16.11. Nomenclature

Symbol	Description	Units
Ak,i	Cross sectional area of component \(k\), in the coolant channel in the axial cell \(i\)	m2
Ak,ca,i	Cross sectional area of component \(k\), in the fuel-pin cavity, in axial cell \(i\).	m2
Aj,k,i	Contact lateral area between component \(j\) and component \(k\) in the axial cell \(i\)	m2
AXMX	Reference cross-sectional area which determines the volume AXMX ⨉ Δzi, over which all component densities are smeared to yield the generalized smeared densities	m2
AFRV	Input, sodium vapor friction coefficient
BFRV	Input, exponent of vapor friction coefficient
CAREA	Coefficient used to define the contact area between two components. Has values between 0 and 1
C’D,Mi,fu,i	Generalized drag coefficient between the gas mixture and the molten fuel in the axial cell \(i\)	Kg/m4
C’in,Mi,fu,i	Generalized inertial force coefficient, used in the definition of the inertial force exerted between the gas mixture and the molten fuel in the axial cell \(i\)	Kg/m3
Cff,cl,i	Coefficient defining the fraction of the cladding perimeter covered by the solid fuel crust in the axial cell \(i\)
Cff,sr,i	Coefficient defining the fraction of the hexcan wall perimeter covered by the solid fuel crust in the axial cell \(i\)
Cfu,cl,i	Coefficient defining the fraction of the cladding perimeter covered by the molten and frozen fuel in the axial cell \(i\)
Cfu,sr,i	Coefficient defining the fraction of the hexcan wall covered by the molten and frozen fuel in the axial cell \(i\)
Cfu,ff,cl,i	Coefficient defining the fraction of the frozen fuel crust on the cladding covered by molten fuel
Cfu,ff,sr,i	Coefficient defining the fraction of the frozen fuel crust on the hexcan wall covered by molten fuel
Cmfu,cl,i	Coefficient defining the fraction of the cladding perimeter covered by molten fuel only, in cell \(i\)
Cmfu,sr,i	Coefficient defining the fraction of the hexcan wall covered by molten fuel only, in cell \(i\)
Cp,fu	Specific heat for the fuel	J/(kg·K)
Cse,ff,cl,i	Coefficient defining the fraction of the frozen fuel crust on the cladding covered by molten steel
Cse,ff,sr,I	Coefficient defining the fraction of the frozen fuel crust on the canwall covered by molten steel
CMNL	Input, liquid sodium compressibility	Pa-1
CMFU	Input, liquid fuel compressibility	Pa-1
DH,Mi,i	Hydraulic diameter for the gas mixture in the coolant channel in cell \(i\)	m
fMi,i	Friction coefficient used to characterize the friction between the gas mixture and the channel walls in cell \(i\)
Farea,bd,lu,i	Fraction of lateral chunk area in contact with the channel boundaries in cell \(i\)
hk,i	Enthalpy of component k in the axial cell \(i\)	J/kg
Hj,k,i	Heat-transfer coefficient between components \(j\) and \(k\) in cell \(i\).	J/(m2s-K)
H’j,k,i	Generalized heat transfer coefficient, similar otherwise to Hj,k,i \({H'}_{j,k,i} = H_{j,k,i} \cdot \frac{A_{j,k,i}}{AXMX\ \ \cdot \ \ \Delta zi}\)	J/(m3s-K)
hNa,liq,i	Enthalpy of liquid sodium at saturation in cell \(i\)	J/kg
hNa,vap,i	Enthalpy of sodium vapor at saturation in cell \(i\)	J/kg
hNa,lg,i	Heat of vaporization for sodium in cell \(i\)	J/kg
hfv,lg,i	Heat of vaporization for fuel	J/kg
kMi,I	Conductivity of the sodium and fission-gas mixture in the axial cell \(i\)	J/(M-s-K)
Lcl,I	Perimeter of all pins in a subassembly in the axial cell \(i\)	m
Lsr,i	Same as above, for the canwall	m
Lff,cl,I	Perimeter of the cladding fuel crust in a subassembly in the axial cell \(i\)	m
Lff,sr,i	Same as above, for the canwall fuel crust	m
lff,cl,i	Thickness of the fuel crust on cladding in the axial cell \(i\)	m
lff,sr,i	Same as above for the canwall fuel crust	m
Mk,i,ic	Mass of component k is the axial cell \(i\) of one subassembly of channel \(\text{ic}\)	kg
Mk,i,ico	Same as above, but referring to the initial conditions	kg
Npins	Number of fuel pins in the subassembly
Pch,i	Total pressure in the coolant channel in the axial cell \(i\)	Pa
Pk,i	Partial pressure of component \(k\) in cell \(i\)	Pa
Pk,sat,i	Saturation pressure for component \(k\) in the cell \(i\), e.g., PNa,sat,i = Psat (TNa,i)	Pa
Qk,i	Energy source in the component \(k\) in cell \(i\)	J/(kg-s)
Qcl,i	Energy source in the cladding in the axial cell \(i\) of one subassembly	J/s
R	Universal gas constant
Rk	Gas constant specific for the component \(k\), \(R_{k} = \frac{R}{M_{k}}\) where \(M_{k}\) is the molar mass of the component \(k\).
Rca,k	Radius of cavity in the axial cell \(k\)	m
Rcl,os,i	Outer radius of the cladding in the axial cell \(i\)	m
Rlu,i	Radius of the fuel/steel chunks in cell \(i\)	m
Re	Reynolds number
Tk,i	Temperature of component \(k\) in cell \(i\)	K
uk,i	Velocity of component \(k\) in the coolant channel at the boundary \(i - 1/2\)	m/s
vNa,i	Specific volume of sodium in cell \(i\)	m3/kg
vNa,liq,i	Specific volume of the liquid sodium at saturation in cell \(i\)	m3/kg
vNa,vap,i	Specific volume of the sodium vapor at saturation in cell \(i\)	m3/kg
Vk,i	Volume occupied by component \(k\) in cell \(i\)	m3
XNa,i	Quality of the two-phase sodium in cell \(i\)
z	Axial coordinate	m
Δzi	Length of axial cell \(i\)	m
ΔTj,k,i	Temperature difference between components \(j\) and \(k\) in the axial cell \(i\)	K
Δt	Time increment	s
ΔRcl,i	Current thickness of the cladding in the axial cell \(i\)	m
ΔRcl0	Thickness of the original cladding in cell \(i\)	m
ρk,i	Physical density of component \(k\) in the cell \(i\).	kg/m3
ρ’k,i	Generalized density of component \(k\) in cell \(i\), \({\rho'}_{k,j} = \rho_{k,i}\ \ \cdot \ \ \frac{A_{k,i}}{\text{AXMX}}\)	Kg/m3
σfu	Liquid fuel surface tension	J/m2
σse	Liquid steel surface tension	J/m2
θk,i	Volume fraction of component k in the axial cell \(i\) \(\theta_{k,i} = \frac{Q_{K,i}}{\text{AXMX}}\)
Subscripts
bd	Refers to a quantity defined at the cell boundary
ca	Cavity
ch	Coolant channel
cl	Cladding
ch,op	Open channel. The open channel at any axial location can become smaller than the original coolant channel due to fuel and steel freezing. It can also increase due to the ablation of the cladding and hexcan wall and to the disruption of the fuel pins
ff	Frozen fuel
ffc	Frozen fuel on cladding
ffs	Frozen fuel on structure
fi	Fission gas
fu	Molten fuel
fv	Fuel vapor
fl	Fuel chunks
i	Cell number, on the channel grid
is	Inner cell of cladding or structure
IN	Inertial
J	Other components in the coolant channel, exchanging mass, momentum or energy with component \(k\)
k	Component subscript, referring to the component being described. Also used as cell number on the fuel-pin grid
liq	Indicates a physical property for the saturated liquid, e.g., hNa,liq,i
lq	Indicates a physical property at liquidus
lu	Solid fuel/steel chunks
lv	Indicates a physical property that characterizes the transition from liquid to gas, e.g. hlv
Mi	Mixture of sodium vapor, fission gas, fuel vapor, steel vapor, and liquid sodium
Mo	Momentum
Na	Sodium
Nl	Liquid sodium
Nv	Sodium vapor
Os	Outer cell of cladding or structure. The “outer” surface is always the surface facing the coolant channel
pin	Fuel pin
sat	Indicates a physical property at saturation, e.g., Tsat (Pk,i)
se	Molten steel
sl	Steel chunks
so	Indicates a physical property at solidus
sr	Structure, i.e., hexcan wall or wall of the experimental loop
st	Refers to a stationary component, such as the solid fuel in the pin
sv	Steel vapor
vap	Indicates a physical property for the saturated dry vapor, e.g., hNa,vap,i
vg	Vapor/gas mixture
Superscripts
cond	Condensation
L	Used to indicate a lateral area, as opposed to a cross-sectional area
N	The value of any quantity at the beginning of the current time step
\(n + 1\)	The value of any quantity at the end of the current time step. If no superscript is present, the default is n
N	Used in relation to the cylindrical chunks, to indicate the area of the lower and upper base
vap	Vaporization