LITFIRE USER'S GUIDE Third Edition · 2.2.2 Radiative Heat Transfer Radiative heat transfer rates...

DOE/ID-01570-5

LITFIRE USER'S GUIDEThird Edition

D.S. Barnett

April 1989

Plasma Fusion CenterMassachusetts Institute of Technology

Cambridge, MA 02139 U.S.A.

*This work was supported by EG&G Idaho, Inc. and theU.S. Department of Energy, Idaho Operations Office

under DOE Contract No. DE-AC07-7611D01570

Reproduction, translation, publication, use and disposalin whole or in part, by or for the United States

government is permitted

PFC/RR-89-4

Abstract

This document contains instructions for using the LITFIRE lithium firesimulation code in its form as of April 1989. The code is capable of simulatingfires in a single compartment connected to an optional second compartment, orin an insulated pan suspended in one compartment. Lithium or lithium-leadeutectic may be used as the fuel, reacting with an atmosphere of oxygen, ni-trogen, water vapor, or any mixture thereof. Any inert gas may be includedin the compartment atmosphere and lithium only may be burned in a carbondioxide atmosphere without oxygen. An option for liquid metal-concrete inter-action exists as well as the following options for mitigating the effects of thefire: gas flooding, emergency space cooling, emergency floor cooling, aerosolremoval and gas injection. The guide also includes the following:

" a description of the workings of the code, including the various optionsavailable 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

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Contents

Abstract

Table of Contents

List of Figures

1 Introduction

2 Program Description2.1 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 . . . . . . . . . . . .

2.2 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 . . . . . . . .2.2.7 Lithium Combustion . . . . . . . . . . . . .2.2.8 Overpressure, Leakage, and Aerosol Behavior2.2.9 Integrals . . . . . . . . . . . . . . . . . . . .2.2.10 Termination Checks . . . . . . . . . . . . . .2.2.11 Time Step Control . . . . . . . . . . . . . .2.2.12 Output Section . . . . . . . . . . . . . . . .2.2.13 Error Pointers . . . . . . . . . . . . . . . . .

2.3 Modeling Options . . . . . . . . . . . . . . . . . . .2.3.1 One Cell Option . . . . . . . . . . . . . . .2.3.2 Two Cell Option . . . . . . . . . . . . . . .2.3.3 Pan Option . . . . . . . . . . . . . . . . . .2.3.4 Concrete Reaction . . . . . . . . . . . . . .2.3.5 Lithium-Lead Combustion . . . . . . . . . .2.3.6 Steam-Air Atmosphere Option . . . . . . . .2.3.7 Torus Fire Option . . . . . . . . . . . . . . .2.3.8 Mitigation Options . . . . . . . . . . . . . .

3 Execution of LITFIRE3.1 Obtaining Copies of LITFIRE and the Input3.2 Organization of LITFIRE for Execution . .

Data Files.

2

1

2

3

192122

3.2.1 One Cell Option ........................ . 223.2.2 Two Cell Option . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.3 Pan, Concrete Reaction and Lithium-Lead Combustion . . . . 253.2.4 Gas Flooding, Emergency Space Cooling, Emergency Floor Liner

Cooling and Gas Injection . . . . . . . . . . . . . . . . . . . . 263.2.5 Steam Injection to Containment . . . . . . . . . . . . . . . . . 263.2.6 Torus Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 PFCVAX Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . 283.4 MFE Crays Execution . . . . . . . . . . . . . . . . . . . . . . . . . . 293.5 Sample Input and Output Files . . . . . . . . . . . . . . . . . . . . . 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 ...... ....................... 142 Two-cell option in LITFIRE ........................ 153 Mass flow in LITFIRE .......................... 164 Pan option in LITFIRE ........................ . 175 Torus fire option in LITFIRE ...... ...................... 20

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1 Introduction

LITFIRE is a computer code which simulates lithium fires in fusion reactors by gen-erating the time histories of the temperature and pressure profiles occurring in areactor 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 inan insulated pan in a single cell. The lithium or lithium-lead may react with anymixture of oxygen, nitrogen or water vapor; an inert gas may also be included inthe cell atmospheres. Lithium only may be burned in a carbon dioxide atmospherewithout oxygen. An option for liquid metal-concrete interaction is available as wellas the following options for mitigating the effects of a fire: gas flooding, emergencyspace cooling, emergency floor cooling, aerosol removal and gas injection. This user'sguide includes a brief description of the physics of lithium fires, the workings of thecode and the options available to users, and also includes a listing of the code with acomplete glossary of variables used in LITFIRE.

The present version of LITFIRE is available on the PFCVAX at MIT and onthe Crays at the National Magnetic Fusion Energy Computer Center (NMFECC,hereafter referred to as MFE) It is written in FORTRAN 77 and is compatible withthe computing facilities at which it is located. The instructions present in this guidewill enable a user to execute the code at either location.

Other information on LITFIRE such as more detailed descriptions of physicalmodels or correlations used in the code are available in the references listed in thereference section of the guide.

2 Program Description

To assist the new user of LITFIRE in understanding the code, a brief descriptivesection is included. The description of the code sections is presented in the order thatthey are executed. For a description of code options, see Section 2.3. This section isbroken down into an initial routine and a dynamic cycle. The initial routine preparesthe code for execution; then the dynamic cycle integrates the time rate of change ofthe code variables over the time step to calculate their values. The dynamic cycle isrepeated until execution is terminated either by the code or as predetermined by theuser.

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

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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 de-scribed in Section 2.3. Input variables are described in Section 3 and examples of theinput 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 ensurethat the input was properly entered into the input files. Misaligned input data is acommon 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. Someconstants are defined and initial conditions are applied using the input data. Inaddition there is a short sub-section where the units of the input data are changed tothe 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 thebeginning of a spill. The amount reacted in the spray is user specified. A difficultydoes arise in that the specific heats of the reaction products are calculated as func-tions of temperature. The spray fire calculation is not a spray fire model per se inthat the lithium reacting in the spray is consumed instantaneously, adiabatically andstoichiometrically, with the equilibrium temperatures being determined by iteration.

2.2 Dynamic Cycle

The dynamic cycle in LITFIRE calculates the temperature, pressure and mass profilesof the reactor containment over the time of the run. Most of the dynamic cycleconsists of calculating the thermal admittances between nodes, which are then usedin conjunction with the nodal temperatures, to determine the time rates of change ofthe nodal temperatures. The heat flow to or from a node is determined by calculatingthe thermal resistances to conduction or convection between adjacent nodes and thenadding on radiative heat transfer to or from nodes within a line of sight. All of the

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calculations performed in the dynamic cycle are listed below in the order which theyare 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 incontainment 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.

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2.2.1 Preliminary Calculations

Before any calculations are performed by the code, the material properties of all of thenodes must be calculated. Most properties are assumed to be constant with respect totemperature, but the specific heats of some gases and combustion products, and mostlithium properties, are calculated as functions of temperature. These are calculatedat the beginning of each time step. The mass fraction and total mass of each of theindividual gases is also calculated so that the total heat capacity of the gas may becalculated.

2.2.2 Radiative Heat Transfer

Radiative heat transfer rates in LITFIRE are calculated using the following basicequation:

Q1--.2 = f Aio(T' - T2) (1)

where Q1-.2 = heat transfer rate (W) from node 1 to node 2A1 = exposed area of node 1f = radiative interchange factor based on A10 = Stefan-Boltzmann constantT,, = temperature of node n

The radiative interchange factor f is determined by the emissivities of the surfacesof the two nodes and the view factor between them. Thus the radiative emissivity ofeach node is required to account for radiative heat transfer within the containmentbuilding.

The emissivities of the solid elements in the containment building are specified bythe input data and are assumed to be constant. The emissivity of the lithium pool isassumed by the code to be governed by the buildup of reaction products (Li 20, Li3 Nand Li2 CO 3 ) on the pool surface.

The emissivity of the cell gas (in the absence of steam) is determined by theaerosol 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 theinput data and the concentration is calculated from the amount of aerosol reactionproduct generated by the fire. In the presence of steam the emissivity of the cell gasis also governed by the partial pressure of the water vapor in the cell. Radiative heattransfer 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 gasrequires that a different method be used to determine the temperature of the gas thanthe integral method described in Section 2.2.9, as the latent heat of vaporization ofthe steam must be taken into account. In this option, the code performs an iterative

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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-condensiblegas, c, is the specific heat of the non-condensible gas, M, is the mass of the steamand u, is the specific internal energy of the steam. Values of the temperature areguessed, and along with the specific volume of the steam (which is known), are usedto determine the other properties of the steam. These values are then used to solve forthe error, TEMP. When TEMP is a sufficiently small fraction of the total gas internalenergy, the final guess is taken as the gas temperature. For further discussion, seereference[2].

2.2.4 Natural Convection Heat Transfer

The heat transfer coefficients for convective heat transfer between surfaces and gasesh 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 co-efficients used are the Uchida heat transfer coefficients determined empirically asfunctions of the ratio of the mass of water to the mass of non-condensibles in the cellatmosphere. 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 heattransfer coefficients for all of the nodes have been calculated, the thermal resistancesbetween the nodes are calculated. Knowledge of the thermal resistance allows thetemperature rate of change due to heat conduction and heat convection to be calcu-lated. In LITFIRE the thermal resistance between adjacent nodes i and j is calculatedas follows:

+ (4)2kA 2k, A

orI. 1

i A = + _A (5)

where 1, = characteristic length (thickness) of node nkn = thermal conductivity of node nA = area of contact between nodes i and jhij = 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).

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The thermal resistance between the lithium pool and the combustion zone isdetermined somewhat differently, as the lithium is considered to vaporize and thenreact with the gases in the combustion zone. Details of the calculation are given inreference[2].

2.2.6 Temperature Rates of Change

The rates of heat transfer between all thermally adjacent nodes are calculated fromthe temperatures of the nodes, and the thermal resistances and radiative interchangefactors between them. Once the rates of heat transfer to and from all of the nodeshave been calculated, they are summed for each node, and the temperature rate ofchange of each node is calculated using its own heat capacity. The heat flow to orfrom a given node is determined by summing the heat flow by conduction, convectionand radiation to and from thermally adjacent nodes:

Q (T1-Ti)+Z fT p 6Q1 = (T O+ AifIjo(T14 - T ) (6)

where: Q, = heat flow rate to or from node 1T, = temperature of node ni = designation for physically adjacent nodeRli = thermal resistance between nodes 1 and i

(see Eqns. 4 and 5)j = designation for optically adjacent nodeA1 = surface area of node 1fij = radiative interchange factor between nodes 1 and j

Temperature rates of change for each node are calculated by dividing the energygain or loss rate by the heat capacity of the node:

dT1 Q, (7)dt - ii

where t is time, mI is the mass of node 1 and cp is the specific heat of node 1. Thecombustion zone node adds the heat of combustion and the heat of vaporization ofthe lithium combusted to the above terms, while the lithium pool subtracts the heatof vaporization of the lithium combusted. That is due to the assumption that thelithium reaction takes place in the vapor phase.

2.2.7 Lithium Combustion

The temperature rates of change in the containment can differ greatly dependingwhether or not the lithium pool is actually combusting (reacting with the containmentatmosphere). The criteria used to determine whether or not the lithium is combustingare:

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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 than11270C

If none of the above conditions are met, then the combustion zone is consideredto be nonexistent, and heat transfer from the lithium to the rest of the containmentbuilding is performed normally. If combustion is occurring, then the combustion rateand the heat liberated by the lithium reactions is calculated.

In LITFIRE the lithium combustion rate is governed by the flow rate of gas or (iflithium-lead is being burned) the diffusion of lithium to the combustion zone. Thegas flow rate is determined by natural convection using Reynold's analogy betweenheat and mass transfer.

Once the gas flow rate to the combustion zone has been calculated, the lithiumreaction rate may be calculated. The lithium is assumed to react with the gas quicklyas it flows to the combustion zone, unless the chemical kinetics serves to further limitthe reaction rate. The unhindered lithium reaction rate is given by:

RRu = Apoo RR; (8)

whereRR, = hmpiR., (9)

where Apool = surface area of the lithium pool

hm = natural convection mass transfer coefficientp; = total density of the gas i (mass/containment volume)R1, = 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 thereaction site. After the gas flow rates of each of the constituent gases of the atmo-sphere have been determined, reaction kinetics effects are applied to the preliminaryreaction rates to determine their final values. Lithium reaction kinetics are coveredin detail in reference[2].

Once the reaction rates have been calculated, the heat generated by combustionis calculated by summing the products of the reaction rates RR; and the heats ofcombustion AH; of each of the reacting gases:

Q= RR.AHi (10)

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2.2.8 Overpressure, Leakage, and Aerosol Behavior

The masses of each cell gas component and the cell gas temperature are integratedin the integration section. From this, the cell gas pressure is determined and thusleakage from containment can be calculated. Aerosol adhesion to the containmentwalls is a user specified option and changes the concentration of aerosol combustionproducts in the containment atmosphere.

2.2.9 Integrals

All time rates of change are integrated over each time step to calculate the values ofthe 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 isthe time dependent rate of change of P.

INTGRL is an integration function that uses a fourth order Runge-Kutta Methodor Simpson's Rule (user specified) to simultaneously solve all of the differential equa-tions 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 over-pressurization

" 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 dynamiccycle. They are:

1. The time step must be smaller than a user defined fraction of the inverse ratesof change:

DELT < RELERR T/ (-)

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2. The conduction heat transfer limit must be satisfied:

aLatat< 0.3(AX)2

3. The user imposed maximum and minimum time steps must be observed. Themaximum 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. Examplesof the output files are shown in Appendix E, generated by the input files found inAppendix D.

2.2.13 Error Pointers

This section is not actually part of the dynamic cycle, although if an error duringexecution should occur, an error message would be written into file outl.dat and codeexecution would halt.

2.3 Modeling Options

The basic version of LITFIRE is capable of simulating a wide variety of spill conditionsas 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 asthe mass and surface area of the lithium spilled. Optional reaction geometries includea primary cell containing the lithium, surrounded by a larger secondary cell; a partiallyinsulated pan holding the lithium inside the basic primary cell; or a primary cellsurrounded by blanket and shield structures producing decay heat, further surroundedby a larger secondary cell. A concrete floor and wall for the containment are optionalas is a liquid metal-concrete reaction routine. Also instead of elemental lithium, alithium-lead eutectic may be selected for the spill with the composition chosen by theuser. Finally an option to simulate a lithium or lithium-lead spill in the presence ofa steam-air atmosphere may be chosen.

In addition to the above options, several options involving the mitigation of lithiumfires are available. These include:

" gas flooding

" emergency space cooling

" emergency floor liner cooling

" aerosol removal

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* 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 otheroptions 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 upto twenty concrete wall or floor nodes of any thickness. As stated earlier all materialproperties may be chosen by the user as may the composition of the containmentatmosphere. Lithium or lithium-lead may react with any mixture of oxygen, nitrogenor water vapor and lithium only may react with carbon dioxide in the absence ofoxygen. Any inert gas may also be included in the cell atmosphere. Lastly, anycontainment or spill geometry may be chosen as stated above.

The heat transfer correlations are fixed by the code so that accurate results maybe obtained, although some modification is possible from the input data as shown inSection 2.2.4. The heat transfer pathways are also fixed by the code and are shownin Figure 1. The heat transfer mechanisms and their applications to the code arefurther 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 fusionreactor and to determine its effects on the structural integrity of the the torus. Inthis option a separate secondary cell with its own material composition, atmosphereand geometry exists surrounding the primary cell. (See Figure 1) The provision fora crack between the primary and secondary cells, allowing the exchange of cell gasesalso exists. The code follows the composition, pressure and temperature of both cellgases during the run. The heat and mass flow paths in two cell LITFIRE are shownin Figures 2 and 3. High velocity gas flows, as would be encountered in the eventof a breach in a vacuum torus have been successfully modeled by LITFIRE. (Seereference[3])

2.3.3 Pan Option

Figure 4 shows the pan option available in LITFIRE. This option may be used witheither the one or two cell option, but not with the concrete reaction option. Thisoption was created to model the lithium fire experiments performed at HEDL. Thepan dimensions and composition are user defined. The pan is surrounded by twoseparate insulation nodes.

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Wall Liner

Ambient Cell Gas

Combustion Zone-

iAhUM JPool

Conret WYl lor LinerCConcrete FWalr

Concete loor- Conductive Heat Transfer

-- Convective Hent Transfer----- Radiative Heat Transfer

Figure 1: One-cell option in LITFIRE

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H

Ambient

Concrete Wall

Secondary Cell Gas

Primary Wall

Primary Cell GasCrack.

SS

SS

SS

SS

I rimary Floor

Combustion Zone

Secondary Wall Liner

__ N

Concrete Floor

Secondary Floor Liner

- Conductive Heat Transfer

- Convective Heat Transfer

--- 0.Radiative Heat Transfer

Figure 2: Two-cell option in LITFIRE

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Inert GasStorage

InertGasFlooding

H2 ,OsN Cjand innt gases viaconvection anddiffusion

Solid ReactionProducts (LiN,Li20, Li 2C2,Li2CO3, an C)

rge AmbientCG2

InjectionGass mGame andAeosols vialeakage

Cell GasConsti-blents

via Crack

Combustionzone

UithiumPool

AmolRemovol viasticking to WaI

PrimaryWal

Reaction Products (LiOH,Li3N, LiW, H2. Li2CO)

UWhimn via vqpri" anddiffusion

Figure 3: Mass flow in LITFIRE

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PrimaryCell Gas

SecondaryCell Gas

Gas StN2, 02,

Ambient

N1

Concrete Wall

] II

Combustion Z

Steel Pan

PanInsulation

Cell Gas Wall Liner

s...

)L P'

Lithium Pool

I

a

Floor Liner

Concrete Floor- Conductive Heat Transfer

- Convective Heat Transfer

Radiative Heat Transfer

Figure 4: Pan option in LITFIRE

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2.3.4 Concrete Reaction

The liquid metal-concrete reaction subroutine allows for the reaction of lithium withthe concrete floor under the liner. This includes lithium reactions with water drivenfrom the concrete and certain components of the concrete itself. For further discus-sion, see reference[2].

2.3.5 Lithium-Lead Combustion

This option allows for the substitution of a lithium-lead eutetic in the place of ele-mental lithium as the source of the fire. All LITFIRE options are compatible withthe lithium-lead combustion option except for the initial spray fire calculation. Inaddition, this option allows the user to choose either a layered or turbulent pool re-action, allowing for optimistic or pessimistic results respectively, depending on theuser's view of lithium-lead fires. Reference[2] discusses the lithium-lead option ingreater detail.

2.3.6 Steam-Air Atmosphere Option

The steam-air atmosphere option allows for the reaction of lithium or lithium-leadwith a mixture of steam and other non-condensible gases. It also includes modifica-tions of the convective heat transfer coefficients to account for condensation and theprovision 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 inSection 2.2.3) to account for the presence of the condensible vapor, rather than in theusual integral method described earlier. The steam in the atmosphere may be presentas humidity or may be injected into the primary or secondary cell atmosphere, withthe time, mass flow rate and enthalpy of the steam injected selected by the user. Thedevelopment 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 plasmachamber of a tokamak during a loss of flow or loss of coolant accident. The reactorblanket and shield structures are represented by six extra nodes surrounding theprimary cell, shown in Figure 5. During a loss of flow accident the nodes are thermallyconnected via conduction. During a loss of coolant accident some of them are alsoconnected via radiation as shown in the figure. The emissivities of, and the viewfactors between the nodes are user specified. The radioactive decay heat generatedin the first wall (primary wall and floor) and the blanket and shield structures isincluded as an extra heat generation term for each node:

dT- q__ (12)dt ,.picpi

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where: i = individual noder = each individual isotope in the node i<L" = initial decay heat density of an isotope rA = decay constant of an isotope rpi = density of node i

Up to three different isotopes may be modeled in each node; the initial decay heatdensity and the decay coefficient are specified by the input data for each isotope. Inthe coding of the torus fire option, the breeder region of the blanket (see Figure 5) isrepresented by the node, in the two-cell option, that normally represents the secondaryextraneous heat capacity. In the torus fire option, the extraneous heat capacity in theouter cell is represented by the magnets node. The torus fire option is incompatiblewith 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 certaintechniques 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 de-sired. These options are discussed further in reference[4].

3 Execution of LITFIRE

The execution of the LITFIRE code requires certain system commands dependingupon 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 followingorder:

1. Obtaining the source code and sample input files

2. Execution on the PFCVAX

3. Execution on the MFE Crays

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to Sec

to Secondary Cell Floor- Convective Heat Transfer

Radiative Heat Transfer

Except across the vacuumgap, all adjacent nodes areconnected via thermalconduction.

Figure 5: Torus fire option in LITFIRE

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to Secondary Cell Wall

ondary Cell Gas Crack

Plasma First.... Chamber Wall-

First Wall

Breeder

Manifold

Shield

Vacuum Gap Blanket Back WallNN

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 canbe found: the PFCVAX at MIT, and the MFE FILEM disk storage.

To use the PFCVAX copy, the user must first obtain a PFCVAX account. Thismay be done by contacting the Plasma Fusion Center at MIT. Introductory informa-tion may be found on the VAX by using the HELP command, which will define mostof 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.datuwmak.wutumak.xutwmak.yuwmak.zsteamop.torus.

After obtaining copies of the input files, they may be viewed by using the type com-mand 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 apersonal 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 maybe moved to a different machine 'n' by using the netout command as follows:

netout flename site=nma

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3.2 Organization of LITFIRE for Execution

One of the most important steps in the execution of LITFIRE is the preparation ofthe input data files. Most errors in code execution occur due to mistakes in the inputdata files. The input data files and the options they control are listed below. Asstated in Section 2.3, some options are incompatible with each other.

uwmak.w: one celluwmak.x: two celluwmak.y: pan, concrete reaction and lithium lead combustionuwmak.z: gas flooding, emergency space cooling, emergency floor liner

cooling, aerosol removal and gas injectionsteamop.: steam injection with steam-air atmospheretorus.: torus fire

3.2.1 One Cell Option

The one cell option is the simplest version of LITFIRE. The first input file must existto run any other code options. The order in which the input variables must appearin the file uwmak.w is shown below (British units are given in the Glossary, SI unitsmay be used for all input data files by setting the input variable IFLAGISI = 1):

22

line variables1 IFLAGW,IFLAGF,IFLAGP,IFLAG2,IFLAGS,IFLAGC,

IFLAGU,IFLAGB,IBLOW,IESC,ISFLC,ISWICH,IAROSL,IFLAGD,IFLAGISI,IFLAGCO,IFLAGTIFLAGR

2 NL,NL13 L(1) to L(NL)4 L1(1) to L1(NL1)5 VP,CHP,CPAP,XMOLA6 TEHCZP,XMEHCPAEHCPCPEHCP,HINECP7 THWC,THFC,GAP,KGAP,KLEAK8 ESTLWP,CPSWP,KSTLWP,RHSWPAWP,THWP9 ESTLFP,CPSFP,KSTLFP,RHSFP,AFPTHFP10 EMLI,CPLI,AKLI,RHLI11 EMCONC,CPCON,KCON,RHCON12 RHOLIO,RHOLIN,RHOLIH,EMGPF,EMCZ,TAUCZ13 QCO1,QCO2,QCN,QCW,QCW214 RCMB01,RCMBO2,RCMBN,RCMBW,RCMBW2,RCMBH215 TMELT,TVAP,QVAPPERCEN16 CONF1,CONF2,C2FAC,FLIOH,FLI2017 HIN,HINGSPHINGSS,HINPS,HINSAM,HINFAN18 HINFGS,HINFSG19 ASLI,SPILL,SPRAY,FRA,RA20 TCZI,TGPZER,TSPZER,TSFPI,TA,TLII21 PAPZER,WO2P,HUM,WAPWCP22 IMETH,DTMIN,TIMEF,RELERR,DELOUT,OUTPUT

The formats for the input lines are:

line format1 (1x,14(il,1x))2 (i4,i4)3,4 (10f5.3)5 (f12.2,3f12.4)6-21 (6f12.4)22 (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 fileis 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 locatedafter 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 forthe second data file (units are given in the glossary as for the first input file):

line variables1 VS,CHS,PASZER,TGSZER,TSSZER,TFSZER2 CRACK,HUM2,WO2S,WAS,CPAS,WCO2S3 TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS4 ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS5 ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS6 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 firstinput 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 inputdata 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 aregiven in the Glossary):

Pan Optionline variables1 KPAN, RHPAN,CPPAN,RHINS,CPINS,EMINS2 TPANZO,APAN,BREDTH,AINS,HINGPF3 THKPAN,THKIN1,THKIN2

Concrete Reaction Optiontline variables1 ZZDIN,QCCONC,CRACON,XMH2OI,TCIGNI,RCMBC

Lithium-Lead Optiontline variables4(1) CPLEAD,KLEAD,RHLEAD,ALLOYI,QDISS,CPLIPB5(2) DFLVAR

t: 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)


open(unit=4,fle= 'len. ame ',statu='old')

must be used. An example of this file (British units) is given in Appendix D.


call link("unit4=flename,read4//")


25

3.2.4 Gas Flooding, Emergency Space Cooling, Emergency Floor LinerCooling and Gas Injection

Each of these options is included in one input data file. The following is a variablelisting for each of the options. Only the variable lines of the options used need beentered, although the lines used must be in the order shown below (British units aregiven in the Glossary):

line1 (gas flooding)23 (emerg. space cooling)4 (emerg. floor cooling)5 (aerosol removal)6 (gas injection)

The format for lines 1-5 is:(3f10.2,6f8.4).

variablesWO2B,WWAB,WN2B,XMOLAB,CPAB,TBLOWBLOWV,EXHSTV,TBLIN,TBLOUT,WABESCR,ESCTIN,ESCENDSFLCR,SFLTIN,SFLENDBETATONE,TTWO,TTHREE,DP1,DP2,DP3,FCT1,FCT2,FCT3

(6f12.4). For the gas injection option (line 6) it is:


open(unit=5,file='filen.ame',status='old')





3.2.5 Steam Injection to Containment

The following is a variable listing for the steam injection to containment available inthe steam-air atmosphere option (British units are given in the Glossary):

line variables1 STMIN,STMOUT,MINJR,HINJ2 STMIN2,STOUT2,MINJR2,HINJ2

The format for all lines is: (6f12.4)

26


open (unit=6,file=' ilen. ame',status='old')





3.2.6 Torus Fire

The following are the variable listing and the formats for the torus fire option. (Britishunits are given in the Glossary).

line variables1 VS,CHS,PASZER,TGSZER,TSSZER,TFSZER2 CRACK,HUM2,WO2S,WAS,CPAS,WCO2S .3 TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS,KEHCS4 ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS5 ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS6 CLEHCS,EEHCS,EBLI,EFWI,VIEWM7 TSHLZ,THSHL,KSHL,XMSHL,CPSHL,ASHL8 ESHL,HINSHL,TMAGZ,AMAG,XMMAG,CPMAG9 HINMAG,KHE,THE,LOCA,VIEWG,VIEWB10 KBLI,THBLI,CPBLI,ABLI,XMBLI,TBLIO11 TSHIO,TSHOO,THSHI,THSHO,XMSHI,XMSHO12 THMAN,XMMAN,CPMAN,AMAN,TMANO,KMAN13 QOFW1,EXPFW1,QOFW2,EXPFW2,QOFW3,EXPFW314 QOBL1,EXPBL1,QOBL2,EXPBL2,QOBL3,EXPBL315 QOBL4,EXPBL4,QOBL5,EXPBL5,QOBL6,EXPBL616 QOBLI1,EXPBI1,QOBLI2,EXPBI2,QOBLI3,EXPBI317 QOSH1,EXPSH1,QOSH2,EXPSH2,QOSH3,EXPSH318 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 firstinput data file.


call link("unit7=fiename,read7//")


3.3 PFCVAX Execution

To execute LITFIRE on the PFCVAX, the user must ensure that all necessary OPENstatements are included for the data files necessary to run the code as indicated inSection 3.2. The input data file head.dat must always be included as it providesheadings for the output data files that LITFIRE will create. The statement necessaryto 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 LITFIREin order to execute the code.

OPEN statements are also needed for the output files created by LITFIRE. Thesestatements are placed right after the OPEN statements for the input data files andtake the form of:

open (unit=1 Ofile='outl.dat',status= 'new')

There are ten output data files named outl.dat through outlO.dat, and an OPENstatement is needed for each one.

Optional output files may be created to allow graphs to be made of code variablesvs. time. These files may be used in conjunction with the graphics routines availableon the PFCVAX to create the actual graphs. The optional files require OPEN state-ments 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 outputsection to write values of TIME and the variable desired to the file. Some optionaloutput file OPEN and WRITE statements which have been commented out may befound in the appropriate sections of the code. The output files created may be usedwith 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 rununtil terminated by a user defined time limit (i.e., TIME=TIMEF) or by the codeitself. (e.g., 'the temperature of the lithium pool has reached the melting point'). Ifthe code stops due to an error, an error message will be given. Refer to AppendixC-Troubleshooting.

3.4 MFE Crays Execution

To execute LITFIRE on the Crays, the necessary CALL LINK statements must bepresent for all of the input data files as indicated in Section 3.2 The input data filehead. dat must be included to provide headings for the output data files that LITFIREwill 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 statementstake the form of:

call link("unitl0=(outi, text, create),printl//")

for each of the ten output files outi through out10. They should be placed directlyafter the CALL LINK statements for the input data files.

To compile, load and run LITFIRE on the Crays, the following commands shouldbe used:

rcftti=itfire,x=xlitfire / t pxitfre / 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 steamoption is being used, in which case up to five minutes may be required (and thepriority would be 10).

t: on the b machine, civic should be used instead of rcft.

29

3.5 Sample Input and Output Files

To check whether LITFIRE has been properly executed, a set of sample input andoutput files are given in Appendices D and E. Execution of the code using the sampleinput files on the PFCVAX or the Crays will produce approximately the same resultsas 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.datout9.dat, outlO.dat, blank

It should be noted that only the input files head.dat, uwmak.w and uwmak.x wereused for the examples in the Appendices.

30

I

A NomenclatureA heat transfer surface areasC user defined heat transfer correlation constant

C, specific heatc', specific heat at constant volume

f radiative interchange factor, including emissivityAH heat of combustionh convective heat transfer coefficienth. convective mass transfer coefficientk, ki thermal conductivityL, l;, characteristic lengthMm mass

q'" decay heat densityQ, dq/dt heat flow rateR;,j thermal resistanceRR reaction ratet timeT temperatureU specific internal energy

U, total internal energyx linear distancea thermal diffusivity

0 coefficient of volumetric expansionp densitya Stefan-Boltzmann constant

31

B Variable Listing

32

AA Exponent used in expression for GRPR or GRPRFABLI Cross sectional area of the blanket back wall (ft2 )ACTVTY Calculates activity of lithium in lithium-lead eutecticAEHCP Surface area of primary extraneous heat capacity (ft2)AEHCS Surface area of secondary extraneous heat capacity (cross sectional

area of breeder with torus fire option) (ft2 )AFP 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 (ft2 )AHT Area of the lithium pool-pan interface (ft2)AINS Outside exposed area of insulating layer on the pan (ft2 )AIRFAC Density weighting factor for calculating steam-air mixture propertiesAK Product of thermal conductivity and Prandtl number of the primary

gas (BTU/sec-ft deg. F.) See associated film temperature T1.AKEXX Function used to calculate heat transfer coefficientsAKLEAD Thermal conductivity of lead (input as BTU/hr-ft deg. F.)AKLI Thermal conductivity of lithium (input as BTU/hr-ft deg. F.)AKLIX Thermal conductivity of lithium used during LC-2 lithium transfer

simulation (BTU/sec-ft-deg. F.)AKVAP Product of thermal conductivity and Prandtl number of water vapor at

the lithium pool surface (BTU/sec-ft deg. F.)ALLOYI Initial atom percent of lithium in lithium-leadALPHA Used to determine whether or not LILP should be fixed at an amount

equal to AKLI/(RHLI*CPLI)ALPHA2 Used in determining PYU. Also tests conduction limit on time step for

the pan or floor liner.AMAG Surface area of the magnets (secondary extraneous heat capacity) (ft2)AMAN Cross sectional area of the blanket manifold (ft2 )AMIN1 FORTRAN function that determines the minimum of the arguments usedAPAN Pan external heat transfer area (ft 2)ASHL Outer surface area of the reactor shield (ft2 )ASLI Surface area of the lithium spilled (ft2)ASURF Surface area of the liquid water pool (ft2)AWP Surface area of the primary wall liner (ft2 )AWS Surface area of the secondary wall liner (ft2)B Used in calculating the thermal resistance between the wall liner, the gap

and the wall concreteBB Analogous to B, but for the floor liner, gap and concreteB1 Coefficient of volumetric expansion for gas (0)

(1/deg. F.) See associated film temperature T1

BETABETABBETAFBIL

BILGE

BLINBLOUTBLOWRBLOWVBREAKS

BREDTHCxxx

C1C2C3C4(i)0506C7C8C9C10(i)C11C12013C14C15C16C17018C19C20C21C22C23C2FACCA'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 minimumtime stepEqual to the minimum value of DT1,DT2,DT3,DT4 or DT5, used incalculating 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 betweencells and leakage. (deg. R./sec)Perimeter of the pan (ft)'C' is used to indicate a thermal admittance between nodes (i.e., theinverse of the product of effective thermal resistance between thenodes and the heat capacity of one of them (hA/mc,) (sec-)Primary gas to primary wall liner in gasPan to primary gas in gasWall liner to concrete in concreteConcrete wall node i to node i+1 in concreteConcrete wall to ambient in concretePrimary gas to primary wall in wall linerWall liner to concrete in wall linerFloor liner to concrete floor in floor linerFloor liner to concrete floor in concreteConcrete floor node i to node i+1 in concreteWall liner to ambient (no concrete option) in wall linerFloor liner to ambient (no concrete option) in floor linerPan to primary gas in panSecondary floor liner to secondary gas in floor linerSecondary floor liner to secondary gas in gasPrimary floor liner to primary gas in floor linerPrimary floor liner to primary gas in gasPrimary floor liner to secondary gas in floor linerPrimary floor liner to secondary gas in gasPrimary wall liner to secondary gas in wall linerSecondary wall liner to secondary gas in wall linerPrimary wall liner to secondary gas in gasSecondary wall liner to secondary gas in gasFraction of Li-CO 2 reaction which produces Li 2C2Coefficient in expression for GRPR or GRPRFBlanket back wall to manifold in manifold

33

'C'BLMANCCZ'C'CZPCD'C'EHCGP'C'EHCGS'C'EHCSH'C'EHCFP'C'EHCWP'C'FPEHC'C'GCZ'C'GLI'C'GPEHC'C'GSEHC'C'GSMAG'C'GSSHLCHPCHS'C'IN1PN'C'IN12'C'IN21CLEHCS'C'LIG'C'LIPAN'C'LIST'C'MAGGS'C'MANBI'C'MANBLCMBRCMBRC2CMBRCO

CMBRHCMBRHHCMBRHICMBRNCMBRNHCMBROCMBRO1CMBRO2

CMBROHCMBRW

Breeder to manifold in manifoldHeat generation rate in the combustion zone (BTU/sec)Lithium pool to combustion zone in poolCoefficient of discharge between the two cells (nea.r unity)Primary extraneous heat capacity to primary gas in gasSecondary extraneous heat capacity to secondary gas in gasBlanket back wall to shield inside region in shield inside regionFirst wall (floor) to breeder in first wall (floor)First wall to breeder in first wallFirst wall (floor) to breeder in breederCombustion zone to primary gas in combustion zoneLithium Pool to primary gas (no combustion) in poolPrimary gas to primary extraneous heat capacity in heat capacitySecondary gas to secondary extraneous heat capacity in heat capacitySecondary gas to magnets in magnetsShield outside region to secondary gas in shield outside regionPrimary cell optical path length (ft)Secondary cell optical path length (ft)Pan to inner insulation in insulationInner pan insulation to outer pan insulation in inner insulationInner pan insulation to outer pan insulation in outer insulationThickness of the breeder node (ft)Lithium pool to primary gas (no combustion) in gasLithium pool to pan in pool (suspended pan option)Lithium pool to primary floor liner in poolMagnets to secondary gas in secondary gasManifold to blanket back wall in blanket back wallManifold to breeder in breederTotal 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-ft2 )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

CMBRWHCMRC2HCMRCOHC02CO2LFSCONDRCONF1CONF2CPxxxCPACPA2CPAB'C'PANLICPAPCPASCPBCPBLICPCARPCPCO2PCPCO2SCPCON'C'PCZCPEHCPCPEHCS

CPFACCPH2CPINSCPLC2PCPLC3PCPLC3SCPLEADCPLICPLIX

CPLIHCPLINCPLINPCPLINSCPLIOCPLIOHCPLIOP

Combustion rate for the water vapor reaction producing Li20(lb Li/sec-ft 2 )CMBRW in g Li/min-cm2

CMBRC2 in g Li/min-cm2

CMBRO2 in g Li/min-cm 2

A subroutine which sets up the pure CO2 atmosphereCarbon dioxide left after spray fire (lb)Condensation mass flow rate (lb/sec)Fraction of Li-CO 2 reaction which produces Li 20Fraction of Li-CO 2 reaction which produces Li 2CO3

Gaseous specific heats are all specific heats at constant volumePrimary 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 panSpecific 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 zoneSpecific heat of primary extraneous heat capacity (BTU/lb deg. F.)Specific heat of secondary extraneous heat capacity (breeder withtorus 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 Li2 CO3 in the primary gas (BTU/lb deg. F.)Specific heat of Li2 CO3 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 transfersimulation (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 Specific heat of lithium oxide in secondary (BTU/Lb deg. F.)CPLIPB Specific heat of lithium-lead (BTU/lb deg. F.)CPLV Specific heat of water for secondary floor liner-secondary water pool

heat transfer (at TAVE) (BTU/deg. F.)CPMAG Specific heat of the magnets (secondary extraneous heat capacity)

(BTU/lb deg. F.)CPMAN Specific heat of the manifold (BTU/lb deg. F.)CPMCOP Heat capacity of carbon dioxide in primary (BTU/deg. F.)CPMCOS Heat capacity of carbon dioxide in secondary (BTU/deg. F.)CPMCZ Effective heat capacity of combustion zone (BTU/deg. F.)CPMH2 Heat capacity of hydrogen in containment (BTU/deg. F.)CPMLCP Heat capacity of lithium carbonate in primary (BTU/deg. F.)CPMLCS Heat capacity of lithium carbonate in secondary (BTU/deg. F.)CPMLOP Heat capacity of lithium oxide in primary (BTU/deg. F.)CPMLOS Heat capacity of lithium oxide in secondary (BTU/deg. F.)CPMNIP Heat capacity of nitrogen in primary (BTU/deg. F.)CPMNIS Heat capacity of nitrogen in secondary (BTU/deg. F.)CPMOXP Heat capacity of oxygen in primary (BTU/deg. F.)CPMOXS Heat capacity of oxygen in secondary (BTU/deg. F.)'C'PNIN1 Pan to inner insulation in panCPN2P Specific heat of nitrogen gas in primary (BTU/lb deg. F.)CPN2S Specific heat of nitrogen gas in secondary (BTU/lb deg. F.)CPSFP Specific heat of primary floor liner (BTU/lb deg. F.)CPSFS Specific heat of secondary floor liner (BTU/lb deg. F.)CPSHL Specific heat of the reactor shield (BTU/lb deg. F.)CPSWP Specific heat of primary wall liner (BTU/lb deg. F.)CPSWS Specific heat of secondary wall liner (BTU/lb deg. F.)CPWV Specific heat of water vapor in primary (BTU/lb deg. F.)CRACON Area of concrete exposed to lithium in concrete combustion model (ft2)CRACK Area of the orifice between the two cells (square inches)'C'SBLI Lithium pool to primary floor liner in floor liner'C'SHEHC Blanket back wall to shield inside region in blanket back wall'C'SHISH Shield bulk to shield inside region in shield bulk'C'SHLGS Shield outside region to secondary gas in secondary gas'C'SHOSH Shield bulk to shield outside region in shield bulk'C'SHSHO Shield bulk to shield outside region in shield outside region'C'SHSHI Shield bulk to shield inside region in shield inside regionCSTM Steam catalytic factorCSTMA Steam catalytic factor in airCSTMN Steam catalytic factor in nitrogenDAB Diffusion coefficient for air and water (ft2 /sec)DCOCZ Depth of concrete combustion zone (ft)

used to calculate volume of zone for heat generationDECBL Total decay heat density in the breeder (BTU/ft3 sec)

36

37

DECBLI Total decay heat density in the blanket back wall (BTU/ft3 sec)DECFW Total decay heat density in the first wall (BTU/ft3 sec)DECMAN Total decay heat density in the manifold (BTU/ft3 sec)DECSH Total decay heat density in the shield bulk (BTU/ft3 sec)DECSHI Total decay heat density in the shield inside region (BTU/ft3 sec)DECSHO Total decay heat density in the shield outside region (BTU/ft3 sec)DELMP Fractional exchange rate of primary gas used in determining the

minimum time step (sec)DELMS Fractional exchange rate of secondary gas used in determining the

minimum time step (sec)DELOUT User defined maximum time step length (sec)DELT Time step length (sec)DFILM Lithium vapor film thickness (ft)DFLIPB Diffusion coefficient for lithium through lead (ft2/sec)DFLVAR Constant used to calculate DFLIPB (6.5E-08) (ft2/sec)DIFF Gas mass diffusion coefficient to the combustion zone (ft2/sec)DIFFLI Lithium diffusion coefficient to the combustion zone (ft2 /sec)DMPBDT Mass rate of change of lead in lead layer (lb/sec)DP1,..DP3 Increase in cell gas pressure due to each injection (psi)DTBDT(i) Concrete floor temperature rate of change, node i (deg. F./sec)DTCDT(i) Concrete wall temperature rate of change, node i (deg. F./sec)DTMIN User defined minimum time step length (sec)DT1..DT5 X/(dx/dt) * RELERR, used in determining the time step length (sec)DT1 X = Lithium pool temperatureDT2 X = Primary gas temperatureDT3 X = Primary wall liner temperatureDT4 X = Combustion rateDT5 X = Combustion zone temperature*.05DYNAMI Subroutine used in controlling integration loopsD1 Kinematic viscosity of the cell gas (squared) at the film temperature

(ft4 /sec 2 ), See related film temperature Ti.EBLI Thermal emissivity of the interior of the blanketEEHCS Thermal emissivity of the exterior of the blanket (facing the shield)EFWI Thermal emissivity of the interior of the first wallEFILM Film depth of depleted zone above combustion zone (in)EMCONC Thermal emissivity of concreteEMCZ Thermal emissivity of combustion zoneEMF Used in fixing minimum emissivity of the lithium pool (.9 in code)EMGP Thermal emissivity of primary gas (minimum of .005 in code)EMGPF Constant used in determining EMGP, usually chosen at .04EMGS Thermal emissivity of secondary gas (minimum of .005 in code)EMINS Thermal emissivity of pan insulation

(There is no page 38.)

38

EMLIESCRESCTINESHLESTAIRESTLFPESTLFSESTLWPESTLWSEW1EXHSTREXHSTVEXPBIn

EXPBLn

EXPBLn

EXPSHn

EXX

EXi

FCO2PFCO2SFCT1,FCT2FCT3FF1,FF2FLI20FLIOHFMLEAKFMLEFTFNIPFNISFOUTPFOUTSFOUTTFOXPFOXSFPGFPWFRA

Thermal emissivity of lithium poolHeat removal rate by emergency space cooling (BTU/sec)Time after spill when ESCR begins (sec)Thermal emissivity of the reactor shieldThermal emissivity of the cell steam-air mixture (without aerosols)Thermal emissivity of the primary floor linerThermal emissivity of the secondary floor linerThermal emissivity of the primary wall linerThermal emissivity of the secondary wall linerThermal emissivity of water vapor at one atmosphere and cell temperatureRate 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

(n=1-3) (sec- 1 )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 diffusioncoefficients (ft- 3 )Used in calculating mass and heat transfer coefficients(ft-') See related film temperature T1.Weight fraction of CO 2 in primary gasWeight fraction of CO 2 in secondary gasFraction of nitrogen in each injection (by number)

Used in heat balance equations for spray fireMass fraction of Li reacting with H2 0 that produces Li 2 0Mass fraction of Li reacting with H2 0 that produces LiOHFraction of mass of gas leaked out of primaryFraction of mass of gas remaining in containmentWeight fraction of nitrogen in primary gasWeight fraction of nitrogen in secondary gasLoss rate of primary gas which is either exhausted or changes cellsLoss rate of secondary gas which is either exhausted or changes cellsTotal loss rate from outermost gas tell (FOUTS+LEAK)Weight fraction of oxygen in primary gasWeight fraction of oxygen in secondary gasRadiative view factor from lithium pool to primary gas (1.0 w/o pan)Radiative view factor from lithium pool to primary wall linerFraction of combustion products evolved into cell gas

39

FWAP Weight fraction of water vapor in primary gasFWAS Weight fraction of water vapor in secondary gasGAP Air gap between floor liner and concrete (ft)GAMMA Ratio of specific heats c,/c, (set to 1.4 in the code)GIN Acceleration due to gravity (32.2 ft/sec2 )GRPR Product of the Grashof and Prandtl numbers of the water pool-gas boundaryGRPRF Product of the Grashof and Prandtl numbers of the water poolH2LEFT Current water content of concrete (lb/ft3 )HA Heat transfer coefficient between exterior wall and ambient (BTU/ft2 sec deg. F.)HAMF Heat transfer coefficient between exterior floor and ambient

(BTU/ft2 sec deg. F.)HB Heat transfer coefficient between lithium pool and primary gas

(BTU/ft2 sec deg. F.)HBINF Equilibrium value of HBHCOND Total heat transfer coefficient between the water pool and the cell

gas (BTU/ft2 sec deg. F.)HEHCP Heat transfer coefficient between primary extraneous heat capacity

and primary gas (BTU/ft2 sec deg. F.)HEHCS Heat transfer coefficient between secondary extraneous heat capacity

and secondary gas (BTU/ft2 sec deg. F.)HEVAP Heat flux to water pool from gas mixture due to evaporation ( BTU/sec-ft 2 )HF Mass transport coefficient to the lithium pool (ft/sec)HFG Latent heat of vaporization of water vapor in the primary gas (BTU/lb)HFG2 Latent heat of vaporization of water vapor in the secondary gas (BTU/lb)HFINF Equilibrium value of HF (BTU/ft2 sec deg. F.)HFPGP Heat transfer coefficient between primary floor liner and primary gas

(BTU/ft2 sec deg. F.)HFPGAS Heat transfer coefficient between primary floor liner and

secondary gas (BTU/ft 2 sec deg. F.)HFSGAS Heat transfer coefficient between secondary floor liner and

secondary gas (BTU/ft 2 sec deg. F.).HGWP Heat transfer coefficient between primary wall and gas (BTU/ft 2 sec deg. F.)HINxxx Heat transfer coefficients are determined by LITFIRE as indicated in

Section 2.2.4. The coefficients C are indicated in the code asHINxxx and are dimensionless

HINECP Correlation for HEHCPHINECS Correlation for HEHCSHINFAM Correlation for HAMFHINFGS Correlation for HFPGASHINFSG Correlation for HFSGASHINGPF Correlation for HFPGP

40

HINGSP Correlation for HGWPHINGSS Correlation for HSECHINJ Specific enthalpy of steam injected to primary cell (BTU/lb)HINJ2 Specific enthalpy of steam injected to secondary cell (BTU/lb)HINMAG Correlation for HMAGHINPS Correlation for HWPGASHINSAM Correlation for HAHINSHL Correlation for HSHLHLP Specific enthalpy of the primary liquid water pool (BTU/b)HLP2 Specific enthalpy of the secondary liquid water pool (BTU/lb)HLPFLR Heat transfer coefficient between the liquid water pool and the

secondary floor liner (BTU/ft2 sec deg. F.)HMAG Heat transfer coefficient between magnets and secondary gas

(BTU/ft 2 sec deg. F.)HPAN Heat transfer coefficient between the pan and primary gas

(BTU/ft 2 sec deg. F.)HPRIME Increased value of HSENS due to a large condensation/evaporation

rate (BTU/ft 2 sec deg. F.)HRATIO Molar fraction of hydrogen in the primary gasHRAT2 Molar fraction of hydrogen in the secondary gasHSAT Specific enthalpy of saturated liquid water at cell pressure (BTU/lb)HSEC Heat transfer coefficient between secondary floor liner and

secondary gas (BTU/ft 2 sec deg. F.)HSENS Sensible heat transfer coefficient from the water pool to the vapor

mixture (BTU/ft 2 sec deg. F.)HSHL Heat transfer coefficient between the shield outside region and

secondary gas (BTU/ft 2 sec deg. F.)HTCPGP Heat capacity of the primary gas (BTU/deg. F.)HTCPGS Heat capacity of the secondary gas (BTU/deg. F.)HU(x,y) Chart of Uchida heat transfer coefficients vs. MRHUCH Uchida heat transfer coefficient for condensing steam (BTU/ft 2 sec deg. F.)HUM Initial relative humidity of the primary cell (1.0=100%)HUM2 Initial relative humidity of the secondary cell (1.0=100%)HWPGAS Heat transfer coefficient between primary wall liner and

secondary gas (BTU/ft 2 sec deg. F.)HWV Specific enthalpy of water vapor in the primary gas (BTU/lb)HWV2 Specific enthalpy of water vapor in the secondary gas (BTU/lb)I General purpose DO loop counterIAM DO loop counter for wall and floor concrete node initializationIB DO loop counter for floor concrete iterationsINIT Initializing subroutine for integrationsINJEC1..3 Flags for gas injection. INJECn indicates the injection has occurred.

41

INTDSxINTGRLIPAGEIPASS

KAIRKAIRB

KAIRGKBKBLIKBNDRYKCONKEHCSKFILMKGAP

KH20KH2OB

KH2OGKHEKIN1KIN2KLEAK

KMANKPANKSHLKSTLFPKSTLFSKSTLWPKSTLWSKWATLLiLEAKLEAKOLIBPLIL

LILC2LILCA

42

Interpolation factor used in reading steam tablesArithmetic statement function for finding integralsNumber of lines of output between headingsUsed during integration routine to tell INTGRL to perform certainspecial functions during the first two executions of the sectionThermal conductivity of non-condensible gas (air) (BTU/sec ft deg. F.)Thermal conductivity of air at the water pool-gas boundary(BTU/sec ft deg. F.)Thermal conductivity of air in a cell gas (BTU/sec ft deg. F.)Water condensation mass transfer coefficient (lb mol/sec-ft 2)Thermal conductivity of the blanket back wall (BTU/hr ft deg. F.)Thermal conductivity of the water pool-gas boundary (BTU/sec ft deg. F.)Thermal conductivity of concrete (input as BTU/hr ft deg. F.)Thermal conductivity of the breeder node (BTU/hr ft deg. F.)Thermal conductivity of pool/combustion zone film (BTU/sec ft deg. F.)Thermal conductivity of the gap between the liner and concrete(BTU/hr ft deg. F.)Thermal conductivity of water vapor (BTU/sec ft deg. F.)Thermal conductivity of water vapor at the water pool-gas boundary(BTU/sec ft deg. F.)Thermal conductivity of water vapor in a cell gas (BTU/sec ft deg. F.)Thermal conductivity of the vacuum (He filled) gap (BTU/hr ft deg. F.)Thermal conductivity of inner insulation layer (BTU/hr ft deg. F.)Thermal conductivity of outer insulation layer (BTU/hr ft deg. F.)Leak rate constant from containment (sec- 1psi-0 5)Reference value: 2.588-10'Thermal conductivity of the manifold (BTU/hr ft deg. F.)Thermal conductivity of the pan (BTU/hr ft deg. F.)Thermal conductivity of the reactor shield (BTU/hr ft deg. F.)Thermal conductivity of the primary floor liner (BTU/hr ft deg. F.)Thermal conductivity of the secondary floor liner (BTU/hr ft deg. F.)Thermal conductivity of the primary wall liner (BTU/hr ft deg. F.)Thermal conductivity of the secondary wall liner (BTU/hr ft deg. F.)Thermal conductivity of liquid water (BTU/sec ft deg. F.)Thickness of a wall concrete node (ft)Thickness of a floor concrete node (ft)Gas leakage rate from outermost cell (sec 1 )Initial gas leakage rate from outermost cell (sec- 1)Lithium consumed in pool fire (lb)Amount of lithium remaining in pool-limited to LIT/10 for numericalstability during calculationsAmount of Li2C 2 in the pool (lb)Amount of Li2CO3 in the pool (lb)

LILCARLILNILILOXLILPLISLITLOCAMAIPMAISMAIRPMAIRSMAPMASMBOILMCO2IPMCO2ISMCO2PMCO2SMCONDEMCONDFMCONDPMCONDWMCONFP

MCONWP

MFABMFAGMFVBMFVGMGBMH2PMH2SMINJRMINJR2MLC2PMLC2SMLC3IPMLC3ISMLC3PMLC3SMLEADMLIHPMLIHS

Amount of carbon in the pool (lb)Amount of Li3 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 linerfrom the secondary gas (lb/sec)Condensation rate of water on the primary wall linerfrom the secondary gas (lb/sec)Molar fraction of air at the water pool-gas boundaryMolar fraction of air in the cell gasMolar fraction of water vapor at the water pool-gas boundaryMolar fraction of water vapor in the cell gasMolecular weight of the mixture at the water pool-gas boundaryMass 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 Initial mass of lithium-nitride in the primary gas (lb)MLINIS Initial mass of lithium-nitride in the secondary gas (lb)MLINP Mass of lithium-nitride in the primary gas (lb)MLINS Mass of lithium-nitride in the secondary gas (lb)MLIOH Mass of LiOH produced (moles)MLIOIP Initial mass of lithium-oxide in primary gas (lb)MLIOIS Initial mass of lithium-oxide in secondary gas (lb)MLIOP Mass of lithium-oxide in primary gas (lb)MLIOS Mass of lithium-oxide in secondary gas (lb)MNIINJ Rate of nitrogen injection during a one minute interval (lb/sec)MNIIP Initial mass of nitrogen in the primary gas (lb)MNIIS Initial mass of nitrogen in the secondary gas (lb)MNIP Mass of nitrogen in the primary gas (lb)MNIS Mass of nitrogen in the secondary gas (lb)MNINJ1..3 Mass of nitrogen injected in gas injection (lb)MOINJ1..3 Mass of oxygen injected in gas injection (lb)MOXINJ Rate of oxygen injection during a one minute interval (lb/sec)MOXIP Initial mass of oxygen in the primary gas (lb)MOXIS Initial mass of oxygen in the secondary gas (lb)MOXP Mass of oxygen in the primary gas (lb)MOXS Mass of oxygen in the secondary gas (lb)MR Mass ratio of air to water vapor in the cell gasMUAIR Viscosity of air in the cell gas (lb/sec-ft)MUAIRB Viscosity of air at the water pool-gas boundary (lb/sec-ft)MUAIRG Viscosity of air in the cell gas (lb/sec-ft)MUB Viscosity of the mixture at the water pool-gas boundary (lb/sec-ft)MUDIFF Viscosity of the mixture at the lithium pool surface (lb/sec-ft)MUV Viscosity of water vapor in the cell gas (lb/sec-ft)MUVB Viscosity of water vapor at the water pool-gas boundary (lb/sec-ft)MUVCZ Viscosity of water vapor at the lithium pool surface (lb/sec-ft)MWL Mass of liquid water in the primary water pool (lb)MWL2 Mass of liquid water in the secondary water pool (lb)MWLV Mass of liquid water in the primary gas (lb)MWLV2 Mass of liquid water in the secondary gas (lb)MWLZ Time rate of change of the mass of liquid water in the primary water

pool (lb/sec)MWLZ2 Time rate of change of the mass of liquid water in the secondary water

pool (lb/sec)MWV Total mass of water in the primary gas (lb)MWV2 Total mass of water in the secondary gas (lb)MWVV Mass of water vapor in the primary gas (lb)MWVV2 Mass of water vapor in the secondary gas (lb)

44

MWVZ Time rate of change of the total mass of water in the primary gas (lb/sec)MWVZ2 Time rate of change of the total mass of water in the secondary gas (lb/sec)N Index used to transfer to section of subroutines, and as a DO loop counterNAME(i) Input variable containing program name and output headingsNL Number of concrete wall nodesNL1 Number of concrete floor nodesNLM1 Number of concrete wall nodes minus oneNL1M1 Number of concrete floor nodes minus oneNS Index used to control transfer to sections of the steam-air subroutinesNULV Kinematic viscosity of water at the secondary floor liner (ft2/sec)OFAC Oxygen inhibition factor (lithium-steam reaction)OUTINT Fraction of the outermost cell gas leaked to ambientOVERPP Primary cell overpressure (psig)OVERPS Secondary cell overpressure (psig)OXLB Mass of oxygen consumed in the fire (lb)OXLBI Mass of oxygen consumed in the spray fire (lb)OXLFS Mass of oxygen remaining after the spray fire (lb)PAP Primary gas pressure (psia)PAPZER Initial primary gas pressure (psia)PAS Secondary gas pressure (psia)PASZER Initial secondary gas pressure (psia)PERCEN Molecular percentage of lithium-peroxide (vs. monoxide) formed

during combustionPH20 Partial pressure of water vapor in the primary gas (psia)PH202 Partial pressure of water vapor in the secondary gas (psia)PH20B Partial pressure of water vapor at the primary water pool-gas

boundary (psia)PH20B2 Partial pressure of water vapor at the secondary water pool-gas

boundary (psia)PHASE =1 if primary cell is saturated, =2 if superheatedPHASE2 =1 if secondary cell is saturated, =2 if superheatedPHIA Baroczy two-phase flow correction factor at the lithium pool surfacePHIW Baroczy two-phase flow correction factor at the lithium pool surfacePHIAWB Baroczy two-phase flow correction factor at the water pool surfacePHIWAB Baroczy two-phase flow correction factor at the water pool surfacePLIV Partial pressure of lithium vapor (psia)PRSC Prandtl number divided by the Schmidt numberPSAT Saturation pressure of water at the primary gas temperature (psia)PSAT2 Saturation pressure of water at the secondary gas temperature (psia)PYU Used in setting the time step length calculated from the heat conduction

rate to the pan or primary floor liner from the lithium poolPZEROP Primary gas pressure after the spray fire (psia)QCxxx Heat of combustion (BTU/lb Li)

45

(There is no page 46.)

46

QCC Li-CO 2 producing lithium carbonate reactionQCCONC Concrete reactionQCN Nitrogen reactionQCO Oxygen reactionQCO1 Monoxide reactionQCO2 Peroxide reactionQCW Water vapor reaction producing LiOHQCW2 Water vapor reaction producing Li20QDISS Heat of dissociation of LiPb (BTU/lb)QIN Heat addition to primary gas from spray fire (BTU)QL2C2 Heat of combustion for the carbon reaction (BTU/lb Li)QLFLR Heat flux from the secondary water pool to the secondary floor liner

(BTU/ft 2)QLIOH Heat of fusion of LiOH (BTU/lb mol)QOFWn Volumetric decay heat generation rate in the first wall for an isotope

(n=1-3) (BTU/sec ft3 )QOBLn Volumetric decay heat generation rate in the breeder for an isotope

(n=1-3) (BTU/sec ft')QOBLn Volumetric decay heat generation rate in the manifold for an isotope

(n=4-6) (BTU/sec ft')QOBLIn Volumetric decay heat generation rate in the blanket back wall for a

(n=1-3) (BTU/sec ft')QOSHn Volumetric decay heat generation rate in the shield bulk for an isoto

(n=1-3) (BTU/sec ft')QOSHIn Volumetric decay heat generation rate in the inside of the shield for

n isotope

an isotope (n=1-3) (BTU/sec ft')QOSHOn Volumetric decay heat generation rate in the outside of the shield for

an isotope (n=1-3) (BTU/sec ft')QOUT1..5 Used in heat balance equations for the spray fire (BTU)

QQQ Used as a counter in the lithium transfer simulationQRADxx Indicates a radiative heat flow (BTU/sec)QRADB Floor liner (or pan) to ambient or floor concreteQRADC Wall liner to ambient or wall concreteQRADCG Pan to primary gasQRADEB Breeder to blanket back wallQRADEM Breeder to manifoldQRADES Blanket back wall to shield inside regionQRADFB First wall (floor) to breederQRADFG Primary floor liner to secondary gasQRADFS Primary floor liner to secondary floor linerQRADG Combustion zone (or Li pool without combustion) to primary gasQRADP Combustion zone to lithium pool (only during combustion)QRADPG Primary wall liner to secondary gas

47

?e

QRADPS Primary wall liner to secondary wall linerQRADS Pan to primary floor linerQRADW Combustion zone (or lithium pool) to primary wall linerQRADWB First wall to breederQRSHFS Radiative heat flow from the shield outside region to the secondary

floor (BTU/sec)QRSHGS Radiative heat flow from the shield outside region to the secondary

gas (BTU/sec)QRSHWS Radiative heat flow from the shield outside region to the secondary

wall (BTU/sec)QU Heat flux from the primary gas to primary wall liner

due to condensation (BTU/sec-ft2 )QVAP Heat of vaporization of lithium (BTU/lb)QVEHC Heat flux from the cell gas to the extraneous heat capacity

due to condensation (BTU/sec-ft2 )QVPAN Heat flux from the primary gas to the pan insulation

due to condensation (BTU/sec-ft2 )QVSEC Heat flux from the secondary gas to secondary wall liner

due to condensation (BTU/sec-ft2 )QVFLR Heat flux from the cell gas to cell floor liner

due to condensation (BTU/sec-ft2 )QVFPGS Heat flux from the secondary gas to primary floor liner

due to condensation (BTU/sec-ft2 )QVWPGS Heat flux from the secondary gas to primary wall liner

due to condensation (BTU/sec-ft 2)RA Mean radius of combustion product particles (microns)RADxxx 'RAD' or 'R' indicates a temperature rate of change in one node due

to radiative heat transfer to or from another (deg. F./sec)'RAD'B Floor liner to ambient or floor concrete'RAD'C Wall liner to ambient or wall concrete'RAD'CB Floor concrete from floor liner'RAD'CC Wall concrete from wall linerRAIR Gas constant for primary non-condensible gas (RIN/XMOLP)RAIR2 Gas constant for secondary non-condensible gas (RIN/XMOLS)'R'BFF Breeder node from first wall (floor)'R'BFW Breeder node from first wall'R'BIEHC Blanket back wall from breederRBREAK Temperature rate of change of primary gas due to leakage (R/sec)RC2 Li-CO 2 reaction rate inhibition factor (Li2 CO3 reaction)RC2LB Rate of carbon consumption (lb/sec)RCMBC Stoichiometric combustion ratio for lithium and concrete

(lb Li/lb concrete)RCMBC2 Stoichiometric combustion ratio for lithium and carbon (lb Li/lb C)

48

RCMBCO Stoichiometric combustion ratio for lithium and carbon dioxidefor lithium carbonate producing reaction (lb Li/lb CO 2)

RCMBCS Stoichiometric ratio of lithium consumed in Li2CO3 producingreaction to Li2 CO3 produced (lb Li/lb Li2CO 3 )

RCMBH2 Stoichiometric combustion ratio for lithium and hydrogen (lb Li/lb H)RCMBN Stoichiometric combustion ratio for lithium and nitrogen (lb Li/lb N)RCMBO Stoichiometric combustion ratio for lithium and oxygen (lb Li/lb 0)RCMB01 Stoichiometric combustion ratio for monoxide reaction (lb Li/lb 0)RCMB02 Stoichiometric combustion ratio for peroxide reaction (lb Li/lb 0)RCMBW Stoichiometric combustion ratio for lithium and water for reaction

producing LiOH (lb Li/lb H20)RCMBW2 Stoichiometric combustion ratio for lithium and water for reaction

producing Li2 0 (lb Li/lb H2 0)RCMCA1 Stoichiometric ratio of lithium consumed in Li-CO 2 reaction

producing Li20 and carbon to carbon produced (lb Li/lb C)RCMCA2 Stoichiometric ratio of lithium consumed in Li-CO 2 reaction

producing Li2 CO3 and carbon to carbon produced (lb Li/lb C)RCMCCO Stoichiometric combustion ratio for lithium and carbon dioxide

for lithium oxide producing reaction (lb Li/lb CO 2)RCOLB Rate of carbon dioxide consumption (lb CO 2/sec)'R'CZG Primary gas from combustion zone'R'CZP Lithium pool from combustion zone'R'CZW Primary wall liner from combustion zone'R'EHCBI Breeder from blanket back wall'R'EHCMN Breeder from manifold'R'EHCSH Blanket back wall from shield inside regionRELERR Fraction of X/(dx/dt) allowed as the maximum time step (sec)'R'FFB First wall (floor) from breeder node'R'FPFS Primary floor liner from secondary floor liner'R'FPGAS Primary floor liner from secondary gas'R'FSFP Secondary floor liner from primary floor liner'R'FSSH Secondary floor liner from shield outside region'R'FWB First wall from breeder node'R'GASFP Secondary gas from primary floor liner'R'GASPA Pan to primary gas'R'GLI Lithium pool to primary gas (without combustion)'R'GSSH Secondary gas from shield ouside regionRHCON Density of concrete (lb/ft3 )RHINS Density of insulation (lb/ft3 )RHLEAD Density of pure lead (lb/ft3 )RHLI Density of pure lithium (lb/ft3 )RHLIX Density of pure lithium (used in LC-2 lithium transfer simulation)

(lb/ft3 )RHOAIP Initial density of primary non-condensible gas (lb/ft3 )

RHOAISRHOAPRHOASRHOBRHOCARRHOLC2RHOLC3RHOLIHRHOLINRHOLIORHOLIVRHOTOTRHPANRHSFPRHSFSRHSWPRHSWSRIFxxxRIFBBIRIFBMRIFCZGRIFCZPRIFESRIFFFBRIFFPSRIFFWBRIFPAGRIFPASRIFPGRIFPGARIFPSRIFPWRIFSCFRIFSCWRIFSLCRIFSFRIFSWRINRINPRINSRISHGS

'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 CO3 (lb/ft3 )Density of LiOH (lb/ft3 )Density of Li3N (lb/ft3 )Density of Li20 (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 transferBreeder node to blanket back wallBreeder node to manifoldCombustion zone and primary gasCombustion zone and primary wall linerBlanket back wall to shield inside regionFirst wall (floor) to breeder nodePrimary floor liner and secondary floor linerFirst wall to breeder nodePan to primary gasPan to floor linerLithium pool to primary gasPrimary wall liner to secondary gasPrimary wall liner to secondary wall linerLithium pool to primary wall linerSecondary floor to concrete floorSecondary wall to concrete wallWall or floor liner to concreteShield outside region to secondary floorShield outside region to secondary wallUniversal 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 thesecondary cell gasGas from lithium pool (without combustion)Wall liner from lithium gool (without combustion)

'R'MNEHCRN2RNxx

RNILBR02ROXLB'R'PAGAS'R'PANSTRRRRTLI'R'SHEHC'R'SHFS'R'SHGS'R'SHWS'R'SPGS'R'STPANRWALB'R'WLI'R'WPGAS'R'WPWS'R'WSSH'R'WSWPSAT(x,y)SFLCRSFLENDSFLTINSH(x,y,z)SIGMASPILLSPRAYSTICK

STMFACSTMINSTMIN2STMOUTSTOUT2TATAUTAUCZ

Manifold from breederLithium-nitrogen reaction rate inhibition factorExpressions used to calculate RN2 as a function of gas composition andlithium temperatureRate of nitrogen combustion (lb/sec)Lithium-oxygen reaction rate inhibition factorRate of oxygen combustion (lb/sec)Primary gas from panPrimary wall liner from panFunction which generates the lithium-nitrogen kinetics limit curveLithium-nitrogen reaction kinetics limit modified by the presence of steamShield inside region from blanket back wallShield outside region from secondary floorShield outside region from secondary gasShield outside region from secondary wallSecondary gas from primary wall linerPan from primary wall linerRate of water vapor consumption (lb/sec)Lithium pool from primary wall liner (without combustion)Primary wall liner from secondary gasPrimary wall liner from secondary wall linerSecondary wall liner from shield outside regionSecondary wall liner from primary wall linerSaturated steam tableHeat 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 tableStefan-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 fireRate at which aerosols are removed from the primary cell due tosticking to the wall. If STICK > 1.0, execution stops.STICK may be reduced by increasing BETA.Density weighting factor for calculating steam-air mixture propertiesTime 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 convectionRadiative transmissivity used to model pool-combustion zone couplingrather than (1.-EMCZ)

51

TAVE Average of secondary floor and secondary water pool temperature (deg. R.)TAVHI Variable used to read steam tablesTAVLO Variable used to read steam tablesTB(i) Temperature of ith node of concrete floor (deg. R.)TBIC(i) Initial temperature of ith node of concrete floor (deg. R.)TxxxxF Corresponding temperature to Txxxx in FahrenheitTBLI Temperature of blanket back wall (deg. R.)TBLIO Initial temperature of blanket back wall (deg. R.)TBLOW Inert gas inlet temperature (deg. R.)TC(i) Temperature of ith node of concrete wall (deg. R.)TCIC(i) Initial temperature of ith node of concrete wall (deg. R.)TCIGNI Ignition temperature of lithium-concrete reaction (deg. R.)TCON Concrete combustion zone temperature (deg. R.)TCZ Combustion zone temperature (deg. R.)TCZI Initial combustion zone temperature (deg. R.)TE Equilibrium temperature resulting from spray fire (deg. R.)TEHCP Primary extraneous heat capacity temperature (deg. R.)TEHCS Secondary extraneous heat capacity (breeder with torus fire option)

temperature (deg. R.)TEHCZP Initial primary extraneous heat capacity temperature (deg. R.)TEHCZS Initial secondary extraneous heat capacity (breeder with torus fire

option) temperature (deg. R.)TETI Used in calculating thermal conductivity of inner pan insulation

See KIN1TET2 Used in calculating thermal conductivity of outer pan insulation

See KIN2TEZ Average of combustion zone temperature and lithium pool temperature

Used in test for combustion (deg. R.)TFEFF Normalized temperature of combustion zone-lithium pool temperature

(deg. R.)TFHI Variable used to read steam tablesTFLO Variable used to read steam tablesTFS Secondary floor liner temperature (deg. R.)TGP Primary gas temperature (deg. R.)TGPZER Initial primary gas temperature (deg. R.)TGS Secondary gas temperature (deg. R.)TGSZER Initial secondary gas temperature (deg. R.)THBLI Thickness of blanket back wall (ft)THE Thickness of vacuum gap (ft)THFC Thickness of concrete floor (ft)THFP Thickness of primary floor liner (ft)THFS Thickness of secondary floor liner (ft)THI 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)THMAN Thickness of blanket manifold (ft)THPB Thickness of lead layer above the lithium-lead pool (ft)THSHI Thickness of inside region of reactor shield (ft)THSHL Thickness of bulk region of reactor shield (ft)THSHO Thickness of outside region of reactor shield (ft)THWC Thickness of concrete wall (ft)THWP Thickness of primary wall liner (ft)THWS Thickness of secondary wall liner (ft)TIME Time elapsed after spill has occurred (sec)TIMEF User defined time to stop execution of the code (sec)TIMEO Time at which code prints output data to a file (sec)TINS1 Inner pan insulation layer temperature (deg. R.)TINS1I Initial inner pan insulation layer temperature (deg. R.)TINS2 Outer pan insulation layer temperature (deg. R.)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.)TLI Lithium pool temperature (deg. R.)TLIBS Lithium pool temperature before spray fire (deg. R.)TLII initial lithium pool temperature (deg. R.)TLO Temporary variable used to read steam tablesTLP 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.TMAN Temperature of the blanket manifold (deg. R.)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.)TSFP Primary floor liner temperature (deg. R.)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 Initial shield bulk region temperature (deg. R.)TSHO Shield outside region temperature (deg. R.)TSHOO Initial shield outside region temperature (deg. R.)TSP Primary wall liner temperature (deg. R.)TSPZER Initial primary wall liner temperature (deg. R.)TSS Secondary wall liner temperature (deg. R.)TSSZER Initial secondary wall liner temperature (deg. R.)TVAP Vaporization temperature of lithium (deg. R.)TI Film temperature between primary gas and lithium pool (deg. R.)T2,T3 Temporary variables used in setting up steam tableUA Internal energy of non-condensible gas in a cell (BTU)UGPB Specific internal energy of saturated water vapor at boiling (BTU/lb)UL Internal energy of the primary water pool (BTU)UL2 Internal energy of the secondary water pool (BTU)ULP Specific internal energy of the primary water pool (BTU/lb)ULP2 Specific internal energy of the secondary water pool (BTU/lb)ULPB Specific internal energy of liquid needed for boiling to occur (BTU/lb)ULZ Time rate of change of UL (BTU/sec)ULZ2 Time rate of change of UL2 (BTU/sec)USUBA Heat transfer coefficient between the outermost containment node and

the ambient (BTU/sec-ft2 -deg. F.)UV Internal energy of the primary gas (BTU)UV2 Internal energy of the secondary gas (BTU)UVZ Time rate of change of the internal energy of the primary gas (BTU/sec)UVZ2 Time rate of change of the internal energy of the secondary gas (BTU/sec)UWV Specific internal energy of water vapor in the primary gas (BTU/lb)UWV2 Specific internal energy of water vapor in the secondary gas (BTU/lb)VA Specific volume of non-condensible primary gas (ft3/lb)VAB Specific volume of non-condensible gas at the water pool-gas boundary (ft3 /lb)VCONC Volume of concrete in the first node of concrete (ft3 )VG Specific volume of water in the primary gas (ft3 /lb)VG2 Specific volume of water in the secondary gas (ft3 /lb)VHI Variable used to read steam tablesVIEWB View factor from the breeder to the blanket back wallVIEWG View factor across the vacuum gapVIEWM View factor from the breeder to the manifoldVL Volume of the primary water pool (ft3 )VL2 Volume of the secondary water pool (ft3 )VLO Variable used to read steam tablesVLP Specific volume of the primary water pool (ft3 /lb)VLP2 Specific volume of the secondary water pool (ft3 /lb)

54

VLPF

VLPV

VPVSVSBVSTVVB

VVB2

VVGVVG2VVTWABWAPWASWATER

WCBWCPWCO2SWN2BWN2PWN2SWO2BWO2PWO2SWWABWWAPWWASXALLOYXAMXBLOWXESCXINJXINJ2XLIXLIDOT

XMAIRPXMAIRS

as time-+ooMass fractionMass fractionMass fractionMass fractionMass fractionMass fractionMass fractionMass fractionMass fractionMass fraction

(lb/ft3 )of carbon dioxide in the flooding gasof carbon dioxide in the primary gasof carbon dioxide in the secondary gasof nitrogen in the flooding gasof nitrogen in the primary gasof nitrogen in the secondary gasof oxygen in the flooding gasof oxygen in the primary gasof oxygen in the secondary gasof water vapor in the flooding gas

Mass fraction of water vapor in the primary gasMass fraction of water vapor in the secondary gasAtom percent of lithium in lithium-lead poolLogarithmic mean molar fraction of air (see MFAB and MFAG)Used in conjunction with IBLOWUsed in conjunction with IESCIndicates whether steam injection to the primary is in effectIndicates whether steam injection to the secondary is in effectMass fraction of lithium in lithium-lead poolMass flow rate of lithium through the lead layer above the Li-Pbpool (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

Specific volume of saturated liquid water at the secondary floor linertemperature (ft3 /lb)Specific volume of saturated liquid water for heat transfer between thesecondary 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 pooltemperature (ft3 /lb)Specific volume of saturated water vapor at the secondary water pooltemperature (ft3/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 condensationMass fraction of inert gas in the flooding gasMass fraction of inert gas in the primary gasMass fraction of inert gas in the secondary gasAmount of water that should be left in the top concrete node

XMBLI Mass of the blanket back wall (lb)XMCOCZ Mass of concrete combustion zone (lb)XMDOT Mass flow rate of gas between primary and secondary cells (lb/sec)XMEHCP Mass of primary extraneous heat capacity (lb)XMEHCS Mass of secondary extraneous heat capacity (breeder with torus fire

option) (lb)XMH20I Initial water content of concrete (lb/ft3 )XMMAG Mass of the magnets (secondary extraneous heat capacity) (lb)XMMAN Mass of the blanket manifold (lb)XMOLP Molecular weight of non-condensible primary gas (lb/lb-mol)XMOLS Molecular weight of non-condensible secondary gas (lb/lb-mol)XMOLA Molecular weight of containment inert gas (lb/lb-mol)XMOLAB Molecular weight of flooding inert gas (lb/lb-mol)XMSHI Mass of shield inside region (lb)XMSHL Mass of shield bulk region (lb)XMSHO Mass of shield outside region (lb)XSFL Indicates whether emergency floor cooling is currently in effectYALIG Effective thermal admittance between the pool and primary gas

(BTU/sec-deg. F.)YAPCZ Effective thermal admittance between the pool and combustion zone

(BTU/sec-deg. F.)YPAGAS Effective thermal admittance between the pan and primary gas

(BTU/sec-deg. F.)ZLI Thickness of the lithium pool (ft)ZP Used to determine EMLI if EMLI < 0.9ZZxxxx Temperature rate of change of a node (deg. R./sec)ZZ1 Lithium poolZZ2 Lithium spill panZZ3 Secondary cell gasZZ4 Primary cell gasZZ5 Primary wall linerZZ6 Combustion zoneZZ7 Primary floor linerZZ8 Inner insulation layerZZ9 Outer insulation layerZZ99 Change in combustion rate with respect to time (lb Li/sec2 ft2)'ZZ'C Concrete combustion zone'ZZ'BLI Blanket back wallZZD Rate of change of concrete combustion zone thickness (ft/sec)ZZDIN Initial rate of change of concrete combustion zone thickness (ft/sec)'ZZ'EP Primary extraneous heat capacity'ZZ'ES Secondary extraneous heat capacity'ZZ'FS Secondary floor liner'ZZ'MAG Magnets (secondary extraneous heat capacity)

56

'ZZ'MAN'ZZ'PB'ZZ's'ZZ'SHI'ZZ'SHL'ZZ'SHO

Blanket manifoldLead layer above Li-Pb poolSecondary wall linerShield inside regionShield bulk regionShield outside region

PROGRAM DECISION FLAGS

IAROSL =1 to use aerosol removal from containment by sticking optionIBLOW =1 Containment flooding with inert gas

=0 No containment floodingICMB =0 No oxygen left after spray fire

=1 Still oxygen left after spray fire (initially =1, reset by code)ICNI =0 Nitrogen reactions not possible

=1 Nitrogen reactions possibleIC021 =1 to use pure CO 2 atmosphereICZ =0 Combustion zone model not used

=1 Combustion zone model usedIESC =1 to use emergency space cooling optionIFLAG2 =1 to use two-cell geometry optionIFLAGB =1 to use lithium-lead optionIFLAGC =1 to use concrete combustion optionIFLAGCO =1 to use pure CO 2 atmosphere optionIFLAGD =1 to use layered lithium-lead pool optionIFLAGF =1 to use floor concrete optionIFLAGISI =1 to enter input data in SI unitsIFLAGP =1 to use pan optionIFLAGR =1 to use torus fire optionIFLAGS =1 to use dry gas injection optionIFLAGT =1 to use steam-air mixture optionIFLAGU =1 to get output in SI unitsIFLAGW =1 to use wall concrete optionILIT =0 No lithium left to burn

=1 Lithium left to burnIMETH =1 Runge-Kutta method of integration used

=3 Simpson's Rule method of integration usedISFLC =1 to use emergency floor cooling optionISWICH =0 Crack size remains constant

Crack size reset to zero after primary and secondary cellgas pressure equilibrate (note: this should not be used wheneither cell is small compared to the other or the volume of gasbeing consumed by the fire)

57

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.

OPTION AND LOGICAL DECISION FLAGS

Two cell geometryInjection of dry gas during runConcrete combustionPure CO 2 containment atmosphereConcrete combustion has stopped (set by code)Lithium-lead layered pool combustion modelFloor concreteCode accepts input in SI unitsLILP 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 combustionPan optionCode prints output in SI unitsSteam-air mixture in containmentTorus fire optionWall concrete

58

C Troubleshooting

"There exists no large computer code which runs perfectly 100% of the time."-ANONYMOUS-

The user of this code may encounter problems while trying to execute LITFIRE.The most common error statement is generated by the computer itself: DIVIDE BYZERO and stops the code. This indicates that an attempt was made to divide by zeroor something very close to zero. The first step when encountering an error messageis to check the output file outl.dat and ensure that the input was properly enteredinto the code. If it was, the error may occur if the value of EXHSTV is too high orLILP 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 totake the square root of a negative number - the code has diverged numerically andthe combustion zone temperature is negative. This may occur when. the combustionrate CMBRH is very small (i.e.,< 1.0 lb Li/hr-ft2 ), the oxygen and nitrogen concen-trations are low, or when the gas pressure is low. This problem occurs when ZZ6and DELT are large enough to produce a negative TCZ. This problern may be solvedby reducing the value of DELOUT to limit the time step size, so extrapolations ofTCZ over a long time step do not cause problems. Unfortunately, this can increasecomputation time considerably. The variation of the combustion zone temperatureover time is a good indicator of whether or not the code is running properly. Duringcombustion, 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 thispoint if the lithium has been consumed, but it is continuously calculated for numericalreasons.) 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 mayindicate that the rate of change of the lithium pool temperature was very large. Thismay be due to the fact that TCZ has diverged to a very large value. This generallyoccurs as LILP nears zero, as the pool then has a lower heat capacity, and a suddeninflux 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, CM-BRH; or time step length DELT. In general, DELT should increase after the start ofthe 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 nothelp solve the problem, print out values of the code quantities like ZZ5 and ZZ6 orUVZ and MWVZ to help find the problem.

Other messages indicate that the user is attempting to use incompatible optionstogether, or that the code has been stopped because there is no point in continu-ing 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 EXECUTIONOF THE CODF LITFIRE

THESE ARE THE OUTPUT VALUES CORRESPONDINGTO THE PRIMARY CELL ENVIRONMENT

TIME DELT TCZF TLIF TGPF PATHESE ARE THE OUTPUT VALUES CORRESPONDINGTO THE SECONDARY CELL ENVIRONMENT

TIME TGSF TFSF PAS XMDOT MOXSTHESE ARE THE OUTPUT VALUES CORRESPONDINGTO THE PAN OUTPUT OPTION

TIME TLIF TPANF TINS1FTHESE ARE ADDITIONAL OUTPUT VALUES CORRESPOJDINGTO THE PRIMARY CELL ENVIRONMENT

TIME MNIP MOXP MCO2PTHESE ARE THE OUTPUT VALUES CORRESONDINGTO THE LITHIUM/LEAD DIFFUSION OPTION

TIME XLIDOT TLEADF MLEAD

P TSPF TSFPF

MNIS

TINS2F

RN2

MCO2S

PAP

R02

THPB

INPUT DATA FILE UWMAK.W

S0 e 0 0 0 0 0 0 0 0 05 5.20 .20 .20 .20 .20.20 .20 .20 .20 .20497.88 10.14 0.1247 39.90725.0 123.00 51.00 0.1199 0.090.833 2.080 0.002 0.015 0.000.15 0.1189 30.00 497.500 572.3 0.050.15 0.1189 30.00 497.500 38.35 0.050.2 0.9960 33.80 30.000.9 0.2650 0.0227 144.00

124.00 86.9400 160.00 0.04 0.9 0.118510.0 0.0 4080.0 13784.0 10964.1

0.8764 0.0 1.487 0.383 0.766 6.93816.60 2916.0 8431.0 0.0

0.87 0.13 0.01 0.11 0.890.16 0.85 0.112 0.07 0.01 0.010.07 0.072.153 22.05 0.000 0.050 5.0

1752.6 851.4 851.2 815.2 530.99 1751.814.70 0.2320 0.0 0.0000 0.0000

00030000000.02000000900.00000000000.00300000001.00000000100.0000

INPUT DA A FILE UWMAK.X

8855700.00000000140.0eOe0000014.70000000538.10000000538.20000000538.300015.5 00.00 0.232 0.0 522.0000 0.0

1482.0 1696200.0 9709.00 0.6921 0.090.85 0.1199 12.40 497.50 188164.00 0.02080.85 0.1199 12.40 497.50 59038.00 0.0208

350.0

60

LIBP

ZLI

8080

INPUl DATA FILE UWMAK.Y

0000030.00000000497.50000000000.12000000008.11500000000.20000000000.90001750.00 7.00 5.9055 12.32 0.09

0.0210 0.1667 0.08330.0350 9.3000 708.0000 0.1700 3315.0000 0000.0415

6.45600E-08

INPUT DATA FILE UWMAK.Z

0000100.00000000000.00000000000.00000000004. ecoeCOOOOO.12470000535.000024.0 0.0 310.0 325.0 0.00

INPUT DATA FILE STEAMOP.

0001000.000000030e0. OOOOOOOeo. 00900001190.300

INPUT DATA FILE TORUS.

8855700.00000000150.00000000014.70000000538.10000000538.20000000538.300015.5 00.70 0.232 0.0 522.0000 0.0

1482.0 115468.0 7796.00 0.1189 0.09 1.4980.85 0.1199 12.40 497.50 188164.00 0.02080.85 0.1199 12.40 497.50 59038.00 0.02081.344 0.500 0.1 0.1 .648

672.0 1.903 14.202 3500000.0 0.1653 12110.00.500 0.0001 538.0 14000.0 9000000.0 0.11990.09 0.000 0.0656 0.889 1.0 .27817.90 .1312 .1189 9472.0 149816.0 1300.0

670.0 585.0 .1312 .1312 260000.0 260000.0.656 522842.0 .188 8890.0 1392.0 11.387

8.16e+00 4.41e-06 4.43e-01 9.57e-08 1.75e-01 2.90e-071.03e-01 4.41e-06 6.46e-03 9.57e-08 1.09e+00 3.08e-028.46e-02 2.56e-08 1.91e+00 7.41e-05 3.32e-02 2.92.-62.84e-02 4.41e-06 8.21e+00 3.08e-03 2.88e-03 2.90e-071.85e+00 7.41e-05 2.72e-03 2.56e-08 1.70e-04 3.84e-121.77e+01 2.81e-02 1.69e-04 7.51e-03 7.34e-06 1.69e-04

350.0

61

mmwk.ftww

E Sample Output Data Files

OUTPUT DATA FILE OUT2.DAT

THESE ARE THE OUTPUT VALUES CORRESPONDINGTO THE PRIMARY CELL ENVIRONMENT

TIME0.0

100.0200.2300.1400.1500.0600.1700.0800.0900.1

DELT0.100.320.470.220.430.820.480.040.170.04

TCZF700.67810.60827.90855.77900.09911.94922.62935.18950.40967.46

TLIF700.22609.64622.37650.31679.50715.02742.62757.36765.30773.17

TGPF200.00198.78197.98197.09196.39195.21194.11193.89193.60193.30

PAP101.70102.11102.89'03.66104.42105.32106.13106.63106.92107.21

progrom execution stopped by programvalues 0.233e+02 0.604e+03 0.181e+03 0.692e+01 0.619e+00

TSPF199.89198.41196.93195.49194.17192.62191.23190.38189.91189.45

OUTPU' DATA FILE OUT3.DAT

THESE ARE THE OUTPUT VALUES CORRESPONDINGTO THE SECONDARY CELL ENVIRONMENT

TIME0.0

100.0200.2300.1400.1500.0600.1700.0800.0900.1

TGSF25.9428.1230.4032.6934.9037.5639.9641.4442.3043.15

TFSF26.0626.0626.0626.0826.1026.1526.2026.2526.2826.31

PAS XMDOT101.38-0.2194e+00102.11102.89103.67104.41105.32106.13106.63106.92107.21

0.0.0.0.0.0.0.3826e-010.0.3610e-01

MOXS0. 1508e+060. 1508e+060. 1508e+060.1508e+060.1508e+060. 1508e+060. 1508e+060.1508e+060.1508e+060. 1508e+06

MNIS0.4994e+060.4994e+060.4994e+060.4994e+060.4994e+060.4994e+060.4994e+060.4994e+060.4994e+060.4994e+06

62

TSFPF179.89489.57573.67613.54643.92680.06709.36725.33733.84741.89

MCO2S0.0.0.0.0.0.0.0.0.0.


THESE ARE ADDITIONAL OUTPUT VALUES CORRESPONDINGTO THE PRIMARY CFLL ENVIRONMENT

TIME0.0

100.020C 2300. 1400.1500.0600.1700.0800.0900.1

MNIP0. 8074e+010.8153e+010. .272e+010.8395e+010.8510e+010.8662e+010.8806e+010.8892e+010.8937e+010.8988e+01

MOXP0. 2439e+010. 2426e+010.2399e+010.2372e+010.2345e+010. 2305e+010. 2264e+010. 2236e+010.2221e+010. 2208e+01

MCO2P0.0.0.0.0.0.0.0.0.0.

RN20.000000.351100.331250.282690.236680.189930.161820.168190.185530.20478


These outputs ore the weights of react 3n products in LB

Time Lilox

0.0100.0200.2300.1400.1500.0600.1700.0800.0900.1

0.0. 193e+000. 503e+000. 837e+000.1 19e+010. 165e+010.209e+010. 238e+010. 255e+010. 273e+01

Lilni Lilco Lilc2 Lilcar Mliop MIc3p

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.

OuJPUT DATA FILE OUT1O.DAT

These outputs are the reaction rates in gram Li/min-cm2

Time Cmbrhh Cmbrnh Cmbroh Cmbrwh Cmrcoh Cmrc2t

0.0 0.100.0 0.3885e-01200.2 0.4243e-01300.1 0.4672e-01400.1 0.5183e-1Ol500.0 0.4680e-01600.1 0.4365e-01700.0 0.4509e-01800.0 0.4833e-01900.1 0.5207e-el

0.3050e-050.2047e-010.2292e-010.2678.-010.3112e-010.2599e-010. 2289e-010. 2433e-010.2739e-010.3091e-0 1

0.2866e-050.1839e-010.1951e-e10.1993e-010.2071e-010.2081e-010.2076e-e10.2076e-010.2094e-010.2116e-01

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.

63

R020.971200.970980.970590.970200.969820.969290.968750.968410.968230.96805

LIBP0.0. 1015e+000.2476e+000.4156e+000.6179e+000.8597e+000. 1074e+010.1209e+010.1297e+010.1393e+01

0.0.0.0.0.0.0.0.0.0.

0.0.0.0.0.0.0.0.0.0.

0.0.101 e-810. 262e-010. 435e-e10.614e-010.846e-010. 107e+000. 121e+000. 128e+000. 136e+00

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, secondedition, August 1987. PFC/RR-87-11.

[21 D.S. Barnett. The Chemical Kinetics of the Reactions of Lithium with Steam-AirMixtures. PhD thesis, Massachusetts Institute of Technology, April 1989.

[3] V.J. Gilberti and M.S. Kazimi. Modeling of Lithium and Lithium-Lead Reactionsin Air Using LITFIRE. Technical Report PFC/RR-83-08, MIT Plasma FusionCenter, January 1983.

[4] D.A. Dube and M.S. Kazimi. Analysis of Design Strategies for Mitigating theConsequences of Lithium Fire Within Containment of Controlled ThermonuclearReactors. Technical Report MITNE-219, Massachusetts Institute of Technology,July 1978.

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