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 … Line_i … Line_N

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 [M_chan =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

[ d_E d_N d_W d_S ]

[: M_E M_N M_W M_S ]

[: nf_E nf_N nf_W nf_S ]

[: nd_E nd_N nd_W nd_S ]

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

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.

Fig. 2 Box geometry example (uniform thickness).

Fig. 3 Box geometry example (thick corners).

pin – pin or pincell

pin PINID [nsect=*Int*] [nring=*Int*] [size=*Int*]

: r₁ r₂ … r_i … r_N

: M₁ M₂ … M_i … M_N [M_out]

[: nr₁ nr₂ … nr_i … nr_N nr_out]

[: ns₁ ns₂ … ns_i … ns_N ns_out]

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 (M_chan) and set to the first member of that class, “M_chan.1.” For example if M_chan=“COOL,” then M_out= “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 M_out, 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

Fig. 4 Pincell meshing variants.

pinmap – pin layout

pinmap

PINID₁

PINID₂ …

PINID_i … PINID_N

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 … | PINID_i … PINID_N

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 …

PINID_i … PINID_N

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 … t_i … t_N

: M₁ M₂ … M_i … M_N

[: nx₁ nx₂ … nx_i … nx_N ]

[: ny₁ ny₂ … ny_i … ny_N ]

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 … p_i=val_i … p_N=val_N]

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 … id_i=val_i … id_N=val_N

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 … id_i=val_i … id_N=val_N

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 … id_i=val_i … id_N=val_N

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%.

w_u234 = 0.007731*(enr) ^1.0837

w_u236 = 0.0046*enr

w_u238 = 100 – w_u234 – enr – w_u236

**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 … M_i=Bool … M_N=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 … M_i=Bool … M_N= 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 … M_i=XTYPE … M_N= 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 … p_i=val_i … p_N=val_N

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 … p_i … p_N]

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 … b_i … b_N]

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 … b_i … b_N]

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 … t_i … t_N]

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 … t_i … t_N]

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 … val_i … val_N

[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 … key_i=val_i … key_N=val_N]

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 … key_i=val_i … key_N=val_N]

Examples:

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

option<BOND> – Bondarenko search

opt BOND [key₁=val₁ key₂=val₂ … key_i=val_i … key_N=val_N]

Examples:

% introduce Bondarenko iterations on total cross section
opt BOND
   MaxIterations=10
   ConvergenceXS="SIGT"

option<DEPL> – depletion

opt DEPL [key₁=val₁ key₂=val₂ … key_i=val_i … key_N=val_N]

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 … key_i=val_i … key_N=val_N]

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 … b_i … b_N ]

[: E₁ E₂ … E_i … E_N-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 … key_i=val_i … key_N=val_N]

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

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

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.