Polaris: 2D Light Water Reactor Lattice Physics Module

M. A. Jessee, J. J. Jarrell, W. A. Wieselquist, M. L. Williams, K. S. Kim, T. M. Evans, S. P. Hamilton, C. A. Gentry

Polaris is a new module for SCALE 6.2 that provides 2D lattice physics analysis capability for light water reactor (LWR) fuel designs. Polaris uses a new multigroup self-shielding method called the Embedded Self Shielding Method (ESSM) and a new transport solver based on the Method of Characteristics (MoC). The ESSM computes multigroup self-shielded cross sections using Bondarenko interpolation methods. The background cross section used in the interpolation is determined by iterative 2D MoC fixed source transport calculations. Polaris is integrated with ORIGEN for depletion calculations. Each pin—or each radial subregion of the pin—is depleted based on the local power distribution. An optional critical spectrum calculation is incorporated into the depletion calculation and the output edits of few-group homogenized cross sections. Few-group cross sections are archived to an xfile016 file, which can be used in subsequent core simulator calculations. Polaris provides an easy-to-use input format to allow users to set up lattice models with minimal lines of input.

Acknowledgments

The authors express gratitude to Brad Rearden and Stephen Bowman for their supervision of Polaris development for the US Nuclear Regulatory Commission (NRC). The author acknowledges Don Algama and Mourad Aissa of the NRC for their support of the project. Appreciation is extended to the ATLAS development team—Jordan Lefebvre, Rob Lefebvre, and Adam Thompson—for their development of the ATLAS Ray Tracing Geometry package used in the Polaris MoC solver. Appreciation is also extended to Ugur Mertyurek, Brian Ade, Ben Betzler, Scott Palmtag, and Andrew Godfrey for testing and benchmarking efforts and also Sheila Walker for finalizing the publication of this document.

Introduction

Polaris is a new module for SCALE 6.2 that provides 2D lattice physics analysis capability for light water reactor (LWR) fuel designs. For multigroup cross section processing, Polaris uses the Embedded Self-Shielding Method (ESSM) [WK12]. Unlike SCALE multigroup sequences that use XSProc, ESSM does not require user-defined unit cell definitions. ESSM computes multigroup cross sections using Bondarenko interpolation methods. The background cross section used in the interpolation is determined by iterative 2D fixed source transport calculations. Both the ESSM fixed source calculations and the keff calculation utilize a new Method of Characteristics (MoC) transport solver developed in the Exnihilo computational package.

Polaris is integrated with ORIGEN for depletion calculations. Each pin—or each radial subregion of the pin—is depleted based on the local power distribution. An optional critical spectrum calculation is incorporated into the depletion calculation and the output edits of few-group homogenized cross sections. Few-group cross sections are archived to an xfile016 file, which can be used in subsequent core simulator calculations. A complete description of the Polaris computational methods is provided in [JWE+14].

Polaris provides an easy-to-use input format to allow users to set up lattice models with minimal lines of input. All recognized Polaris commands are shown in Table 1. Note that many commands support short and long forms. The allowed basic Types for input are described in Table 2. The special Polaris TYPES are shown in Table 3. The convention used in this manual is that basic types appear italicized and capitalized (Type), while special Polaris types appear in all caps (TYPE).

Table 1 Polaris commands.

card

long

command

short

command(s)

system

system

sys

geometry

geometry

geom

composition

composition

comp

property

property

prop

material

material

mat

burnup

bu or dbu

power

power

pow

options

option

opt

time

t or dt

state

state

branch block

branch

pin geometry component

pin

assembly pin map

pinmap

assembly channel

channel

assembly half gap

hgap

channel box

box

shield

shield

deplete

deplete

slab geometry component

slab

power basis materials

basis

assembly inserts

insert

assembly control elements

control

Table 2 Basic Types in Polaris input.

basic Type

description

examples

incorrect examples

Word

starts with a character A-Z or a-z and includes characters, numbers, underscores

uox

bor_water_500pp m

FUEL

uox_enr5.1

316SS
uox-3.1

Int

integer

17

92235

2

565

31.4 uox

Bool

boolean/logical

yes

false

TRUE No

Real

any number

565

10.257

1.5e-6

yes bor_water

String

a single or double quoted string

“INFMED”

“Includes spaces”

‘NONE’

Includes spaces

Value

any non-word

Int|Bool|Real|String

Table 3 Special Polaris Types.

Polaris Type

description

Variants

STYPE

system type

PWR|BWR

GTYPE

geometry type

ASSM|REFL

CTYPE

composition type

NUM|WT|FORM|CONC|LW|UOX

PTYPE

property type

SOLP

ETYPE

control element type

RODLET

OTYPE

option type

KEFF|BOND|ESSM|CRITS PEC|FG|* DEPL*|RUN|PRINT

The Polaris input supports a very flexible input scheme that allows some elements to be suppressed for better readability. With key=value type input, when the standard order of keys is used, the keys may be suppressed. Consider the following input specification as an example.

geometry GNAME : ASSM npins=Int ppitch=Real [sym=FULL|SE]

The geometry card requires a geometry name (GNAME) in the first group, then a geometry type (GTYPE) which is ASSM here indicating an assembly geometry. The remaining arguments have keys: “npins” with an integer value, “ppitch” with a real value, and the optional “sym” with either FULL or SE values (optional arguments are always shown in square brackets: [sym=*FULL*|SE]. The default value is underlined: (FULL). The pipe “|” shows an or relation i.e., FULL or SE is an acceptable value).

geometry FuelNode : ASSM npins=15 ppitch=1.43 sym=FULL
geometry FuelNode : ASSM 15 1.43 FULL
geometry FuelNode : ASSM sym=FULL ppitch=1.43 npins=15
geometry FuelNode : ASSM 15 1.43
geometry FuelNode ASSM 15 1.43

The group separator “:” is suppressed in the last variant. This is possible in any situation where (1) the group is implicitly terminated by running out of arguments or (2) the next type does not match the expected type in the current group. For example, consider the hgap card:

hgap [ d ] [: M ]

In this card, d and M are values (without keys) defined as Real and material name (MNAME), respectively. The following form would automatically bypass the Real value, which allows a default, and set the interassembly gap material name as COOL.2.

hgap COOL.2

Setup

The cards in this section generally appear at the beginning of an input file. Note that the manual is organized with each card starting a new page. This is especially convenient when printing a few cards across different sections.

title – case title lines

title Line1 Line2 … Linei … LineN

param

type

name

details

default

Linei

String

line

used in output file headers

“DEFAULT TITLE”

Examples:

title "Westinghouse 15x15"

title "Westinghouse 15x15"
        "Condition: Hot Full Power"
        "Date: 10/18/2012"

Comments:

The title card gives a title to this Polaris case, which appears as a descriptive header on the output file. The additional lines may be used to document a subcase or to embed additional information in the output file in an orderly way (e.g., author, date, project identifier).

The title card is optional.

See also:

lib

library – nuclear data libraries

lib [mg=*String*]

param

type

name

details

default

mg

String

multigroup library

multigroup cross section library

“fine_n”

Examples:

% a name of library in the DATA directory
% use SCALE 252g ENDF/B-VII.1 library
lib "fine_n"   % SAME AS "V7-252"

% use SCALE 56g ENDF/B-VII.1 library
lib mg="broad_n"   % SAME AS mg="V7-56"

% a name of a local library in the temporary working directory
% (useful in SAMPLER calculations)
lib "perturbed_xs_library"

% fully specified path
lib "C:\scale6.2\data\scale.rev04.xn252v7.1"

Comments:

The lib card specifies the multigroup library location. See SCALE’s FileNameAliases.txt file in the installation directory for up-to-date library aliases for the fine and broad group libraries provided in SCALE’s data directory. Only the 252-group and the 56-group cross section libraries can be used in Polaris. Full specification of the file path is acceptable, as in the final example shown above.

The lib card is optional.

See also:

title

Geometry

The highest level structures in the model are named and defined with a geometry card. The general outline for a geometry definition is shown below. Two types of geometry are currently supported, ASSM for pressurized water reactor (PWR) or boiling water reactor (BWR) assemblies with fuel elements in a square-pitch, and REFL for an assembly-adjacent reflector.

geom GNAME : GTYPE arguments

argument

type

name

details

default

GNAME

Word

geometry name

GTYPE

-

geometry type

ASSM

assembly

see pin & pinmap

REFL

reflector

see slab

arguments

remaining arguments

depends on GTYPE

The control element geometry is also enumerated with types, as shown below. To model PWR-type rod cluster control assemblies (RCCAs), the RODLET element type is used in conjunction with pin definitions. In future releases of Polaris, other control element types, such as BWR-type control blades will be supported.

control INAME : ETYPE arguments

Argument

type

name

details

default

INAME

Word

control element name

ETYPE

-

control element type

RODLET

PWR-type RCCA

requires PINIDs

arguments

remaining arguments

depends on ETYPE

For accurate solutions to lattice physics problems using the method of characteristics (MoC), the input geometry must be subdivided into smaller regions called cells. Although the defaults should be applicable in most cases, the capability to change the number of cells is provided through meshing options appearing at the end of many geometry cards. See the slab, pin, box, and hgap cards for details.

geometry<ASSM> – assembly

geom GNAME :
ASSM
npins=Int
ppitch=Real
[sym=*FULL|SE*]

param

type

name

details

default

GNAME

Word

assembly name

GTYPE

ASSM

npins

Int

number of pins

on each side of the assembly

ppitch

Real

pin pitch

units: cm

sym

FULL|SE

symmetry

assembly symmetry FULL: no symmetry SE: south-east quarter

FULL

Examples:

% simple pincell
geom MyPin : ASSM 1 1.5

% 17x17 Westinghouse with 1.26 cm pin pitch in quarter symmetry
geom FuelNode : ASSM 17 1.26 sym=SE

Comments:

The assembly geometry describes the basic elements of an assembly. The pin and pinmap cards are required to finalize the assembly geometry. The hgap card specifies the interassembly half gap, and the channel specifies the channel material for the assembly.

See also:

pinmap, pin, hgap, box, channel, control, insert

geometry<REFL> – reflector

geom GNAME :
REFL
thick=REAL

param

type

name

details

default

GNAME

Word

reflector name

GTYPE

REFL

thick

Real

thickness

units: cm

Examples:

% defines a 20 cm reflector
geom ReflectorNode : REFL 20.0

Comments:

The reflector geometry describes the basic elements of a simple slab-type reflector. The slab card can be used to define geometric dimensions and mesh for the reflector geometry.

See also:

slab

channel – materials and mesh options

channel [Mchan =MCLASS]

param

type

name

details

default

Mchan

MCLASS

material class

initializes materials in outermost pin zone

*

*By default, Mchan will be set to COOL by “system PWR” and “system BWR.” Otherwise, Mchan is required.

Examples:

% define the channel material class to be COOL
channel COOL

Comments:

The channel card is used to set the default channel material class for the outermost region of each pin, typically containing reactor coolant. See the material card for a description of material classes.

See also:

pin, material, geometry<ASSM>

hgap – half distance between assemblies

hgap
[ dE dN dW dS ]
[: ME MN MW MS ]
[: nfE nfN nfW nfS ]
[: ndE ndN ndW ndS ]

param

type

name

details

default

di

Real

list of widths with i:

E: east

N: north

W: west

S: south

accepts 1, 2, or 4 values

E: all hgaps are same

E+N: dE =dS and dN =dW

units: cm

0.0

Mi

MNAME

list of

material names

requires same # as di

*

meshing options

nfi

Int

list of

number of faces per pin

requires same # as di

2

ndi

Int

list of

number of divisions

requires same # as di

1

*By default, hgap material will be set to COOL.1 by “system PWR.” For “system BWR,” the east and south hgap materials will be set to MOD.2, and the west and north hgap materials will be set to MOD.1. Otherwise hgap material is required.

Examples:

% defines a 17x17 Westinghouse assembly with 1.26 cm pin pitch
% with 0.04 cm half-gap filled with material COOL.1
geom w17x17 : ASSM 17 1.26 sym=SE
hgap 0.04 COOL.1

% defines a GE 7x7 assembly with 1.88 cm pin pitch
%   0.48 cm narrow gap on east and south edge
%   0.95 cm wide gap on north and west edge
%   narrow gap mesh is 3
%   wide gap mesh is 4
%   faces per pin is 2 for both narrow and wide gap
geom ge7x7 : ASSM 7 1.88
hgap 0.48 0.95 : MOD.1 MOD.1 : 2 2 : 3 4

Comments:

The hgap specifies the outermost geometry region in an assembly. If a channel box exists, then hgap specifies the material and mesh from outer channel box edge to the problem boundary. Otherwise, hgap specifies the material and mesh from the edge of the fuel array to the problem boundary. In both cases, hgap represents the half-distance between adjacent assemblies for single assembly calculations. Fig. 1 shows some of the hgap meshing options. Referring to the south edge of the assembly, the number of faces per pin refers to the extra cells introduced by “splitting” the pin cell boundary, and the number of divisions refers to extra horizontal lines dividing half gap into smaller width cells.

See also:

pinmap, control, insert, geometry<ASSM>, channel, box

_images/fig1102.png

Fig. 1 Interassembly half gap meshing variants.

box [thick=*Real*] [rad=*Real*] [icdist=*Real*] [xrad=*Real*] [xlen=*Real*] [Mbox=MNAME]

param

type

name

details

default

thick

Real

nominal thickness (cm)

must be >0

none

rad

Real

inner corner radius (cm)

must be >0,

additional constraints listed below

none

icdist

Real

in-channel distance (cm)

must be >0

none

xrad

Real

extra corner thickness (cm)

must be >= 0

0

xlen

Real

extra corner length (cm)

excludes rounded corner length

0

Mbox

MNAME

box material

*

*By default, box material will be set to CAN.1 by “system BWR.” Otherwise box material is required.

Examples:

% GE 7x7 assembly with 1.88 cm pin pitch
%   0.48 cm narrow gap
%   0.95 cm wide gap
system BWR
geom ge7x7 : ASSM 7 1.88
hgap 0.48 0.95

% Box geometry
%   0.2 thickness
%   0.97 inner corner radius
%   0.14 in-channel distance
box 0.2 0.97 0.14

% Same example, all variables
box 0.2 0.97 0.14 0 0 CAN.1

Comments:

The box specifies the channel box geometry and material that surround the array of fuel pins.

Fig. 2 and Fig. 3 show different box geometries, with and without thick corners respectively.

_images/fig214.png

Fig. 2 Box geometry example (uniform thickness).

_images/fig313.png

Fig. 3 Box geometry example (thick corners).

pin – pin or pincell

pin PINID [nsect=*Int*] [nring=*Int*] [size=*Int*]
: r1 r2 … ri … rN
: M1 M2 … Mi … MN [Mout]
[: nr1 nr2 … nri … nrN nrout]
[: ns1 ns2 … nsi … nsN nsout]

param

type

name

details

default

PINID

Word|

Int

pin identifier

size

Int

pin will be placed in a size x size pincell grid

used to create large water rods in CE PWRs and GE BWRs (see pinmap)

ri

Real

list of

radii

for each radial zone from center out

units: cm

Mi

MNAME

list of

pin materials

material in each radial zone

.1 added if given MCLASS, e.g., FUELFUEL.1

Mout

MNAME

material

in outermost zone

material in outermost zone

.1 added if given MCLASS, e.g., FUELFUEL.1

*

meshing options

nsect

Int

number of sectors

azimuthal sections of the pin cell, value applies to all nsi

and nso ut

nring

Int

number of rings

value applies to all nri

and nrout

nri

Int

number of rings

number of rings in each radial zone

1

nrout

Int

number of rings

in outermost zone

number of rings in the outermost zone

1

nsi

Int

number of sectors

number of sectors in each radial zone

1

nsout

Int

number of sectors

in outermost zone

number of sectors in the outermost zone

1

*If not specified, the material class MCLASS is taken from the channel card (Mchan) and set to the first member of that class, “Mchan.1.” For example if Mchan=“COOL,” then Mout= “COOL.1.”

Examples:

%standard fuel pin
pin 1 : 0.4096 0.418 0.475
      : FUEL   GAS   CLAD

%empty guide tube
pin E :        0.561 0.602
      :       COOL.1 CLAD.1

%pyrex
pin P : 0.214 0.231 0.241 0.427 0.437 0.484 0.561 0.602
      : GAS   TUBE  GAS   BP.3  GAS   TUBE  COOL  CLAD

%standard fuel pin with explicit material in the outermost region
pin 1 : 0.4096 0.418 0.475
      : FUEL   GAS   CLAD   COOL.6


%standard fuel pin with explicit ring and sector mesh
pin 1 : 0.4096 0.418 0.475
      : FUEL   GAS   CLAD
      : 5      1     1      0   %5 rings in fuel
      : 8      1     1      1   %8 sectors only in fuel


%large central 2x2 water rod in 4x4 assembly
pin W size=2 : 0.8
             : COOL

%pinmap must show adjacent Ws
pinmap
F F F F
F W W F
F W W F
F F F F

Comments:

The pin card is one of the basic building blocks of the assembly model. It is the only geometry component which allows an integer (Int) identifier as well as a Word—all other geometric identifiers use Word. Note that the materials are required, except for the last Mout, which can be used to overwrite the material given by a channel for the outermost region in the pincell. The various pin cell meshing options are displayed in Fig. 3.2.4. Note that extra rings in the radial zones create equal area regions, whereas rings in the outermost region create equal distance divisions between the last radius and the pincell boundary. Extra sectors create additional azimuthal divisions. A negative value of sectors is allowed and can be used to rotate the sector mesh by a half angle, e.g., ns=4 looks like ⊕ and ns=-4 looks like ⊗.

The total number of cells used in the transport calculation is determined from both the number of rings and the number of sectors. With the MoC transport solver, the fidelity of the solution is also dictated by the number of azimuthal and polar angles and ray spacing. These parameters are changed on the option<KEFF> card.

Due to self-shielding and depletion, each cell could be modeled as a unique material with its own cross section data. However, this is prohibitively memory intensive and typically not necessary. The shield card provides the mechanism to control the additional self-shielded materials introduced.

See also:

pinmap, control, insert, channel, system, option<KEFF>, shield

_images/fig413.png

Fig. 4 Pincell meshing variants.

pinmap – pin layout

pinmap
PINID1
PINID2
PINIDi … PINIDN

param

type

name

details

default

PINIDi

Word|

Int

list of

pin identifiers

supports full, quarter, or octant symmetry

quarter: assumes southeast (SE)

octant: assumes south-by-so utheast (SSE)

Examples:

%Westinghouse 17x17 pinmap in octant symmetry
pinmap
  2
  1 1
  1 1 1
  3 1 1 3
  1 1 1 1 1
  1 1 1 1 1 3
  3 1 1 3 1 1 1
  1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1

%Westinghouse 17x17 pinmap in quarter symmetry
pinmap
  2 1 1 3 1 1 3 1 1
  1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1
  3 1 1 3 1 1 3 1 1
  1 1 1 1 1 1 1 1 1
  1 1 1 1 1 3 1 1 1
  3 1 1 3 1 1 1 1 1
  1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1

%Westinghouse 17x17 pinmap in full
pinmap
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 3 1 1 3 1 1 3 1 1 1 1 1
  1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 3 1 1 3 1 1 2 1 1 3 1 1 3 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 3 1 1 1 1 1 1 1 1 1 3 1 1 1
  1 1 1 1 1 3 1 1 3 1 1 3 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

%large central 2x2 water rod in 6x6 assembly
%pinmap must show adjacent Ws
pin W size=2 : 0.8
             : COOL
pinmap
F F F F F F
F F F F F F
F F W W F F
F F W W F F
F F F F F F
F F F F F F

Comments:

The pinmap card defines the layout of pin cells in the assembly. The symmetry is determined by the number of pin identifiers given on the card and must not be more general than the symmetry option given on the assembly geometry card (i.e., do not define a full pin map for a sym=SE assembly model).. If the pin has a large size specifier, size>1, then the pinmap must reflect that with those pins occurring in blocks of size × size.

See also:

geometry<REFL> – reflector , control, insert

control<RODLET> – RCCA-type layout

|control INAME : RODLET | PINID1 | PINID2 … | PINIDi … PINIDN

param

type

name

details

default

INAME

Word

insert name

ETYPE

RODLET

PINIDi

Word|

Int

list of

pin identifiers

same format as pinmap

“_” indicate empty locations

Examples:

% B4C control rods
mat GAS.1  : FILLGAS
mat CLAD.1 : ZIRC4
mat MOD.1  : LW
mat TUBE.1 : SS304
mat CNTL.1 : B4C

pin B : 0.214  0.231 0.241 0.427 0.437 0.484 0.561 0.602
      : GAS    TUBE  GAS   CNTL  GAS   TUBE  MOD   CLAD

control  BankD  : RODLET
  _
  _ _
  _ _ _
  B _ _ B
  _ _ _ _ _
  _ _ _ _ _ B
  B _ _ B _ _ _
  _ _ _ _ _ _ _ _
  _ _ _ _ _ _ _ _ _

Comments:

Note that control elements and inserts share the INAME identifiers, so an insert and a control element cannot have the same name. Different control rod banks may be included in a single input file using more than one control card with unique INAMEs. The main difference between the inserts defined by control element and insert cards is that by default, control element materials are not depleted, whereas insert materials are depleted.

The outer dimensions of the tube must be included in the pin card that is inserted.

See also:

pinmap, control, insert, state

insert – insert layout

insert INAME :
PINID1
PINID2
PINIDi … PINIDN

param

type

name

details

default

INAME

Word

insert name

PINIDi

Word|

Int

list of

pin identifiers

same format as pinmap

“_” indicate empty locations

Examples:

%pyrex inserts
pin P : 0.214  0.231 0.241 0.427 0.437 0.484 0.561 0.602
      : GAS    TUBE  GAS   BP.3  GAS   TUBE  COOL  CLAD

insert PyrexInserts :
  _
  _ _
  _ _ _
  P _ _ P
  _ _ _ _ _
  _ _ _ _ _ P
  P _ _ P _ _ _
  _ _ _ _ _ _ _ _
  _ _ _ _ _ _ _ _ _

Comments:

The insert card defines a set of pins to be used to model inserts such as WABA. When the insert is “in,” the insert pins replace overlapping regions of the pins defined on the assembly pinmap. An underscore (_) is used to indicate locations without inserts. See the notes on the control<RODLET> card for additional guidelines.

See also:

pinmap, control, insert

slab – slab geometry

slab [SLABID]
: t1 t2 … ti … tN
: M1 M2 … Mi … MN
[: nx1 nx2 … nxi … nxN ]
[: ny1 ny2 … nyi … nyN ]

param

type

name

details

default

SLABID

Word

slab geometry identifier

reflector GNAME

ti

Real

list of

slab thicknesses

units: cm

Mi

MNAME

list of

material names

meshing options

nxi

Int

list of

number of x-divisions

1

nyi

Int

list of

number of y-divisions

1

Examples:

% a reflector definition
% 2.22 cm of baffle
% 15 cm of moderator
geom ReflectorNode : REFL 17.22
  slab 2.22 15 : BAFFLE.1  MOD.1

Comments:

The slab card may be used to define three things: (1) the materials and thicknesses of a reflector initiated on a geometry card, (2) slabs in a control blade, and (3) spacer grids. If the first argument identifier is not present, then the first purpose of describing the various material thicknesses in a reflector is assumed. The meshing options allow each material slab to be spatially refined in x and y, increasing the number of cells in the transport problem. The meshing option for the number of x divisions creates the equivalent of additional “sub-slabs” in each user-defined slab thickness. The y-divisions create additional cells vertically. The default of one y-division corresponds to the entire assembly.

See also:

geometry<REFL>

Materials

A material contains two main types of information: (1) the composition, or distribution of nuclides, and (2) the properties which include basic (required) properties like density and temperature, and as well as (optional) properties like soluble poison content, void, or grid spacer smearing. The composition is defined by a composition card. The basic specification for a material is shown below.

mat MNAME : CNAME [dens=*Real*] [temp=*Real*] [: properties]

argument

type

name

details

default

MNAME=

MCLASS.MSUB

Word.Int

material name

used to reference this material

CNAME

Word

composition name

dens

Real

density

basic property

units: g/cm3

composition reference density, if defined

temp

Real

temperature

basic property

units: K

293

properties

Word=Value

properties

extra properties are defined with property

cards

no extra properties

A material name has two parts, the material class, or MCLASS, and a member identifier, or MSUB. For example, FUEL.2 has an MCLASS=FUEL and an MSUB=2. All properties are defined by MCLASS. The composition referenced by CNAME is created with a composition card, as shown below.

comp CNAME : CTYPE arguments

argument

type

Name

details

default

CNAME

Word

composition name

used to reference this composition later in materials and property definitions

CTYPE

-

composition type

General Composition Constructor s <#basis-power-basis-materials>__

NUM

number fraction

WT

weight fraction

FORM

Formula

CONC

Concentrations

Reactor Composition Constructor s

LW

borated light water

UOX

uranium oxide fuel

arguments

remaining arguments

depends on CTYPE

Additional properties are defined with the property card, which defines the property PNAME for a material class MCLASS. The property type, PTYPE, determines the remaining arguments.

prop PNAME MCLASS : PTYPE arguments

argument

type

name

details

default

PNAME

Word

property name

used to reference this property

PTYPE

PTYPE

property type

SOLP

soluble poison

used to define soluble boron content

arguments

remaining arguments

depends on PTYPE

material – material

mat MNAME : CNAME [dens=*Real*] [temp=*Real*]
[: p1=val1 p2=val2 … pi=vali … pN=valN]

argument

type

name

details

default

MNAME

Word.Int

material name

uses form MCLASS.MSUB

CNAME

Word

composition name

dens

Real

density

basic property

units: g/cm3

composition

reference density

temp

Real

temperature

basic property

units: K

293

pi =vali

PNAME=Value

properties

additional properties

0

Examples:

% define a gas gap material
mat GAP.1  : FILLGAS

% define a 3.5% enriched fuel material
comp uox_e350 : UOX 3.5
mat FUEL.1 : uox_e350 dens=10.257 temp=900

% define a cladding material
mat CLAD.1 : ZIRC4

% define a guide tube material
mat TUBE.1 : SS304

% define a control rod material
mat CNTL.1 : AIC

Comments:

Material properties may be set on either a material card or on a state card. If a temperature is specified rather than a density, the “temp=” key must be used to skip over the density argument.

See also:

state, composition, property

composition<NUM|WT> – general atom/wt fraction

comp CNAME : NUM|WT
[scale= PCT|ABS|PPM]
[norm=*Bool*]
[refdens=*Real*]
[structure=*Function]*
id1=val1 id2=val2 … idi=vali … idN=valN

param

type

name

details

default

CNAME

Word

composition name

CTYPE

NUM

number fraction

WT

weight fraction

scale

PCT|ABS|PP M

scaling factor

all values are divided by this factor PCT: percentage

(divide by 100) PPM: parts per million (divide by 1e6)

ABS: absolute (divide by 1)

PCT

norm

Bool

normalize

normalize values to 1

false

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

*

structure

Function

structure

see Table X.X.X

FREE

idi =vali

Word|Int=Real

id/value pairs

value<0 fills the remainder up to value

see acceptable id forms below

*The density property must be defined for each material either explicitly on the material card itself or implicitly through the “reference density” of the material’s composition.

Examples:

% create a plutonium vector and then plutonium oxide
comp puvec : WT scale=PCT
  Pu238=1.2
  Pu239=63.3
  Pu240=21.0
  Pu241=8.6
  Pu242=5.9
comp puox : FORM puvec=1 O=2

% create an 85/10/5 Ag/In/Cd composition
% using 10% In, 5% Cd,
% and filling the remainder up to 100% with Ag
comp aic : WT In=10 Cd=5 Ag=-100

Comments:

IDs in weight or number fraction-based compositions may be any of the following:

  • nuclide IDs (Int), e.g., 92235,

  • nuclide names (Word), e.g., U235 or u235,

  • element Z numbers (Int), e.g., 92,

  • element names (Word), e.g., U or u, or

  • other composition names (CNAME).

See also:

composition<FORM>

composition<FORM> – general chemical formula

comp CNAME : FORM * [refdens=*Real]

[structure=*Function*]
id1=val1 id2=val2 … idi=vali … idN=valN

param

Type

name

details

default

CNAME

Word

composition name

CTYPE

FORM

formula

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

*

structure

Function

structure

see Table X.X.X

FREE

idi =vali

Word|Int=Real

id/value pairs

see acceptable id forms below

values in atoms per molecule

(e.g., H2 O is given as “H”=2 “O”=1)

*The density property must be defined for each material either explicitly on the material card itself or implicitly through the “reference density” of the material’s composition.

Examples:

% define Gd2O3 using element names
% (using elements implies natural abundances used in isotopics)
comp gd2o3 : FORM Gd=2 O=3

% define Gd2O3 using 100% Gd 155
comp gd2o3 : FORM Gd155=2 O=3

% define D2O using nuclide IDs and element names
comp d2o : FORM 1002=2 8000=3
comp d2o : FORM H2=2 O=3

Comments:

IDs in formula-based composition may be any of the following:

  • nuclide IDs (Int), e.g., 92235,

  • nuclide names (Word), e.g., U235 or u235,

  • element Z numbers (Int), e.g., 92,

  • element names (Word), e.g., U or u, or

  • other composition names (CNAME).

See also:

composition<NUM|WT>, composition<CONC>

composition<CONC> – general number density

comp CNAME : CONC [refdens=Real]
id1=val1 id2=val2 … idi=vali … idN=valN

param

type

name

details

default

CNAME

Word

composition name

CTYPE

CONC

concentration

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

**

idi =vali

Int=Real

id/value pairs

see acceptable id forms below

note: cannot use other CNAMEs for IDs in CONC input

units: #/barn-cm

**A reference density is automatically calculated from concentrations input. If specified, it will simply scale up concentrations linearly.

Examples:

% pyrex composition
comp pyrex_e125 : CONC
         5010=9.63266E-04
         5011=3.90172E-03
         8016=4.67761E-02
        14028=1.81980E-02
        14029=9.24474E-04
        14030=6.10133E-04

% fuel composition
comp uox_e310_gd180 : CONC
        92234=3.18096E-06
        92235=3.90500E-04
        92236=1.79300E-06
        92238=2.10299E-02
        64152=3.35960E-06
        64154=3.66190E-05
        64155=2.48606E-04
        64156=3.43849E-04
        64157=2.62884E-04
        64158=4.17255E-04
        64160=3.67198E-04
         8016=4.53705E-02

% wet annular burnable absorber (WABA) composition
comp waba : CONC
         5010=2.98553E-03
         5011=1.21192E-02
         6000=3.77001E-03
         8016=5.85563E-02
        13027=3.90223E-02

Comments:

IDs in concentration-based composition may be any of the following:

  • nuclide IDs (Int), e.g., 92235;

  • nuclide names (Word), e.g., U235 or u235;

  • element Z numbers (Int), e.g., 92;

  • element names (Word), e.g., U or u; and

  • SCALE-specific Nuclide IDs (Int), e.g., 3006000 (Only available for comp(CONC) card).

Other composition names (CNAME) cannot be used in a concentration definition. To easily ensure consistency of input when comparing codes, the composition input should be used in the concentrations described here. In all other cases, the other composition constructors are recommended because they are much simpler and easier to use.

See also:

composition<FORM>, composition<NUM|WT>

composition<LW> – borated light water

comp CNAME : LW [borppm=*Real*] [refdens=*Real*]

param

Type

name

details

default

CNAME

Word

composition name

CTYPE

LW

light water

borppm

Real

boron

parts per million by weight of natural boron (B) in light water (H2 O)

*

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

0.0

*The density property must be defined for each material either explicitly on the material card itself or implicitly through the “reference density” of the material’s composition.

Examples:

% define a 600ppm boron moderator composition
comp mod_600ppm : LW 600

% same composition using FORM and WT
comp mod : FORM H=2 O=1
comp mod_600ppm : WT scale=PPM norm=yes
                  mod=1e6 B=600

Comments:

Internally, the borated light water composition is built from composition<FORM> and composition<WT> cards assuming natural boron. To use different boron isotopics such as depleted or enriched boron, the more general composition cards should be used.

See also:

composition<FORM>, composition<WT>

composition<UOX> –UO2 fuel

comp CNAME : UOX enr=Real [bu=*Real*] [refdens=*Real*]

param

type

name

details

default

CNAME

Word

composition name

CTYPE

UOX

uranium dioxide

enr

Real

enrichment

U-235 wt. %

(see composition<ENRU> for formula)

bu

Real

burnup

only available for 0≤bu≤100

units: GWd/MTU

0*

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

**

*Generally, the burnup parameter should not be specified. It is provided for testing purposes only to create a fixed, representative, burned fuel composition. The composition is interpolated using linear interpolation from an internal burnup- and enrichment-dependent data matrix.

**The density property must be defined for each material either explicitly on the material card itself or implicitly through the “reference density” of the material’s composition.

Examples:

% define a 4.95% enriched fuel composition with a reference density
comp uox_495 : UOX 4.95 refdens=10.25

% same result as above
comp u_495 : ENRU 4.95
comp uox_495 : FORM u_495=1 O=2

Comments:

Internally, the UO2 composition is built from composition<FORM> and composition<ENRU> cards.

See also:

composition<ENRU>, composition<FORM>

composition<ENRU> – enriched uranium

comp CNAME : ENRU enr=Real [refdens=*Real*]

param

type

name

details

default

CNAME

Word

composition name

CTYPE

UOX

uranium dioxide

enr

Real

enrichment

*U-235 wt.%

refdens

Real

reference density

default density for materials using this composition

units: g/cm3

**

*The following formula from [BS96] is used to determine the 234U and 236U wt% from the 235U enrichment. Note that this formula is only valid for U-235 enrichments less than 10 wt%.
wu234 = 0.007731*(enr) 1.0837
wu236 = 0.0046*enr
wu238 = 100 – wu234 – enr – wu236

**The density property must be defined for each material either explicitly on the material card itself or implicitly through the “reference density” of the material’s composition.

Examples:

% 5% enriched metal fuel
comp umetal : ENRU 5

Comments:

This composition for enriched uranium is used internally to create UO2 using the composition<UOX> card.

See also:

composition<UOX>

Standard molecular compositions

CNAME

Description

H2O

B4C

Er2O3

Gd2O3

SiC

ZrH

Zr5H8

ZrH2

fillgas

light water with structure=BOND(H2O)

Boron carbide burnable poison material

Erbium oxide burnable poison material

Gadolinium oxide burnable poison material

Silicon carbide

zirconium hydride alloy with structure=CRYS(orthorhombic_zrh)

zirconium hydride alloy with structure=CRYS(cubic_zrh)

zirconium hydride alloy with structure=CRYS(tetragonal_zrh)

Helium gas

Standard reactor mixtures and alloys

CNAME

Description

aic

pyrex

zirc2

zirc4

ss304

ss316

inc718

water

Ag-In-Cd control rod absorber material

Pyrex glass

Zircaloy-2 clad material

Zircaloy-4 clad material

Stainless Steel 304

Stainless Steel 316

Inconel 718

H2O with trace amount of boron

pyroc

Pyrolytic carbon, C with structure=CRYS(pyrolytic_c)

graphite

Graphite, C with structure=CRYS(hexagonal_c)

Structure names

structure

Description

Nuclide

** Cross section** ID

BOND(H2O)

H,O in liquid water

H-1→1001

H-2→1002

FREE

atoms allowed to orient freely (no structure)

H-1→8001001

H-2→8001002

CRYS(orthorhombic_zrh)

Zr,H in zirconium hydride alloy with orthorhombic crystal structure (gamma phase)

H-1→7001001

Zr-90→1040090

Zr-91→1040091

Zr-92→1040092

Zr-93→1040093

Zr-94→1040094

Zr-95→1040095

Zr-95→1040096

CRYS(cubic_zrh)

Zr,H in zirconium hydride alloy with cubic crystal structure (delta phase)

H-1→7001001

Zr-90→1040090

Zr-91→1040091

Zr-92→1040092

Zr-93→1040093

Zr-94→1040094

Zr-95→1040095

Zr-95→1040096

CRYS(tetragonal_zrh)

Zr,H in zirconium hydride alloy with tetragonal crystal structure (epsilon phase)

H-1→7001001

Zr-90→1040090

Zr-91→1040091

Zr-92→1040092

Zr-93→1040093

Zr-94→1040094

Zr-95→1040095

Zr-95→1040096

CRYS(pyrolytic_c)

C in pyrolytic crystal structure (graphite)

C→3006000

CRYS(hexagonal_c)

C in pyrolytic carbon (additional covalent bonds compared to graphite)

C→3006000

*Note: the cross section IDs can only be used on composition cards with the CONC variant to input number densities directly.

property<SOLP> – soluble poison by weight

prop PNAME M1 … : SOLP poison [scale=PPM|PCT|ABS]

param

Type

name

details

default

PNAME

Word

property name

property value p≥ 0

M1 …

MCLASS

material class

one or more material classes to gain this property

PTYPE

SOLP

soluble poison

poison

CNAME

soluble poison composition name

scale

PCT|ABS|PP M

scaling factor

all values are divided by this factor PCT: percentage

(divide by 100) PPM: parts per million (divide by 1e6)

ABS: absolute (divide by 1)

PPM

Examples:

% define a soluble boron property for moderator
% and coolant material classes
% using natural boron
prop boron MOD COOL : SOLP B

% investigate coolant crud/impurity activation
%  1. define a general impurity property to mix in coolant,
  comp crud : NUM Ni=12.7 Cr=2.3 Fe=-100 %mostly Fe
  prop impurity COOL : SOLP crud
% 2. create coolant material with 100ppm of crud
  mat COOL.1 : LW dens=0.75 : impurity=100
% 3. make sure to "deplete" coolant so crud gets activated
  deplete COOL=true

Comments:

None

See also:

pinmap, control, insert

deplete – material depletion and decay

deplete M1=Bool M2=Bool … Mi=Bool … MN=Bool

param

type

name

details

default

Mi

MNAME|MCLAS S

list of

material names or

material classes

use ALL for all materials

Note

Only one deplete card is allowed in an input.

Note

ALL only applies in the first position

Examples:

% turn on depletion/decay for two new materials
sys PWR
deplete MyMaterial=true MyOtherMaterial=true

% activate/deplete/decay every material
deplete ALL=true

% impose strict conditions
sys PWR
deplete ALL=false FUEL=true CLAD=true

Comments:

The deplete card not only instructs Polaris to deplete a material, but also to solve the Bateman equations with ORIGEN for that material. Thus if the flux/power is zero, only materials that are flagged to “deplete” will undergo decay. The deplete card modifies the depletables included in a system card to avoid the situation in which “deplete MyMaterial=true” would make only MyMaterial depletable. Thus to completely re-specify the depletable materials, “ALL=false” should be used as the first argument. This is in contrast to the basis card, which completely specifies a new power basis.

See also:

material, shield, basis

basis – power basis materials

basis M1=Bool M2=Bool … Mi=Bool … MN= Bool

param

type

name

details

default

Mi

MNAME|MCLAS S

list of

material names or

material classes

use ALL for all materials

ALL

Note

Only one basis card is allowed per input.

Note

ALL is only allowed in the first position.

% use only FUEL materials as the basis
basis ALL=no FUEL=YES

% Specify FUEL.3 as the basis
basis ALL=no FUEL.3=YES

Comments:

The basis card is used to specify the materials to use in power normalization. By default, the energy release from all materials is taken into account, including (n,gamma) reactions in structural materials such as cladding. It is not recommended to change the default of ALL in most situations. Exceptions include (1) when comparing results to other codes that only use fuel in the basis and (2) fixing the power in a specific pin is known—a material should be created only for that pin, and the power basis should be specified for that material only. The basis card overrides any power basis imposed by a system card. Thus it behaves differently than a deplete card, which is combined with depletable materials imposed by a system card.

See also:

material, shield, deplete

shield – cross section self-shielding expansion specification

shield M1=XTYPE M2=XTYPE … Mi=XTYPE … MN= XTYPE

param

type

name

Details

default

Mi

MNAME|MCLAS S

list of

material names or

material classes

use ALL for all materials

XTYPE

N|P|R|S

self-shield ing expansion type

shield across various mesh elements

N: no expansion

P: pins

R: rings (P implicit)

R

Note

Only one shield card is allowed per input.

Note

ALL is only allowed in the first position.

Examples:

%create a unique self-shielded FUEL cross sections in each pin
%consider all other materials to have a single self-shielded cross section
shield ALL=N FUEL=P

%assess effect of self-shielding each pin’s cladding
shield CLAD=P

%re-specify self-shielding to be P by default, R for the FUEL
shield ALL=P FUEL=R

Comments:

The shield card controls how materials are internally expanded for self-shielding purposes. By default, Polaris expands all materials across pins and rings (R). For example, a fuel region defined on a pin card as having 10 rings will be expanded internally to have 10 different self-shielded cross sections. Because the R option also implicitly includes the P option, each instance of that pin will also get different cross sections.

When using specific systems (e.g., system PWR), this card is generally not needed. The shield card modifies the self-shielding options included in a system card. Thus, to completely re-specify the expansion, use “ALL=N” as the first argument. This is in contrast to the basis card, which completely specifies a new power basis.

See also:

material, deplete, system

State

The idea of a “state” or “statepoint” is a standard concept in lattice physics calculations. In Polaris, the concept of state is mostly tied to the values of material properties. The base state for a calculation is determined as follows:

  1. The base state is initialized with any property values set on material cards.

  2. The base state is updated with any state cards that apply to ALL.

  3. The base state is updated with any other state cards, and the power card is used to set the base state power.

This sequence ensures that the state does not change, even if the order of inputs changes. A time or burnup card is then used to initiate a calculation as a function of time or burnup, thus producing a sequence of states. A branch block is used to perform branches off the base state at specific times or burnups.

state<MNAME> – material state

state MNAME|MCLASS :
p1=val1 p2=val2 … pi=vali … pN=valN

param

type

name

details

default

MNAME|MCLAS S

material name or

material class

use ALL for all materials

pi

PNAME

property name

vali

Value

property value

Examples:

% reset to hot zero power conditions
state ALL  : temp=565
state COOL : dens=0.75


% set channel/bypass materials to different ppm boron
state COOL : boron=0
state BYP  : boron=600

% set all materials with a boron property
state ALL : boron=300

Comments:

The state card declares the base state for materials and the base state of possible control elements or insert elements.

See also: material, deplete, system

state<INAME> – insert/control state

state INAME : in=Bool

param

type

name

details

default

INAME

insert name or

control element name

in

Bool

insertion

“in=” is required

Examples:

% insert bank D control rods
state BankD : in=true
% remove inserts named Ins6A
state Ins6A false
% perform reflector calculation
state ReflectorNode : in=true

Comments:

This form of the state card is required to insert any control element or inserts. By default, inserts and control elements are out when defined.

See also:

material, deplete, system

state<GNAME> – geometry state

state GNAME : pres=Bool

param

type

name

details

default

GNAME

geometry name

pres

Bool

present

“pres=” is required

Examples:

% disable reflector calculation even though
% reflector geometry is present
state ReflectorNode : pres=false

Comments:

The geometry version of the state card is used to declare which geometric elements are present in the system. The geometry version of the add card is useful for performing branch calculations for reflector nodes. Note that an assembly geometry must be present to perform a calculation.

See also:

geometry<REFL>, state<MNAME>, state<INAME>

power – total power

pow [: p1 p2 … pi … pN]

param

type

Name

details

default

pi

Real

list of specific powers in W/g initial heavy metal

0

Examples:

% set power to 35 W/gIHM
power 35.0

% provide a power history
% must have same number of values as following time/burnup card
power : 35.0 40.0 45.0 45.0 40.0 5.0 0.0
time  : 10   20   30   40   50   60  70

Comments:

The power card specifies the total power of the basis materials specified by a basis card. The power value may be specified only once.

See also:

t, bu, history, basis, state<MNAME>

bu – initiate calculation with cumulative burnups

bu [units=*GWD/MTIHM*|MWD/MTIHM] : [b1 b2 … bi … bN]

param

Type

name

details

default

units

GWD/MTIHM|

MWD/MTIHM

burnup units

GWD/MTIHM

bi

Real

list of

absolute burnups

0

Examples:

% simple depletion case with constant power and absolute/cumulative burnups
power 40
bu 0 5 10 15 20 30 40 50 60 80

% using MWd/MTIHM units with variable power
% 40 W/gIHM for 05000 MWD/MTIHM, then 30 W/gIHM for 500010000 MWD/MTIHM
power  40    30
bu MWD/MTIHM: 0 5000 10000

% combine burn/time cards
% 20 W/gIHM for 05 then 510 GWD/MTIHM steps, then
% 40 W/gIHM for a 5-day step then 30 W/gIHM for a 5-day step
power 20
bu   GWD/MTIHM :  5 10 GWD/MTIHM
power 40 30
dt  DAYS :   5  5

Comments:

The bu card initiates a calculation for a given sequence of cumulative burnups. A burnup or time card usually follows a power card, the two effectively specifying the power history. If multiple burnups are given, then the power card must have either a single power or a list of powers the same size as the list times. A value of 0 is implicit at the beginning of the first burnup list. Multiple burnup/time cards may be specified in an input. This can be convenient for switching units or changing from burnup-based to time-based depletion. Internal automatic substeps are always in effect unless modified with the option<DEPL> card.

See also:

t, dt, dbu, power, option<DEPL>, branch, deplete

dbu – initiate calculation with incremental burnups

dbu [units=*GWD/MTIHM*|MWD/MTIHM] : [b1 b2 … bi … bN]

param

Type

name

details

default

units

GWD/MTIHM|

MWD/MTIHM

burnup units

GWD/MTIHM

bi

Real

list of

incremental burnups

0

Examples:

% incremental burnups equivalent to
%   power 40
%   bu 0 5 10 15 20 30 40 50 60 80
power 40
dbu 5 5 5 5 10 10 10 10 20

Comments:

The dbu card initiates a calculation for a given sequence of incremental burnups. Otherwise, it is identical to the bu card for specifying cumulative burnups.

See also:

t, dt, bu, power, option<DEPL>, branch, deplete

t – initiate calculation by cumulative time

t [units=*SECONDS*|MINUTES|HOURS|DAYS|YEARS] : [t1 t2 … ti … tN]

param

Type

name

details

default

units

SECONDS|MINUTE S|

HOURS| DAYS|YEARS

time units

DAYS

ti

Real

list of

times

0

0

Examples:

% burn with 40 W/gIHM for 300 days in 100-day increments
power 40
t 100 200 300

% simulate 2 cycles of time-dependent irradiation with shutdown cooling
% note that time defaults to DAYs
%
% cycle 1
power 40   30   30   30
t    100  200  300  400
power  0
t    415
%
% cycle 2
power 30   20   20   20
t    515  615  715  815
power  0
t    830

Comments:

The t card initiates a calculation for a given sequence of cumulative/absolute times. One of the time cards (t, dt, or ti) is required to model periods of decay in conjunction with power 0. Otherwise, the time card t is similar in functionality to the burnup bu card but with different units.

See also:

dt, bu, dbu, power, option<DEPL>, branch, deplete

dt – initiate calculation by incremental time

dt [units=*SECONDS*|MINUTES|HOURS|DAYS|YEARS] : [t1 t2 … ti … tN]

param

Type

name

details

default

units

SECONDS|MINUTE S|

HOURS| DAYS|YEARS

time units

DAYS

ti

Real

list of

times

0

0

Examples:

% burn with 40 W/gIHM for 300 days in 100-day increments equivalent to
%     power 40
%     t 100 200 300
power 40
dt 100 100 100

% decay for 30 minutes
power 0
dt 30 MINUTES

Comments:

The dt card is identical to the cumulative time card t except that the values given are incremental.

See also:

t, bu, dbu, power, option<DEPL>, branch, deplete

branch – instantaneous change

read branch [BNAME]
add
[add …]
end branch

param

type

Name

details

default

BNAME

Word

branch name

DEFAULT

allowed cards in branch block

Add

-

adds a list of states to branch on

Examples:

% fuel temperature and boron branches (results in 7 total states) read branch   add FUEL : temp=800 1000 1200   add COOL : boron=0 400 800 1400 end branch

% branch to different % fuel temp/coolant temp/coolant density, synchronizing % states (results in 3 total states) read branch

% state 1 2 3

  add FUELtemp=800 1000 1200

COOL : temp=565   585  620

  COOL : dens=0.73 0.71 0.68 end branch

Comments:

The branch card initiates so-called “branch” calculations, i.e., instantaneous changes of state at specific burnups/times during the base depletion sequence of calculations. The syntax for the add card is identical to the state card except, instead of taking a list of different properties and their values, it takes a single property and a list of values. Note that a time or burnup card is not necessary—if not found, branches will be performed at every burnup/time specified in the base state. The initial state for any branch card is the base state as specified in the main file. This means branch cards have no knowledge of one another.

See also:

add, bu, t, title

add<MNAME> – material branch

add MNAME|MCLASS
[incr=*Bool*]
[scale=*ABS*|PCT] :
PNAME=val1 val2 … vali … valN
[MNAME|MCLASS
… ]

param

type

name

details

default

MNAME|MCLAS S

material name or

material class

use ALL for all materials

incr

Bool

increment

values are added to reference value

false

scale

ABS|PCT

Scaling

scaling

ABS: absolute units

PCT: percentage units

ABS

PNAME

property name

vali

Value

list of

property values

Examples:

% fuel temperature branches using incremental
% changes from the base state of 900 K
state FUEL : temp=900
read branch
  add FUEL incr=true : temp=-200 -100 +100 +200 +500
end branch


% material properties may be varied together (synchronized)
% by chaining additional material/properties together
% the first block below results in 2 states
% the second is 6 states
read branch
  add FUEL : temp=900 1200
      FUEL : dens=10.4 10.3
      COOL : dens=0.7  0.65
end branch
read branch
  add FUEL : temp=900 1200
  add FUEL : dens=10.4 10.3
  add COOL : dens=0.7  0.65
end branch

Comments:

The add card is only valid inside a branch block. This version adds a set of branches for a specific material name (MNAME) or class (MCLASS). Branches are always with respect to the base state. Although similar to the state card, the add card has a single property name and a list of values. The state card has a list of property=value pairs.

See also:

material, state<MNAME>

add<INAME> – insert/control branch

add INAME : in=Bool1[Bool2]

param

type

name

details

default

INAME

insert name or

control element name

in

Bool

list of insertion states

“in=” is required

Examples:

% branch to remove WABA inserts
state InsWABA4 : in=true
read branch
  add InsWABA4 : in=false
end branch

% synchronize rods in with material branches (5 states)
read branch
  add BankD : in=true false false false true
      FUEL  : temp=600 900 1200 2000 2000
end branch

% swap control banks
read branch
  add BankB : in=true  false false
      BankC : in=false true  false
      BankD : in=false false true
end branch

Comments:

This form of the add card is required to add branches to insert/remove control elements or inserts. Given that only two possible states exist, specifying “true false” will result in a calculation at the other state not specified by the base state.

See also:

insert, control, state<INAME>

add<GNAME> – geometry branch

add GNAME : pres=Bool1[Bool2]

param

type

name

details

default

GNAME

geometry name

pres

Bool

list of geometry states

“pres=” is required

Examples:

% perform a reflector calculation on a branch
state ReflectorNode : pres=no
read branch
  add ReflectorNode : pres=yes
end branch

Comments:

This form of the add card is required to add branches for new geometry, such as reflector calculations. Given that only two possible states exist, specifying “true false” will result in a calculation at the other state not specified by the base state.

See also:

geometry, state<GNAME>

Options

An extensive set of options is provided for manipulating the solvers and output. Most option cards support a key=value style of input, with reasonable defaults in place for all parameters.

option<KEFF> – eigenvalue

opt KEFF [key1=val1 key2=val2 … keyi=vali … keyN=valN]

_images/3-2-6-1-tab.svg

Examples:

% change the MOC ray spacing for the
% eigenvalue calculation to 0.01 cm
opt KEFF RaySpacing=0.01

%P3 scattering
opt KEFF PnOrder=3

option<ESSM> – embedded self-shielding

opt ESSM

[key1=val1 key2=val2 … keyi=vali … keyN=valN]

_images/3-2-6-2-tab.svg

Examples:

% change within group solver to use source iterations
opt ESSM WithinGroupSolver=SOURCE

option<DEPL> – depletion

opt DEPL [key1=val1 key2=val2 … keyi=vali … keyN=valN]

_images/3-2-6-4-tab.svg

Examples:

% Set the number of origen substeps per time steps to 2
% (may be useful for convergence studies)
opt DEPL
   NumSubsteps=2

% disable the addition of depletion nuclides to input materials
opt DEPL TrackingSet="NONE"

% use CRAM solver
opt DEPL Solver="CRAM"

option<CRITSPEC> – critical spectrum

opt CRITSPEC [key1=val1 key2=val2 … keyi=vali … keyN=valN]

_images/3-2-6-5-tab.svg

Examples:

% enable critical buckling search using B1 equations for a buckling of 1e-3
opt CRITSPEC
  Mode="SPECIFIED"
  B2=1e-3
  Method="B1"

option<PRINT> – printing

key

value type

details

default

XSSummary

Bool

print a cross section summary in the output file

yes

CritSpecSummary

String

print critical spectrum summary

“NONE”: no print out

“BUCKLING”: limited buckling info

“SPECTRUM”: full spectrum

“BUCKLING”

XFile16

Bool

output a TRITON xfile016 nodal data library

no

InputDataContai ner

Bool

print out the input data container

yes

InputCompositio nSummary

Bool

print compostion card input summary

yes

InputMaterialSu mmary

Bool

print material card input summary

yes

LibrarySummary

Bool

print cross section library summary

no

MaterialSummary

Bool

print material summary at each statepoint

no

Examples:

% print the xfile016
% if input file is polaris.inp, file name will be polaris.x16
opt PRINT XFile16=yes

% print summaries
opt PRINT XSSummary=yes
          CritSpecSummary="SPECTRUM"
          InputCompositionSummary=yes
          InputMaterialSummary=yes
          LibrarySummary=yes
          MaterialSummary=yes   % disabled for now

option<FG> – few-group cross section generation

opt FG
[AdjointMode=String InvVelMode=String]
[: b1 b2 … bi … bN ]
[: E1 E2 … Ei … EN-1 ]

param

type

details

default

AdjointMode

String

type of adjoint calculation to use in few-group data generation

“INFMED”: infinite medium adjoint

“CRITICAL”: critical spectrum adjoint

“UNIFORM”: uniform adjoint

“INFMED”

InvVelMode

String

weighting option for few-group inverse velocities

“FORWARD”: forward flux weighting

“ADJOINT”: adjoint flux weighting

“FORWARD”

bi

Real

list of burnups to include in output few-group cross section database, e.g., XFile16 output

units: GWd/MTHM

all burnups available

Ei

Real

note descending order and only N-1 divisions are needed for an N group structure

E0 is maximum energy (typically 2e7 eV)

EN is minimum (typically 1e-5 eV)

units: eV

0.625 eV division (two groups)

Examples:

% enable the critical spectrum adjoint
opt FG AdjointMode="CRITICAL"

%only include 0,10,15,20 GWd/MTHM burnups in few-group outputs, including XFile16
opt FG : 0 10 15 20

%redefine group energy divisions for 3 groups with divisions at 10 and 0.625 eV
opt FG : : 10 0.625

option<RUN> – run time

opt RUN [key1=val1 key2=val2 … keyi=vali … keyN=valN]

key

value type

details

default

CheckOnly

Bool

check input and terminate

true

HomogenizeGrains

Bool

homogenize grains

false

Examples:

% check input
opt RUN CheckOnly=true

% homogenize grains
opt RUN HomogenizeGrains=yes

See also:

property<GRAIN>

System

The system cards provide a way to initialize a set of defaults to simplify input and add robustness for a well-known and well-characterized system.

system STYPE

argument

Type

name

details

default

STYPE

-

system type

PWR

pressurized water reactor

BWR

boiling water reactor

The system card performs the following actions:

  1. defines a set of materials and properties, imposing standard names for the materials and properties;

  2. warns user of potential mistakes; and

  3. uses heuristics to modify unspecified mesh and solver options for robust results.

system<PWR> – pressurized water reactor

sys PWR

Definitions

_images/3-2-7-1-tab.svg

Description

Twelve reactor materials are initialized with compositions and densities from the predefined composition set. In most cases, all that remains is to define fuel materials, all material temperatures, and properties such as COOL/MOD soluble boron and density. Note that some rules are based on naming conventions. For example, burnable poisons (the material class BP) are declared to be depletable materials, whereas the CNTL (control elements) class of materials is not.

Examples:

% a complete input file for a PWR pincell model
=polaris
system PWR
geom MyPin : ASSM 1 1.5
comp f35 : UOX 3.5
mat FUEL.1 : f35 dens=10.25
pin 1 : 0.5 0.6 : FUEL CLAD
state ALL : temp=565
state MOD : dens=0.743
state COOL: dens=0.743
state ALL : boron=600
power 40
burn 0 0.1 0.2 0.5 1 2 5 10 15
     20 25 30 35 40 45 50 55 60
end

system<BWR> – boiling water reactor

sys BWR

Definitions

_images/3-2-7-2-tab.svg

Sample problems

Within the SCALE distribution, 27 Polaris sample problems are provided to demonstrate the differences in calculation and geometry options, and 21 sample problems consider the Consortium for Advanced Simulation of Light Water Reactors (CASL) Virtual Environment for Reactor Applications (VERA) benchmark problems for pin cell and lattice configurations described in [God14]. The VERA pin cell problems are identified as polaris_1a_252g.inp through polaris_1e_252g.inp. The VERA lattice problems are identified as polaris_2a_252g.inp through polaris_2k_252g.inp, polaris_2l_56g.inp through polaris_2m_56g.inp, polaris_2o_252g.inp, and polaris_2p_252g.inp.

The remaining six sample problems are described as follows:

  • polaris_TMI1_Cycle1-2.inp – 15 × 15 PWR geometry model with branch block definition for lattice physics calculations

  • polaris_bench_taka3_sf97-4_assm.inp, polaris_bench_taka3_sf97-4_pin.inp - Takahama UOX depletion benchmark for radiochemical assay NT3G24-SF97-4 described in [RE13].

  • polaris_bwr10x10.inp, polaris_bwr7 × 7.inp – example BWR geometry models for 10 × 10 and 7 × 7 fuel.

  • polaris_dv1a.inp – simple PWR pin cell depletion calculation.

BS96

S. M. Bowman and T. Suto. SCALE-4 Analysis of Pressurized Water Reactor Critical Configurations: Volume 5. 1996.

God14

Andrew T. Godfrey. VERA core physics benchmark progression problem specifications. Consortium for Advanced Simulation of LWRs, 2014.

JWE+14

Matthew Anderson Jessee, William A. Wieselquist, Thomas M. Evans, Steven P. Hamilton, Joshua J. Jarrell, Kang Seog Kim, Jordan P. Lefebvre, Robert A. Lefebvre, Ugur Mertyurek, and Adam B. Thompson. Polaris: a new two-dimensional lattice physics analysis capability for the SCALE code system. Technical Report, Oak Ridge National Lab.(ORNL), Oak Ridge, TN (United States), 2014.

RE13

B. Roque and M. Erlund. International Comparison of a Depletion Calculation Benchmark on Fuel Cycle Issues, Results from Phase 1 on UOx Fuels. Technical Report, NEA/NSC/DOC, 2013.

WK12

Mark L. Williams and Kang Seog Kim. The embedded self-shielding method. PHSYOR, 2012.