USER'S GUIDE Third Edition

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DOE/ID-01570-5
PFC/RR-89-4
LITFIRE USER'S GUIDE
Third Edition
D.S. Barnett
April 1989
Plasma Fusion Center
Massachusetts Institute of Technology
Cambridge, MA 02139 U.S.A.
*This work was supported by EG&G Idaho, Inc. and the
U.S. Department of Energy, Idaho Operations Office
under DOE Contract No. DE-AC07-7611D01570
Reproduction, translation, publication, use and disposal
in whole or in part, by or for the United States
government is permitted
Abstract
This document contains instructions for using the LITFIRE lithium fire
simulation code in its form as of April 1989. The code is capable of simulating
fires in a single compartment connected to an optional second compartment, or
in an insulated pan suspended in one compartment. Lithium or lithium-lead
eutectic may be used as the fuel, reacting with an atmosphere of oxygen, nitrogen, water vapor, or any mixture thereof. Any inert gas may be included
in the compartment atmosphere and lithium only may be burned in a carbon
dioxide atmosphere without oxygen. An option for liquid metal-concrete interaction exists as well as the following options for mitigating the effects of the
fire: gas flooding, emergency space cooling, emergency floor cooling, aerosol
removal and gas injection. The guide also includes the following:
" a description of the workings of the code, including the various options
available to the user
" a description of the physics of lithium fires and heat and mass transfer
" instructions for running the code
" a list of sample input ifies
" a listing of the code with a glossary defining code variables
1
Contents
Abstract
1
Table of Contents
2
List of Figures
3
1
Introduction
2
Program Description
2.1
2.2
2.3
3
Initial Routine .....................
2.1.1 Input Data . . . . . . . . . . . . . . .
2.1.2 Print out the Input . . . . . . . . . . .
2.1.3 Variable Initialization . . . . . . . . . .
2.1.4 Spray Fire Calculations . . . . . . . . .
Dynamic Cycle . . . . . . . . . . . . . . . . .
2.2.1 Preliminary Calculations . . . . . . . .
2.2.2 Radiative Heat Transfer . . . . . . . .
2.2.3 Gas Node Temperature Determination
2.2.4 Natural Convection Heat Transfer . . .
2.2.5 Conductive Heat Transfer . . . . . . .
2.2.6 Temperature Rates of Change . . . . .
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2.2.7
Lithium Combustion . . . . . . . . . . . . .
2.2.8
2.2.9
2.2.10
2.2.11
2.2.12
2.2.13
Overpressure, Leakage, and
Integrals . . . . . . . . . .
Termination Checks . . . .
Time Step Control . . . .
Output Section . . . . . .
Error Pointers . . . . . . .
Aerosol
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Behavior
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Modeling Options . . . . . . . . . . . . . . . . . . .
2.3.1
One Cell Option
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2.3.2
Two Cell Option
. . . . . . . . . . . . . . .
2.3.3
2.3.4
Pan Option . . . . . . . . . . . . . . . . . .
Concrete Reaction . . . . . . . . . . . . . .
2.3.5
Lithium-Lead Combustion . . . . . . . . . .
2.3.6
2.3.7
2.3.8
Steam-Air Atmosphere Option . . . . . . . .
Torus Fire Option . . . . . . . . . . . . . . .
Mitigation Options . . . . . . . . . . . . . .
Execution of LITFIRE
3.1 Obtaining Copies of LITFIRE and the Input Data Files.
3.2 Organization of LITFIRE for Execution . .
2
19
21
22
3.2.1
3.2.2
One Cell Option
Two Cell Option
........................
.
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22
24
3.2.3
3.2.4
Pan, Concrete Reaction and Lithium-Lead Combustion . . . .
Gas Flooding, Emergency Space Cooling, Emergency Floor Liner
Cooling and Gas Injection . . . . . . . . . . . . . . . . . . . .
Steam Injection to Containment . . . . . . . . . . . . . . . . .
25
3.2.5
26
26
3.3
3.2.6 Torus Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PFCVAX Execution . . . . . . . . . . . . . . . . . . . . . . . . . . .
27
28
3.4
3.5
MFE Crays Execution . . . . . . . . . . . . . . . . . . . . . . . . . .
Sample Input and Output Files . . . . . . . . . . . . . . . . . . . . .
29
30
A Nomenclature
31
B Variable Listing
32
C Troubleshooting
59
D Sample Input Data Files
60
E Sample Output Data Files
62
F Listing of the LITFIRE code
63
Bibliography
152
List of Figures
1
One-cell option in LITFIRE ......
2
3
4
5
Two-cell option in LITFIRE ........................
Mass flow in LITFIRE ..........................
Pan option in LITFIRE ........................
Torus fire option in LITFIRE ......
......................
.......................
3
14
.
15
16
17
20
1
Introduction
LITFIRE is a computer code which simulates lithium fires in fusion reactors by generating the time histories of the temperature and pressure profiles occurring in a
reactor containment in response to a lithium or lithium-lead eutectic spill and fire.
The fire may take place in a single cell connected to an optional second cell, or in
an insulated pan in a single cell. The lithium or lithium-lead may react with any
mixture of oxygen, nitrogen or water vapor; an inert gas may also be included in
the cell atmospheres. Lithium only may be burned in a carbon dioxide atmosphere
without oxygen. An option for liquid metal-concrete interaction is available as well
as the following options for mitigating the effects of a fire: gas flooding, emergency
space cooling, emergency floor cooling, aerosol removal and gas injection. This user's
guide includes a brief description of the physics of lithium fires, the workings of the
code and the options available to users, and also includes a listing of the code with a
complete glossary of variables used in LITFIRE.
The present version of LITFIRE is available on the PFCVAX at MIT and on
the Crays at the National Magnetic Fusion Energy Computer Center (NMFECC,
hereafter referred to as MFE) It is written in FORTRAN 77 and is compatible with
the computing facilities at which it is located. The instructions present in this guide
will enable a user to execute the code at either location.
Other information on LITFIRE such as more detailed descriptions of physical
models or correlations used in the code are available in the references listed in the
reference section of the guide.
2
Program Description
To assist the new user of LITFIRE in understanding the code, a brief descriptive
section is included. The description of the code sections is presented in the order that
they are executed. For a description of code options, see Section 2.3. This section is
broken down into an initial routine and a dynamic cycle. The initial routine prepares
the code for execution; then the dynamic cycle integrates the time rate of change of
the code variables over the time step to calculate their values. The dynamic cycle is
repeated until execution is terminated either by the code or as predetermined by the
user.
2.1
Initial Routine
The four parts of the initial routine are:
1. read in the input data
2. write the input data to a file
4
3. initialize the variables
4. spray fire calculation
2.1.1
Input Data
The input data consists of titles and headings, control flags for the choice of options,
geometries, initial conditions and material properties. User chosen options are described in Section 2.3. Input variables are described in Section 3 and examples of the
input data files are given in Appendix D.
2.1.2
Print out the Input
The input is printed out to a file, which should be examined by the user to ensure
that the input was properly entered into the input files. Misaligned input data is a
common source of error that can easily be caught by examining the printed input.
2.1.3
Variable Initialization
The initialization section sets all time rates of change to zero for the first step. Some
constants are defined and initial conditions are applied using the input data. In
addition there is a short sub-section where the units of the input data are changed to
the following to become consistent with the rest of the code:
BTU, pounds mass, feet, seconds
2.1.4
Spray Fire Calculations
The spray fire calculation simulates the effect of lithium reacting as a spray at the
beginning of a spill. The amount reacted in the spray is user specified. A difficulty
does arise in that the specific heats of the reaction products are calculated as functions of temperature. The spray fire calculation is not a spray fire model per se in
that the lithium reacting in the spray is consumed instantaneously, adiabatically and
stoichiometrically, with the equilibrium temperatures being determined by iteration.
2.2
Dynamic Cycle
The dynamic cycle in LITFIRE calculates the temperature, pressure and mass profiles
of the reactor containment over the time of the run. Most of the dynamic cycle
consists of calculating the thermal admittances between nodes, which are then used
in conjunction with the nodal temperatures, to determine the time rates of change of
the nodal temperatures. The heat flow to or from a node is determined by calculating
the thermal resistances to conduction or convection between adjacent nodes and then
adding on radiative heat transfer to or from nodes within a line of sight. All of the
5
calculations performed in the dynamic cycle are listed below in the order which they
are performed:
1. Perform gas injection if necessary
2. Calculate temperature dependent heat capacities
3. Calculate individual gas fractions
4. Calculate gas emissivities and radiative interchange factors
5. Perform an energy balance to determine the gas temperature if the steam in
containment option is used
6. Calculate natural convection gas heat transfer coefficients
7. Calculate thermal admittances
8. Perform steam injection if necessary
9. Perform lithium-lead diffusion calculation if necessary
10. Test for and calculate lithium or lithium-lead combustion
11. Calculate temperature rates of change from heat flow
12. Calculate lithium-concrete reaction if necessary
13. Calculate gas overpressure and leakage
14. Calculate aerosol removal rate via aerosol sticking
15. Perform integrations
16. Check for terminating execution
17. Perform time step control
18. Write the output to data files
19. Display error pointers if necessary
Short descriptions of the subsections appear below.
6
2.2.1
Preliminary Calculations
Before any calculations are performed by the code, the material properties of all of the
nodes must be calculated. Most properties are assumed to be constant with respect to
temperature, but the specific heats of some gases and combustion products, and most
lithium properties, are calculated as functions of temperature. These are calculated
at the beginning of each time step. The mass fraction and total mass of each of the
individual gases is also calculated so that the total heat capacity of the gas may be
calculated.
2.2.2
Radiative Heat Transfer
Radiative heat transfer rates in LITFIRE are calculated using the following basic
equation:
Q1--.2 = f Aio(T' - T2)
(1)
where Q1-.2 = heat transfer rate (W) from node 1 to node 2
A1
= exposed area of node 1
f
= radiative interchange factor based on A1
0
T,,
= Stefan-Boltzmann constant
= temperature of node n
The radiative interchange factor f is determined by the emissivities of the surfaces
of the two nodes and the view factor between them. Thus the radiative emissivity of
each node is required to account for radiative heat transfer within the containment
building.
The emissivities of the solid elements in the containment building are specified by
the input data and are assumed to be constant. The emissivity of the lithium pool is
assumed by the code to be governed by the buildup of reaction products (Li 2 0, Li 3 N
and Li 2 CO 3 ) on the pool surface.
The emissivity of the cell gas (in the absence of steam) is determined by the
aerosol size and concentration in the gas and by the optical path length in the cell.
The aerosol particle area and the optical path length are defined by the user in the
input data and the concentration is calculated from the amount of aerosol reaction
product generated by the fire. In the presence of steam the emissivity of the cell gas
is also governed by the partial pressure of the water vapor in the cell. Radiative heat
transfer is discussed in greater detail in reference[2].
2.2.3
Gas Node Temperature Determination
If the steam in containment option is being used, the presence of a condensible gas
requires that a different method be used to determine the temperature of the gas than
the integral method described in Section 2.2.9, as the latent heat of vaporization of
the steam must be taken into account. In this option, the code performs an iterative
7
energy balance by solving the equation:
TEMP = U, - Mci.T - Mu,
(2)
where U, is the total internal energy of the gas, At is the mass of the non-condensible
gas, c, is the specific heat of the non-condensible gas, M, is the mass of the steam
and u, is the specific internal energy of the steam. Values of the temperature are
guessed, and along with the specific volume of the steam (which is known), are used
to determine the other properties of the steam. These values are then used to solve for
the error, TEMP. When TEMP is a sufficiently small fraction of the total gas internal
energy, the final guess is taken as the gas temperature. For further discussion, see
reference[2].
2.2.4
Natural Convection Heat Transfer
The heat transfer coefficients for convective heat transfer between surfaces and gases
h are calculated from the temperature of the surface T,, the temperature of the gas
T9, and the density of the gas p,:
h = CF(T,,T, pg)
(3)
where C is a user defined constant. In the presence of steam the hest transfer coefficients used are the Uchida heat transfer coefficients determined empirically as
functions of the ratio of the mass of water to the mass of non-condensibles in the cell
atmosphere. A more detailed description is given in reference[2].
2.2.5
Conductive Heat Transfer
Once the heat capacities, the radiative interchange factors and the convective heat
transfer coefficients for all of the nodes have been calculated, the thermal resistances
between the nodes are calculated. Knowledge of the thermal resistance allows the
temperature rate of change due to heat conduction and heat convection to be calculated. In LITFIRE the thermal resistance between adjacent nodes i and j is calculated
as follows:
+
(4)
2k, A
2kA
or
I.
i=
A
+
1
_A
(5)
where 1, = characteristic length (thickness) of node n
kn = thermal conductivity of node n
A = area of contact between nodes i and j
hij = convective heat transfer coefficient between nodes i and j,
depending on whether or not node j is a solid (Equation 4) or a gas (Equation 5).
8
The thermal resistance between the lithium pool and the combustion zone is
determined somewhat differently, as the lithium is considered to vaporize and then
react with the gases in the combustion zone. Details of the calculation are given in
reference[2].
2.2.6
Temperature Rates of Change
The rates of heat transfer between all thermally adjacent nodes are calculated from
the temperatures of the nodes, and the thermal resistances and radiative interchange
factors between them. Once the rates of heat transfer to and from all of the nodes
have been calculated, they are summed for each node, and the temperature rate of
change of each node is calculated using its own heat capacity. The heat flow to or
from a given node is determined by summing the heat flow by conduction, convection
and radiation to and from thermally adjacent nodes:
Q
(T1-Ti)+Z
O+
fT
where:
p
AifIjo(T14 - T )
Q1 = (T
Q,
=
heat flow rate to or from node 1
T,
=
temperature of node n
i
=
designation for physically adjacent node
Rli
=
thermal resistance between nodes 1 and i
6
(6)
(see Eqns. 4 and 5)
= designation for optically adjacent node
A 1 = surface area of node 1
fij = radiative interchange factor between nodes 1 and j
Temperature rates of change for each node are calculated by dividing the energy
gain or loss rate by the heat capacity of the node:
j
Q,
dT1
dt
(7)
ii
-
where t is time, mI is the mass of node 1 and cp is the specific heat of node 1. The
combustion zone node adds the heat of combustion and the heat of vaporization of
the lithium combusted to the above terms, while the lithium pool subtracts the heat
of vaporization of the lithium combusted. That is due to the assumption that the
lithium reaction takes place in the vapor phase.
2.2.7
Lithium Combustion
The temperature rates of change in the containment can differ greatly depending
whether or not the lithium pool is actually combusting (reacting with the containment
atmosphere). The criteria used to determine whether or not the lithium is combusting
are:
9
9
Liquid lithium must be available (between 180 and 13470C)
" Oxygen, nitrogen, carbon dioxide or water vapor must be available
* If only nitrogen is present, the combustion zone temperature must be less than
11270C
If none of the above conditions are met, then the combustion zone is considered
to be nonexistent, and heat transfer from the lithium to the rest of the containment
building is performed normally. If combustion is occurring, then the combustion rate
and the heat liberated by the lithium reactions is calculated.
In LITFIRE the lithium combustion rate is governed by the flow rate of gas or (if
lithium-lead is being burned) the diffusion of lithium to the combustion zone. The
gas flow rate is determined by natural convection using Reynold's analogy between
heat and mass transfer.
Once the gas flow rate to the combustion zone has been calculated, the lithium
reaction rate may be calculated. The lithium is assumed to react with the gas quickly
as it flows to the combustion zone, unless the chemical kinetics serves to further limit
the reaction rate. The unhindered lithium reaction rate is given by:
RRu = Apoo
RR;
(8)
where
RR, = hmpiR.,
where Apool
hm
p;
R1,
(9)
=
=
=
=
surface area of the lithium pool
natural convection mass transfer coefficient
total density of the gas i (mass/containment volume)
stoichiometric combustion ratio between lithium and the gas i
(mass of lithium/mass of gas)
The kinetics of the lithium reactions with nitrogen, oxygen and steam may serve
to either reduce the reaction rates below those expected from the gas flow rate to the
reaction site. After the gas flow rates of each of the constituent gases of the atmosphere have been determined, reaction kinetics effects are applied to the preliminary
reaction rates to determine their final values. Lithium reaction kinetics are covered
in detail in reference[2].
Once the reaction rates have been calculated, the heat generated by combustion
is calculated by summing the products of the reaction rates RR; and the heats of
combustion AH; of each of the reacting gases:
Q=
RR.AHi
10
(10)
2.2.8
Overpressure, Leakage, and Aerosol Behavior
The masses of each cell gas component and the cell gas temperature are integrated
in the integration section. From this, the cell gas pressure is determined and thus
leakage from containment can be calculated. Aerosol adhesion to the containment
walls is a user specified option and changes the concentration of aerosol combustion
products in the containment atmosphere.
2.2.9
Integrals
All time rates of change are integrated over each time step to calculate the values of
the quantities during the execution of the code. The form of the integrals is:
P = INTGRL P., -
(11)
where P, is the initial value of function P (mass, temperature or energy), and 4 is
the time dependent rate of change of P.
INTGRL is an integration function that uses a fourth order Runge-Kutta Method
or Simpson's Rule (user specified) to simultaneously solve all of the differential equations used in the code. For a more detailed description, see the listing of the code,
Appendix F.
2.2.10
Termination Checks
The conditions that will terminate the code are:
" the lithium temperature reaches a value at which the lithium vaporizes (13470C)
or solidifies (1800C)
" the primary cell gas temperature returns to ambient temperature with no overpressurization
" the code reaches the user specified stopping point (TIME>TIMEF)
2.2.11
Time Step Control
Three criteria are used to determine the size of the time step used during each dynamic
cycle. They are:
1. The time step must be smaller than a user defined fraction of the inverse rates
of change:
DELT < RELERR T/
11
(-)
2. The conduction heat transfer limit must be satisfied:
aLatat<
(AX)2
0.3
3. The user imposed maximum and minimum time steps must be observed. The
maximum time step is indicated by DELOUT and the minimum by DTMIN.
DELOUT and DTMIN are read from the first input file.
2.2.12
Output Section
The output from LITFIRE is written into data files as the code is executed. Examples
of the output files are shown in Appendix E, generated by the input files found in
Appendix D.
2.2.13
Error Pointers
This section is not actually part of the dynamic cycle, although if an error during
execution should occur, an error message would be written into file outl.dat and code
execution would halt.
2.3
Modeling Options
The basic version of LITFIRE is capable of simulating a wide variety of spill conditions
as indicated by the user in the first input data file. The containment volume, height,
wall and floor areas, atmosphere, and material composition may be specified as well as
the mass and surface area of the lithium spilled. Optional reaction geometries include
a primary cell containing the lithium, surrounded by a larger secondary cell; a partially
insulated pan holding the lithium inside the basic primary cell; or a primary cell
surrounded by blanket and shield structures producing decay heat, further surrounded
by a larger secondary cell. A concrete floor and wall for the containment are optional
as is a liquid metal-concrete reaction routine. Also instead of elemental lithium, a
lithium-lead eutectic may be selected for the spill with the composition chosen by the
user. Finally an option to simulate a lithium or lithium-lead spill in the presence of
a steam-air atmosphere may be chosen.
In addition to the above options, several options involving the mitigation of lithium
fires are available. These include:
" gas flooding
" emergency space cooling
" emergency floor liner cooling
" aerosol removal
12
* gas injection
Each option is discussed below.
2.3.1
One Cell Option
The single cell model is the simplest version of LITFIRE that may be run. All other
options are constructed as subroutines added on to the one cell version of the code.
The nodes existing in the one cell version are shown in Figure 1 There may be up
to twenty concrete wall or floor nodes of any thickness. As stated earlier all material
properties may be chosen by the user as may the composition of the containment
atmosphere. Lithium or lithium-lead may react with any mixture of oxygen, nitrogen
or water vapor and lithium only may react with carbon dioxide in the absence of
oxygen. Any inert gas may also be included in the cell atmosphere. Lastly, any
containment or spill geometry may be chosen as stated above.
The heat transfer correlations are fixed by the code so that accurate results may
be obtained, although some modification is possible from the input data as shown in
Section 2.2.4. The heat transfer pathways are also fixed by the code and are shown
in Figure 1. The heat transfer mechanisms and their applications to the code are
further discussed in reference[2].
2.3.2
Two Cell Option
The two cell option was developed to model the effects of a fire inside a tokamak fusion
reactor and to determine its effects on the structural integrity of the the torus. In
this option a separate secondary cell with its own material composition, atmosphere
and geometry exists surrounding the primary cell. (See Figure 1) The provision for
a crack between the primary and secondary cells, allowing the exchange of cell gases
also exists. The code follows the composition, pressure and temperature of both cell
gases during the run. The heat and mass flow paths in two cell LITFIRE are shown
in Figures 2 and 3. High velocity gas flows, as would be encountered in the event
of a breach in a vacuum torus have been successfully modeled by LITFIRE. (See
reference[3])
2.3.3
Pan Option
Figure 4 shows the pan option available in LITFIRE. This option may be used with
either the one or two cell option, but not with the concrete reaction option. This
option was created to model the lithium fire experiments performed at HEDL. The
pan dimensions and composition are user defined. The pan is surrounded by two
separate insulation nodes.
13
Wall Liner
Ambient
Cell Gas
Combustion Zone-
iAhUM
Conret WYl
CConcrete
JPool
lor Liner
FWalr
Concete
loor-
Conductive Heat Transfer
-Convective Hent Transfer
----- Radiative Heat Transfer
Figure 1: One-cell option in LITFIRE
14
H
Secondary Cell Gas
Primary Wall
Ambient
Primary Cell Gas
Crack.
S
S
S
S
Combustion Zone
S
S
S
S
I rimary Floor
Secondary Wall Liner
N
__
Secondary Floor Liner
Concrete Wall
Concrete Floor
-
Conductive Heat Transfer
Convective Heat Transfer
--- 0.Radiative Heat Transfer
Figure 2: Two-cell option in LITFIRE
15
Gas St rge
02, CG2
Ambient
N2,
Inert Gas
Storage
Injection
Gass
m
Game
and
Aeosols via
leakage
Cell Gas
Inert
Gas
Flooding
ConstiPrimary
Cell Gas
blents
Secondary
Cell Gas
via Crack
AmolRemovol via
sticking to WaI
Primary
Wal
H2 ,OsN Cj
and innt gases via
convection and
diffusion
Combustion
zone
Solid Reaction
Products (LiN,
Li 20, Li 2C 2,
Li2CO3 , an C)
Uithium
Pool
Reaction Products (LiOH,
Li 3N, LiW, H2. Li2CO)
UWhimn via vqpri"
and
diffusion
Figure 3: Mass flow in LITFIRE
16
Cell Gas
Wall Liner
Ambient
N1
s...
Combustion Z )L
P'
Steel Pan
Lithium Pool
] II
Pan
Insulation
I
a
Floor Liner
Concrete Wall
Concrete Floor
-
Conductive Heat Transfer
Convective Heat Transfer
Radiative Heat Transfer
Figure 4: Pan option in LITFIRE
17
2.3.4
Concrete Reaction
The liquid metal-concrete reaction subroutine allows for the reaction of lithium with
the concrete floor under the liner. This includes lithium reactions with water driven
from the concrete and certain components of the concrete itself. For further discussion, see reference[2].
2.3.5
Lithium-Lead Combustion
This option allows for the substitution of a lithium-lead eutetic in the place of elemental lithium as the source of the fire. All LITFIRE options are compatible with
the lithium-lead combustion option except for the initial spray fire calculation. In
addition, this option allows the user to choose either a layered or turbulent pool reaction, allowing for optimistic or pessimistic results respectively, depending on the
user's view of lithium-lead fires. Reference[2] discusses the lithium-lead option in
greater detail.
2.3.6
Steam-Air Atmosphere Option
The steam-air atmosphere option allows for the reaction of lithium or lithium-lead
with a mixture of steam and other non-condensible gases. It also includes modifications of the convective heat transfer coefficients to account for condensation and the
provision for steam condensation into a water pool node above the cell floor liner.
Gas temperature is determined by an iterative energy balance routine (as shown in
Section 2.2.3) to account for the presence of the condensible vapor, rather than in the
usual integral method described earlier. The steam in the atmosphere may be present
as humidity or may be injected into the primary or secondary cell atmosphere, with
the time, mass flow rate and enthalpy of the steam injected selected by the user. The
development of the steam-air atmosphere option is discussed in reference[2].
2.3.7
Torus Fire Option
This option allows LITFIRE to model a lithium or lithium-lead fire inside the plasma
chamber of a tokamak during a loss of flow or loss of coolant accident. The reactor
blanket and shield structures are represented by six extra nodes surrounding the
primary cell, shown in Figure 5. During a loss of flow accident the nodes are thermally
connected via conduction. During a loss of coolant accident some of them are also
connected via radiation as shown in the figure. The emissivities of, and the view
factors between the nodes are user specified. The radioactive decay heat generated
in the first wall (primary wall and floor) and the blanket and shield structures is
included as an extra heat generation term for each node:
dTdt
q__
,.picpi
18
(12)
where:
i
r
<L"
A
=
=
=
=
individual node
each individual isotope in the node i
initial decay heat density of an isotope r
decay constant of an isotope r
pi = density of node i
Up to three different isotopes may be modeled in each node; the initial decay heat
density and the decay coefficient are specified by the input data for each isotope. In
the coding of the torus fire option, the breeder region of the blanket (see Figure 5) is
represented by the node, in the two-cell option, that normally represents the secondary
extraneous heat capacity. In the torus fire option, the extraneous heat capacity in the
outer cell is represented by the magnets node. The torus fire option is incompatible
with the two-cell, pan and concrete reaction options.
2.3.8
Mitigation Options
The following is a list of options available to evaluate the effectiveness of certain
techniques used to attempt to mitigate the consequences of a lithium fire:
* gas flooding
* emergency space cooling
* emergency floor liner cooling
* aerosol removal
* gas injection
Each option allows the user to select additional heat removal mechanisms as desired. These options are discussed further in reference[4].
3
Execution of LITFIRE
The execution of the LITFIRE code requires certain system commands depending
upon the location at which it is being run. The specific commands for compiling,
loading (linking), and running the code will be discussed in this section in the following
order:
1. Obtaining the source code and sample input files
2. Execution on the PFCVAX
3. Execution on the MFE Crays
19
to Secondary Cell Wall
Crack
to Sec ondary Cell Gas
....
Plasma
Chamber
First
Wall-
First Wall
Breeder
Manifold
Shield
N
N
Vacuum Gap
Blanket Back Wall
to Secondary Cell Floor
-
Convective Heat Transfer
Radiative Heat Transfer
Except across the vacuum
gap, all adjacent nodes are
connected via thermal
conduction.
Figure 5: Torus fire option in LITFIRE
20
3.1
Obtaining Copies of LITFIRE and the Input Data Files
There are currently two locations at which a copy of the source code of LITFIRE can
be found: the PFCVAX at MIT, and the MFE FILEM disk storage.
To use the PFCVAX copy, the user must first obtain a PFCVAX account. This
may be done by contacting the Plasma Fusion Center at MIT. Introductory information may be found on the VAX by using the HELP command, which will define most
of the commands used on the PFCVAX.
To get a copy of LITFIRE for personal use, the following commands must be used:
copy [barnett.litfire]litfire.for[username]*.*
This will copy the code litfire.for into the user's main directory.
To get a copy of the sample input files, the copy command must also be used,
substituting the following filenames for litfire.for:
head.dat
uwmak.w
utumak.x
utwmak.y
uwmak.z
steamop.
torus.
After obtaining copies of the input files, they may be viewed by using the type command or edited by using any line or text editor. (e.g. EMACS or EDT).
To obtain a copy of the LITFIRE source code on one of the MFECC machines,
the user must be logged onto a machine and then use the flem command to obtain a
personal copy:
filem read .15467 litfire
This will copy litfire into the user's personal directory on that particular machine.
To obtain copies of the input files, the command
read .15467 flename
must be used for each input file (the names are the same for MFE and the PFCVAX)
while still in filem.
Once copies of LITFIRE and the sample input files have been obtained, they may
be moved to a different machine 'n' by using the netout command as follows:
netout flename site=nma
21
3.2
Organization of LITFIRE for Execution
One of the most important steps in the execution of LITFIRE is the preparation of
the input data files. Most errors in code execution occur due to mistakes in the input
data files. The input data files and the options they control are listed below. As
stated in Section 2.3, some options are incompatible with each other.
uwmak.w: one cell
uwmak.x: two cell
uwmak.y: pan, concrete reaction and lithium lead combustion
uwmak.z:
gas flooding, emergency space cooling, emergency floor liner
cooling, aerosol removal and gas injection
steamop.: steam injection with steam-air atmosphere
torus fire
torus.:
3.2.1
One Cell Option
The one cell option is the simplest version of LITFIRE. The first input file must exist
to run any other code options. The order in which the input variables must appear
in the file uwmak.w is shown below (British units are given in the Glossary, SI units
may be used for all input data files by setting the input variable IFLAGISI = 1):
22
variables
line
1
IFLAGW,IFLAGF,IFLAGP,IFLAG2,IFLAGS,IFLAGC,
2
3
4
IFLAGU,IFLAGB,IBLOW,IESC,ISFLC,ISWICH,
IAROSL,IFLAGD,IFLAGISI,IFLAGCO,IFLAGT
IFLAGR
NL,NL1
L(1) to L(NL)
L1(1) to L1(NL1)
5
6
7
VP,CHP,CPAP,XMOLA
TEHCZP,XMEHCPAEHCPCPEHCP,HINECP
THWC,THFC,GAP,KGAP,KLEAK
8
9
10
11
ESTLWP,CPSWP,KSTLWP,RHSWPAWP,THWP
ESTLFP,CPSFP,KSTLFP,RHSFP,AFPTHFP
EMLI,CPLI,AKLI,RHLI
EMCONC,CPCON,KCON,RHCON
12
13
RHOLIO,RHOLIN,RHOLIH,EMGPF,EMCZ,TAUCZ
QCO1,QCO2,QCN,QCW,QCW2
14
15
RCMB01,RCMBO2,RCMBN,RCMBW,RCMBW2,RCMBH2
TMELT,TVAP,QVAPPERCEN
16
CONF1,CONF2,C2FAC,FLIOH,FLI20
17
18
19
20
21
22
HIN,HINGSPHINGSS,HINPS,HINSAM,HINFAN
HINFGS,HINFSG
ASLI,SPILL,SPRAY,FRA,RA
TCZI,TGPZER,TSPZER,TSFPI,TA,TLII
PAPZER,WO2P,HUM,WAPWCP
IMETH,DTMIN,TIMEF,RELERR,DELOUT,OUTPUT
The formats for the input lines are:
line
1
2
3,4
format
(1x,14(il,1x))
(i4,i4)
(10f5.3)
5
(f12.2,3f12.4)
6-21
22
(6f12.4)
(i4,5f12.4)
An example of this data file (British units) is uwmak.w in Appendix D.
PFCVAX
The statement:
open(unit=2,file='uwmak.w',status='old'
must be included in the code for the code to execute, assuming that the input data file
is named uwmak.w. A similar OPEN statement must be included for each input data
23
file used by the code. These statements are currently located after the "common"
blocks at the beginning of the code.
MFE Crays
For these machines the statement:
call link("unit1=filename,read1//")
must be used for each input data file. These statements are also currently located
after the "common" blocks at the beginning of the code.
3.2.2
Two Cell Option
If the two cell option is chosen, the following are the variable listing and formats for
the second data file (units are given in the glossary as for the first input file):
line
1
2
3
4
5
6
variables
VS,CHS,PASZER,TGSZER,TSSZER,TFSZER
CRACK,HUM2,WO2S,WAS,CPAS,WCO2S
TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS
ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS
ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS
TSWICH
The format for all lines is: (6f12.4)
PFCVAX
If this option is used, the statement:
open(unit=3,jle=flen. ame',status='old')
must be included in LITFIRE in the same place as the OPEN statement for the first
input data file. An example of this data file (British units) is given in Appendix D.
MFE Crays
For these machines, the statement:
call link("unit3=flename,read3//")
must be used in the same location as the CALL LINK statement for the first input
data file.
24
3.2.3
Pan, Concrete Reaction and Lithium-Lead Combustion
The following is a variable listing for each of the above options (British units are
given in the Glossary):
t:
line
1
2
3
Pan Option
variables
KPAN, RHPAN,CPPAN,RHINS,CPINS,EMINS
TPANZO,APAN,BREDTH,AINS,HINGPF
THKPAN,THKIN1,THKIN2
line
1
Concrete Reaction Optiont
variables
ZZDIN,QCCONC,CRACON,XMH2OI,TCIGNI,RCMBC
line
4(1)
5(2)
Lithium-Lead Optiont
variables
CPLEAD,KLEAD,RHLEAD,ALLOYI,QDISS,CPLIPB
DFLVAR
The pan option cannot be chosen with the concrete reaction option.
t: Lithium-lead data is entered on line 1 if the concrete reaction option is not chosen.
The format for all lines except 5(2) for the lithium-lead option is:
(6f12.4) The
format for line 5(2) is: (e12.5)
PFCVAX
The statement:
open(unit=4,fle='len. ame ',statu='old')
must be used. An example of this file (British units) is given in Appendix D.
MFE Crays
For these machines, the statement:
call link("unit4=flename,read4//")
must be used in the same location as the CALL LINK statement for the first input
data file.
25
3.2.4
Gas Flooding, Emergency Space Cooling, Emergency Floor Liner
Cooling and Gas Injection
Each of these options is included in one input data file. The following is a variable
listing for each of the options. Only the variable lines of the options used need be
entered, although the lines used must be in the order shown below (British units are
given in the Glossary):
line
1
(gas flooding)
2
3
4
5
6
(emerg. space cooling)
(emerg. floor cooling)
(aerosol removal)
(gas injection)
The format for lines 1-5 is:
variables
WO2B,WWAB,WN2B,XMOLAB,CPAB,TBLOW
BLOWV,EXHSTV,TBLIN,TBLOUT,WAB
ESCR,ESCTIN,ESCEND
SFLCR,SFLTIN,SFLEND
BETA
TONE,TTWO,TTHREE,DP1,DP2,DP3,FCT1,FCT2,FCT3
(6f12.4).
For the gas injection option (line 6) it is:
(3f10.2,6f8.4).
PFCVAX
The statement:
open(unit=5,file='filen.ame',status='old')
must be used. An example of this file (British units) is given in Appendix D.
MFE Crays
For these machines, the statement:
call link("unit5=filename,read5//")
must be used in the same location as the CALL LINK statement for the first input
data file.
3.2.5
Steam Injection to Containment
The following is a variable listing for the steam injection to containment available in
the steam-air atmosphere option (British units are given in the Glossary):
line
variables
1
STMIN,STMOUT,MINJR,HINJ
2
STMIN2,STOUT2,MINJR2,HINJ2
The format for all lines is: (6f12.4)
26
PFCVAX
The statement:
open(unit=6,file=' ilen.ame',status='old')
must be used. An example of this file (British units) is given in Appendix D.
MFE Crays
For these machines, the statement:
call link("unit6=filename,read6//")
must be used in the same location as the CALL LINK statement for the first input
data file.
3.2.6
Torus Fire
The following are the variable listing and the formats for the torus fire option. (British
units are given in the Glossary).
variables
line
1
VS,CHS,PASZER,TGSZER,TSSZER,TFSZER
2
CRACK,HUM2,WO2S,WAS,CPAS,WCO2S .
TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS,KEHCS
3
4
ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS
5
ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS
CLEHCS,EEHCS,EBLI,EFWI,VIEWM
6
TSHLZ,THSHL,KSHL,XMSHL,CPSHL,ASHL
7
8
ESHL,HINSHL,TMAGZ,AMAG,XMMAG,CPMAG
HINMAG,KHE,THE,LOCA,VIEWG,VIEWB
9
10
KBLI,THBLI,CPBLI,ABLI,XMBLI,TBLIO
11
TSHIO,TSHOO,THSHI,THSHO,XMSHI,XMSHO
12
THMAN,XMMAN,CPMAN,AMAN,TMANO,KMAN
13
QOFW1,EXPFW1,QOFW2,EXPFW2,QOFW3,EXPFW3
14
QOBL1,EXPBL1,QOBL2,EXPBL2,QOBL3,EXPBL3
15
QOBL4,EXPBL4,QOBL5,EXPBL5,QOBL6,EXPBL6
16
QOBLI1,EXPBI1,QOBLI2,EXPBI2,QOBLI3,EXPBI3
17
QOSH1,EXPSH1,QOSH2,EXPSH2,QOSH3,EXPSH3
18
QOSHI1,QOSHI2,QOSHI3,QOSHO1,QOSHO2,QOSHO3
The format for lines 1-12 is: (6f12.4)
The format for lines 13-18 is: (6e9.2)
27
PFCVAX
If this option is used, the statement:
open (unit=7,file='fien.ame',status='old')
must be included in LITFIRE in the same place as the OPEN statement for the first
input data file.
MFE Crays
For these machines, the statement:
call link("unit7=fiename,read7//")
must be used in the same location as the CALL LINK statement for the first input
data file.
3.3
PFCVAX Execution
To execute LITFIRE on the PFCVAX, the user must ensure that all necessary OPEN
statements are included for the data files necessary to run the code as indicated in
Section 3.2. The input data file head.dat must always be included as it provides
headings for the output data files that LITFIRE will create. The statement necessary
to include head.dat is:
open(unit=1,fie='head.dat',status='old')
It should be noted that all input data files must be in the same directory as LITFIRE
in order to execute the code.
OPEN statements are also needed for the output files created by LITFIRE. These
statements are placed right after the OPEN statements for the input data files and
take the form of:
open (unit=1Ofile='outl.dat',status='new')
There are ten output data files named outl.dat through outlO.dat, and an OPEN
statement is needed for each one.
Optional output files may be created to allow graphs to be made of code variables
vs. time. These files may be used in conjunction with the graphics routines available
on the PFCVAX to create the actual graphs. The optional files require OPEN statements like the ones for outl.dat through outlO.dat, but use the filename forOnn.dat,
where nn is any number from 01 to 99. Steps must be added to the code in the output
section to write values of TIME and the variable desired to the file. Some optional
output file OPEN and WRITE statements which have been commented out may be
found in the appropriate sections of the code. The output files created may be used
with the McCool graphics routine available on the PFCVAX to create the graphs.
There are three separate steps involved in the execution of LITFIRE: compiling,
linking and running the code.
To compile LITFIRE, the command:
28
for litfire.for
must be used and will create the file litfire.obj.
To link LITFIRE, the command:
link litfire.obj
must be used and will create the file litfire.exe.
To run LITFIRE, the command:
run litfire.exe
must be used. If the input data files were entered properly, the code should run
until terminated by a user defined time limit (i.e., TIME=TIMEF) or by the code
itself. (e.g., 'the temperature of the lithium pool has reached the melting point'). If
the code stops due to an error, an error message will be given. Refer to Appendix
C-Troubleshooting.
3.4
MFE Crays Execution
To execute LITFIRE on the Crays, the necessary CALL LINK statements must be
present for all of the input data files as indicated in Section 3.2 The input data file
head.dat must be included to provide headings for the output data files that LITFIRE
will create. The statement needed to include head.dat is:
call link("unitl=head.dat,readl//")
CALL LINK statements are needed for the ten output files as well. Those statements
take the form of:
call link("unitl0=(outi,text, create),printl//")
for each of the ten output files outi through out10. They should be placed directly
after the CALL LINK statements for the input data files.
To compile, load and run LITFIRE on the Crays, the following commands should
be used:
rcftti=itfire,x=xlitfire/ t p
xitfre / t p
where t is the total CPU time allowed in minutes and p sets the priority of the run.
One minute and a priority of 2 should be sufficient to run xlitfire unless the steam
option is being used, in which case up to five minutes may be required (and the
priority would be 10).
t: on the b machine, civic should be used instead of rcft.
29
I
3.5
Sample Input and Output Files
To check whether LITFIRE has been properly executed, a set of sample input and
output files are given in Appendices D and E. Execution of the code using the sample
input files on the PFCVAX or the Crays will produce approximately the same results
as given in the sample output files.
Using the input data files:
head.dat, uwmak.w, uwmak.x, uwmak.y, uwmak.z, steamop., torus.,
the following output files should be generated:
outl.dat, out2.dat, out3.dat, out4.dat, out5.dat, out6.dat, out7.dat, out8.dat
out9.dat, outlO.dat, blank
It should be noted that only the input files head.dat, uwmak.w and uwmak.x were
used for the examples in the Appendices.
30
A
Nomenclature
heat transfer surface areas
user defined heat transfer correlation constant
specific heat
specific heat at constant volume
radiative interchange factor, including emissivity
f
heat of combustion
AH
convective heat transfer coefficient
h
h.
convective mass transfer coefficient
k, ki
thermal conductivity
characteristic length
L, l;,
mass
Mm
decay heat density
q'"
Q, dq/dt heat flow rate
thermal resistance
R;,j
reaction rate
RR
t
time
temperature
T
A
C
C,
c',
U
specific internal energy
U,
x
a
0
p
a
total internal energy
linear distance
thermal diffusivity
coefficient of volumetric expansion
density
Stefan-Boltzmann constant
31
B
Variable Listing
AA
ABLI
ACTVTY
AEHCP
AEHCS
AFP
Exponent used in expression for GRPR or GRPRF
Cross sectional area of the blanket back wall (ft2 )
Calculates activity of lithium in lithium-lead eutectic
Surface area of primary extraneous heat capacity (ft2 )
Surface area of secondary extraneous heat capacity (cross sectional
area of breeder with torus fire option) (ft 2 )
Surface area of primary floor liner, must be equal to or greater than
the area of the lithium spill ASLI. (ft2 )
AFS
Surface area of the secondary floor liner (ft 2 )
AHT
Area of the lithium pool-pan interface (ft2 )
AINS
AIRFAC
AK
AMAG
AMAN
AMIN1
APAN
Outside exposed area of insulating layer on the pan (ft2 )
Density weighting factor for calculating steam-air mixture properties
Product of thermal conductivity and Prandtl number of the primary
gas (BTU/sec-ft deg. F.) See associated film temperature T1.
Function used to calculate heat transfer coefficients
Thermal conductivity of lead (input as BTU/hr-ft deg. F.)
Thermal conductivity of lithium (input as BTU/hr-ft deg. F.)
Thermal conductivity of lithium used during LC-2 lithium transfer
simulation (BTU/sec-ft-deg. F.)
Product of thermal conductivity and Prandtl number of water vapor at
the lithium pool surface (BTU/sec-ft deg. F.)
Initial atom percent of lithium in lithium-lead
Used to determine whether or not LILP should be fixed at an amount
equal to AKLI/(RHLI*CPLI)
Used in determining PYU. Also tests conduction limit on time step for
the pan or floor liner.
Surface area of the magnets (secondary extraneous heat capacity) (ft 2 )
Cross sectional area of the blanket manifold (ft2 )
FORTRAN function that determines the minimum of the arguments used
Pan external heat transfer area (ft 2 )
ASHL
ASLI
Outer surface area of the reactor shield (ft2 )
Surface area of the lithium spilled (ft2 )
ASURF
Surface area of the liquid water pool (ft 2 )
AWP
Surface area of the primary wall liner (ft2 )
AWS
B
Surface area of the secondary wall liner (ft2 )
Used in calculating the thermal resistance between the wall liner, the gap
and the wall concrete
Analogous to B, but for the floor liner, gap and concrete
Coefficient of volumetric expansion for gas (0)
(1/deg. F.) See associated film temperature T1
AKEXX
AKLEAD
AKLI
AKLIX
AKVAP
ALLOYI
ALPHA
ALPHA2
BB
B1
32
BETA
BETAB
BETAF
BIL
BILGE
BLIN
BLOUT
BLOWR
BLOWV
BREAKS
BREDTH
Cxxx
C1
C2
C3
C4(i)
05
06
C7
C8
C9
C10(i)
C11
C12
013
C14
C15
C16
C17
018
C19
C20
C21
C22
C23
C2FAC
CA
'C'BIMAN
Inverse sticking coefficient for particles impinging on the wall (sec.)
Volumetric expansion coefficient 3 for the water pool-gas boundary (1/deg. F.
Volumetric expansion coefficient P for the water pool (1/deg. F.)
Fractional change between BILGE and DELT, used in determining minimum
time step
Equal to the minimum value of DT1,DT2,DT3,DT4 or DT5, used in
calculating the time step length (sec.)
Time after spill at which inert gas flooding and exhaust begins (sec.)
Time after spill at which inert gas flooding and exhaust ends (sec.)
Inert gas input rate (lbm/sec)
Inert gas volumetric input rate (ft3 /sec)
Outer cell gas temperature rate of change due to gas flow between
cells and leakage. (deg. R./sec)
Perimeter of the pan (ft)
'C' is used to indicate a thermal admittance between nodes (i.e., the
inverse of the product of effective thermal resistance between the
nodes and the heat capacity of one of them (hA/mc,) (sec-)
Primary gas to primary wall liner in gas
Pan to primary gas in gas
Wall liner to concrete in concrete
Concrete wall node i to node i+1 in concrete
Concrete wall to ambient in concrete
Primary gas to primary wall in wall liner
Wall liner to concrete in wall liner
Floor liner to concrete floor in floor liner
Floor liner to concrete floor in concrete
Concrete floor node i to node i+1 in concrete
Wall liner to ambient (no concrete option) in wall liner
Floor liner to ambient (no concrete option) in floor liner
Pan to primary gas in pan
Secondary floor liner to secondary gas in floor liner
Secondary floor liner to secondary gas in gas
Primary floor liner to primary gas in floor liner
Primary floor liner to primary gas in gas
Primary floor liner to secondary gas in floor liner
Primary floor liner to secondary gas in gas
Primary wall liner to secondary gas in wall liner
Secondary wall liner to secondary gas in wall liner
Primary wall liner to secondary gas in gas
Secondary wall liner to secondary gas in gas
Fraction of Li-CO 2 reaction which produces Li 2 C 2
Coefficient in expression for GRPR or GRPRF
Blanket back wall to manifold in manifold
33
'C'BLMAN
CCZ
'C'CZP
CD
'C'EHCGP
'C'EHCGS
'C'EHCSH
'C'EHCFP
'C'EHCWP
'C'FPEHC
'C'GCZ
'C'GLI
'C'GPEHC
'C'GSEHC
'C'GSMAG
'C'GSSHL
CHP
CHS
'C'IN1PN
'C'IN12
'C'IN21
CLEHCS
'C'LIG
'C'LIPAN
'C'LIST
'C'MAGGS
'C'MANBI
'C'MANBL
CMBR
CMBRC2
CMBRCO
CMBRH
CMBRHH
CMBRHI
CMBRN
CMBRNH
CMBRO
CMBRO1
CMBRO2
CMBROH
CMBRW
Breeder to manifold in manifold
Heat generation rate in the combustion zone (BTU/sec)
Lithium pool to combustion zone in pool
Coefficient of discharge between the two cells (nea.r unity)
Primary extraneous heat capacity to primary gas in gas
Secondary extraneous heat capacity to secondary gas in gas
Blanket back wall to shield inside region in shield inside region
First wall (floor) to breeder in first wall (floor)
First wall to breeder in first wall
First wall (floor) to breeder in breeder
Combustion zone to primary gas in combustion zone
Lithium Pool to primary gas (no combustion) in pool
Primary gas to primary extraneous heat capacity in heat capacity
Secondary gas to secondary extraneous heat capacity in heat capacity
Secondary gas to magnets in magnets
Shield outside region to secondary gas in shield outside region
Primary cell optical path length (ft)
Secondary cell optical path length (ft)
Pan to inner insulation in insulation
Inner pan insulation to outer pan insulation in inner insulation
Inner pan insulation to outer pan insulation in outer insulation
Thickness of the breeder node (ft)
Lithium pool to primary gas (no combustion) in gas
Lithium pool to pan in pool (suspended pan option)
Lithium pool to primary floor liner in pool
Magnets to secondary gas in secondary gas
Manifold to blanket back wall in blanket back wall
Manifold to breeder in breeder
Total combustion rate (lb Li/sec-ft2 )
Combustion rate for the carbon reaction (lb Li/sec-ft 2 )
Combustion rate for the lithium-carbonate producing reaction
(lb Li/sec-ft 2 )
Total combustion rate (lb Li/hr-ft 2 )
CMBRH in g Li/min-cm 2
Initial combustion rate (lb Li/hr-ft 2 )
Combustion rate for the nitrogen reaction (lb Li/sec-ft 2 )
CMBRN in g Li/min-cm 2
Total of CMBRO1 and CMBRO2 (lb Li/sec-ft 2 )
Combustion rate for the oxygen reaction (lb Li/sec-ft 2 )
Combustion rate for the Li-CO 2 reaction producing lithium-oxide
(lb Li/sec-ft2 )
CMBRO in g Li/min-cm 2
Combustion rate for the water vapor reaction producing LiOH
(lb Li/sec-ft 2 )
CMBRW2
Combustion rate for the water vapor reaction producing Li 2 0
(lb Li/sec-ft 2 )
CMBRWH
CMRC2H
CMRCOH
C02
CO2LFS
CONDR
CONF1
CONF2
CPxxx
CPA
CPA2
CPAB
'C'PANLI
CPAP
CPAS
CPB
CPBLI
CPCARP
CPCO2P
CPCO2S
CPCON
'C'PCZ
CPEHCP
CPEHCS
CPFAC
CPH2
CPINS
CPLC2P
CPLC3P
CPLC3S
CPLEAD
CPLI
CPLIX
CPLIH
CPLIN
CPLINP
CPLINS
CPLIO
CPLIOH
CPLIOP
CMBRW in g Li/min-cm 2
CMBRC2 in g Li/min-cm 2
CMBRO2 in g Li/min-cm 2
A subroutine which sets up the pure CO2 atmosphere
Carbon dioxide left after spray fire (lb)
Condensation mass flow rate (lb/sec)
Fraction of Li-CO 2 reaction which produces Li 2 0
Fraction of Li-CO 2 reaction which produces Li 2 CO 3
Gaseous specific heats are all specific heats at constant volume
Primary non-condensible gas specific heat (BTU/lb deg. F.)
Secondary non-condensible gas specific heat (BTU/lb deg. F.)
Flooding gas specific heat (BTU/lb deg. F.)
Lithium pool to pan in pan
Specific heat of primary cell inert gas (BTU/lb deg. F.)
Specific heat of secondary cell inert gas (BTU/lb deg. F.)
Specific heat of the water pool-gas boundary (BTU/lb deg. F.)
Specific heat of the blanket back wall (BTU/lb deg. F.)
Specific heat of carbon in the primary gas (BTU/lb deg. F.)
Specific heat of carbon dioxide in the primary gas (BTU/lb deg. F.)
Specific heat of carbon dioxide in the secondary gas (BTU/lb deg. F.)
Heat capacity of floor and wall concrete (BTU/lb deg. F.)
Lithium pool to combustion zone in combustion zone
Specific heat of primary extraneous heat capacity (BTU/lb deg. F.)
Specific heat of secondary extraneous heat capacity (breeder with
torus fire option) (BTU/lb deg. F.)
Used in calculating CPLI (CPFAC=.004938TL-6.20741)
Specific heat of hydrogen gas (2.48 BTU/lb deg. F.)
Specific heat of insulation (BTU/lb deg. F.)
Specific heat of lithium carbide in the primary gas (BTU/lb deg. F.)
Specific heat of Li 2 CO 3 in the primary gas (BTU/lb deg. F.)
Specific heat of Li 2 CO 3 in the secondary gas (BTU/lb deg. F.)
Specific heat of pure lead (BTU/lb deg. F.)
Specific heat of lithium (BTU/lb deg. F.)
Specific heat of lithium (used during LC-2 lithium transfer
simulation (BTU/lb deg. F.))
Specific heat of lithium hydroxide (0.67 BTU/lb deg. F.)
Specific heat of lithium nitride (BTU/lb deg. F.)
Specific heat of lithium nitride in primary (BTU/lb deg. F.)
Specific heat of lithium nitride in secondary (BTU/lb deg. F.)
Specific heat of lithium oxide (BTU/lb deg. F.)
Molar specific heat of lithium hydroxide (BTU/lb-mol deg. F.)
Specific heat of lithium oxide in primary (BTU/lb deg. F.)
35
CPLIOS
CPLIPB
CPLV
CPMAG
CPMAN
CPMCOP
CPMCOS
CPMCZ
CPMH2
CPMLCP
CPMLCS
CPMLOP
CPMLOS
CPMNIP
CPMNIS
CPMOXP
CPMOXS
'C'PNIN1
CPN2P
CPN2S
CPSFP
CPSFS
CPSHL
CPSWP
CPSWS
CPWV
CRACON
CRACK
'C'SBLI
'C'SHEHC
'C'SHISH
'C'SHLGS
'C'SHOSH
'C'SHSHO
'C'SHSHI
CSTM
CSTMA
CSTMN
DAB
DCOCZ
DECBL
Specific heat of lithium oxide in secondary (BTU/Lb deg. F.)
Specific heat of lithium-lead (BTU/lb deg. F.)
Specific heat of water for secondary floor liner-secondary water pool
heat transfer (at TAVE) (BTU/deg. F.)
Specific heat of the magnets (secondary extraneous heat capacity)
(BTU/lb deg. F.)
Specific heat of the manifold (BTU/lb deg. F.)
Heat capacity of carbon dioxide in primary (BTU/deg. F.)
Heat capacity of carbon dioxide in secondary (BTU/deg. F.)
Effective heat capacity of combustion zone (BTU/deg. F.)
Heat capacity of hydrogen in containment (BTU/deg. F.)
Heat capacity of lithium carbonate in primary (BTU/deg. F.)
Heat capacity of lithium carbonate in secondary (BTU/deg. F.)
Heat capacity of lithium oxide in primary (BTU/deg. F.)
Heat capacity of lithium oxide in secondary (BTU/deg. F.)
Heat capacity of nitrogen in primary (BTU/deg. F.)
Heat capacity of nitrogen in secondary (BTU/deg. F.)
Heat capacity of oxygen in primary (BTU/deg. F.)
Heat capacity of oxygen in secondary (BTU/deg. F.)
Pan to inner insulation in pan
Specific heat of nitrogen gas in primary (BTU/lb deg. F.)
Specific heat of nitrogen gas in secondary (BTU/lb deg. F.)
Specific heat of primary floor liner (BTU/lb deg. F.)
Specific heat of secondary floor liner (BTU/lb deg. F.)
Specific heat of the reactor shield (BTU/lb deg. F.)
Specific heat of primary wall liner (BTU/lb deg. F.)
Specific heat of secondary wall liner (BTU/lb deg. F.)
Specific heat of water vapor in primary (BTU/lb deg. F.)
Area of concrete exposed to lithium in concrete combustion model (ft 2)
Area of the orifice between the two cells (square inches)
Lithium pool to primary floor liner in floor liner
Blanket back wall to shield inside region in blanket back wall
Shield bulk to shield inside region in shield bulk
Shield outside region to secondary gas in secondary gas
Shield bulk to shield outside region in shield bulk
Shield bulk to shield outside region in shield outside region
Shield bulk to shield inside region in shield inside region
Steam catalytic factor
Steam catalytic factor in air
Steam catalytic factor in nitrogen
Diffusion coefficient for air and water (ft2 /sec)
Depth of concrete combustion zone (ft)
used to calculate volume of zone for heat generation
Total decay heat density in the breeder (BTU/ft3 sec)
36
DECBLI
DECFW
DECMAN
DECSH
DECSHI
DECSHO
DELMP
DELOUT
DELT
DFILM
DFLIPB
DFLVAR
DIFF
DIFFLI
DMPBDT
DP1,..DP3
DTBDT(i)
DTCDT(i)
DTMIN
DT1..DT5
DT1
DT2
DT3
Total decay heat density in the blanket back wall (BTU/ft3 sec)
Total decay heat density in the first wall (BTU/ft3 sec)
Total decay heat density in the manifold (BTU/ft3 sec)
Total decay heat density in the shield bulk (BTU/ft3 sec)
Total decay heat density in the shield inside region (BTU/ft3 sec)
Total decay heat density in the shield outside region (BTU/ft3 sec)
Fractional exchange rate of primary gas used in determining the
minimum time step (sec)
Fractional exchange rate of secondary gas used in determining the
minimum time step (sec)
User defined maximum time step length (sec)
Time step length (sec)
Lithium vapor film thickness (ft)
Diffusion coefficient for lithium through lead (ft2 /sec)
Constant used to calculate DFLIPB (6.5E-08) (ft2 /sec)
Gas mass diffusion coefficient to the combustion zone (ft2 /sec)
Lithium diffusion coefficient to the combustion zone (ft2 /sec)
Mass rate of change of lead in lead layer (lb/sec)
Increase in cell gas pressure due to each injection (psi)
Concrete floor temperature rate of change, node i (deg. F./sec)
Concrete wall temperature rate of change, node i (deg. F./sec)
User defined minimum time step length (sec)
X/(dx/dt) * RELERR, used in determining the time step length (sec)
X = Lithium pool temperature
X = Primary gas temperature
X = Primary wall liner temperature
DT4
X = Combustion rate
DT5
DYNAMI
D1
X = Combustion zone temperature*.05
Subroutine used in controlling integration loops
Kinematic viscosity of the cell gas (squared) at the film temperature
(ft4 /sec 2 ), See related film temperature Ti.
Thermal emissivity of the interior of the blanket
Thermal emissivity of the exterior of the blanket (facing the shield)
Thermal emissivity of the interior of the first wall
Film depth of depleted zone above combustion zone (in)
Thermal emissivity of concrete
Thermal emissivity of combustion zone
Used in fixing minimum emissivity of the lithium pool (.9 in code)
Thermal emissivity of primary gas (minimum of .005 in code)
Constant used in determining EMGP, usually chosen at .04
Thermal emissivity of secondary gas (minimum of .005 in code)
Thermal emissivity of pan insulation
DELMS
EBLI
EEHCS
EFWI
EFILM
EMCONC
EMCZ
EMF
EMGP
EMGPF
EMGS
EMINS
37
(There is no page 38.)
EMLI
ESCR
ESCTIN
ESHL
ESTAIR
ESTLFP
ESTLFS
ESTLWP
ESTLWS
EW1
EXHSTR
EXHSTV
EXPBIn
EXPBLn
EXPBLn
EXPSHn
EXX
Thermal emissivity of lithium pool
Heat removal rate by emergency space cooling (BTU/sec)
Time after spill when ESCR begins (sec)
Thermal emissivity of the reactor shield
Thermal emissivity of the cell steam-air mixture (without aerosols)
Thermal emissivity of the primary floor liner
Thermal emissivity of the secondary floor liner
Thermal emissivity of the primary wall liner
Thermal emissivity of the secondary wall liner
Thermal emissivity of water vapor at one atmosphere and cell temperature
Rate of primary gas exhaust (lb/sec)
Rate of primary gas exhaust (ft3 /sec)
Decay constant of decay heat producing isotope in the blanket back wall
1
(n=1-3) (sec- )
Decay constant of decay heat producing isotope in the breeder node
(n=1-3) (sec-)
Decay constant of decay heat producing isotope in the manifold
(n=4-6) (sec 1 )
Decay constant of decay heat producing isotope in the reactor shield
(n=1-3) (sec 1 )
Temporary variable used in calculating heat and mass diffusion
coefficients (ft- 3 )
EXi
Used in calculating mass and heat transfer coefficients
(ft-') See related film temperature T1.
FCO2P
FCO2S
FCT1,FCT2
FCT3
FF1,FF2
FLI20
FLIOH
FMLEAK
FMLEFT
FNIP
FNIS
FOUTP
FOUTS
FOUTT
FOXP
FOXS
FPG
FPW
FRA
Weight fraction of CO 2 in primary gas
Weight fraction of CO 2 in secondary gas
Fraction of nitrogen in each injection (by number)
Used in heat balance equations for spray fire
Mass fraction of Li reacting with H2 0 that produces Li 2 0
Mass fraction of Li reacting with H2 0 that produces LiOH
Fraction of mass of gas leaked out of primary
Fraction of mass of gas remaining in containment
Weight fraction of nitrogen in primary gas
Weight fraction of nitrogen in secondary gas
Loss rate of primary gas which is either exhausted or changes cells
Loss rate of secondary gas which is either exhausted or changes cells
Total loss rate from outermost gas tell (FOUTS+LEAK)
Weight fraction of oxygen in primary gas
Weight fraction of oxygen in secondary gas
Radiative view factor from lithium pool to primary gas (1.0 w/o pan)
Radiative view factor from lithium pool to primary wall liner
Fraction of combustion products evolved into cell gas
39
FWAP
FWAS
GAP
GAMMA
GIN
GRPR
GRPRF
Weight fraction of water vapor in primary gas
Weight fraction of water vapor in secondary gas
Air gap between floor liner and concrete (ft)
Ratio of specific heats c,/c, (set to 1.4 in the code)
Acceleration due to gravity (32.2 ft/sec2 )
Product of the Grashof and Prandtl numbers of the water pool-gas boundary
Product of the Grashof and Prandtl numbers of the water pool
H2LEFT
Current water content of concrete (lb/ft3 )
HA
HAMF
Heat transfer coefficient between exterior wall and ambient (BTU/ft 2 sec deg. F.)
Heat transfer coefficient between exterior floor and ambient
(BTU/ft 2 sec deg. F.)
Heat transfer coefficient between lithium pool and primary gas
(BTU/ft 2 sec deg. F.)
Equilibrium value of HB
Total heat transfer coefficient between the water pool and the cell
gas (BTU/ft 2 sec deg. F.)
Heat transfer coefficient between primary extraneous heat capacity
and primary gas (BTU/ft2 sec deg. F.)
Heat transfer coefficient between secondary extraneous heat capacity
and secondary gas (BTU/ft2 sec deg. F.)
Heat flux to water pool from gas mixture due to evaporation ( BTU/sec-ft 2 )
Mass transport coefficient to the lithium pool (ft/sec)
Latent heat of vaporization of water vapor in the primary gas (BTU/lb)
Latent heat of vaporization of water vapor in the secondary gas (BTU/lb)
Equilibrium value of HF (BTU/ft 2 sec deg. F.)
Heat transfer coefficient between primary floor liner and primary gas
(BTU/ft 2 sec deg. F.)
Heat transfer coefficient between primary floor liner and
HB
HBINF
HCOND
HEHCP
HEHCS
HEVAP
HF
HFG
HFG2
HFINF
HFPGP
HFPGAS
secondary gas (BTU/ft 2 sec deg. F.)
HFSGAS
HGWP
HINxxx
HINECP
HINECS
HINFAM
HINFGS
HINFSG
HINGPF
Heat transfer coefficient between secondary floor liner and
secondary gas (BTU/ft 2 sec deg. F.).
Heat transfer coefficient between primary wall and gas (BTU/ft 2 sec deg. F.)
Heat transfer coefficients are determined by LITFIRE as indicated in
Section 2.2.4. The coefficients C are indicated in the code as
HINxxx and are dimensionless
Correlation for HEHCP
Correlation for HEHCS
Correlation for HAMF
Correlation for HFPGAS
Correlation for HFSGAS
Correlation for HFPGP
40
HINGSP
HINGSS
HINJ
HINJ2
HINMAG
HINPS
HINSAM
HINSHL
HLP
HLP2
HLPFLR
HMAG
HPAN
HPRIME
HRATIO
HRAT2
HSAT
HSEC
HSENS
HSHL
HTCPGP
HTCPGS
HU(x,y)
HUCH
HUM
HUM2
HWPGAS
HWV
HWV2
I
IAM
IB
INIT
INJEC1..3
Correlation for HGWP
Correlation for HSEC
Specific enthalpy of steam injected to primary cell (BTU/lb)
Specific enthalpy of steam injected to secondary cell (BTU/lb)
Correlation for HMAG
Correlation for HWPGAS
Correlation for HA
Correlation for HSHL
Specific enthalpy of the primary liquid water pool (BTU/b)
Specific enthalpy of the secondary liquid water pool (BTU/lb)
Heat transfer coefficient between the liquid water pool and the
secondary floor liner (BTU/ft2 sec deg. F.)
Heat transfer coefficient between magnets and secondary gas
(BTU/ft 2 sec deg. F.)
Heat transfer coefficient between the pan and primary gas
(BTU/ft 2 sec deg. F.)
Increased value of HSENS due to a large condensation/evaporation
rate (BTU/ft 2 sec deg. F.)
Molar fraction of hydrogen in the primary gas
Molar fraction of hydrogen in the secondary gas
Specific enthalpy of saturated liquid water at cell pressure (BTU/lb)
Heat transfer coefficient between secondary floor liner and
secondary gas (BTU/ft 2 sec deg. F.)
Sensible heat transfer coefficient from the water pool to the vapor
mixture (BTU/ft 2 sec deg. F.)
Heat transfer coefficient between the shield outside region and
secondary gas (BTU/ft 2 sec deg. F.)
Heat capacity of the primary gas (BTU/deg. F.)
Heat capacity of the secondary gas (BTU/deg. F.)
Chart of Uchida heat transfer coefficients vs. MR
Uchida heat transfer coefficient for condensing steam (BTU/ft 2 sec deg. F.)
Initial relative humidity of the primary cell (1.0=100%)
Initial relative humidity of the secondary cell (1.0=100%)
Heat transfer coefficient between primary wall liner and
secondary gas (BTU/ft 2 sec deg. F.)
Specific enthalpy of water vapor in the primary gas (BTU/lb)
Specific enthalpy of water vapor in the secondary gas (BTU/lb)
General purpose DO loop counter
DO loop counter for wall and floor concrete node initialization
DO loop counter for floor concrete iterations
Initializing subroutine for integrations
Flags for gas injection. INJECn indicates the injection has occurred.
41
INTDSx
INTGRL
IPAGE
IPASS
Interpolation factor used in reading steam tables
Arithmetic statement function for finding integrals
Number of lines of output between headings
Used during integration routine to tell INTGRL to perform certain
special functions during the first two executions of the section
KAIR
Thermal conductivity of non-condensible gas (air) (BTU/sec ft deg. F.)
KAIRB
Thermal conductivity of air at the water pool-gas boundary
(BTU/sec ft deg. F.)
KAIRG
Thermal conductivity of air in a cell gas (BTU/sec ft deg. F.)
KB
Water condensation mass transfer coefficient (lb mol/sec-ft 2 )
Thermal conductivity of the blanket back wall (BTU/hr ft deg. F.)
KBLI
KBNDRY Thermal conductivity of the water pool-gas boundary (BTU/sec ft deg. F.)
KCON
Thermal conductivity of concrete (input as BTU/hr ft deg. F.)
KEHCS
Thermal conductivity of the breeder node (BTU/hr ft deg. F.)
KFILM
Thermal conductivity of pool/combustion zone film (BTU/sec ft deg. F.)
KGAP
Thermal conductivity of the gap between the liner and concrete
(BTU/hr ft deg. F.)
KH20
Thermal conductivity of water vapor (BTU/sec ft deg. F.)
KH2OB
Thermal conductivity of water vapor at the water pool-gas boundary
(BTU/sec ft deg. F.)
KH2OG
Thermal conductivity of water vapor in a cell gas (BTU/sec ft deg. F.)
KHE
Thermal conductivity of the vacuum (He filled) gap (BTU/hr ft deg. F.)
KIN1
Thermal conductivity of inner insulation layer (BTU/hr ft deg. F.)
KIN2
Thermal conductivity of outer insulation layer (BTU/hr ft deg. F.)
KLEAK
Leak rate constant from containment (sec- 1 psi- 0 5)
Reference value: 2.588-10'
KMAN
Thermal conductivity of the manifold (BTU/hr ft deg. F.)
KPAN
Thermal conductivity of the pan (BTU/hr ft deg. F.)
KSHL
Thermal conductivity of the reactor shield (BTU/hr ft deg. F.)
KSTLFP
Thermal conductivity of the primary floor liner (BTU/hr ft deg. F.)
Thermal conductivity of the secondary floor liner (BTU/hr ft deg. F.)
KSTLFS
KSTLWP Thermal conductivity of the primary wall liner (BTU/hr ft deg. F.)
KSTLWS Thermal conductivity of the secondary wall liner (BTU/hr ft deg. F.)
KWAT
Thermal conductivity of liquid water (BTU/sec ft deg. F.)
L
Thickness of a wall concrete node (ft)
Li
Thickness of a floor concrete node (ft)
LEAK
Gas leakage rate from outermost cell (sec 1 )
LEAKO
Initial gas leakage rate from outermost cell (sec- 1 )
LIBP
Lithium consumed in pool fire (lb)
LIL
Amount of lithium remaining in pool-limited to LIT/10 for numerical
stability during calculations
LILC2
Amount of Li 2 C 2 in the pool (lb)
LILCA
Amount of Li 2 CO 3 in the pool (lb)
42
LILCAR
LILNI
LILOX
LILP
LIS
LIT
LOCA
MAIP
MAIS
MAIRP
MAIRS
MAP
MAS
MBOIL
MCO2IP
MCO2IS
MCO2P
MCO2S
MCONDE
MCONDF
MCONDP
MCONDW
MCONFP
MCONWP
MFAB
MFAG
MFVB
MFVG
MGB
MH2P
MH2S
MINJR
MINJR2
MLC2P
MLC2S
MLC3IP
MLC3IS
MLC3P
MLC3S
MLEAD
MLIHP
MLIHS
Amount of carbon in the pool (lb)
Amount of Li 3 N in the pool (lb)
Amount of Li 20 in the pool (lb)
True amount of lithium in the pool (lb)
Amount of lithium consumed in the spray fire (lb)
Initial mass of lithium in the pool (lb)
View factor between the first wall and the breeder node (may be zero)
Initial mass of inert gas in the primary gas (lb)
Initial mass of inert gas in the secondary gas (lb)
Mass of primary non-condensible gas (lb)
Mass of secondary non-condensible gas (lb)
Mass of inert gas in the primary gas (lb)
Mass of inert gas in the secondary gas (lb)
Mass of water boiled off from the water pool in one time step (lb)
Initial mass of carbon dioxide in the primary gas (lb)
Initial mass of carbon dioxide in the secondary gas (lb)
Mass of carbon dioxide in the primary gas (lb)
Mass of carbon dioxide in the secondary gas (lb)
Condensation rate of water on an extraneous heat capacity (lb/sec)
Condensation rate of water on the secondary floor liner (lb/sec)
Condensation rate of water on the pan insulation (lb/sec)
Condensation rate of water on a wall liner (lb/sec)
Condensation rate of water on the primary floor liner
from the secondary gas (lb/sec)
Condensation rate of water on the primary wall liner
from the secondary gas (lb/sec)
Molar fraction of air at the water pool-gas boundary
Molar fraction of air in the cell gas
Molar fraction of water vapor at the water pool-gas boundary
Molar fraction of water vapor in the cell gas
Molecular weight of the mixture at the water pool-gas boundary
Mass of hydrogen in the primary gas (lb)
Mass of hydrogen in the secondary gas (lb)
Mass flow rate of steam injected to primary cell (lb/sec)
Mass flow rate of steam injected to secondary cell (lb/sec)
Mass of lithium carbide in the primary gas (lb)
Mass of lithium carbide in the secondary gas (lb)
Initial mass of lithium carbonate in the primary gas (lb)
Initial mass of lithium carbonate in the secondary gas (lb)
Mass of lithium carbonate in the primary gas (lb)
Mass of lithium carbonate in the secondary gas (lb)
Mass of lead in the lead layer above the lithium-lead pool (lb)
Mass of lithium-hydroxide in the primary gas (lb)
Mass of lithium-hydroxide in the secondary gas (lb)
43
MLINIP
MLINIS
MLINP
MLINS
MLIOH
MLIOIP
MLIOIS
MLIOP
MLIOS
MNIINJ
MNIIP
MNIIS
MNIP
MNIS
MNINJ1..3
MOINJ1..3
MOXINJ
MOXIP
MOXIS
MOXP
MOXS
MR
MUAIR
MUAIRB
MUAIRG
MUB
MUDIFF
MUV
MUVB
MUVCZ
MWL
MWL2
MWLV
MWLV2
MWLZ
MWLZ2
MWV
MWV2
MWVV
MWVV2
Initial mass of lithium-nitride in the primary gas (lb)
Initial mass of lithium-nitride in the secondary gas (lb)
Mass of lithium-nitride in the primary gas (lb)
Mass of lithium-nitride in the secondary gas (lb)
Mass of LiOH produced (moles)
Initial mass of lithium-oxide in primary gas (lb)
Initial mass of lithium-oxide in secondary gas (lb)
Mass of lithium-oxide in primary gas (lb)
Mass of lithium-oxide in secondary gas (lb)
Rate of nitrogen injection during a one minute interval (lb/sec)
Initial mass of nitrogen in the primary gas (lb)
Initial mass of nitrogen in the secondary gas (lb)
Mass of nitrogen in the primary gas (lb)
Mass of nitrogen in the secondary gas (lb)
Mass of nitrogen injected in gas injection (lb)
Mass of oxygen injected in gas injection (lb)
Rate of oxygen injection during a one minute interval (lb/sec)
Initial mass of oxygen in the primary gas (lb)
Initial mass of oxygen in the secondary gas (lb)
Mass of oxygen in the primary gas (lb)
Mass of oxygen in the secondary gas (lb)
Mass ratio of air to water vapor in the cell gas
Viscosity of air in the cell gas (lb/sec-ft)
Viscosity of air at the water pool-gas boundary (lb/sec-ft)
Viscosity of air in the cell gas (lb/sec-ft)
Viscosity of the mixture at the water pool-gas boundary (lb/sec-ft)
Viscosity of the mixture at the lithium pool surface (lb/sec-ft)
Viscosity of water vapor in the cell gas (lb/sec-ft)
Viscosity of water vapor at the water pool-gas boundary (lb/sec-ft)
Viscosity of water vapor at the lithium pool surface (lb/sec-ft)
Mass of liquid water in the primary water pool (lb)
Mass of liquid water in the secondary water pool (lb)
Mass of liquid water in the primary gas (lb)
Mass of liquid water in the secondary gas (lb)
Time rate of change of the mass of liquid water in the primary water
pool (lb/sec)
Time rate of change of the mass of liquid water in the secondary water
pool (lb/sec)
Total mass of water in the primary gas (lb)
Total mass of water in the secondary gas (lb)
Mass of water vapor in the primary gas (lb)
Mass of water vapor in the secondary gas (lb)
44
MWVZ
MWVZ2
N
NAME(i)
NL
NL1
NLM1
NL1M1
NS
NULV
OFAC
OUTINT
OVERPP
OVERPS
OXLB
OXLBI
OXLFS
PAP
PAPZER
PAS
PASZER
PERCEN
PH20
PH202
PH20B
PH20B2
PHASE
PHASE2
PHIA
PHIW
PHIAWB
PHIWAB
PLIV
PRSC
PSAT
PSAT2
PYU
PZEROP
QCxxx
Time rate of change of the total mass of water in the primary gas (lb/sec)
Time rate of change of the total mass of water in the secondary gas (lb/sec)
Index used to transfer to section of subroutines, and as a DO loop counter
Input variable containing program name and output headings
Number of concrete wall nodes
Number of concrete floor nodes
Number of concrete wall nodes minus one
Number of concrete floor nodes minus one
Index used to control transfer to sections of the steam-air subroutines
Kinematic viscosity of water at the secondary floor liner (ft2 /sec)
Oxygen inhibition factor (lithium-steam reaction)
Fraction of the outermost cell gas leaked to ambient
Primary cell overpressure (psig)
Secondary cell overpressure (psig)
Mass of oxygen consumed in the fire (lb)
Mass of oxygen consumed in the spray fire (lb)
Mass of oxygen remaining after the spray fire (lb)
Primary gas pressure (psia)
Initial primary gas pressure (psia)
Secondary gas pressure (psia)
Initial secondary gas pressure (psia)
Molecular percentage of lithium-peroxide (vs. monoxide) formed
during combustion
Partial pressure of water vapor in the primary gas (psia)
Partial pressure of water vapor in the secondary gas (psia)
Partial pressure of water vapor at the primary water pool-gas
boundary (psia)
Partial pressure of water vapor at the secondary water pool-gas
boundary (psia)
=1 if primary cell is saturated, =2 if superheated
=1 if secondary cell is saturated, =2 if superheated
Baroczy two-phase flow correction factor at the lithium pool surface
Baroczy two-phase flow correction factor at the lithium pool surface
Baroczy two-phase flow correction factor at the water pool surface
Baroczy two-phase flow correction factor at the water pool surface
Partial pressure of lithium vapor (psia)
Prandtl number divided by the Schmidt number
Saturation pressure of water at the primary gas temperature (psia)
Saturation pressure of water at the secondary gas temperature (psia)
Used in setting the time step length calculated from the heat conduction
rate to the pan or primary floor liner from the lithium pool
Primary gas pressure after the spray fire (psia)
Heat of combustion (BTU/lb Li)
45
(There is no page 46.)
QCC
QCCONC
QCN
QCO
QCO1
QCO2
QCW
QCW2
QDISS
QIN
QL2C2
QLFLR
QLIOH
QOFWn
QOBLn
QOBLn
QOBLIn
QOSHn
QOSHIn
Li-CO 2 producing lithium carbonate reaction
Concrete reaction
Nitrogen reaction
Oxygen reaction
Monoxide reaction
Peroxide reaction
Water vapor reaction producing LiOH
Water vapor reaction producing Li 2 0
Heat of dissociation of LiPb (BTU/lb)
Heat addition to primary gas from spray fire (BTU)
Heat of combustion for the carbon reaction (BTU/lb Li)
Heat flux from the secondary water pool to the secondary floor liner
(BTU/ft 2 )
Heat of fusion of LiOH (BTU/lb mol)
Volumetric decay heat generation rate in the first wall for an isotope
3
(n=1-3) (BTU/sec ft )
Volumetric decay heat generation rate in the breeder for an isotope
(n=1-3) (BTU/sec ft')
Volumetric decay heat generation rate in the manifold for an isotope
(n=4-6) (BTU/sec ft')
Volumetric decay heat generation rate in the blanket back wall for a n isotope
(n=1-3) (BTU/sec ft')
Volumetric decay heat generation rate in the shield bulk for an isoto ?e
(n=1-3) (BTU/sec ft')
Volumetric decay heat generation rate in the inside of the shield for
QRADC
QRADCG
QRADEB
an isotope (n=1-3) (BTU/sec ft')
Volumetric decay heat generation rate in the outside of the shield for
an isotope (n=1-3) (BTU/sec ft')
Used in heat balance equations for the spray fire (BTU)
Used as a counter in the lithium transfer simulation
Indicates a radiative heat flow (BTU/sec)
Floor liner (or pan) to ambient or floor concrete
Wall liner to ambient or wall concrete
Pan to primary gas
Breeder to blanket back wall
QRADEM
QRADES
Breeder to manifold
Blanket back wall to shield inside region
QRADFB
QRADFG
QRADFS
QRADG
QRADP
QRADPG
First wall (floor) to breeder
Primary floor liner to secondary gas
Primary floor liner to secondary floor liner
Combustion zone (or Li pool without combustion) to primary gas
Combustion zone to lithium pool (only during combustion)
Primary wall liner to secondary gas
QOSHOn
QOUT1..5
QQQ
QRADxx
QRADB
47
QRADPS
QRADS
QRADW
QRADWB
QRSHFS
QRSHGS
QRSHWS
QU
QVAP
QVEHC
QVPAN
QVSEC
QVFLR
QVFPGS
QVWPGS
RA
RADxxx
'RAD'B
'RAD'C
'RAD'CB
'RAD'CC
RAIR
RAIR2
'R'BFF
'R'BFW
'R'BIEHC
RBREAK
RC2
RC2LB
RCMBC
RCMBC2
Primary wall liner to secondary wall liner
Pan to primary floor liner
Combustion zone (or lithium pool) to primary wall liner
First wall to breeder
Radiative heat flow from the shield outside region to the secondary
floor (BTU/sec)
Radiative heat flow from the shield outside region to the secondary
gas (BTU/sec)
Radiative heat flow from the shield outside region to the secondary
wall (BTU/sec)
Heat flux from the primary gas to primary wall liner
due to condensation (BTU/sec-ft 2 )
Heat of vaporization of lithium (BTU/lb)
Heat flux from the cell gas to the extraneous heat capacity
due to condensation (BTU/sec-ft 2 )
Heat flux from the primary gas to the pan insulation
due to condensation (BTU/sec-ft 2 )
Heat flux from the secondary gas to secondary wall liner
due to condensation (BTU/sec-ft 2 )
Heat flux from the cell gas to cell floor liner
due to condensation (BTU/sec-ft 2 )
Heat flux from the secondary gas to primary floor liner
due to condensation (BTU/sec-ft2 )
Heat flux from the secondary gas to primary wall liner
due to condensation (BTU/sec-ft 2 )
Mean radius of combustion product particles (microns)
'RAD' or 'R' indicates a temperature rate of change in one node due
to radiative heat transfer to or from another (deg. F./sec)
Floor liner to ambient or floor concrete
Wall liner to ambient or wall concrete
Floor concrete from floor liner
Wall concrete from wall liner
Gas constant for primary non-condensible gas (RIN/XMOLP)
Gas constant for secondary non-condensible gas (RIN/XMOLS)
Breeder node from first wall (floor)
Breeder node from first wall
Blanket back wall from breeder
Temperature rate of change of primary gas due to leakage (R/sec)
Li-CO 2 reaction rate inhibition factor (Li 2 CO 3 reaction)
Rate of carbon consumption (lb/sec)
Stoichiometric combustion ratio for lithium and concrete
(lb Li/lb concrete)
Stoichiometric combustion ratio for lithium and carbon (lb Li/lb C)
48
RCOLB
'R'CZG
'R'CZP
'R'CZW
'R'EHCBI
'R'EHCMN
'R'EHCSH
RELERR
'R'FFB
'R'FPFS
'R'FPGAS
'R'FSFP
'R'FSSH
'R'FWB
'R'GASFP
'R'GASPA
'R'GLI
'R'GSSH
Stoichiometric combustion ratio for lithium and carbon dioxide
for lithium carbonate producing reaction (lb Li/lb CO 2 )
Stoichiometric ratio of lithium consumed in Li 2 CO 3 producing
reaction to Li 2 CO3 produced (lb Li/lb Li 2 CO 3 )
Stoichiometric combustion ratio for lithium and hydrogen (lb Li/lb H)
Stoichiometric combustion ratio for lithium and nitrogen (lb Li/lb N)
Stoichiometric combustion ratio for lithium and oxygen (lb Li/lb 0)
Stoichiometric combustion ratio for monoxide reaction (lb Li/lb 0)
Stoichiometric combustion ratio for peroxide reaction (lb Li/lb 0)
Stoichiometric combustion ratio for lithium and water for reaction
producing LiOH (lb Li/lb H2 0)
Stoichiometric combustion ratio for lithium and water for reaction
producing Li 2 0 (lb Li/lb H2 0)
Stoichiometric ratio of lithium consumed in Li-CO 2 reaction
producing Li 2 0 and carbon to carbon produced (lb Li/lb C)
Stoichiometric ratio of lithium consumed in Li-CO 2 reaction
producing Li2 CO 3 and carbon to carbon produced (lb Li/lb C)
Stoichiometric combustion ratio for lithium and carbon dioxide
for lithium oxide producing reaction (lb Li/lb CO 2 )
Rate of carbon dioxide consumption (lb CO 2 /sec)
Primary gas from combustion zone
Lithium pool from combustion zone
Primary wall liner from combustion zone
Breeder from blanket back wall
Breeder from manifold
Blanket back wall from shield inside region
Fraction of X/(dx/dt) allowed as the maximum time step (sec)
First wall (floor) from breeder node
Primary floor liner from secondary floor liner
Primary floor liner from secondary gas
Secondary floor liner from primary floor liner
Secondary floor liner from shield outside region
First wall from breeder node
Secondary gas from primary floor liner
Pan to primary gas
Lithium pool to primary gas (without combustion)
Secondary gas from shield ouside region
RHCON
Density of concrete (lb/ft3 )
RHINS
RHLEAD
RHLI
RHLIX
Density
Density
Density
Density
(lb/ft3 )
RHOAIP
Initial density of primary non-condensible gas (lb/ft3 )
RCMBCO
RCMBCS
RCMBH2
RCMBN
RCMBO
RCMB01
RCMB02
RCMBW
RCMBW2
RCMCA1
RCMCA2
RCMCCO
of insulation (lb/ft3 )
of pure lead (lb/ft3 )
of pure lithium (lb/ft3 )
of pure lithium (used in LC-2 lithium transfer simulation)
RHOAIS
RHOAP
RHOAS
RHOB
RHOCAR
RHOLC2
RHOLC3
RHOLIH
RHOLIN
RHOLIO
RHOLIV
RHOTOT
RHPAN
RHSFP
RHSFS
RHSWP
RHSWS
RIFxxx
RIFBBI
RIFBM
RIFCZG
RIFCZP
RIFES
RIFFFB
RIFFPS
RIFFWB
RIFPAG
RIFPAS
RIFPG
RIFPGA
RIFPS
RIFPW
RIFSCF
RIFSCW
RIFSLC
RIFSF
RIFSW
RIN
RINP
RINS
RISHGS
'R'LIG
'R'LIW
Initial density of secondary non-condensible gas (lb/ft3 )
Density of primary non-condensible gas (lb/ft3 )
Density of secondary non-condensible gas (lb/ft3 )
Density of the water pool-gas boundary layer (lb/ft3 )
Density of carbon (lb/ft3 )
Density of Li 2 C2 (lb/ft3 )
Density of Li 2 CO 3 (lb/ft3 )
Density of LiOH (lb/ft3 )
Density of Li 3 N (lb/ft3 )
Density of Li 2 0 (lb/ft3 )
Density of lithium vapor above the pool (lb/ft3 )
Total gas density at the lithium pool surface (lb/ft3 )
Density of lithium spill pan (lb/ft3 )
Density of primary floor liner (lb/ft3 )
Density of secondary floor liner (lb/ft3 )
Density of primary wall liner (lb/ft3 )
Density of secondary wall liner (lb/ft3 )
Radiative interchange factor-used in radiative heat transfer
Breeder node to blanket back wall
Breeder node to manifold
Combustion zone and primary gas
Combustion zone and primary wall liner
Blanket back wall to shield inside region
First wall (floor) to breeder node
Primary floor liner and secondary floor liner
First wall to breeder node
Pan to primary gas
Pan to floor liner
Lithium pool to primary gas
Primary wall liner to secondary gas
Primary wall liner to secondary wall liner
Lithium pool to primary wall liner
Secondary floor to concrete floor
Secondary wall to concrete wall
Wall or floor liner to concrete
Shield outside region to secondary floor
Shield outside region to secondary wall
Universal gas constant (1545 ft-lbf/lb-mol-deg. F.)
Gas constant for the primary gas (RIN/XMOLP)
Gas constant for the secondary gas (RIN/XMOLS)
Radiative interchange factor between the shield outer region and the
secondary cell gas
Gas from lithium pool (without combustion)
Wall liner from lithium gool (without combustion)
'R'MNEHC
RN2
RNxx
RNILB
R02
ROXLB
'R'PAGAS
'R'PANST
RR
RRTLI
'R'SHEHC
'R'SHFS
'R'SHGS
'R'SHWS
'R'SPGS
'R'STPAN
RWALB
'R'WLI
'R'WPGAS
'R'WPWS
'R'WSSH
'R'WSWP
SAT(x,y)
SFLCR
SFLEND
SFLTIN
SH(x,y,z)
SIGMA
SPILL
SPRAY
STICK
STMFAC
STMIN
STMIN2
STMOUT
STOUT2
TA
TAU
TAUCZ
Manifold from breeder
Lithium-nitrogen reaction rate inhibition factor
Expressions used to calculate RN2 as a function of gas composition and
lithium temperature
Rate of nitrogen combustion (lb/sec)
Lithium-oxygen reaction rate inhibition factor
Rate of oxygen combustion (lb/sec)
Primary gas from pan
Primary wall liner from pan
Function which generates the lithium-nitrogen kinetics limit curve
Lithium-nitrogen reaction kinetics limit modified by the presence of steam
Shield inside region from blanket back wall
Shield outside region from secondary floor
Shield outside region from secondary gas
Shield outside region from secondary wall
Secondary gas from primary wall liner
Pan from primary wall liner
Rate of water vapor consumption (lb/sec)
Lithium pool from primary wall liner (without combustion)
Primary wall liner from secondary gas
Primary wall liner from secondary wall liner
Secondary wall liner from shield outside region
Secondary wall liner from primary wall liner
Saturated steam table
Heat removal rate by emergency cooling of floor liner (BTU/sec)
Time after spill when SFLCR ends (sec)
Time after spill when SFLCR begins (sec)
Superheated steam table
Stefan-Boltzmann constant (1.713-10-9 BTU/ft2 -hr-deg. R. 4 )
Total mass of lithium spilled (lb)
Mass fraction of lithium consumed in the spray fire
Rate at which aerosols are removed from the primary cell due to
sticking to the wall. If STICK > 1.0, execution stops.
STICK may be reduced by increasing BETA.
Density weighting factor for calculating steam-air mixture properties
Time to begin steam injection to primary cell (sec)
Time to begin steam injection to secondary cell (sec)
Time to end steam injection to primary cell (sec)
Time to end steam injection to secondary cell (sec)
Ambient temperature (deg. R.)
Time constant for transient natural convection
Radiative transmissivity used to model pool-combustion zone coupling
rather than (1.-EMCZ)
51
TAVE
TAVHI
TAVLO
TB(i)
TBIC(i)
TxxxxF
TBLI
TBLIO
TBLOW
TC(i)
TCIC(i)
TCIGNI
TCON
TCZ
TCZI
TE
TEHCP
TEHCS
TEHCZP
TEHCZS
TETI
TET2
TEZ
TFEFF
TFHI
TFLO
TFS
TGP
TGPZER
TGS
TGSZER
THBLI
THE
THFC
THFP
THFS
THI
Average of secondary floor and secondary water pool temperature (deg. R.)
Variable used to read steam tables
Variable used to read steam tables
Temperature of ith node of concrete floor (deg. R.)
Initial temperature of ith node of concrete floor (deg. R.)
Corresponding temperature to Txxxx in Fahrenheit
Temperature of blanket back wall (deg. R.)
Initial temperature of blanket back wall (deg. R.)
Inert gas inlet temperature (deg. R.)
Temperature of ith node of concrete wall (deg. R.)
Initial temperature of ith node of concrete wall (deg. R.)
Ignition temperature of lithium-concrete reaction (deg. R.)
Concrete combustion zone temperature (deg. R.)
Combustion zone temperature (deg. R.)
Initial combustion zone temperature (deg. R.)
Equilibrium temperature resulting from spray fire (deg. R.)
Primary extraneous heat capacity temperature (deg. R.)
Secondary extraneous heat capacity (breeder with torus fire option)
temperature (deg. R.)
Initial primary extraneous heat capacity temperature (deg. R.)
Initial secondary extraneous heat capacity (breeder with torus fire
option) temperature (deg. R.)
Used in calculating thermal conductivity of inner pan insulation
See KIN1
Used in calculating thermal conductivity of outer pan insulation
See KIN2
Average of combustion zone temperature and lithium pool temperature
Used in test for combustion (deg. R.)
Normalized temperature of combustion zone-lithium pool temperature
(deg. R.)
Variable used to read steam tables
Variable used to read steam tables
Secondary floor liner temperature (deg. R.)
Primary gas temperature (deg. R.)
Initial primary gas temperature (deg. R.)
Secondary gas temperature (deg. R.)
Initial secondary gas temperature (deg. R.)
Thickness of blanket back wall (ft)
Thickness of vacuum gap (ft)
Thickness of concrete floor (ft)
Thickness of primary floor liner (ft)
Thickness of secondary floor liner (ft)
Temporary variable used to read steam tables
52
THKIN1
Thickness of inner pan insulation (ft)
THKIN2
Thickness of outer pan insulation (ft)
THKPAN Thickness of spill pan (ft)
Thickness of blanket manifold (ft)
THMAN
THPB
Thickness of lead layer above the lithium-lead pool (ft)
Thickness of inside region of reactor shield (ft)
THSHI
Thickness of bulk region of reactor shield (ft)
THSHL
Thickness of outside region of reactor shield (ft)
THSHO
THWC
Thickness of concrete wall (ft)
Thickness of primary wall liner (ft)
THWP
Thickness of secondary wall liner (ft)
THWS
Time elapsed after spill has occurred (sec)
TIME
User defined time to stop execution of the code (sec)
TIMEF
Time at which code prints output data to a file (sec)
TIMEO
Inner pan insulation layer temperature (deg. R.)
TINS1
Initial inner pan insulation layer temperature (deg. R.)
TINS1I
Outer pan insulation layer temperature (deg. R.)
TINS2
TINS2I
Initial outer pan insulation layer temperature (deg. R.)
TLEAD
Temperature of the lead layer above the Li-Pb pool (deg. R.)
TLEADI
Initial temperature of the lead layer above the Li-Pb pool (deg. R.)
Lithium pool temperature (deg. R.)
TLI
Lithium pool temperature before spray fire (deg. R.)
TLIBS
TLII
initial lithium pool temperature (deg. R.)
TLO
Temporary variable used to read steam tables
TLP
Temperature of the primary liquid pool (deg. R.)
TMAG
Temperature of the magnets (secondary extraneous heat capacity) (deg. R.)
TMAGZ
Initial temperature of the magnets (secondary extraneous heat capacity) (deg.
Temperature of the blanket manifold (deg. R.)
TMAN
TMANO
Initial temperature of the blanket manifold (deg. R.)
TMELT
Melting temperature of lithium (deg. R.)
TO
Primary gas temperature before spray fire (deg. R.)
TONE,TTWO,TTHREE Time at which each injection occurs (sec)
TPAN
Pan temperature (deg. R.)
TPANZO Initial pan temperature (deg. R.)
TSAT
Saturation temperature of water based on its partial pressure (deg. F.)
Primary floor liner temperature (deg. R.)
TSFP
TSFPI
Initial primary floor liner temperature (deg. R.)
TSFSI
Initial secondary floor liner temperature (deg. R.)
TSHI
Shield inside region temperature (deg. R.)
TSHIO
Initial shield inside region temperature (deg. R.)
TSHL
Shield bulk region temperature (deg. R.)
53
TSHLZ
TSHO
TSHOO
TSP
TSPZER
TSS
TSSZER
TVAP
TI
T2,T3
UA
UGPB
UL
UL2
ULP
ULP2
ULPB
ULZ
ULZ2
USUBA
UV
UV2
UVZ
UVZ2
UWV
UWV2
VA
VAB
VCONC
VG
VG2
VHI
VIEWB
VIEWG
VIEWM
Initial shield bulk region temperature (deg. R.)
Shield outside region temperature (deg. R.)
Initial shield outside region temperature (deg. R.)
Primary wall liner temperature (deg. R.)
Initial primary wall liner temperature (deg. R.)
Secondary wall liner temperature (deg. R.)
Initial secondary wall liner temperature (deg. R.)
Vaporization temperature of lithium (deg. R.)
Film temperature between primary gas and lithium pool (deg. R.)
Temporary variables used in setting up steam table
Internal energy of non-condensible gas in a cell (BTU)
Specific internal energy of saturated water vapor at boiling (BTU/lb)
Internal energy of the primary water pool (BTU)
Internal energy of the secondary water pool (BTU)
Specific internal energy of the primary water pool (BTU/lb)
Specific internal energy of the secondary water pool (BTU/lb)
Specific internal energy of liquid needed for boiling to occur (BTU/lb)
Time rate of change of UL (BTU/sec)
Time rate of change of UL2 (BTU/sec)
Heat transfer coefficient between the outermost containment node and
the ambient (BTU/sec-ft2 -deg. F.)
Internal energy of the primary gas (BTU)
Internal energy of the secondary gas (BTU)
Time rate of change of the internal energy of the primary gas (BTU/sec)
Time rate of change of the internal energy of the secondary gas (BTU/sec)
Specific internal energy of water vapor in the primary gas (BTU/lb)
Specific internal energy of water vapor in the secondary gas (BTU/lb)
Specific volume of non-condensible primary gas (ft3 /lb)
Specific volume of non-condensible gas at the water pool-gas boundary (ft3 /lb)
Volume of concrete in the first node of concrete (ft3 )
Specific volume of water in the primary gas (ft3 /lb)
Specific volume of water in the secondary gas (ft3 /lb)
Variable used to read steam tables
View factor from the breeder to the blanket back wall
View factor across the vacuum gap
View factor from the breeder to the manifold
VL
VL2
Volume of the primary water pool (ft3 )
Volume of the secondary water pool (ft3 )
VLO
VLP
VLP2
Variable used to read steam tables
Specific volume of the primary water pool (ft3 /lb)
Specific volume of the secondary water pool (ft3 /lb)
54
VLPF
VLPV
VP
VS
VSB
VST
VVB
VVB2
VVG
VVG2
VVT
WAB
WAP
WAS
WATER
WCB
WCP
WCO2S
WN2B
WN2P
WN2S
WO2B
WO2P
WO2S
WWAB
WWAP
WWAS
XALLOY
XAM
XBLOW
XESC
XINJ
XINJ2
XLI
XLIDOT
XMAIRP
XMAIRS
Specific volume of saturated liquid water at the secondary floor liner
temperature (ft3 /lb)
Specific volume of saturated liquid water for heat transfer between the
secondary floor liner and the secondary water pool (ft3 /lb)
Volume of primary cell (ft3 )
Volume of secondary cell (ft3 )
Specific volume of water vapor at the water pool-gas boundary (ft3 /lb)
Specific volume of water vapor at the lithium pool surface (ft3 /lb)
Specific volume of saturated water vapor at the primary water pool
temperature (ft3 /lb)
Specific volume of saturated water vapor at the secondary water pool
temperature (ft 3 /lb)
Specific volume of saturated water vapor in the primary gas (ft3 /lb)
Specific volume of saturated water vapor in the secondary gas (ft3 /lb)
Temporary variable used to determine steam properties for condensation
Mass fraction of inert gas in the flooding gas
Mass fraction of inert gas in the primary gas
Mass fraction of inert gas in the secondary gas
Amount of water that should be left in the top concrete node
as time-+oo (lb/ft3 )
Mass fraction of carbon dioxide in the flooding gas
Mass fraction of carbon dioxide in the primary gas
Mass fraction of carbon dioxide in the secondary gas
Mass fraction of nitrogen in the flooding gas
Mass fraction of nitrogen in the primary gas
Mass fraction of nitrogen in the secondary gas
Mass fraction of oxygen in the flooding gas
Mass fraction of oxygen in the primary gas
Mass fraction of oxygen in the secondary gas
Mass fraction of water vapor in the flooding gas
Mass fraction of water vapor in the primary gas
Mass fraction of water vapor in the secondary gas
Atom percent of lithium in lithium-lead pool
Logarithmic mean molar fraction of air (see MFAB and MFAG)
Used in conjunction with IBLOW
Used in conjunction with IESC
Indicates whether steam injection to the primary is in effect
Indicates whether steam injection to the secondary is in effect
Mass fraction of lithium in lithium-lead pool
Mass flow rate of lithium through the lead layer above the Li-Pb
pool (lb/sec)
Amount of non-condensible primary gas after spray fire (lb-mol)
Amount of non-condensible secondary gas after spray fire (lb-mol)
55
XMBLI
XMCOCZ
XMDOT
XMEHCP
XMEHCS
Mass of the blanket back wall (lb)
Mass of concrete combustion zone (lb)
Mass flow rate of gas between primary and secondary cells (lb/sec)
Mass of primary extraneous heat capacity (lb)
Mass of secondary extraneous heat capacity (breeder with torus fire
option) (lb)
XMH20I
Initial water content of concrete (lb/ft3 )
XMMAG
XMMAN
XMOLP
XMOLS
XMOLA
XMOLAB
XMSHI
XMSHL
XMSHO
XSFL
YALIG
ZLI
ZP
ZZxxxx
ZZ1
ZZ2
ZZ3
ZZ4
ZZ5
ZZ6
ZZ7
ZZ8
ZZ9
Mass of the magnets (secondary extraneous heat capacity) (lb)
Mass of the blanket manifold (lb)
Molecular weight of non-condensible primary gas (lb/lb-mol)
Molecular weight of non-condensible secondary gas (lb/lb-mol)
Molecular weight of containment inert gas (lb/lb-mol)
Molecular weight of flooding inert gas (lb/lb-mol)
Mass of shield inside region (lb)
Mass of shield bulk region (lb)
Mass of shield outside region (lb)
Indicates whether emergency floor cooling is currently in effect
Effective thermal admittance between the pool and primary gas
(BTU/sec-deg. F.)
Effective thermal admittance between the pool and combustion zone
(BTU/sec-deg. F.)
Effective thermal admittance between the pan and primary gas
(BTU/sec-deg. F.)
Thickness of the lithium pool (ft)
Used to determine EMLI if EMLI < 0.9
Temperature rate of change of a node (deg. R./sec)
Lithium pool
Lithium spill pan
Secondary cell gas
Primary cell gas
Primary wall liner
Combustion zone
Primary floor liner
Inner insulation layer
Outer insulation layer
ZZ99
'ZZ'C
Change in combustion rate with respect to time (lb Li/sec2 ft 2 )
Concrete combustion zone
'ZZ'BLI
ZZD
ZZDIN
'ZZ'EP
'ZZ'ES
'ZZ'FS
'ZZ'MAG
Blanket back wall
Rate of change of concrete combustion zone thickness (ft/sec)
Initial rate of change of concrete combustion zone thickness (ft/sec)
Primary extraneous heat capacity
Secondary extraneous heat capacity
Secondary floor liner
Magnets (secondary extraneous heat capacity)
56
YAPCZ
YPAGAS
'ZZ'MAN
'ZZ'PB
'ZZ's
'ZZ'SHI
'ZZ'SHL
'ZZ'SHO
Blanket manifold
Lead layer above Li-Pb pool
Secondary wall liner
Shield inside region
Shield bulk region
Shield outside region
PROGRAM DECISION FLAGS
IAROSL
IBLOW
ICMB
ICNI
IC021
ICZ
IESC
IFLAG2
IFLAGB
IFLAGC
IFLAGCO
IFLAGD
IFLAGF
IFLAGISI
IFLAGP
IFLAGR
IFLAGS
IFLAGT
IFLAGU
IFLAGW
ILIT
IMETH
ISFLC
ISWICH
=1 to use aerosol removal from containment by sticking option
=1 Containment flooding with inert gas
=0 No containment flooding
=0 No oxygen left after spray fire
=1 Still oxygen left after spray fire (initially =1, reset by code)
=0 Nitrogen reactions not possible
=1 Nitrogen reactions possible
=1 to use pure CO 2 atmosphere
=0 Combustion zone model not used
=1 Combustion zone model used
=1 to use emergency space cooling option
=1 to use two-cell geometry option
=1 to use lithium-lead option
=1 to use concrete combustion option
=1 to use pure CO 2 atmosphere option
=1 to use layered lithium-lead pool option
=1 to use floor concrete option
=1 to enter input data in SI units
=1 to use pan option
=1 to use torus fire option
=1 to use dry gas injection option
=1 to use steam-air mixture option
=1 to get output in SI units
=1 to use wall concrete option
=0 No lithium left to burn
=1 Lithium left to burn
=1 Runge-Kutta method of integration used
=3 Simpson's Rule method of integration used
=1 to use emergency floor cooling option
=0 Crack size remains constant
Crack size reset to zero after primary and secondary cell
gas pressure equilibrate (note: this should not be used when
either cell is small compared to the other or the volume of gas
being consumed by the fire)
57
OPTION AND LOGICAL DECISION FLAGS
FLAG2 = .TRUE.
FLAGAS = .TRUE.
FLAGC = .TRUE.
FLAGCO = .TRUE.
FLAGD = .TRUE.
FLAGDF = .TRUE.
FLAGF = .TRUE.
FLAGISI = .TRUE.
FLAGL =.TRUE.
FLAGM = .TRUE.
FLAGN = .TRUE.
FLAGPB = .TRUE.
FLAGPN = .TRUE.
FLAGSI = .TRUE.
FLAGST = .TRUE.
FLAGTR = .TRUE.
FLAGW = .TRUE.
Two cell geometry
Injection of dry gas during run
Concrete combustion
Pure CO 2 containment atmosphere
Concrete combustion has stopped (set by code)
Lithium-lead layered pool combustion model
Floor concrete
Code accepts input in SI units
LILP is fixed at a minimum (set by code)
Sonic gas flow between cells (set by code)
Indicates first run through a subroutine (set by code)
Lithium-lead combustion
Pan option
Code prints output in SI units
Steam-air mixture in containment
Torus fire option
Wall concrete
58
C
Troubleshooting
"There exists no large computer code which runs perfectly 100% of the time."
-ANONYMOUSThe user of this code may encounter problems while trying to execute LITFIRE.
The most common error statement is generated by the computer itself: DIVIDE BY
ZERO and stops the code. This indicates that an attempt was made to divide by zero
or something very close to zero. The first step when encountering an error message
is to check the output file outl.dat and ensure that the input was properly entered
into the code. If it was, the error may occur if the value of EXHSTV is too high or
LILP is too low. This problem may be mitigated to an extent by reducing DTMIN,
the minimum time step length, although this will increase computation time.
Another common error message is generated by LITFIRE: EXX IS NEGATIVE
- CANNOT TAKE ROOT When this occurs, it indicates that the code is trying to
take the square root of a negative number - the code has diverged numerically and
the combustion zone temperature is negative. This may occur when. the combustion
rate CMBRH is very small (i.e.,< 1.0 lb Li/hr-ft 2 ), the oxygen and nitrogen concentrations are low, or when the gas pressure is low. This problem occurs when ZZ6
and DELT are large enough to produce a negative TCZ. This problern may be solved
by reducing the value of DELOUT to limit the time step size, so extrapolations of
TCZ over a long time step do not cause problems. Unfortunately, this can increase
computation time considerably. The variation of the combustion zone temperature
over time is a good indicator of whether or not the code is running properly. During
combustion, TCZ should be 100' F. or more higher than TLI. Once combustion stops,
TCZ should drop rapidly to a value just barely above TLI. (TLI is hypothetical at this
point if the lithium has been consumed, but it is continuously calculated for numerical
reasons.) If TCZ oscillates rapidly or falls below TLI, it is an indication of trouble.
As stated earlier, this may be mitigated by decreasing the value of DELOUT.
If the statement: LITHIUM TEMP. ABOVE BOILING POINT occurs, this may
indicate that the rate of change of the lithium pool temperature was very large. This
may be due to the fact that TCZ has diverged to a very large value. This generally
occurs as LILP nears zero, as the pool then has a lower heat capacity, and a sudden
influx of energy would cause the pool to heat up rapidly.
Other signs of trouble include a rapid drop in containment gas mass (MNIP,
MOXP), or an oscillating combustion zone temperature, TCZ; combustion rate, CMBRH; or time step length DELT. In general, DELT should increase after the start of
the run and then level off until combustion stops, when it may change more rapidly.
Sudden large changes in DELT indicate that the temperature rates of change are
varying rapidly, which usually should not be the case. If reducing DELT does not
help solve the problem, print out values of the code quantities like ZZ5 and ZZ6 or
UVZ and MWVZ to help find the problem.
Other messages indicate that the user is attempting to use incompatible options
together, or that the code has been stopped because there is no point in continuing further (i.e. the lithium temperature has dropped below the melting point, or
containment gas temperature and pressure have returned to normal).
59
D
Sample Input Data Files
INPUT DAIA FILE HEAD.DAT
THIS IS THE INPUT DATA FOR THE EXECUTION
OF THE CODF LITFIRE
THESE ARE THE OUTPUT VALUES CORRESPONDING
TO THE PRIMARY CELL ENVIRONMENT
TIME
DELT
TCZF
TLIF
TGPF
THESE ARE THE OUTPUT VALUES CORRESPONDING
TO THE SECONDARY CELL ENVIRONMENT
TIME
TGSF
TFSF
PAS
XMDOT
PA P
TSPF
MOXS
TSFPF
MNIS
MCO2S
THESE ARE THE OUTPUT VALUES CORRESPONDING
TO THE PAN OUTPUT OPTION
TIME
TLIF
TPANF
TINS1F
THESE ARE ADDITIONAL OUTPUT VALUES CORRESPOJDING
TO THE PRIMARY CELL ENVIRONMENT
TIME
MNIP
MOXP
MCO2P
TINS2F
RN2
PAP
R02
LIBP
THESE ARE THE OUTPUT VALUES CORRESONDING
TO THE LITHIUM/LEAD DIFFUSION OPTION
TIME
XLIDOT
TLEADF
THPB
MLEAD
ZLI
INPUT DATA FILE UWMAK.W
e0 0 0 0 0 0 0 0 0
S0
5
.20
.20
5
.20
.20
.20
.20
.20
.20
.20
.20
497.88
10.14
725.0
0.833
0.15
123.00
2.080
0.1189
0.1189
0.9960
0.2650
86.9400
0.0
0.0
2916.0
0.13
0.85
0.07
22.05
851.4
0.2320
0.15
0.2
0.9
124.00
18510.0
0.8764
816.60
0.87
0.16
0.07
2.153
1752.6
14.70
0.1247
39.90
51.00
0.002
30.00
0.015
0.09
0.00
497.500
572.3
30.00
497.500
33.80
0.0227
160.00
4080.0
1.487
8431.0
0.01
0.112
0.000
851.2
0.0
0.1199
30.00
144.00
0.04
13784.0
0.383
0.0
0.11
0.07
0.050
815.2
0.0000
0.05 80
0.05 80
38.35
0.1
0.9
10964.1
0.766
6.93
0.89
0.01
5.0
530.99
0.0000
0.01
1751.8
00030000000.02000000900.00000000000.00300000001.00000000100.0000
INPUT DA A FILE UWMAK.X
8855700.00000000140.0eOe0000014.70000000538.10000000538.20000000538.3000
0.0
0.0
522.0000
0.232
00.00
15.5
0.09
0.6921
9709.00
1696200.0
1482.0
188164.00
0.0208
0.1199
12.40
497.50
0.85
0.0208
59038.00
497.50
12.40
0.85
0.1199
350.0
60
mmwk.ftww
INPUl DATA FILE UWMAK.Y
0000030.00000000497.50000000000.12000000008.11500000000.20000000000.9000
0.09
12.32
5.9055
7.00
1750.00
0.0833
0.1667
0.0210
0000.0415
3315.0000
0.1700
708.0000
9.3000
0.0350
6.45600E-08
INPUT DATA FILE UWMAK.Z
0000100.00000000000.00000000000.00000000004.ecoeCOOOOO.12470000535.0000
0.00
325.0
310.0
0.0
24.0
INPUT DATA FILE STEAMOP.
0001000.000000030e0.
00900001190.300
OOOOOOOeo.
INPUT DATA FILE TORUS.
8855700.00000000150.00000000014.70000000538.10000000538.20000000538.3000
0.0
522.0000
0.0
0.232
00.70
15.5
1.498
0.09
0.1189
7796.00
115468.0
1482.0
0.0208
188164.00
497.50
12.40
0.1199
0.85
0.0208
59038.00
497.50
12.40
0.85
0.1199
.648
0.1
0.1
0.500
1.344
0.1653 12110.0
14.202 3500000.0
1.903
672.0
0.1199
9000000.0
14000.0
538.0
0.0001
0.500
.278
1.0
0.889
0.0656
0.000
0.09
1300.0
149816.0
9472.0
.1189
.1312
17.90
260000.0
.1312 260000.0
.1312
585.0
670.0
11.387
1392.0
8890.0
.188
.656 522842.0
8.16e+00 4.41e-06 4.43e-01 9.57e-08 1.75e-01 2.90e-07
1.03e-01 4.41e-06 6.46e-03 9.57e-08 1.09e+00 3.08e-02
8.46e-02 2.56e-08 1.91e+00 7.41e-05 3.32e-02 2.92.-6
2.84e-02 4.41e-06 8.21e+00 3.08e-03 2.88e-03 2.90e-07
1.85e+00 7.41e-05 2.72e-03 2.56e-08 1.70e-04 3.84e-12
1.77e+01 2.81e-02 1.69e-04 7.51e-03 7.34e-06 1.69e-04
350.0
61
E
Sample Output Data Files
OUTPUT DATA FILE OUT2.DAT
THESE ARE THE OUTPUT VALUES CORRESPONDING
TO THE PRIMARY CELL ENVIRONMENT
TIME
0.0
DELT
TCZF
TLIF
TGPF
0.10
700.67
700.22 200.00
100.0
0.32
810.60
609.64 198.78
0.47
200.2
827.90
622.37 197.98
300.1 0.22
650.31 197.09
855.77
400.1
0.43
900.09
679.50 196.39
500.0 0.82
911.94
715.02 195.21
600.1 0.48
922.62
742.62 194.11
700.0
0.04
757.36 193.89
935.18
800.0 0.17
950.40
765.30 193.60
900.1 0.04
967.46
773.17
193.30
progrom execution stopped by program
values 0.233e+02 0.604e+03 0.181e+03 0.692e+01
TSPF
TSFPF
199.89
198.41
179.89
PAP
101.70
102.11
102.89
'03.66
104.42
105.32
106.13
106.63
106.92
107.21
196.93
195.49
194.17
192.62
191.23
190.38
189.91
189.45
489.57
573.67
613.54
643.92
680.06
709.36
725.33
733.84
741.89
0.619e+00
OUTPU' DATA FILE OUT3.DAT
THESE ARE THE OUTPUT VALUES CORRESPONDING
TO THE SECONDARY CELL ENVIRONMENT
TIME
0.0
100.0
200.2
300.1
400.1
500.0
600.1
700.0
800.0
900.1
TGSF
25.94
28.12
30.40
32.69
34.90
37.56
39.96
41.44
42.30
43.15
TFSF
26.06
26.06
26.06
26.08
26.10
26.15
26.20
26.25
26.28
26.31
MOXS
0.1508e+06
0. 1508e+06
0.1508e+06
0.1508e+06
0.1508e+06
0.1508e+06
0.1508e+06
0.1508e+06
0.1508e+06
107.21 0.3610e-01 0.1508e+06
XMDOT
PAS
101.38-0.2194e+00
102.11 0.
102.89 0.
103.67 0.
104.41 0.
105.32 0.
106.13 0.
106.63 0.3826e-01
106.92 0.
62
MNIS
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
0.4994e+06
MCO2S
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
OUTPUT DATA FILE OUT5.DAT
THESE ARE ADDITIONAL OUTPUT VALUES CORRESPONDING
TO THE PRIMARY CFLL ENVIRONMENT
TIME
0.0
100.0
20C 2
300. 1
400.1
500.0
600.1
700.0
800.0
900.1
MNIP
0.8074e+01
0.8153e+01
0..272e+01
0.8395e+01
0.8510e+01
0.8662e+01
0.8806e+01
0.8892e+01
0.8937e+01
0.8988e+01
MOXP
0.2439e+01
0.2426e+01
0.2399e+01
0.2372e+01
0.2345e+01
0. 2305e+01
0.2264e+01
0. 2236e+01
0.2221e+01
0.2208e+01
RN2
0.00000
0.35110
0.33125
0.28269
MCO2P
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
R02
0.97120
0.97098
0.97059
0.97020
0.96982
0.96929
0.23668
0.18993
0.16182
0.16819
0.18553
0.96875
0.96841
0.96823
0.96805
0.20478
LIBP
0.
0.1015e+00
0.2476e+00
0.4156e+00
0.6179e+00
0.8597e+00
0.1074e+01
0.1209e+01
0.1297e+01
0.1393e+01
OUTPUT DATA FILE OUT9.DAT
These outputs ore the weights of react 3n products in LB
Lilox
Time
0.0
100.0
200.2
300.1
400.1
500.0
600.1
700.0
800.0
900.1
0.
0.193e+00
0.503e+00
0.837e+00
0.1 19e+01
0.165e+01
0.209e+01
0.238e+01
0.255e+01
0.273e+01
Lilni
Lilco
0.
0.
0.205e+00 0.
e.474e+00 0.
0.802e+00 0.
0.124e+01 0.
0.173e+01 0.
0.213e+01 0.
0.238e+01 0.
0.255e+01 0.
0.275e+01 0.
Lilc2
Lilcar
Mliop
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
MIc3p
0.
0.
0.101 e-81 0.
0.262e-01 0.
0. 435e-e1 0.
0.614e-01 0.
0.846e-01 0.
0.107e+00 0.
0.121e+00 0.
0.128e+00 0.
0.136e+00 0.
OuJPUT DATA FILE OUT1O.DAT
These outputs are the reaction rates in gram Li/min-cm2
Time
0.0
100.0
200.2
300.1
400.1
500.0
600.1
700.0
800.0
900.1
Cmbrhh
Cmbrnh
0.3050e-05 0.2866e-05
0.
0.3885e-01 0.2047e-01 0.1839e-01
0.4243e-01 0.2292e-01 0.1951e-e1
0.4672e-01 0.2678.-01 0.1993e-01
0.5183e-1Ol 0.3112e-01 0.2071e-01
0.4680e-01 0.2599e-01 0.2081e-01
0.4365e-01 0.2289e-01 0.2076e-e1
0.4509e-01 0. 2433e-01 0.2076e-01
0.4833e-01 0.2739e-01 0.2094e-01
0.5207e-el 0.3091e-0 1 0.2116e-01
63
Cmrc2t
Cmrcoh
Cmbrwh
Cmbroh
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
0.
F
Listing of the LITFIRE code
64
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References
[1] D.S. Barnett, et al. LITFIRE User's Guide. MIT Plasma Fusion Center, second
edition, August 1987. PFC/RR-87-11.
[21 D.S. Barnett. The Chemical Kinetics of the Reactions of Lithium with Steam-Air
Mixtures. PhD thesis, Massachusetts Institute of Technology, April 1989.
[3] V.J. Gilberti and M.S. Kazimi. Modeling of Lithium and Lithium-Lead Reactions
in Air Using LITFIRE. Technical Report PFC/RR-83-08, MIT Plasma Fusion
Center, January 1983.
[4] D.A. Dube and M.S. Kazimi. Analysis of Design Strategies for Mitigating the
Consequences of Lithium Fire Within Containment of Controlled Thermonuclear
Reactors. Technical Report MITNE-219, Massachusetts Institute of Technology,
July 1978.
152
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