14.10. Nomenclature

Symbol	Definition	Units
\(l\)	Linear
n	Time step n
‘	Prime always indicates that a quantity refers to a unit of generalized smear volume
Subscripts
ac	Acoustic
an	Annular
bb	Bubbly or bubble
bk	Lower boundary of node K
ca	Cavity
ch	Coolant channel
cl	Cladding
co	Condensation
deet	De-entrainment
drag	Drag
ej	Ejected or ejection
et	Entrained or entrainment
fc	Fuel/clad interface
ff	Frozen fuel
ffcl	Frozen fuel on cladding
ffsr	Frozen fuel on structure
fi	Free fission gas in coolant channel
fica	Free fission gas in molten pin cavity
ficaxx	Used for special fission gas volume fraction calculation (see Eq. (14.2-46))
fm	Film (stationary liquid sodium film or moving annular fuel film)
fr	Friction
friction	Friction
FR1	Flow regime 1 - particulate fuel flow
FR3	Flow regime 3 - partially or fully annular flow
FR4	Flow regime 4 - bubbly fuel flow
fsca	Dissolved fission gas in the molten pin cavity
fs	Dissolved fission gas in the coolant channel
fu	Liquid and/or mobile solid fuel in the coolant channel
fuca	Mobile fuel in the molten pin cavity
fuch	Mobile fuel in the coolant channel (including fuel vapor)
fufi	Fuel and fission gas
fv	Fuel vapor in the coolant channel
fvca	Fuel vapor in the molten pin cavity
fz	Freezing, frozen
hoop	Hoop (stress)
Ht	Heat transfer
i	Axial coolant channel index, specific enthalpy
IB	Uppermost slug segment of lower sodium slug
if	Interface
in	Inner (middle) clad node or structural node facing neighboring hexan wall
inlet	Subassembly inlet
IT	Lowermost slug segment of upper sodium slug
K	Axial pin or cavity index
k	Material component k; this can also be cladding or structure
l	Dummy index
liq	Liquidus
ls	Lower slug
m	m = 1 indicates upward flow, m = 2 downward flow
me	Melting, melt-in
mi	Mixture of sodium and fission gas
min	Minimum
mv	Moving
mx	Maximum
Na	Sodium
Nl	Liquid sodium
Nm	Moving sodium liquid and sodium vapor
node	Node
Nv	Sodium vapor
op	Open channel - channel volume or cross section remaining open after plateout has occurred
or	Orifice
os	Outer surface of clad or structure of fuel film or fuel crust. All these surfaces are facing the coolant channel.
outlet	Subassembly outlet
p	Subscript of specific heat for constant pressure
Pa	Fuel particle
pin,pi	Pin
PL	PLUTO2
power	Power
radial	Radial
rl	Dissolved fission-gas release
S’	Sink or source per unit of generalized smear volume
sol	Solidus
sonic	Sonic
sr	Structure
un	Uncompressed
us	Upper liquid sodium slug
UTS	Ultimate tensile strength
vg	Vapor and gas
vi	Viscous
x	Auxiliary subscript
z	Axial location z
zi	Designates bottom of a liquid sodium slug segment
Greek Symbols	Definition	Units
\(\alpha\)	Void fraction
\(\beta\)	Delayed neutron fraction
\(\gamma\)	Cp/Cv
\(\delta\)	Partial derivative
\(\Delta\)	Derivative in finite differences
\(\kappa\)	Compressibility
\(\pi\)	Circumference of a circle divided by its diameter
\(\rho\)	Theoretical density
\(\rho'\)	Generalize linear density
\(\sigma\)	Surface tension
\(\theta\)	Generalized volume fraction
Regular Symbols	Description	Units
A	Cross section area
A’	Interaction or surface area per unit of generalized smear volume
AFR	Input, liquid sodium friction coefficient
AFRV	Input, sodium vapor friction coefficient
AHELP	Auxiliary quantity in momentum conservation
AMIIN	Auxiliary quantity in momentum conservation
ARCH	Cross section area of coolant channel per pin
ARCL	Cladding surface area per unit of generalized smear volume
AREA	Area
ARFF	Cross section area of plated-out fuel pin
ARMF	Cross section area of moving fuel per pin
ARSR	Structure surface area per unit of generalized smear volume
AXMX	Input, reference cross section area; recommended input value is subassembly cross section area
BFR	Input, exponent of liquid friction coefficient
BFRV	Input, exponent of vapor friction coefficient
BHELP	Auxiliary quantity in the momentum equation
BMIIN	Auxiliary quantity in the momentum equation
C	Specific heat
CDFU	Input, fuel conductivity
CDNL	Input, liquid sodium conductivity
CDVG	Input, conductivity of sodium vapor
CFCOFV	Input, fuel vapor condensation coefficient
CFFFCL	Fraction of channel perimeter covered by plated-out fuel
CFFRMF	Friction coefficient for annular fuel
CFFUCL	Fraction of cladding and structure covered by moving or plated-out fuel
CFMELT	Fraction of frozen fuel remelting per PLUTO2 time step
CFMFCL	Fraction of channel perimeter covered by moving fuel
CFMFFF	Fraction of plated-out fuel covered by moving fuel
CFNACL	Fraction of channel perimeter that is in contact with sodium
CFNACN	Input, sodium vapor condensation coefficient	J/(m2·s·K)
CFNAEV	Input, sodium evaporation coefficient	J/(m2·s·K)
CIANIN	Input, determines when a complete annular fuel flow begins
CIA1	Input, constant in the fuel particle-to-sodium heat transfer
CIA2	Input, constant in the fuel particle-to-sodium heat transfer
CIA3	Input, constant in the Deissler heat-transfer correlation
CIA4	Input, controls range of interpolation between boiling heat transfer coefficient and single-phase gas heat-transfer coefficient
CIA5	Input, controls drag dependence in void fraction in the particulate flow regime
CIA6	Input, controls drag in the bubbly flow regime
CIBBIN	Input, controlling onset of bubbly flow regime
CIETFU	Input, controls effect of fuel particles on sodium film entrainment
CIFRFU	Input, part of the fuel friction calculation
CIFUFZ	Input, controls mode of fuel freezing
CIFUMO	Input, controls axial fuel momentum low on ejection from pin
CINAFO	Input, initial and maximum sodium film fraction
CIREFU	Input, Reynolds number above which fully turbulent fuel flow is assumed for friction calculation
CIRTFS	Input, controls dissolved gas release	1/s
CIVOID	Input, controls liquid sodium fraction below which single-phase heat-transfer and friction laws are used
CMFU	Input, liquid fuel compressibility	1/Pa
CMNL	Input, liquid sodium compressibility	1/Pa
COFICH	Convective fission-gas mass flux in coolant channel	kg/(s·m2)
COFUCH	Convective fuel mass flux in coolant channel	kg/(s·m2)
COFUOS	Convective fuel energy flux in the channel	J/(s·m2)
CONACH	Convective sodium mass flux in coolant channel	kg/(s·m2)
CPFU	Input, fuel heat capacity	J/(s·m2)
CTFRFU	Fraction of the moving fuel that is in contact with clad or plated-out fuel
C1	Input, part of liquid sodium heat-transfer correlation
C2	Input, part of liquid sodium heat-transfer correlation
C3	Input, part of liquid sodium heat-transfer correlation
C1VIPR	Input, used for the artificial viscous pressure calculation in the pin
C2VIPR	Input, used for the artificial viscous pressure calculation in the pin
D	Diameter, hydraulic diameter	m
DEFICH	Generalized smear density of free fission gas in the coolant channel	kg/m3
DEFUCH	Generalized smear density of the moving fuel in the coolant channel	kg/m3
DEFVCH	Generalized smear density of fuel vapor in the coolant channel	kg/m3
DENACH	Generalized smear density of sodium in the coolant channel	kg/m3
DENMCH	Generalized smear density of moving sodium in the coolant channel	kg/m3
DZPLIN	Input, minimum length of a Lagrangian edge cell	m
e	Internal energy	J/kg
EGBBLY	Input, internal fuel energy below which fuel freezing begins	J/kg
EGFULQ	Input, internal fuel energy at the solidus	J/kg
EGFUSO	Input, internal fuel energy at the solidus	J/kg
EGMN	Input, internal fuel energy below which fuel cannot switch from the particulate to a continuous flow regime	J/kg
EPCH	Input, controls use of advanced pressure in in-pin calculation
f	Factor used in interphase drag term
F	Friction factor
FF	Mass of fuel ejected per time step and per unit of generalized smear volume	kg/m2
FIFNGB	Input, fraction of fission gas on grain boundaries which becomes available as free gas upon fuel melting
FNARME	Input, cross section area of pin cavity/cross section area of fuel above which failure of this node is allowed to occur
FNFUAN	Input, controls when annular fuel flow in molten pin cavity is assumed
FNMECA	Fraction of node width of radial heat-transfer node on cavity boundaries which melts in pure PLUTO2 time step
FNMELT	Input, controls locus of cavity boundary
FNPI	Fraction of all the pins in a subassembly which have failed
FNPOHE	Relative power level
FN	Fraction of the molten fuel in a ejection cell which is ejected per PLUTO2 time step
FUELMS	Initial fuel mass in a radial fuel-pin mode	kg
FUMASS	Initial total fuel mass in an axial fuel node	kg
FUMS	Current fuel mass in the radial fuel pin node on the cavity boundary	kg
F.R. 1	Particulate fuel flow regime
F.R. 3	Partially or fully annular flow regime
F.R. 4	Bubbly fuel flow regime
g	Gravity	m/s2
GAMSS	Input, fraction of power going into direct heating of structure
GAMTNC	Input, fraction of power going into direct heating of coolant
GAMTNE	Input, fraction of power going into direct heating of cladding
h	Heat-transfer coefficient	J/(m2·s·K)
H	Heat-transfer coefficient times heat-transfer area	J/(s·K)
HCCLMI	Input, heat-transfer coefficient between hot cladding and a two-phase sodium/gas mixture	J/(m2·s·K)
HCFFMI	Input, heat-transfer coefficient between frozen fuel crust surface and two-phase sodium/gas mixture	J/(m2·s·K)
HCFUBB	Input, heat-transfer coefficient between the interior of the molten fuel and bubble surface	J/(m2·s·K)
h1	Auxiliary heat-transfer coefficient	J/(m2·s·K)
h2	Auxiliary heat-transfer coefficients	J/(m2·s·K)
I	Axial node index in coolant channel
IB	Channel zone in which the uppermost segment of the lower slug is located
IDIFF	Offset between pin and channel grid. The first pin node is at the same elevation as channel node IDIFF + 1
IFLAG	Pointer array which gives the flow regime number for each axial channel node
IMAX	Uppermost slug segment of upper sodium slug
IT	Channel zone in which the lowermost segment of the upper slug is located
k	Conductivity	J/(m·s·K)
K	Axial index in the pin
KKMX	Uppermost node in the molten pin cavity
KZPIN	Coolant channel zone which contains the fuel pins
KK1	Lowermost node in the molten pin cavity
L	Length	m
L1	Length of the Lagrangian node at one end of the interaction region	m
L2	Length of Lagrangian node at the other end of the interaction region	m
N’	Number per unit of generalized smear volume
NCPLEV	Input, number of cladding nodes which have to be molten in to lead to switch to LEVITATE
NGRDSP	Input, number of grid spacers in the channel zone containing fuel pins
NRPI	Number of pins per subassembly
NT	Number of radial fuel pin nodes
Nu	Nusselt number
P	Pressure	Pa
PECH	Perimeter of the coolant channel associated with one pin	M
PORFR	Porosity fraction
POW	Input, power in highest rated axial fuel pin node	W
POWCOF	Exponent in the exponential function which give the power history during main time step
PRFAIL	Input, failure pressure for non-mechanistic clad failure Propagation	Pa
Pr	Prandtl number
PSHAPE	Input, axial pin power shape
PSHAPR	Input, radial power shape in a pin
Q	Fission heat source	W/kg
r	Radius	M
R	Gas constant or radius	J/(kg·K)
RAFPLA	Input, radius of large particles	m
RAFPSM	Input, radius of small particles (which have been generated due to the decay of the larger particles after TIFP seconds)	kg
RETFG2	Retained fission-gas mass in the original radial fuel-pin node at the cavity boundary before it began melting into the cavity
Re	Reynold’s number
RGAS	Input, gas constant for fission gas	J/(kg·K)
RGNA	Sodium vapor gas constant which is a calculated quantity in PLUTO2	J/(kg·K)
S	Mass sink or source	kg/s
S’	Mass sink or source per unit of generalized smear volume	kg/(s·m3)
St	Stanton number
t	Time	s
T	Temperature	K
TECLMN	Input, cladding temperature above which frozen fuel will not stick to the cladding	K
TECLRL	Input, cladding temperature above which the frozen fuel crust will be released	K
TEFAIL	Input, cladding failure temperature in nonmechanistic failure criteria	K
TESOL	Input, steel solidus temperature	K
TIFP	Input, time delay for fragmentation of large particles into small ones	s
TKFF	Thickness of frozen fuel crust	m
u	Velocity	m/s
UFCH	Fuel velocity in the channel	m/s
UMCH	Sodium/gas mixture velocity in the channel	m/s
VCONST	Auxiliary quantity in the sodium film entrainment calculation
VFNALQ	Input, liquid sodium fraction below which a particulate flow regime can become a continuous one
VFNARE	Input, liquid sodium fraction below which a particular flow regime can become a continuous one
VIFG	Input, viscosity of sodium vapor	kg/(m·s)
VIFULQ	Input, viscosity of liquid sodium	kg/(m·s)
VOLUME	Volume	m3
w	Width	m
W	Mass flow rate	kg/s
x	Sodium quality
XKORGD	Input, orifice coefficient of a single grid spacer
XKORV	Input, expansion, contraction, or orifice coefficient
z	Axial coordinate	m