DOE/ID-01570-5 PFC/RR-89-4 LITFIRE USER'S GUIDE Third Edition D.S. Barnett April 1989 Plasma Fusion Center Massachusetts Institute of Technology Cambridge, MA 02139 U.S.A. *This work was supported by EG&G Idaho, Inc. and the U.S. Department of Energy, Idaho Operations Office under DOE Contract No. DE-AC07-7611D01570 Reproduction, translation, publication, use and disposal in whole or in part, by or for the United States government is permitted Abstract This document contains instructions for using the LITFIRE lithium fire simulation code in its form as of April 1989. The code is capable of simulating fires in a single compartment connected to an optional second compartment, or in an insulated pan suspended in one compartment. Lithium or lithium-lead eutectic may be used as the fuel, reacting with an atmosphere of oxygen, nitrogen, water vapor, or any mixture thereof. Any inert gas may be included in the compartment atmosphere and lithium only may be burned in a carbon dioxide atmosphere without oxygen. An option for liquid metal-concrete interaction exists as well as the following options for mitigating the effects of the fire: gas flooding, emergency space cooling, emergency floor cooling, aerosol removal and gas injection. The guide also includes the following: " a description of the workings of the code, including the various options available to the user " a description of the physics of lithium fires and heat and mass transfer " instructions for running the code " a list of sample input ifies " a listing of the code with a glossary defining code variables 1 Contents Abstract 1 Table of Contents 2 List of Figures 3 1 Introduction 2 Program Description 2.1 2.2 2.3 3 Initial Routine ..................... 2.1.1 Input Data . . . . . . . . . . . . . . . 2.1.2 Print out the Input . . . . . . . . . . . 2.1.3 Variable Initialization . . . . . . . . . . 2.1.4 Spray Fire Calculations . . . . . . . . . Dynamic Cycle . . . . . . . . . . . . . . . . . 2.2.1 Preliminary Calculations . . . . . . . . 2.2.2 Radiative Heat Transfer . . . . . . . . 2.2.3 Gas Node Temperature Determination 2.2.4 Natural Convection Heat Transfer . . . 2.2.5 Conductive Heat Transfer . . . . . . . 2.2.6 Temperature Rates of Change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.7 Lithium Combustion . . . . . . . . . . . . . 2.2.8 2.2.9 2.2.10 2.2.11 2.2.12 2.2.13 Overpressure, Leakage, and Integrals . . . . . . . . . . Termination Checks . . . . Time Step Control . . . . Output Section . . . . . . Error Pointers . . . . . . . Aerosol . . . . . . . . . . . . . . . . . . . . . . . . . Behavior . . . . . . . . . . . . . . . . . . . . . . . . . Modeling Options . . . . . . . . . . . . . . . . . . . 2.3.1 One Cell Option . . . . . . . . . . . . . . . 2.3.2 Two Cell Option . . . . . . . . . . . . . . . 2.3.3 2.3.4 Pan Option . . . . . . . . . . . . . . . . . . Concrete Reaction . . . . . . . . . . . . . . 2.3.5 Lithium-Lead Combustion . . . . . . . . . . 2.3.6 2.3.7 2.3.8 Steam-Air Atmosphere Option . . . . . . . . Torus Fire Option . . . . . . . . . . . . . . . Mitigation Options . . . . . . . . . . . . . . Execution of LITFIRE 3.1 Obtaining Copies of LITFIRE and the Input Data Files. 3.2 Organization of LITFIRE for Execution . . 2 19 21 22 3.2.1 3.2.2 One Cell Option Two Cell Option ........................ . . . . . . . . . . . . . . . . . . . . . . . . . . 22 24 3.2.3 3.2.4 Pan, Concrete Reaction and Lithium-Lead Combustion . . . . Gas Flooding, Emergency Space Cooling, Emergency Floor Liner Cooling and Gas Injection . . . . . . . . . . . . . . . . . . . . Steam Injection to Containment . . . . . . . . . . . . . . . . . 25 3.2.5 26 26 3.3 3.2.6 Torus Fire . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PFCVAX Execution . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 28 3.4 3.5 MFE Crays Execution . . . . . . . . . . . . . . . . . . . . . . . . . . Sample Input and Output Files . . . . . . . . . . . . . . . . . . . . . 29 30 A Nomenclature 31 B Variable Listing 32 C Troubleshooting 59 D Sample Input Data Files 60 E Sample Output Data Files 62 F Listing of the LITFIRE code 63 Bibliography 152 List of Figures 1 One-cell option in LITFIRE ...... 2 3 4 5 Two-cell option in LITFIRE ........................ Mass flow in LITFIRE .......................... Pan option in LITFIRE ........................ Torus fire option in LITFIRE ...... ...................... ....................... 3 14 . 15 16 17 20 1 Introduction LITFIRE is a computer code which simulates lithium fires in fusion reactors by generating the time histories of the temperature and pressure profiles occurring in a reactor containment in response to a lithium or lithium-lead eutectic spill and fire. The fire may take place in a single cell connected to an optional second cell, or in an insulated pan in a single cell. The lithium or lithium-lead may react with any mixture of oxygen, nitrogen or water vapor; an inert gas may also be included in the cell atmospheres. Lithium only may be burned in a carbon dioxide atmosphere without oxygen. An option for liquid metal-concrete interaction is available as well as the following options for mitigating the effects of a fire: gas flooding, emergency space cooling, emergency floor cooling, aerosol removal and gas injection. This user's guide includes a brief description of the physics of lithium fires, the workings of the code and the options available to users, and also includes a listing of the code with a complete glossary of variables used in LITFIRE. The present version of LITFIRE is available on the PFCVAX at MIT and on the Crays at the National Magnetic Fusion Energy Computer Center (NMFECC, hereafter referred to as MFE) It is written in FORTRAN 77 and is compatible with the computing facilities at which it is located. The instructions present in this guide will enable a user to execute the code at either location. Other information on LITFIRE such as more detailed descriptions of physical models or correlations used in the code are available in the references listed in the reference section of the guide. 2 Program Description To assist the new user of LITFIRE in understanding the code, a brief descriptive section is included. The description of the code sections is presented in the order that they are executed. For a description of code options, see Section 2.3. This section is broken down into an initial routine and a dynamic cycle. The initial routine prepares the code for execution; then the dynamic cycle integrates the time rate of change of the code variables over the time step to calculate their values. The dynamic cycle is repeated until execution is terminated either by the code or as predetermined by the user. 2.1 Initial Routine The four parts of the initial routine are: 1. read in the input data 2. write the input data to a file 4 3. initialize the variables 4. spray fire calculation 2.1.1 Input Data The input data consists of titles and headings, control flags for the choice of options, geometries, initial conditions and material properties. User chosen options are described in Section 2.3. Input variables are described in Section 3 and examples of the input data files are given in Appendix D. 2.1.2 Print out the Input The input is printed out to a file, which should be examined by the user to ensure that the input was properly entered into the input files. Misaligned input data is a common source of error that can easily be caught by examining the printed input. 2.1.3 Variable Initialization The initialization section sets all time rates of change to zero for the first step. Some constants are defined and initial conditions are applied using the input data. In addition there is a short sub-section where the units of the input data are changed to the following to become consistent with the rest of the code: BTU, pounds mass, feet, seconds 2.1.4 Spray Fire Calculations The spray fire calculation simulates the effect of lithium reacting as a spray at the beginning of a spill. The amount reacted in the spray is user specified. A difficulty does arise in that the specific heats of the reaction products are calculated as functions of temperature. The spray fire calculation is not a spray fire model per se in that the lithium reacting in the spray is consumed instantaneously, adiabatically and stoichiometrically, with the equilibrium temperatures being determined by iteration. 2.2 Dynamic Cycle The dynamic cycle in LITFIRE calculates the temperature, pressure and mass profiles of the reactor containment over the time of the run. Most of the dynamic cycle consists of calculating the thermal admittances between nodes, which are then used in conjunction with the nodal temperatures, to determine the time rates of change of the nodal temperatures. The heat flow to or from a node is determined by calculating the thermal resistances to conduction or convection between adjacent nodes and then adding on radiative heat transfer to or from nodes within a line of sight. All of the 5 calculations performed in the dynamic cycle are listed below in the order which they are performed: 1. Perform gas injection if necessary 2. Calculate temperature dependent heat capacities 3. Calculate individual gas fractions 4. Calculate gas emissivities and radiative interchange factors 5. Perform an energy balance to determine the gas temperature if the steam in containment option is used 6. Calculate natural convection gas heat transfer coefficients 7. Calculate thermal admittances 8. Perform steam injection if necessary 9. Perform lithium-lead diffusion calculation if necessary 10. Test for and calculate lithium or lithium-lead combustion 11. Calculate temperature rates of change from heat flow 12. Calculate lithium-concrete reaction if necessary 13. Calculate gas overpressure and leakage 14. Calculate aerosol removal rate via aerosol sticking 15. Perform integrations 16. Check for terminating execution 17. Perform time step control 18. Write the output to data files 19. Display error pointers if necessary Short descriptions of the subsections appear below. 6 2.2.1 Preliminary Calculations Before any calculations are performed by the code, the material properties of all of the nodes must be calculated. Most properties are assumed to be constant with respect to temperature, but the specific heats of some gases and combustion products, and most lithium properties, are calculated as functions of temperature. These are calculated at the beginning of each time step. The mass fraction and total mass of each of the individual gases is also calculated so that the total heat capacity of the gas may be calculated. 2.2.2 Radiative Heat Transfer Radiative heat transfer rates in LITFIRE are calculated using the following basic equation: Q1--.2 = f Aio(T' - T2) (1) where Q1-.2 = heat transfer rate (W) from node 1 to node 2 A1 = exposed area of node 1 f = radiative interchange factor based on A1 0 T,, = Stefan-Boltzmann constant = temperature of node n The radiative interchange factor f is determined by the emissivities of the surfaces of the two nodes and the view factor between them. Thus the radiative emissivity of each node is required to account for radiative heat transfer within the containment building. The emissivities of the solid elements in the containment building are specified by the input data and are assumed to be constant. The emissivity of the lithium pool is assumed by the code to be governed by the buildup of reaction products (Li 2 0, Li 3 N and Li 2 CO 3 ) on the pool surface. The emissivity of the cell gas (in the absence of steam) is determined by the aerosol size and concentration in the gas and by the optical path length in the cell. The aerosol particle area and the optical path length are defined by the user in the input data and the concentration is calculated from the amount of aerosol reaction product generated by the fire. In the presence of steam the emissivity of the cell gas is also governed by the partial pressure of the water vapor in the cell. Radiative heat transfer is discussed in greater detail in reference[2]. 2.2.3 Gas Node Temperature Determination If the steam in containment option is being used, the presence of a condensible gas requires that a different method be used to determine the temperature of the gas than the integral method described in Section 2.2.9, as the latent heat of vaporization of the steam must be taken into account. In this option, the code performs an iterative 7 energy balance by solving the equation: TEMP = U, - Mci.T - Mu, (2) where U, is the total internal energy of the gas, At is the mass of the non-condensible gas, c, is the specific heat of the non-condensible gas, M, is the mass of the steam and u, is the specific internal energy of the steam. Values of the temperature are guessed, and along with the specific volume of the steam (which is known), are used to determine the other properties of the steam. These values are then used to solve for the error, TEMP. When TEMP is a sufficiently small fraction of the total gas internal energy, the final guess is taken as the gas temperature. For further discussion, see reference[2]. 2.2.4 Natural Convection Heat Transfer The heat transfer coefficients for convective heat transfer between surfaces and gases h are calculated from the temperature of the surface T,, the temperature of the gas T9, and the density of the gas p,: h = CF(T,,T, pg) (3) where C is a user defined constant. In the presence of steam the hest transfer coefficients used are the Uchida heat transfer coefficients determined empirically as functions of the ratio of the mass of water to the mass of non-condensibles in the cell atmosphere. A more detailed description is given in reference[2]. 2.2.5 Conductive Heat Transfer Once the heat capacities, the radiative interchange factors and the convective heat transfer coefficients for all of the nodes have been calculated, the thermal resistances between the nodes are calculated. Knowledge of the thermal resistance allows the temperature rate of change due to heat conduction and heat convection to be calculated. In LITFIRE the thermal resistance between adjacent nodes i and j is calculated as follows: + (4) 2k, A 2kA or I. i= A + 1 _A (5) where 1, = characteristic length (thickness) of node n kn = thermal conductivity of node n A = area of contact between nodes i and j hij = convective heat transfer coefficient between nodes i and j, depending on whether or not node j is a solid (Equation 4) or a gas (Equation 5). 8 The thermal resistance between the lithium pool and the combustion zone is determined somewhat differently, as the lithium is considered to vaporize and then react with the gases in the combustion zone. Details of the calculation are given in reference[2]. 2.2.6 Temperature Rates of Change The rates of heat transfer between all thermally adjacent nodes are calculated from the temperatures of the nodes, and the thermal resistances and radiative interchange factors between them. Once the rates of heat transfer to and from all of the nodes have been calculated, they are summed for each node, and the temperature rate of change of each node is calculated using its own heat capacity. The heat flow to or from a given node is determined by summing the heat flow by conduction, convection and radiation to and from thermally adjacent nodes: Q (T1-Ti)+Z O+ fT where: p AifIjo(T14 - T ) Q1 = (T Q, = heat flow rate to or from node 1 T, = temperature of node n i = designation for physically adjacent node Rli = thermal resistance between nodes 1 and i 6 (6) (see Eqns. 4 and 5) = designation for optically adjacent node A 1 = surface area of node 1 fij = radiative interchange factor between nodes 1 and j Temperature rates of change for each node are calculated by dividing the energy gain or loss rate by the heat capacity of the node: j Q, dT1 dt (7) ii - where t is time, mI is the mass of node 1 and cp is the specific heat of node 1. The combustion zone node adds the heat of combustion and the heat of vaporization of the lithium combusted to the above terms, while the lithium pool subtracts the heat of vaporization of the lithium combusted. That is due to the assumption that the lithium reaction takes place in the vapor phase. 2.2.7 Lithium Combustion The temperature rates of change in the containment can differ greatly depending whether or not the lithium pool is actually combusting (reacting with the containment atmosphere). The criteria used to determine whether or not the lithium is combusting are: 9 9 Liquid lithium must be available (between 180 and 13470C) " Oxygen, nitrogen, carbon dioxide or water vapor must be available * If only nitrogen is present, the combustion zone temperature must be less than 11270C If none of the above conditions are met, then the combustion zone is considered to be nonexistent, and heat transfer from the lithium to the rest of the containment building is performed normally. If combustion is occurring, then the combustion rate and the heat liberated by the lithium reactions is calculated. In LITFIRE the lithium combustion rate is governed by the flow rate of gas or (if lithium-lead is being burned) the diffusion of lithium to the combustion zone. The gas flow rate is determined by natural convection using Reynold's analogy between heat and mass transfer. Once the gas flow rate to the combustion zone has been calculated, the lithium reaction rate may be calculated. The lithium is assumed to react with the gas quickly as it flows to the combustion zone, unless the chemical kinetics serves to further limit the reaction rate. The unhindered lithium reaction rate is given by: RRu = Apoo RR; (8) where RR, = hmpiR., where Apool hm p; R1, (9) = = = = surface area of the lithium pool natural convection mass transfer coefficient total density of the gas i (mass/containment volume) stoichiometric combustion ratio between lithium and the gas i (mass of lithium/mass of gas) The kinetics of the lithium reactions with nitrogen, oxygen and steam may serve to either reduce the reaction rates below those expected from the gas flow rate to the reaction site. After the gas flow rates of each of the constituent gases of the atmosphere have been determined, reaction kinetics effects are applied to the preliminary reaction rates to determine their final values. Lithium reaction kinetics are covered in detail in reference[2]. Once the reaction rates have been calculated, the heat generated by combustion is calculated by summing the products of the reaction rates RR; and the heats of combustion AH; of each of the reacting gases: Q= RR.AHi 10 (10) 2.2.8 Overpressure, Leakage, and Aerosol Behavior The masses of each cell gas component and the cell gas temperature are integrated in the integration section. From this, the cell gas pressure is determined and thus leakage from containment can be calculated. Aerosol adhesion to the containment walls is a user specified option and changes the concentration of aerosol combustion products in the containment atmosphere. 2.2.9 Integrals All time rates of change are integrated over each time step to calculate the values of the quantities during the execution of the code. The form of the integrals is: P = INTGRL P., - (11) where P, is the initial value of function P (mass, temperature or energy), and 4 is the time dependent rate of change of P. INTGRL is an integration function that uses a fourth order Runge-Kutta Method or Simpson's Rule (user specified) to simultaneously solve all of the differential equations used in the code. For a more detailed description, see the listing of the code, Appendix F. 2.2.10 Termination Checks The conditions that will terminate the code are: " the lithium temperature reaches a value at which the lithium vaporizes (13470C) or solidifies (1800C) " the primary cell gas temperature returns to ambient temperature with no overpressurization " the code reaches the user specified stopping point (TIME>TIMEF) 2.2.11 Time Step Control Three criteria are used to determine the size of the time step used during each dynamic cycle. They are: 1. The time step must be smaller than a user defined fraction of the inverse rates of change: DELT < RELERR T/ 11 (-) 2. The conduction heat transfer limit must be satisfied: aLatat< (AX)2 0.3 3. The user imposed maximum and minimum time steps must be observed. The maximum time step is indicated by DELOUT and the minimum by DTMIN. DELOUT and DTMIN are read from the first input file. 2.2.12 Output Section The output from LITFIRE is written into data files as the code is executed. Examples of the output files are shown in Appendix E, generated by the input files found in Appendix D. 2.2.13 Error Pointers This section is not actually part of the dynamic cycle, although if an error during execution should occur, an error message would be written into file outl.dat and code execution would halt. 2.3 Modeling Options The basic version of LITFIRE is capable of simulating a wide variety of spill conditions as indicated by the user in the first input data file. The containment volume, height, wall and floor areas, atmosphere, and material composition may be specified as well as the mass and surface area of the lithium spilled. Optional reaction geometries include a primary cell containing the lithium, surrounded by a larger secondary cell; a partially insulated pan holding the lithium inside the basic primary cell; or a primary cell surrounded by blanket and shield structures producing decay heat, further surrounded by a larger secondary cell. A concrete floor and wall for the containment are optional as is a liquid metal-concrete reaction routine. Also instead of elemental lithium, a lithium-lead eutectic may be selected for the spill with the composition chosen by the user. Finally an option to simulate a lithium or lithium-lead spill in the presence of a steam-air atmosphere may be chosen. In addition to the above options, several options involving the mitigation of lithium fires are available. These include: " gas flooding " emergency space cooling " emergency floor liner cooling " aerosol removal 12 * gas injection Each option is discussed below. 2.3.1 One Cell Option The single cell model is the simplest version of LITFIRE that may be run. All other options are constructed as subroutines added on to the one cell version of the code. The nodes existing in the one cell version are shown in Figure 1 There may be up to twenty concrete wall or floor nodes of any thickness. As stated earlier all material properties may be chosen by the user as may the composition of the containment atmosphere. Lithium or lithium-lead may react with any mixture of oxygen, nitrogen or water vapor and lithium only may react with carbon dioxide in the absence of oxygen. Any inert gas may also be included in the cell atmosphere. Lastly, any containment or spill geometry may be chosen as stated above. The heat transfer correlations are fixed by the code so that accurate results may be obtained, although some modification is possible from the input data as shown in Section 2.2.4. The heat transfer pathways are also fixed by the code and are shown in Figure 1. The heat transfer mechanisms and their applications to the code are further discussed in reference[2]. 2.3.2 Two Cell Option The two cell option was developed to model the effects of a fire inside a tokamak fusion reactor and to determine its effects on the structural integrity of the the torus. In this option a separate secondary cell with its own material composition, atmosphere and geometry exists surrounding the primary cell. (See Figure 1) The provision for a crack between the primary and secondary cells, allowing the exchange of cell gases also exists. The code follows the composition, pressure and temperature of both cell gases during the run. The heat and mass flow paths in two cell LITFIRE are shown in Figures 2 and 3. High velocity gas flows, as would be encountered in the event of a breach in a vacuum torus have been successfully modeled by LITFIRE. (See reference[3]) 2.3.3 Pan Option Figure 4 shows the pan option available in LITFIRE. This option may be used with either the one or two cell option, but not with the concrete reaction option. This option was created to model the lithium fire experiments performed at HEDL. The pan dimensions and composition are user defined. The pan is surrounded by two separate insulation nodes. 13 Wall Liner Ambient Cell Gas Combustion Zone- iAhUM Conret WYl CConcrete JPool lor Liner FWalr Concete loor- Conductive Heat Transfer -Convective Hent Transfer ----- Radiative Heat Transfer Figure 1: One-cell option in LITFIRE 14 H Secondary Cell Gas Primary Wall Ambient Primary Cell Gas Crack. S S S S Combustion Zone S S S S I rimary Floor Secondary Wall Liner N __ Secondary Floor Liner Concrete Wall Concrete Floor - Conductive Heat Transfer Convective Heat Transfer --- 0.Radiative Heat Transfer Figure 2: Two-cell option in LITFIRE 15 Gas St rge 02, CG2 Ambient N2, Inert Gas Storage Injection Gass m Game and Aeosols via leakage Cell Gas Inert Gas Flooding ConstiPrimary Cell Gas blents Secondary Cell Gas via Crack AmolRemovol via sticking to WaI Primary Wal H2 ,OsN Cj and innt gases via convection and diffusion Combustion zone Solid Reaction Products (LiN, Li 20, Li 2C 2, Li2CO3 , an C) Uithium Pool Reaction Products (LiOH, Li 3N, LiW, H2. Li2CO) UWhimn via vqpri" and diffusion Figure 3: Mass flow in LITFIRE 16 Cell Gas Wall Liner Ambient N1 s... Combustion Z )L P' Steel Pan Lithium Pool ] II Pan Insulation I a Floor Liner Concrete Wall Concrete Floor - Conductive Heat Transfer Convective Heat Transfer Radiative Heat Transfer Figure 4: Pan option in LITFIRE 17 2.3.4 Concrete Reaction The liquid metal-concrete reaction subroutine allows for the reaction of lithium with the concrete floor under the liner. This includes lithium reactions with water driven from the concrete and certain components of the concrete itself. For further discussion, see reference[2]. 2.3.5 Lithium-Lead Combustion This option allows for the substitution of a lithium-lead eutetic in the place of elemental lithium as the source of the fire. All LITFIRE options are compatible with the lithium-lead combustion option except for the initial spray fire calculation. In addition, this option allows the user to choose either a layered or turbulent pool reaction, allowing for optimistic or pessimistic results respectively, depending on the user's view of lithium-lead fires. Reference[2] discusses the lithium-lead option in greater detail. 2.3.6 Steam-Air Atmosphere Option The steam-air atmosphere option allows for the reaction of lithium or lithium-lead with a mixture of steam and other non-condensible gases. It also includes modifications of the convective heat transfer coefficients to account for condensation and the provision for steam condensation into a water pool node above the cell floor liner. Gas temperature is determined by an iterative energy balance routine (as shown in Section 2.2.3) to account for the presence of the condensible vapor, rather than in the usual integral method described earlier. The steam in the atmosphere may be present as humidity or may be injected into the primary or secondary cell atmosphere, with the time, mass flow rate and enthalpy of the steam injected selected by the user. The development of the steam-air atmosphere option is discussed in reference[2]. 2.3.7 Torus Fire Option This option allows LITFIRE to model a lithium or lithium-lead fire inside the plasma chamber of a tokamak during a loss of flow or loss of coolant accident. The reactor blanket and shield structures are represented by six extra nodes surrounding the primary cell, shown in Figure 5. During a loss of flow accident the nodes are thermally connected via conduction. During a loss of coolant accident some of them are also connected via radiation as shown in the figure. The emissivities of, and the view factors between the nodes are user specified. The radioactive decay heat generated in the first wall (primary wall and floor) and the blanket and shield structures is included as an extra heat generation term for each node: dTdt q__ ,.picpi 18 (12) where: i r <L" A = = = = individual node each individual isotope in the node i initial decay heat density of an isotope r decay constant of an isotope r pi = density of node i Up to three different isotopes may be modeled in each node; the initial decay heat density and the decay coefficient are specified by the input data for each isotope. In the coding of the torus fire option, the breeder region of the blanket (see Figure 5) is represented by the node, in the two-cell option, that normally represents the secondary extraneous heat capacity. In the torus fire option, the extraneous heat capacity in the outer cell is represented by the magnets node. The torus fire option is incompatible with the two-cell, pan and concrete reaction options. 2.3.8 Mitigation Options The following is a list of options available to evaluate the effectiveness of certain techniques used to attempt to mitigate the consequences of a lithium fire: * gas flooding * emergency space cooling * emergency floor liner cooling * aerosol removal * gas injection Each option allows the user to select additional heat removal mechanisms as desired. These options are discussed further in reference[4]. 3 Execution of LITFIRE The execution of the LITFIRE code requires certain system commands depending upon the location at which it is being run. The specific commands for compiling, loading (linking), and running the code will be discussed in this section in the following order: 1. Obtaining the source code and sample input files 2. Execution on the PFCVAX 3. Execution on the MFE Crays 19 to Secondary Cell Wall Crack to Sec ondary Cell Gas .... Plasma Chamber First Wall- First Wall Breeder Manifold Shield N N Vacuum Gap Blanket Back Wall to Secondary Cell Floor - Convective Heat Transfer Radiative Heat Transfer Except across the vacuum gap, all adjacent nodes are connected via thermal conduction. Figure 5: Torus fire option in LITFIRE 20 3.1 Obtaining Copies of LITFIRE and the Input Data Files There are currently two locations at which a copy of the source code of LITFIRE can be found: the PFCVAX at MIT, and the MFE FILEM disk storage. To use the PFCVAX copy, the user must first obtain a PFCVAX account. This may be done by contacting the Plasma Fusion Center at MIT. Introductory information may be found on the VAX by using the HELP command, which will define most of the commands used on the PFCVAX. To get a copy of LITFIRE for personal use, the following commands must be used: copy [barnett.litfire]litfire.for[username]*.* This will copy the code litfire.for into the user's main directory. To get a copy of the sample input files, the copy command must also be used, substituting the following filenames for litfire.for: head.dat uwmak.w utumak.x utwmak.y uwmak.z steamop. torus. After obtaining copies of the input files, they may be viewed by using the type command or edited by using any line or text editor. (e.g. EMACS or EDT). To obtain a copy of the LITFIRE source code on one of the MFECC machines, the user must be logged onto a machine and then use the flem command to obtain a personal copy: filem read .15467 litfire This will copy litfire into the user's personal directory on that particular machine. To obtain copies of the input files, the command read .15467 flename must be used for each input file (the names are the same for MFE and the PFCVAX) while still in filem. Once copies of LITFIRE and the sample input files have been obtained, they may be moved to a different machine 'n' by using the netout command as follows: netout flename site=nma 21 3.2 Organization of LITFIRE for Execution One of the most important steps in the execution of LITFIRE is the preparation of the input data files. Most errors in code execution occur due to mistakes in the input data files. The input data files and the options they control are listed below. As stated in Section 2.3, some options are incompatible with each other. uwmak.w: one cell uwmak.x: two cell uwmak.y: pan, concrete reaction and lithium lead combustion uwmak.z: gas flooding, emergency space cooling, emergency floor liner cooling, aerosol removal and gas injection steamop.: steam injection with steam-air atmosphere torus fire torus.: 3.2.1 One Cell Option The one cell option is the simplest version of LITFIRE. The first input file must exist to run any other code options. The order in which the input variables must appear in the file uwmak.w is shown below (British units are given in the Glossary, SI units may be used for all input data files by setting the input variable IFLAGISI = 1): 22 variables line 1 IFLAGW,IFLAGF,IFLAGP,IFLAG2,IFLAGS,IFLAGC, 2 3 4 IFLAGU,IFLAGB,IBLOW,IESC,ISFLC,ISWICH, IAROSL,IFLAGD,IFLAGISI,IFLAGCO,IFLAGT IFLAGR NL,NL1 L(1) to L(NL) L1(1) to L1(NL1) 5 6 7 VP,CHP,CPAP,XMOLA TEHCZP,XMEHCPAEHCPCPEHCP,HINECP THWC,THFC,GAP,KGAP,KLEAK 8 9 10 11 ESTLWP,CPSWP,KSTLWP,RHSWPAWP,THWP ESTLFP,CPSFP,KSTLFP,RHSFP,AFPTHFP EMLI,CPLI,AKLI,RHLI EMCONC,CPCON,KCON,RHCON 12 13 RHOLIO,RHOLIN,RHOLIH,EMGPF,EMCZ,TAUCZ QCO1,QCO2,QCN,QCW,QCW2 14 15 RCMB01,RCMBO2,RCMBN,RCMBW,RCMBW2,RCMBH2 TMELT,TVAP,QVAPPERCEN 16 CONF1,CONF2,C2FAC,FLIOH,FLI20 17 18 19 20 21 22 HIN,HINGSPHINGSS,HINPS,HINSAM,HINFAN HINFGS,HINFSG ASLI,SPILL,SPRAY,FRA,RA TCZI,TGPZER,TSPZER,TSFPI,TA,TLII PAPZER,WO2P,HUM,WAPWCP IMETH,DTMIN,TIMEF,RELERR,DELOUT,OUTPUT The formats for the input lines are: line 1 2 3,4 format (1x,14(il,1x)) (i4,i4) (10f5.3) 5 (f12.2,3f12.4) 6-21 22 (6f12.4) (i4,5f12.4) An example of this data file (British units) is uwmak.w in Appendix D. PFCVAX The statement: open(unit=2,file='uwmak.w',status='old' must be included in the code for the code to execute, assuming that the input data file is named uwmak.w. A similar OPEN statement must be included for each input data 23 file used by the code. These statements are currently located after the "common" blocks at the beginning of the code. MFE Crays For these machines the statement: call link("unit1=filename,read1//") must be used for each input data file. These statements are also currently located after the "common" blocks at the beginning of the code. 3.2.2 Two Cell Option If the two cell option is chosen, the following are the variable listing and formats for the second data file (units are given in the glossary as for the first input file): line 1 2 3 4 5 6 variables VS,CHS,PASZER,TGSZER,TSSZER,TFSZER CRACK,HUM2,WO2S,WAS,CPAS,WCO2S TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS TSWICH The format for all lines is: (6f12.4) PFCVAX If this option is used, the statement: open(unit=3,jle=flen. ame',status='old') must be included in LITFIRE in the same place as the OPEN statement for the first input data file. An example of this data file (British units) is given in Appendix D. MFE Crays For these machines, the statement: call link("unit3=flename,read3//") must be used in the same location as the CALL LINK statement for the first input data file. 24 3.2.3 Pan, Concrete Reaction and Lithium-Lead Combustion The following is a variable listing for each of the above options (British units are given in the Glossary): t: line 1 2 3 Pan Option variables KPAN, RHPAN,CPPAN,RHINS,CPINS,EMINS TPANZO,APAN,BREDTH,AINS,HINGPF THKPAN,THKIN1,THKIN2 line 1 Concrete Reaction Optiont variables ZZDIN,QCCONC,CRACON,XMH2OI,TCIGNI,RCMBC line 4(1) 5(2) Lithium-Lead Optiont variables CPLEAD,KLEAD,RHLEAD,ALLOYI,QDISS,CPLIPB DFLVAR The pan option cannot be chosen with the concrete reaction option. t: Lithium-lead data is entered on line 1 if the concrete reaction option is not chosen. The format for all lines except 5(2) for the lithium-lead option is: (6f12.4) The format for line 5(2) is: (e12.5) PFCVAX The statement: open(unit=4,fle='len. ame ',statu='old') must be used. An example of this file (British units) is given in Appendix D. MFE Crays For these machines, the statement: call link("unit4=flename,read4//") must be used in the same location as the CALL LINK statement for the first input data file. 25 3.2.4 Gas Flooding, Emergency Space Cooling, Emergency Floor Liner Cooling and Gas Injection Each of these options is included in one input data file. The following is a variable listing for each of the options. Only the variable lines of the options used need be entered, although the lines used must be in the order shown below (British units are given in the Glossary): line 1 (gas flooding) 2 3 4 5 6 (emerg. space cooling) (emerg. floor cooling) (aerosol removal) (gas injection) The format for lines 1-5 is: variables WO2B,WWAB,WN2B,XMOLAB,CPAB,TBLOW BLOWV,EXHSTV,TBLIN,TBLOUT,WAB ESCR,ESCTIN,ESCEND SFLCR,SFLTIN,SFLEND BETA TONE,TTWO,TTHREE,DP1,DP2,DP3,FCT1,FCT2,FCT3 (6f12.4). For the gas injection option (line 6) it is: (3f10.2,6f8.4). PFCVAX The statement: open(unit=5,file='filen.ame',status='old') must be used. An example of this file (British units) is given in Appendix D. MFE Crays For these machines, the statement: call link("unit5=filename,read5//") must be used in the same location as the CALL LINK statement for the first input data file. 3.2.5 Steam Injection to Containment The following is a variable listing for the steam injection to containment available in the steam-air atmosphere option (British units are given in the Glossary): line variables 1 STMIN,STMOUT,MINJR,HINJ 2 STMIN2,STOUT2,MINJR2,HINJ2 The format for all lines is: (6f12.4) 26 PFCVAX The statement: open(unit=6,file=' ilen.ame',status='old') must be used. An example of this file (British units) is given in Appendix D. MFE Crays For these machines, the statement: call link("unit6=filename,read6//") must be used in the same location as the CALL LINK statement for the first input data file. 3.2.6 Torus Fire The following are the variable listing and the formats for the torus fire option. (British units are given in the Glossary). variables line 1 VS,CHS,PASZER,TGSZER,TSSZER,TFSZER 2 CRACK,HUM2,WO2S,WAS,CPAS,WCO2S . TEHCZS,XMEHCS,AEHCS,CPEHCS,HINECS,KEHCS 3 4 ESTLWS,CPSWS,KSTLWS,RHSWS,AWS,THWS 5 ESTLFS,CPSFS,KSTLFS,RHSFS,AFS,THFS CLEHCS,EEHCS,EBLI,EFWI,VIEWM 6 TSHLZ,THSHL,KSHL,XMSHL,CPSHL,ASHL 7 8 ESHL,HINSHL,TMAGZ,AMAG,XMMAG,CPMAG HINMAG,KHE,THE,LOCA,VIEWG,VIEWB 9 10 KBLI,THBLI,CPBLI,ABLI,XMBLI,TBLIO 11 TSHIO,TSHOO,THSHI,THSHO,XMSHI,XMSHO 12 THMAN,XMMAN,CPMAN,AMAN,TMANO,KMAN 13 QOFW1,EXPFW1,QOFW2,EXPFW2,QOFW3,EXPFW3 14 QOBL1,EXPBL1,QOBL2,EXPBL2,QOBL3,EXPBL3 15 QOBL4,EXPBL4,QOBL5,EXPBL5,QOBL6,EXPBL6 16 QOBLI1,EXPBI1,QOBLI2,EXPBI2,QOBLI3,EXPBI3 17 QOSH1,EXPSH1,QOSH2,EXPSH2,QOSH3,EXPSH3 18 QOSHI1,QOSHI2,QOSHI3,QOSHO1,QOSHO2,QOSHO3 The format for lines 1-12 is: (6f12.4) The format for lines 13-18 is: (6e9.2) 27 PFCVAX If this option is used, the statement: open (unit=7,file='fien.ame',status='old') must be included in LITFIRE in the same place as the OPEN statement for the first input data file. MFE Crays For these machines, the statement: call link("unit7=fiename,read7//") must be used in the same location as the CALL LINK statement for the first input data file. 3.3 PFCVAX Execution To execute LITFIRE on the PFCVAX, the user must ensure that all necessary OPEN statements are included for the data files necessary to run the code as indicated in Section 3.2. The input data file head.dat must always be included as it provides headings for the output data files that LITFIRE will create. The statement necessary to include head.dat is: open(unit=1,fie='head.dat',status='old') It should be noted that all input data files must be in the same directory as LITFIRE in order to execute the code. OPEN statements are also needed for the output files created by LITFIRE. These statements are placed right after the OPEN statements for the input data files and take the form of: open (unit=1Ofile='outl.dat',status='new') There are ten output data files named outl.dat through outlO.dat, and an OPEN statement is needed for each one. Optional output files may be created to allow graphs to be made of code variables vs. time. These files may be used in conjunction with the graphics routines available on the PFCVAX to create the actual graphs. The optional files require OPEN statements like the ones for outl.dat through outlO.dat, but use the filename forOnn.dat, where nn is any number from 01 to 99. Steps must be added to the code in the output section to write values of TIME and the variable desired to the file. Some optional output file OPEN and WRITE statements which have been commented out may be found in the appropriate sections of the code. The output files created may be used with the McCool graphics routine available on the PFCVAX to create the graphs. There are three separate steps involved in the execution of LITFIRE: compiling, linking and running the code. To compile LITFIRE, the command: 28 for litfire.for must be used and will create the file litfire.obj. To link LITFIRE, the command: link litfire.obj must be used and will create the file litfire.exe. To run LITFIRE, the command: run litfire.exe must be used. If the input data files were entered properly, the code should run until terminated by a user defined time limit (i.e., TIME=TIMEF) or by the code itself. (e.g., 'the temperature of the lithium pool has reached the melting point'). If the code stops due to an error, an error message will be given. Refer to Appendix C-Troubleshooting. 3.4 MFE Crays Execution To execute LITFIRE on the Crays, the necessary CALL LINK statements must be present for all of the input data files as indicated in Section 3.2 The input data file head.dat must be included to provide headings for the output data files that LITFIRE will create. The statement needed to include head.dat is: call link("unitl=head.dat,readl//") CALL LINK statements are needed for the ten output files as well. Those statements take the form of: call link("unitl0=(outi,text, create),printl//") for each of the ten output files outi through out10. They should be placed directly after the CALL LINK statements for the input data files. To compile, load and run LITFIRE on the Crays, the following commands should be used: rcftti=itfire,x=xlitfire/ t p xitfre / t p where t is the total CPU time allowed in minutes and p sets the priority of the run. One minute and a priority of 2 should be sufficient to run xlitfire unless the steam option is being used, in which case up to five minutes may be required (and the priority would be 10). t: on the b machine, civic should be used instead of rcft. 29 I 3.5 Sample Input and Output Files To check whether LITFIRE has been properly executed, a set of sample input and output files are given in Appendices D and E. Execution of the code using the sample input files on the PFCVAX or the Crays will produce approximately the same results as given in the sample output files. Using the input data files: head.dat, uwmak.w, uwmak.x, uwmak.y, uwmak.z, steamop., torus., the following output files should be generated: outl.dat, out2.dat, out3.dat, out4.dat, out5.dat, out6.dat, out7.dat, out8.dat out9.dat, outlO.dat, blank It should be noted that only the input files head.dat, uwmak.w and uwmak.x were used for the examples in the Appendices. 30 A Nomenclature heat transfer surface areas user defined heat transfer correlation constant specific heat specific heat at constant volume radiative interchange factor, including emissivity f heat of combustion AH convective heat transfer coefficient h h. convective mass transfer coefficient k, ki thermal conductivity characteristic length L, l;, mass Mm decay heat density q'" Q, dq/dt heat flow rate thermal resistance R;,j reaction rate RR t time temperature T A C C, c', U specific internal energy U, x a 0 p a total internal energy linear distance thermal diffusivity coefficient of volumetric expansion density Stefan-Boltzmann constant 31 B Variable Listing AA ABLI ACTVTY AEHCP AEHCS AFP Exponent used in expression for GRPR or GRPRF Cross sectional area of the blanket back wall (ft2 ) Calculates activity of lithium in lithium-lead eutectic Surface area of primary extraneous heat capacity (ft2 ) Surface area of secondary extraneous heat capacity (cross sectional area of breeder with torus fire option) (ft 2 ) Surface area of primary floor liner, must be equal to or greater than the area of the lithium spill ASLI. (ft2 ) AFS Surface area of the secondary floor liner (ft 2 ) AHT Area of the lithium pool-pan interface (ft2 ) AINS AIRFAC AK AMAG AMAN AMIN1 APAN Outside exposed area of insulating layer on the pan (ft2 ) Density weighting factor for calculating steam-air mixture properties Product of thermal conductivity and Prandtl number of the primary gas (BTU/sec-ft deg. F.) See associated film temperature T1. Function used to calculate heat transfer coefficients Thermal conductivity of lead (input as BTU/hr-ft deg. F.) Thermal conductivity of lithium (input as BTU/hr-ft deg. F.) Thermal conductivity of lithium used during LC-2 lithium transfer simulation (BTU/sec-ft-deg. F.) Product of thermal conductivity and Prandtl number of water vapor at the lithium pool surface (BTU/sec-ft deg. F.) Initial atom percent of lithium in lithium-lead Used to determine whether or not LILP should be fixed at an amount equal to AKLI/(RHLI*CPLI) Used in determining PYU. Also tests conduction limit on time step for the pan or floor liner. Surface area of the magnets (secondary extraneous heat capacity) (ft 2 ) Cross sectional area of the blanket manifold (ft2 ) FORTRAN function that determines the minimum of the arguments used Pan external heat transfer area (ft 2 ) ASHL ASLI Outer surface area of the reactor shield (ft2 ) Surface area of the lithium spilled (ft2 ) ASURF Surface area of the liquid water pool (ft 2 ) AWP Surface area of the primary wall liner (ft2 ) AWS B Surface area of the secondary wall liner (ft2 ) Used in calculating the thermal resistance between the wall liner, the gap and the wall concrete Analogous to B, but for the floor liner, gap and concrete Coefficient of volumetric expansion for gas (0) (1/deg. F.) See associated film temperature T1 AKEXX AKLEAD AKLI AKLIX AKVAP ALLOYI ALPHA ALPHA2 BB B1 32 BETA BETAB BETAF BIL BILGE BLIN BLOUT BLOWR BLOWV BREAKS BREDTH Cxxx C1 C2 C3 C4(i) 05 06 C7 C8 C9 C10(i) C11 C12 013 C14 C15 C16 C17 018 C19 C20 C21 C22 C23 C2FAC CA 'C'BIMAN Inverse sticking coefficient for particles impinging on the wall (sec.) Volumetric expansion coefficient 3 for the water pool-gas boundary (1/deg. F. Volumetric expansion coefficient P for the water pool (1/deg. F.) Fractional change between BILGE and DELT, used in determining minimum time step Equal to the minimum value of DT1,DT2,DT3,DT4 or DT5, used in calculating the time step length (sec.) Time after spill at which inert gas flooding and exhaust begins (sec.) Time after spill at which inert gas flooding and exhaust ends (sec.) Inert gas input rate (lbm/sec) Inert gas volumetric input rate (ft3 /sec) Outer cell gas temperature rate of change due to gas flow between cells and leakage. (deg. R./sec) Perimeter of the pan (ft) 'C' is used to indicate a thermal admittance between nodes (i.e., the inverse of the product of effective thermal resistance between the nodes and the heat capacity of one of them (hA/mc,) (sec-) Primary gas to primary wall liner in gas Pan to primary gas in gas Wall liner to concrete in concrete Concrete wall node i to node i+1 in concrete Concrete wall to ambient in concrete Primary gas to primary wall in wall liner Wall liner to concrete in wall liner Floor liner to concrete floor in floor liner Floor liner to concrete floor in concrete Concrete floor node i to node i+1 in concrete Wall liner to ambient (no concrete option) in wall liner Floor liner to ambient (no concrete option) in floor liner Pan to primary gas in pan Secondary floor liner to secondary gas in floor liner Secondary floor liner to secondary gas in gas Primary floor liner to primary gas in floor liner Primary floor liner to primary gas in gas Primary floor liner to secondary gas in floor liner Primary floor liner to secondary gas in gas Primary wall liner to secondary gas in wall liner Secondary wall liner to secondary gas in wall liner Primary wall liner to secondary gas in gas Secondary wall liner to secondary gas in gas Fraction of Li-CO 2 reaction which produces Li 2 C 2 Coefficient in expression for GRPR or GRPRF Blanket back wall to manifold in manifold 33 'C'BLMAN CCZ 'C'CZP CD 'C'EHCGP 'C'EHCGS 'C'EHCSH 'C'EHCFP 'C'EHCWP 'C'FPEHC 'C'GCZ 'C'GLI 'C'GPEHC 'C'GSEHC 'C'GSMAG 'C'GSSHL CHP CHS 'C'IN1PN 'C'IN12 'C'IN21 CLEHCS 'C'LIG 'C'LIPAN 'C'LIST 'C'MAGGS 'C'MANBI 'C'MANBL CMBR CMBRC2 CMBRCO CMBRH CMBRHH CMBRHI CMBRN CMBRNH CMBRO CMBRO1 CMBRO2 CMBROH CMBRW Breeder to manifold in manifold Heat generation rate in the combustion zone (BTU/sec) Lithium pool to combustion zone in pool Coefficient of discharge between the two cells (nea.r unity) Primary extraneous heat capacity to primary gas in gas Secondary extraneous heat capacity to secondary gas in gas Blanket back wall to shield inside region in shield inside region First wall (floor) to breeder in first wall (floor) First wall to breeder in first wall First wall (floor) to breeder in breeder Combustion zone to primary gas in combustion zone Lithium Pool to primary gas (no combustion) in pool Primary gas to primary extraneous heat capacity in heat capacity Secondary gas to secondary extraneous heat capacity in heat capacity Secondary gas to magnets in magnets Shield outside region to secondary gas in shield outside region Primary cell optical path length (ft) Secondary cell optical path length (ft) Pan to inner insulation in insulation Inner pan insulation to outer pan insulation in inner insulation Inner pan insulation to outer pan insulation in outer insulation Thickness of the breeder node (ft) Lithium pool to primary gas (no combustion) in gas Lithium pool to pan in pool (suspended pan option) Lithium pool to primary floor liner in pool Magnets to secondary gas in secondary gas Manifold to blanket back wall in blanket back wall Manifold to breeder in breeder Total combustion rate (lb Li/sec-ft2 ) Combustion rate for the carbon reaction (lb Li/sec-ft 2 ) Combustion rate for the lithium-carbonate producing reaction (lb Li/sec-ft 2 ) Total combustion rate (lb Li/hr-ft 2 ) CMBRH in g Li/min-cm 2 Initial combustion rate (lb Li/hr-ft 2 ) Combustion rate for the nitrogen reaction (lb Li/sec-ft 2 ) CMBRN in g Li/min-cm 2 Total of CMBRO1 and CMBRO2 (lb Li/sec-ft 2 ) Combustion rate for the oxygen reaction (lb Li/sec-ft 2 ) Combustion rate for the Li-CO 2 reaction producing lithium-oxide (lb Li/sec-ft2 ) CMBRO in g Li/min-cm 2 Combustion rate for the water vapor reaction producing LiOH (lb Li/sec-ft 2 ) CMBRW2 Combustion rate for the water vapor reaction producing Li 2 0 (lb Li/sec-ft 2 ) CMBRWH CMRC2H CMRCOH C02 CO2LFS CONDR CONF1 CONF2 CPxxx CPA CPA2 CPAB 'C'PANLI CPAP CPAS CPB CPBLI CPCARP CPCO2P CPCO2S CPCON 'C'PCZ CPEHCP CPEHCS CPFAC CPH2 CPINS CPLC2P CPLC3P CPLC3S CPLEAD CPLI CPLIX CPLIH CPLIN CPLINP CPLINS CPLIO CPLIOH CPLIOP CMBRW in g Li/min-cm 2 CMBRC2 in g Li/min-cm 2 CMBRO2 in g Li/min-cm 2 A subroutine which sets up the pure CO2 atmosphere Carbon dioxide left after spray fire (lb) Condensation mass flow rate (lb/sec) Fraction of Li-CO 2 reaction which produces Li 2 0 Fraction of Li-CO 2 reaction which produces Li 2 CO 3 Gaseous specific heats are all specific heats at constant volume Primary non-condensible gas specific heat (BTU/lb deg. F.) Secondary non-condensible gas specific heat (BTU/lb deg. F.) Flooding gas specific heat (BTU/lb deg. F.) Lithium pool to pan in pan Specific heat of primary cell inert gas (BTU/lb deg. F.) Specific heat of secondary cell inert gas (BTU/lb deg. F.) Specific heat of the water pool-gas boundary (BTU/lb deg. F.) Specific heat of the blanket back wall (BTU/lb deg. F.) Specific heat of carbon in the primary gas (BTU/lb deg. F.) Specific heat of carbon dioxide in the primary gas (BTU/lb deg. F.) Specific heat of carbon dioxide in the secondary gas (BTU/lb deg. F.) Heat capacity of floor and wall concrete (BTU/lb deg. F.) Lithium pool to combustion zone in combustion zone Specific heat of primary extraneous heat capacity (BTU/lb deg. F.) Specific heat of secondary extraneous heat capacity (breeder with torus fire option) (BTU/lb deg. F.) Used in calculating CPLI (CPFAC=.004938TL-6.20741) Specific heat of hydrogen gas (2.48 BTU/lb deg. F.) Specific heat of insulation (BTU/lb deg. F.) Specific heat of lithium carbide in the primary gas (BTU/lb deg. F.) Specific heat of Li 2 CO 3 in the primary gas (BTU/lb deg. F.) Specific heat of Li 2 CO 3 in the secondary gas (BTU/lb deg. F.) Specific heat of pure lead (BTU/lb deg. F.) Specific heat of lithium (BTU/lb deg. F.) Specific heat of lithium (used during LC-2 lithium transfer simulation (BTU/lb deg. F.)) Specific heat of lithium hydroxide (0.67 BTU/lb deg. F.) Specific heat of lithium nitride (BTU/lb deg. F.) Specific heat of lithium nitride in primary (BTU/lb deg. F.) Specific heat of lithium nitride in secondary (BTU/lb deg. F.) Specific heat of lithium oxide (BTU/lb deg. F.) Molar specific heat of lithium hydroxide (BTU/lb-mol deg. F.) Specific heat of lithium oxide in primary (BTU/lb deg. F.) 35 CPLIOS CPLIPB CPLV CPMAG CPMAN CPMCOP CPMCOS CPMCZ CPMH2 CPMLCP CPMLCS CPMLOP CPMLOS CPMNIP CPMNIS CPMOXP CPMOXS 'C'PNIN1 CPN2P CPN2S CPSFP CPSFS CPSHL CPSWP CPSWS CPWV CRACON CRACK 'C'SBLI 'C'SHEHC 'C'SHISH 'C'SHLGS 'C'SHOSH 'C'SHSHO 'C'SHSHI CSTM CSTMA CSTMN DAB DCOCZ DECBL Specific heat of lithium oxide in secondary (BTU/Lb deg. F.) Specific heat of lithium-lead (BTU/lb deg. F.) Specific heat of water for secondary floor liner-secondary water pool heat transfer (at TAVE) (BTU/deg. F.) Specific heat of the magnets (secondary extraneous heat capacity) (BTU/lb deg. F.) Specific heat of the manifold (BTU/lb deg. F.) Heat capacity of carbon dioxide in primary (BTU/deg. F.) Heat capacity of carbon dioxide in secondary (BTU/deg. F.) Effective heat capacity of combustion zone (BTU/deg. F.) Heat capacity of hydrogen in containment (BTU/deg. F.) Heat capacity of lithium carbonate in primary (BTU/deg. F.) Heat capacity of lithium carbonate in secondary (BTU/deg. F.) Heat capacity of lithium oxide in primary (BTU/deg. F.) Heat capacity of lithium oxide in secondary (BTU/deg. F.) Heat capacity of nitrogen in primary (BTU/deg. F.) Heat capacity of nitrogen in secondary (BTU/deg. F.) Heat capacity of oxygen in primary (BTU/deg. F.) Heat capacity of oxygen in secondary (BTU/deg. F.) Pan to inner insulation in pan Specific heat of nitrogen gas in primary (BTU/lb deg. F.) Specific heat of nitrogen gas in secondary (BTU/lb deg. F.) Specific heat of primary floor liner (BTU/lb deg. F.) Specific heat of secondary floor liner (BTU/lb deg. F.) Specific heat of the reactor shield (BTU/lb deg. F.) Specific heat of primary wall liner (BTU/lb deg. F.) Specific heat of secondary wall liner (BTU/lb deg. F.) Specific heat of water vapor in primary (BTU/lb deg. F.) Area of concrete exposed to lithium in concrete combustion model (ft 2) Area of the orifice between the two cells (square inches) Lithium pool to primary floor liner in floor liner Blanket back wall to shield inside region in blanket back wall Shield bulk to shield inside region in shield bulk Shield outside region to secondary gas in secondary gas Shield bulk to shield outside region in shield bulk Shield bulk to shield outside region in shield outside region Shield bulk to shield inside region in shield inside region Steam catalytic factor Steam catalytic factor in air Steam catalytic factor in nitrogen Diffusion coefficient for air and water (ft2 /sec) Depth of concrete combustion zone (ft) used to calculate volume of zone for heat generation Total decay heat density in the breeder (BTU/ft3 sec) 36 DECBLI DECFW DECMAN DECSH DECSHI DECSHO DELMP DELOUT DELT DFILM DFLIPB DFLVAR DIFF DIFFLI DMPBDT DP1,..DP3 DTBDT(i) DTCDT(i) DTMIN DT1..DT5 DT1 DT2 DT3 Total decay heat density in the blanket back wall (BTU/ft3 sec) Total decay heat density in the first wall (BTU/ft3 sec) Total decay heat density in the manifold (BTU/ft3 sec) Total decay heat density in the shield bulk (BTU/ft3 sec) Total decay heat density in the shield inside region (BTU/ft3 sec) Total decay heat density in the shield outside region (BTU/ft3 sec) Fractional exchange rate of primary gas used in determining the minimum time step (sec) Fractional exchange rate of secondary gas used in determining the minimum time step (sec) User defined maximum time step length (sec) Time step length (sec) Lithium vapor film thickness (ft) Diffusion coefficient for lithium through lead (ft2 /sec) Constant used to calculate DFLIPB (6.5E-08) (ft2 /sec) Gas mass diffusion coefficient to the combustion zone (ft2 /sec) Lithium diffusion coefficient to the combustion zone (ft2 /sec) Mass rate of change of lead in lead layer (lb/sec) Increase in cell gas pressure due to each injection (psi) Concrete floor temperature rate of change, node i (deg. F./sec) Concrete wall temperature rate of change, node i (deg. F./sec) User defined minimum time step length (sec) X/(dx/dt) * RELERR, used in determining the time step length (sec) X = Lithium pool temperature X = Primary gas temperature X = Primary wall liner temperature DT4 X = Combustion rate DT5 DYNAMI D1 X = Combustion zone temperature*.05 Subroutine used in controlling integration loops Kinematic viscosity of the cell gas (squared) at the film temperature (ft4 /sec 2 ), See related film temperature Ti. Thermal emissivity of the interior of the blanket Thermal emissivity of the exterior of the blanket (facing the shield) Thermal emissivity of the interior of the first wall Film depth of depleted zone above combustion zone (in) Thermal emissivity of concrete Thermal emissivity of combustion zone Used in fixing minimum emissivity of the lithium pool (.9 in code) Thermal emissivity of primary gas (minimum of .005 in code) Constant used in determining EMGP, usually chosen at .04 Thermal emissivity of secondary gas (minimum of .005 in code) Thermal emissivity of pan insulation DELMS EBLI EEHCS EFWI EFILM EMCONC EMCZ EMF EMGP EMGPF EMGS EMINS 37 (There is no page 38.) EMLI ESCR ESCTIN ESHL ESTAIR ESTLFP ESTLFS ESTLWP ESTLWS EW1 EXHSTR EXHSTV EXPBIn EXPBLn EXPBLn EXPSHn EXX Thermal emissivity of lithium pool Heat removal rate by emergency space cooling (BTU/sec) Time after spill when ESCR begins (sec) Thermal emissivity of the reactor shield Thermal emissivity of the cell steam-air mixture (without aerosols) Thermal emissivity of the primary floor liner Thermal emissivity of the secondary floor liner Thermal emissivity of the primary wall liner Thermal emissivity of the secondary wall liner Thermal emissivity of water vapor at one atmosphere and cell temperature Rate of primary gas exhaust (lb/sec) Rate of primary gas exhaust (ft3 /sec) Decay constant of decay heat producing isotope in the blanket back wall 1 (n=1-3) (sec- ) Decay constant of decay heat producing isotope in the breeder node (n=1-3) (sec-) Decay constant of decay heat producing isotope in the manifold (n=4-6) (sec 1 ) Decay constant of decay heat producing isotope in the reactor shield (n=1-3) (sec 1 ) Temporary variable used in calculating heat and mass diffusion coefficients (ft- 3 ) EXi Used in calculating mass and heat transfer coefficients (ft-') See related film temperature T1. FCO2P FCO2S FCT1,FCT2 FCT3 FF1,FF2 FLI20 FLIOH FMLEAK FMLEFT FNIP FNIS FOUTP FOUTS FOUTT FOXP FOXS FPG FPW FRA Weight fraction of CO 2 in primary gas Weight fraction of CO 2 in secondary gas Fraction of nitrogen in each injection (by number) Used in heat balance equations for spray fire Mass fraction of Li reacting with H2 0 that produces Li 2 0 Mass fraction of Li reacting with H2 0 that produces LiOH Fraction of mass of gas leaked out of primary Fraction of mass of gas remaining in containment Weight fraction of nitrogen in primary gas Weight fraction of nitrogen in secondary gas Loss rate of primary gas which is either exhausted or changes cells Loss rate of secondary gas which is either exhausted or changes cells Total loss rate from outermost gas tell (FOUTS+LEAK) Weight fraction of oxygen in primary gas Weight fraction of oxygen in secondary gas Radiative view factor from lithium pool to primary gas (1.0 w/o pan) Radiative view factor from lithium pool to primary wall liner Fraction of combustion products evolved into cell gas 39 FWAP FWAS GAP GAMMA GIN GRPR GRPRF Weight fraction of water vapor in primary gas Weight fraction of water vapor in secondary gas Air gap between floor liner and concrete (ft) Ratio of specific heats c,/c, (set to 1.4 in the code) Acceleration due to gravity (32.2 ft/sec2 ) Product of the Grashof and Prandtl numbers of the water pool-gas boundary Product of the Grashof and Prandtl numbers of the water pool H2LEFT Current water content of concrete (lb/ft3 ) HA HAMF Heat transfer coefficient between exterior wall and ambient (BTU/ft 2 sec deg. F.) Heat transfer coefficient between exterior floor and ambient (BTU/ft 2 sec deg. F.) Heat transfer coefficient between lithium pool and primary gas (BTU/ft 2 sec deg. F.) Equilibrium value of HB Total heat transfer coefficient between the water pool and the cell gas (BTU/ft 2 sec deg. F.) Heat transfer coefficient between primary extraneous heat capacity and primary gas (BTU/ft2 sec deg. F.) Heat transfer coefficient between secondary extraneous heat capacity and secondary gas (BTU/ft2 sec deg. F.) Heat flux to water pool from gas mixture due to evaporation ( BTU/sec-ft 2 ) Mass transport coefficient to the lithium pool (ft/sec) Latent heat of vaporization of water vapor in the primary gas (BTU/lb) Latent heat of vaporization of water vapor in the secondary gas (BTU/lb) Equilibrium value of HF (BTU/ft 2 sec deg. F.) Heat transfer coefficient between primary floor liner and primary gas (BTU/ft 2 sec deg. F.) Heat transfer coefficient between primary floor liner and HB HBINF HCOND HEHCP HEHCS HEVAP HF HFG HFG2 HFINF HFPGP HFPGAS secondary gas (BTU/ft 2 sec deg. F.) HFSGAS HGWP HINxxx HINECP HINECS HINFAM HINFGS HINFSG HINGPF Heat transfer coefficient between secondary floor liner and secondary gas (BTU/ft 2 sec deg. F.). Heat transfer coefficient between primary wall and gas (BTU/ft 2 sec deg. F.) Heat transfer coefficients are determined by LITFIRE as indicated in Section 2.2.4. The coefficients C are indicated in the code as HINxxx and are dimensionless Correlation for HEHCP Correlation for HEHCS Correlation for HAMF Correlation for HFPGAS Correlation for HFSGAS Correlation for HFPGP 40 HINGSP HINGSS HINJ HINJ2 HINMAG HINPS HINSAM HINSHL HLP HLP2 HLPFLR HMAG HPAN HPRIME HRATIO HRAT2 HSAT HSEC HSENS HSHL HTCPGP HTCPGS HU(x,y) HUCH HUM HUM2 HWPGAS HWV HWV2 I IAM IB INIT INJEC1..3 Correlation for HGWP Correlation for HSEC Specific enthalpy of steam injected to primary cell (BTU/lb) Specific enthalpy of steam injected to secondary cell (BTU/lb) Correlation for HMAG Correlation for HWPGAS Correlation for HA Correlation for HSHL Specific enthalpy of the primary liquid water pool (BTU/b) Specific enthalpy of the secondary liquid water pool (BTU/lb) Heat transfer coefficient between the liquid water pool and the secondary floor liner (BTU/ft2 sec deg. F.) Heat transfer coefficient between magnets and secondary gas (BTU/ft 2 sec deg. F.) Heat transfer coefficient between the pan and primary gas (BTU/ft 2 sec deg. F.) Increased value of HSENS due to a large condensation/evaporation rate (BTU/ft 2 sec deg. F.) Molar fraction of hydrogen in the primary gas Molar fraction of hydrogen in the secondary gas Specific enthalpy of saturated liquid water at cell pressure (BTU/lb) Heat transfer coefficient between secondary floor liner and secondary gas (BTU/ft 2 sec deg. F.) Sensible heat transfer coefficient from the water pool to the vapor mixture (BTU/ft 2 sec deg. F.) Heat transfer coefficient between the shield outside region and secondary gas (BTU/ft 2 sec deg. F.) Heat capacity of the primary gas (BTU/deg. F.) Heat capacity of the secondary gas (BTU/deg. F.) Chart of Uchida heat transfer coefficients vs. MR Uchida heat transfer coefficient for condensing steam (BTU/ft 2 sec deg. F.) Initial relative humidity of the primary cell (1.0=100%) Initial relative humidity of the secondary cell (1.0=100%) Heat transfer coefficient between primary wall liner and secondary gas (BTU/ft 2 sec deg. F.) Specific enthalpy of water vapor in the primary gas (BTU/lb) Specific enthalpy of water vapor in the secondary gas (BTU/lb) General purpose DO loop counter DO loop counter for wall and floor concrete node initialization DO loop counter for floor concrete iterations Initializing subroutine for integrations Flags for gas injection. INJECn indicates the injection has occurred. 41 INTDSx INTGRL IPAGE IPASS Interpolation factor used in reading steam tables Arithmetic statement function for finding integrals Number of lines of output between headings Used during integration routine to tell INTGRL to perform certain special functions during the first two executions of the section KAIR Thermal conductivity of non-condensible gas (air) (BTU/sec ft deg. F.) KAIRB Thermal conductivity of air at the water pool-gas boundary (BTU/sec ft deg. F.) KAIRG Thermal conductivity of air in a cell gas (BTU/sec ft deg. F.) KB Water condensation mass transfer coefficient (lb mol/sec-ft 2 ) Thermal conductivity of the blanket back wall (BTU/hr ft deg. F.) KBLI KBNDRY Thermal conductivity of the water pool-gas boundary (BTU/sec ft deg. F.) KCON Thermal conductivity of concrete (input as BTU/hr ft deg. F.) KEHCS Thermal conductivity of the breeder node (BTU/hr ft deg. F.) KFILM Thermal conductivity of pool/combustion zone film (BTU/sec ft deg. F.) KGAP Thermal conductivity of the gap between the liner and concrete (BTU/hr ft deg. F.) KH20 Thermal conductivity of water vapor (BTU/sec ft deg. F.) KH2OB Thermal conductivity of water vapor at the water pool-gas boundary (BTU/sec ft deg. F.) KH2OG Thermal conductivity of water vapor in a cell gas (BTU/sec ft deg. F.) KHE Thermal conductivity of the vacuum (He filled) gap (BTU/hr ft deg. F.) KIN1 Thermal conductivity of inner insulation layer (BTU/hr ft deg. F.) KIN2 Thermal conductivity of outer insulation layer (BTU/hr ft deg. F.) KLEAK Leak rate constant from containment (sec- 1 psi- 0 5) Reference value: 2.588-10' KMAN Thermal conductivity of the manifold (BTU/hr ft deg. F.) KPAN Thermal conductivity of the pan (BTU/hr ft deg. F.) KSHL Thermal conductivity of the reactor shield (BTU/hr ft deg. F.) KSTLFP Thermal conductivity of the primary floor liner (BTU/hr ft deg. F.) Thermal conductivity of the secondary floor liner (BTU/hr ft deg. F.) KSTLFS KSTLWP Thermal conductivity of the primary wall liner (BTU/hr ft deg. F.) KSTLWS Thermal conductivity of the secondary wall liner (BTU/hr ft deg. F.) KWAT Thermal conductivity of liquid water (BTU/sec ft deg. F.) L Thickness of a wall concrete node (ft) Li Thickness of a floor concrete node (ft) LEAK Gas leakage rate from outermost cell (sec 1 ) LEAKO Initial gas leakage rate from outermost cell (sec- 1 ) LIBP Lithium consumed in pool fire (lb) LIL Amount of lithium remaining in pool-limited to LIT/10 for numerical stability during calculations LILC2 Amount of Li 2 C 2 in the pool (lb) LILCA Amount of Li 2 CO 3 in the pool (lb) 42 LILCAR LILNI LILOX LILP LIS LIT LOCA MAIP MAIS MAIRP MAIRS MAP MAS MBOIL MCO2IP MCO2IS MCO2P MCO2S MCONDE MCONDF MCONDP MCONDW MCONFP MCONWP MFAB MFAG MFVB MFVG MGB MH2P MH2S MINJR MINJR2 MLC2P MLC2S MLC3IP MLC3IS MLC3P MLC3S MLEAD MLIHP MLIHS Amount of carbon in the pool (lb) Amount of Li 3 N in the pool (lb) Amount of Li 20 in the pool (lb) True amount of lithium in the pool (lb) Amount of lithium consumed in the spray fire (lb) Initial mass of lithium in the pool (lb) View factor between the first wall and the breeder node (may be zero) Initial mass of inert gas in the primary gas (lb) Initial mass of inert gas in the secondary gas (lb) Mass of primary non-condensible gas (lb) Mass of secondary non-condensible gas (lb) Mass of inert gas in the primary gas (lb) Mass of inert gas in the secondary gas (lb) Mass of water boiled off from the water pool in one time step (lb) Initial mass of carbon dioxide in the primary gas (lb) Initial mass of carbon dioxide in the secondary gas (lb) Mass of carbon dioxide in the primary gas (lb) Mass of carbon dioxide in the secondary gas (lb) Condensation rate of water on an extraneous heat capacity (lb/sec) Condensation rate of water on the secondary floor liner (lb/sec) Condensation rate of water on the pan insulation (lb/sec) Condensation rate of water on a wall liner (lb/sec) Condensation rate of water on the primary floor liner from the secondary gas (lb/sec) Condensation rate of water on the primary wall liner from the secondary gas (lb/sec) Molar fraction of air at the water pool-gas boundary Molar fraction of air in the cell gas Molar fraction of water vapor at the water pool-gas boundary Molar fraction of water vapor in the cell gas Molecular weight of the mixture at the water pool-gas boundary Mass of hydrogen in the primary gas (lb) Mass of hydrogen in the secondary gas (lb) Mass flow rate of steam injected to primary cell (lb/sec) Mass flow rate of steam injected to secondary cell (lb/sec) Mass of lithium carbide in the primary gas (lb) Mass of lithium carbide in the secondary gas (lb) Initial mass of lithium carbonate in the primary gas (lb) Initial mass of lithium carbonate in the secondary gas (lb) Mass of lithium carbonate in the primary gas (lb) Mass of lithium carbonate in the secondary gas (lb) Mass of lead in the lead layer above the lithium-lead pool (lb) Mass of lithium-hydroxide in the primary gas (lb) Mass of lithium-hydroxide in the secondary gas (lb) 43 MLINIP MLINIS MLINP MLINS MLIOH MLIOIP MLIOIS MLIOP MLIOS MNIINJ MNIIP MNIIS MNIP MNIS MNINJ1..3 MOINJ1..3 MOXINJ MOXIP MOXIS MOXP MOXS MR MUAIR MUAIRB MUAIRG MUB MUDIFF MUV MUVB MUVCZ MWL MWL2 MWLV MWLV2 MWLZ MWLZ2 MWV MWV2 MWVV MWVV2 Initial mass of lithium-nitride in the primary gas (lb) Initial mass of lithium-nitride in the secondary gas (lb) Mass of lithium-nitride in the primary gas (lb) Mass of lithium-nitride in the secondary gas (lb) Mass of LiOH produced (moles) Initial mass of lithium-oxide in primary gas (lb) Initial mass of lithium-oxide in secondary gas (lb) Mass of lithium-oxide in primary gas (lb) Mass of lithium-oxide in secondary gas (lb) Rate of nitrogen injection during a one minute interval (lb/sec) Initial mass of nitrogen in the primary gas (lb) Initial mass of nitrogen in the secondary gas (lb) Mass of nitrogen in the primary gas (lb) Mass of nitrogen in the secondary gas (lb) Mass of nitrogen injected in gas injection (lb) Mass of oxygen injected in gas injection (lb) Rate of oxygen injection during a one minute interval (lb/sec) Initial mass of oxygen in the primary gas (lb) Initial mass of oxygen in the secondary gas (lb) Mass of oxygen in the primary gas (lb) Mass of oxygen in the secondary gas (lb) Mass ratio of air to water vapor in the cell gas Viscosity of air in the cell gas (lb/sec-ft) Viscosity of air at the water pool-gas boundary (lb/sec-ft) Viscosity of air in the cell gas (lb/sec-ft) Viscosity of the mixture at the water pool-gas boundary (lb/sec-ft) Viscosity of the mixture at the lithium pool surface (lb/sec-ft) Viscosity of water vapor in the cell gas (lb/sec-ft) Viscosity of water vapor at the water pool-gas boundary (lb/sec-ft) Viscosity of water vapor at the lithium pool surface (lb/sec-ft) Mass of liquid water in the primary water pool (lb) Mass of liquid water in the secondary water pool (lb) Mass of liquid water in the primary gas (lb) Mass of liquid water in the secondary gas (lb) Time rate of change of the mass of liquid water in the primary water pool (lb/sec) Time rate of change of the mass of liquid water in the secondary water pool (lb/sec) Total mass of water in the primary gas (lb) Total mass of water in the secondary gas (lb) Mass of water vapor in the primary gas (lb) Mass of water vapor in the secondary gas (lb) 44 MWVZ MWVZ2 N NAME(i) NL NL1 NLM1 NL1M1 NS NULV OFAC OUTINT OVERPP OVERPS OXLB OXLBI OXLFS PAP PAPZER PAS PASZER PERCEN PH20 PH202 PH20B PH20B2 PHASE PHASE2 PHIA PHIW PHIAWB PHIWAB PLIV PRSC PSAT PSAT2 PYU PZEROP QCxxx Time rate of change of the total mass of water in the primary gas (lb/sec) Time rate of change of the total mass of water in the secondary gas (lb/sec) Index used to transfer to section of subroutines, and as a DO loop counter Input variable containing program name and output headings Number of concrete wall nodes Number of concrete floor nodes Number of concrete wall nodes minus one Number of concrete floor nodes minus one Index used to control transfer to sections of the steam-air subroutines Kinematic viscosity of water at the secondary floor liner (ft2 /sec) Oxygen inhibition factor (lithium-steam reaction) Fraction of the outermost cell gas leaked to ambient Primary cell overpressure (psig) Secondary cell overpressure (psig) Mass of oxygen consumed in the fire (lb) Mass of oxygen consumed in the spray fire (lb) Mass of oxygen remaining after the spray fire (lb) Primary gas pressure (psia) Initial primary gas pressure (psia) Secondary gas pressure (psia) Initial secondary gas pressure (psia) Molecular percentage of lithium-peroxide (vs. monoxide) formed during combustion Partial pressure of water vapor in the primary gas (psia) Partial pressure of water vapor in the secondary gas (psia) Partial pressure of water vapor at the primary water pool-gas boundary (psia) Partial pressure of water vapor at the secondary water pool-gas boundary (psia) =1 if primary cell is saturated, =2 if superheated =1 if secondary cell is saturated, =2 if superheated Baroczy two-phase flow correction factor at the lithium pool surface Baroczy two-phase flow correction factor at the lithium pool surface Baroczy two-phase flow correction factor at the water pool surface Baroczy two-phase flow correction factor at the water pool surface Partial pressure of lithium vapor (psia) Prandtl number divided by the Schmidt number Saturation pressure of water at the primary gas temperature (psia) Saturation pressure of water at the secondary gas temperature (psia) Used in setting the time step length calculated from the heat conduction rate to the pan or primary floor liner from the lithium pool Primary gas pressure after the spray fire (psia) Heat of combustion (BTU/lb Li) 45 (There is no page 46.) QCC QCCONC QCN QCO QCO1 QCO2 QCW QCW2 QDISS QIN QL2C2 QLFLR QLIOH QOFWn QOBLn QOBLn QOBLIn QOSHn QOSHIn Li-CO 2 producing lithium carbonate reaction Concrete reaction Nitrogen reaction Oxygen reaction Monoxide reaction Peroxide reaction Water vapor reaction producing LiOH Water vapor reaction producing Li 2 0 Heat of dissociation of LiPb (BTU/lb) Heat addition to primary gas from spray fire (BTU) Heat of combustion for the carbon reaction (BTU/lb Li) Heat flux from the secondary water pool to the secondary floor liner (BTU/ft 2 ) Heat of fusion of LiOH (BTU/lb mol) Volumetric decay heat generation rate in the first wall for an isotope 3 (n=1-3) (BTU/sec ft ) Volumetric decay heat generation rate in the breeder for an isotope (n=1-3) (BTU/sec ft') Volumetric decay heat generation rate in the manifold for an isotope (n=4-6) (BTU/sec ft') Volumetric decay heat generation rate in the blanket back wall for a n isotope (n=1-3) (BTU/sec ft') Volumetric decay heat generation rate in the shield bulk for an isoto ?e (n=1-3) (BTU/sec ft') Volumetric decay heat generation rate in the inside of the shield for QRADC QRADCG QRADEB an isotope (n=1-3) (BTU/sec ft') Volumetric decay heat generation rate in the outside of the shield for an isotope (n=1-3) (BTU/sec ft') Used in heat balance equations for the spray fire (BTU) Used as a counter in the lithium transfer simulation Indicates a radiative heat flow (BTU/sec) Floor liner (or pan) to ambient or floor concrete Wall liner to ambient or wall concrete Pan to primary gas Breeder to blanket back wall QRADEM QRADES Breeder to manifold Blanket back wall to shield inside region QRADFB QRADFG QRADFS QRADG QRADP QRADPG First wall (floor) to breeder Primary floor liner to secondary gas Primary floor liner to secondary floor liner Combustion zone (or Li pool without combustion) to primary gas Combustion zone to lithium pool (only during combustion) Primary wall liner to secondary gas QOSHOn QOUT1..5 QQQ QRADxx QRADB 47 QRADPS QRADS QRADW QRADWB QRSHFS QRSHGS QRSHWS QU QVAP QVEHC QVPAN QVSEC QVFLR QVFPGS QVWPGS RA RADxxx 'RAD'B 'RAD'C 'RAD'CB 'RAD'CC RAIR RAIR2 'R'BFF 'R'BFW 'R'BIEHC RBREAK RC2 RC2LB RCMBC RCMBC2 Primary wall liner to secondary wall liner Pan to primary floor liner Combustion zone (or lithium pool) to primary wall liner First wall to breeder Radiative heat flow from the shield outside region to the secondary floor (BTU/sec) Radiative heat flow from the shield outside region to the secondary gas (BTU/sec) Radiative heat flow from the shield outside region to the secondary wall (BTU/sec) Heat flux from the primary gas to primary wall liner due to condensation (BTU/sec-ft 2 ) Heat of vaporization of lithium (BTU/lb) Heat flux from the cell gas to the extraneous heat capacity due to condensation (BTU/sec-ft 2 ) Heat flux from the primary gas to the pan insulation due to condensation (BTU/sec-ft 2 ) Heat flux from the secondary gas to secondary wall liner due to condensation (BTU/sec-ft 2 ) Heat flux from the cell gas to cell floor liner due to condensation (BTU/sec-ft 2 ) Heat flux from the secondary gas to primary floor liner due to condensation (BTU/sec-ft2 ) Heat flux from the secondary gas to primary wall liner due to condensation (BTU/sec-ft 2 ) Mean radius of combustion product particles (microns) 'RAD' or 'R' indicates a temperature rate of change in one node due to radiative heat transfer to or from another (deg. F./sec) Floor liner to ambient or floor concrete Wall liner to ambient or wall concrete Floor concrete from floor liner Wall concrete from wall liner Gas constant for primary non-condensible gas (RIN/XMOLP) Gas constant for secondary non-condensible gas (RIN/XMOLS) Breeder node from first wall (floor) Breeder node from first wall Blanket back wall from breeder Temperature rate of change of primary gas due to leakage (R/sec) Li-CO 2 reaction rate inhibition factor (Li 2 CO 3 reaction) Rate of carbon consumption (lb/sec) Stoichiometric combustion ratio for lithium and concrete (lb Li/lb concrete) Stoichiometric combustion ratio for lithium and carbon (lb Li/lb C) 48 RCOLB 'R'CZG 'R'CZP 'R'CZW 'R'EHCBI 'R'EHCMN 'R'EHCSH RELERR 'R'FFB 'R'FPFS 'R'FPGAS 'R'FSFP 'R'FSSH 'R'FWB 'R'GASFP 'R'GASPA 'R'GLI 'R'GSSH Stoichiometric combustion ratio for lithium and carbon dioxide for lithium carbonate producing reaction (lb Li/lb CO 2 ) Stoichiometric ratio of lithium consumed in Li 2 CO 3 producing reaction to Li 2 CO3 produced (lb Li/lb Li 2 CO 3 ) Stoichiometric combustion ratio for lithium and hydrogen (lb Li/lb H) Stoichiometric combustion ratio for lithium and nitrogen (lb Li/lb N) Stoichiometric combustion ratio for lithium and oxygen (lb Li/lb 0) Stoichiometric combustion ratio for monoxide reaction (lb Li/lb 0) Stoichiometric combustion ratio for peroxide reaction (lb Li/lb 0) Stoichiometric combustion ratio for lithium and water for reaction producing LiOH (lb Li/lb H2 0) Stoichiometric combustion ratio for lithium and water for reaction producing Li 2 0 (lb Li/lb H2 0) Stoichiometric ratio of lithium consumed in Li-CO 2 reaction producing Li 2 0 and carbon to carbon produced (lb Li/lb C) Stoichiometric ratio of lithium consumed in Li-CO 2 reaction producing Li2 CO 3 and carbon to carbon produced (lb Li/lb C) Stoichiometric combustion ratio for lithium and carbon dioxide for lithium oxide producing reaction (lb Li/lb CO 2 ) Rate of carbon dioxide consumption (lb CO 2 /sec) Primary gas from combustion zone Lithium pool from combustion zone Primary wall liner from combustion zone Breeder from blanket back wall Breeder from manifold Blanket back wall from shield inside region Fraction of X/(dx/dt) allowed as the maximum time step (sec) First wall (floor) from breeder node Primary floor liner from secondary floor liner Primary floor liner from secondary gas Secondary floor liner from primary floor liner Secondary floor liner from shield outside region First wall from breeder node Secondary gas from primary floor liner Pan to primary gas Lithium pool to primary gas (without combustion) Secondary gas from shield ouside region RHCON Density of concrete (lb/ft3 ) RHINS RHLEAD RHLI RHLIX Density Density Density Density (lb/ft3 ) RHOAIP Initial density of primary non-condensible gas (lb/ft3 ) RCMBCO RCMBCS RCMBH2 RCMBN RCMBO RCMB01 RCMB02 RCMBW RCMBW2 RCMCA1 RCMCA2 RCMCCO of insulation (lb/ft3 ) of pure lead (lb/ft3 ) of pure lithium (lb/ft3 ) of pure lithium (used in LC-2 lithium transfer simulation) RHOAIS RHOAP RHOAS RHOB RHOCAR RHOLC2 RHOLC3 RHOLIH RHOLIN RHOLIO RHOLIV RHOTOT RHPAN RHSFP RHSFS RHSWP RHSWS RIFxxx RIFBBI RIFBM RIFCZG RIFCZP RIFES RIFFFB RIFFPS RIFFWB RIFPAG RIFPAS RIFPG RIFPGA RIFPS RIFPW RIFSCF RIFSCW RIFSLC RIFSF RIFSW RIN RINP RINS RISHGS 'R'LIG 'R'LIW Initial density of secondary non-condensible gas (lb/ft3 ) Density of primary non-condensible gas (lb/ft3 ) Density of secondary non-condensible gas (lb/ft3 ) Density of the water pool-gas boundary layer (lb/ft3 ) Density of carbon (lb/ft3 ) Density of Li 2 C2 (lb/ft3 ) Density of Li 2 CO 3 (lb/ft3 ) Density of LiOH (lb/ft3 ) Density of Li 3 N (lb/ft3 ) Density of Li 2 0 (lb/ft3 ) Density of lithium vapor above the pool (lb/ft3 ) Total gas density at the lithium pool surface (lb/ft3 ) Density of lithium spill pan (lb/ft3 ) Density of primary floor liner (lb/ft3 ) Density of secondary floor liner (lb/ft3 ) Density of primary wall liner (lb/ft3 ) Density of secondary wall liner (lb/ft3 ) Radiative interchange factor-used in radiative heat transfer Breeder node to blanket back wall Breeder node to manifold Combustion zone and primary gas Combustion zone and primary wall liner Blanket back wall to shield inside region First wall (floor) to breeder node Primary floor liner and secondary floor liner First wall to breeder node Pan to primary gas Pan to floor liner Lithium pool to primary gas Primary wall liner to secondary gas Primary wall liner to secondary wall liner Lithium pool to primary wall liner Secondary floor to concrete floor Secondary wall to concrete wall Wall or floor liner to concrete Shield outside region to secondary floor Shield outside region to secondary wall Universal gas constant (1545 ft-lbf/lb-mol-deg. F.) Gas constant for the primary gas (RIN/XMOLP) Gas constant for the secondary gas (RIN/XMOLS) Radiative interchange factor between the shield outer region and the secondary cell gas Gas from lithium pool (without combustion) Wall liner from lithium gool (without combustion) 'R'MNEHC RN2 RNxx RNILB R02 ROXLB 'R'PAGAS 'R'PANST RR RRTLI 'R'SHEHC 'R'SHFS 'R'SHGS 'R'SHWS 'R'SPGS 'R'STPAN RWALB 'R'WLI 'R'WPGAS 'R'WPWS 'R'WSSH 'R'WSWP SAT(x,y) SFLCR SFLEND SFLTIN SH(x,y,z) SIGMA SPILL SPRAY STICK STMFAC STMIN STMIN2 STMOUT STOUT2 TA TAU TAUCZ Manifold from breeder Lithium-nitrogen reaction rate inhibition factor Expressions used to calculate RN2 as a function of gas composition and lithium temperature Rate of nitrogen combustion (lb/sec) Lithium-oxygen reaction rate inhibition factor Rate of oxygen combustion (lb/sec) Primary gas from pan Primary wall liner from pan Function which generates the lithium-nitrogen kinetics limit curve Lithium-nitrogen reaction kinetics limit modified by the presence of steam Shield inside region from blanket back wall Shield outside region from secondary floor Shield outside region from secondary gas Shield outside region from secondary wall Secondary gas from primary wall liner Pan from primary wall liner Rate of water vapor consumption (lb/sec) Lithium pool from primary wall liner (without combustion) Primary wall liner from secondary gas Primary wall liner from secondary wall liner Secondary wall liner from shield outside region Secondary wall liner from primary wall liner Saturated steam table Heat removal rate by emergency cooling of floor liner (BTU/sec) Time after spill when SFLCR ends (sec) Time after spill when SFLCR begins (sec) Superheated steam table Stefan-Boltzmann constant (1.713-10-9 BTU/ft2 -hr-deg. R. 4 ) Total mass of lithium spilled (lb) Mass fraction of lithium consumed in the spray fire Rate at which aerosols are removed from the primary cell due to sticking to the wall. If STICK > 1.0, execution stops. STICK may be reduced by increasing BETA. Density weighting factor for calculating steam-air mixture properties Time to begin steam injection to primary cell (sec) Time to begin steam injection to secondary cell (sec) Time to end steam injection to primary cell (sec) Time to end steam injection to secondary cell (sec) Ambient temperature (deg. R.) Time constant for transient natural convection Radiative transmissivity used to model pool-combustion zone coupling rather than (1.-EMCZ) 51 TAVE TAVHI TAVLO TB(i) TBIC(i) TxxxxF TBLI TBLIO TBLOW TC(i) TCIC(i) TCIGNI TCON TCZ TCZI TE TEHCP TEHCS TEHCZP TEHCZS TETI TET2 TEZ TFEFF TFHI TFLO TFS TGP TGPZER TGS TGSZER THBLI THE THFC THFP THFS THI Average of secondary floor and secondary water pool temperature (deg. R.) Variable used to read steam tables Variable used to read steam tables Temperature of ith node of concrete floor (deg. R.) Initial temperature of ith node of concrete floor (deg. R.) Corresponding temperature to Txxxx in Fahrenheit Temperature of blanket back wall (deg. R.) Initial temperature of blanket back wall (deg. R.) Inert gas inlet temperature (deg. R.) Temperature of ith node of concrete wall (deg. R.) Initial temperature of ith node of concrete wall (deg. R.) Ignition temperature of lithium-concrete reaction (deg. R.) Concrete combustion zone temperature (deg. R.) Combustion zone temperature (deg. R.) Initial combustion zone temperature (deg. R.) Equilibrium temperature resulting from spray fire (deg. R.) Primary extraneous heat capacity temperature (deg. R.) Secondary extraneous heat capacity (breeder with torus fire option) temperature (deg. R.) Initial primary extraneous heat capacity temperature (deg. R.) Initial secondary extraneous heat capacity (breeder with torus fire option) temperature (deg. R.) Used in calculating thermal conductivity of inner pan insulation See KIN1 Used in calculating thermal conductivity of outer pan insulation See KIN2 Average of combustion zone temperature and lithium pool temperature Used in test for combustion (deg. R.) Normalized temperature of combustion zone-lithium pool temperature (deg. R.) Variable used to read steam tables Variable used to read steam tables Secondary floor liner temperature (deg. R.) Primary gas temperature (deg. R.) Initial primary gas temperature (deg. R.) Secondary gas temperature (deg. R.) Initial secondary gas temperature (deg. R.) Thickness of blanket back wall (ft) Thickness of vacuum gap (ft) Thickness of concrete floor (ft) Thickness of primary floor liner (ft) Thickness of secondary floor liner (ft) Temporary variable used to read steam tables 52 THKIN1 Thickness of inner pan insulation (ft) THKIN2 Thickness of outer pan insulation (ft) THKPAN Thickness of spill pan (ft) Thickness of blanket manifold (ft) THMAN THPB Thickness of lead layer above the lithium-lead pool (ft) Thickness of inside region of reactor shield (ft) THSHI Thickness of bulk region of reactor shield (ft) THSHL Thickness of outside region of reactor shield (ft) THSHO THWC Thickness of concrete wall (ft) Thickness of primary wall liner (ft) THWP Thickness of secondary wall liner (ft) THWS Time elapsed after spill has occurred (sec) TIME User defined time to stop execution of the code (sec) TIMEF Time at which code prints output data to a file (sec) TIMEO Inner pan insulation layer temperature (deg. R.) TINS1 Initial inner pan insulation layer temperature (deg. R.) TINS1I Outer pan insulation layer temperature (deg. R.) TINS2 TINS2I Initial outer pan insulation layer temperature (deg. R.) TLEAD Temperature of the lead layer above the Li-Pb pool (deg. R.) TLEADI Initial temperature of the lead layer above the Li-Pb pool (deg. R.) Lithium pool temperature (deg. R.) TLI Lithium pool temperature before spray fire (deg. R.) TLIBS TLII initial lithium pool temperature (deg. R.) TLO Temporary variable used to read steam tables TLP Temperature of the primary liquid pool (deg. R.) TMAG Temperature of the magnets (secondary extraneous heat capacity) (deg. R.) TMAGZ Initial temperature of the magnets (secondary extraneous heat capacity) (deg. Temperature of the blanket manifold (deg. R.) TMAN TMANO Initial temperature of the blanket manifold (deg. R.) TMELT Melting temperature of lithium (deg. R.) TO Primary gas temperature before spray fire (deg. R.) TONE,TTWO,TTHREE Time at which each injection occurs (sec) TPAN Pan temperature (deg. R.) TPANZO Initial pan temperature (deg. R.) TSAT Saturation temperature of water based on its partial pressure (deg. F.) Primary floor liner temperature (deg. R.) TSFP TSFPI Initial primary floor liner temperature (deg. R.) TSFSI Initial secondary floor liner temperature (deg. R.) TSHI Shield inside region temperature (deg. R.) TSHIO Initial shield inside region temperature (deg. R.) TSHL Shield bulk region temperature (deg. R.) 53 TSHLZ TSHO TSHOO TSP TSPZER TSS TSSZER TVAP TI T2,T3 UA UGPB UL UL2 ULP ULP2 ULPB ULZ ULZ2 USUBA UV UV2 UVZ UVZ2 UWV UWV2 VA VAB VCONC VG VG2 VHI VIEWB VIEWG VIEWM Initial shield bulk region temperature (deg. R.) Shield outside region temperature (deg. R.) Initial shield outside region temperature (deg. R.) Primary wall liner temperature (deg. R.) Initial primary wall liner temperature (deg. R.) Secondary wall liner temperature (deg. R.) Initial secondary wall liner temperature (deg. R.) Vaporization temperature of lithium (deg. R.) Film temperature between primary gas and lithium pool (deg. R.) Temporary variables used in setting up steam table Internal energy of non-condensible gas in a cell (BTU) Specific internal energy of saturated water vapor at boiling (BTU/lb) Internal energy of the primary water pool (BTU) Internal energy of the secondary water pool (BTU) Specific internal energy of the primary water pool (BTU/lb) Specific internal energy of the secondary water pool (BTU/lb) Specific internal energy of liquid needed for boiling to occur (BTU/lb) Time rate of change of UL (BTU/sec) Time rate of change of UL2 (BTU/sec) Heat transfer coefficient between the outermost containment node and the ambient (BTU/sec-ft2 -deg. F.) Internal energy of the primary gas (BTU) Internal energy of the secondary gas (BTU) Time rate of change of the internal energy of the primary gas (BTU/sec) Time rate of change of the internal energy of the secondary gas (BTU/sec) Specific internal energy of water vapor in the primary gas (BTU/lb) Specific internal energy of water vapor in the secondary gas (BTU/lb) Specific volume of non-condensible primary gas (ft3 /lb) Specific volume of non-condensible gas at the water pool-gas boundary (ft3 /lb) Volume of concrete in the first node of concrete (ft3 ) Specific volume of water in the primary gas (ft3 /lb) Specific volume of water in the secondary gas (ft3 /lb) Variable used to read steam tables View factor from the breeder to the blanket back wall View factor across the vacuum gap View factor from the breeder to the manifold VL VL2 Volume of the primary water pool (ft3 ) Volume of the secondary water pool (ft3 ) VLO VLP VLP2 Variable used to read steam tables Specific volume of the primary water pool (ft3 /lb) Specific volume of the secondary water pool (ft3 /lb) 54 VLPF VLPV VP VS VSB VST VVB VVB2 VVG VVG2 VVT WAB WAP WAS WATER WCB WCP WCO2S WN2B WN2P WN2S WO2B WO2P WO2S WWAB WWAP WWAS XALLOY XAM XBLOW XESC XINJ XINJ2 XLI XLIDOT XMAIRP XMAIRS Specific volume of saturated liquid water at the secondary floor liner temperature (ft3 /lb) Specific volume of saturated liquid water for heat transfer between the secondary floor liner and the secondary water pool (ft3 /lb) Volume of primary cell (ft3 ) Volume of secondary cell (ft3 ) Specific volume of water vapor at the water pool-gas boundary (ft3 /lb) Specific volume of water vapor at the lithium pool surface (ft3 /lb) Specific volume of saturated water vapor at the primary water pool temperature (ft3 /lb) Specific volume of saturated water vapor at the secondary water pool temperature (ft 3 /lb) Specific volume of saturated water vapor in the primary gas (ft3 /lb) Specific volume of saturated water vapor in the secondary gas (ft3 /lb) Temporary variable used to determine steam properties for condensation Mass fraction of inert gas in the flooding gas Mass fraction of inert gas in the primary gas Mass fraction of inert gas in the secondary gas Amount of water that should be left in the top concrete node as time-+oo (lb/ft3 ) Mass fraction of carbon dioxide in the flooding gas Mass fraction of carbon dioxide in the primary gas Mass fraction of carbon dioxide in the secondary gas Mass fraction of nitrogen in the flooding gas Mass fraction of nitrogen in the primary gas Mass fraction of nitrogen in the secondary gas Mass fraction of oxygen in the flooding gas Mass fraction of oxygen in the primary gas Mass fraction of oxygen in the secondary gas Mass fraction of water vapor in the flooding gas Mass fraction of water vapor in the primary gas Mass fraction of water vapor in the secondary gas Atom percent of lithium in lithium-lead pool Logarithmic mean molar fraction of air (see MFAB and MFAG) Used in conjunction with IBLOW Used in conjunction with IESC Indicates whether steam injection to the primary is in effect Indicates whether steam injection to the secondary is in effect Mass fraction of lithium in lithium-lead pool Mass flow rate of lithium through the lead layer above the Li-Pb pool (lb/sec) Amount of non-condensible primary gas after spray fire (lb-mol) Amount of non-condensible secondary gas after spray fire (lb-mol) 55 XMBLI XMCOCZ XMDOT XMEHCP XMEHCS Mass of the blanket back wall (lb) Mass of concrete combustion zone (lb) Mass flow rate of gas between primary and secondary cells (lb/sec) Mass of primary extraneous heat capacity (lb) Mass of secondary extraneous heat capacity (breeder with torus fire option) (lb) XMH20I Initial water content of concrete (lb/ft3 ) XMMAG XMMAN XMOLP XMOLS XMOLA XMOLAB XMSHI XMSHL XMSHO XSFL YALIG ZLI ZP ZZxxxx ZZ1 ZZ2 ZZ3 ZZ4 ZZ5 ZZ6 ZZ7 ZZ8 ZZ9 Mass of the magnets (secondary extraneous heat capacity) (lb) Mass of the blanket manifold (lb) Molecular weight of non-condensible primary gas (lb/lb-mol) Molecular weight of non-condensible secondary gas (lb/lb-mol) Molecular weight of containment inert gas (lb/lb-mol) Molecular weight of flooding inert gas (lb/lb-mol) Mass of shield inside region (lb) Mass of shield bulk region (lb) Mass of shield outside region (lb) Indicates whether emergency floor cooling is currently in effect Effective thermal admittance between the pool and primary gas (BTU/sec-deg. F.) Effective thermal admittance between the pool and combustion zone (BTU/sec-deg. F.) Effective thermal admittance between the pan and primary gas (BTU/sec-deg. F.) Thickness of the lithium pool (ft) Used to determine EMLI if EMLI < 0.9 Temperature rate of change of a node (deg. R./sec) Lithium pool Lithium spill pan Secondary cell gas Primary cell gas Primary wall liner Combustion zone Primary floor liner Inner insulation layer Outer insulation layer ZZ99 'ZZ'C Change in combustion rate with respect to time (lb Li/sec2 ft 2 ) Concrete combustion zone 'ZZ'BLI ZZD ZZDIN 'ZZ'EP 'ZZ'ES 'ZZ'FS 'ZZ'MAG Blanket back wall Rate of change of concrete combustion zone thickness (ft/sec) Initial rate of change of concrete combustion zone thickness (ft/sec) Primary extraneous heat capacity Secondary extraneous heat capacity Secondary floor liner Magnets (secondary extraneous heat capacity) 56 YAPCZ YPAGAS 'ZZ'MAN 'ZZ'PB 'ZZ's 'ZZ'SHI 'ZZ'SHL 'ZZ'SHO Blanket manifold Lead layer above Li-Pb pool Secondary wall liner Shield inside region Shield bulk region Shield outside region PROGRAM DECISION FLAGS IAROSL IBLOW ICMB ICNI IC021 ICZ IESC IFLAG2 IFLAGB IFLAGC IFLAGCO IFLAGD IFLAGF IFLAGISI IFLAGP IFLAGR IFLAGS IFLAGT IFLAGU IFLAGW ILIT IMETH ISFLC ISWICH =1 to use aerosol removal from containment by sticking option =1 Containment flooding with inert gas =0 No containment flooding =0 No oxygen left after spray fire =1 Still oxygen left after spray fire (initially =1, reset by code) =0 Nitrogen reactions not possible =1 Nitrogen reactions possible =1 to use pure CO 2 atmosphere =0 Combustion zone model not used =1 Combustion zone model used =1 to use emergency space cooling option =1 to use two-cell geometry option =1 to use lithium-lead option =1 to use concrete combustion option =1 to use pure CO 2 atmosphere option =1 to use layered lithium-lead pool option =1 to use floor concrete option =1 to enter input data in SI units =1 to use pan option =1 to use torus fire option =1 to use dry gas injection option =1 to use steam-air mixture option =1 to get output in SI units =1 to use wall concrete option =0 No lithium left to burn =1 Lithium left to burn =1 Runge-Kutta method of integration used =3 Simpson's Rule method of integration used =1 to use emergency floor cooling option =0 Crack size remains constant Crack size reset to zero after primary and secondary cell gas pressure equilibrate (note: this should not be used when either cell is small compared to the other or the volume of gas being consumed by the fire) 57 OPTION AND LOGICAL DECISION FLAGS FLAG2 = .TRUE. FLAGAS = .TRUE. FLAGC = .TRUE. FLAGCO = .TRUE. FLAGD = .TRUE. FLAGDF = .TRUE. FLAGF = .TRUE. FLAGISI = .TRUE. FLAGL =.TRUE. FLAGM = .TRUE. FLAGN = .TRUE. FLAGPB = .TRUE. FLAGPN = .TRUE. FLAGSI = .TRUE. FLAGST = .TRUE. FLAGTR = .TRUE. FLAGW = .TRUE. Two cell geometry Injection of dry gas during run Concrete combustion Pure CO 2 containment atmosphere Concrete combustion has stopped (set by code) Lithium-lead layered pool combustion model Floor concrete Code accepts input in SI units LILP is fixed at a minimum (set by code) Sonic gas flow between cells (set by code) Indicates first run through a subroutine (set by code) Lithium-lead combustion Pan option Code prints output in SI units Steam-air mixture in containment Torus fire option Wall concrete 58 C Troubleshooting "There exists no large computer code which runs perfectly 100% of the time." -ANONYMOUSThe user of this code may encounter problems while trying to execute LITFIRE. The most common error statement is generated by the computer itself: DIVIDE BY ZERO and stops the code. This indicates that an attempt was made to divide by zero or something very close to zero. The first step when encountering an error message is to check the output file outl.dat and ensure that the input was properly entered into the code. If it was, the error may occur if the value of EXHSTV is too high or LILP is too low. This problem may be mitigated to an extent by reducing DTMIN, the minimum time step length, although this will increase computation time. Another common error message is generated by LITFIRE: EXX IS NEGATIVE - CANNOT TAKE ROOT When this occurs, it indicates that the code is trying to take the square root of a negative number - the code has diverged numerically and the combustion zone temperature is negative. This may occur when. the combustion rate CMBRH is very small (i.e.,< 1.0 lb Li/hr-ft 2 ), the oxygen and nitrogen concentrations are low, or when the gas pressure is low. This problem occurs when ZZ6 and DELT are large enough to produce a negative TCZ. This problern may be solved by reducing the value of DELOUT to limit the time step size, so extrapolations of TCZ over a long time step do not cause problems. Unfortunately, this can increase computation time considerably. The variation of the combustion zone temperature over time is a good indicator of whether or not the code is running properly. During combustion, TCZ should be 100' F. or more higher than TLI. Once combustion stops, TCZ should drop rapidly to a value just barely above TLI. (TLI is hypothetical at this point if the lithium has been consumed, but it is continuously calculated for numerical reasons.) If TCZ oscillates rapidly or falls below TLI, it is an indication of trouble. As stated earlier, this may be mitigated by decreasing the value of DELOUT. If the statement: LITHIUM TEMP. ABOVE BOILING POINT occurs, this may indicate that the rate of change of the lithium pool temperature was very large. This may be due to the fact that TCZ has diverged to a very large value. This generally occurs as LILP nears zero, as the pool then has a lower heat capacity, and a sudden influx of energy would cause the pool to heat up rapidly. Other signs of trouble include a rapid drop in containment gas mass (MNIP, MOXP), or an oscillating combustion zone temperature, TCZ; combustion rate, CMBRH; or time step length DELT. In general, DELT should increase after the start of the run and then level off until combustion stops, when it may change more rapidly. Sudden large changes in DELT indicate that the temperature rates of change are varying rapidly, which usually should not be the case. If reducing DELT does not help solve the problem, print out values of the code quantities like ZZ5 and ZZ6 or UVZ and MWVZ to help find the problem. Other messages indicate that the user is attempting to use incompatible options together, or that the code has been stopped because there is no point in continuing further (i.e. the lithium temperature has dropped below the melting point, or containment gas temperature and pressure have returned to normal). 59 D Sample Input Data Files INPUT DAIA FILE HEAD.DAT THIS IS THE INPUT DATA FOR THE EXECUTION OF THE CODF LITFIRE THESE ARE THE OUTPUT VALUES CORRESPONDING TO THE PRIMARY CELL ENVIRONMENT TIME DELT TCZF TLIF TGPF THESE ARE THE OUTPUT VALUES CORRESPONDING TO THE SECONDARY CELL ENVIRONMENT TIME TGSF TFSF PAS XMDOT PA P TSPF MOXS TSFPF MNIS MCO2S THESE ARE THE OUTPUT VALUES CORRESPONDING TO THE PAN OUTPUT OPTION TIME TLIF TPANF TINS1F THESE ARE ADDITIONAL OUTPUT VALUES CORRESPOJDING TO THE PRIMARY CELL ENVIRONMENT TIME MNIP MOXP MCO2P TINS2F RN2 PAP R02 LIBP THESE ARE THE OUTPUT VALUES CORRESONDING TO THE LITHIUM/LEAD DIFFUSION OPTION TIME XLIDOT TLEADF THPB MLEAD ZLI INPUT DATA FILE UWMAK.W e0 0 0 0 0 0 0 0 0 S0 5 .20 .20 5 .20 .20 .20 .20 .20 .20 .20 .20 497.88 10.14 725.0 0.833 0.15 123.00 2.080 0.1189 0.1189 0.9960 0.2650 86.9400 0.0 0.0 2916.0 0.13 0.85 0.07 22.05 851.4 0.2320 0.15 0.2 0.9 124.00 18510.0 0.8764 816.60 0.87 0.16 0.07 2.153 1752.6 14.70 0.1247 39.90 51.00 0.002 30.00 0.015 0.09 0.00 497.500 572.3 30.00 497.500 33.80 0.0227 160.00 4080.0 1.487 8431.0 0.01 0.112 0.000 851.2 0.0 0.1199 30.00 144.00 0.04 13784.0 0.383 0.0 0.11 0.07 0.050 815.2 0.0000 0.05 80 0.05 80 38.35 0.1 0.9 10964.1 0.766 6.93 0.89 0.01 5.0 530.99 0.0000 0.01 1751.8 00030000000.02000000900.00000000000.00300000001.00000000100.0000 INPUT DA A FILE UWMAK.X 8855700.00000000140.0eOe0000014.70000000538.10000000538.20000000538.3000 0.0 0.0 522.0000 0.232 00.00 15.5 0.09 0.6921 9709.00 1696200.0 1482.0 188164.00 0.0208 0.1199 12.40 497.50 0.85 0.0208 59038.00 497.50 12.40 0.85 0.1199 350.0 60 mmwk.ftww INPUl DATA FILE UWMAK.Y 0000030.00000000497.50000000000.12000000008.11500000000.20000000000.9000 0.09 12.32 5.9055 7.00 1750.00 0.0833 0.1667 0.0210 0000.0415 3315.0000 0.1700 708.0000 9.3000 0.0350 6.45600E-08 INPUT DATA FILE UWMAK.Z 0000100.00000000000.00000000000.00000000004.ecoeCOOOOO.12470000535.0000 0.00 325.0 310.0 0.0 24.0 INPUT DATA FILE STEAMOP. 0001000.000000030e0. 00900001190.300 OOOOOOOeo. INPUT DATA FILE TORUS. 8855700.00000000150.00000000014.70000000538.10000000538.20000000538.3000 0.0 522.0000 0.0 0.232 00.70 15.5 1.498 0.09 0.1189 7796.00 115468.0 1482.0 0.0208 188164.00 497.50 12.40 0.1199 0.85 0.0208 59038.00 497.50 12.40 0.85 0.1199 .648 0.1 0.1 0.500 1.344 0.1653 12110.0 14.202 3500000.0 1.903 672.0 0.1199 9000000.0 14000.0 538.0 0.0001 0.500 .278 1.0 0.889 0.0656 0.000 0.09 1300.0 149816.0 9472.0 .1189 .1312 17.90 260000.0 .1312 260000.0 .1312 585.0 670.0 11.387 1392.0 8890.0 .188 .656 522842.0 8.16e+00 4.41e-06 4.43e-01 9.57e-08 1.75e-01 2.90e-07 1.03e-01 4.41e-06 6.46e-03 9.57e-08 1.09e+00 3.08e-02 8.46e-02 2.56e-08 1.91e+00 7.41e-05 3.32e-02 2.92.-6 2.84e-02 4.41e-06 8.21e+00 3.08e-03 2.88e-03 2.90e-07 1.85e+00 7.41e-05 2.72e-03 2.56e-08 1.70e-04 3.84e-12 1.77e+01 2.81e-02 1.69e-04 7.51e-03 7.34e-06 1.69e-04 350.0 61 E Sample Output Data Files OUTPUT DATA FILE OUT2.DAT THESE ARE THE OUTPUT VALUES CORRESPONDING TO THE PRIMARY CELL ENVIRONMENT TIME 0.0 DELT TCZF TLIF TGPF 0.10 700.67 700.22 200.00 100.0 0.32 810.60 609.64 198.78 0.47 200.2 827.90 622.37 197.98 300.1 0.22 650.31 197.09 855.77 400.1 0.43 900.09 679.50 196.39 500.0 0.82 911.94 715.02 195.21 600.1 0.48 922.62 742.62 194.11 700.0 0.04 757.36 193.89 935.18 800.0 0.17 950.40 765.30 193.60 900.1 0.04 967.46 773.17 193.30 progrom execution stopped by program values 0.233e+02 0.604e+03 0.181e+03 0.692e+01 TSPF TSFPF 199.89 198.41 179.89 PAP 101.70 102.11 102.89 '03.66 104.42 105.32 106.13 106.63 106.92 107.21 196.93 195.49 194.17 192.62 191.23 190.38 189.91 189.45 489.57 573.67 613.54 643.92 680.06 709.36 725.33 733.84 741.89 0.619e+00 OUTPU' DATA FILE OUT3.DAT THESE ARE THE OUTPUT VALUES CORRESPONDING TO THE SECONDARY CELL ENVIRONMENT TIME 0.0 100.0 200.2 300.1 400.1 500.0 600.1 700.0 800.0 900.1 TGSF 25.94 28.12 30.40 32.69 34.90 37.56 39.96 41.44 42.30 43.15 TFSF 26.06 26.06 26.06 26.08 26.10 26.15 26.20 26.25 26.28 26.31 MOXS 0.1508e+06 0. 1508e+06 0.1508e+06 0.1508e+06 0.1508e+06 0.1508e+06 0.1508e+06 0.1508e+06 0.1508e+06 107.21 0.3610e-01 0.1508e+06 XMDOT PAS 101.38-0.2194e+00 102.11 0. 102.89 0. 103.67 0. 104.41 0. 105.32 0. 106.13 0. 106.63 0.3826e-01 106.92 0. 62 MNIS 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 0.4994e+06 MCO2S 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. OUTPUT DATA FILE OUT5.DAT THESE ARE ADDITIONAL OUTPUT VALUES CORRESPONDING TO THE PRIMARY CFLL ENVIRONMENT TIME 0.0 100.0 20C 2 300. 1 400.1 500.0 600.1 700.0 800.0 900.1 MNIP 0.8074e+01 0.8153e+01 0..272e+01 0.8395e+01 0.8510e+01 0.8662e+01 0.8806e+01 0.8892e+01 0.8937e+01 0.8988e+01 MOXP 0.2439e+01 0.2426e+01 0.2399e+01 0.2372e+01 0.2345e+01 0. 2305e+01 0.2264e+01 0. 2236e+01 0.2221e+01 0.2208e+01 RN2 0.00000 0.35110 0.33125 0.28269 MCO2P 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. R02 0.97120 0.97098 0.97059 0.97020 0.96982 0.96929 0.23668 0.18993 0.16182 0.16819 0.18553 0.96875 0.96841 0.96823 0.96805 0.20478 LIBP 0. 0.1015e+00 0.2476e+00 0.4156e+00 0.6179e+00 0.8597e+00 0.1074e+01 0.1209e+01 0.1297e+01 0.1393e+01 OUTPUT DATA FILE OUT9.DAT These outputs ore the weights of react 3n products in LB Lilox Time 0.0 100.0 200.2 300.1 400.1 500.0 600.1 700.0 800.0 900.1 0. 0.193e+00 0.503e+00 0.837e+00 0.1 19e+01 0.165e+01 0.209e+01 0.238e+01 0.255e+01 0.273e+01 Lilni Lilco 0. 0. 0.205e+00 0. e.474e+00 0. 0.802e+00 0. 0.124e+01 0. 0.173e+01 0. 0.213e+01 0. 0.238e+01 0. 0.255e+01 0. 0.275e+01 0. Lilc2 Lilcar Mliop 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. MIc3p 0. 0. 0.101 e-81 0. 0.262e-01 0. 0. 435e-e1 0. 0.614e-01 0. 0.846e-01 0. 0.107e+00 0. 0.121e+00 0. 0.128e+00 0. 0.136e+00 0. OuJPUT DATA FILE OUT1O.DAT These outputs are the reaction rates in gram Li/min-cm2 Time 0.0 100.0 200.2 300.1 400.1 500.0 600.1 700.0 800.0 900.1 Cmbrhh Cmbrnh 0.3050e-05 0.2866e-05 0. 0.3885e-01 0.2047e-01 0.1839e-01 0.4243e-01 0.2292e-01 0.1951e-e1 0.4672e-01 0.2678.-01 0.1993e-01 0.5183e-1Ol 0.3112e-01 0.2071e-01 0.4680e-01 0.2599e-01 0.2081e-01 0.4365e-01 0.2289e-01 0.2076e-e1 0.4509e-01 0. 2433e-01 0.2076e-01 0.4833e-01 0.2739e-01 0.2094e-01 0.5207e-el 0.3091e-0 1 0.2116e-01 63 Cmrc2t Cmrcoh Cmbrwh Cmbroh 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. F Listing of the LITFIRE code 64 -4 0 a 00 A44 0., S0 4444 4444 44444444 44444444 44444444 44444444 44 444.-I 44 1. 445 44 44 44 4443 44 44--I 44e-I 44 44 44 44 44 00 0-.4 00 0 1 0 -. 44 44.0 44 0 0 10 44 440 44.-I 44 .1 01444 044 4444 44 -4 -a 0 044 -da 440044* 0 o 44 44 -I -. 4 0044* w w 0 -- 0m 4 1 a 00 4 - 0 14 - M .4 0 0 -.4 0 \ ..- 444.-.44 4'444'4-.e 0 -.4 - - 0 00a0i. 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X 0.11w 4l&5 0 -4 0. II 0 0 0. 14 '4 II N II II 0 0 V m 44 93 ,.0 V IIr -edII .1 Nl 9: II -eiA AII AIIewN nII 91 II lfaN II V00 - N A0 . 0930 4-0 .0 II 0 > II 0 4 1 0 e 4l 4 0 4 44 0 11400m *11454 -4 0 0 0 44 -r4 -4 -4 -44&- --p.04045 4 -4 -4 0. 0 45 -4 e-4 .0 .. 0.,0 -e4 45 - 4 0 e0 0 400 0. 4 a -404- AC -w V V Aj 4 0 444 0.14 0.0. 0sA.C.0 .. 0..0 0.0 -4 4 4.0 0 0 .1 4 14 5 45 5 45 0 0 ' ' A 0 04 0 -A D0' 0*'0 -4 I 0 m 0 0 0 %D.4 I .4 0 ee 00 oC w 0 V eI CO4 Cot '00505050o4050o N O N N.-44 04 .4 0m 4 0 0 ! e 'o 4 0 0 0'N 4J -0. .4 151 -II -d u 0 N go -Al .A 0 0'MN 4V C: 4 0 U 4 041 a 4 0 0 : N u0~ 0 C4 0 e 9 4 1 1 1 0. 14 e 'C M N eU an w a c:4 000 II 45 45 45 e 0 0 0 4y (. 0 .-4 p e 140 References [1] D.S. Barnett, et al. LITFIRE User's Guide. MIT Plasma Fusion Center, second edition, August 1987. PFC/RR-87-11. [21 D.S. Barnett. The Chemical Kinetics of the Reactions of Lithium with Steam-Air Mixtures. PhD thesis, Massachusetts Institute of Technology, April 1989. [3] V.J. Gilberti and M.S. Kazimi. Modeling of Lithium and Lithium-Lead Reactions in Air Using LITFIRE. Technical Report PFC/RR-83-08, MIT Plasma Fusion Center, January 1983. [4] D.A. Dube and M.S. Kazimi. Analysis of Design Strategies for Mitigating the Consequences of Lithium Fire Within Containment of Controlled Thermonuclear Reactors. Technical Report MITNE-219, Massachusetts Institute of Technology, July 1978. 152