP:N=1 THP=1.4400299E-7 VOL=1.5305957 $ gap TFE28
4 -8.4286 256 -257 -9 3 4 IMP:N=1 TMP=1.0109033E-7 VOL=3.3574357 8 collec
10 -3.56 257 -258 -9 3 4 IMP:N=1 TMP=1.0022863E-7 VOL=1.8268400 $ sheath
4 -8.4286 258 -259 -9 3 4 /34P:N=1 TMP=7.7565925E-8 VOL=1.9255881 8 claddi
5 -0.75 259 -260 -9 3 4 IMP:N=1 TMP- 7.75659259 -8 VOL=11.109162 $ coolant
4 -8.4286 260 -261 -9 3 4 IMP:N=1 TMP=7.7565925E-8 $ liner TFE28
VOL=2.4736401E-1
0 -262 -9 3 1MP:N=1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE29
1 -10.0 262 -263 -9 3 IMP:N=1 TMP=1.6399443E-7 VOL=13.330994 $ fuel TFE29
14 -18.8 263 -264 -9 3 IMP:N =1 TMP=1.4417533E-7 VOL-7.9985968 $ emitter
3 0 264 -265 -9 3 IMP:N =1 TMP=1.4400299E-7 VOL=3.0611913 $ gap TFE29
4 -8.4286 265 -266 -9 3 IMP:N =1 114P=1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 266 -267 -9 3 ID49:N=1 TMP=1.0022863E-7 VOL=3.6536800 $ sheath IT
4 -8.4286 267 -268 -9 3 /4P:N=1 TMP=7.7565925E-8 VOL- 3.8511762 $ cladding
5 -0.75 268 -269 -9 3 IMP:N=1 THP=7.7565925E-8 vOL=22.218324 $ coolant IF
4 -8.4286 269 -270 -9 3 144P:N=1 T44P=7.7565925E-8 VOL=4.9472802E-1 $ liner
0 -271 -9 3 I4P:11=1 TMP=1.6399443E-7 VOL=8.8873298E-1 $ void TFE30
1 -10.0 271 -272 -9 3 IMP:N=1 TH1..1.6399443E-7 VOL=13.330994 $ fuel Trt30
14 -18.8 272 -273 -9 3 I24P:N=1 TMP=1.4417533E-7 VOL=7.9985968 f emitter T
124
279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325326327328329330331332333334335336337338339340341342343344345346347348349350351352353354355356357358359360361362363364365366367368369370371372373374375376377378379380381-
271
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278
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282
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286
287
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322
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331
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370
371
372
3 0 273 -274 -9 3 I4P:N1 TMP1.4400299E-7 VOL3.0611913 $ gap TFE30
4 -8.4286 274 -275 -9 3 IMP:101 TMP1.0109033E-7 V01=6.7148714 $ collecto
10 -3.56 275 -276 -9 3 I4P:N1 TMP1.0022863E-7 VOL3.6536800 8 sheath IF
4 -8.4286 276 -277 -9 3 IMP:N1 TWP7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 277 -278 -9 3 IMP:N.1 TMP.7.7565925E-8 VOL=22.210324 0 coolant IF
liner
4 -8.4286 278 -279 -9 3 IMP:N1 TMP7.7565925E-8 VOL4.9472802E-1
0 -280 -9 3 I49:N1 TWP1.6399443E-7 VOL8.8873298E-1 8 void TFE31
1 -10.0 280 -281 -9 3 TMP:N1 TMP- 1.6399443E -7 VOL.13.330994 $ fuel TFE31
14 -18.8 281 -282 -9 3 I4P:N=1 TMP1.4417533E-7 VOL.7.9985968 $ emitter T
3 0 282 -283 -9 3 IMP:N=1 THP=1.4400299E-7 VOL=3.0611913 8 gap TFE31
4 -8.4286 283 -284 -9 3 fl :N =1 TWP1.0109033E-7 VOL=6.7148714 0 collecto
10 -3.56 284 -285 -9 3 DIP:N1 TMP1.0022863E-7 VOL3.6536800 $ *heath Tr
4 -8.4286 285 -286 -9 3 IMP:N.1 TM:P=7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 286 -287 -9 3 IM9):N1 THP7.7565925E-8 VOL.22.218324 $ coolant TF
4 -8.4286 287 -288 -9 3 I4P:N.1 TI4P7.7565925E-8 VOL4.9472802E-1 $ liner
0 -289 -9 3 I4P:N1 THP1.6399443E-7 VOL8.8873298E-1 8 void TFE32
1 -10.0 289 -290 -9 3 D49:N=1 THP.1.6399443E-7 VOL13.330994 $ fuel TFE32
14 -18.8 290 -291 -9 3 E4P:N1 TMP1.4417533E-7 VOL7.9985968 $ emitter T
3 0 291 -292 -9 3 IMP:N1 THP=1.4400299E-7 VOL3.0611913 8 gap TFE32
4 -8.4286 292 -293 -9 3 II4P:N1 TWP=1.0109033E-7 VOL.6.7148714 $ collecto
10 -3.56 293 -294 -9 3 MHP:Wd THP1.0022863E-7 VOL3.6536800 8 sheath TF
4 -8.4286 294 -295 -9 3 IMP:N1 TWP7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 295 -296 -9 3 IMP:N1 THP-7.7565925E-8 VOL.22.218324 $ coolant TF
4 -8.4286 296 -297 -9 3 TI4P:N.1 TW27.7565925E-8 VOL=4.9472802E-1 8 liner
0 -298 -9 3 IMP:N=1 TWP1.6399443E-7 VOL8.8873298E-1 $ void TFE33
1 -10.0 298 -299 -9 3 IMP:N1 THP.1.6399443E-7 VOL.13.330994 8 fuel TFE33
14 -18.8 299 -300 -9 3 1WP:N=1 TH21.4417533E-7 VOL=7.9985968 $ emitter T
3 0 300 -301 -9 3 DIP:N=1 TMP=1.4400299E-7 V0103.0611913 $ gap 11133
4 -8.4286 301 -302 -9 3 IMP:N=1 THP=1.0109033E-7 VOL6.7148714 8 collecto
10 -3.56 302 -303 -9 3 I4P:N=1 TWP1.0022863E-7 VOL.3.6536800 8 sheath TF
4 -8.4286 303 -304 -9 3 IMP:N1 TMP7.75659251-8 V01=3.8511762 $ cladding
5 -0.75 304 -305 -9 3 I4P:N=1 TH9.7.7565925E-8 VOL.22.218324 $ coolant TF
4 -8.4286 305 -306 -9 3 IMP:N1 TWP=7.7565925E-8 VOL4.9472802E-1 8 liner
0 -307 -9 3 I4P:N=1 THP1.6399443E-7 VOL.8.8873298E -1 8 void TFE34
1 -10.0 307 -308 -9 3 IMP:N1 TH2.1.6399443E-7 VOL=13.330994 0 fuel TFE34
14 -18.8 308 -309 -9 3 MMP:N=1 THP1.4417533E-7 VOL7.9985968 $ emitter T
3 0 309 -310 -9 3 7249:N1 TWP=1.4400299E-7 VOL3.0611913 $ gap TFE34
4 -8.4286 310 -311 -9 3 IMP:N1 TWP=1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 311 -312 -9 3 MMP:N=1 THP=1.00228631-7 VOL=3.6536800 $ sheath TF
4 -8.4286 312 -313 -9 3 IMP:N1 174P=7.75659251-8 VOL3.8511762 $ cladding
5 -0.75 313 -314 -9 3 IMP:N=1 TWP7.7565925E-8 VOL22.218324 $ coolant TF
liner
4 -8.4286 314 -315 -9 3 IMP:N1 TMP=7.7565925E-8 VOL.4.9472802E-1
0 -316 -9 3 I4P:N1 THP1.63994431-7 VOL8.8873298E-1 $ void TFE35
1 -10.0 316 -317 -9 3 IMP:N=1 THP.1.6399443E-7 VOL=13.330994 $ fuel TFE35
14 -18.8 317 -318 -9 3 IMP:N.1 TM-1.4417533E-7 VOL.7.9985968 8 emitter T
3 0 318 -319 -9 3 IMP:N=1 TMP1.4400299E-7 VOL.3.0611913 $ gap TF135
4 -8.4286 319 -320 -9 3 3)49:81 15411.0109033E-7 VOL.6.7148714 $ collecto
10 -3.56 320 -321 -9 3 I4P:81 TWP1.0022863E-7 VOL.3.6536800 8 sheath TF
4 -8.4286 321 -322 -9 3 I0:14=1 TMP7.7565925E-8 VOL.3.8511762 $ cladding
5 -0.75 322 -323 -9 3 IMP:N=1 THIP7.75659251-8 VOL.22.218324 8 coolant TF
4 -8.4286 323 -324 -9 3 IMP:N.1 1W17.75659251-8 VOL4.9472802E-1 $ liner
0 -325 -9 3 TI4P:N1 THY-1.6399443E-7 VOL8.8873298E-1 $ void TFE36
1 -10.0 325 -326 -9 3 IMP:N1 TMP1.63994431-7 VOL13.330994 8 fuel TFE36
14 -18.8 326 -327 -9 3 IMP:N1 THP1.44175331-7 VOL7.9985968 8 emitter T
3 0 327 -328 -9 3 340:81 189=1.4400299E-7 VOL=3.0611913 $ gap 1FE36
4 -8.4286 328 -329 -9 3 IMP:N=1 TWP1.0109033E-7 VOL.6.7148714 $ collecto
10 -3.56 329 -330 -9 3 I1P:N1 THP1.00228631-7 VOL.3.6536800 $ sheath IF
4 -8.4286 330 -331 -9 3 IMP:N=1 TWP7.75659251-8 VOL=3.8511762 8 cladding
5 -0.75 331 -332 -9 3 IMP:N1 7MP-7.7565925E-8 VOL=22.218324 $ coolant IF
liner
4 -8.4286 332 -333 -9 3 3)0:51 150=7.75659251-8 VOL.4.9472802E-1
0 -334 -9 3 IMP:N1 THP1.63994431-7 VOL8.8873298E-1 $ void 1FE37
1 -10.0 334 -335 -9 3 1MP:20.1 1e-1.6399443E-7 VOL13.330994 $ fuel TFE37
14 -18.8 335 -336 -9 3 350:81 THP1.4417533E-7 VOL.7.9985968 $ emitter T
3 0 336 -337 -9 3 I4P:10.1 THP1.4400299E-7 VOL3.0611913 $ gap TFE37
4 -8.4286 337 -338 -9 3 10:8.1 T501.01090331-7 VOL=6.7148714 $ collecto
10 -3.56 338 -339 -9 3 11442.:8=1 T)01.0022863E-7 VOL3.6536800 $ sheath IF
4 -8.4286 339 -340 -9 3 I4P:N1 TMP=7.75659251-8 VOL3.8511762 $ cladding
5 -0.75 340 -341 -9 3 3)0:51 THY...7.7565925E-8 VOL22.218324 $ coolant IF
4 -8.4286 341 -342 -9 3 254P:N1 189=7.75659251-8 VOL4.9472802E-1 $ liner
0 -343 -9 3 IMP:N=1 THP1.63994431-7 VOLm6.8873298E-1 $ void TFE38
1 -10.0 343 -344 -9 3 IMP:N1 THY...1.6399443E-7 VOL.13.330994 $ fuel TFE38
14 -18.8 344 -345 -9 3 IMP:N.1 TMP=1.44175331-7 VOL7.9985968 8 emitter T
3 0 345 -346 -9 3 I4P:N=1 TWP=1.44002991-7 VOL.3.0611913 8 gap TFE38
4 -8.4286 346 -347 -9 3 I4P:5 .1 TWP=1.0109033E-7 VOL6.7148714 8 collecto
10 -3.56 347 -348 -9 3 1MP:51 TWP1.002286315-7 VOL=3.6536800 $ sheath TF
4 -8.4286 348 -349 -9 3 3)0:81 MP-7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 349 -350 -9 3 IMP:N1 TWP7.75659251-8 VOL=22.218324 0 coolant TF
4 -8.4286 350 -351 -9 3 IMP:N1 TWP=7.7565925E-8 VOL 4.94728021 -1 $ liner
0 -352 -9 3 4 I4P:N=1 TMP1.6399443E-7 VOL4.4436649E-1 $ void 1FE39
1 -10.0 352 -353 -9 3 4 IMP:N=1 THP=1.63994431-7 VOL6.6654973 $ fuel TFE
14 -18.8 353 -354 -9 3 4 1M0:N1 TMP1.4417533E-7 VOL3.9992984 $ emitter
3 0 354 -355 -9 3 4 3)449:51 1501.44002991-7 VOL1.5305957 $ gap 11E39
4 -8.4286 355 -356 -9 3 4 IMP:N.1 TMP1.0109033E-7 VOL.3.3574357 $ collec
10 -3.56 356 -357 -9 3 4 1MP:8.1 TMP-1.0022863E-7 VOL=1.8268400 $ sheath
4 -8.4286 357 -358 -9 3 4 IMP:N=1 TMP7.75659251-8 VOL.1.9255881 $ claddi
5 -0.75 358 -359 -9 3 4 IMP:N=1 THP=7.7565925E-8 V01=11.109162 $ coolant
4 -8.4286 359 -360 -9 3 4 IMP:N=1 THP7.75659251-8 $ liner TFE39
VOL.2.4736401E-1
0 -361 -9 3 IMP:N=1 THP.1.63994431-7 V01.8.8873298E-1 $ void TFE40
1 -10.0 361 -362 -9 3 E41:N=1 TH2..1.6399443E-7 VOL.13.330994 $ fuel TFE40
14 -18.8 362 -363 -9 3 IMP:N=1 n2.1.4417533E-7 VOL=7.9985968 8 emitter T
3 0 363 -364 -9 3 3)441:571 1M1=1.4400299E-7 VOL.3.0611913 8 gap 11E40
4 -8.4286 364 -365 -9 3 142:51 1501.01090331-7 VOL6.7148714 $ collecto
10 -3.56 365 -366 -9 3 142:N1 T10..1.0022863E-7 VOL3.6536800 8 sheath TF
4 -8.4286 366 -367 -9 3 IMP:N.1 1W9=7.7565925E-8 VOL=3.8511762 8 cladding
5 -0.75 367 -368 -9 3 IMP:N1 THP.7.7565925E-8 VOL.22.218324 8 coolant IF
4 -8.4286 368 -369 -9 3 I0:N1 THP7.75659251-8 VOL.4.9472802E-1 $ liner
0 -370 -9 3 I4P:N1 1549 1.63994431-7 VOL.8.8873298E-1 $ void TFE41
1 -10.0 370 -371 -9 3 2519:11 150=1.63994431-7 VOL13.330994 $ fuel 11E41
14 -18.8 371 -372 -9 3 3)0:81 9441.44175331-7 VOL7.9985968 $ emitter T
3 0 372 -373 -9 3 I4P:N=1 TMP1.4400299E-7 VOL3.0611913 8 gap TFE41
4 -8.4286 373 -374 -9 3 I4P:N1 THP1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 374 -375 -9 3 I4P:11 THP1.00228631-7 VOL.3.6536800 $ sheath TF
125
382383384385386387388389390391392393394395396397398399400401402403404405406407408409410411412413414415416417418419420421422423424425426427428429430431432433434435436437438439440441442443444445446447448449450451452453454455456457458459460461462463464465466467468469470471472473474475476477478479480481482483484-
373
374
375
376
377
378
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380
381
382
383
384
385
386
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415
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1
2
*3
*4
5
*6
7
8
9
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11
12
13
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19
20
21
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23
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44
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46
47
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50
51
52
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54
4 -8.4286 375 -376 -9 9 1MP:N1 TMP=7.7565925E-8 VOLp3.8511762 f cladding
5 -0.75 376 -377 -9 3 IMP:Nml TMP7.756592512-8 VOL=22.218324 $ coolant Tr
4 -8.4286 377 -378 -9 3 IMP:N1 TMP7.7565925E-8 VOL4.9472802E-1 $ liner
0 -379 -9 3 IMP:NI TMP1.6399443E-7 VOL8.8873298E-1 $ void TFE42
1 -10.0 379 -380 -9 3 IMP:N1 TMP1.6399443E-7 VOL=13.330994 $ fuel TFE42
14 -18.8 380 -381 -9 3 IMP:N1 TMP1.4417533E-7 V0L.7.9985968 $ emitter T
3 0 381 -382 -9 3 IMP:N=1 TMP1.4400299E-7 V0L=3.0611913 $ gap TFE42
4 -8.4286 382 -383 -9 3 1MP:N.1 TMP1.0109033E-7 VOL=6.7148714 0 collecto
10 -3.56 383 -384 -9 3 1MP:N1 MP-1.0022863E-7 VOL3.6536800 0 sheath SF
4 -8.4286 384 -385 -9 3 1WP:N1 TMP=7.7565925E-8 V0L3.8511762 $ cladding
5 -0.75 385 -386 -9 3 MP:N1 MP7.756592512-8 VOL=22.218324 $ coolant TT
4 -8.4286 386 -387 -9 3 MP:N.1 5M97.756592512-8 V0L.4.9472802E-1 $ liner
0 -388 -9 3 MP:N1 TMP1.6399443E-7 VOL.8.8873298E-1 $ Void TFE43
1 -10.0 388 -389 -9 3 MP:N1 TMP1.6399443E-7 VOL13.330994 $ fuel TFE43
14 -18.8 389 -390 -9 3 IMP:N=1 TMP=1.4417533E-7 vOL- 7.9985968 $ emitter T
3 0 390 -391 -9 3 IMP:N1 TMP1.4400299E-7 VOLm3.0611913 $ gap TFE43
4 -8.4286 391 -392 -9 3 IM0:N1 TMP=1.0109033E-7 V0L=6.7148714 $ collect°
10 -3.56 392 -393 -9 3 EMP:Mml TMP1.0022863E-7 VOL3.6536800 $ sheath Tr
4 -8.4286 393 -394 -9 3 1MP:N.1 TMP7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 394 -395 -9 3 EMP:N1 /MP-7.7565925E-8 V0L22.218324 $ coolant IF
4 -8.4286 395 -396 -9 3 MP:N=1 1MP-7.7565925E-8 VOL.4.9472802E-1 $ liner
0 -397 -9 3 1M99:N.1 TMP=1.6399443E-7 V01.8.8873298E-1 $ void TFE44
1 -10.0 397 -398 -9 3 MP:N1 TMP.1.6399443E-7 VOL13.330994 0 fuel TFE44
14 -18.8 398 -399 -9 3 /MP:N1 TMP1.4417533E-7 VOL=7.9985968 $ emitter T
3 0 399 -400 -9 3 MP:N=1 TMP1.4400299E-7 VOL=3.0611913 $ gap TFE44
4 -8.4286 400 -401 -9 3 1M0:N1 TMP-1.0109033E-7 VOL6.7148714 $ collecto
10 -3.56 401 -402 -9 3 MP:N=1 TMP1.0022863E-7 V0Lm3.6536800 f sheath Tr
4 -8.4286 402 -403 -9 3 MP:Nml TMP7.7565925E-8 VOL3.8511762 $ cladding
5 -0.75 403 -404 -9 3 MP:N.1 THP=7.75659252-8 VOL22.218324 $ coolant TT
4 -8.4286 404 -405 -9 3 /4P:N1 TMP7.7565925E-8 V0L.4.9472802E-1 $ liner
0 -406 -9 3 1MP:N1 TMP=1.6399443E-7 VOL-8.8873298E-1 0 void TFE45
1 -10.0 406 -407 -9 3 5)0:51 5142=1.639944312-7 V0L.13.330994 0 fuel TFE45
14 -18.8 407 -408 -9 3 MP:N=1 TMP=1.4417533E-7 V0L7.9985968 $ emitter T
3 0 408 -409 -9 3 IMP:N1 M1..1.4400299E-7 VOL.3.0611913 $ gap TFE45
4 -8.4286 409 -410 -9 3 IM0:N1 TMP=1.0109033E-7 V0L6.7148714 $ collecto
10 -3.56 410 -411 -9 3 TIMP:N=1 TMP1.0022863E-7 VOL3.6536800 $ sheath TF
4 -8.4286 411 -412 -9 3 IM0:N1 TMP=7.7565925E-8 VOL 3.8511762 0 cladding
5 -0.75 412 -413 -9 3 MP:N=1 MP=7.7565925E-8 V0L.22.218324 $ coolant IF
4 -8.4286 413 -414 -9 3 IMP:N=1 TMP.7.7565925E-8 vOL4.9472802E-1 $ liner
0 -415 -9 3 IMP:N=1 TMP=1.6399443E-7 V01.8.8873298E-1 $ void TFE46
1 -10.0 415 -416 -9 3 IMP:N=1 TMP1.6399443E-7 VOL=13.330994 $ fuel TFE46
14 -18.8 416 -417 -9 3 ZMP:N1 TMP-1.4417533E-7 VOL7.9985968 $ emitter T
9 0 417 -418 -9 3 MP:N=1 THP1.4400299E-7 VOL=3.0611913 $ gap TFE46
4 -8.4286 418 -419 -9 3 1MP:N1 TMP.1.0109033E-7 VOL=6.7148714 $ collecto
10 -3.56 419 -420 -9 3 IMP:N1 TMP1.0022863E-7 V0L3.6536800 $ sheath TF
4 -8.4286 420 -421 -9 3 MP:N.1 TMP7.7565925E-8 VOL=3.8511762 $ cladding
5 -0.75 421 -422 -9 3 114P:N.1 1MP-7.7565925E-8 VOL22.218324 $ coolant TF
4 -8.4286 422 -423 -9 3 IMP:N=1 MP7.7565925E-8 VOL4.9472802E-1 $ liner
SO 1000 $ infinity
PZ 27.5 $ top of core
PZ 0 $ midplane
PX 0 $ X symmetric plane
CZ 32 $ reflector cylinder
PY 0 $ Y symmetric plane
CZ 24 $ cylinder of core
PE 19.522 0 top of rod
PZ 12.573 $ top of fuel
C/2 0 1R 0.15 $ TFE1
C/2 0 1R 0.6 $ TFE1
C/2 0 1R 0.75 $ TEEM
C/2 0 1R 0.8 $ TFE1
C/2 0 1R 0.9 $ TFE1
C/2 0 1R 0.95 $ TFE1
C/2 0 1R 1.0 $ TFE1
C/Z 0 1R 1.25 $ TFE1
C/2 0 IR 1.255 $ TFE1
C/2 3.263
0.15 $ TFE2
C/2 3.263
0.6 $ TFE2
C/2 3.263
0.75 $ TFE2
C/2 3.263
0.8 $ TFE2
C/2 3.263
0.9 $ TFE2
C/2 3.263
0.95 $ TFE2
C/2 3.263
1.0 $ TFE2
C/2 3.263
1.25 $ TFE2
C/Z 3.263
1.255 $ TFE2
C/2 6.526
0.15 $ TFE3
C/2 6.526
0.6 $ TFE3
C/2 6.526
0.75 $ TFE3
C/2 6.526
0.8 $ TFE3
C/2 6.526
0.9 $ TFE3
C/2 6.526
0.95 $ TFE3
C/2 6.526
1.0 $ TFE3
C/2 6.526
1.25 $ TFE3
C/2 6.526
1.255 $ TFE3
C/2 9.789
0.15 $ TFE4
C/2 9.789
0.6 $ TFE4
C/2 9.789
0.75 $ TFE4
C/2 9.789
0.8 $ TFE4
C/Z 9.789
0.9 $ TFE4
C/2 9.789
0.95 $ TFE4
C/2 9.789
1.0 $ TFE4
C/2 9.789
1.25 $ TFE4
C/2 9.789
1.255 $ TFE4
C/2 13.052
0.15 $ TFE5
C/2 13.052
0.6 $ TEES
C/2 13.052
0.75 $ TFE5
C/2 13.052
0.8 $ TFE5
C/2 13.052
0.9 $ TEES
C/2 13.052
0.95 $ TFE5
C/2 13.052
1.0 $ TFE5
C/2 13.052
1.25 $ TFE5
C/2 13.052
1.255 4 TFE5
126
485486487488489490491492493494495496497498499500501502503504505506507508509510511512513514515516517518519520521522523524525526527528529530531532533534535536537538539540541542543544545546547548549550551552553554555556557558559560561562563564565566567568569570571572573574575576577578579580581582583584585586587-
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C/S 16.315
0.15 $ TFE6
C/Z 16.315
0.6 $ TFE6
C/S 16.315
0.75 $ TFE6
C/S 16.315
0.8 $ TFE6
C/S 16.315
0.9 $ TFE6
C/S 16.315
0.95 $ TFE6
C/S 16.315
1.0 8 TFE6
C/Z 16.315
1.25 $ TFE6
C/S 16.315
1.255 8 TFE6
C/Z 19.578
0.15 $ TFE7
C/S 19.578
0.6 $ TFE7
C/S 19.578
0.75 8 TFE7
C/Z 19.578
0.8 $ TFE7
C/S 19.578
0.9 $ TFE7
C/S 19.578
0.95 8 TFE7
C/S 19.578
1.0 $ TFE7
C/S 19.578
1.25 8 TFE7
C/S 19.578
1.255 $ TFE7
C/S 1.6315 .8259211 0.15 6 TFE8
C/Z 1.6315 .8259211 0.6 $ TFE8
C/S 1.6315 .8259211 0.75 $ TFE8
C/S 1.6315 .8259211 0.8 $ TFE8
C/S 1.6315 .8259211 0.9 $ TFE8
C/S 1.6315 .8259211 0.95 0 TEES
C/S 1.6315 .8259211 1.0 id TFE8
C/S 1.6315 .8259211 1.25 $ TFE8
C/S 1.6315 .8259211 1.255 $ TFE8
C/S 4.8945 .8259211 0.15 $ TFE9
C/S 4.8945 .8259211 0.6 8 TFE9
C/S 4.8945 .8259211 0.75 $ TFE9
C/Z 4.8945
.8259211 0.8 $ TFE9
C/S 4.8945
.8259211 0.9 8 TFE9
C/Z 4.8945
.8259211 0.95 $ TFE9
C/Z 4.8945
.8259211 1.0 $ TFE9
C/S 4.8945
.8259211 1.25 $ TFE9
C/Z 4.8945
.8259211 1.255 $ TFE9
C/S 8.1575
.8259211 0.15 $ TFE10
C/S 8.1575
.8259211 0.6 $ TFE10
C/S 8.1575
.8259211 0.75 $ TFE10
C/S 8.1575
.8259211 0.8 $ TFE10
C/Z 8.1575
.8259211 0.9 $ TFE10
C/S 8.1575
.8259211 0.95 $ TFE10
C/S 8.1575
.8259211 1.0 $ TFE10
C/S 8.1575
.8259211 1.25 8 TFE10
C/S 8.1575 .8259211 1.255 $ TFE10
C/Z 11.4205 2.8259211 0.15 $ TFE11
C/Z 11.4205 2.8259211 0.6 8 TFE11
C/S 11.4205 2.8259211 0.75 $ TFE11
C/S 11.4205 2.8259211 0.8 $ TFE11
C/S 11.4205 2.8259211 0.9 $ TFE11
C/Z 11.4205 2.8259211 0.95 $ TFE11
C/Z 11.4205 2.8259211 1.0 $ TFE11
C/Z 11.4205 2.8259211 1.25 $ TFE11
C/S 11.4205 2.8259211 1.255 $ TFE11
C/Z 14.6835 2.8259211 0.15 $ TFE12
C/S 14.6835 2.8259211 0.6 8 TFE12
C/Z 14.6835 2.8259211 0.75 $ TFE12
C/S 14.6835 2.8259211 0.8 8 TFE12
C/S 14.6835 2.8259211 0.9 8 TFE12
C/Z 14.6835 2.8259211 0.95 $ TFE12
C/S 14.6835 2.8259211 1.0 8 TFE12
C/Z 14.6835 2.8259211 1.25 8 TFE12
C/S 14.6835 2.8259211 1.255 $ TFE12
C/S 17.9465 2.8259211 0.15 $ TFE13
C/S 17.9465 2.8259211 0.6 8 TFE13
C/Z 17.9465 2.8259211 0.75 $ TFE13
C/S 17.9465 2.8259211 0.8 $ TFE13
C/S 17.9465 2.8259211 0.9 $ TFE13
C/S 17.9465 2.8259211 0.95 8 TFE13
C/Z 17.9465 2.8259211 1.0 $ TFE13
C/S 17.9465 2.8259211 1.25 $ TFE13
C/S 17.9465 2.8259211 1.255 $ TFE13
C/S 21.2095 2.8259211 0.15 6 TFE14
C/Z 21.2095 2.8259211 0.6 $ TFE14
C/Z 21.2095 2.8259211 0.75 $ TFE14
C/S 21.2095 2.8259211 0.8 $ TFE14
C/S 21.2095 2.8259211 0.9 $ TFE14
C/S 21.2095 2.8259211 0.95 $ TFE14
C/S 21.2095 2.8259211 1.0 8 TFE14
C/Z 21.2095 2.8259211 1.25 $ TFE14
C/S 21.2095 2.8259211 1.255 8 TFE14
C/S 0 5.6518423 0.15 $ TFE15
C/S 0 5.6518423 0.6 $ TFE15
C/S 0 5.6518423 0.75 $ TFE15
C/S 0 5.6518423 0.8 $ TFE15
C/Z 0 5.6518423 0.9 $ TFE15
C/Z 0 5.6518423 0.95 $ TFE15
C/Z 0 5.6518423 1.0 8 TFE15
C/S 0 5.6518423 1.25 $ TFE15
C/S 0 5.6518423 1.255 $ TFE15
C/S 3.263 5.6518423 0.15 $ TFE16
C/S 3.263 5.6518423 0.6 $ TFE16
C/Z 3.263 5.6518423 0.75 $ TFE16
C/S 3.263 5.6518423 0.8 $ TFE16
C/S 3.263 5.6518423 0.9 $ TFE16
C/Z 3.263 5.6518423 0.95 $ TFE16
C/S 3.263 5.6518423 1.0 $ TFE16
C/S 3.263 5.6518423 1.25 $ TFE16
C/S 3.263 5.6518423 1.255 8 TFE16
C/S 6.526 5.6518423 0.15 $ TFE17
C/S 6.526 5.6518423 0.6 $ TFE17
C/S 6.526 5.6518423 0.75 $ TFE17
C/Z 6.526 5.6518423 0.8 $ TFE17
127
588589590591592593594595596597598599600601602603604605606607608609610611612613614615616617618619620621622623624625626627628629630631632633634635636637638639640641642643644645646647648649650651652653654655656657658659660661662663664665666667668669670671672673674675676677678679680681682683684685686687688689690-
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C/Z 6.526 5.6518423 0.9 $ TFE17
C/S 6.526 5.6518423 0.95 $ TFE17
C/Z 6.526 5.6518423 1.0 $ TFE17
C/Z 6.526 5.6518423 1.25 $ TFE17
C/S 6.526 5.6518423 1.255 $ TFE17
C/S 9.789 5.6518423 0.15 $ TFE18
C/2 9.789 5.6518423 0.6 $ TFE18
C/8 9.789 5.6518423 0.75 $ TFE18
C/8 9.789 5.6518423 0.8 $ TFE18
C/Z 9.789 5.6518423 0.9 $ Trine
C/Z 9.789 5.6518423 0.95 $ TFE18
C/S 9.789 5.6518423 1.0 $ TFE18
C/Z 9.789 5.6518423 1.25 $ TFE18
C/S 9.789 5.6518423 1.255 $ TFE18
C/8 13.052 5.6518423 0.15 $ TFE19
C/8 13.052 5.6518423 0.6 $ TFE19
C/8 13.052 5.6518423 0.75 $ TFE19
C/Z 13.052 5.6518423 0.8 $ TFE19
C/Z 13.052 5.6518423 0.9 $ TFE19
C/8 13.052 5.6518423 0.95 $ TFE19
C/S 13.052 5.6518423 1.0 $ TFE19
C/S 13.052 5.6518423 1.25 $ TFE19
C/S 13.052 5.6518423 1.255 $ TFE19
C/S 16.315 5.6518423 0.15 $ TFE20
C/Z 16.315 5.6518423 0.6 $ TFE20
C/Z 16.315 5.6518423 0.75 $ TFE20
C/Z 16.315 5.6518423 0.8 $ TFE20
C/Z 16.315 5.6518423 0.9 $ TFE20
C/Z 16.315 5.6518423 0.95 $ TFE20
C/Z 16.315 5.6518423 1.0 $ TFE20
C/8 16.315 5.6518423 1.25 $ TFE20
C/Z 16.315 5.6518423 1.255 $ TFE20
C/8 19.578 5.6518423 0.15 $ TFE21
C/8 19.578 5.6518423 0.6 $ TFE21
C/8 19.578 5.6518423 0.75 $ TFE21
C/S 19.578 5.6518423 0.8 $ TFE21
C/8 19.578 5.6518423 0.9 $ TFE21
C/8 19.578 5.6518423 0.95 $ TFE21
C/8 19.578 5.6518423 1.0 $ TFE21
C/Z 19.578 5.6518423 1.25 $ TFE21
C/S 19.578 5.6518423 1.255 $ TFE21
C/S 1.6315 8.4777634 0.15 $ TFE22
C/Z 1.6315 8.4777634 0.6 $ TFE22
C/Z 1.6315 8.4777634 0.75 $ TFE22
C/8 1.6315 8.4777634 0.8 $ TFE22
C/Z 1.6315 8.4777634 0.9 $ TFE22
C/Z 1.6315 8.4777634 0.95 $ TFE22
C/Z 1.6315 8.4777634 1.0 $ TFE22
C/Z 1.6315 8.4777634 1.25 $ TFE22
C/Z 1.6315 8.4777634 1.255 $ TFE22
C/Z 4.8945 8.4777634 0.15 $ TFE23
C/8 4.8945 8.4777634 0.6 $ TFE23
C/Z 4.8945 8.4777634 0.75 $ TFE23
C/S 4.8945 8.4777634 0.8 $ TFE23
C/S 4.8945 8.4777634 0.9 $ TFE23
C/Z 4.8945 8.4777634 0.95 $ TFE23
C/Z 4.8945 8.4777634 1.0 $ TFE23
C/8 4.8945 8.4777634 1.25 $ TFE23
C/8 4.8945 8.4777634 1.255 $ TFE23
C/8 8.1575 8.4777634 0.15 $ TFE24
C/8 8.1575 8.4777634 0.6 $ TFE24
C/8 8.1575 8.4777634 0.75 $ TFE24
C/8 8.1575 8.4777634 0.8 $ TFE24
C/Z 8.1575 8.4777634 0.9 $ TFE24
C/8 8.1575 8.4777634 0.95 $ TFE24
C/8 8.1575 8.4777634 1.0 $ TFE24
C/8 8.1575 8.4777634 1.25 $ TFE24
C/8 8.1575 8.4777634 1.255 $ TFE24
C/8 11.4205 8.4777634 0.15 $ TFE25
C/8 11.4205 8.4777634 0.6 $ TFE25
C/8 11.4205 8.4777634 0.75 $ TFE25
C/8 11.4205 8.4777634 0.8 $ TFE25
C/E 11.4205 8.4777634 0.9 $ TFE25
C/8 11.4205 8.4777634 0.95 $ TFE25
C/8 11.4205 8.4777634 1.0 $ TFE25
C/Z 11.4205 8.4777634 1.25 $ TFE25
C/S 11.4205 8.4777634 1.255 $ TFE25
C/Z 14.6835 8.4777634 0.15 $ TFE26
C/Z 14.6835 8.4777634 0.6 $ TFE26
C/S 14.6835 8.4777634 0.75 $ TFE26
C/8 14.6835 8.4777634 0.8 $ TFE26
C/8 14.6835 8.4777634 0.9 $ TFE26
C/8 14.6835 8.4777634 0.95 $ TFE26
C/Z 14.6835 8.4777634 1.0 $ TFE26
C/8 14.6835 8.4777634 1.25 $ TFE26
C/2 14.6835 8.4777634 1.255 $ TFE26
C/8 17.9465 8.4777634 0.15 $ TFE27
C/8 17.9465 8.4777634 0.6 $ TFE27
C/8 17.9465 8.4777634 0.75 $ TFE27
C/Z 17.9465 8.4777634 0.8 $ TFE27
C/S 17.9465 8.4777634 0.9 $ TFE27
C/8 17.9465 8.4777634 0.95 8 TFE27
C/Z 17.9465 8.4777634 1.0 $ TFE27
C/Z 17.9465 8.4777634 1.25 $ TFE27
C/8 17.9465 8.4777634 1.255 $ TFE27
C/Z 0 11.303684 0.15 $ TFE28
C/8 0 11.303684 0.6 $ TFE28
C/8 0 11.303684 0.75 $ TFE28
C/Z 0 11.303684 0.8 $ TFE28
C/8 0 11.303684 0.9 $ TFE28
C/8 0 11.303684 0.95 $ TFE28
C/8 0 11.303684 1.0 $ TFE28
C/Z 0 11.303684 1.25 $ TFE28
128
691692693694695696697698699700701702703704705706707708709710711712713714715716717718719720721722723724725726727728729730731732733734735736737738739740741742743744745746747748749750751752753754755756757758759760761762763764765766767768769770771772773774775776777778779780781782783784785786787788789790791792793-
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C/8 0 11.303684 1.255 $ TFE28
C/8 3.263 11.303684 0.15 $ 2rE29
C/8 3.263 11.303684 0.6 $ TFE29
C/8 9.263 11.303684 0.75 $ TFE29
C/S 3.263 11.303684 0.8 $ TFE29
C/8 3.263 11.303684 0.9 $ TFE29
C/S 3.263 11.303684 0.95 $ TFE29
C/S 3.263 11.303684 1.0 $ TFE29
C/8 3.263 11.303684 1.25 $ TFE29
C/S 3.263 11.303684 1.255 5 TFE29
C/8 6.526 11.303684 0.15 $ TFE30
C/S 6.526 11.303684 0.6 $ TFE30
C/8 6.526 11.303684 0.75 $ TFE30
C/8 6.526 11.303684 0.8 $ TFE30
C/S 6.526 11.303684 0.9 $ TFE30
C/8 6.526 11.303684 0.95 8 TFE30
C/8 6.526 11.303684 1.0 $ TFE30
C/S 6.526 11.303684 1.25 0 TFE30
C/8 6.526 11.303684 1.255 $ TFE30
C/S 9.789 11.303684 0.15 $ TFE31
C/8 9.789 11.303684 0.6 $ TFE31
C/S 9.789 11.303684 0.75 0 TFE31
C/8 9.789 11.303684 0.8 $ TFE31
C/Z 9.789 11.303684 0.9 $ TFE31
C/8 9.789 11.303684 0.95 $ TFE31
C/S 9.789 11.303684 1.0 $ 58E31
C/S 9.789 11.303684 1.25 $ TFE31
C/8 9.789 11.303684 1.255 8 5rE31
C/8 13.052 11.303684 0.15 $ TFE32
C/8 13.052 11.303684 0.6 $ TFE32
C/8 13.052 11.303684 0.75 $ TFE32
C/8 13.052 11.303684 0.8 $ TFE32
C/8 13.052 11.303684 0.9 $ TFE32
C/8 13.052 11.303684 0.95 $ TFE32
C/8 13.052 11.303684 1.0 $ TFE32
C/8 13.052 11.303684 1.25 $ TFE32
C/8 13.052 11.303684 1.255 $ TFE32
C/8 16.315 11.303684 0.15 $ TFE33
C/8 16.315 11.303684 0.6 $ TFE33
C/Z 16.315 11.303684 0.75 $ TFE33
C/8 16.315 11.303684 0.8 $ TFE33
C/8 16.315 11.303684 0.9 $ TFE33
C/8 16.315 11.303684 0.95 $ TFE33
C/S 16.315 11.303684 1.0 8 TFE33
C/8 16.315 11.303684 1.25 $ TFE33
C/S 16.315 11.303684 1.255 0 TFE33
C/Z 1.6315 14.129605 0.15 $ TFE34
C/S 1.6315 14.129605 0.6 $ TFE34
C/8 1.6315 14.129605 0.75 $ TFE34
C/S 1.6315 14.129605 0.8 $ TFE34
C/S 1.6315 14.129605 0.9 $ TFE34
C/8 1.6315 14.129605 0.95 $ TFE34
C/8 1.6315 14.129605 1.0 $ TFE34
C/8 1.6315 14.129605 1.25 $ TFE34
C/8 1.6315 14.129605 1.255 $ TFE34
C/Z 4.8945 14.129605 0.15 $ TFE35
C/S 4.8945 14.129605 0.6 $ TFE35
C/Z 4.8945 14.129605 0.75 $ TFE35
C/11 4.8945 14.129605 0.8 $ TFE35
C/S 4.8945 14.129605 0.9 $ TFE35
C/Z 4.8945 14.129605 0.95 $ TFE35
C/S 4.8945 14.129605 1.0 $ TFE35
C/8 4.8945 14.129605 1.25
C/8 4.8945 14.129605 1.255 $ TFE35
C/8 8.1575 14.129605 0.15 $ TFE36
C/8 8.1575 14.129605 0.6 8 TFE36
C/8 8.1575 14.129605 0.75 $ TFE36
C/S 8.1575 14.129605 0.8 $ TFE36
C/8 8.1575 14.129605 0.9 $ TFE36
C/Z 8.1575 14.129605 0.95 $ TFE36
C/8 8.1575 14.129605 1.0 $ 58E36
C/S 8.1575 14.129605 1.25 $ TFE36
C/S 8.1575 14.129605 1.255 $ 58E36
C/8 11.4205 14.129605 0.15 $ TFE37
C/S 11.4205 14.129605 0.6 $ TFE37
C/Z 11.4205 14.129605 0.75 $ 58E37
C/S 11.4205 14.129605 0.8 $ TFE37
C/S 11.4205 14.129605 0.9 $ TFE37
C/S 11.4205 14.129605 0.95 $ TFE37
C/S 11.4205 14.129605 1.0 $ TFE37
C/S 11.4205 14.129605 1.25 $ TFE37
C/8 11.4205 14.129605 1.255 $ TFE37
C/S 14.6835 14.129605 0.15 4 TFE38
C/S 14.6835 14.129605 0.6 $ TFE38
C/8 14.6835 14.129605 0.75 $ TFE38
C/8 14.6835 14.129605 0.8 $ TFE38
C/S 14.6835 14.129605 0.9 $ TFE38
C/8 14.6835 14.129605 0.95 $ 53E38
C/S 14.6835 14.129605 1.0 $ TFE38
C/8 14.6835 14.129605 1.25 $ TFE38
C/8 14.6835 14.129605 1.255 $ TFE38
C/8 0 16.955526 0.15 $ TFE39
C/S 0 16.955526 0.6 $ TFE39
C/S 0 16.955526 0.75 $ TFE39
C/8 0 16.955526 0.8 $ TFE39
C/8 0 16.955526 0.9 $ TFE39
C/S 0 16.955526 0.95 $ TFE39
C/Z 0 16.955526 1.0 $ TFE39
C/S 0 16.955526 1.25 $ TFE39
C/8 0 16.955526 1.255 $ TFE39
C/8 3.263 16.955526 0.15 $ TFE40
C/S 3.263 16.955526 0.6 $ TFE40
C/S 3.263 16.955526 0.75 $ TFE40
129
794795796797798799800801802803804805806807808809810811812813814e15816817818819820821822823824825826827828829830831832833834835836837838839840841842843844845846847848849850851852853854855856857858859860861862863864865866867868869870871872873874875876877878879880881882883884885886887888889890891892893894895896-
364
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NM
MS
MT8
N5
M14
A11
M4
NS
NIO
M7
MT7
F4:N
F7:N
C/Z 3.263 16.955526 0.8 $ TFE40
C/S 3.263 16.955526 0.9 $ TFE40
C/S 3.263 16.955526 0.95 $ TFE40
C/Z 3.263 16.955526 1.0 $ TFE40
C/Z 3.263 16.955526 1.25 $ TFE40
C/Z 3.263 16.955526 1.255 $ TFE40
C/S 6.526 16.955526 0.15 $ TFE41
C/S 6.526 16.955526 0.6 $ TFE41
C/S 6.526 16.955526 0.75 $ TFE41
C/S 6.526 16.955526 0.8 $ TFE41
C/Z 6.526 16.955526 0.9 $ TFE41
C/Z 6.526 16.955526 0.95 $ TFE41
c/z 6.526 16.955526 1.0 $ TFE41
C/8 6.526 16.955526 1.25 $ TFE41
C/Z 6.526 16.955526 1.255 $ TFE41
C/Z 9.789 16.955526 0.15 $ TFE42
C/S 9.789 16.955526 0.6 $ TFE42
C/Z 9.789 16.955526 0.75 $ TFE42
C/8 9.789 16.955526 0.8 $ TFE42
C/S 9.789 16.955526 0.9 $ TFE42
C/S 9.789 16.955526 0.95 $ TFE42
C/8 9.789 16.955526 1.0 $ TFE42
C/S 9.789 16.955526 1.25 $ TFE42
C/8 9.789 16.955526 1.255 $ TFE42
C/Z 13.052 16.955526 0.15 $ TFE43
C/8 13.052 16.955526 0.6 $ TFE43
C/S 13.052 16.955526 0.75 $ TFE43
C/S 13.052 16.955526 0.8 $ TFE43
C/S 13.052 16.955526 0.9 0 TFE43
C/S 13.052 16.955526 0.95 $ TFE43
C/Z 13.052 16.955526 1.0 $ TFE43
C/S 13.052 16.955526 1.25 $ TFE43
C/8 13.052 16.955526 1.255 $ TFE43
C/Z 1.6315 19.781448 0.15 $ TFE44
C/8 1.6315 19.781448 0.6 $ TFE44
C/S 1.6315 19.781448 0.75 $ TFE44
C/2 1.6315 19.781448 0.8 $ TFE44
C/8 1.6315 19.781448 0.9 $ TFE44
C/S 1.6315 19.781448 0.95 $ TFE44
C/S 1.6315 19.781448 1.0 $ TFE44
C/S 1.6315 19.781448 1.25 $ TFE44
C/S 1.6315 19.781448 1.255 $ TFE44
C/S 4.8945 19.781448 0.15 $ TFE45
C/S 4.8945 19.781448 0.6 $ TFE45
C/8 4.8945 19.781448 0.75 $ TFE45
C/Z 4.8945 19.781448 0.8 $ TFE45
C/Z 4.8945 19.781448 0.9 $ TFE45
C/S 4.8945 19.781448 0.95 $ TFE45
C/S 4.8945 19.781448 1.0 $ TFE45
C/Z 4.8945 19.781448 1.25 $ TFE45
C/Z 4.8945 19.781448 1.255 $ TFE45
C/Z 8.1575 19.781448 0.15 $ TFE46
C/Z 8.1575 19.781448 0.6 $ TFE46
C/Z 8.1575 19.781448 0.75 $ TFE46
C/Z 8.1575 19.781448 0.8 $ TFE46
C/Z 8.1575 19.781448 0.9 $ TFE46
C/Z 8.1575 19.781448 0.95 $ TFE46
C/S 8.1575 19.781448 1.0 $ TFE46
C/Z 8.1575 19.781448 1.25 $ TFE46
C/8 8.1575 19.781448 1.255 $ TFE46
$ BURNUP CELL MUST CONTAIN ALL 20 ISOTOPES IN ORDER.
$ 15-233 ISOTOPE NO. 1
1.00000000000000-300
$ 15-234 ISOTOPE NO. 2
1.00000000000000-300
$ 15-235 ISOTOPE NO. 3
9.50000000000000-001
$ U-236 ISOTOPE NO. 4
1.00000000000000-300
$ 15-237 ISOTOPE NO. 5
1.00000000000000-300
6
$ 15-238 ISOTOPE NO.
5.0000000000000D-002
$ U-239 ISOTOPE NO. 7
1.00000000000000 -300
8
$ 15-240 ISOTOPE NO.
1.00000000000000-300
$ NP237 ISOTOPE NO. 9
1.00000000000000-300
$ NON
$ NP238 ISOTOPE NO. 10
1.0000000000000D-300
$ NON
$ NP239 ISOTOPE NO. 11
1.00000000000000 -300
$ NON
$ NP240 ISOTOPE NO. 12
1.0000000000000D-300
$ PU238 ISOTOPE NO. 13
94238
1.00000000000000-300
$ PU239 ISOTOPE NO. 14
94239
1.00000000000000-300
$ PU240 ISOTOPE NO. 15
94240
1.00000000000000-300
$ PU241 ISOTOPE NO. 16
94241
1.00000000000000-300
$ PU242 ISOTOPE NO. 17
94242
1.00000000000000-300
$ A94241 ISOTOPE NO. 18
95241
1.00000000000000-300
ISOTOPE NO. 19
50999
1.00000000000000-300
$ F.P
$ 1-135 ISOTOPE NO. 20
$ NON
1.0000000000000D-300
$ XE135 ISOTOPE NO. 21
54135
1.00000000000000-300
$ PM149 ISOTOPE NO. 22
$ NON
1.0000000000000D-300
$ 5W149 ISOTOPE NO. 23
62149
1.00000000000000-300
8016
2.00000000000000+000
$ OXY0 ISOTOPE NO. 24
$ GANAT ISOTOPE NO. 25
64000
1.00000000000000-300
40000 1 1001 1.84 $ zrit
H/SR.05T SR/H.05T
11023 -0.78 19000 -0.22 $ NaK
74184 1 $ pure W-184
42000 -0.329 4009 -0.0402 8016 -0.08 74000 -0.106 41093 -0.444 0 top rod
41093 1 $ Nb
1001 1 $ cesium
13027 2 8016 3 $ A1203
4009 1 8016 1 $ Be0
BE.05T
8 17 26 35 44 53 62 71 SO 89 98 107 116 125 134 143 152 161 170
179 188 197 206 215 224 233 242 251 260 269 278 287 296 305 314
323 332 341 350 359 368 377 386 395 404 413
8 17 26 35 44 53 62 71 80 89 98 107 116 125 134 143 152 161 170
179 188 197 206 215 224 233 242 251 260 269 278 287 296 305 314
323 332 341 350 359 368 377 386 395 404 413
92233
92234
92235
92236
92237
92238
92239
92240
93237
130
897898899900901902903904905906907908909910911-
KCODE
KSRC
1000 1. 5 250
0.15 2R
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
BURN
8831.544737
1
46875
46875
13
15
46875
46875
60
90
46875
185
46875
365
46875
730
46875
1095 46875
1
46875
DENSITY
GRAM
DENSITY
0.00000E+00
0.00000E+00
1.42558E-01
1.42558E-01
2.04547E-02
1.02897E-01
0.00000E+00
6.76165E-02
0.00000E+00
0.00000E+00
2.96000E+00
2.96000E+00
1.86000E+00
5.60000E+00
0.00000E+00
1.00000E+01
ATOM
//
//
CELL
MAT
1
2
1
0
2
0
3
3
4
4
7
5
5
11
6
7
8
6
7
8
8
0
1
7
VOLUME
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
2.22183E-01
3.33275E+00
TRUNCATED MANUALLY DUE TO LENGTH OF DOCUMENT
419
420
419
420
5
4
1.78649E-02
5.46330E-02
7.50000E-01
8.42860E+00
TOTAL
NUMBER OF BURNUP STEPS
CORE TOTAL VOLUME (CC)
CORE FUEL REGION FRACTION
CORE TOTAL NTIHM
AVERAGE CORE LOADING (0/CC)
VOLUME
CC
LATTICE
8
17
26
35
44
53
62
71
80
89
98
107
116
125
134
143
152
161
170
179
188
197
206
215
224
233
242
251
260
269
278
287
296
305
314
323
332
341
350
359
368
377
386
395
404
413
MCNI,
5.4181E+01
1.0836E+02
1.0836E+02
1.0836E+02
1.0836E+02
1.0836E+02
1.0836E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
1.0836E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
1.0836E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
1.0836E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
2.1673E+02
1 STARTS AT
ENDS AT
STEP INPUT THERMAL POWER:
!
2.22183E+01
4.94728E-01
1.66637E+01
4.16986E+00
2.53515E+03
1.65682E+04
10
8.83154E+03
6.15111E-02
4.78195E-03
5.41462E-01
LOADING
G/CC
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
5.4146E-01
MASS
GRAM
2.9337E+01
5.8674E+01
5.8674E+01
5.8674E+01
5.8674E+01
5.8674E+01
5.8674E+01
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
5.8674E+01
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
5.8674E+01
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
5.8674E+01
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
1.1735E+02
/BURNUP/ VERSION 393
BURNUP STEP
MASS
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
0.00000E+00
3.33275E+01
09/01/93
0.000
1.00
DAYS
DAYS
4.6875E+04 WATTS.
22:03:58.90
14
00300 W0 W0 0 WW0 00 0 0000000 0 W0 0 0 0 W0 0 0 0 0 0 0 0000000000.41
0000000000000000000000000000000000000000000000M
0 00000000003000000000 0 0 0 0 0 00 0 0 0000 00000 00 0 0 0 0 0 01+1 H
HPHHHHHHHHHHI,PHHI..HF.HHPHI.. +++++ HpHHHWHI.HHF.F.HPHHH
WWW00000MOMWWWWWWWW0MM0M00000MOW00000WWWW00000
0000000000000000000000000000000000000000000000
mNwmmmmtvmmi.m.MMNKINIONmmivmnaNKINNNNtommtomr4NNNmmmMNN
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWH
MPIMMMWMPIMMMMIIMOIMMMMPIMMMMPIMMVIMMMMMMMMMMMMINMNPIMRn
0000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000 H
oZ
wWWWWwwWWwwwWWWWW,WWWWWWWWWW,WWWWWWWW,VWWWVVWWWWW
i.O.WWWWWWWWWWWNPONNWONNMAINF.HHFAHHWHHHH
1..0,00J0NWW.D.WNHOWW4OWd.WNHOWMJJmWOWNF.OWWW-40,1WPWNH
W.1.0m..10wOHNW.F.OMJWMOYMW&WMJMW01.MWO.Wm.40.00HMWs.WMJ0
H0
................................................
1...HHHHHI+HI.,HYHHHHHHHHHPHI.,rialayHHHHHpl...F.HHeYHH,WH
J.4.4.JJ,JJ.4.4JJJJ-JJ.4JJJJ-JJJJ4J.J,74JJJJJJ-JJJJJJJ,I,JJJWO
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWHZ
TTITTT7TVITITTMITIVITYITTITTVITTITTITTTTITIVi
Falah.HHI..F.HHHHHHHHHHH1,1-.HHHI+HHHPHHI,HHHHHPPI,I,R
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW %
0000000000000000000000000000000000000000000000W
rommi.roloton,NmNhamMmmtoNtomWommt.mr.mr4NrotomMMN,rommNfolviommt0H0
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWM%
VITITIVVVITIVITYTITTITTITITVITITITTTITT7TV7777
0000000000000000000000000000000000000000000000 p
0000000000000000000000000000000000000000000000
WWWWWMWNwMWWWWWWWWNWWWWWWWWWWWWNWNWWWWWNNNNmmN
OM$NMWAVARtWOAWItarVIRMAtarARAVVAV
,++,
+++ ++, +
0000000000000000000000000000000000000000000000
WOMw.C.4.6.m0WMWJwA0mdsOCONosOtoHc.wNroHo.W.I.WWWW.J.10wWOH
++ ++++ +++++ ++ +++++ +++++++
1.1.,1.1-.Hwl+WHWHHHHHF.HHmHHHHHHotHWHHHHHOO.WmmmW
F.HHWOm0H4000H0OHFAE.H0OHMNHOON,,,W0H00HMW&HmJWWw0
JmwmPcoNHWMNOw000.e.w.1.0WmWWwWf..M00.1>WmWONWWAOMmvJWJP4
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW%
AT,Va4lgtanggMaRNVNNRIMARga4Pg$APNIRM4ANARn
+++++++++++++++++++++++++++++++++
+,+++++++++++Hoo
00000000000000000000000000000000000000000000000H
0000000000000000000000000000000000000000000000%0z
i
PoNNKINMmMNIoNtoroNloMMN.ONNMNNN.NMPorotototorololoNNNNI,~014NNN
WWWWW.A.C.WP&PaWl.d.S.C.C.W +++++ W ++++++ W ++++++ Wdadap0o0 \M
001 40w1+0FamF.HI,MmF.HNHF,m1-.t.toHy.%1-.MHMI,NMHHI...4.H0NHyHYHHM
%
PRArRAgMAVRAMAAIMARRPM4W4MaRVNPNARRaRRrn
+ +++++++++++++++++++++++++++++++++++++++++++++ O
0
1...HH1-1+1,1+HHHHHI..1.1-.1-.1-HHHP1...HHHHHHH0
NoWAWW0...P.Mm00.0.140wWWmlowHJw&OweOMMOC.PwAHNC.O.PNWWQ
WWI.W.WMmWMmJWPMJ4000emJOHHWMCDWHNNWOJw.HWWW00
0..WWWWWWC.OMMOWWw0HOHOWWHOMOOPWWWwt.OJwW0i.ONO&NwM%
WWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWWW
WiMM.I.IMMMIMMIT,M$1.1.M$1111MfMq
MIIFITYTMWTTOMfff$MqffMffMTOMForl
0000000000000000000000000000000000000000000000H0
Pl...Hp..1..HHI..H.F.HFAHHI..PyHHI-.1-.HHHHHHHHHI..HHHHIMM
mt..NNNForotommmmNNMNNIOMMMNNWNNMmmioPolotoNtoNNWMP0MNKINNO%
NW.taNalAchmWa.mJal&WQMwwWmJWOHWWJwIst.NNOJoHMWC.mMHI,MWID
.4.1..WYN01-..wWWOHmWalmJmOWJJWM4Wm&PWCON.00.m0NN,JOMMHMO
OWWWW00..m0OWOOMOWwWWW0WH.C.owSad.JP&WM0000M0
F.Hh.p.1-.H1+Hi+HF.H1...HHP..HWHHHHMNI+HHHNNMFAHHHMNAIHHHNNKINZM
H HHYHHPHF..1... +++++ HHFAHHIaHHHPHI...1,HHHHI.,PPHHHHHPHHHI-.1-.
AAApWNNIOWNNNWAMmWWW&WWWWWWMWWWWW.1.1010WWWWWI.WWWWWZ
01-.4.0W01-.WJMMOMOMMHNoTOJHmOOMMNHOwOMOIMNNJS.047M0-.4.0N
MI.OWPWWW000%00%01-.4.WHOOWPWWw0WWWWOOmmWmoN0WPIOJWg
OJW,0001-.0lne..ommiqmMMW.1.01...wm&m0WmJUIJMMWPO0MHHN.w.1
NwNAWMms.JJ0MW.INWWW0W0MOWHHJwWmmmi.WOMM0WOHJWWOHn
MOIMMMMPIMMMMMMMPIMMNPIMMNPIMMMMNVIMMMMNPIMMMMMNPIMMMM
+ ++4++++++++++++++++ +++++++++++++++++++ + ++++++
1...Hi..p..11+1..ii...1-.1....i...faH1+1+1-PHP,P.I.,laiapi+1-.Mr.
As.WWWWWWWWWWWWMNMMMNIoNNNPF.PHHHHHI+HH
F.O.DMJMWOPWNH000JmPWHOwOJJWd.W101-.0w00JM
W.I.OmJ0wOHNWPWOJ0wOHMW&WmJ0.DOHNWPOMJ0WOHmWs.OmJ0
N
t-.
..
OW
4.0
OJ
roJ
M%
1+
00
1,0
R
rnK
AN
HZ
R40
li
H
g
132
CRITICALITY:
ESTIMATOR
K(COLLISION)
K(ABSOR3T/ON)
K(TRK LENGTH)
CYCLE
250
1.096337
1.096392
1.096257
COMBINATION
K(COL/ABS)
K(ABS/TR LK)
K(TK LN/COL)
245
AVE OF
1.105479
1.104952
1.106174
SIMPLE AVERAGE
1.105216 0.0014
1.105563 0.0017
1.105827 0.0017
CYCLES
0.0015
0.0014
0.0024
COMINED AVERAGE
CORR
0.9231
0.4789
0.5623
1.105010 0.0014
1.105044 0.0014
1.105514 0.0015
CELL:
ISOTOPE
ATOM DENS.
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
0.000000E+00
0.000000E+00
2.141189E-02
0.000000E+00
0.000000E+00
1.126941E-03
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
4.507765E-02
0.000000E+00
6.761648E-02
(atom/b.cm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
BURNUP CONVERSION FACTOR
CELL:
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
WEIGHT %
0.0000E+00
0.0000E+00
9.4939E+01
0.0000E+00
0.0000E+00
5.0607E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
1.0000E+02
B CHANGE
FROM DIN
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
WEIGHT B
/HM
0.0000E+00
0.0000E+00
9.4939E+01
0.0000E+00
0.0000E+00
5.0607E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
1.0000E+02
B CHANGE
FROM INN
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000 B
413
ISOTOPE
ATOM DENS.
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
0.000000E+00
0.000000E+00
2.141189E-02
0.000000E+00
0.000000E+00
1.126941E-03
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
0.000000E+00
4.507765E-02
0.000000E+00
6.761648E-02
(atom/b.om)
1
CURRENT
LOAD(GM)
0.0000E+00
0.0000E+00
2.7852E+01
0.0000E+00
0.0000E+00
1.4847E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0,0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
3.9904E+00
0.0000E+00
3.3327E+01
BURNUP CONVERSION FACTOR
CURRENT
LOAD(G4)
0.0000E+00
0.0000E+00
1.1141E+02
0.0000E+00
0.0000E+00
5.9387E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
0.0000E+00
1.5962E+01
0.0000E+00
1.3331E+02
0.0000 B
1TALLY FLUCTUATION CHARTS
TALLY
NPS
16000
32000
48000
64000
80000
96000
112000
128000
144000
160000
176000
192000
208000
224000
240000
250128
TALLY
4
MEAN
6.39876E-03
6.13161E-03
6.49375E-03
6.65824E-03
6.62109E-03
6.53186E-03
6.67282E-03
6.62925E-03
6.58786E-03
6.63142E-03
6.65875E-03
6.58774E-03
6.55713E-03
6.55829E-03
6.56010E-03
6.60305E-03
ERROR
0.0761
0.0514
0.0401
0.0342
0.0310
0.0282
0.0258
0.0240
0.0225
0.0212
0.0202
0.0194
0.0185
0.0178
0.0172
0.0168
FOM
7.3E+00
6.4E+00
6.6E+00
6.6E+00
6.3E+00
6.3E+00
6.4E+00
6.4E+00
6.3E+00
6.5E+00
6.5E+00
6.5E+00
6.5E+00
6.5E+00
6.6E+00
6.6E+00
7
MEAN
2.02122E-02
1.79999E-02
1.96604E-02
1.91061E-02
1.81909E -02
1.77042E-02
1.82804E-02
1.77824E-02
1.79419E-02
1.80767E-02
1.79750E-02
1.75852E-02
1.78721E-02
1.78471E-02
1.78488E-02
1.79677E-02
ERROR
TOM
0.1527
0.0984
0.0760
0.0639
0.0559
0.0505
0.0459
0.0431
0.0404
0.0386
0.0371
0.0355
0.0344
0.0330
0.0318
0.0310
1.8E+00
1.8E+00
1.8E+00
1.9E+00
1.9E+00
2.0E+00
2.0E+00
2.0E+00
2.0E+00
2.0E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
133
TALLY
NPS
16000
32000
48000
64000
80000
96000
112000
128000
144000
160000
176000
192000
208000
224000
240000
250128
MOM
24
MEAN
ERROR
POW
1.65261E-02 0.1527 1.8E+00
1.47172E-02 0.0984 1.8E+00
1.60749E-02
1.56217E-02
1.48734E-02
1.44754E-02
1.49466E-02
1.45394E-02
1.466985-02
1.47800E-02
1.46969E-02
1.43781E-02
1.461275-02
1.45923E-02
1.45937E-02
1.46909E-02
0.0760
0.0639
0.0559
0.0505
0.0459
0.0431
0.0404
0.0386
0.0371
0.0355
0.0344
0.0330
0.0318
0.0310
/BURNUP/ VERSION 383
BURNUP STEP
2 STARTS AT
ENDS AT
8
17
IRRADIATION
NMD/TE
1.3723E+02
1.3723E+02
// TRUNCATED
//
MCNP
Q- FISSION
17
26
35
44
53
62
71
80
89
98
107
116
125
134
143
152
161
170
179
188
197
206
215
224
233
242
251
260
269
278
287
296
305
314
323
332
341
350
359
368
377
386
395
404
413
DAYS
DAYS
NU-FISSION
N /FISSION
2.4436E+00
2.4424E+00
FISION RATE
FISSION/8
1.6175E+15
1.6175E+15
MANUALLY DUE TO LENGTH OF DOCUMENT I
/BURNUP/ VERSION 383
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
8
07:13:57.37
4.6875E+04 WATTS.
5.3077E+00 KW/LITER
8.8876E-01
MeV/FISSION
1.8088E+02
1.8088E+02
BURNUP STEP 10 STARTS AT
ENDS AT
CELL
09/02/93
1.00
14.0
STEP INPUT THERMAL POWER:
AVERAGE POWER DENSITY:
POWER NORMALIZATION FACTOR:
CELL
1.8E+00
1.9E+00
1.9E+00
2.0E+00
2.0E+00
2.0E+00
2.0E+00
2.0E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
1.9E+00
IRRADIATION
NMD/TE
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
2.5045E+04
09/05/93
0.255E+04 DAYS
0.255E+04 DAYS
4.6875E+04 WATTS.
5.3077E+00 KW/LITER
8.8855E-01
Q-FISSION
NAV/FISS/ON
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
1.8088E+02
NU-FISSION
N/FISSION
2.4425E+00
2.4422E+00
2.4408E+00
2.4420E+00
2.4434E+00
2.4418E+00
2.4383E+00
2.4430E+00
2.4425E+00
2.4418E+00
2.4424E+00
2.4431E+00
2.4409E+00
2.4355E+00
2.4423E+00
2.4421E+00
2.4424E+00
2.4420E+00
2.4421E+00
2.4413E+00
2.4359E+00
2.4420E+00
2.4421E+00
2.4427E+00
2.4427E+00
2.4417E+00
2.4369E+00
2.4426E+00
2.4419E+00
2.4417E+00
2.4415E+00
2.4405E+00
2.4369E+00
2.4419E+00
2.4420E+00
2.4416E+00
2.4407E+00
2.4364E+00
2.4413E+00
2.4411E+00
2.4406E+00
2.4391E+00
2.4353E+00
2.4374E+00
2.4367E+00
2.4360E+00
FISION RATE
FISSION/S
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
1.6175E+15
08:35:00.58
134
CELL
THERMAL FLUX
N/cM/CM/S
3.7406E+11
3.7372E+11
3.6357E+11
3.5151E+11
2.9738E+11
2.7357E+11
3.3839E+11
3.8976E+11
3.6938E+11
3.6853E+11
3.2204E+11
2.9818E+11
2.8940E+11
4.1497E+11
3.8534E+11
3.6506E+11
3.5632E+11
3.3896E+11
2.9857E+11
3.0792E+11
3.9757E+11
3.5374E+11
3.5342E+11
3.0635E+11
3.0449E+11
2.8932E+11
4.1526E+11
3.2950E+11
3.3735E+11
3.1656E+11
3.0058E+11
2.9739E+11
4.1950E+11
3.1444E+11
2.7825E+11
2.7893E+11
2.9303E+11
3.9062E+11
2.9812E+11
2.9544E+11
2.9262E+11
3.3867E+11
4.1985E+11
4.2497E+11
4.1037E+11
4.2136E+11
8
17
26
35
44
53
62
71
80
89
98
107
116
125
134
143
152
161
170
179
188
197
206
215
224
233
242
251
260
269
278
287
296
305
314
323
332
341
350
359
368
377
386
395
404
413
FAST FLUX
N/Cm/Cm/s
2.3725E+13
2.2806E+13
2.1737E+13
2.0720E+13
1.8299E+13
1.6178E+13
1.4162E+13
2.2949E+13
2.2607E+13
2.1078E+13
1.9478E+13
1.7538E+13
1.5128E+13
1.2756E+13
2.3121E+13
2.2169E+13
2.1792E+13
1.9986E+13
1.7854E+13
1.5825E+13
1.3240E+13
2.1528E+13
2.0839E+13
1.9668E+13
1.8147E+13
1.6330E+13
1.3736E+13
1.9930E+13
1.9571E+13
1.8681E+13
1.7247E+13
1.5776E+13
1.4234E+13
1.8424E+13
1.7414E+13
1.6703E+13
1.5090E+13
1.3597E+13
1.6576E+13
1.5935E+13
1.4988E+13
1.4379E+13
1.2845E+13
1.3967E+13
1.3914E+13
1.2873E+13
TOTAL FLUX
N/Cm/cMVS,
2.4099E+13
2.3179E+13
2.2101E+13
2.1071E+13
1.8597E+13
1.6452E+13
1.4500E+13
2.3339E+13
2.2976E+13
2.1447E+13
1.9800E+13
1.7836E+13
1.5417E+13
1.3171E+13
2.3507E+13
2.2534E+13
2.2148E+13
2.0325E+13
1.8153E+13
1.6133E+13
1.3638E+13
2.1882E+13
2.1192E+13
1.9975E+13
1.8452E+13
1.6619E+13
1.4151E+13
2.0260E+13
1.9908E+13
1.8998E+13
1.7548E+13
1.6074E+13
1.4653E+13
1.8738E+13
1.7692E+13
1.6982E+13
1.5383E+13
1.3988E+13
1.6874E+13
1.6231E+13
1.5281E+13
1.4717E+13
1.3265E+13
1.4392E+13
1.4324E+13
1.3295E+13
sp. POWER
MW/TE
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
9.8025E+00
POWER
WATTS
3.5298E+02
6.8388E+02
6.7330E+02
6.3563E+02
5.4971E+02
4.9875E+02
5.3646E+02
1.3784E+03
1.3681E+03
1.2877E+03
1.1663E+03
1.0407E+03
9.7250E+02
1.1511E+03
6.8593E+02
1.3312E+03
1.3042E+03
1.2085E+03
1.0768E+03
1.0086E+03
1.1206E+03
1.2819E+03
1.2530E+03
1.1563E+03
1.0930E+03
1.0304E+03
1.1751E+03
5.9314E+02
1.2001E+03
1.1528E+03
1.0601E+03
1.0261E+03
1.1963E+03
1.1240E+03
1.0544E+03
1.0264E+03
9.8930E+02
1.154E1E+03
5.2725E+02
9.9723E+02
9.8703E+02
1.0551E+03
1.1678E+03
1.1854E+03
1.1883E+03
1.1685E+03
CRITICALITY:
ESTIMATOR
K(COLLISION)
MA3SORPTION)
K(TRK LENGTH)
COMBINATION
K(cOL/ABS)
K(ABS/TK LN)
K(TK Lei/COL)
CYCLE
250
1.053118
1.050015
1.034105
AVE OF
245
1.104660
1.104737
1.102887
SIMPLE AVERAGE
1.104699 0.0015
1.103812 0.0017
1.103774 0.0018
CYCLES
0.0016
0.0015
0.0024
COMBINED AVERAGE
1.104729 0.0015
1.104588 0.0015
1.104527 0.0016
CORR
0.9236
0.5540
0.6148
CELL:
ISOTOPE
ATOM DENS.
92233
92234
92235
92236
92237
92238
92239
92240
93237
93238
93239
93240
94238
94239
94240
94241
94242
95241
50999
53135
54135
61149
62149
8016
64000
3.738768E-10
3.771509E-07
2.041589E-02
2.116602E-04
6.008454E-08
1.116368E-03
8.580546E-11
1.999594E-16
8.083827E-06
5.530366E-10
1.240661E-08
1.463797E-17
1.557947E-07
9.075157E-06
2.228952E-07
2.030942E-08
2.016433E-10
1.633537E-09
9.794067E-04
7.372805E-09
1.085584E-08
1.045006E-08
2.745823E-06
4.507675E-02
0.000000E+00
6.782086E-02
(atam/b.cm)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TOTAL:
BURNUP CONVERSION FACTOR
CURRENT
LOAD(OM)
4.8219E-07
4.8850E-04
2.6557E+01
2.7650E-01
7.8849E-05
1.4707E+00
1.1355E-07
2.6574E-13
1.0605E-02
7.2858E-07
1.6414E-05
1.9447E-14
2.0525E-04
1.2006E-02
2.9612E-04
2.7103E-05
2.7012E-07
2.1792E-06
6.3417E-01
5.5072E-06
8.1051E-06
8.6124E-06
2.2630E-03
3.9903E+00
0.0000E+00
3.2955E+01
WEIGHT 8
1MM
1.6436E-06
1.6651E-03
9.0523E+01
9.4249E-01
2.6877E-04
5.0132E+00
3.8707E-07
9.0580E-13
3.6149E-02
2.4835E-06
5.5948E-05
6.6287E-14
6.9962E-04
4.0925E-02
1.0094E-03
9.2383E-05
9.2076E-07
7.4283E-06
2.1617E+00
1.8772E-05
2.7627E-05
2.9357E-05
7.7136E-03
0.0000E+00
0.0000E+00
9.8729E+01
0.0446 %
// TRUNCATED MANUALLY DUE TO LENGTH OF DOCUMENT
//
!
8 CHANGE
FROM THIN
1.6588E-06
1.6733E-03
-4.4190E+00
9.3909E-01
2.6658E-04
-4.6914E-02
3.8070E-07
8.8718E-13
3.5866E-02
2.4537E-06
5.5046E-05
6.4946E-14
6.9123E-04
4.0265E-02
9.8894E-04
9.0109E-05
8.9465E-07
7.2477E-06
4.3454E+00
3.2712E-05
4.8165E-05
4.6365E-05
1.2183E-02
-4.0071E-03
0.0000E+00
9.0679E-01
135
Burnable Poison in Selected TFEs
B.
This is a partial listing similar to the standard but shows the changes in the
poisoned TFEs.
MCNP
123456789-
10111213-
/BURNUP/ VERSION 383
01:21:27.05
09/06/93
pitch.1.3 cm /burnup/
ati driver reactor reference startup radlus=24 cm
0 (-3:-4:-6:2:5) -1 IMP:N=0 TMP6.9896795E-8 $ outside reactor Void outsi
1
0 (-3:-4:-6:2:5) 1 IMP:N.0 TMP6.9896795E-8 $ infinity Void outside react
2
7 -2.96 -7 8 -2 4 6 IMP:N.1 TIMP6.9896795E-8 $ top reflector Reflector
3
7 -2.96 7 -5 -2 3 4 6 IMP:N=1 TMP=6.9896795E-8 8 outer reflector Reflect°
4
11 -1.86 -7 9 -8 4 6 IMP:N=1 7MP-6.9896795E-8 $ top of core region Reflec
5
6
8 -5.6 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 0 moder
171 180 189 198 207 216 225 234 243 252 261 270 279 288 297 306
315 324 333 342 351 360 369 378 387 396 405 414 423 -9 -7 3 4 6
IMP:N=1 TMP=6.9896795E-8
0 -10 -9 3 4 6 IMP:N=1 TMF1.6399443E-7 VOL- 2.2218324E -1 $ void TFE1
7
101 -10.0 10 -11 -9 3 4 6 I4P:14.1 TMP1.6399443E-7 VOL=3.3327486 $ fuel T
8
9
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138
MATRIX OPERATOR MATHEMATICS
APPENDIX III:
The following theory and solution was adopted in subroutine SOLVER and its
auxiliary subroutines is from work done for the computer code LEAF (Lee & Foley, 1976).
The theory presented here is based on that work modified to fit the variables and
parameter in this work.
if the matricent AttoR (Lee, Apperson, & Foley, 1976) is defined ass
A:0(R) = I
+
IdtR(t) + Idt R(t) Ida R(a)
to
to
(1)
to
converges absolutely and uniformly in every closed interval in which R(t) is continuous,
then one may write the solution
X(t) = A:0(R) X(t)
.
(2)
Dividing the interval (to,t) into N parts by introducing the intermediate points t; (1 5 i 5 N-1)
and setting At = t 1 - t
for 1 5 I 5. N-1 with t=tN and t=to, it is readily shown that
Atto(R)
eR,2At2 eR,1,6113
= lim [ eRt,,AtN
(3)
At,)0
The various values of the matrix function R(t) are, in general, not permutable in the time
subinterval At,. In the very special case in which they are permutable, namely
( R[, R[/) = Ri Rf
Rte Rtt
(4)
for t', t", (to, t), then eq.(2) becomes
Ids R,
Atto(R) = e
(5)
For example, if Rt. = constant for VE (to, t), then eq.(3) is satisfied and substitution of eq.(1)
5
I is the identity matrix.
139
yields the solution
(6)
X(t) = Xto eR
This solution is valid for the assumption that the flux is constant in a time interval (to, t).
the matrix operator eRt is defined by
eRt E
(RT)!
(7)
P!
which is exactly the result obtained from evaluating the matricent AtotR in eq.(49) of the
thesis text. provided eq.(3) is satisfied. Since R has eigenvalues with negative real parts,
it is trivially true that et is non - negatives and has eigenvalues
p(eRt)=
e-'
r
(8)
where A and r are the real and imaginary parts of the eigenvalues of (RXAT. Hence,
0
1p I
Now consider the explicit evaluation of eRt.
(9)
1
Although by eq.(8) the magnitude of the
eigenvalues of the e5T are bounded by unity, and eq.(6) is uniformly and absolutely
convergent, the direct usage of eq.(6) for cases such that IIRTII >> 1 can lead to a
computational catastrophe.
Rewriting eq.(5) as
X(t) = X(to) + CD(C) X(to)
which is an identity if C=Ilt(t-t0),
and defining
D(C) =
Ct
=
(10)
" (P-1-1)!
Clearly the matrix D(C) exists even if C is singular'.
Although the eigenvalue of p, eq.(7), are bounded by unity, and the eigenvalues of C are
is non-negative.
6
if Rik > 0 for j#1c, et = 1+ R T
7
for example, for a decay scheme involving a stable isotope, C is singular.
140
bounded, the fact that the eigenvalues C, (A ± iF)T, are not necessarily bounded by unity
is what causes the difficulty in evaluating eq.(6) or eq.(9) directly. Using the laws of
exponentiation (Lee, Apperson, & Foley, 1976) the matrix C may readily be scaled until
its eigenvalues are bounded by unity and then compute e using a recursion relationship
to scale back up to RT. If the matrix H defined by
H = 24D C
to have eigenvalues less than unity, then P may be determined from
(12)
2P > E I Cjk 12
j,k
or
ISk 12)
(13)
j,k
In 2
where LN is the natural logarithm. Now from eq.(9)
D(H) = H-1(e"-.1)
C = 2P H
,
(14)
(15)
The following is a derivation and proof of the recursion relationship by induction. If P=0
D(H)=D(C)
if P=1, and since (H,H)=0, then
D(C) = D(2H)
= (2H)-1(e2H-1)
= H-1(e"-1)1/2(eH+1)
= D(H)(I+Y2HD(H))
Now, by induction it can be shown that
141
D(2PH) = D(2"H)(1+(2P-1H)D(2P-1H))
(16)
2
D(C)
Suppose eq.(15), which is true for P =O, 1, is true for P=n, then evaluate D(2"1 H) as
D(2" H) = (2"H)(e2n""- I)
(e2n" -I)(e2nH +I)
= (2"1-1)
= D(2"1-I)(1+
2
(2°H)D(2" H)
(17)
2
and the only equation used is eq.(16) and (H,H)=0. Therefore, since eq.(15) has the
same form as eq.(16), then by induction it is true for all PX).
The evaluation of the matrix D(H) is approximated, of course, by a finite number of terms.
Denote this approximation by
Dm(H)
=E
H1 F1-1(eH-1)
(p +1)!
2
(18)
and evaluate it as a factorial matrix polynomial
Dm(H) = H(I+_ (1+...(--- (1+ )-.))))
H
H
H
2
2
(19)
m
From the mth term backwards, where m is a suitably chosen integer. If it is assumed that
IHI < 1/2
,
then the first term omitted contributes one error, Env of order
£m =
1
11-1
(m+2)!
(20)
2m41(m+2)!
For example, for m=1 the error is of order 4.17 X 10-2 and for m=20, Em= 4.24 X 10-28.
The direct evaluation of
D(C) =C-1 (ec
i) =
C"
E (n+1)!
(21)
n=0
would prove difficult computationally, rather the matrix C can be scaled so that the
eigenvalues are bounded by unity.
142
Define
B = 2-P C
where P is determined by IBI <1/2 or
1n(E I
P=
C..12)
(22)
"
2 In2
Since
= T AU, where
= At/2"P then
In(E I
P=
TA..12)
In (1E Aq 12 IT 12)
ij
2In2
2 In2
In(E I C412)
P=
(24)
"
2 In2
In(E 1
P=
"
A412) An IT 12
"
(25)
2 In2
In(E I Au 12) +2 In 1T1
P=
(23)
(26)
2 In2
When NP = 0 then P can be determined as
In(E P4)+2 In (A)
P=
2 1n2
D(B) matrix operator is then approximated by a finite number of terms m,
(27)
143
m
Dm (B) = E
B"
(28)
r14) (n +1)!
m is determined such that the excluded terms have an error less than some e, or
E
= 0, i
1131mA
1
(m +2)!
2""l(m +2)!
(29)
j
B71 = 1, i = j
Fm =
1
m +2 --k
DTi = Fm x B71
k=1, m
(30)