NUREG/CR-4561

LA-10678-M.'.

FIRAC User's."Manual:

A Computer Code to Simulate..

.-.. Fire Accidents in Nuclear Facilities

Manuscript Completed: ,February 1986

Date. Published: April 1986

Prepared by

B. D. Nichols, W. S. Gregory

Los Alamos National Laboratory

,..Los Alamos, NM 87545

Prepared for

Division of Fuel Cycle and Material Safety

Office of Nuclear Material Safety and Safeguards

U.S. Nuclear Regulatory Commission

Washington, D.C. 20555

NRC FIN A7152

CONTENTS

ABSTRACT ............................ .................................. 1

I. INTRODUCTION 2....................

2

II. PHYSICAL MODELS .......................... 3

A. Gas Dynamics Models ............................ 3

B. Material Transport Models ..... ................................... 9

C. Duct Heat Transfer Model..... ................................. 14

D. FIRIN Fire and Radioactive Source Term Simulation ................ 15

III. SYSTEM MODELING STRATEGIES FOR FIRE-INDUCED TRANSIENTS ............... 19

A. General ..................... ........ 19

B. Fire Accident System Modeling ..................... ............ 19

C. System Modeling:Examiples ......................................... 23

IV. USER INFORMATION AND PROGRAMMING DETAILS ..................... ...... 35

A. Input Organization ........................................... 35

B. Input Format ..................................................... 37

C. Improved FIRAC Input Specifications ............................ 38

D. Input Processing ............................................. 111

E. Output Processing ............. .................................. 111

F. Diagnostic Messages ............... ............................. 118

G. FIRAC Programming Details .......................... .......... 119

H. Compiling, Loading, and Executing Instructions .................. 122

I. General User Hints and Suggestions... ........................ 128

J. Time and Cost Estimates .......................................... 130

V. SAMPLE PROBLEMS... •................... ........................... 130

A. Introduction ... ............................................. 130

B. Sample Problem 1 .................................................. 131

,C. Sample Problem 2 ............................................ 161

APPENDIX A. GAS DYNAMICS SUMMARY . ......... .............................. 185

APPENDIX B. DUCT HEAT TRANSFER THEORY AND METHODS ........................ 189

APPENDIX C. MATERIAL TRANSPORT THEORY ................................. 203

APPENDIX D. BLOWER MODEL ............. ................ o2......... . 229

APPENDIX E. CONTROL DAMPER MODEL ...................................... 231

APPENDIX F. MODELING DUCTS AND VALVES ................................. 233

APPENDIX G. SAMPLE OUTPUT..! .................................. ........ 236

REFERENCES ................................................................. 300

iii

NOME NCLATURE

T.' Duct inlet gas temperature in

Tout Duct outlet ýgas temperature

Tg Average gas temperature in duct

TN Duct wall temperature on outside surface

Ti Duct wall temperature on inside surface

•Tj Duct wall temperature at node j

To 0 Air temperature outside duct

Qj Net amount

because of

Qci Net amount

because of

Qri Net amount

because of

Qo Net amount

environment

Qco Net amount

environment

Q.__ Net amount

of energy transfer,. from the gas to the duct inside-7surface

forced convection and radiation heat transfer

of energy transfer from the gas to the duct inside surface

forced convection heat transfer

of energy transfer from the gas to the duct inside surface

radiation heat transfer

of energy transfer from the duct outside surface to the

because of natural convection and radiation heat transfer

of energy transfer from the duct outside surface, to the

* because of natural convection heat transfer

of energy transfer from the duct outside surface to the "ro

.A

D

Ig

g"I

w

Re

Pr

Gr

C

p

Cpw

m

k

k

Wh

environment because of radiation heat transfer

Neat transfer area of wall

Duct .equivalent diameter (four times the cross-sectional area divided

the perimeter)

Radiation intensity-factor-evaluated at the average gas temperature

Radiation intensity factor evaluated'at the inside wall temperature

Reynolds number

Prandtl number

Grashof number

Gas specific heat at constant pressure

Wall specific heat at constant pressure

Duct mass flow rate

Gas or air thermal conductivity

Duct wall thermal conductivity

Heat transfer coefficient (natural or forced convection)

by

v
p Duct wall density

t Time

At Time-step size

Ax Thickness of each wall node

a Stephan-Boltzman constant.

Ci Emissivity of duct inside surface

Emissivity of duct outside surface evaluated at the outside duct wall

temperature

'Absorptivity of the duct outside surface evaluated at the outside air

temperature

vi
FIRAC USER'S MANUAL

A COMPUTER CODE TO SIMULATE FIRE ACCIDENTS IN NUCLEAR FACILITIES

by

B. D. Nichols and W. S. Gregory

ABSTRACT

This user's manual supports the fire accident analysis computer code FIRAC. FIRAC is designed to estimate radioactive and

nonradioactive sourcelterms and to predict fire-induced flows

.and thermal and material transport within the ventilation systems of nuclear fuel cycle facilities. FIRAC has been expanded

and modified to include the capabilities of the zone-type compartment fire model computer code FIRIN developed by Battelle

-Pacific Northwest Laboratories. The two codes have been coupled

to provide an improved simulation of a fire-induced transient

within a facility. The basic material transport capability of*

FIRAC has, been retained and includes estimates of entrainment,

convection, deposition", and-filtration of material. Also, the

interrelated effects of filter plugging, heat transfer,, gas dynamics, material transport, and fire and radioactive source

terms are simulated.

This report summarizes the physical. models that describethe

gas dynamic, material transport, heat transfer, and source termprocesses and illustrates how a typical facility is modeled us-•_

ing the code. The modifications-required to couple the code to

FIRIN also are presented. Finally, the input and code-calculated 'output for several sample problems *that illustrate some of

the capabilities of the code are described.

1
1. INTRODUCTION

This user's manual supports an expanded and modified version of the computer code FIRAC. The expanded version is designed to predict the radioactive

and nonradioactive source terms that lead to gas dynamic, material transport,

and heat transfer transients in a nuclear facility when it is subjected to a

fire. The code's capabilities are directed toward nuclear fuel cycle facilities and the primary release pathway--the ventilation system. However, the

code is applicable to other. facilities and can be used to model other airflow

pathways within a structure.

This is one in a family of codes designed to provide improved safety analysis methods for the nuclear industry. Its predecessors include

0 TVENT (a code to analyze tornado-induced gas dynamics1 ),

0 TORAC (a code to analyze tornado-induced gas dynamics and material

transport 2), and

a EXPAC (a code to analyze explosion-induced gas dynamics and material

transport 3).

The FIRAC computer code now includes ,the capabilities of the zone-type compartment fire model FIRIN, 4 which was developed by Battelle Pacific Northwest

Laboratories (PNL). The two codes have been coupled to. allow an improved simulation of a fire-induced transient within a facility.

The physical models used in the code may be divided into four principal

categories.

* Gas dynamics models

0 Material transport models

@ .Heat transfer models

* FIRIN fire and radioactive source term models

These models are summarized in Sec. II, and a detailed description of the models (except for the FIRIN fire and radioactive source terms4 ) is presented

in the appendixes. Setting up a computer model to simulate a given system's

response to a fire transient is discussed in Sec. III. Modeling strategies and

examples for several flow networks are given.

Translating the computer model to the actual deck that the code uses as

input is discussed in Sec. IV. The data deck organization and input card

specifications are presented, and the output from the computer code also is

discussed. This includes both expected results and diagnostic messages that

2
may be returned in case of program abort. Also, several system-dependent features of the code are discussed in Sec. IV. Information concerning installing

the code on a computing system, computer storage requirements, file requirements, and system-dependent subprograms is presented.

An illustration of the modeling strategies for several flow networks is

discussed in Sec. V. Also, the initial inputs needed to run the selected sample problems are discussed, and the data (input) deck required to run the sample problems is provided. Finally, typical selected output results are presented and discussed.

II. PHYSICAL MODELS

A. Gas Dynamics Models

A system is modeled using a flow network. The flow network consists of

two distinct types of components: nodes and branches. A node can be either a

boundary node, where the conditions (pressure and temperature) are known as a

function of time, or a room node, where the laws of conservation of mass and

energy are applied. Branches connect any two nodes, and branch models are provided to represent

* ducts,

0 dampers or valves,

* filters, and

0 blowers or fans.

The physical models representing these components are quite varied, and are summarized below. The equations used and the numerical solution method for the

resulting equations are detailed in Appendix A.

1. Ducts. Ducts are modeled using a momentum equation that includes the

effects of inertia, friction, heat transfer, and gravity (buoyancy). In the

case of high flow rates, the momentum equation is replaced by a choking condition. A distinguishing characteristic of the duct model is the nonlinear

steady-state pressure drop relationship:

2 Ap = Rpv

3
where Ap is the pressure drop across the duct, p is the density, v is the gas

velocity, and R is a constant resistance coefficient. The code will calculate

the value of the resistance coefficient based on input values of pressure drop

and flow. A user-specified resistance coefficient also may be used. The resistance coefficients are used to obtain both the steady-state and transient

results.

Because a lumped-parameter formulation is used in this code (Appendix A),

no spatial distribution of parameters along the length of the duct is calculated. However, the user may obtain more spatial detail by dividing the duct into a number of smaller sections. For example, a 100-ft-long (30.48 m) duct

could be treated as 10 10-ft (3.05-m)-long ducts in series. This method is

illustrated in one of the sample problems in Sec. V.

Heat transfer effects along the length of the duct will be calculated if

requested by the user; otherwise, they are ignored. More details on the available heat transfer models are given in Sec. II.C and Appendix B.

2. Filters. Filters are modeled as elements that exhibit only resistance

to flow (that is, no inertia, buoyancy, or heat transfer). The fundamental

aspects of filter behavior are reviewed in Appendix C. In general, the pressure drop across a clean filter consists of a sum of linear and quadratic dependencies on the flow rate. The equation is of the form

2 Ap 0 = aQ +.bpQ2, (1)

where Ap0 is the filter pressure drop, Q is the volumetric flow rate, p is

the gas density, and a and b are constants. In general, only the linear part

of the curve (b = o) is applicable to fire situations. In this case, the code

will calculate the value of the resistance coefficient, a, based on input values of pressures and flow rates. If necessary, the complete equation may be

specified, which requires additional user input.

A filter plugging model is provided that modifies Eq. (1) when there is

materialfaccumulation on the filter. This model is derived in Appendix C. The

net result is that a filter with material accumulated on it is modeled by a relation of the form

4
apa Apo0 a

where Ap0 is the pressure drop for a clean filter (at the same flow rate), Ap

is the pressure drop for the dirty filter, Ma is the material mass on the

filter, and a is the filter plugging factor dependent on filter and material

properties and has units of the reciprocal of mass. The resistance for dirty

filters usually is estimated as 2 to 5 times that for clean filters.

3. Dampers and Valves. Dampers and valves are modeled as elements that

exhibit only resistance to flow. The pressure drop across these elements is

modeled as a quadratic dependence on the flow rate,

Ap =RQ2

The resistance coefficient, R, may be calculated by the code or entered by the

user (similar to the input for ducts).

4. Blowers and Fans. The model of a blower or fan is discussed in

Appendix D. The model essentially depends on the performance curve of the

blower obtained at standard conditions. The model then adjusts these data to

predict the blower performance at off-design conditions. The blower head/flow

characteristic curve is input as a number of points on the curve obtained from

the manufacturers' data and measured at standard conditions Cp = 0.075 lb/ft 3

(1.20 kg/im3 )]. The curve then is approximated by a number of straight-line

segments as shown in Fig. 1. As discussed in Appendix D, all the segments

should have a negative slope.

A fire event usually will not lead to blower performance in the outrunning

(0P negative) or backflow (Q negative) regions. If this is the case, points on

the curve in these regions need not be entered. However, estimates must be made

if it is necessary to enter data in these regions because there is little manufacturer data for these regions. The Los Alamos National Laboratory has obtained

blower data in the outrunning and backflow regions from which such estimates can

be obtained. An example of these data is shown in Fig. 2. This information is

preliminary, and more data are needed before the blowers can be modeled accurately in the abnormal flow regions. However, this information can be used as a

5
qn -

S20

• 10-

~-20

rz•

M -30 -

-401

-10000 0 10000 20000 30000 40000

FLOW (cf m)

Fig. 1.

Computer model representation of a

typical blower characteristic curve.

6
307

2U)

-OW

10

I20 -

M- -30

-40

-40- . , , , ,

-10000 0 10000 20000 30000 40000

FLOW (cfm)

Fig. 2.

Quasi-steady-state characteristic curve

for a 24-in. (0.61-m) centrifugal blower.

7
guideline for estimating the blower performance in these regions. Asan approximation, we use the same slope in the backflow quadrant as that to the

right of the typical operating point in our blower model inputs.

5. Rooms, Cells, or Plenums. Components that have a finite volume (such

as rooms, gloveboxes, plenums, and cells) are modeled using capacitance nodes

or room nodes. The capacitance of the node is represented by its volume. Duct

volume should be taken into account by including its volume in an adjacent

room(s). (See Sample Problem 1 in Sec. V for an example of this concept.)

Mass and energy storage at these nodes is taken into account by using the conservation of mass and energy equations. The conservation equations are applied

to the room nodes using a lumped-parameter formulation assuming a homogeneous

mixture and thermodynamic equilibrium. Therefore, spatial details within the

nodes are not predicted.

An ideal gas (air) equation of state is assumed in the conservation equations. In the room nodes, the user may specify various combinations of pressure and temperature transient values along with various combinations of energy

and mass sources. If the quantities are not specified, they are calculated by

the code.

6. Boundary Nodes. Any node for which the pressure and temperature can

be specified is considered a boundary node. An example is the supply and exhaust openings from a ventilation system to the atmosphere. The computer model

of a system must have at least two boundary nodes. These nodes serve as boundary conditions for the remainder of the system. Both pressure and temperature

must be specified for any boundary nodes contained in the computer model. The

values of these quantities may be held constant for the transient, or they may

be varied by a user-defined time function.

In addition to the standard boundary node described above, the coupled

version of the code requires that the model of the system under study have at

least two internal boundary nodes if FIRIN is used to simulate the fire-induced

transient. The internal boundary nodes are necessary to represent the fire

compartment within the network. An internal boundary node should not be confused with an internal node representing a room (volume). The internal boundary

node is not treated as a capacitance node but is treated like a standard boundary node within the FIRAC computational formulation. The details and importance of the internal boundary node will be discussed and explained in

Sec. II.D.

8
7. Leakage. Leakage paths from the system to the atmosphere may be approximated in the model by using a boundary node and a fictitious duct. The

initial specified duct flow rate is the desired leak rate. During the course

of a transient, the leak rate will vary, depending on the calculated system

pressure response.

B. Material Transport Models

1. Introduction. The material transport portion of the code estimates

the movement of material (aerosol or gas) in an interconnected network of ventilation system components representing a given fuel cycle facility. Using

this capability, the code can calculate material concentrations and material

mass flow rates at any location in the network. Furthermore, the code will

perform these transport calculations for various gas dynamic transients. The

code solves the entire network for transient flow and in so doing takes into

account system interactions.

A generalized treatment of material transport under fire-induced accident

conditions could become very complex. Several different types of materials

could be transported, and more than one phase could be involved, including

solids, liquids, and gases with phase transitions. Chemical reactions could

occur during transport that lead to the formation of new species. Further,

for each type of material there will be a size distribution that varies with

time and position depending on the relative importance of effects such as homogeneous nucleation, coagulation (material interaction), diffusion (both by

Brownian motion and by turbulence), and gravitational sedimentation. We know

of no codes that can model transient-flow-induced material transport in a network system subject to the possibility of all of these.complications. The

transport portion of the code does not include this level of generality either.

However, this version of the code does provide a simple material transport capability.

The material transport components of this code are

1. material characteristics,

2. transport initiation,

3. convective transport,

4. aerosol depletion, and

5. filtration.

9
Material characteristics and transport initiation are areas that must be considered by the user as he begins to set up the code to solve a given:problem.

Calculations of convective transport, aerosol depletion, and filtration are

performed automatically by the code. Items 2--5 are actually separate subroutines or modules within the code. Item 3, convective transport, is a key subroutine that calls on items 2, 4, and 5 as needed during the course of the calculation. Each of the components listed above is subject to certain:limitations and assumptions that will be brought out below or in Appendix C. We also

will specify the required user inputs and provide appropriate references for

the theory in each case.

2. Material Characteristics. The material transport models have some

limitations with regard to the physical and chemical characteristics of the

material. The pneumatically transportablecontaminant material can consist of

any number of aerosol or gaseous species. However, no phase transitions or

chemical reactions are allowed., For example, condensation and gas-to-particle

conversion are not permitted. If the contaminant is an aerosol (solid particles or liquid droplets suspended in air), a size distribution can be simulated. In this case, within each size range, the material will be treated as

monodisperse (equal-sized), homogeneous (uniform density), spherical particles

or droplets during a given code run. Both the size and density of each specie

must be specified by the user. If the contaminant is a gas, then it is assumed

to be inert. User guidance in the area of aerosol and gas characteristics is

provided in Appendix C. Some suggestions are made for describing fuel-grade

plutonium and uranium oxide powders.

3. Transport Initiation. To calculate material transport using the code,

the analyst must determine or assume the location, distribution, and total

quantity of contaminant material. This material can be located or generated

in rooms, internal boundary nodes representing the fire compartment, cells,

gloveboxes, corridors, or rectangular ductwork. (An assumption about material

distribution is only necessary when the user wishes to exercise the calculated

aerodynamic entrainment of dry powder from thick beds option discussed below.)

A total quantity (mass of material) must be known or assumed.

There are three options for material transport initiation: user-specified, calculated aerodynamic entrainment, and FIRIN-calculated material generation. The user-specified option allows the analyst considerable flexibility

10
but requires engineering judgment to specify input to the code. This option

involves preparing a table or graph of material generation rate or mass injection rate (kilogram per second) vs time. The data are supplied to the code on

the input deck TIME FUNCTION DEFINITION DATA CARDS.

For example, a given cell can have a given quantity of fuel-grade uranium

or plutonium powder injected at a specified. rate. The injected material also

could be a gas. This user-specified option may be selected to calculate the

consequences of a hypothetical aerosol or gaseous release and is recommended

for the case of'reentrainment from thin beds (dirty cells or ductwork). The

code was developed assuming that off-design flows are the primary cause of

source term initiation. Los Alamos is developing other codes specifically to

assess the consequences of tornados and explosions. For accidents that do not

disrupt the normal ventilation system flow significantly, such as pressurized

release, spills, and equipment failures, a general purpose utility code may be

used. Guidance for the user to estimate source terms may be found in

Appendix C.

The user may wish to specify a material generation rate vs time. This

procedure is exactly the same as that discussed above. That is, a table or

graph of mass injection rate can be specified to simulate the injection of

material associated with the event.

The calculated entrainment option specifically refers to a subroutine

designed to calculate aerodynamic entrainment of dry powder from thick beds.

This subroutine can be useful for analyzing material transport initiation. It

uses a new semi-empirical analytical approach for calculating entrainment that

takes advantage of detailed flow information produced by the gas dynamics module. To arrive at our estimate of mass of material entrained at each time step

of calculation, this subroutine calculates when the surface particles will begin to move. To do this, particle, surface, and flow characteristics are taken

into account. It also accounts for the aerodynamic, interparticle (cohesion),

and surface to particle (adhesion) forces that may be acting. This procedure

was used previously (Ref. 5) and is discussed more fully in Appendix C. The

calculated entrainment option may be used whenever powder beds are known or

assumed to be present. The code must be provided with particle size and density (Appendix C), total mass of contaminant, and the floor area of the (assumed

duct) surface over which the powder is uniformly distributed.

11
The FIRIN module (subroutine) calculates various particulate and gaseous

specie generation rates and concentrations for the fire compartment. If the

user selects the FIRIN models..to simulate the release of particulate material,

up to 13 particulate and 3 gaseous species can be transported by the FIRAC material transport. models. The first two particulate species (nspecie = 1 and

nspecie = 2) are the total smoke and total radioactive particulates, respectively. The total radioactive particulate mass released as a result of the

fire has been divided into 11 particle size distributions. These particle size

distributions are generated within the FIRIN radioactive source term subroutines and are transported as the remaining 11 particulate species (nspecie = 3

through nspecie 13). The. particle size distributions are shown in Table I.

TABLE I

FIRIN-GENERATED SPECIES AND SPECIE IDENTIFI'CATION

Particul ate

Smoke particulate

Total radioactive particulate

Specie Identification Number

nspecie* = 1

nspecie = 2

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

Radioactive

particul ate

particulate

particulate

particulate

particulate

particulate

particulate

particulate

particulate

particulate

< 0.1 m

between 0.1 and 0.3 Um

nspecie = 3

nspecie* = 4

between

between

between

between

between

between

between

between

0.3 and 0.5 pm

0.5 and 0.7 um

0.7 and 0.9 um

0.9 and 1.1 um

1.1 and 2 ur.

2 and 6 um

6 and 10 um

10 and -20 um

nspecie

nspecie

nspecie

nspecie

nspecie

nspec1e

nspecie

nspecie

=5

- 6

=7

: 8

=9

10

11

= 12

particulate > 20.0 pm nspecie = 13

Gaseous-Species

Oxygen

Carbon dioxide

Carbon monoxide

Specie Identification

ngspecie* = 1

ngspecie = 2

ngspecie = 3

*See input specifications for RUN CONTROL CARD II.

12
'The sum of the materialhapportioned within particulate-species 3 through 13 is

equivalent.-to the total radioactive particulate material (mass) represented by

nspecie 2.

The userhas two options to transport radioactive p~articulate generated by

FIRIN. The user can transport all 11 radioactive 'particle size's or only the

total radioactive particulate (nspecie = 2.). If the distribution of material

is to be transported., the code Will restrict the transport of the totalbparticulate quantity automatically. The system would contain twice the amount of

radioactive material actually available if nspecie = 2 through nspecie.= 13

were transported. The transport of only the total radioactive particulate requires that the user set the number of particulate.species .(input parameter

nspecies) equal to 2 and select a representative'particle diameter and density. The transport of mater-ial does contribute to the total time (cost) for a

fire-induced flow simulation. (See Sec. IVA.d,) In some cases it may be possible for the user to, reduce the number of species (using the option described

above) and thus reduce the running time (cost) for a calculation without losing detail.

4. Convective Transport-. The, code includes a simple material, transport

model with the.capability of p,.edicting airborne materialdistribution in a

flow network and its release to.the environment. Accidental release to the

environment from a fire is a major concern'in nuclear facilities because the

airborne material could be radioactive or chemically toxic.. The model is based

on the assumptions that the particle size is,•small and its.mass fraction is

small relative to the gas mass in the same volume. This allows us to assume

that the material and the gas form a homogeneous mixture and that they are in

dynamic equilibrium. In this case, the gas dynamic aspectofjthe problem is

not affected by the presence of the airborne material, and the particulate or

material velocity is the same as the gas velocity at any location and time.

-Accordingly, the only relation needed to describe the motion of the material isthe continuity. equation. 'This modeling ,.and the underlying assumptions are, •

presented in more detail in Appendix C.

13
5'. Material Depletion. Once the user has chosen to exercise material'

transport, he can calculate aerosol'losses caused by gravitational sed-imentation in horizontal, rectangular, or round ducts. Aerosol depletion may be

calculated throughout the network during transient flow. The theory is basedon quasi-steady-state settling with the terminal settling velocity corrected

by the Cunningham slip factor. The flow in ducts and rooms 'is assumed to be

well-mixed so that the aerosolconcentration is uniform within the volume.

The user must. supply the aerosol diameter, density, and duct height to this

model.- Th'e aerosol may consist of solid particles or liquid droplets. (More

detail and references may be found in Appendix C.)

6. Filter Loading. A phenomenological approach to filter loading is

presented. The filter gas dynamic performance can be changed by the accumulation of airborne material on the filter, which in turn causes an increase in

resistance. 'A linear model is used in which the increase in resistance is

linearly; proportional to the amount of material on the filter. The proportionality constant is a function of the fuel source and filter properties. The user

supplies the filter efficiency and plugging factor. Some information on the

filter plugging factor is given in Appendix C.

C. Duct Heat Transfer Model

The purp6se of the duct heat transfer model is to predict how the combustion gas in the system heats up or cools down as it flows throughout the ducts

in the ventilating system. The model predicts the exit gas temperature for any

section-of the duct if the inlet temperature and gas properties are known. An

ancillary result of the calculation is the duct wall temperature. A heat

transfer calculation is performed for a duct component. Furthermore, the calculation is performed in a given duct only if that branch has been flagged in

the input deck. Experience in using the code has shown that duct heat transfer calculations can'increase the computer running time"by a factor of 2.

Therefore,we advise that duct heat transfer calculations be performed only

where needed. Generally, the main region ofinterest and concern is those

ducts downstream from the firre compartment and especially between the fire compartment and any filters downstream from it.

The overall model is composed of fivedistinct sub-models of heat transfer processes along with a numerical solution procedure to evaluate them. The

following heat transfer processes are modeled.

14
* Forced-convectionheat transfer between the.combustion gas and the

inside duct walls

e "Radiation heat transfer ,between the combustion gas, and the inside duct

walls

@ Heat conduction through the duct wall

0 Natural convection heat transfer from the outside duct walls to the

surroundings

0 Radiation heat.transfer from the outside duct. walls to the atmosphere

Details concerning *the physical assumptions and simplifications as well as the

heat transfer correlations and their. ranges of applicability-are given in

Appendi~x B. There it is shown that the. total amount of.energy removed from

the gas as it flows through the duct. is the solution-.of a set of four nonlinear

algebraic equations. The solution procedure used to solve these equations also

is presented in Appendix B.,-

The user inputs required to execute the duct heat transfer model include

the following duct properties.

0 Equivalent diameter and. heat transfer area

e Outside wall. emissivity and absorptivity

0 Wall density, thermal conduct-ivity,.specific heat, and thickness.

A typical application of the duct. heat.transfer model is.shown in one.of

the sample problems presented in Sec. V.-. The-actual -code inputs are shown, and

typical output -results. are discussed for a full-scale.(but simple) system..

D. FIRIN Fire and Radioactive Source Term Simulation

1. Summary. Fire-generated radioactive and nonradioactive source terms

are estimated in the FIRIN module of the FIRAC code....The FIRIN code, which

was developed by PNL under the sponsorship of the Division of Risk.Analys.i.s-.-of

the US Nuclear Regulatory Commission, uses a zone-type compartment fire model.

A zone-type fire compartment assumes that the gas in the room is divided into

two homogeneous regions,, or layers, during, a fire. One, layer (the hot layer)

develops near the ceiling and contains the hot combustion products released

from the burning material. The cold layer, which is between the hot layer and

the floor, contains fresh air. FIRIN predicts the fire source mass loss rate,

,energy generation rate,ý and fire room conditions (temperatures of the two

layers and room pressure) as a function of time. It also calculates the mass

15
generation rate and particle size distributions for radioactive and.nonradioactive particles that can become airborne for a given fi:re accident scenario.

The radioactive release factors incorporated-within, the FIRIN module are primarily those developed in experimental work at PNL, and the combustion product

data were developed from a literature search of combustibles that-commonly are

found in nuclear'facilities. 4 More information on the fire and radioactive

source term models and FIRIN code assumptions is available in Ref. 4.

2. FIRAC/FIRIN Integration.

a. Introduction. The coupling scheme chosen for integrating FIRAC and

FIRIN uses internal boundary nodes to represent the fire compartment within the

network. Internal boundary nodes are boundary nodes that are located within

the network. Typically, boundary nodes are used to define the conditions at

the inlet and outlet of the network. The use of internal boundary nodes within a system required that FIRAC and FIRIN be modified to produce an interactive

code version.

An interactive version of the code was obtained by requiring that FIRIN

calculate the fire compartment'thermodynamic conditions'(pressure and-temperature for each layer) and the particulate and gaseous releases (in the form of

concentrations) at each time step. This FIRIN-supplied information is transferred to FIRAC through'the internal boundary node scheme. The internal boundary nodes that represent the fire compartment are assigned the FIRIN-calculated

pressures, temperatures, particulate, and gaseous species concentrations at

each time step. Within the computational formulation of FIRAC, the internal

boundary nodes are treated. as.standard boundary nodes; that. is, the internal.,

boundary nodes can have pressures and temperatures specified as, a function of

time. Because boundary nodes are-zero-capacitance -nddes, several modifications

to the material transport subroutines were made to permit material concentrations to be assigned at the internal boundary nodes. When the FIRIN-calculated

fire compartment conditions for that time step have been transferred to FIRAC

(as boundary node conditions), the network response (system flows, material;.

transport, and heat transfer) can be determined by FIRAC. The FIRAC-calculated

total inlet and outlet volumetric flow rates for the fire compartment (based

on the current fire compartment conditions) are transferred to FIRIN to complete one computational cycle. ýA schematic of the coupling 'scheme is presented in Fig. 3.

16
FIRE COMPARTMENT

DESCRIPTION

FIRIN

FIRE COMPARTMENT

CONDITIONS

4

N

ACCIDENT DESCRIPTION

SOURCE TERMS.

PRESSURE

HOT LAYER TEMPERATURE

SMOKE CONCENTRATION

RADIOACTIVE PARTICLE CONCENTRATIONS

VARIOUS GASEOUS SPECIES CONCENTRATIONS

INITIAL

CONDITIONS

AEROSOL

RELEASE

RATE

FIRAC

SYSTEM RESPONSE TO

FIRE COMPARTMENT

CONDITIONS

FACILITY

DESCRIPTION

VPRESSURES

TEMPERATURES

FLO RAES

FACILITY

AEROSOL

DISTRIBUTION

Fig. 3.

Schematic of FIRAC/FIRIN coupling.

17
At least two internal boundary nodes are required to represent the fire

compartment because the FIRIN-zone-type model requires an inflow and outflow

condition for the compartment. Three internal boundary nodes can be used to

extend the fire compartment model. The additional internal boundary node is

not required but could be used to simulate a potential leak path or an additional compartment flow condition. For example, if there were several inflow/

outflow conditions that needed to be modeled, it could be beneficial to use the

third internal boundary node instead of lumping the flow conditions into a major inflow/outflow condition.- (See Sec. III.C.)

b. FIRAC Input Changes. The input specifications for FIRAC requires

several values in addition to the necessary FIRIN input data.• These additional

input values assist in the transfer of information between the FIRIN module and

the FIRAC subroutines. The FIRIN input and the new input variables that assist

in the coupling of the two codes are incorporated within the input specifications section of the manual. (See Sec. IV.C.).

c. Internal Boundary Node Pressures and Temperatures. The FIRIN twolayer, fire compartment model calculates a pressure, a cold-layer temperature,

and a hot-layer temperature for the compartment. The two internal boundary

nodes are assigned the FIRIN-calculated compartment pressure at each time step.

Based on the user-specified duct elevation and diameter of the inlet or outlet

of the fire compartment and the position of the hot layer, the internal boundary nodes are assigned a value of the FIRIN-calculated cold layer, hot layer,

or an averaged temperature value. If the hot layer is positioned above the

duct centerline elevation plus one-half the duct'diameter,..the internal boundary node representing the fire compartment inlet or outlet would be assigned a

temperature value equal to the FIRIN-cold-layer temperature. Similarly, if the

hot layer is positioned below the duct centerline eleVation minus one-half the

duct diameter, the internal boundary node is assigned the value of the FIRIN

hot-layer temperature. .' When the hot. layer is positioned within, the region of

the flow boundary, the internal boundary node is assigned a-temperature value

that is a function of the hot- and cold-layer temperatures and the position of

the hot layer with respect to the flow boundary centerline elevation. The user

must enter the duct elevations and diameters for the internal boundary nodes

in the fire compartment initial conditions and noding data cards.

d. Internal Boundary Node Material Transport. The improved FIRAC code

version is capable of transporting 13 particulate species and 3 gaseous species

18
generated by.FIRIN. Eleven of the thirteen particulate species are radioactive

particles ranging in size from less than 0.1 rnm.in diameter to greater than

20 urm in diameter.. The remaining particulate species are the.total smoke and

radioactive particulate generated by the fire. The three. gaseous species that

.can be transported are the hot-layer combustion products (oxygen, carbon dioxide, and carbon monoxide). The values of the smoke, radioactive particles,

oxygen, carbon dioxide, and carbon monoxide concentrations calculated by the

FIRIN subroutine are transferred to FIRAC at each time step. Based on the userspecified physical properties of the species, the FIRAC material transport models (convection, deposition, entrainment, and so on) are used to determine the

time-dependent transport characteristics and concentration of the particulate

and gaseous species throughout the system.

III. SYSTEM MODELING STRATEGIES FOR FIRE-INDUCED TRANSIENTS

A. General

FIRAC is designed to predict airflows in an arbitrarily connected network

system. In a nuclear facility, this network system could include process

cells, canyons, laboratories..offices, corridors, and offgas systems. In

addition, an integral part of this network is the ventilation system. The

ventilation system is used to move air into; through, and out of the facility. Therefore, the code must becapable of predicting flow through a network

system that also includes ventilation system components such as filters, dampers, ducts, and blowers. These ventilation system components are connected

to the rooms and corridors of the facility to form a complete network for

moving air through the structure and perhaps maintaining pressure levels in

certain areas.

B. Fire Accident System Modeling

1. Model Set Up. The first and most critical step is setting up a model

of the air pathways in a nuclear facility, which requires a schematic showing

the system components and their interconnections. Drawings, specifications,

material lists, safety analysis reports, and existing schematics are sources

that can be used in deriving a system description. A physical inspection of

the facility and consultations with the designer(s) before and after the schematic is drawn may be necessary to verify that it is correct. Frequently,

there is a lack of needed data at this step. Although there is no substitute

19
for accurate data, certain .assumptions, averaging, or conservative.estimates

can be used to make the problem manageable.. Figures 4 and 5 show how a simple

ventilation system within a facility structure can be transformed into a network schematic. We will illustrate the system modeling concepts in the next:

section and then provide additional detail for the flow and material transport

modeling.

2. System Definitions. Three terms are used to describe the construction of a model and are used extensively in the remainder of this report.

0 System - A network of components (branches) joined together at points

called nodes.

0 Branch - A connecting member between upstream and downstream nodal

points. A branch contains one component such as a duct, valve, damper, filter, or blower. Gas flow, pressure differential, and material

flow are associated with branches.

* Node - A connection point or junction for one or more branches. Volume elements such as rooms, gloveboxes, and plenums are defined as

capacitance nodes. ýEven a long duct or slow pathway is divided into

a series of volume nodes. Compressibility of the system fluid is

taken into account at these capacitance nodes. Boundary points also

are defined at nodes; gas pressure, density, temperature, material

concentration, and mass fraction are specified at nodes. The improved FIRAC code version has a third type of junction or point, the

internal boundary node. As mentioned earlier (Sec. II.D.2), internal

boundary nodes are required to represent the fire if the FIRIN fire

compartment effects subroutine (module)' is selected.

3. Fire Compartment Modeling Options. The organization of the ventilation system components that will form the complete network will depend on the

user-specified fire simulation option. Two options are available in FIRAC to

simulate a fire within a ventilation system. One is to use the FIRIN fire compartment model that has been integrated within FIRAC. The second is to apply

the user-specified time function capability. This option enables the user to

simulate a fire in a capacitance node by inputting an energy release rate (to

simulate heat addition to the'room) and particulate and gaseous species generation rates (to simulate combustion particles and gases and radioactive particle releases)'for that V.iume.

20
Fig. 4.

Example of a simple facility with a ventilation system.

N3
CELL L i

BUILDING

Fig. 5.

Network schematic of a simple facility with a ventilation system.
If the user selects the FIRIN fire compartment module, internalboundary

nodes must be used to represent the fire compartment (room). The remainderobf

the system can be modeled with the more conventional components (branches and'

capacitance and boundary nodes). If the user-specified time function option

is selected, the system model requires the use of conventional:components only.

Internal boundary nodes should be used only if the user plans to enable the

FIRIN module.

Typically, the user would select one of the two possible options to simulate a fire. However, both options could be used simultaneously to simulate

several fires in a facility. The FIRIN module can be used to simulate a fire

in only one location of the facility network; however, the user-specified time

function option could be used to represent additional fires in..other capacitance nodes.

C. System Modeling Examples

Network ,systems.for airflow through a.nuclear facility may be constructed

using a building block approach. The building blocks that are used.toconstruct fire network analysis systems are shown in Fig. 6 and can be arranged

as shown in Figs. 7(a) and 7(b) to form arbitrary systems. These building

block symbols will be used throughout this report. An exampled showing how the

building block schematic corresponds to a simple network system for the userspecified time function fire simulation option is presented in Fig. 8(a).

Nodes 1 and 11 in Fig. 8(a) are boundary nodes. A capacitance node (node 4)

represents the sampling room where the fire is postulated to occur. Branches

are shown in Fig. 8(a) at the tips of arrows. The branch numbers are enclosed

in parentheses adjacent to their corresponding branches. Note that branch 3

is connected on the upstream side by node 3 and on the downstream side by

node 4.

Figure 8(b) illustrates how the example shown in Fig. 8(a) would be modified to accomodate the FIRIN option for a postulated fire in node 4. The nodes

representing the intake and exhaust conditions (nodes-1 and 12) are boundary

nodes. The sampling room and postulated fire location that was represented by

a capacitance node (node 4) in Fig. 8(a) is replaced with two internal boundary
DAMPER

-HXJ----FILTER

II~j~INTERNAL BOUNDARY NODE

(REPRESENTING A FIRE ROOM)

~ ROOM (ONLY AT INTERNAL

NODES)

BLOWER

-Av~---oDUCT'

Fi g. 6.

Fire network analysis building blocks.

24
BOUNDARY NODES

INTERNAL NODES

1

(1) (2)

Arbitrary

Fig. 7(a)aitn, nds system using capacitance nodes.

M.3

L,
M)3

BOUNDARY NODES

- INTERNAL NODES

INTERNAL BOUNDARY

.- NODES 7

Fig. 7(b),

Arbitrary system using capacitanc'e

and internal boundary nodes.
INTAKE

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Fig. 8(a). Building block correspondence with standard noding.
rNCO

INTAKE

L-i, I=I-- ,- &- W ""Li=

(1) (2) (3) (4) (5) (6) ý(7) (8) (9) (10)

Fig. 8(b).

Building block correspondence with internal boundary noding.
nodes (nodes 4 and 5) as shown in Fig. 8(b). Two internal boundary nodes are

required to model the room's intake and exhaust. In the input deck, the user

will specify the fire room intake and exhaust branch identification parameters,

duct elevations and diameters, the two internal boundary node identification

parameters, and other information that will enable the FIRIN compartment model

and the FIRAC systems code to be interactive.

We have illustrated extremely simple network systems. A slightly more

complex system is shown in Fig. 9, and the corresponding schematics are shown

in Figs. 10(a) and 10(b). The conventionally modeled system shown in

rig. 10(a) illustrates a room (node 2) with three connected branches (1, 2,

and 3), and a leakage path around the cell (node 3) access hatch also is modeled using branch 5 and node 5. If a fire were postulated to occur in the

cell, the user could specify the necessary time function data for node 3

(energy release rate, particulate and gaseous species release rates, and so

on) to simulate the fire accident. If the user selected the FIRIN model option, the flow network computer schematic shown in Fig. 10(b) presents an

example of one possible noding arrangement for this option. The cell can be

represented by three internal boundary nodes. Internal boundary nodes 3 and 4

model the intake and exhaust to the cell, and internal boundary node 5 models

the potential leak path (access hatch). FIRAC can model three main connections (requiring three internal boundary nodes) to a FIRIN fire compartment

(Sec. ll.D.2). If more than three inflow/outflow conditions are specified for

the room that will represent the fire compartment, several approximations.may

be required. The selection of the inflow/outflow approximations is an important consideration because the flow conditions influence the mass and energy

balance in the fire compartment. For example, if the fire compartment had the

inflow/outflow conditions as shown in Fig. 11(a), two feasible modeling options

are possible [Figs. 11(b) and 11(c)]. The first option would be to combine the

inflow conditions of intakes 2 and 3 because these intakes represent a fraction of the total inflow condition and are located at the same room elevation.

Another possibility would be to combine all three intakes [Fig. 11(c)]. This

arrangement would require an average inflow room elevation and duct diameter

(required fire compartment input parameters) based on the three intakes.

29
ACCESS HATCH

(POTENTIAL LEAK) STACK-

%l-II / DAMPER -

ROOM

~.EaLaIJ

F! LTER

DAMPER

Fig. 9.

Simple flow network with leak path.

30
5

(5)~

1

(1) (3) (6) (7) (8)

Fig. 10(a).

FIRAC model of the simple flow network

with leak path using standard noding.

CA)
6

(5)

a • 0

1

(1) (3) (6) (7) (8)

Fig. 10(b).

FIRAC model of the single flow network with

leak path using internal boundary noding.
EXHAUST

INTAKE 1

INTAKE 3

INTAKE 2

SFig. 11(a).

Fire compartment example with several inflow ventilators.

33
INTAKE I EXHAUST

INTAKE 2

INTAKE 3

Fig. 11(b).

Fire compartment representation with three internal boundary nodes.

INTAKE 1

INTAKE 2

INTAKE 3

EXHAUST

Fig. 11(c).

Fire compartment representation with two internal boundary nodes.

34
This configuration would not be as accurate because of the engineering approximations for the inflow elevation and duct diameter. In some cases the user

may be confronted. w.ith using, approximations and. may need to perform a sensitivity study to determine the importance of the approximations selected.

IV. USER INFORMATION AND PROGRAMMING DETAILS

A. Input Organization

The improved FIRAC input deck is divided into 10 sections: problem control, branch geometry, specie description, boundary node, time function, capacitance node, component, initial conditions, FIRIN module, and time-step. These

blocks of data are read in -the order shown in Fig. 12 and compose the FIRAC

input file FIN. The problem control data cards contain general problem control information including title cards for problem identification, output and

plotting package control, steady-state or transient run options, iteration convergence criteria, and geometry, component, FIRIN simulation option and time

function control options. The branch geometry data, blocks specify the branch

general geometric characteristics (branch identifier, adjacent nodes, length,

flow area, and so on) and branch heat transfer characteristics if the heat

transfer option is enabled.

- The boundary node data block section contains initial values, for the

boundary node, pressure, and/or temperature time 'function identifiers and the

boundary node type. Internal boundary nodes are required if the FIRIN simulation option is selected. (See Secs. II and III.)

If particulate and gaseous species are present and indicated in the problem-control data block, the data for the species selected will follow the

branch geometry input. For particulate species,, the user must. specify the

particle identifier, diameter, and density and can input initial mass fractions and initial wall mass if desired. For the gaseous species, the user

must specify the gaseous species identifier and can select initial volume

fractions. The selection of particulate and gaseous specie identifiers is re

stricted by internal modifications made to FIRAC to accomodate FIRIN. These

restrictions are discussed in Sec. II B.3 and only apply if FIRIN is selected

to simulate the transient.

35
Fig. 12.

Improved FIRAC input deck organization.

36
The time function data contain time-dependent, data for boundary nodes and

capacitance nodes. -Pressure and temperature time functions can be-defined for

boundary and-capacitance (room) nodes, and energy addition, mass addition,

particulate, and gaseous species-sources also can be~defined for room nodes..

The required room data block that follows the time function information specifies the room, node identifier, room volume, cross-sectional, area, elevation,

and time functionzidentifiers.

Component data cards define the input parameters for the-blower and filter,

components of the system. An identifier and performance curve are required

input for the blower. The filter:data card specifies the filter identifier,

.efficiency, and plugging factor.

Initial pressure and/or.temperature conditions can be defined for each

system node if desired. The pressure and/or temperature control parameter in

the problemrcontrol data blockýmust be enabled for this-optional input.

If the user selects the FIRIN module to simulate the nonradioactive and/or

radioactive releases caused by fire, the user must define the fire growth concept; the type, quantity, and burn area of the fuel; output control parameters

that specify the edit frequency for the FIRIN-generated data; the dimensional

and material characteristics of the burn room; and the type and amount of radioactive' contaminant and the release mechanisms-associated with that contaminant. Also,.ýthe user can specify additional flow path connections to the fire

compartment, potentiallequipment heat sinks, and pressurized vessel

failures. if desired.

The last set of input information.,-is the time step cards that control the

calculation. ,The problem transient time can be divided into time domains.

Each time domain can have different time-step sizes-and output edit intervals.

B. Input Format

The FIRAC input specifications (Sec. IV.C) give the organization of the

input deck (FIN) that must be followed. If the FIN fixed formats are not followed (the location of card information is prescribed), the program will attempt to read data from an adjacent column or from the next line of input and

probably will abort with a format error. Input diagnostic messages have been

incorporated within the input processor to help the user debug improperly formatted input.

37
There are three types of input data in FIRAC: .(a) A/N, alphanumeric data

(any combination of letters and numbers); (b) FP, floating.point data; and

(c) I, integer data.: Alphanumeric data should be left-justified.with,.respectto the first column of the field definition (data should startAin the.first

column of the~field). Integer data should be right-justified in the data

field (the last data character should appear in the right-most column,-of the

field). For example, the integer 6 placed in column 4 of the first branch

description card would be .interpreted as branch 60 because the field definition encompasses columns 1 through 5. If branch 6 were to be specified, it

should be placed in column 5. Floating point data also are right-justified.

Only large or small floating point numbers require the-form +nnnE+_mm where n

and m are integers; Intermediate floating point numbers may be specified as

+nn-.nnnn- with, the decimal point given. Values of data occurring under the

heading "Default Value" are used ifthe input data field is left blank.

C. Improved FIRAC Input Specifications

In the FIRAC input deck (Table II), the sets of information are separated

by data separator cards. These cards must be included in the positions indicatedin the specifications (Table III) and should be used to identify the

data that will follow. The sets of information that form the input deck data

cards. Each data card. description has four parts: data card descriptor, card,*

comments, data type, format and. variables, and data.description. The data

type, format, and variables follow the data card comments. The data type

(alphanumeric, floating point, or integer) is indicated by the actual.format

used in the: code. The!.variables are presented.in the orderthey occur on the

data card. The data description section contains a brief description of the

data, the variable name associated with the data, the card location (column)

of that variable, the variable default value, and the variable's maximum value.

User-oriented comments.pertaining to that particular data card are presented

after.the data descriptor and .occasionally following the data description

section.

38
TABLE I I

FIRAC INPUT DECK ORGANIZATION

Card Identif~ication. General Information

Data separator

TITLE User-specified problem identification

Data separator

RUN CONTROL I Run option, initial output time, time step

for output, last output

time,, and special output times

Data separator

PRINT/PLOT CONTROL, CARD 1

PRINT/PLOT CONTROL, CARD 2

Units for output-lists and plots,

additional output times, number of plot

frames of each type

Number of plots of various information for

each specie

Data separator

PLOT FRAME Number of curves on each frame and

identification number of node or branch

Data separator

RUN CONTROL II Maximum. iterations,.convergence criterion,

calculated deposition and entrainment

options, relaxation parameter, initial

pressure input option, initial temperature

input option,-initial particulate species

mass fraction option, initial gaseous

species volume fraction option, number of

gaseous species, number of particulate

, species, natural convection option, and

fire simulation options

Number of boundary nodes, atmospheric pressure and temperature, and total number

of each time function (pressure,

temperature, energy, mass, particulate

.species, and gaseous species)

Data separator

BOUNDARY CONTROL

Data separator

39
TABLE II (CONT)

Card Identification General Information

GEOMETRY AND COMPONENT CONTROL

Data separator

BRANCH DESCRIPTION DATA, CARD 1

BRANCH DESCRIPTION DATA, CARD 2

BRANCH DESCRIPTION DATA, CARD 3

Data separator

PARTICULATE SPECIES DATA, CARD 1

PARTICULATE SPECIES DATA, CARD 2

PARTICULATE SPECIES DATA, CARD 3

Data separator

GASEOUS SPECIES DATA, CARD 1

GASEOUS SPECIES DATA, CARD 2

Total number of branches, nodes, rooms,

blower function types, filter types, and

control dampers

Branch number, upstream node, downstream

node, initial flow estimate, flow area,

duct. length, component type, differential

pressure, and blower function

identification

Forward'and backward resistance

coefficients, filter type duct height,

duct floor area, and heat transfer option

Duct equivalent diameter, heat transfer

area, wall thickness, emissivity,

absorptivity, thermal conductivity,

density, specific heat, initial wall

temperature, and number of wall heat

transfer nodes

Particulate species identification,

diameter, and particle density

Initial particulate species mass fraction

at each node

Initial particulate specieswall mass

Data separator

BOUNDARY NODE DATA

Data separator

PRESSURE TIME FUNCTION

DATA CONTROL

PRESSURE/TIME DATA

Gaseous species identification

Initial gaseous species volume fraction at

each node

Node number, node type, initial pressure,

pressure time function number, initial

temperature, temperature time function

number, and elevation

Function identification number and number

of sets of points

Coordinates - value of time and pressure

40
TABLE II (CONT)

Card Identification General Information

Data separator

TEMPERATURE TIME FUNCTION

DATA CONTROL

TEMPERATURE/ TIME DATA

Data separator

ENERGY TIME FUNCTION

DATA CONTROL

ENERGY/TIME DATA

Data separator

MASS TIME FUNCTION

DATA CONTROL

MASS/TIME DATA

Data separator

PARTICULATE SPECIESTIWE FUNCTION DATA CONTROL

PARTICULATE-SPECIES/TIME DATA

Data separator

GASEOUS SPECIES TIME FUNCTION

DATA CONTROL

GASEOUS-SPECIES/TIME DATA

Data separator

ROOM DATA, CARD 1

ROOM DATA, CARD 2

.Function identification number and number

of sets

Coordinates - value of time and temperature

Function identification number and number

of sets

Coordinates - value of time and energy rate

Function identification number, number of

sets, and temperature function associated

with injected mass

Coordinates - value of time and mass rate

Function identification number and number

of sets

Coordinates - value of time and mass rate

Function identification number and number

of sets

Coordinates - value of time and mass rate

Node number, volume, energy, mass,

pressure, and temperature time function

identification numbers, and initial values

of energy, mass, pressure, and temperature

Cross-sectional area of room, number of

particulate species time functions, number

of gaseous species time functions, and

elevation

41
TABLE II (CONT)

Card Identification General Information

ROOM DATA, CARD 3

ROOM DATA, CARD 4

Data separator

CONTROL DAMPER

Data separator

BLOWER CURVE CONTROL

BLOWER CURVE DATA

Particulate species number corresponding to

source function, time function number, and

initial value of the source function

Gaseous species number corresponding to

source function, time function number, and

initial value of source function

Controlled. node, branch number, damper

type, pressure range, initial damper angle,

rate of damper angle change

Function identification number and number

of points

Coordinates - flow and. head

Data separator

FILTER DATA

Data separator

PRESSURE INPUT

Data separator

TEMPERATURE INPUT

Data separator

Filter identification number, filter

efficiency, filter plugging factor, number

of species, and turbulent and laminar

coefficients.

Initial value of pressure at each node

Initial value of temperature at each node

SCENARIO CONTROL SPECIFICATIONS,

CARD 1

SCENARIO CONTROL SPECIFICATIONS,

CARD 2

Data. separator

INITIAL CONDITIONS

INFLOW SPECIFICATIONS

Fire duration, output

frequency, and fire growth option

Fire growth option, number of

additional flow paths, number of pieces of

equipment and vessels, and third, fire

compartment node identifier

Initial compartment temperature and pressure

Inflow branch number, inflow node number,

and height and diameter of inlet ventilator

42
TABLE II (CONT)

Card Identification General Information

OUTFLOW SPECIFICATIONS

THIRD COMPARTMENT NODE

SPECIFICATIONS

Data separator

FUEL MASS DATA

FUEL SURFACE AREA DATA

Outflow branch number, outflow.node .number,

and height and diameter of outlet ventilator

Third node branch number, third node.

number, and height and diameter of extra

ventil ator

Mass of fuels

Surface area of fuels

Data separator

FIRE COMPARTMENT GEOMETRY

Data Separator

Length, width, and height of compartment;

thickness of ceiling, wall, and floor; and

height of flame base

Ceiling, wall, and floor construction

materials

Identification of combustibles

FIRE COMPARTMENT MATERIALS

COMBUSTIBLES IDENTIFICATION

Data separator

EQUIPMENT/VESSEL IDENTIFIER

EQUIPMENT/VESSEL GEOMETRY

EQUIPMENT/VESSEL CONTENT

Data separator

Identification of equipment and vessels at

risk

Width, length, and height of equipment/

vessels; construction materials; and weight

Volume of contents,. moisture content,

initial surface temperature, initial inside

temperature, and failure (rupture) pressure

of equipment/vessel

Failure times of additional flow paths,

heights of paths, pressures at outlets, and

diameters of paths

Number of radioactive source terms

Form of radioactive contaminant,

material identification, tracking number,

and burning order

ADDITIONAL FLOW PATH DATA

Data separator

RADIOACTIVE SOURCE IDENTIFIER

CONTAMINATED COMBUSTIBLE SOLID

IDENTIFIER

43
Card Identification

CONTAMINATED COMBUSTI BLE

SOLID MASS

CONTAMINATED COMBUSTIBLE LIQUID

IDENTIFIER

CONTAMINATED COMBUSTIBLE LIQUID

MASS

CONTAMINATED SURFACE

UNPRESSURIZED RADIOACTIVE LIQUID

PRESSURIZED RADIOACTIVE POWDER

PRESSURIZED RADIOACTIVE LIQUID

RADIOACTIVE PYROPHONIC SOLID

TIME STEP CARDS

TABLE II (CONT)

General Information

Mass of radioactive material

Form of radioactive contaminant, material

identification, tracking number, and

burning order

Mass of radioactive material

Tracking number and mass of radioactive

material

Identification number, tracking number,

mass of radioactive material

Identification number, tracking number,

mass of radioactive material

Identification number, tracking number,

mass of radioactive material

Tracking number, burning order, mass of

radioactive material, and size of metal

Time step size, end of time domain, and

print edit interval

and

and

and

44
TABLE III

FIRAC INPUT DATA DECK

'DATA SEPARATOR CARDS

Col.(s) Data Description

1-80 These cards may be left blank or may contain alphanumeric

data. These cards are used to separate different types of

data cards. The contents of these cards are not used by the

FIRAC.

Only one data separator card is shown here, but these cards should be

placed in the input deck in the positions indicated in Table .H.

TITLE CARD

Col.(s) Data Description

1-80 Eighty columns of alphanumeric data are available to the

user. This title is used for headings on output lists and

user identification of the problem.

45
RUN CONTROL I CARD

(FORMAT 3X, A2, 2F5.0, E10.0, 15, 5F5.0) RUNT, TINIT, DTI, TOT, NSPOUT,

SOUT(I), (I = 1,5)

Default Maximum

Col.(s) Variable Data Description Value Value

4-5 RUNT Run option ST

SS - steady-state solution only

ST - steady-state plus transient

6-10 TINIT First output time(s) 0.0

11-15 DTI Time between outputs(s) 0.01

16-25 TOT Last output time(s) 1.0

30 NSPOUT Number of special outputs 0 5

31-35 SOUT (1) First special output time(s) 0.0

36-40 SOUT (2) Second special output time(s) 0.0

41-45 SOUT (3) Third special output time(s) 0.0

46-50 SOUT (4) Fourth special output time(s) 0.0

51-55 SOUT (5) Fifth special output time(s) 0.0

Transient values of pressure, temperature, mass, and volume flows are

saved for listing and plotting. These values are spaced uniformly between the

first output time'and the last output time. Additionally, up to five special

output times may be requested.

46
PRINT/PLOT CONTROL CARDý "

(FORMAT A2, A3,. 61.5). LUNITS, .PLTOPT, NPFRMS, NQFRMS,

NMFRMS, NAFRMS,-NTFRMS, NSPECC

,...Default Maximum

Col.(s) Variable Data Description Value Value

1-2

3-5

6-10

11-15

16-20

21-25

26-30

31-35

LUNITS Units for output lists and

plots. SI specified here'

yields pressures (kPa), 3

flows(m /s), and

temperatures (K).

PLTOPT Entering the letters

"ALL" produces lists

of pressures, flows,

temperatures, and

differential pressures at

every output time (Jncl.uding

special outputs).

NPFRMS Numberof pressure plot frames.

NQFRMS Number of volumetric flow rate

plot frames _:

NMFRMS Number of •massiflow rate plot..,,,-

frames

NTFRMS Number of temperature plot frames

NAFRMS Number of' damper blade angle..

frames.

NSPECC Number of particulate species

for which plots will be

requested (next. set-.of data cards)

(BLANK)zyields

- :pressures

(in. w.g. at..60 0 F),

flows (cfm), and

temperatures.(°F).

(BLANK) Lists

produced only

at star.t time,

total run

time, and

special. out-_

put. times.

0 10

0 10

0

0

0

0

10

10

10

5

The maximum number of plot frames that can be requested is 25; therefore,

the sum of pressure frames, volumetric flow rate frames, mass flow rate frames,

temperature frames, and particulate species frames must not exceed 25. These

entries may be left blank if printer plots are not desired.

47
PRINT/PLOT CONTROL CARD

(Second Card -- Particulate Species Specification Card)

These cards are provided only if NSPECC is > 0. This quantity is

specified in Cols. 36--40 of the first PRINT/PLOT control card. NSPECC cards

must be provided.

(FORMAT 715) KNDSPC(I) NFLXFR(I), NPMOFR(I), NWMAFR(I), NSRCFR(I), NSINFR(I),

NYFRMS(I), (I = 1, NSPECC)

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 KNDSPC Particulate species number 0

6-10 NFLXFR Number of particulate flow rate 0 10

plots for this particulate

species number

11-15 NPMOFR Number 'ofintegrated particulate 0 10

flow rate through branch plots for

this particulate species number

16-20 NWMAFR Number of particulate mass on 0 10

duct wall plots for this

particulate species number

21-25 NSRCFR Number of entrainment rate 0 10

plots for this particulate

species number

26-30 NSINFR Number of deposition rate 0 10

plots for this particulate

species number

31-35 NYFRMS .,Number of mass fraction 0 10

plots for this particulate

species number

48
PLOT FRAME CARDR

(FORMAT 515, F10.0) NCRVS(K), NCID(1,K), NCID(2,•K), NCID(3,K) NC[D(4,K),

XSCL(K), (K = 1, NFMT)

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 NCRVS Total number of curves this frame 0 4

6-10 NCID Node/branch. number for first curve 0 100

11-15 NCID Node/branch number for second curve 0 100

16-20 NCID Node/branch number for third curve 0 100

21-25 NCID Node/branch number for fourth curve 0 100

26-35 XSCL Scale limit for frame BLANK

Pressures, temperatures, and mass fraction quantities are available for

plotting at each node. Volumetric flow rate'and mass flow rate are available

for plotting at each branch. Particulate flow rate, integrated particulate flow

rate, particulate mass on duct wall, entrainment rate, and deposition rate are

available for plotting for each duct type branch. Thi~s.card identifies how many

and which nodes or branches are to appear as-curves on the print/plot frame.

Different quantities cannot:be mixed on the ýsame frame. There is one plot-frame

card for each frame. These'cards. may be omitted if plot frames are not requested on the print/plot control card. A scale limit may be specified for the

frame; otherwise the plot routine finds the maximum value of: all the pressures,

flows, or temperatures on the frame and uses this value as 100% of full scale.

49
RUN CONTROL II CARD

(FORMAT 15, FIO.O, 4X, 11, 4X, 11,• 4X, A1, 4X, Al, 215,. 5X, 15, 5X, 315) MAXIT,

CONVRG, IDEP, IENT

PINP,TINP, IAINP,

IGINP, IF[RIN,

NGSPECE,NSPECES, INC

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 MAXIT Maximum iterations permitted per 1000

time step. The program will

abort if convergence (discussed

in App. A) has not been achieved

for this number of iterations.

Ten times this number is permitted for steady-state calculations.

6-15 CONVRG Criterion for iteration conver-> 0.0001

gence (App. A)..

20 IDEP Calculated particulate deposition 0

option. If IDEP =1, deposition

is calculated.

25 IENT Calculated part-iculate entrainment 0

option. If IENT = 1, entrainment is

calculated.

30 PINP Initial pressure input option. (BLANK)

Insert the letter lp" in this no input

column if pressures at nodal pressures

points are to be supplied, supplied

35 TINP Initial temperature input option. (BLANK)

Insert the letter "T" in this implies all

column if temperatures at nodal ambient

points are to be supplied. values

50
RUN CONTROL II CARD (CONT)

(FORMAT 15, F1O.O, 4X, I1, 4X, I1, 4X,-A1 4X, Al, 215, 5X,. 15, 5X, 315) MAXIT,

CONVRG, PINIP,

TINP, IAINP, IGINP,

IFIRIN, NGSPECE,

NSPECES, INC

Default Maximum

Col.(s) .variable Data Description Value Value

40 IAINIP 1. if initial particulate specie 0

mass fractions are *to be input.

45 IGINP 1 if initial gas species volume 0 •

fractions are to be input.

55 IFIRIN 1 if timefunctions are to be used 0

to simulate the fire

0 if the FIRIN module is to simulate

'the fire.* See Sec-. III on modeling

strategies.

61-65 NGSPECE Number of gaseous species.. 0 5'

66-70 NSPECES Number of particulate species 0 5

75 INC I if buoyancy term in Eq. (A-3) (BLANK)

is to be included. L(BLANK)

(recommended) results in

neglecting this term.]

*If the FIRIN module simulates the fire, the fire accident will not begin until

the problem time equals 2.0 s.

51
BOUNDARY CONTROL CARD

(FORMAT 215, 2F10.O, 515) NPFN, NBNODS, PZERO, TAMB, NTFN, NEFN, NMFN, NCFN,

NGFN

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 NPFN Total number of pressure- 0 5

time functions

6-10 NBNODS Total number of boundary nodes 0 10

11-20 PZERO Value for atmospheric pressure 14.7

(psia)

21-30 TAMB Value for atmospheric 60

temperature (*F)

35 NTFN Total number of temperature- 0 5

time functions

40 NEFN Total number of energy- 0 5

time functions

45 NMFN Total number of mass-time functions 0 5

50 NCFN Total number of particulate species 0 5

addition time functions

55 NGFN Total number of gaseous species 0 5

addition time functions

The code is limited to handle a maximum of 10 boundary nodes and a maximum

of 5 time functions of each type.

52
GEOMETRY AND COMPONENT CONTROL CARD

(FORMAT 215, 5X, 315) NBRCH, NNODES, NROOMS, NBLFNS, NFILRS

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 NBRCH Number of branch description 0 100

data card sets

6-10 NNODES Number of nodes defined for 0 100

problem (includes boundary nodes)

16-20 NROOMS Total number of rooms 0 100

21-25 NBLFNS Total number of blower 0 15

characteri'stic functions

26-30 NFILRS Total number of special filter types 0 20

31-35 NCDAMP Total number of control dampers 0 100

Values of these parameters control the reading of input data and should

not exceed maximum values.

53
BRANCH DESCRIPTION DATA,. CARD 1

(FORMAT 315, 3F10.0, Al, 4X, F10.2ý, lOX, 12) IBRN, INDU(IBRN), INDD(IBRN),

Q(IBRN), FA(IBRN), XL(IBRN),

ICPTYP(IBRN), DP(IBRN), IBCN

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 IBRN Branch number 0 100

6-10 INDU Upstream node number 0 100

11-15 INDD Downstream node number 0 100

16-25 Q Initial estimate of flow (cfm). (0.1 x FA)

This value is used to calculate

damper, filter, and duct resistance

coefficients.

26-35 FA Flow area (ft 2) 1.0

36-45 XL Duct length (ft) ( FA) 5 /12

46 ICPTYP Component type 0

V ... .. 'Damper

F ..... Filter

B ..... Blower

D ..... Duct

51-60 DP Branch.pressure differential 0.0

(in. w.g. at 60 0 F)

71-72 IBCN Blower curve identification 0 15

Identifies which blower curve to

use for component type B.

54
BRANCH DESCRIPTION DATA, CARD 2

(FORMAT 2E10.O, 110, 20X, 2EI0.O, 9X, II) FZ, RZ, NFE, HEIGHT(IBRN),

FLAREA(IBRN), IHNT(IBRN)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 FZ Forward resistance coefficient Codefor branch. If > 0, this value calculated

overrides that calculated by the value

code from pressure differential

and initial flow.

11-20 RZ Rear resistance coefficient, for Codebranch. If > 0, this value over- calculated

rides that calculated by the code value

from pressure differential and

initial flow.

21-30 NFE Filter type. .0

51-60 HEIGHT Duct height (use h D2 .foiý round 0

duct) (ft).

2 61-70 FLAREA Duct floor area (ft2). 0

80 IHNT Heat transfer option = 1 if heat 0

transfer calculation is to be

performed for this branch.

Two cards. are required per branch. The branch pressure differential is

used with the initial estimate of branch flow to calculate a resistance coefficient. The differential pressures also are used to calculate initial starting

.point system pressures if these pressures are not input separately.

The BRANCH DESCRIPTION CARDS need not be ordered in the input deck

(branch 10 might precede branch 5,). However, the number of cards should agree

with that specified in Cols. 1--5 of the GEOMETRY AND COMPONENT CONTROL card.

55
The blower curve~identification refers to the blower curve number identifier specified later on the BLOWER CURVE CONTROL CARD.

The filter type refers to special type filters for which a plugging calculation is to be'performed. The filter types are specified on the FILTER DATA

CARD(S). The filter type may be left blank if a plugging calculation (detailed

in App. C) is not requested.

BRANCH DESCRIPTION DATA, CARD 3

This card is read only if duct heat transfer is requested on the second

branch description data card (Col. 80).

(FORMAT 2E8.0, 18, .7E8.0) DIA, HTAREA, NODES, THICK, EMISS, ABST, KWALL, RHOW,

CPW, TWALL

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 DIA Duct equivalent diameter (ft) 0.0

2 9-16 HTAREA Duct heat transfer area (ft2) 0.0

17-24 NODES Number of heat transfer nodes 1

in wall

25-32 THICK Duct wall thickness (in.) 0.0

33-40 EMISS Duct emissivity (outside) 0.0

41-48 ABST Duct..:absorptivity (outside) 0.0

49-56 KWALL Wall thermal conductivity 0.0

(Btu/h/ft-° F)

57-64 RHOW Wall density (Ibm/ft 3 ) 0.0

65-72 CPW Wall specific heat (Btu/Ib-°F) 0.0

73-80 TWALL Initial wall temperature (°F) 0.0

56
PARTICULATE SPECIES DATA, 'CARD 1.

These cards are read only if NSPECIES is > 0. This quantity is in

Cols. 66--70 of RUN CONTROL CARD II. Provide NSPECIES sets of these cards.

(One for each particulate specie.)

(FORMAT 110, 2X, A8, 2EI0.O) ISPEC, IDSPEC, DIAP, RHOP

.'Default Maximum

Col.(s) Variable Data Description. Value Value

1-10 ISPEC Species Number 0 NSPECIES

13-20 IDSPEC Identification of this species BLANK

(up to eight characters)

21-30 DIAP Particle diameter (pm) 0.0

31-40 RHOP Particle density (g/cm3) 0.0

57ý
PARFICULATE SPECIES DATA, CARD 2

Initial Particulate Species Wall Mass

The following card should be present only if RUN CONTROL CARD II (Col. 40)

indicates that initial particulate specie quantities are to be input. The dLfault for these quantities is zero. Use as many cards as necessary to define

the initial particulate specie mass fraction at all nodes. The number of quantities to be provided should be the same as specified in Cols..6--lO of the

GEOMETRY AND COMPONENT CONTROL CARD. Values that are left b.lank are assumed to

be zero.

(Format 5E15.0)

58
PARTICULATE SPECIES, DATA CARD 3

Initial Particulate Specie Wall MasS

The following card should be present only if RUN CONTROL CARD II (Col. 40)

indicates, that initial particulate specie quantitiesý are to be input. The default for these quantities is. zero. Use as many cards as necessary to. define

the initial particulate specie mass contai.ned on the walls.-of each branch. The

number of. quantities to.be provided should be the same as specified in Cols,. 1--5

of the GEOMETRY AND COMPONENT CONTROL CARD. Values that are left blank are assumed to be zero.

(FORMAT 5E15.0)

Default Maximum

Col-.-(s) Data'Description Value Value

1-15 Wall mass in the first branch 0.0

16-30 Wall mass in the second branch 0.0

31-45 Wall mass in the third branch 0.0

46-60 Wall mass in the fourth branch 0.0

61-75 Wall mass in the fifth branch 0.0

'.59
GASEOUS SPECIES DATAiý.CARD 1

These cards are read, only if NGSPECIES is...> 0. This quantity is in

Cols..61-65 of RUN CONTROL CARD II. Provide NGSPECIES sets of these cards

(one for each, gaseous specie).

(FORMAT .I10, 2X, A8-) ISPEC,. IDSPEC

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 ISPEC Species No. 1 < ISPEC < NGSPECIES 0

13-20 IDSPEC Identification of this species BLANK

(Up to eight characters)

60
GASEOUS SPECIES DATA, CARD 2

Initial Gaseous Species Volume Fraction

The following card should be present only ,ifRUN CONTROL CARD II (Col. 45)

indicates that initial gaseous specie quantities are to be input. The default

for these quantities is zero. Use as many cards as necessary to define the initial volume fraction of this specie at all nodes.. ;The number of "quantities provided should be the same as specified in Cols. 6--10. of the GEOMETRY AND COMPONENT CONTROL CARD.

(FORMAT 5E15.0)

Default Maximum

Col.(s) Data Description Value Value

1-15 Volume fraction in the first node .0.0

16-30 Volume fraction in the second node 0.0

3.1-45 Volume fraction in the third node OO'

46-60 Volume fraction in the fourth node 0.0

61-75 Volume fraction in the fifth node 0.0
BOUNDARY NODE DATA CARD

(FORMAT 15, 12, F11.O, F1O.O, 15, FIO.O) IBNNR(I), ITYPBN(I), PB(I), IBPFN(I),

TBI(I), IBTFN(I), ELEV[IBNNR(I)],

[I = 1, NBNODS]

ý ,Default Maximum

Col. (s) Variable Data' Description Value Value

1-5 IBNNR Boundary node number 0 10

6-7 ITYPBN Boundary node type (ITYPBN = 1 0

denotes an internal boundary

node)

8-18 PB Initial value of pressure at node atmo-

(in. w.g. at 60 0 F) spheric

19-22 IBPFN Identification number of pressure- 0 5

time function at the boundary node (Steady

(See Time Function Data card.) value of

pressure)

23-32 TBI Initial value of temperature .(OF) atmospheric

33-37 IBTFN Identification of temperature- 0 5

timefunction number

at this boundary node

38-47 ELEV Elevation (ft)

62
TIME FUNCTION -DATA-1,:CONTROL UCARD

(FORMAT 215, 3X, 12) IFN, NP(IFN), ITEM(IFN)..'•

Default Maximum

Col.( s) Variable Data Description Value Value

1-5 IFN Time function identifier. 0 5

6-10 NP Number of data points in time 0 20

function definition. A data

point is defined as an ordered"

pair of values-oftime and function

of time.

14-15 ITEM Temperature function number for mass 0 5

injection.

This card controls-the reading of .subsequent TIME FUNCTION DEFINITION cards

and-should precede each time function definition. The TIME FUNCTION DATA CONTROL card is followed by one or more TIME FUNCTION DEFINITION data cards. This

set of'cards;-may be present, but it.is not required for steady-state runs.

63.
TIME FUNCTION DEFINITION DATA CARD

(Format 3(2F1O.O)).T(I,IFN), FT(I,IFN), i(I =-1, INP) REPEATED

Default Maximum

Col. (s). Variable Data Description Value Value

1-10 T Value ,of time for first time 0.0

function data point.

11-20 FT Value of-variable-for first time 0.0

function, data point.

21-30 T Value.:of time for second time 0.0

function data point.

31-40 FT Value of variable for second time 0.0

function data point.

41-50 T Value of time for third time 0.0

function data point.

51-60 FT Value of variable for third time 0.0

function data point.

Insert. as. many TIME FUNCTION DEFINITION cardsi.as needed to define all -the''.

data points. The TIME FUNCTION data card sets are used to define all the timedependent user-specified data for the problem. This includes time-dependent

data for both boundary nodes and capacitance nodes (rooms). Each type of time

function must be preceded by a data separator card.

Use as many TIME FUNCTION DATA CARD DESCRIPTION and TIME FUNCTION DEFINITION

DATA CARD DESCRIPTION sets as-necessary to define all the time function sets

required by the problem. The card sets must be in the following order and in

the quantities provided in the indicated units.

9 Pressure (psig)

9 Temperature (OF)

@ Energy (kW)

e Mass (Ibm/h)

* Particulate species (g/s)

9 Gaseous species (cfm)

The defining times must bein ascending order.

64
ROOM DATA, CARD 1;

'(FORMAT 15, FiOAo, 415;1 4FIO.O)AIND(K), VOL(K), NOE(K), NOM(K),' NOP(K), NOT(K),

REDOT(K),.RMDOT(K), RPý(K), RT(K), (K =1, NROOMS)

Default Maximum

'Col.(s) Variable Data Description .Value Value

1-5 IND Node number for room 0 100

3ý 6-15 VOL Room volume (ft) .0.0.

20 NOE Energy"tiime function. number 0 5

25 NOM Mass addition time function number 0 5

30 NOP Pressure time function number 0 5

35 NOT Temperature time funct'ion n'umber 0 5

36-45 REDOT Initial value of energy. (.kW) .0.0

46-55. RMDOT Initial value of mass (Ibm/h) 0.0

56-65 RP Initial value of pressure

(in. w.g. at 60 0 F) 0.0

66-75 RT Initial value .of temperature (OF) atmospheric

Two cards are-required per room. The volume dimension is used in the calculation of-capacitance coefficients, and zero volume is not, permitted. Room

volumes are required input for steady-state runs. Duct volume (if significant)

must be input as a pseudo-room requiring an additional node. Rooms cannot be

located at boundary nodes. The ROOM DATA cards need not be in numerical order.

65
ROOM DATA, CARD 2

(FORMAT E1O.O, 2110, lOX, ElO.,O) RFA(K), (K = 1, NROOMS), NOPFNS, NOGFNS,.

ELEV (IND(K))

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 RFA Room area (ft ) (flow area) 0.0

11-20 NOPFNS No. of particulate species source

time functions for this room 0

21-30 NOGFNS No. of gaseous. species source time 0

functions for this room

41-50 ELEV Elevation (ft) - 0.0

66
ROOM DATA, CARD'3

•..Particulate Species Source Specification Card

These cards are present 'only if there are p.articulate, specie sources in

this room (Cols. 11-20 on the second room data card). There'is one card for

each particulate time function requested for-this room. The,.total number of

cards must be the.same as the number of.particulate sources specified in

Cols. 11-20 of the second room data card.

(FORMAT 2110, E1O.O) ISPEC, IPTFNO, PCDOT

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 ISPEC Species number for this source 0

must agree with that stated on the

particulate species data cards)

11-20 IPTFNO Time function number describing 0

this source

21-30 PCDOT Initial value of the particulate 0.0

source (kg/s)

67
ROOM DATA, CARD 4

(Gaseous Species Source Specification Cards)

These card's are present only if there are gaseous specie sources in this

room (Cols. 21--30 on the second room data card). There is one card for each

gaseous species time function requested for this room. The total number of

cards must be the same as the number of gaseous species sources specified in

Cols. 21--30 of the second ROOM DATA CARD.

(FORMAT 2110, E1O.O) ISPEC, IGTFNO, GCDOT

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 ISPEC Species number for this source 0

(must agree with that stated on

the gaseous species data cards)

11-20 IGTFNO Time function number describing 0

this source

21-30 GCDOT Initial value of the gaseous 0.0

specie source (cfm)

68
CONTROL DAMPER CARD :.-

Format (315,. 5F4.,O) .CTLNODE,,.DArNUM, TYPE, PMIN, PMAX,

THETA, dTHETA, tDELAY

Default Maximum

Col.(s). Variable Data Description. Value Value

1-5 CTLNODE The node at .which a pressure is being 100

maintained.

6-10 DAMPNUM The branch number of the controlling 100

damper.. 11-15 TYPE The damper type. 1 3

1 - opposed-blade medium duty.

2 - opposed-blade light duty

3 - parrallel-blade light duty

16-25 PMIN The minimum pressure allowed at the 0

controlled node (in. wg.).

26-35 PMAX The maximum pressure allowed at the 0

controlled node (iTn. wg.).

36-45 THETA The initial angle of the damper 0 g90

blade.

900 - open

00 - closed

46-55 DTHETA The number of degrees'Athfat the Do 900

blower opens if the pre~ssure is',

above PMAX or.:closes if the pressure.

is below PMIN (negative if the damper

closes at high pressures).,

56-65 TOELAY The time-that the pressure must 0°

remain above or below the limits

before the damper will respond (s).

The control damper model can be used to model fixed dampers by setting

THETA to the blade angle of the damper and dTHETA to 00. Additional damper

types can be added to FIRAC by the procedure explained in Appendix E.. Control

dampers respond by closing or opening DTHETA degrees after the pressure has

been outside of the specified range for TDELAY seconds. After the damper responds, it will wait another TDELAY seconds before responding again. To obtain

"continous" opening or closing of a damper use a TDELAY equal to the timestop

and a DTHETA to match.

69
BLOWER CURVE CONTROL CARD

(FORMAT 215) JB, NPBC(JB)

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 JB Blower curve number identifier. 0 15

6-10 NPBC Number of points defining this 0 20

blower curve. A point is defined

as an ordered pair of values of

flow (cfm) and head (in. w.g.

at 60 0 F).

The blower curve data are ordered in the same way as time function data--a

curve input control card is followed by one or more curve description cards.

One curve control card is required for each blower type. The order of the

blower curves is unimportant (curve 3 might precede curve 1); however, this

card is used in reading the following blower curve data points and must appear

just before the appropriate curve description card(s).

70
BLOWER CURVE -- DATA CARD

(FORMAT 3(2F10.O)) XB,(I, JB), FXB(I, JB), [I = 1, NPBC(JB)] REPEATEDDefault Maximum

CoI.(S) Variable Data Description Value. Value

1-10 XB Flow (cfm) for-the first point 0,0.

'11-20 FXB Blower. head (in. w.g. at 60°F) for. 0.0

the first point.

21-30 XB Flow for the second point 0.0

31-40 FXB Blower head for the second point 0.0

41-50 XB Flow for the third point

51-60 FXB Blower head for the third point 0.0

71
FILTER .DATA CARD(S)

(FORMAT 110, 4F10.2) NFE, FEF(NFE), ALF1(NFE), AKL(NFE), AKT(NFE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 NFE Filter type number (required) 0 NFILRS

11-20 FEF Filterefficiency (required) 0.0

21-30 ALF1 Filter plugging factor (1/kg) 0.0

(optional)

31-40 AKL Laminar filter factor KL 0.0

41-50 AKT Turbulent filter factor KT 0.0

One card for each

GEOMETRY AND COMPONENT

special filter

CONTROL CARD.

type specified in Cols. 26--30 of the

Special filter types refer to filters for

which a plugging calculation is

plugging factor is given in Eq.

tors are defined by Eqs. ,(C-39)

to be performed. The definition of the filter

(C-42). The laminar and turbulent filter facand (C-40).

72
PRESSURE INPUT CARD

(FORMAT 5E15.0) P(I), (I = 1, NNODES) (Five entries per card)

Default Maximum

Col.(s) Variable Data Description Value Value

1-15 P Pressure (in. w.g. at 60 0 F) at the 0.0

first node

16-30 Pressure at the second node 0.0

31-45 Pressure at the third node 0.0

46-60 Pressure at the fourth node 0.0

61-75 Pressure at the fifth node 0.0

These cards are required only if Col. 30 of the RUN CONTROL II CARD is set

to P. The values of pressure for boundary nodes may be left blank because these

values are supplied on the BOUNDARY NODE DATA cards. Use as many cards as required to define all the system pressures.

73
TEMPERATURE INPUTý CARD

(FORMAT 5E15.0) T(I), (I= 1, NNODES) Five entries per card

Default Maximum

Col.(s) Variable Data Description Value Value

1-15 T Temperature (OF) at the first node 0.0

16-30 Temperature at the second node 0.0

31-45 Temperature at the third node 0.0

46-60 Temperature at the fourth node 0.0

61-75 Temperature at the fifth node 0.0

These cards are required only if Col. 35 of the RUN CONTROL II CARD is set

to T. The values of temperature for boundary nodes may be left blank because

these values are supplied on the BOUNDARY NODE DATA cards. Use as many cards

as required to define all the system temperatures.

74
SCENARIO.CONTROL SPECIFICATIONS, CARD 1

(FORMAT FIO.2, 2110) TSPEC, IPRNT, MIBO

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 TSPEC User-specified fire duration in 0.0

real-time seconds (used only in

FIRIN module).

11-20 IPRNT User-specified frequency of time 0

step intervals for whichthe

computed data are printed into the

output unit fi:les. For example,.

if the time-step interval (DTMAX) is

0.1 s and the user wi'shes to obtain

computed data every 1Os in real

time of the fire, IPRNT = 100

should be specified.

2-30 MIBO .One way to approximate fire growth 0 5

with the FIRIN module; users

must estimate the orders':of fuel

consumption.:(burning order) in the

fire if more than one combustible

material is specified at risk in the

compartment. MIBO is the.maximum

*"number'of burning orders, and it

governs the number. of physical card

requirements for FIRESOURCETERM

DATA CARDS.

75
SCENARIO CONTROL SPECIFICATIONS, CARD 2

(FORMAT 110, F10.1, 110, F1O.1, 2110) IGNITE, PFLOW, NFP, EQUIP, WJE, IFLOW3

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IGNITE A less conservative way to ap- 0

proximate fire growth with the

FIRIN module is using the igni.-

tion energy concept. This ap-,

proximation.allows auto-ignition

of combustibles at risk if the heat

flux levels generated by the.initial

burning combustibles in the compartment are sufficient. The ýignition

energy levels required for autoignition of the combustibles depend

on material properties, and they are

stored in the program. To use this

concept for.approximation, IGNITE = 1

must be i-nput;,otherwise, IGNITE 0

must be specified. When this concept

is applied, MIBO = 2 must be specified where the first burning order

(IBO = 1), the fuel quantity, and

the surface area are input for initial

burning materials, and for.second

burning order (IBO = 2), the quantity

and surface area of combustibles at

risk (because of possible auto-ignition) are specified.

76
SCENARIO CONTROL SPECIFICATIONS, CARD 2 (CONT)

Default Maximum

Col.(s) Variable Data Description Value Value

11-20 PFLOW Numeric identifier for additional 0.0

flow paths to/from the fire

compartment.

FLOW = 1.0 (additional

flow paths), or.

FLOW = 0.0 (no additional

flow paths).

If FLOW = 0.0 is specified, no

input data are required for additional FLOW PATH DATA CARDS.

21-30 NFP Number of additional flow paths 0 50

to/from the fire compartment. A

glovebox is an example of a compartment that has glove ports as its

additional flow paths where the

gloves attached to it have burnt

off. The value selected for NFP

governs the number of physical card

requirements for additional FLOW

PATH DATA CARDS. If NFP = 0, no

data input is required for these

cards.

31-40 EQUIP Numeric identifier for equipment 0.0

and vessels at risk in the fire

compartment.

EQUIP = 1.0 (equipment

and vessels)

EQUIP = 0.0 (no equipment

or vessels)

77
SCENARIO CONTROL SPECIFICATIONS, CARD 2, (CONT)

Default Maximum

Col.(s) Variable Data Description Value Value

If EQUIP = 0.0 is specified, no

input data are required for

EQUIPMENT/VESSEL GEOMETRY CARDS

or EQUIPMENT/VESSEL CONTENT DATA

CARDS.

41-50

51-60

MW E

IFLOW3

Number of pieces of equipment and

vessels at risk inside the fire

compartment. The number assigned

for MIE is the number required for

each type of EQUIPMENT/VESSEL

GEOMETRY CARDS.

Numeric identifier for third

fire compartment node.

IFLOW3 = 1 Third node contributes

to inflow at steadystate conditions.

IFLOW3 = 0 No third node.

IFLOW3.= -1 Third node contributes

to outflow at steadystate conditions.

0 10

0

78
INITIAL.•CONDITIONS CARD

(FORMAT FIO.2, F10.6) TENIT, PINIT

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 TENIT Initial temperature ( 0 F) of the ,0.0

fire compartment

11-20 PINIT Initial pressure (in. w.g.) inside 0.0

the fire compartment

INFLOW SPECIFICATIONS CARD

(FORMAT 2110, 2F10.2) IBRCHI, IFCND1, ZIF, DIF

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IBRCHI Fire compartment inflow branch 0

number

11-20 IFCND1 Fire compartment inflow node 0

number

21-30 ZIF Height of elevation (ft) of the 0.0

center plane of inlet ventilator

from the floor, level in the

compartment

31-40 DIF Diameter (ft) of inlet ventilator 0.0

79
OUTFLOW SPECIFICATIONS CARD

(FORMAT 2110, 2F10.2) IBRCHO, IFCND2, ZOF, DOF

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IBRCHO Fire compartment outflow branch 0

number

11-20 IFCND2 Fire compartment outflow node 0

number

21-30 ZOF Height of elevation (ft) of the 0.0

center plane of outlet ventilator

from the floor level in the

compartment

31-40 DOF Diameter (ft) of outlet 0.0

ventilator

80
THIRD COMPARTMENT NODE SPECIFICATIONS CARD

This card is not required if IFLOW3 = 0 (SCENARI-O CONTROL SPECIFICATIONS

CARD 2).

(FORMAT 2110, 2F10.2) IBRCH3, IFCND3, ZIOF3, DIOF3

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IBRCH3 Third compartment node branch 0

number

11-20 IFCND3 Third compartment node number 0

21-30 ZIOF3 Height of elevation (ft) of the 0.0

center plane of extra ventilator

(option of either inflow or out

flow) from the floor level in the

compartment

31-40 DIOF3 ,-Diame.ter (ft) of extra, ventilator 0.0

81
FUEL SOURCE TERMS DATA CARDS

The number of sets of the following two card types is governed by the number of burning orders, MIBO (SCENARIO CONTROL SPECIFICATIONS CARD 1). MIBO sets

must be entered in sequence, and all FUEL MASS DATA CARDS must be entered before

any FUEL SURFACE AREA DATA CARDS

FUEL MASS DATA CARDS

(FORMAT 9F8.2) FUEL (I, IBO), (I G 1, 9; IBO;= 1, MIBO)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 FUEL Mass' (pounds) of nine different 0.0

9-16 types of combustible fuel, mate17-24 rials (I 1, 9) commonly found

25-32 in fLel cycle facilities andl.

33-40 possibly present in the fire com41-48 partment. I is the numeric identi49-56 fier for types of fuels, which are

57-64 described in Table IV*. IBO is the

65-72 burning order (that is, first, second, third, fourth, and so on) of

fuels specified by the user. ýPut

O.O.in the corresponding columns of

:each physical card where that particular fuel is notinvolved in the

fire. Currently, up to nine combust-

*ible materials can be burning all

at once, and burning orders can be up

to MIBO = 5.

*Table IV follows the completion of Table III on p. 110.

ý82
•,,FUEL SURFACE AREA DATTA CARDS

(FORMAT 9F8.2) AREC (I, IBO), Il.i19; IBO = 1,.-MIB

Default Maximum

Col.(s) Variable Data Description Value Value

2

1-8 AREC Surface area (ft2) of 0.0

9-16 fuels for nine different types of.

17-24 combustible materials (I = 1, 9).

25-32 A value'of 0.0 should be entered

33-40 in the corresponding columns, of

41-48 each physical card when that49-56 particular fuel is not involved

57-64 in the fire. A total of nine values

65-72 should be filled for for. each*

physical: -ard as in;FUEL .(I, IBO).

83
FIRE COMPARTMENT GEOEETRY CARD

(FORMAT 7F10.3) RL, WR, ZR, XCEIL, XWALL, XFLOOR, ZFIRE

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 RL Length (ft) of fire compartment. 0.0

11-20 WR 'Width (ft) of fire compartment. 0.0

21-30 ZR Height (ft) of fire compartment. 0.0

31-40 XCEIL Thickness (ft) of compartment 0.0

ceiling.

41-50 XWALL Thickness (ft) of compartment 0.0

wall.

51-60 XFLOOR Thickness (ft) of compartment 0.0

floor. If the compartment is on

floor level with no other

compartment below it, a large

value for XFLOOR is suggested

for heat transfer considerations.

61-70 ZFIRE Normalized height (ft) of 0.0

the flame base from the floor

level. Spec'ifying this value

requires the user's judgment. For

exanmle, when a glovebox is in

a fire, ZFIRE is the height of

the glovebox floor from the

ground level. In all cases,

ZFIRE must be given a positive,

nonzero value.

84
FIRE COMPARTMENT MATERIALS CARD

(FORMAT 3110) MATERC, MATERW, MATERF

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 MATERC Ceiling construction material. 0

Use the numeric identifier

MATERC = 1, 2,...15 (Table V*)

for noncombustible solid

materials. MATERC = 1 denotes

concrete as the Ceiling material.

11-20 MATERW Wall construction material. Use 0

the numeric identifier as for

MATE RC.

21-30 MATERF Floor construction material. Use 0

the numeric identifier as for

MATE RC.

*Table V follows the completion of Table III on p.. 110.

85
COMBUSTIBLES IDENTIFICATION CARD

This card type is required only when the ignition energy concept-is applied, IGNITE I (SCENARIO CONTROL SPECIFICATIONS, CARD-2).

(FORMAT 915) NBO(1), (I = 1, 9)

Default Maximum

Col.(s) Variable Data Description Value Value

1-5 NBO Numeric identifier for the nine 0 3

6-10 combustibles at risk.

11-15 Input. NBO(I) = 0 for material that

16-20 burns initially in

21-25 the fire.

26-30 NBO(1) =.1 for combustibles that

31-35 are at risk and that

36-40 can contribute to the

41-45 fire.through the ignition energy .concept.

NBO(1) = 2 for any of the nine

combustible types that

will not contribute to

the .fire at all.

NBO(I) : 3 formaterial types that

burn at the start of

the fire and.are also

at risk because of ignition energy concept.

Nine input values, are required on this

card. Enter NBO(I) = 2 for combustibles

*not involved in the fire.

86
EQUIPMENT/VESSEL IDENTIFIER CARD

This card is required only if equipment or vessels'.are at risk.inside the

fire compartment. For this to be true, MJE > 0 (SCENARIO CONTROL SPECIFICATIONS,.

CARD 2). Only one card is necessary.

(Format 4F10.2) NVES (IE), (IE = 1, 4)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10. NVES Number of pieces of equipment or 0 10

11-20 vessel of type 1E 1, 2, 3, and 4

21-30 Type 1 , simple heat sink

31-40 Type 2 - pressurized containers

of-powder

Type 3 - pressurized containers

of liquid

Type 4 - open liquid containers

Enter NVES(1E) = 0 if Type,-IE is not

found in the fire compartment.

87
EQUIPMENT/VESSEL GEOMETRY CARDS

The following five card types decribe the pieces of equipment and vessels

at risk inside the fire compartment. The number of sets of cards is governed

by the number of pieces, MJE (SCENARIO CONTROL SPECIFICATION, CARD 2), one set

for every piece of equipment or vessel. If MJE = 0, no cards are required.

EQUIPMENT/VESSEL GEOMETRY, CARD 1

(FORMAT 4F10.2) WD(IE, JE), (IE = 1, 4; JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 WD Width (ft) of the equipment 0.0

11-20 and/or vessels. The FIRIN module

21-30 is limited to only four types of

31-40 equipment or vessels (IE = 1, 4):

simple heat sink, pressurized

containers of powder, pressurized

liquid containers, and open liquid

containers. JE denotes number of

each type of equipment or vessels,

up to 10 for each type (MJE = 10).

88
.EQUIRMENT/. VESSEL GEOME2,TRY- , CA RD,2

(FORMAT 4F10.2) HEQ(IE, JE),9 (IE = 1, 94; JE . •I EIJE.

Default Maximum

co Variable Data Description Value Value

1-10 HEQ Length (kft). ftof the equipment 0.0,-

11-20 (diameter of cyl i~nder, s,.- Ilength

21-30 exposed to fire: for,:boxes) and/or

31-40 vessel s :p.resent•,.;in the fire

cpmpartment,;.f"Same.Ainput

requirement as WD.(IE.,JE) above".

EQ UI PMENT/VESSEL GEOMETRY CARD 3

(FORMAT.4FIO.2) HTF(IE, JE), (IE = 1, 4;-:..JE = 1, MJE)

Default Maximum

.Col.(s) Variable Data Description Value Value

1-10 HTF Height (ft) of the base of ,"0.0

11-20 equipment and/or vessels from the

21-30 ........floor level. Same input require

31140 ment as WD(IE, JE) above.

89-
EQUIPIENT/ VESSEL GEOIvETRY,•t CARD 4

(FORMAT 4110) MATERE (IE, JE), (IE = 1;- 4 JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 MATERE Construction material .of the four 0

11-20 types of equipment or vessels

21-30 mentioned above (IE = 1, 4).

31-40 MATERE is a numeric identifier for

types of noncombustible materials.

IE denotes number of each *type of

equipment or vessels, with up to

seven types of possible construction material. For example,

MATERE (IE, JE) = 3 denotes the

JEth piece of equipment or vessel

Type IE constructed of stainless

steel.-See Table VI.*

EQUIPMENT-/VESSEL GEOMETRY, CARD 5

(FORMAT 4F10.2) WMASS (IE, JE), (IE = 1, 4; JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value.

1-10 WMASS Weight (pounds) of equipment or 0.0

11-20 vessels. Similar input require21-30 ments as for WD(IE,JE), HFT(IE,JE),

31-40 and HEQ(IE,JE).

*Table VI follows the completion of Table III on p. 111.

90
EQUIPMENT/VESSEL .CONTENTS CARDS

The following .15 card types describe the contents of the equipment and vessels at risk in the fire compartment. The number of entries on each card must

equal.:the number of pieces of equipment and vessels, MJE (SCENARIO CONTROL SPECIFICATIONS CARD 2). :If MJE = 0.0, no.1cards are required; otherwise, each card

type must be entered.

EQUIPMENT/VESSEL CONTENTS, CARD I

(FORMAT 10F8.2) VGAS2 (JE), (JE 1, MJE)

'Default Maximum

Col.(s) Variable Data Description Value Value

1-8, VGAS2 Gas volume (ft) inside 0.0

every 8 Vessel Type 2 (IE = 2, pressurized

container). MJE values must be

input on this card; for equipment

or vessels not Type 2, enter 0.0 in

the corresponding array, spaces.

91
EQUI PMENT/ VESSEL CONTENTS, CARD 2

(FORMAT 10F8.2) VPWD(JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 VPWD Volume of powder (ft ) inside 0.0

every 8 Vessel Type 2 (IE = 2, pressurized

container). See EQUIPMENT/VESSEL

CONTENTS, CARD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 3

(FORMAT 10F8.2) WH202 (JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 WH202 Moisture content (pounds) inside 0.0

every 8 Vessel Type 2. See EQUIPMENT/VESSEL

CONTENTS, CARD 1.

92
EQUIPMENT/VESSEL CONTENTS, CARD 4

(FORMAT 10F8.2) VGAS3(JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

A-8 VGAS3 Volume of gas (ft inside 0.0

every 8 Vessel Type 3 (IE = 3, pressurized

liquid containers). See EQUIPMENT/

VESSEL CONTENTS CARD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 5

(FORMAT 10F8.2) WH203(JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 WH203 Moisture content (pounds) inside 0.0

every 8 Vessel Type 3. See EQUIPMENT/

VESSEL CONTENTS, CARD 1.

93
EQUIPMENT/VESSEL CONTENTS, CARD 6

(FORMAT 1OF8.2) FVOL(JE), (JE = 1, MJE)

Default Maximum

Col.(s)• Variable Data Description Value Value

1-8 FVOL Liquid volume (ft3) inside 0.0

every 8 Vessel Type 4 (IE : 4, open liquid

containers). See EQUIPMENT/VESSEL

CONTENTS, CAQD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 7

(FORMAT 10F8.2) TE1(JE), (JE = 1, MJE)

Default Maximum

Col..(s) Variable Data Description Value Value

1-8 TEl Initial surface temperature (OF) of 0.0

every 8 equipment or Vessel Type 2

(IE : 2, pressurized containers).

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

94
EQUIPMENT/VESSEL' CONTENTS, CARD8

-(FORMAT 1OF8.2) TE2.(JE), (JE = i, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 TE2 Initial surface temperature (OF) 0.0

every 8 of equipment;,or Vessel Type 2

(IE = 2, pressurized containers).

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 9

(FORMAT 1OF8.2) TE3(JE), (JE = 1, KIE)

Default Maximum

Col. Variable Data Description Value Value

1-8 TE3 'Initial surface temperature (°F) of 0.0

every 8 equipment or Vessel Type3 (IE = 3,

pressurized liquid containers).

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

95
EQ UI PMENT/ VESSELL CONTENTS, -CARD '10

(FORMAT 1OF8.2) TE4(JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 TE4 Initial surface temperature (°F) of 0.0

every 8 equipment or Vessel Type 4

(IE = 4, open l~iquid containers).

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

EQUIPMENT/ VESSEL CONTENTS, CARD 11

(FORMAT 10F8.2) TI2(JE), (JE = 1, MJE)

Default Maximum

Col.(s) Variable Data Description Value Value

1-8 T12 Initial inside temperature (OF) of 0.0

every 8 equipment or-Vessel Type 2.,.

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

96
EQUIPMENT/VESSEL CONTENTS, CARD 12

•(FORMAT 10F8.2) T13(JE), (JE = 1, MJE)

Default Maximum

Col.(s). Variable Data Description Value. Value

1-8 TI3 Initial inside temperature ( 0 F) of 0.0

every 8 ý1,equipment or Vessel Type 3..

See EQUIPMENT/VESSEL CONTENTS, CARD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 13

(FORMAT 10F8.2) TL(JE), (JE = 1, MJE)

Default Maximum

Col.(s).. Variable Data Description Value. Value

1-8 TL Initial-liquid-temperature (°F) of 0.0

every 8 Vessel Type; 4. See EQUIPMENT/

VESSEL CONTENTS, CARD 1.

97
EQUIPMENT/VESSEL ..CONTENTS, CARD 14

(FORMAT 10F8.2) PF2(JE), (JE = 1, MJE)

Default .Maximum

Col. (s) Variable Data Description Value Value

1-8 PF2 Failure (or rupture) pressure (psia) 0.0

every 8 of equipment or Vessel Type 2. See

EQUIPMENT/VESSEL CONTENTS, CARD 1.

EQUIPMENT/VESSEL CONTENTS, CARD 15

(FORMAT 1OF8.2) PF3(JE), (JE 1,.MJE)

Default -Maximum

Col.(s) Variable Data Description Value Value

1-8 PF3 Failure- (or rupture) pressure (psia) 0.0

every 8 of equipment or Vessel Type 3. See

EQUIPMENT/VESSEL CONTENTS, CARD 1.

98
ADDITIONAL FLOW PATH DATA CARDS

Description cards of the additional flow paths' into the firep:,ompartmentz,ý .

The number of cards required is equal to the number .of flow paths, NFP (SCENAR- ,

10 CONTROL SPECIFICATIONS, CARD'2). If NFP = 0, no cards are required.

(FORMAT 4F10.2) TFP(IFP), HFP(IFP), PFP(IFP), DFP(IFP:), (IFP = 1, W NFP.).11.-...

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 TFP Failure times .(s) of..the. 0.0

additional flow paths to.the fire

compartment during the~course of

the fire.

11-20 HFP Heights (ft).of the additional 0.0

flow paths.

21-30 PFP * Pressures.,(psia) at the outlets of 0.0

the additional flow paths to the

compartment.,

31-40 DFP Diameters (ft) of the additional 0.0

fl ow paths to the compartment.

99
RADIOACTIVE SOURCE IDENTIFIER CARD

(FORMAT 7110) NRAD(J)-, (J= 1, 7)

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 NRAD Number of radioactive source terms 0

11-20, that will be generated under the

21-30 Jth type of release mechanism. J

31-40 is the numeric identifier for the

41-50 total of.seven types of radioactive

51-60 release mechanisms described in

61-70 ''Table VI. Zeros are'required to

fill in the format of seven integers

if the mechanism(s) is/are not involved. Thus, NRAD(1) = 2 denotes

that there are two radioactive source

terms resulting from burning two

types of contaminated combustible

solids. The values specified for

NRAD(J) are the numbers of physical

cards required for the .next nine

card types.

100
CONTAMINATED COMBUSTIBLE SOLID IDENTIFIER CARD

Number of this card type is governed by NRAD(1) (RADIOACTIVE SOURCE .

IDENTIFIER CARD). If NRAD(1) 0 0, no cards are required

(FORMAT 4110) IFORM, I, JACT, IBO

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IFORM The physical form of radioactive 0

contaminant found on the combustible solid.

IFORM = 1 (powder)

IFORM = 2 (liquid)

11-20 I The numeric identifier for types 0

of combustible materials, where

I = 1, 9. See Table IV for the

combustible materials and their

corresponding numeric identifiers.

21-30 JACT Any integer ranging from 1 to 20 0 20

assigned to a source term for

identification among other possible

source terms in a single fire

scenario. Up to 20 radioactive

source terms can be tracked.

31-40 IBO The burning order of the contami- 0

nated combustible sol-ids. See

descriptions for FUEL SOURCE TERMS

DATA CARDS.

101
CONTAMINATED COMBUSTIBLE SOLID MASS CARD

Number of this card, type is governed by NRAD(1) (RADIOACTIVE SOURCE IDENTIFIER CARD). If NRAD(1) = 0, no cards are required.

(FORMAT E10.4) QRAD1

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 QRAD1 Estimated total mass (pounds) of 0.0

radioactive material

102
CONTAMINATE D..COMBUSTI BLE..L IQ-UID ..I DENT IF IER, CARD

Number of .this card.type is governed by. NRAD(2) (RADIOACTIVE. SOURCE IDENTIFIER CARD). If NRAD(2) = 0, no cards are required.

(FORMAT 4110) IFORM, I, JACT, IBO

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IFORM The physical form of.,radioactive 0

contaminant found on the combustible solid.

IFORM = 1 (powder)

IFORM = 2 (liquid)

11-20 I The numeric identifier for types 0

of combustible materials, where

I = 1, 9. See Table IV for the

combustible, materials and their

corresponding numeric, identifiers.

21-30 JACT Any integer ranging from 1 to 20 0 20

assigned to a source term for

identification among other possible

source terms in a single fire

scenario. Up to 20 radioactive

-source terms can be-tracked.

31-40 IBO The burning order of the contami- 0

nated combustible solids. See

descriptions for FUEL SOURCE TERMS

DATA CARDS.

103
CONTAMINATED COMBUSTIBLE LIQUID MASS CARD

Number of this card type is governed by NRAD(2) (RADIOACTIVE SOURCE

IDENTIFIER CARD). If NRAD(2) = 0, no cards are required.

(FORMAT E10.4) QRAD2

Default Maximum

Col.(s) Variable Data Description Value. Value

1-10 QRAD2 Estimated total mass (pounds) of 0.0

radioactive material

CONTAMINATED SURFACE CARD

Number of this card type is governed by NRAD(3) (RADIOACTIVE SOURCE IDENTIFIER CARD). If NRAD(3) 0 0, no cards are required.

(FORMAT 110, E1O.4) JACT, QRAD3

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 JACT See JACT, CONTAMINATED COMBUSITBLE 0 20

SOLID IDENTIFIER CARD.

11-20 QRAD3 Estimated mass (pounds) of radio- 0.0

active material on the surface

heated by the fire.

104
UNPRESSURIZED RADIOACTIVE LIQUID CARD

Number of this card type is governed by NRAD(4) (RADIOACTIVE :SOURCE

IDENTIFIER CARD). If NRAD(4) = O,.no cards are required.

(Format 2110, E10.4) IVES, JACT, QRAD4

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IVES A number from 1 to 10 identifying 0 10

up to 10 vessels of radioactive

liquid.

11-20 JACT See JACT, CONTAMINATED COMBUSTIBLE 0 20

SOLID IDENTIFIER CARD.

21-30 QRAD4 Estimated mass (pounds) of radio- 0.0

active material in the liquid

105
PRESSURIZED RADIOACTIVE POWDER CARD

Number of this card type is governed by NRAD(5) (RADIOACTIVE SOURCE

IDENTIFIER CARD). If NRAD(5) = O,.no cards are required.

(FORMAT 2110, E10.4) IVES, JACT, QRAD5

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IVES A number from 1 to 10 identifying 0 10

up to 10 vessels of radioactive

powder.

11-20 JACT See JACT, CONTAMINATED COMBUSTIBLE 0 20

SOLID IDENTIFIER CARD.

21-30 QRAD5 Estimated mass (pounds) of radio- 0.0

active material in the liquid

106
PRESSURIZED RADIOACTIVE LIQUID CARD

Number of this card type is governed by NRAD(6) (RADIOACTIVE SOURCE

IDENTIFIER CARD). If NRAD(6) 0 0, no cards are required.

(FORMAT 2110, E1O.4) IVES, JACT, QRAD6

Default Maximum

Col.(s) Variable Data Description Value Value

1-10 IVES See IVES, UNPRESSURIZED 0 10

RADIOACTIVE LIQUID CARD.

11-20 JACT See JACT, CONTAMINATED COMBUSTIBLE 0 20

SOLID IDENTIFIER CARD.

21-30 QRAD6 Estimated mass (pounds) of radio- 0.0

active material in the liquid

107
RADIOACTIVE PYROPHONIC.SOLID CARD

Number',of this card type is governed by NRAD(7) (RADIOACTIVE SOURCE•

IDENTIFIER CARD). If NRAD(7) = 0, no cards are required.

(FORMAT 2110, 2E10.4) JACT, IBO, QRAD7, SQ

Default Maximum

Cl.( S). Variable Data Description Value Value

1-10- JACT See JACT, CONTAMINATED COMBUSTIBLE 0 20

SOLID IDENTIFIER CARD.

11-10 IBO See IBO, CONTAMINATED.COMBUSTIBLE 0 MIBO

SOLID IDENTIFIER CARD.

21-30 QRAD7 Estimated mass (pounds) of metal 0.0

burned.

31-40 SQ Size (pounds) of radioactive metal. 0.0

108
TIMvE STEP CARDS

The time spanjis separated into domains. Each domain may have different

time-step sizes and edit, intervals, and one card is required per domai.n.- At

least one card must be entered.

(FORMAT lOX, 4E10.O.) DTMAX, TEND .EDINT

Default Maximum

Col.(s) Variable Data Description Val ue Val ue'

11-20 DTMAX Time:step size (s) for this time 0.0

domain.

21-30 TEND.- End of this time. domain (s) 0.0

31-40 EDINT Print edit interval (s) for this 0.0

domain

41-50 FRFINT Graphics interval 0.0

i09
TABLE" IV:

COMBUSTIBLE MATERIALS FOR THE FIRE COMPARTMENT

Material No. Combustible Material

1 Polymethylmethacryl ate

2 Polystyrene

3 Polyvinylchloride

4 Polychloroprene

5 Cellulose (Oak)a

6 Cellulosic Material

•7 Kerosene

8 User's Option

9 User's Option

aOak was selected to represent wood products.based on the extensive

information available.

TABLE V

NONCOMBUSTIBLE MATERIAL OPTIONS FOR THE FIRE COMPARTMENT

Material No. Noncombustible Material

1. Concrete

2 Fire brick

3 Stainless Steel

4 Steel

5 Al umi num

6 Copper

7 Brass

8 to 15 User's Option

1 10.
TABLE VI

SUBROUTINES FOR ESTIMATING RADIOACTIVE RELEASES

Subroutine Name J Release Mechanisma

RST1 1 Burning of contaminated combustible solids

RST2 2 Burning of contaminated-combustible liquids

RST3 3 Heating of contaminated surface

RST4 4 Heating of unpressurized radioactive liquids

RST5b 5 Pressurized releases of radioactive powders

RST6b 6 Pressurized releases of radioactive liquids

RST7 7 Burning of radioactive pyrophonic metals

aspilling of radioactive materials has yet to be incorporated into FIRINI.

bA release factor is used to model pressurized releases at this time. A more

realistic model is currently under development and will be incorporated when

completed.

D. Input Processing

Before the system response to the selected transients can be calculated,

the FIRAC input infomation must be examined by the input processor subroutine.

The information supplied to the input processor (subroutine INPROC) is obtained

from the user-prepared input deck FIN. As the input is retrieved from the input file, the user-selected input parameters are checked to ensure the problem

set-up is consistent. If inconsistencies are found, diagnostic or error messages will appear in the output file FOUT and locally on the user's terminal.

Typically, the error messages reveal the type of input error and its location

when corrections are needed. Several input diagnostic messages and examples

are shown~in Sec. IV.

.E. Output Processing

The improved FIRAC code produces seven primary output files: FOUT, PRINTI,

PRINT2, PRINT3, RST, TAPEIO, TAPE14 (shown in Fig. 13) and three secondary output files: TAPEll, TAPE13, and FCOMP. Tables VII and VIII present a description of the information stored on each primary and secondary output file, respectively. The first five primary output files listed are in a printed format

Ili
N3

IPRINT D FIPRINT

FIR

Fig. 13.

Improved FIRAC primary output files.

MINT 3
TA BLE VII

PRIMARY OUTPUT DATA FILES

File Name

FOUT

P RI NT1

P RI NT2

P RI NT3

RST

TAP El 0

TAP E14

Subroutine(s)

Generating Information

OUTPROC

FIRIN

FIRIN

FIRIN

FIRIN

OUTP ROC

'TFNS and FIRIN

Type of-;:Information'Stored/File:Purpose

System gas dynamic and material

transport parameters

Fire compartment parameters

Fire source term parameters--

Fire compartment particulate at flow

boundaries

Radioactive source term parameters

File used for FOUT-line-printer

processed graphics of gas dynamic and

material transport parametersFile used for post-processed graphics

of fire compartment parameters

TABLE VIII

SECONDARY OUTPUT DATA FILES

File Name

TAPE11

TAPE13

Subroutine(s)

Generating Informati

GCOMP

OUTFLE and WPSPEC

on Type.of Information Stored/File Purpose

File used for post-processed graphics

of gas dynamic and material- transport

parameters

File used for conversion of system gas'

dynamic and material.-transport

parameters

FCOMP FIRIN Additional fire compartment parameters

113
.and contain helpful information for analyzing and possibly debugging the calculation. FOUT presents the gas dynamic parameters plus material concentrations, mass fractions, material flow rates, and material accumulations. The

pressures, temperatures, and densities are calculated at nodal points; volume

flows, mass flows, pressure differentials, and heat transfer parameters are

calculated for branches. The material concentrations and mass fractions are

calculated at nodal points, but the material flow rates and the amount passing

through branches or the accumulations on filters are calculated for branches.

A complete table of pressures, temperatures, and flows always is given for the

first and last calculation time step. These "archival data" also are broken'`

down into.component pressures and flows. Filter material accumulation data

are given for all filters in the system in tabular form. Pressures, temperatures, and mass and volume flows are-available on time plots if requested in

the program control section of the input.

..A summary of extreme values spanning the entire period of the problem is

produced at the end of the problem. Pressures and flows are inspected at each

time step during the calculation in compiling data for this list so that extreme values are not missed>by poor selection of output frequency. Frequently,

one mfght wish output lists for a specific point in time not covered in the!

selection of output frequency. A maximum of five special output times may be

selected. These special output times do not appear in the printer plots because the points must be equidistant in- time. The printed data are broken

down into the following 14 categories.

A-I An exact listing (echo) of the input file

A-II A summary of the controlling information and any diagnostics for

missing or inconsistent data

A-Ill A summary of problem parameters

A-IV - A summary of model parameters

A-V A summary of nodal-information (type, initial pressure, and Connecting branches)

A-VI. Dimensionless friction factors aand critical mach numbers for choking

A-VII Filter branch data

A-VIII Blower branch data

A-IX Summary of solution parameters

114
A-X Archival list of output parametersA-XI Breakdown of archival ddatai accord.ing.'to componentý type.

A-XII Pressure differential between rooms

A-XIII Summary of extreme values for calculation time (step)

A-XIV Summary of extreme values for entire problem

The PRINT family of files (PRINT1, PRINT2, and PRINT3) contains the FIRIN--

calculated results for the fire compartment. PRINTI presents-the volumetric

flow rates at the boundaries, the average hot-layer temperature, the hot-layer

thickness, the oxygen concentration near the burning'material, and the compart-

•ment pressure. The fire source term information on PRINT2 contains the total

smoke and soot generation rates, the total mass los's ratelfrom burning combustible materials, the total heat rate to the gases, and the total heat loss rate

to the surrounding heat sinks in the compartment. PIRINT3 presents the smoke,

soot, :and radioactive mass at the flow boundaries. The FIRIN radioactive

source term output file RST contains -mass flow rates for each radioactive particle size distribution and the total mass flow, rate of radioactive particles

released by the fire. Table IX summarizes the FIRIN-generated output. information for -the four FIRIN output files. ,The output frequency for the FIRIN output is specified in the FIRIN data section of.the input file.

A sample of the FIRAC and FIRIN output is found in Appendix E. The FOUT

sample includes all output from the code in.reaching a steady-state solution

and the output from the last time step.,

If plots are requested in the problem control. data block, TAPE1O and

TAPE11 will be*.generated and will contain information for the-FOUT line printer

plotting package and the post-processed graphics program GOPLOT. For the line

printer plots, a maximum of 25 frames can be requested with a maximum of 4

curves per frame. Each curve is identified by an alphabetic character A

through D. Overlapping curves are shown-by the character X at the point of

overlap., The program partially fil.ls the plot frame page when the number of.

output times is sparse by spacing with blank, lines between points. The extreme

value summaries can serve as valuable guides in selecting"the node or branch

candidates for plotting. Further, the final extreme value surmnary can be

checked for missing extrema on the plots.- Printer plots are not precise; however, they can give the analyst a good picture of the system response.

115
TABLE IX

FIRIN OUTPUT INFORMATION

File Variable Description

P RI N T1

PCOMP Fire compartment pressure (atm)

FM02 Oxygen concentration near the burning objective

ZHL Thickness of the hot layer (m)

VIP Volumetric flow rate (m3 /s) at the inlet ventilator

VOF Volumetric flow rate (m3 /s) at the outlet ventilator

THLUC ..Average temperature in the hot layer (OF)

PRINT2'

TIME --.Fire transient real time (s)

QLOSSN Total heat loss rate (10-3 Btu/h) to equipment,

vessels,,wal.ls,ceiling and floor from a fire.

(negative indicates heat loss)

TQNET Total heat rate (10-3 Btu/h) to the gases from a

fire (negative indicates heat loss or heat transfer

from the gases)

TSMOKN Total smoke generation rate (g/s) from burning of

combustible materi al s

TSOOTN Total soot generation rate j(gs) from burning of

combustible materials. TSOOTN is fraction of TSMOKN

TMASSN Total mass loss rate (10-3 lb/h) from burning

combustible materials

P RI NT3

WSMIF Smoke (g) at the inlet

WSOIF Soot (g) at the inlet

WRADIF Radioactive materials (g) at the inlet

WSMOF SmOke (g) at theoutlet

WSOOF ,Soot (g) at the outlet

WRADOF Radioactive materials (g) at the outlet

116
TABLE IX (CONT)

File Variable Description

RST

JACT Source term identifier allowing isotopes with

different levels of activity to be traced (for

example, JACT = 2 could indicate radioactive particles

form heating contaminated surfaces, whereas JACT = 1

could indicate particles given off from the burning

gloves). Mass rate is given for the particle size

bins indicated in the output file. In this way, the

particle size distribution for the radioactive source

terms is provided.

TOTAL Total mass rate (g/s) of radioactive particles given

off in a fire. It is the sum of the mass rates of all

size ranges.

TAPE1O contains FIRAC-generated output data formatted for using the GOPLOT

graphics post-processor program. GOPLOT uses the DISSPLA library and other Los

Alamos computing system libraries to produce the graphic results and is compiled

with the FORTRAN-4 extended, language compiler. This compiler is available under

control of the CDC 7600 computer and produces a controller (or absolute binary

file) that can be executed on the Livermore Time Sharing System (LTSS). GOPLOT

produces a binary output file, FIREPL, that can be examined by the Los Alamos

utility PSCAN on a graphics terminal. The plots requested in the problem control data for the line printer plots will produce the data for the more precise

plots that can be created by GOPLOT automatically. The line printer plots and

the GOPLOr-generated plots are identical in content and format.

The FIRIN-generated output written to TAPE14 can be post-processed by the

FOPLOT graphics program. TAPE14 will be generated only if FIRIN is selected to

simulate the fire transient. FOPLOT uses the DISSPLA library and other Los

Alamos computing system libraries to produce the graphic results. FOPLOT also

is compiled with the FORTRAN-4 extended language compiler. F(PLOT produces a

binary output file PLOT that can be viewed on a high-resolution graphics terminal by the Los Alamos utility PSCAN. The information written to TAPE14 is rigidly formatted. That is, the user has no control over the number and types of

plots that will be generated. The user can specify only the edit frequency by

using the print edit frequency parameter in the FIRIN data block. Table X presents the order and descriptions of the plots that are generated automatically

in the FIRIN module.

117
TABLE X

AVAILABLE PLOTS FROM FIRIN PLOTTING PACKAGE

Plot No.

1

2

3

4

5

6

7

8

9

10

11

12

Description

Hot layer height vs time

Fire compartment pressure vs time

Oxygen concentration vs time

Carbon dioxide concentration vs time

Carbon monoxide concentration vs time

Total smoke concentration vs time

Total radioactive particle concentration vs

time

Radioactive particle concentrations ,(size

distributions <0.1 to 0.8 pm) vs time

Radioactive particle concentrations (size

distributions 0.8 to 4 jim) vs time

Radioactive particle concentrations (size

distributions 8 to >20 pm) vs time

Fuel mass vs.time

Fuel burning rate vs time

Because GOPLOT and FOPLOT use and require Los Alamos computing facility li,

braries and utilities, we recommend that these graphics post-processors not be

used unless the user has access to LTSS.

F. Diagnostic Messages

Diagnostic (warning or error) messages are provided to help the user isolate possible input data or modeling errors. In most cases, the error is easily

discerned from the message; however, out-of-order or missing cards tend to produce confusing messages,. In these cases, a careful check of the input return

list and a. review of input.specifications (Sec. IV.C.) usually can isolate the

problem.

118
Diagnostic messages are produced during input processing or the system solver calculations; hence, there ismno set pattern-to their location in the output. ***DIAGNOSTIC MESSAGES always precedes these messages, and if the error

is fatal, either ERROR WITH INPUT CAN'T CONTINUE or  FATAL ERROR** **'SEE

PREVIOUS MESSAGES is printed following the message. See Fig. 14 for an example

Of the mixture of informative (nonfatal) messages and fatal error messages that

can occur.

G. FIRAC Programming Details

This code was developed to be executed on the CDC 7600 computing system.

The FORTRAN source code consists of 9149 lines of coding and is compiled with

the FORTRAN-4 extended language compiler on LTSS. This compiler is available

under control of the SCOPE 2 system for the CDC 7600 computer and produces a

controllee (or absolute binary file) that requires 154 713 words of SCM and

275 040 words of LCM to execute on LTSS.

In addition to the above required storage capacity, 11 additional disk

files [10 formatted (BCD) and 1 unformatted (binary)] are used. The names of

these files, their types, and brief descriptions of their functions are shown

in Table XI.

BRANCH 6 FLOW NEGATIVE, UP'AND DOWN-STREAM NODES 6 5 REVERSED BY PROGRAM

----------- PRESSURES READ

INPUT RESISTANCE

INPUT RESISTANCE

CAN'T CALC. RESISTANCE

INPUT RESISTANCE

INPUT RESISTANCE

INPUT RESISTANCE

INPUT RESISTANCE

BRANCH COUNT IMPOSSI BLE

I. OOOOOE-04

6.94400E-07

(SET TO MIN.

6. 94400E-07

1.42800E-03

6. 944OOE-07

3.08600E-07

FOR NODE 1

IN (NOT CALC, FROM DP)

USED FOR BRANCH

USED FOR BRANCH

VALUE) FOR BRANCH

USED FOR BRANCH

USED FOR BRANCH

USED FOR BRANCH

USED FOR BRANCH

COUNT = 1

4

5

6

13

14

23

24

BRANCH COUNT IMPOSSIBLE FOR NODE 25 COUNT = 1

******FATAL ERROR*****SEE PREVIOUS MESSAGES

Fig. 14.

Example of a multiple diagnostic list.

119
TABLE XI -

NAME, TYPE, AND PURPOSE OF THE 11 FILES USED IN CODE EXECUTION

Name Type Purpose

FIN BCD User-prepared input file.

FOUT BCD Code-generated output file. Code results

are contained in this file.

PRINT1 BCD FIRIN output data from compartment effects

(compartment history).

PRINT2 BCD FIRIN output data from file source terms

computation.

PRINT3 BCD- FIRIN output data from compartment effects

(filter accumulations).

RST BCD FIRIN1 output data from radioactive source

temporary file.

FCOMP BCD Additional FIRIN fire compartment output

data.

TAPE1O BCD Output for FIRAC graphics package.

TAPE13 Binary Temporary file.

TAPE14 BCD Output for FIRIN graphics package.

TAPE59 BCD Code-generated output file. Brief error

messages are contained in this file if

abnormal termination of the run has.occurred.

To allow a high degree of interchangeability of this code for other operating systems, US standard FORTRAN language has been used wherever practicable.

We have identified five procedures used in the code that are not necessarily

required to be supplied by the compiler in US Standard FORTRAN. In most cases,

the majority of these programs will be included in a standard FORTRAN complier.

To facilitate conversion of this code to other systems, information concerning

'120
these five programs is given in Table XII. These programs conveniently are

divided into two catagories and are not required to be included in standard

FORTRAN compilers but are included in the FORTRAN-4 extended language compiler.

TABLE XII

SUBROUTINES THAT ARE STANDARD IN FORTRAN-4 EXTENDED

Program Name

and Arguments

EOF (LUN)

MOVLEV (SOURCE, SINK ,NW)

DATE (IDATE)

TIME (ITIME)

Called ifrom

Subroutine Purpose

IEOF

SCC OP Y

MAIN

MAIN

Routine to.test for:-end of file.

LUN--Logical unit. number

EOF--1--End of file or end of

information encountered on unit'LUN

-0--No end of file or end of

information encountered on unit LUN

Routine to copy contiguous.blocks

of data.

SOURCE-First word address of

source data block.

SINK--First word addresss of sink

data block.

NW--Number of words to be copied.

Routine to return the current date

IDATE--current date in the form

IOH mm/dd/yy, where mm is the

number of the month, ,dd is .the

number of the day within the

month, and yy is the year.

Routine to return the current

reading of the system clock.

ITIME-current time in the form

IOH hh.mm.ss, where hh, mm, and

ss'are the number of hours,

minutes, and seconds, respectively.

Routine to return the central

,processor time.

CPTIME-the central processortime

from start-of-job in seconds.

SECOND (CPTIME)

121
If any of these routines is not available, the brief description of their functions given in Table XII should allow the user to substitute an equivalent

routine.

Dimensioned arrays used in the code limit the types of problems that may

be run. The maximum size of key parameters has been selected as a compromise

between absolute binary file size (63 400 words) and the ability to run realistic problems without modifying DIMENSION statements in the source code. Current input parameter limits defining restrictions on the code are listed in

Table XIII. These restrictions can be modified-easily by changing the DIMENSION statements within the source program.

.Also, LTSS requires that several of the larger arrays be allocated to

large core memory (LCM) with LEVEL 2 statements. The LEVEL 2 statement is

applicable only to Control Data CYBER 170 Model 176, CYBER 70 Model 76, and

CDC 7600 computers.

H. Compiling, Loading, and Executing Instructions

The compiling, loading, and executing procedures for the improved FIRAC

source code on LTSS are outlined. The, executing procedures for the graphics

post-processor executable files GOPLOT and FOPLOT also are described. Even

though the outlined procedures are specific to LTSS, a similar set of procedures exists for other computing systems. If the user plans to use LTSS to

execute FIRAC, we recommend that the LTSS primer and LTSS user's guide be obtained from the Computing Division Documentation Group at Los Alamos.

1. Compiling and Loading the FIRAC Program. Before the improved code

version can be compiled, loaded, or executed, the source file (program), which

is supplied on magnetic tape, must be installed on the user's system. The user

should contact the system's'computing services information group to obtain the

details of how a program written on a magnetic tape is placed on the system.

When the program has been installed, the user should attempt to compile and

load the program. A simple execute line called the ftn control statement is

used to compile and load a FORTRAN program on LTSS. The control statement

form recommended for LTSS is ftn (i = source, cname = exec).

122
TABLE XIII

MAXIMUM PROBLEM SIZE

System Parameter Maximum No.

Branches 100

Nodes 100

Room 100

Blowers 40

Boundary nodes 10

Internal boundary. nodes 3

Time functions of each type 5

Points per time function 50

Blower functions 15

Filter types 20

Points per blower function 20

Points per plot 100

Plots per frame 4

Frames 25

Number of particulate species 5

information to be plotted

123
After the ftn statement is submitted, LTSS will respond with the following.

* * * running ftn compiler * * *

* ofile,source/pa.

* dfile,alistqz.

* cfile,alistqz/pr.

* dfile,atmpbin.

* cfile,atmpbin/ab.

* dfile,aqoqzzi.

* lfc(a,i=source,l=alistqz,lcm=i,z,b=-atmpbin).

14.164 cp seconds compilation time

* goto,1.

* 1,exit.

$ cpu time 14.350 sec

$ sys time 0.468 sec

4 i/o time 10.372 sec

$ total = 0.419 minutes

* * * finished ftn compiler * * *

* * * lod summary * * *

code bloc exec written

file size=- 0162736 0030520

fld Igth= 0275536 0155411

all done

The i parameter specifies the input file or program name. This file must

be in packed-ASCII format. The cname parameter specifies the name of the absolute binary file (controllee) that will be loaded automatically. The name file

is the file that will be used to execute the program. The sym parameter attaches the symbol table to the end of the controllee. The symbol table is

necessary to debug the program if the program terminates as the result of an

error (aborts).

1 24
The load summary indicated that the controller exec has been written. The

first number in the file size line is the controller size:; the second number is

the symbol table size. The first number in the fld lgth line is the large-core

field length; the second number is the small-core field length.

If FORTRAN errors are present, they can be located by examining the listftn

file located in the user's local file space. If system-related errors (such as

maximum file size exceeded) occur during the compilation or loading of the program, the user should contact the system's consultant office for assistance.

2. Executing the FIRAC Program. After the program has been loaded and

compiled on the system without errors and the input deck has been created and

placed in the user's local file space, the user can attempt to execute (run),`the

program. The program is executed simply by typing in the following statement.

exec

This executable file will run the program until the time limit specified for the

execution has expired or until the simulation has been completed. A normal exit

or termination for FIRAC is shown below.

end of time step cards reached -- normal exit

total iterations for problem ; 5887

0 points written'to the plot file

stop ftn normal termination from main program

exec itss time 343.020 seconds

cpu= 286.301 i/o= 1.183' mem= 55.536

all done

A summary of the compilation, loading, and execution procedures is shown in

Table XIV. More information on computer time-limit requirements is presented in

Sec. IV.J.

3. Executing the Graphics Post-Processors. The two graphic post-processor

files, GOPLOT and FOPLOT, are absolute binary files (controllers) and therefore

require no compilation and loading instructions. The programs are executed by

typing in the file name. For example, to excute GOPLOT, the user would enter

the following.

goplot

125
TABLE XIV

COMFILATION, LOADING, AND EXECUTION SUMMARY

files

27542r source

all done

ftn (i=source,cname=exec,sym=)

* * *running ftn compiler * * *

* ofile,source/pa.

*dfile,alistqz.

*cfile,alistqz/pr.

* dfile,atmpbin.

* cfile,atmpbin/ab.

* dfile,aqoqzzi.

* lfc(a,i=source,l=alistqz,lcm=i,z,b=atmpbin).

14.224 cp seconds compilation time

*.goto, l.

* 1,exit.

cpu time 14.410 sec

$ sys time 0.448 sec

i/o time 15.870 sec

$ total = 0.512 minutes

* * * finished ftn compiler * * *

* * * lod summary * * *

code bloc exec written

file size = 0162736 0030520

fld lgth = 0275536 0155411

all done

files

162736r exec

234571d igo

126
'TABLE XIV (CONT)

564566r listftn

5513 map

275424r source

all done

files

162736r exec

1251r fin

234571d 1go

564566r listftn

5513 map

275424r source

all done

exec

The excutable file goplot willl; run the program until the time limit' specified

for the execution has expired or until all the plot frames have been generated.

A normal exit for GOPLOT is shown below.

firepl done. pages =

graphics cl = u

14 plot frames with

goplot Itss time

cpu= 10.118 1/0=

15. words = 34852 -I

-4

5 points for representative facility

1i3.358 seconds

1.562 memr= 1.679

In this example GOPLOT produced 14 plot frames consisting of 34 852 words. The

14 plot frames located in the file firepl can be examined with the LTSS utility

PSCAN. Documentation on the PSCAN utility can be obtained from the computing

facility documentation group at Los Alamos.

127
If the user elects) to use the FIRIN graphics post-processor FOPLOT, the

execution-procedures outlined for GOPLOT should be followed. The results of

FOPLOT are contained in a binary file named plot. This file can be examined by

PSCAN also. A normal exit for FOPLOT is shown below.

PLOT DONE. PAGES = 14. WORDS = 35316

GRAPHICS CL = U

END FTN MAIN.

FOPLOT LTSS TIME 15.373 SECONDS

CPU= 11.667 I/0= 2.053 MEM= 1.653

all done

Source files for, GOPLOT and FOPLOT are not supplied to the user because

:the programs are constructed around Los Alamos computing facility libraries and

utilities. These programs cannot be used unless the user has access to LTSS.

I. General User Hints and Suggestions

The suggestions and hints given in this section are divided primarily into

the areas of input, output, and system modeling strategy.

The task of defining resistance coefficients (friction characteristics) for

a system may be simplified and self-checked if the program is allowed to calculate these values from a "known" set of flows, pressures, and filter and blower

characteristics for the system. The alternative approach is to prescribe a resistance coefficient for each branch separately. Such a set of data usually is

referenced to a normal steady-state operating condition. In the case of a new

system, information about the friction characteristics and flows must be estimated. This can be done using the method described in Appendix G. This

approach usually allows the user to reach a steady-state solution the first.•

time.

1,28
The amount of output obtained in the case of an abort caused by an input

error depends on the time during the solution when this error is encountered.

For example, an incorrect format specified in the input resulting from data being out of order will limit the output to Table A-I (echo of input). Modeling

inconsistencies are diagnosed when the input echo is read in or when the input

data are reworked before entering the solution. Appropriate messages are

printed when this happens. An abort during the solution occurs when a particular time-step calculation fails to converge. A message to this effect is

printed along with a partial dump of the mass flow rates, pressures, densities,

and correction terms being used followed by a printout of Table A-VI through

Table A-XII for time = 0.0 s and the last time step before the abort occurred.

The output is designed to help the user easily find discrepancies in the

input that result in an incomplete or incorrect solution. For example, an

echo of the input file is presented first to help uncover format errors. If the

problem aborts at this point, some diagnostic messages follow that suggest possible reasons why this happened. When the input data are free of format errors

and consistent, the program prepares for the solution. This preparation produces additional data that give the user an opportunity to check the accuracy of the input. This portion of the output also contains any default values.

The steady-state and transient calculations are performed next. If a particular time-step calculation fails to converge, a dump of pertinent parameters

and a list of possible reasons will be printed. The results of the previous

time-step will be printed.

All the categories of data are printed automatically and cannot be suppressed or changed by the user. However, the user has control over the amount

of output generated. Two options are available.

0 If printed plots are requested, only the results from the first and

last calculation times will be printed. This assumes that the plots

will be sufficient for a cursory look at the results and that these

very limited results are enough to bracket the solution.

0 If prints of all the intermediate results are desired as well, the

word "ALL" on the PRINT/PLOT CONTROL card will cause all the results

to be output.

129
e Up to five special output times can be requested. This option serves

two purposes: (1) it permits the user to specify outputs between the

evenly spaced times computed by the program, and (2) it permits the

printouts-when the intermediate output times are suppressed.

If time, filter, and blower functions are not to be used in the described

solution, they still may appear in the input if their existence is specified.

This feature provides the flexibility that is especially useful in parametric

studies.

J. Time and Cost Estimates

The CPU and. problem times required for the two sample problems are compared below.

Number of

Sample Problem Burn Particulate

Problem CPU(s) Time(s) Time(s), Species Branches Nodes

1 1470 1000 -763 13 17 18

2 3575 1000 -810 13 37 22

The Sample Problem 1 CPU time was approximately one-half the CPU time required

for Sample Problem 2 because of the differences in system model, size. The Sample Problem 2 model required more than twice the number of branches than the

system model for 'Sample Problem 1. If the user had elected to transport the

total radioactive particulate species (instead of each individual particle

size). for the Sample Problem 2 calculation, the CPU time would have been

reduced -10

V. SAMPLE PROBLEMS

A. Introduction

The Sample Problems are given to help the user prepare the input deck and

implement several important user options. Sample Problem 1 illustrates the

FIRIN module auto-ignition concept and the FIRAC duct heat transfer and material depletion options for a compartment fire in a simple facility as shown in

130
Fig. 15. The FIRIN sequential burning option for a compartment fire in a more

complex facility (Fig. 16) is demonstrated in Sample Problem 2. Both ample

problems predict releases from a compartment fire where radioactive materials

are at risk. Sample Problem 1 predicts the release of material resulting from

the heating of a contaminated surface and the burning of a contaminated

combustible liquid. The radioactive release resulting from the burning of acontaminated combustible liquid is calculated in Sample Problem 2.

B. Sample Probleml1

1. Description and Computer Model of the Facility. This sample problem

illustrates the application of the code to a simple ventilation:system as shown

in Fig. 15. This simple system is modeled after the Lawrence Livermore National Laboratory (LLNL) full-scale fire test facility. In this sample calcula- -

tion, the fire compartment has a volume of approximately 5100 ft 3 . The walls,

ceiling, and floor of the compartmen.t consist of an A12 03 - Sl02 refractory

.material with the following properties.

Walls Ceiling/Floor

Density (Ibm/ft 3 ) 89.90 119.906

(kg/m 3 ) 1440.00 1920.00

Thermal conductivity (Btu/ft h°F) 0.23 0.35

(W/m K) 0.41 0.63

Specific heat (Btu/Ibm°F) 0.25 0.25

(J/kg K) 1046.00 1046.00

The fire compartment floor is assumed to be 3.3 ft (1.0 m) thick, and the

ceiling and walls are assumed to be 0.5 ft (0.15 m) thick. The fire compartment

has two flow boundaries. Fresh air drawn in by the blower enters the compartment near the floor, and air/combustion products are exhausted through a 26-in. 2

(0.017-m2 ) duct located near the ceiling. A high-efficiency particulate air

131
FIRE COMPARTMENT 0 -ROOM NODE

o - STANDARD BOUNDARY NODE

1 - IWTERNAL BOUNDARY NODE

HEPA

FILTER BLOWER 17

VOLUME=4059 V1*

INTAKE

26-IN. SQ. DUCT 12-IN. DIA. DUCT

32-Fl. LONG 25-Ft. LONG

Fig. 15.

Schematic of the system used in sample problem *1.

132
REPRESENTATIVE FACILITY

19

------- --------

21

9

22

.......... ........ wos Alamos

Fig. 16.

Schematiic of the system used in sample problem 2.

-- 1
(HEPA) filter is located 32 ft (10 m) downstream of the fire compartment. A

centrifugal blower with an exhaust damper is located approximately 25 ft (8 m)

downstream of the HEPA filter. The filter and blower are connected by a 12-in.

(0.30-m)-diam, 25-ft (8-m)-long duct. Air or combustion products passing

through the damper are exhausted to the atmosphere. The 32-ft (9.75-m)-long

duct is assumed-to have 1/4-in. (6.3-mm)-thick steel walls; the 25-ft (8-m)-long

duct is assumed to have 1/16-in. (O.16-mn)-thick steel walls.

Eighteen nodes and seventeen branches were used to model the facility.

Nodes 1 and 18 are boundary nodes representing the assumed atmospheric conditions. Fourteen-capacitance nodes were used to model the inlet to the fire compartment and the 32-ft (9.75-m)-long and the 25-ft (8-m)-long ducts. The fire

compartment exhaust duct [32-ft (9.75-m)-long] is finely noded (11 nodes) to

predict the temperature distribution between the fire compartment and the HEPA

filter. The volume specified for each of the capacitance nodes is shown in

Table XV. Note that the 26-in. (O.17-m 0 ) duct volume is distributed equally

between 11 duct nodes, and the 12-in. (O.30-m)-diam round duct volume is distributed equally between nodes 16 and 17. The 17 branches used to connect.

adjacent nodes consist of 13 ducts, 2 dampers, 1 filter, and 1 blower. The

branch types, along with their related flow and heat-transfer areas, are shown

in Table XVI. The blower characteristic curve for this problem is shown in

Table XVII.

Because the FIRIN module will be used to simulate the nonradioactive and

radioactive source terms, two internal boundary nodes (nodes 3 and 4) were used

to represent the fire compartment. The important fire compartment input parameters are outlined in Table XVIII.-

In addition to the above information, a description of the system initial

conditions as described in Sec. IV is required. The steady state of the system

may be obtained by prescribing branch resistances, the nodal pressures, or a

combination of branch resistances and nodal pressures. For this sample problem

description, an assumed pressure distribution and user-prescribed branch resistances were used to obtain a steady-state solution. This information represents a data base sufficient for the code to establish a consistent steady state

of all the calculated variables corresponding to any ambient temperature (560F

for this sample problem). A complete listing of the computer code input file

(FIN) used to execute Sample Problem 1 is shown in Table XIX.

134
TABLE XV

INITIAL DATA FOR EACH NODE

Vo 1 ume

(ft3 Node )

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

*

1.00

13.64

13.64

13.64

13.64

13.64

13.* 64

13.64

13.64

13.64

14.64

13.64

9.80

9.80

Initial Pressure

(in. w.g.)

0.0

-0.06

0.0

0.0

-0.02

-0.04

-0.06

-0.08

-0.10

-0.12

-0.14

-0.16

-0.18

-0.20

-1.165

-1.365

0.035

0.0

*Boundary node - no volume specified.

135
Branch

No.

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Branch

Type

Damper

Duct

Duct

Duct

Duct

Duct

Duct

Duct

Duct

Duct

Duct

Duct

Filter

Duct

Blower

Damper

TABLE XVI

BRANCH DATA

TABLE XVII

Flow

Area

(f t 2 )

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

4.6940

0.7854

0.7854

0.7854

0.7854

HeatTransfer

Area

(ft 2 )

0.0

0.0

27.8

27.8

27.8

27.8

27.8

27.8

27.8

27.8

27.8

27.8

0.0

78.5

0.0

0.0

DIGITIZED BLOWER CHARACTERISTIC CURVE

FOR SAMPLE PROBLEM

Volumetric flow

(ft 3 /min)

-8000

0

1123

6000

Head

(in. w.g.)

8.0

1.8

1.5278

0.0

136
TABLE XVIII

Parameter(s)

IPRINT

MIBO

IGNITE

PFLOW, NFP

EQUIP, MJE,

IFLOW3

TENIT

PINIT

IBRCHI

IFCND1

ZIF

.DIF

IBRCHO

IFCND2

FIRIN INPUT

Value(s)

100

2

1

0

56.0

-0.20

2

3

1.084

2.166

3

4

PARAMETERS.FOR SAMPLE PROBLEM.1

Description(s)/Comment(s)

Edit frequency for FIRIN output

Number of burning orders

Ignition energy concept option-this requires

MIBO = 2

These options were not used for this calculation

Initial fire compartment temperature (°F)

Initial fire compartment pressure (in. w.g.)

Fire compartment inflow branch identities

Fire compartment internal boundary node

connected to IBRCHI

Elevation if the centerline plane of the inlet

ventilation from the compartment floor (ft)

Diameter of the inlet ventilator (ft)

Fire compartment outflow branch identifier

Fire compartment internal boundary node

connected to IBRCHO

Elevation of the centerline plans of the outflow

ventilator from the compartment floor (ft)

Diameter of the outflow ventilator (ft)

Amount of kerosene fuel -burning order 1 (Ibm)

Amount of kerosene fuel--burning order 2 (Ibm)

Burn area of fuel--burning order 1 (ft 2 )

Burn area of fuel--burning order 2 (ft 2 )

Fire compartment length (ft)

ZOF

DOF

FUEL (7, 1)

FUEL(7,2)

AREC (7, 1)

AREC(7,2)

RL

11.76

2.166

5.75

2.16

4.0

2.0

20.0

137
TABLE XVIII (CONT)

Parameter( s) Value(s) Description( s)/Comment(s)

WR

ZR

XCEIL

X WALL

XFLOOR

ZFI RJE

MATERW

17.0

15.0

0.492

0.492

3.281

0.452

8

Fire compartment width (ft)

Fire compartment height (ft)

Ceiling thickness (ft)

Wall thickness (ft)

Floor thickness (ft)

Height of the flame base from the floor (ft)

Wall material identifiers

Floor material identifier

Combustibles at risk to auto-ignition concept

identifier. NBO = 2 signifies the combustible

is not at risk, NBO = 1 signifies the

combustible is at risk to auto-ignition

MATERF

NBO(1-6)

NBO(7)

NBO(8-9)

NRAD(1,4-7)

NRAD (2)

NRAD(3)

9

2

1

2

0 Radioactive release mechanism identifiers:

NRAD = 0 indicates that these release mechanisms

will not be used, NRAD(2) = NRAD(3) = 1

indicates that the second and third release

mechanisms will be used

1

1

IFORM 1 The following fire input values correspond to

the NRAD(2) release mechanism. IFORM = 1

indicates that the contaminant found on the

combustible is in powder form. I = 7 indicates

that fuel type 7 (kerosene) is a contaminated

combustible. JACT = 1 identifies the source

term and IBO = 2 indicates the burning order of

the contaminated combustible. QRAD 1 = 0.2205

specifies the total mass of radioactive material

in/on thecombustible.

I 7

JACT 1

IBU 2

138
TABLE XVIII (CONT)

Parameter(s) Value(s) Description(s)/Comment(s)

QRAD1 0.2205

JACT 2 The last two FIRIN input values describe the

NRAD(3) release mechanism. JACT = 2 is the

identifier associated with the source term and

QRAD3 = 0.1653 specifies the total mass of

radioactive material on the contaminated surface.

QRAD3 0.1653

139
TABLE XIX

COPY OF INPUT DECK USED TO RUN

SAMPLE PROBLEM 1

I

2 sample problem 1

3 # run control card 1

4 st 1. 999.0

5 # print / plot control card

6 all 2 1 1 2 5

7 1 I I

8 2 1 1

9 3 1 1

10 10 1 I

11 13 1 1

12 # plot frame description card

13 4 2 3 4 5

14 4 4 14 Is 17

15 4 2 3 13 15

16 4 2 3 8 15

17 4 2 3 4 5

18 4 9 14 16 17

19 4 2 3 13 14

20 4 2 3 13 14

21 4 2 3 13 14

22 4 2 3 13 14

23 4 2 3 13 14

24 4 2 3 13 14

25 4 2 3 13 14

26 4 2 3 13 14

27 4 2 3 13 14

28 4 2 3 13 14

29 # run control card 2

30 t

31 # boundary control card

32 0 4 56.

33 # geomotry and component control card

34 16 18 14 1 1

35 # branch description data cards

36 1 1 2 1200. 4.6944 .25 v

37

38 2 2 3 1200. 4.6944 .25 d

39 9.5000e-08

40 3 4 5 1200. 4.6944 3.2 d

41 1.389e-08

42 2.167 27.77 1 .25 .3 .3

43 4 5 6 1200. 4.6944 3.2 d

44

45 2.167 27.77 1 .25 .3 .3

46 5 6 7 1200. 4.6944 3.2 d

47

48 2.167 27.77 1 .25 .3 .3

49 6 7 8 1200. 4.6944 3.2 d

50

51 2.167 27.77 t .25 .3 .3

52 7 8 9 1200. 4.6944 3.2 d

53

54 2.167 27.77 1 .25 .3 .3

55 8 9 10 1200. 4.6944 3.2 d

56

57 2.167 27.77 I .25 .3 .3

58 9 10 11 1200. 4.6944 3.2 d

59

60 2.167 27.77 1 .25 .3 .3

61 10 1t 12 1200. 4.6944 3.2 d

62

63 2.167 27.77 1 .25 .3 .3

64 11 12 13 1200. 4.6944 3.2 d

"If irln"

0 0 13

.06

.14

.02

2. 1666 6.9333

26.2 489. 12

.02

2.1666 6.9333

26.2 489. .12

.02

2.1666 6.9333

26.2 489. 12

.02

2.1666 6.9333

26.2 489. .12

.02

2.1666 6.9333

26.2 489. .12

.02

2.1666 6.9333

26.2 489. .12

.02

2.1666 6.9333

26.2 489. .12

.02

2.1666 6.9333

26.2 489. .12

.02

1

56.

1

56.

1

56.

1

56.

.61

56.

1

56.

140
TABLE- XIX, (CONT)

65

66

67

68

69

70

71

72

73

74

75

76

77

78

79 #

80

81

82

83

84

85

86

87

88

89

90

91

92

93 #

94

95

96

97

98 #

99

100

101

102

103

104

105

106

107

108

109

110

III

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127 #

128

2.167 27.77

12 13 14

2.167 27.77

13 14 15

14 15 16

1. 78.5

15 16 17

16 17 18

I.Oe-07

1 .25

1200. 4.6944

1 .25

1200. .7854

1

2.1666 6.9333

.3 .3 26.2 489. .12

3.2 d .02

2.1666 6.9333

.3 .3 26.2 489. 12

f :965

1

56.

56.

1

56.

1200. .7854

1 .0625

1200. .7854

25. d .2

2-.

.3 .3 26.2 489.

b -1.4

75.

.12

1

1200.

particulate specie

I smoke

2 total rad part

3 rad part .1

4 radpart .2.

5 rad part .4'.

6 rad part .6

7 rad part .. 8,,

8 rad part 1.

9 rad part 1.5

10 rad part 1.9

11 rad part 8.

12 rad part 15.

13 rad part 20.

boundary node

.7854 0.5

data cards

100.

20.

.1

.2

.4.

.6.8

1•.

1.5

1.9

15.

20.

data

56.

56.

56.

56.

V .2

1.

'1.

1.

.1.

.1.

*1.

1.

1.•

1*.

1.

10 0.

31 0.

41 0.

18 0 0.

room

2 1.0

4.6944

5 13.636

4.6944

6 13.636

4.6944

•7 13.636

4.6944.

8 13.636

4.6944

9 13.636

4.6944

10 13.636

4. 6944

11 13.636

4z6944

12 13.636

4.6944

13 13.636

4.6944

14 13.636

4.6944

15 13.636

.7854

16 9.8

.7854

17 9.8

.7854

b

data

lower curve cards

141
TABLE-1XIX. (CONT.)

129 -I

130 6(

131 #

132

133 #

134

135

136

137

138 #

139

140

141 #

142

143

144

145 #

146

147

148

149

150 #

151

152

153 0

154

155 #

156

157

158

159

160 #

161

162

163

8000

000.

). 8. 0.

0.

filter data

.9995

1. 8 1200 1.5278

1 .

temperature data

56. '56. 56.

56. 56. 56.

56. 56. 56.

56. 56. 56.

fire scenario control specifications

1100. 10O 2

1 0.0 0 0.0 0

fire compartment initial conditions and noding

56.0 -. 20

56.

56.

56.

56.

56.

56.

if low3"

0

2 3 1.084 2. 166

3 4.. 11.76 2.166

fuel type. mass *and burn area

0.0 0.0 0.0 0.0 0.0 0.0 5.750

0.0 0.0 0.0 0.0 0.0 0.0 2.150,

0.0 0.0 0.0 0.0 0.0 0.0 4.0

0.0 0.0 0.0 0.0 0.0 0.0 2.0

fire compartment dimensions and materials

20.0 17.0 15.0- 0.492 0.492 3.281

•9 8 9

combustible identifier card (required if ignite > 0)

2 2 2 .2 2 2 1 ' 2 2

radioactive source term input 0 . I 1 0 0 0

0.0 0.0

0.0. 0.0

0.0 0.0

0.0 0.0

0.492

0 I

.22050

2

7 I 2

0.1653

time step cards

.001

.01

.05

3.0

10.0

999.0

1.0

1.0

50.0

,142
2. Fire Accident Scenario. In Sample P-roblem 1, it is postulated that

two o pen cans of flammable solvent (kerosene) are located within the fire compartment. One of the cans of kerosene is -assumed to be contaminated, with a

mixed oxide powder; the other can is not contaminated. ..The uncontaminated can

is assumed to have, an exposed surface area of 4.0 ft 2 (0.37 m2 ) and a mass of

5.75 Ibm (2.61 kg). The smaller contaminated can has an exposed surface area

•'of 2.0 ft 2 (0.18 m2 ) and a mass of 2.16 lbm.(0.98 kg). To initiate the accident sequence, it is postulated that the uncontaminated can becomes ignited.

The second (contaminated) can Of flammable solvent'has been contaminated with

0.22 Ibm (0.10 kg) of mixed oxide powder and is susceptible to ignition via

the FIRIN auto-ignition model. 'The auto-ignition model assumes that the combustible at risk to. ignition from other burning combustibles within the fire

compartment will ignite if the heat flUx levels are sufficient. In addition

to the contaminated flammable solvent, 0.165 lbm' (0.075 kg.) of mixed .oxide powder is assumed to be distributed evenly over the compartment floor. This material can become airborne as a result of the fire-induced hEa~ting-9of the contaminated surface' (fIoor).

3. Calculated Results.

",a. System Response. The fire (ignition of:the uncontaminated kerosene)

begins 2.0 s into the transient and initfates the accident sequence. The sequence.of events for this sample'calculation is presented in Table XX. The

fire compartment (represented by nodes 3 and 4) rapidly pressurizes from its

.ý steady- state value of -20 in. w. g. ý(,50.0 cm w.g.) to a valueapproaching

0.10 in. w.g. (0.25 cm w.g.) as a result of the rapid vol~umetr.ic expansion of

the gases within the compartment. The heating of the air within the compartment

of the fire causes the rapid expansion. Figures 17 and 18 show the pressure

response of the system. The pressures near thefilter and blower locations of.

the system are perturbed s'lightly. The system capacitance represented by the

duct volume located between the fire compartment and filter and blower positions dampens the influence of the fire. Also, as a result of the rapid pressure increase in the fire compartment, a reversal of flow at the inlet and increase of exit flow to the fire compartment is calculated by.FIRAC. The system

volumetric and mass flow results are presented in Figs. 19 and 20. The system

mass flow rates exhibit trends similar to those shown in the volumetric flow.

Once the hot layer has descended to the centerline elevation::of theexit branch

(node 4, branch 3), the mass flow rates are reduced as the warmer gases are

143
TABLE XX

TRANSIENT EVENT SEQUENCE FOR SAM'LE PROBLEM 1

Event Time,(s)

Uncontaminated kerosene ignites 2

Maximum. fire compartment pressure (0.05 in. w.g.) attained -10

(hot layer descends to elevationf outflow boundary) "12

Contaminated kerosene ignites via auto-ignition -582

Transport of radioactive material: initiated -582

(hot layer descends to centerline elevation of inflow boundary) -621

Maximum system temperature (-240°F) attained -7631

Fire terminated& ;763

Release of radioactive material from continued heating of the

residue .- 763

End of ýcalculation 1060

144
SAMPLE PROBLEM 1

TIME (S)

Fig. 17.

Pressure response for nodes 2, 3, 4, and 5.

145
SAMPLE PROBLEM 1

400.0 500.0 600.0 700.0 800.0

TiME (S)

Fig. 18.:

Pressure response for nodes 4, 14, 15, and .17.,

146
SAMPLE PROBLEM 1

U,

0

-J

'./.

o-

:!

0

>

N

.0 100. 200.0 300.0 .400.0 500.0 600.0 700.0 800.0 900A(

T ME (S)

Fig. 19.

Volumetric flow rates for branches 2, 3, 13, and 15.

147
9

SAMPLE PROBLEM 1

100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0

T I ME (S)

Fig. 20.

Mass flow rates for branches 2, 3, 8, and 15.

148
transported through the exhaust duct. The hot-layer position and temperature

vs time are shown in Figs. 21 and 22, respectively. System temperature profiles

in and around the fire compartment are shown in Fig. 23, and the temperature

profiles midway between the fire compartment and the filter and at the filter

inlet and blower exit are shown. in Fig. 24. At any time during the transient,

the decrease in gas temperature with increasing distance from the fire compartment is a result of the gas heat losses because of convection and radiation heat

transfer occurring in the exhaust duct. After the hot layer has descended below

the exhaust elevation of the fire compartment, the system response (pressures,

flow rate, and temperatures) remains stable. At -500 s, the hot layer has descended near the elevation of the inflow (node 3, branch 2). As the hot layer

passes over the inflow boundary, node 3 is assigned an averaged hot-layer temperature value (Fig. 23). Until this time in the transient, the uncontaminated

kerosene has been the only energy source for the fire. The other fuel source

is the contaminated can of solvent susceptible to ignition via the ,FIRIN autoignition option. At -582 s, FIRIN calculates that the fire compartment heat

flux levels have reached the required level to ignite the second'fuel source..

The autoignition of the additional fuel is indicated in several of the'graphic

results. For example, the system pressures and flows are perturbed again as

additional-heat is added to the system. The pressures are calculated to increase throughout the system, whereas the inlet flow is reduced and the exhaust

flow is slightly enhanced. Also, the additional heat source assists in the

growth of the hot layer, an increase in hot-layer temperature, and an increased

fuel burning rate. After the contaminated can of kerosene has ignited, the hot

layer descends to the floor very quickly, and the inflow boundary node (node 3)

achieves a value equivalent to the hot-layer temperature. Another assumption

of the FIRIN auto-ignition concept is combining of fuels and fuel surface areas

after auto-ignition has been achieved. The model assumes that the fuel (mass)

remaining from the initial fuel source is lumped with the at-risk fuel mass and

that the fuel surface burn areas are combined. For this calculation, the fuel

burn area after -582 s was 6.0 ft 2 (0.6 mi2 ). Combining the burn areas enhances

the burning rate (consumption of fuel) as shown in Figs. 25 and 26. After the

hot layer has descended to the floor, the inlet air becomes mixed with the hot

149
SAMPLE PROBLEM I

q

0

I-.

C,!9

OUTFLOW DUCT

~~~............ ................

INFLO T .............................. ............................. ...... a

',

0.0 iO.0 200.0 360. 400.0 500.0 ow.0 700.0 00.0 900.0 1000. TIME (S)

Fig. 21.

Hot-layer height vs time.

150
SAMPLE PROBLEM -1

TIME (S)

Fig. 22.

Hot-layer temperature vs time.

. 51
SAMPLE PROBLEM 1

TIME (S)

Fig. 23.

Temperature response for nodes 2, 3, 4, and 5.

152
SAMPLE PROBLEM 1

0.0 100.0 200.0 300.0 400.0 500.0 600:0

TIME I(S)

Fig. 24.

Temperature response for nodes 9, 14, 16, 17.

153
SAMPLE PROBLEM I

300.0 400.0 500.0 600.0 700.0 800.0

TI ME (S)

Fig. 25.

Fuel burning rate vs time.

154
SAMPLE PROBLEM 1

TIME (S).

Fig. 26. - Fuel mass vs. time.

155
gases of the hot layer and is no longer supplying the fire with fresh air. The

fire, which is assumed to be located approximately 0.6 ft (0.2 m) above the

floor, begins to entrain a mixture of air and combustion products, which decreases the overall oxygen concentration of the compartment (Fig. 27). All the

combustible materials were consumed by -763 s. After the fire has terminated,

the system begins to recover and reestablish the initial steady-state conditions.

b. Material Transport. The transport of smoke particulate and radioactive

particulate was calculated for the sample problem. The quantity of smoke particulate generated by the burning of the kerosene and transported to the filter

is shown in Fig. 28. This plot reveals that a significant portion of the smoke

particulate wasnot transported to the filter because of deposition. As a result of the filter remaining unplugged, the blower performance was not affected

by the smoke. The smoke particulate diameter was shown to be unrealistically

large (-10&pm) so that the effects of particle size on the deposition rate

could be seen in the results. Deposition is an important consideration and can

affect the results of a calculation. For example, improper selection of particle diameter could lead to an unrealistic deposition rate that inhibits 'material

from challenging the HEPA filter in a facility. This could lead to misleading

results in terms of fire strength/duration and radioactive particle release

rates.

During this fire transient, the radioactive release mechanisms were used to

simulate the release of radioactive material. Heating of a contaminated surface

and burning-,of a contaminated combustible liquid were the two:mechanisms. The

release resulting from the heating of the contaminated floor is not evident in

the results. The release rate for this mechanism is several orders of magnitude

less than the release rate for burning of a contaminated liquid. As -a result,

the particulate flow rate -and accumulations for the:20-pm.particles shown in

Figs. 29 and 30 do'not indicate a significant release before -600 s. 'The 20-pm

particulate size distribution is released by both mechanisms. After -600 s,

the burning of the contaminated combustible liquid produces the particle flow

rate and. accumulations shown in the figures. This mechanism has two stages for

particulate release. Stage one is the burning phase, and stage two is the continued heating of the residue after the burning .has stopped. Stage one occurs

between ~600 s and -763 s, and stage two occurs between -763 s and 1000 s. *The

156
SAMPLE PROBLEM I

0 -

0

0v

z o

w

CLL

0 i'

0..

8

h.5-

10.0 0.0, 200.0 300.0 4&0.0 5.0.0 600.0 700.0 0.o 0•0.0 1000.

TIME (S)

Fig. 27.

Fire compartment oxygen concentration vs time.

157
SAMPLE PROBLEM I * -BRANCHIZ2

* -BRANCH 3

I-BRANCH13I

C4

tNd

0

Z

L/) V) ~

0.0 100.0 200.0 300.0 400.0 . 500.0 600.0 700.0 800.0 900.0 1000

TI ME (S)

Fig. 28.

Accumulated smoke particulate mass for' branches 2, 3, 13, and 14.

158
--J I ' Liii

0 I

LA-.

I-

-LJ

1'>**

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000 TIME (S-'

Fig. 29.

20-vim radioactive particulate mass -floW rates for branches 2, 3, 13, and 14.

159
SAMPLE PROBLEM 1

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000

TI ME (S)

Fig. 30.

Accumulated 20-vim radioactive particulate mass for branches 2, 3, 13, and 14.

160
FIRIN rate of release mechanism assumes that the heating of the residue

continues 10 min after the burning has stopped.

4. Summary. Sample Problem 1 demonstrated several user options of the im-.

proved FIRAC: auto-ignition.of a contaminated combustible, release o.f radioactive material-by the release mechanisms; heatihg of a contaminated surface

and burning of a Contaminated combustible liquid;2 internal boundary nodes

representing the fire compartment; transport of 11 radioactive-particle size

distributions and depletion of material; and duct heatltransfer capability.

This- sample problem indicates how Complicated the interpretation.offthe calculated results can become when several options have beenh enabled.,/ The user

should become familiar with all the options and how they will affect the calculation. Also, the interactions that-can occur between the various options.*

should be anticipated to.assist in th e analysis of the results.

.C. .Sample Problem 2;.

1. DescriptionIand Computer Model iof the Facility. To ililustrate how the

improved fire code can be applied to -a more complex facility, consider the system schematic- shown-,in Fig. 16. The facility presented, in the ,,schematic is

representative of most nuclear.fuel cycle-ventilation systems in that it -contains multiple fans, compartments,.:dampers,ý filter systems, and parallel/series:

flow configurations." For this scenario, 'the fire is assumed to occur in the

compartment representedby internal boundary- nodes 9, 21, and. 22. Three- internal boundary nodes were required because the compartment has three flow connections:* two inflow (branches 16 and 17) and one outflow (branch 14) connection.

The inlet and outlet branches (ducts).to the fire compartment have been positioned so that the general ventilation flow direction in-the room is downward.

Most compartment ventilation ducts in fuel cycle facilitiiesare configured in

thins manner to help settle contaminated airborne .part~iculates, ..which reduces

the.risk of contamination throughout the facility. Akcloseup of the fire

compartment noding is shown in Fig. 31.

The fire compartment is assumed to be 39 ft (12 m) long, 39 ft (12-1m) wide

and 20 ft (6..m) high..' The centerline elevation •(measured from the floor) of the

*A-maximum of three internal boundary nodes can be used to represent,.the

FIRIN fire compartment. For this sample calculation,.two internal boundary

- nodes could have been used (Sec. III.C).

. 161
a.)

FROM SUPPLY.

TO FACILITY

•EXHAUST FILTER

I NODE 15

NODE"6

1 BRANCH 16

*r CAPACITANCE

NODES

INTERNAL

BOUNDARY

NODES

FIRE I.:.COMPARTMENT

BRANCH 14

BRANCH 17

NODE 11

FROM CORRIDOR

Fig. 31.

Close-up system schematic near the fire compartment for Sample Problem 2.
two inlet ventilations is 18.74 ft (5.71 m), and the centerline elevation of the

outlet ventilationhis.3.0 ft (0.9 m). Also, the fire.compartment is assumedto

have a concrete floor, ceiling, and walls. The ceiling and floor are assumed to

..be 1.0 ft (0.3 m) thick, and the walls are assumed to be 0.5 ft (0.2 m) thick.

When the system is operating under'steady-state conditions,the fire compartment has a pressure of -0.30 in. w.g..(-O.76 cm w.g.) at a temperature of

70°F (21 0C). The two inlet ventilators (branches 16 and 17) supply 3679 ft 3 /min

.(1.736 m3 /s) and 290 ft 3 /min (0.137*m3 /s) of air to the compartment. The outlet

3 3 ventilator exhausts 3969 ft /min (1.873 mi s) under steady-state conditions. The

fire compartment/overall system steady state was achieved by selecting an initial system pressure distribution and using resistance coefficients,. The fire 2

compartment exhaust filter (branch 17) is assumed to-be 99.95 efficient and

have a plugging factor of 20.1/kg. A large filter plugging factor'was selected

to illustrate the importance of the filter plugging model on the calculated,

results.

The facility model features 37 branches, 22 nodes [17 capacitance (room)

nodes, 2 standard boundary, and 3 internal boundary], 2 blowers, and 9 filters.

A complete listing of the input deck for sample problem 2 showing the assumed

blower curves, initial system pressure distribution, fire compartment input.

specifications, and so on is presented in Table XXI.

2. Fire Accident Scenario. The purpose of sample problem 2 is to illustrate the use of the FIRIN sequential burning option. Two fuels (kerosene and

* polystyrene) will be burned sequent~ially in:.the calculation. The fire compartment is assumed to contain 3.0 Ibm:(1.4 kg),of uncontaminated kerosene. The

f2 i 2 container of kerosene has an exposed surface (burn) area of 5.0 ft2(0.5 m).

In addition to the kerosene, the. compartment contains 30.0 lbm (13.6 kg) of con-.

taminated polystyrene. The polystyrene is assumed to have an exposed surface

area of 7.0 ft 2 (0.7 m2 ) and is contaminated with 0.22.lbm (0.10 kg).of mixed

oxide powder.

Because the scenario assumed that the two combustibles at risk within the

fire compartment will burn sequentially, the maximum number of burning orders

(input parameter. MIBO) is 2. The kerosene was selected to initiate the accident

sequence and has a burning order (IBO) of 1. After all the kerosene has been

consumed, the polystyrene (burning order IBO = 2) will ignite to continue the

.fire-induced.transient. When using the sequential burning option, the combustibles input information must be entered according to the burning order. For

163
TABLE XXI

INPUT DECK LISTING FOR SAMPLE PROBLEM 

2

2

3 

#

4

5#6789

10

12 #

13

14

15

16

17

18

19

20,

21

22

23

24

25

26

27 #

28

29 

#

30

31 

#

3233 

A

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

55

56

57

58

59

60

61

62

63

64

sample problem 

2 run control I

st 0. I. 999.

print plot

all I 1 1 

1

2 1 1

2 1 1 11 1 1

12 1 

1

13 1 I

frame description cards

4 9 15 21 22

control card 5

3344444444444

14

149

14

14

14 

r

14

14

14

14

14

14

14

16-

16

15

34

34

34

34

34

34

34

34

34

34

run

17

17

21 22

35 36

35 36

35 36

35 36

35 36

35 36

35 36

35 36

35 36

35 36

control

F, boundary5

geometry

37 22

branches

I I

0.

2 

2

0.

3 

3

0. (

4 

4

0.

5 

5

0.

6 

7

0.

7 

6

0.

*•8 6

0.'

9 11

0.

10 

8

0.'

11 6

0. 

•

12 

6

0.

13 1l

0.

14 21

2.6000-04

15 

6

0.

control

and component

17 

2

24

0.

6

0.

15

0.

7. 0.

11

0.

7

0.

15

0.

0.

0.

8

0.

8

0.

15

0.

11

0.

17600.00

17600.00

17600.00

17600.00

7710.00

578.00

413,.00

50.00

143.00

433.00

50.0

290. 00

143.00

3766.00

100.00

card 

2

p t

(p. t. e. m)

70.

control 3

12.000 1(

12.000

12.000,

12.000 1'

5.000 1I

.380

•290 2'

.290

.100

.290

.290

.200 2

.100

2.500

2

0.100

3. O00v

0.000f

0. O00b

5. 000v

O. 000v

0.000f

0. ooov

i. ooov

I. 00Ov

0.000f

I. O000V

0. 000v

I. 000v

0.000f

i. O00v

"if rin" 0 0 13

3.464

3.464

3.464

3.464

2.236

.6164

.5385

.5385

.3162

.5385

.5385

.4472

.3162

1.581

.3162

16 6 9 3480.00 2.300 20.O00v

164
-TABLE"•• XXI (CONT)..

65

66

67

68

69

..70

71

72

73

74 : r75,

76

77

78

7990

81

82

83

8485

86

87

88

8990

9192

93

94

95

96

97

98

99

100,

101

102

103

104

105

106

107

108

109

110

1Il

112

113

114'

115..

116

117

118

119

120

121

122

123

124

125

126

127

128

2.875eW08 0.

17 A1 22

0. ý:, 0.

18 10 15

0. 0.

19 6 11

0. o.

20 . 10 0. 0.

21 11 10

0. O.

.22 5 11

0. 0.

23 5 20

0. 0.

24 5 12

0. 0.

25 12 15

0. 0.

26 13 15

0 '. -0.ý : 27 11 :13

0. 0.

28 20 13

o. 0.

"29 20 11

0., 0. 30• 14 15

0.. 0 ° 31 201 - 11

0. 0.

32 20 14

0. 0.

33 11 14

0 0.. 0.O

34,. 15 1

0. 0.

35 -16 17

0 . . . 0 . . . •+36. 17 18

0. w0

37 18 ,19

2860.00

.2000.00ý

100.00

1714.00

286.00

930.00

7260.00

1700.00

1700.00

3746.00

286.00

3460.00

100.00

3886.00

100.00

3600.00

•86 .00-

17•600.00.

17600.00

17 7.6-0. 00

17600.00

190

2.'300

I

0. 100

2.100

190

.620

4•.800

1.100

1.100

2.400

.190

2.300

.070

2. 500

.070

2. 400

•190

12.000

12.000"

,3

12. 000;-4

12.000"

i.O00Ov

0. 000f

1. O00v

20. O00v

I. O00v

10. O00v

20 00%v

20. OOOv

10o. 00o?

0'. POOf

I. 00v

0. 000v

20. 00v

I .0ov

:l0.o ...t .00vf ooov

1O;0. 0v ...

-1,. 517

'.4359

1.517

.,3162

1.449

.. 4359

.7874

2.191

1"049

.4359

.2646:

.2.646.

1.549

...4359

:3.464

3-.46 154

"1. 44

1.

A,

~0

N

particulate specie data cards I smoke.1.

2 total rad parti 20.

3 rad part-.1 . , 4 rad part .2 .2

.5, ad part ,4 -, ' .4

6 rad part :6 -. .6

7 rad part .8 -/ .8

U rad part 1. ,i.

9 rad part 1.5 .1.5

,0 rad part 1.9 1.9

11 I ad p art. 8W. 8.

12 r-ad part '15. 15. 13 rad part 20. .20.

boundary data

1 0

9 1 -0.3

19 0

21 1

22 1

room data

70.

1,470.

70.

70.

70.

(e. m. p. t)

165
TABLE: XX I (CONT)-.

129 2 500.00

130 120.000

131 3 500.00

132 120.000

133 4 500.00

134 120.000

135 5 500.00

136 120.000

137 6 500.00

138 50.000

139 7 3600.00

140 180.00

141 8 4440.00

142 222.00

143 10 87400.00

144 4370.0

145 11 10200.00

146 510.00

147 12-117300.00

149 5865.0

149 13 20000.00

150 1000.0

151 14 20000.00

152 1000.0

153 15 500.00

154 120.000

155 16 500.00

156 120.000

157 17 500.00

158 120.000

159 18 500.00

160 120.000

161 20 500.00

162 50.00

163 # blower curves

164 1 6

165 -5600.00 13.80 0.00 9.80,' 12000.00 9.70

166 17600.00 8.15 25200.00 4.00 30800.00 0.00

167 2 6

168 -7700.00 18.10 0.00 12.10 8000.00 12.00

169 17600.00 11.10 26700.00 6.00 34400.00 0.00

170 # filter data

171 1 .9995 0.

172 2 .9995 20. 173 3 .9995 0.

174 # pressures

175 0.0000 -5.1500 -7.1500 1.0000 .5000

176- 0.0000 -. 3000 -. 3000 -. 3000 -. 3000

177 -. 1500 -. 1500 -. 3000 -. 3000 -1.v3480

178 -7.6000 - 10. 6000 .5000 0.0000 0.0000

179 0.0000 Q.0000

180 # temperatures

18t 70.0 70.0 70.0 70.0 70.0

182 70.0 70.0 70.0 70.0 70.0

183 70.0 70.0 '70.0 70.0 70.0

184 70.0 70.0 70.0 70.0 70.0

185 70.0 70.0

186 # fire scenario control specifications "iflow3*

187 1100. 100 2

188 0 0.0 0 0.0 0

189 # fire compartment initial conditions and noding

190 70.0 -0.30

191 16 9 18.74 1.517

192 14 21 3.000 1.581

1.66
TABLE XXI (CONT).,

193

194 #

195

196

197

i98

199 #

200

201

202

203

204

,205

206 #

207

208

'209

17 22 18.74 .4359

fuel type,"mass ,and burn area

0.0 0.0 0.0 0.0 0.0

0.0 30.0 0.0 0.0 0.0

0.0 0.0 0.0 0.0 0.0

0.0 7.0 0.0 0.0 0.0

fire compartment dimensions and

39.0 39.0 20.0 1.000 1 I I

0.0

0. 0

0.0

0.0

materials w 0.500

3.00

0.0

5.0

0.0

0.0 0.0

0.0 0.0

0.0 0.0

0.0 0.0

1.000 1 .500

radioactive source term Input (polystyrene)

1 0 0 0 0

1 2 1t 2

.2205

0 0

time step cards

.001 3.001

.01 .10.01

.05 999.05

0.5-1.0:

50.

167
this problem, the amount (mass)i _.of" kerosene precedes .the input value for the

amount of polystyrene.• The same format follows for the input of the respective

fuel burn areas.

The radioactive source term input for the release rates resulting from the

burning of the contaminated. polystyrene requires that NRAD(1) = 1. *This input

value for NRAD(1) indicates the radioactive release of particulates will be

estimated in the :contaminated combustible solid release subroutine. The assumption that the contamination is in the form of a powder requires input parameter

IFORM be assigned a value of 1. The combustibles material identifier (1) has

been selected to be 2--polystyrene is fuel type (combustibles identifier) 2.

The burning order (IBO) of the polystyreneis2,,,, and the total mass of powder

contaminate (QRAD 1) is 0.22 lbm (0.10 kg).

3. Sample Problem 2 Results.'

a. System Response. The sequence of events for the Sample Problem 2 calculation is given in Table XXII. The kerosene ignition initiates the accident

TABLE XXII

TRANSIENT EVENT SEQUENCE FOR SAMPLE PROBLEM 2

Event Time (s)

Kerosene ignites 2

Hot layer descends to centerline elevation of inflow boudaries -12

Hot layer descends "to centerline elevation of outflow boundary -190

-Contaminated polystyrene ignites -265

Transport of radioactive material initiated -265

Fire compartment exhaust filter begins to plug -325

Maximum system temperature (-1900 F) attained -806

Fire terminated -806.

End of calculation 1000

168
sequence 2 s into the simulation. The fire compartment (represented by nodes

9, 21, and 22 in the system model) rapidly pressurizes from its steady-state

operating value of -0.30 in. w.g. (-0.76 cm w.g.) to approximately 0.5 in. w.g.

(1.3 cm w.g.) because of the rapid Volumetric expansion of the gases within the

compartment caused by the fire. Figure 32 shows the fire compartment pressure

response for the entire transient. As a result of the pressure increase in the

compartment, a reduction in flow at the intakes (branches 16 and 17) and an

increase in flow at the compartment exhaust (branch 14) is calculated by FIRAC.

Volumetric and mass flow rate results for the fire compartment are presented in

Figs. 33 and 34, respectively.

Between 2 and -200 s, the hot layer gradually expands and descends toward

the outflow ventilator (Fig. 35). As the outflow ventilator begins to exhaust

the hot combustion products/gases composing the hot layer, the fire compartment

begins to depressurize. The volumetric and mass flows at the intakes to the

compartment are enhanced by the depressurization. The compartment exhaust flow

rate decreases because of the depressurization and the presence of the hot

(less dense) combustion gases at the outflow ventilator. The temperature history for the fire compartment is shown in Fig. 36.

The system is perturbed again as the kerosene fire terminates and the contaminated'polystyrene ignites via the sequential burning option. This Fig; 32

transition occurs between -250 and -275 s as shown in Figs. 37 and 38. The ignition of the polystyrene repressurizes the fire compartment to approximately

1.0 in. w.g. (2.5 cm w.g.). The flow rates to the compartment are affected by

the repressurization: enhanced exhaust flow (branch 14) and reduced flow at

the intakes (branches 16 and 17). As the polystyrene burns, the compartment

remains pressurized at approximately 0.9 in. w.g. (2.3 cm w.g.) and becomes

more concentrated with smoke particulates. Burning polystyrene releases a

significantly larger amount of smoke then does burning kerosene as shown in

Fig. 39. The introduction of smoke at a faster rate within the compartment

begins to deplete the amount of oxygen available to the fire (Fig. 40). The

polystyrene continues to burn until -806 s. At this time, all the combustible

materials within the fire compartment have been consumed, and the system begins

to recover to 'a new steady-state operating condition.

b. Material Transport. The combination of the smoke release rate of the

burning-polystyrene material and a fire compartment exhaust filter plugging

factor of 20.1/kg significantly influences the system response to the fire.

169
SAMPLE PROBLEM 2

TI ME (S)

Fig. 32.

Pressure response for nodes 9, 1.5, 21, and 22.

170
SAMPLE PROBLEM 2

TI ME (S)

Fig. 33.

Fire compartment volumetric flow rates (branches 14,16, and 17).

171
SAMPLE PROBLEM 2

Fig. 34.

Fire compartment mass flow rates (branches 14-, 16, and 17).

172
SAMPLE PROBLEM 2

400.0 50.0

TI ME (S)

Fig. 35.

Hot-layer height vs time.

173
SAMPLE PROBLEM 2

LEGEND

'NOE 9

oNODE 15

-NODE 21

=NODE 22

6

Lii

Lii

0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 800.0 900.0 1000

- TIME (S')

Fi g. 36.

Temperature response for nodes 9, 15, 21, and 22.

174
SAMPLE PROBLEM 2

V.

EU -

0

0w

0~

uii Vn

Ir-0

oz

0

-J0

9-)

0

c;

FUEL TYPE.7 -- KEROSENE

0.0 100.0 20 o.o -00.60 ,06o.o 56o.o 600.0 700.0

TIME (S)

Fig. 37.

Kerosene burning rate vs time.

800.0 900.0 1000.

175
SAMPLE- PROBLEM 2

in

0 I 0

c;

to

0.

0

0

in

-)

10 ,

hi

Uno.,

to

00

Z

Lii

DC4,

UJ0

La4

q07

b1o.

-o

z l'

I',

mo•

FUEL TYPE 2 -- POLYSIYRENE

U. £

0.0 100.0 200.0 300.0 ,00.0 500.0 600.0 700.0 30o.o 90oo 10oo

TIME (S)

Fig. 38.

Polystyrene. burning rateý vs time.

176
SAMPLE PROBLEM 2

0

z

W0

I,-

I--

z

l-.J

0

0

Vz)

0.0 -100.0 200.0 ''300.0 400.0 500.0 600.0 700.0

TIME; (S)

Fig. 39.

Fire compartment smoke concentration +vs time.

177
4~444

14

SAMPLE PROBLEM 2

44

(.

N

0

0

06--

LiJ

0.ýý

C,~4

0 0

40

0

0*

~ 0

N

0

444.,-!<. <•.. ':.• 4-4d.>! 4-! 

4 . 47

4 .

44 -~ 44

44 4444-4 4 4

4 4 4

4.4

4 44

4 -44

4444

444

444 44

44 4 ~44

4 <44444~

4 4- 4 4

4 4 4 .4. 4 144

44 44 4.

4 A -

44-44 4 44 4

444 444

-4 44

44-4

44,

.4

44 444 -4

44 .4

44-4

44 -44

.14

44 44 4

4 4 4444

-4 444

I 44 I II , I 

0.0 100.0 200.0 30'0,0 400.0 50.. 600.0. 700.0 . 800.0 9000 .0 1 000: o TIME S " i:=..

4 4-4 4 4 -4 444 #44

4 .~'Fig. 40.

4Fljr~e com'partment oygen-.concentration vs timne.

4 -44-4 ~44 -4 44

44/

4 4 4 4 4 4.

4 44 4 -444 4-4 -4

44 4 4 4 -4 -4

4 4 4 -44

~,44-.4~

4 4 4 -4

4. 444 4 4

4 -4 14

44 44

4444 44

444 .4 4 4

.44 44 4.4 '44

4 4 4 4

4 4 4 44 4-44 4

. : "'¢.i .•#;• 4: 4.;;7{ 4777 .:..:; ' ;: .::

: 4"4G•. :• -"•7.•7: 4 >•i••;•"•:-:

4 4 -4
.The system flow to and from the fire compartment is reduced gradually (after

.300 s) as the compartment exhaust filter (branch 14, filter no. 2). plugs with

the smoke particulate., As the filter plugs, the polystyrene burns at a constant

burning rate, thereby maintaining a constant fire compartment pressure. Even

though the intake flows to the compartment are being reduced, a.sufficient oxygen concentration level (>15%) is available to sustain a constant fuel burning

rate (Fig. 40). Figures 41 and 42. present the smoke mass flow rate and mass

accumulation on the compartment exhaust filter and at several locations near

the exit to the facility. The smoke particulate release rates indicate an increasing accumulation rate in branch 14. After -300 s, the flow rate in branch

14 decreases with.time,(Fig. 33); however, the smoke concentration in~the hot

layer (Fig..39) steadily increases. The net result is the mass flow rate profile in Fig. 41.

The release mechanism for radioactive material-is the burning of a contaminated combustible solid (polystyrene). Because the burning order (IBO) for the

polystryrene is 2 and the kerosene was assumed to be uncontaminated, radioactive

material is not transported through the system until the polystyrene has been

ignited. The radioactive particulate mass flow rate and mass accumulations for

the 20-pm particle size distribution are presented in Figs. 43 :and 44. .The

radioactive particulate results are similar to the smoke particulate' results

and can be explained similarly.

Following the termination of the fire (-806 s), the smoke and.radioactive.

particulate flow rate begins to decrease as the particulate concentrations in

the hot layer decrease and as the compartment exhaust flow decreases. The system gradually will establish new steady-state operating conditions based on the

consequences of the fire. By -1000 s, more than 1.21 Ibm (0.55 kg) pf,.smoke

particulate has. been deposited on the fire compartment exhaust filter. To the

system, the particulate mass on the filter represents an increase in resistance

for branch 14. The system will readjust and establish new steady-state conditions based on the increase in flow path resistance for branch 14.

C. Summary

Sample Problem 2 illustrated how FIRAC can be applied to a more complex

facility. Also implementation of the FIRIN sequential burning option, the

influence of the filter plugging factor option,,the release of radioactive

material by burning a contaminated conbustible solid, three internal boundary

179
SAMPLE PROBLEM 2 I-BRANCH 14I

IoBRANCH 34I

BR~AW-,:iLJ3

100.0 200.0 -300.0 400.0 00o:o

TIME (S)

Fig.i 41.

Smoke particulate mass 1flow-rates for branches-14, 34, 35, and-36.

180
-SAMPLE PROBLEM 2

ToOt"

'n

I.iz

O0

9-

V.

" 0.0 -100;0 : 200.0 .300.0. -4.00.0 500.0 ....600.0 700.0 8 00.0 - 900.0 1000

'"~ TI ME (S) -

F ig. 42.

Accumulated smoke particulate mass for branches 14, 34, 35, and, 36.

181
SAMPLE PROBLEM 2 T- BRANCH 14I o -BRANCH .34 I.BRANCH 35I

BRANCH 3

00

LLJ

LUJ

0>

ILL C1~4

F- co

C;

Fig. 43.

20--m radioactive particulate mass flow rates for branches 14, 34, 35, and 36.

182
SAMPLE PROBLEM 2 S LEGEND '

T = BRANCH 14

S=-BRANCH 34

* -BRANCH 35 0 - BRANCH:I. 36

1000

TI ME (S)

Fig. 44.

20-pm radioactive particulate mass for branches 14, 34, 35, and 36.

183
nodes representing the fire compartment, and the transport of 11 radioactive

particle sizes and smoke particulate were demonstrated. Sample Problem 2 also

indicates how complicated the interpretation of the calculated results can become when several user options are enabled. For this sample problem, the filter

plugging factor provedto be an important input variable. The system's response

to the fire would have been different if the filter plugging option had not been

used. If the user plans to make a best-estimate calculation, input variables

and code options that influence the results significantly should be recognized

and used with consideration.

ACKNOWLEDGMENT

This manual represents the work of many individuals over a period of several years. The principal structure of the code was developed by J. W. Bolstad.

The gas dynamics and material convection concepts were made by P. K. Tang. The

material depletion mechanisms were implemented by R. A. Martin. M. W. Burkett

was responsible for coupling the Pacific Northwest Laboratories' fire model with

the FIRAC computer code and performing sensitivity studies with it. ;F. R. Krause

contributed in the fire source simulation area. R. D. Foster's contribution was

assisting in, the development of heat transfer modules. R. W. Andrae assisted

with programming and debugging the gas dynamics used in the code. D. V..:Talbott

converted the code to the CRAY, VAX, and PC computers; he also developed- the

damper model used in the code.

184
APPENDIX A

GAS DYNAMICS SUMMARY

I. INTODUCTION

This discussion includes-a very brief summary of the gas dynamics used in..,

the code. The formulation of the equations is similar to those used in the

3 EXPAC. code,3 and a more detailed discussion of the theoretical and numerical"

formul'ation of the working equations is describ ed.there.

The l umped.-parameter method iisr:. the basitcformul ation. ,that describes -the

..system. . No spatial-distribution of. parameters is consider~ed-jn t~his approach,

but an effect of spatial-distribution .can b.e approximated. by noding. .Network

theory, using the lumped-parameter method, includes a number of system elements,

called branches, joined at certain points, called nodes. Ventilation system

components that, exhibit flow resistance and inertia, such as dampers, ducts,

valves, and. filters, and that :e&xhibitt flow potential ,.sUch asolýoSwers", are

located within the branches of the.system.

The connection points of branches are nodes for components that have finite

.,volumes, such as rooms, gloveboxes, and p.l~enums, and for boundaries where the

volume is practically infinite. Ther'ef'ore,- all in~ternal nodes possess: s..me. finite volume where fluid mass and. energy storage are accounted for.

II. MASS EQUATI.ON

The. contnuity equation (conservation: of mass) is applied at. each internal 1

node. The mass equation,-for such nodal pointsis

P= :+ i d t - " . k : s -.• (A-I)

k

where mk is the mass flow rate in branch k, and p is the density of the node.,

M is the user-specified mass source per unit time for the volume, and V is the 5

volume of the node. The convention used here is that positive mass flows represent flow into the ,node.

185
III. ENERGY EQUATION

The energy equation used in the code is

.2 .

dp R; CpT + + CT +E (A-2)

Tt CVT w k Cp I , spS 5]

v

The nodal pressure is p, and R, Cv and C represent-the gas constant, specific v p

heat at constant volume, and specific heat at constant pressure, respectively.

Tk and vk are the branch gas temperature and velocity. The temperature associated with mass add4i-tion is T and the energy addition is E A perfect gas law

has been used to obtain this expression.-

IV. MOMENTUM EQUATION

A momentum equation of incompressible form for a duct with constant area

is used.

;dinm* p•I f 1 m. ,+Igm

P1 2 P ~g Az

where i and A are the duct length and cross-section area, p is the average density in the branch, g is the acceleration of. gravity, and Az is the elevation

change across the branch. The values f and D represent the Moody f-riction factor and hydraulic diameter. For a branch with sudden area Change, the following

momentum equation is obtained:,

idm Ip \ m'ml + p--g AZ

- = i-j effA 2p .

186
where

I -i , and 2A 2A

f_ +f(A_

ef f (_20 (i) (ýA ) '2Dj

I represents the inertia effect of the flow path between nodal points i and j.

This includes the rooms as well as the duct. Keff is the total effective resistance coefficient; the minor losses, such as turning, entrance, and exit are

represented by the K's.

V. CHOKING OF COMPRESSIBLE FLOW WITH DISSIPATION

The steady-state flow rate in incompressible flow is determined by the

pressure drop. In compressible flow, the flow rate will reach a maximum value

regardless of how much the downstream pressure is decreased if the uistream

pressure is constant. This phenomenon is called choking.

We treat the quasi-steady compressible flo&v inside a constant area duct,

where the usual one-dimensional approximation is assumed. Heat transfer is not

taken into account, but friction is. For a duct with friction loss, the Mach

number at the duct entrance (location 1) can reach a maximum, and the value is

less than 1. This upstream critical Mach number M1 is uniquely related to

the friction loss, so that

m=pvlA =AM, yplpl

This is the maximum allowable mass flow rate that a particular branch can supply

for a given condition at 1. This flow rate will be compared with that from the

momentum equation. Choked flow is used if the former is smaller.

187
An implicit numerical scheme is used to solve for the pressure and density

corrections at each node. The iterative process continues until both the pressure and density corrections, sp and 6e, approach zero and the system is balanced. Additional detail can be found in Ref. 6.

The result of the gas dynamic transient provides the driving force for material convection and also interacts with the material source and sink. These

effects are presented in Appendix C.

188
APPENDIX B

DUCT HEAT TRANSFER THEORY AND METHODS

I. INTRODUCTION

The purpose of this Appendix is to give the details of the heat transfer

correlations and methods used in the duct heat transfer module. This module

evaluates the gas temperature (T t) leaving any section of the duct if the gas out

velocity and inlet temperature (Tin) are known. This temperature is the temperature (Tk) needed to evaluate the energy equation in the gas dynamics module

[Eq. (A-2)]. In .addition, this module.describes how the combustion gas in the

system heats up or cools down as it flows through the ducts in the ventilating

system. These temperatures and the physical geometry are shown on Fig. B-i.

The user may divide the duct into one or more sections by breaking the duct

into a number of branches. Each section of the duct (or branch) is characterized by an.average gas temperature (T ) for that branch. This average temper- 9

ature is simply the mean of its inlet and outlet temperatures. The outlet temperature is a function of the inlet temperature and the amount of energy the gas

loses as'it passes through this section of the duct. This energy loss is'a sum

of two terms, Qr and Qc" Qr is the net amount of energy loss .because of radiation from the gas to the duct wall. Qc is the energy lossresulting from forced

convection heat transfer from the gas to the duct wall.

It will be shown that the gas temperature is a function of the energy loss,

but furthermore, the energy loss is a function of the gas temperature and wall

temperature (Ti), which itself is a function of the energy loss. Because the

,heat-transfer processes are nonlinear in temperature, solving the equations requires that a set of nonlinear coupled differential and algebraic equations be

solved. This set of equations is solved using an iterative method.

189
ONE SECTION- 4

OF DUCT

WALL SECTION

OF DUCT

I 0 T 0 I Do~

Fig. B-I.

Definition of temperatures and physical geometry

used in the duct heat transfer module.

190
II. MODEL DESCRIPTION

A. Energy;Equation for Duct,

We consider a section of duct with a known inlet temperature and mass flow

rate. We wish to determine the outlet temperature to solve the energy balance

for the downstream room node. The energy balance across. this section of *duct

gives

Qi

u mC

P

where Qi is the net amount of energy transferred from the gas to the duct

wall, m is the mass flow rate through the duct, and C is the gas specific

heat. The net amount of energy transferred is the sum of convection and radiation heat transfer processes from the flowing gas to the duct inside wall. The

solution of Eq. (B-i) for the duct outlet temperature is the net result of the

duct heat transfer model. The quantites mC and T. are known, and thus the

p i

evaluation of the net energy transfer Qi will allow the solution of the equation.

B. Heat Transfer from Combustion Gas to Inside Duct Walls

The net energy transfer between the combustion gas and duct walls may be

broken into two components,

Qi.= Qci + Qri '(B-2)

where Qci is the net amount of energy transferred from the gas to the duct

inside surface because of forced-convection heat transfer and Qri is the net

amount of energy transferred from the gas to the duct wall because of radiation

heat transfer. Each of these quantities may be determined independently. They

are evaluated using standard correlations based on experimental data. These

correlations are described in the following sections.

191
1. Forced-Convection Heat Transfer (Inside Duct). In general, the

forced-convection heat transfer may be calculated from an equation of the form

Qci= h A (Tg Ti) (B-3)

where A is the wall (heat transfer) surface area, T is the bulk gas temperag

ture, Ti is the inside duct wall temperature, and h is the heat transfer coefficient. There are many available correlations for h. The best correlation

for a particular application depends on many factors. Many correlations for

forced convection are summarized in Ref. 8. A particularly suitable correlation

for cooling of gases is

h= .023 (Re)" 8 (Pr) 3 hD • (B-4)

where Re is the Reynolds number, Pr is the Prandtl number, k is the gas thermal

conductivity, and D is the duct equivalent diameter. 9 This is the correlation

used in the model, and it applies when the Prandtl number is between 0.7 and

120, the Reynolds number is in the range 10 000--120 000, and the length of the

duct is at least 60 equivalent diameters. 4 0 For small temperature differences

[(T -Ti) < 1000 F] the physical properties are evaluated at the gas (bulk) temperature. For larger temperature differences, the properties are evaluated at

the average of the two temperatures. Thus, the heat transfer coefficient is a

function of the duct geometry, fluid properties, gas mass flow rate, and the gas

and duct wall temperatures. For a fixed geometry, Eq. (B-3) has the functional

dependence

Q ci =f(Tg, Ti) .,(B-75

The gas temperature is known, but the wall temperature must be described by an

additional model to evaluate the forced-convection heat transfer.

192
2. Radiation Heat Transfer (Inside Duct). For the case of airflow in a

duct, the emissivity and absorptivity go to zero, and radiation heat transfer

is unimportant. HottelI 0 states that-gases with symnetric molecules (for example, hydrogen, oxygen, and nitrogen) do not have emissivities of sufficient

magnitude to cause radiation heat transfer to-be an important effect.

On the other hand, if the gas contains any heterpolar constituents (for

example CO2 , H2 0, SO2 , and hydrocarbons), radiation heat transfer from the gas

to the structure may become significant. It becomes even more significant if

the gas contains luminous flames, glowing char particles, soot, or black particles. In this case, the emissivity and absorptivity are complex functions of

their temperature, partial pressure, superimposed radiation, and system geometry.

A complete treatment of radiation heat transfer that includes these complications is beyond the scope of this project. Furthermore, the basic code

structure into which this model is intended to be integrated does not account

for the various possible gas constituents. Therefore, we have chosen to include a simple gas radiation model that does not include many of the abovementioned complexities but still includes many of the salient features of the

physical process as. it is germane to this problem.

This model is intended to be applied in ducts away from the fire source.

,Therefore, we may assume that luminous flames do not exist in the region. This

simplifies matters somewhat because the radiation from luminous flames depends

on the concentration of particles, flame size and shape, and geometric factors.

The second simplification results from the duct geometry. For this geometry,

essentially all of the radiation emitted by the gas will be intercepted by the

duct walls. Furthermore, we may assume that the duct length is much larger

than its diameter, and for this case, the geometric considerations are greatly

simplified. 1 Finally, we may assume that the gas pressure is near atmospheric

pressure because variations from this pressure in a typical ventilation system

are small. This fact greatly simplifies the use and interpretation of experimental data, which are generally available at 1 atm.

193
Taking into account the above assumptions, the net radiation energy transfer from a nonluminous gas to its surroundings (that is, the duct wall) may be

found from

Qri = Aci(1g - IS) . (B-6)

In this equation, ci is the emissivity of the surface, Ig is an intensity factor that is a function of the gas composition and temperature, and Is is

an intensity factor that is a function of the gas composition and wall temperature.

The intensity factors have been tabulated for a variety of individual

1,4

gases and compositions of gases. To evaluate the intensity factors appearing in Eq. (B-6), we have selected a typical gas consisting of 0.8 mole .of water vapor per mole of carbon dioxide. A fit of these data for typical duct

geometries gives the following equation for both the intensity factors (that

is, Ig and I s).

I(T) 190 ((T +;460) 5 (B7) 760 /

where T is either the gas temperature or wall temperature and I(T) is in units

2 of Btu/h-ft . Using Eq. (B-7) in Eq. (B-6), we have an expression for the

net radiation energy transfer between the combustion gas and the duct wall.

It takes the form

Qri - f(Tg4 ' Tin) " (B-8)

Using Eqs. (B-5) and (B-8) in Eq. (B-2), we have an expression for the total

net energy transfer between the combustion gas and duct walls. It is of the

form

194
f(TT T 4 Ti 4 ) (B-9)

Therefore, we see that the total energy transfer is a function of the wall temperature as well as the gas temperature. Therefore, we cannot evaluate this

term without a model for the duct wall temperature. This model is -discussed

below.

C. Heat Conduction Through the Duct Wall

The model for heat conduction through the duct wall is based on standard

12 models such as Patankar and will only be summarized here. The direction

of heat flow is perpendicular to the direction of tile gas flow, and axial conduction (along the wall) is neglected. The method may be understood by considering the quantities shown on Fig. B-2. This figure is an expanded view of the

wall section of duct shown on Fig. B-I. On the inside of the wall. there is an

energy input, Qi, given by Eq. (B-9); similarly, on the outside we have an

energy loss, Qo" Yet the origin of the coordinate system, be at the inside

of the structure with positive direction out. We will calculate the temperature at specified points within the wall, xj with j = 1, N. The number of

nodal points could be only 1, in which case the temperature is the average duct

wall temperature. For N = 2, the model will give the inside and outside wall

temperatures. For N > 2, the model will give the wall temperatures as well as

.temperatures at interior nodes. (The nodes are assumed to be equally spaced.)

An energy balance at each node gives the following set of coupled differential

equations.

d (pCT) 1 T Cl T2 + Qi

d ' ' ( - O

-t (PC pwTj aj Tj-1 + b j j T j+1

d -f (oC p pwT N) a aN N T N-1 + b N T N + Qo

195
INSIDE OF DUCT

Fig. B-2.

Definition of geometry and noding for one-dimensional

heat conduction through the duct wall.
where p is the density of the wall, C is the constant .pressure specific heat

pw I '. I I"

of the wall, and a bj• and c. are constants. To solve the set of equations,

the derivative terms are put into a finite difference form:

dTj . - T

dt At

Here Tn signifies the temperature at node j and time tn. Using this expression in Eq. (B-10) reduces the set of differential equations to the following

set of algebraic equations.

d1 e1 Tln+I Qi

c2 d 2 e 2 0 0

ci di T n+1 bi +

0 (B-1I)

0

c N dN T n+1 bN Qo

The constants in the equations are functions of the wall properties p, Cpw,

and k w the geometry Ax; the time-step size At; and the nodal temperatures

at the previous (known) time. These constants are defined as

k

1 Aw

Ax

197
pC AX k

d At AX ,

k,

SAX w and

epCwAX. ~

b T n

1 At 1

The set of equations.in Eq. (B-11) may be written in the compact mat.rix form

E Tn+l B +Q

The E matrix is tridiagonal as shown in Eq. (B-11). It is easily inverted by

the tridiagonal-matrix algorithm detailed in Ref. 12 with the result

Tn+_ E-1B + E-1Q , (B-12)

where E is the inverse of matrix E. Thus, if the energy deposition on both

sides of. the duct wall is known (that is, Qi and Q ), all temperatures at an

advanced time, tn+1, can be obtained from those at a previous time tn.

Eq. (B-9) gives an expression for Qi; however, Eq. (B-12) shows that we

still need to evaluate Q before we can solve for the temperatures. Furthermore, Eq. (B-9) shows that we must solve Eq. (B-12) for the temperatures before

the energy source: [Eq. (B-9)] can be evaluated.

D. Heat Transfer from Outside Duct Walls to the Atmosphere

The net energy transfer between the duct outside surface and the

surroundings may be broken into two components:

Qo Qco +' Q ro ' (B-713)

198
where Q'o is the net amount of energy transferred fromthe duct Wall because.

of natural convectionh.heat transfer and Qro is the net amount of energy transferred from the outside duct wall to the atmosphere resulting from radiation

heat transfer. Each of these quantities may"be'determined independently. The

correlations used to evaluate these quantities are described in the following

sections.

1. Natural Convection Heat Transfer (Outside Duct). Experimental data

show' 3 that natural convection heat transfer from horizontal ducts may be correlated well with the functional form

Qco = h A (TN - To) 1 (B-14)

where h is a heat-transfer coefficient based on experimental data, A is the

duct outside heat-transfer area, TN is the duct outside wall temperature,

and T is the air temperature. The correlation used for h is divided into

two distinct regimes.

h = 0.53 k (GrPr)" 2 5

hl= 0.094249 (GrPr)/3

GrPr < 109 , and

(B-15)

9 GrPr> 10

Here k is the air thermal conductivity, D is the duct equivalent diameter, Gr

is the Grashof number, and Pr is the Prandtl number. All thermodynamic quantities are evaluated at the film temperature (average of wall and air temperatures).

2. Radiation Heat Transfer (Outside Duct). The net energy interchange

between the outside duct walls and the environment may be approximated by the - 141 formula for the energy transfer between a diffuse-gray surface and a black

surface:

Qro =aA (eT N 4 -aT 04 ) (B-16)

199
Here a is the Stephan-Boltzman constant, A is the duct outside heat-transfer

area, c is the emissivity of the outside duct.wall evaluated at temperature

TN, and a is the absorptivity of the duct wall evaluated at temperature TO.

Using Eqs. (B-14) through (B-16) in Eq. (B-13) gives the final expression

for the total net energy transfer between the outside duct wall and the environment. It is of the form

Q0 = f (TN4(B-I) ) 

III. THE SOLUTION METHOD FOR THE EQUATIONS

The net result of the duct heat-transfer model is to predict the gas

temperature (Tout) leaving any section of duct if the gas properties and

inlet temperature (Tin) are known. The outlet temperature is given by the

equation

Qi

T =Tin -T (B-18)

m Cp

However, as shown above, the net energy transferred from the gas (Qi) is

dependent on the duct wall temperatures. In fact, the quantity Q. is the

partial solution of the following set of four equations in four unknowns.

Q. e f (Tg, Ti, T g, T. 4 )

Q0 f (T )4

Ti f (Qi' Q TN) ,and

TN = f (QiQoTi) T

200
.The equations are nonlinear, and a direct solution is not possible. .The heattransfer module solves these four equations using an iterative method. To

solve these equations, we define the tilde (temporary) quantities. These are

the best (latest) estimates of the exact Solution of the coupled equations.

For the first iteration in a time step, these quantities are estimated to be

the solution of the equations at the previous time step. The tilde quantities

are calculated in the following order.

Qo =f JT"T) ..

Q f(TgT~

Qi =f(T T)

Ti = f (Qo0 Qi) , and

Tn =f Wo Qi)

where the functional form is defined by the above models. The duct outlet

temperature then is evaluated:

Qi

T -T out in

p

This duct outlet temperature is used as the room inlet temperature in the gas

dynamics energy equation for a downstream room node. A solution of the room

energy equations produces new'duct gas temperatures (T and T. ), and the

g in

process is repeated until convergence is achieved in the gas dynamics iteration.

201
IV. SUMMARY

'The duct heat transfer module evaluates the gas temperature leaving any

duct for given, duct inlet temperatures and gas properties. Four distinct heattransfer regimes are modeled. These are forced convection and radiation heat

transfer between the combustion products and the inside duct wall and natural

convection and radiation heat transfer between the outside duct wall' and the

environment. The total amount of energy removed from the gas as it flows

through the duct is shown to be the solution of a set of four coupled nonlinear

algebraic equations. These equations are solved using an iterative procedure.

The primary output from this module is the downstream (outlet) duct temperature. A secondary quantity calculated is the duct wall temperatures. The inputs necessary to execute the module include the following.

e Duct equivalent diameter

* Duct heat transfer area

• Duct outside walil emissivity

• Duct outside wall absorptivity

e Duct wall thermal conductivity

e Duct wall density

* Duct wall specific heat

e Number of heat transfer nodes in, duct wall

* Duct wall thickness

* Duct wall temperatures at previous time step

* Environmental temperature outside duct

* Upstream (duct inlet) gas-temperature

a Duct average gas temperature

0 Duct average gasrvelocity

* Duct average gas density

* Time step size

202
APPENDIX C

MATERIAL TRANSPORT THEORY

I. INTRODUCTION

The purpose of the material transport algorithms in the code is to provide

an estimate of the aerosol or gas transport within a nuclear fuel cycle facility. Ultimately, we would like to predict the quantity and physical and chemical

characteristics of hazardous material that may be released from the facility as

a result of an explosion. 'The transport can occur through rooms, cells, canyons, corridors, gloveboxes, and ductwork installed within the facility. The

entire flow pathway forms, in many cases, a complex interconnected network system.,. Using'the computer code, material concentrations and material mass flow

rates can be calculated at any location in the network, including the supply and

exhaust of the network system. Most importantly, the code will perform the

transport calculations as a function of time for an arbitrary user-specified

explosive transient. There is no need to assume steady flow as required in some

material transport codes, but-we can use the code..to determine material transport under steady flow conditions if. desired.

A generalized treatment of material transport under accident conditions

could become very complex. Several different types of.-materials could be transported. More than one phase also-could be involved including solids, liquids,

and gases with phase transitions. Chemical reactions, could occur during transport and lead to the formation of new species. Further, there will be a size

distribution function for each type of material that varies with time and position, depending on the relative importance of effects such as homogeneous nucleation, coagulation (material interaction), diffusion (both by Brownian motion

and by turbulence), and gravitational sedimentation. We know of no computer

code that can handle transient-flow-induced material transport in a network sys-" J

tem subject to the possibility of all of these complications. The transport

portion of this code does not include this level of generality either. This

initial material transport capability consists of the following.

0 Gas dynamics decoupled from material transport

* Homogeneous mixture and dynamic equilibrium

203
. Material transport- provided for an arbitrary -number of particulate and

gaseous species

9 No material interaction during transport

* Material deposition based on gravitational settling using relationships

from the literature

e Turbulent and Brownian diffusion, and thermophoretic effects are neglected

a Phase change, chemical reaction, and electrical migration not allowed

* Material entrainment can be specified arbitrarily using tabular inputs

or calculated using semi-empirical relationships based on wind tunnel

data

The code is organized into modules so that improved versions can be incorporated

easily. This is discussed in the following section followed by information on

material characteristics that may be useful to the analyst. The sections that

follow are detailed descriptions of the material transport modules found within

this version of the code..

II. MODULAR STRUCTURE

Movement or transport oft material by a flowing fluid involves several

basic mechanisms. The primary mechanism for movement is the flow of the fluid

itself. This process will carry along material and is referred to as material

convection.. This mechanism isthelprimary material transport process. The

other mechanisms involve physical models that could be upgraded as the state of

the art improves. The basic mechanisms that we will consider in a fire-induced

flow environment are

* transport initiation,

9 convective transport,

e transport interaction, and

* transport depletion.'

The material transport capability uses all of the basic mechanisms except transport interaction. In addition, the transport depletion module is restricted to

gravitational settling and filtration.

.204
11T.'"MATERIAL CHARACTERISTICS

In .applying the. material transport capability, the usermust "identify the

type.(aerosol or gas),, quanti~ty, and location of material at r.isk. If the material is a solid or liquid aerosol,, a characteristic size and density must be

specified. For example, if the. user is concerned primarily with the transport

of aerosols in the size range.of D < 12 um and with densities of.O.5 < .

3 p _

< 12 g/cm , he could run the-code for some assumed cases- of (D ,.Pp) to

p *p determine entrainment or deposition' sensitivity.

The user may wish to characterize a nonideal aerosol contaminant with

approximate or idealized values of (D0, pp). We advise caution in this because

p p. 'there are'many different ways to characterize the diameter of aerosols of irregular shape and nonuniform density. For example, diameters representing a mean

value relative to total count,.surface area, volume, weight, or terminal settlitig velocity may betestimated based on frequencyof occurrence data.

For the case of aerosol transport along fuel cycle facil-ity pathways, we

are interested in changes in aerosol concentration resulting from entrainment,

dilution, deposition, and filtration. Entrai.nment, deposition,'and filtration

all depend on the quasi-steady aerodynamic drag characteristics-of the-aerosol..

Unless the aerosol is very small (less than 0.5 urm), the probability that a

..spherical particle or droplet will deposit depends on themagnitude of its terminal settling"velocity'u5

•us= ppDCgI18u (Cl)

where

.p actual density,

D =.diameter,

p

C = Cunningham slip *factor,

g = gravitational acceleration, and

, = air dynamic viscosity.

205
Most aerosols (spherical or not) having the same settling velocity-will be distributed throughout a ventilation system network in a similar manner. The recommended deposition parameter is the aerodynamic diameter or Stokes diameter.

(1) Aerodynamic diameter, Da, is the diameter of a sphere of unit density

having the same terminal speed as the contaminant.

(2) Stokes diameter, Ds, is the diameter of a sphere with the same bulk

density and terminal speed as the contaminant.

These diameters are related by the .equation

us p D 2 C g/18P = p Da 2CCg/18- (c•2)

where Cs and Ca are the slip factors associated with Ds and, Das respectively,

and p0 is unit density. For the contaminant of interest, D or Da may be measured directly using such aerodynamic classification devices as impactors, centrifuges, sedimentometers, or air elutriators. These devices are suitable for

measuring the size of irregularly shaped particles. An aerodynamic diameter

measurement should be based on activity if possible. Otherwise, we recommend

using Da based on mass measurements.

If count frequency data (for example, based on projected area diameter for

irregular shaped particles) are available for the contaminant, it must be converted to aerodynamic diameter. Such data should be plotted on log-probability

paper and fit with a straight line. If this straight-line fit to the data is

acceptable, the size distribution is approximately log-normally distributed and

may be described completely by two parameters, geometric count median diameter,

Dgc, and geometric standard deviation, ag* Most fine particle systems formed

by comminution of a bulk material or grown by accretion have log-normal size

distributions; therefore, this assumption is recommended.

Thus, the user can obtain D and a from log-normally distributed

gc g 15

count frequency data. Now the set of Hatch-Choate transformation equations

apply. These equations relate Dgc and a to a number of other median and.

mean diameters that may be important depending on how the toxic substance or

"activity" is related to the physical properties of the particle. For example,

the activity may be proportional to the total number, total surface area, or

206
total mass'of the particles. We choose to work on a mass basis. The user may

calculate the geometric mass median diameter Dgm, the volume mean diameter

Dv, and the weight mean diameter Dw from

log D = log gc + 6.908 log 2 ag

log Dv = log Dgc + 3.454 log 2 ag , and (C-3)

log D = log D + 8.023 og2 a ,

w gc g

where the logarithms are calculated using base 10. The median diameters:referenced above divide the count-based and mass-based size distributions in half.

For example, half of the mass of the sample lies above Dgm and half below. A

mean diameter is the diameter of a hypothetical particle that is intended to

represent the total number of particles in the sample.

In the absence of specific information on the aerodynamic properties of the

aerosol of interest, Stockham15 recommends using D0 as an approximation to aerow

dynamic size. An alternative is to convert Dv to an aerodynamic diameter. (If

we assume the material density to be uniform, independent of size, and known,

the mass of the particle with size D is a mean mass.) To do this, use

v

D 0=p oc/K 1/2D (C-4) a = 6/n pp/ 0 a 3/K r12D v (,'4

where

a3 = volume shape factor, and

K = resistance shape factor.

r

Values of •3' K are listed in Mercer, where this calculation is discussed. 16

31 r

We also advise caution in estimating aerosol density. The aerosol produced

by accident conditionsmay consist of flocculi and agglomerates with actual densities well below the theoretical density of the pure parent materials. The

207
floc densities may be as much as an order of magnitude less than the normal density. Pertinent information concerning fuel grade powder size and density is

given in Refs. 17 and 18, and useful information concerning drop sizes and densities is given in Ref. 17.

IV. TRANSPORT INITIATION

The code provides the analyst with two options for transport initiation:

(1) user specification of mass injection rate vs time and (2) calculated aerodynamic entrainment. These options are quite different. They require different

levels of effort and judgment from the analyst. In this section, we will provide background to help the user supply numbers for source term initiation using

option (I). We will describe the procedure and equations used with option (2)

in detail. The primary cause of initiation is assumed to be transient flow induced by an accident. Two examples illustrating the use of option (1) will be

discussed first.

As a first example, consider a decomissioned fuel reprocessing facility

with contaminated enclosures. The analyst can estimate the preaccident aerosol

concentrations in these areas using the resuspension factor concept. The resuspension factor K was used extensively to quantify airborne contamination levels

in operational fuel cycle facilities. By definition,

K = aerosol concentration (g/m3) 1/m

surface loading (g/m )

Sutter19 has tabulated ranges of K that were compiled from numerous references.

The tables include values of K derived from measurements of airborne contamination resulting from numerous and varied cases of outdoor wind stresses and indoor mechanical stresses. Sutter's summary tables are useful for obtaining

bracketing or bounding values of K. With assumed or measured values of K and

surface loading, the user can calculate the airborne material concentration subject to transport. Based on the enclosure volume, a quantity or mass of contaminant subject to transport can be calculated from the concentration. This

mass can be injected using the user-specified option at the system node representing the enclosure of interest. Mass injection rate must be specified by

the analyst.

208
Healy?0 reviewed many measurements and applications of this simplistic

resuspension factor concept. Several of its limitations are noteworthy. First,:

measured values of K range over 11 orders of magnitude. For benign conditions

where K is most reliable, the uncertainty is at-least 2 orders of magnitude.

Further, K fails to account for particle, surface, or local flow characteristics

except as they existed during a particular measurement., Thus,' werecommend us-

*ing the resuspension factor only for estimating preaccident.airborne mass subject to transport as suggested by this example.

As a second example, consider a mixed-oxide fuel fabrication facility in

which bulk MOX powder is being protected. The user may elect to model this

facility and run the code for a transient without.:mater~ial transport. This

preliminary run would, supply an estimate of system flow rates and pressure drops

.during the accident. Some controlled areas may be subjected to abnormally high

air velocities that could lead to entrainment because of aerodynamic stress. A

knowledge of the air velocity time history will'be useful to estimate the quantity of material made airborne.

We will.summarize briefly three methods that can be used to estimate aerodynamic entrainment of aerosol material. Sutter' 9 has reviewed:and compiled

data from numerous papers under the heading "aerodynamic entrainment."' This

paper is a good source of reference information. The analysts' objective here

should be. to estimate a quantity of material made airborne during the first part

of or during the-entire tornado transient. This quantity must be converted to

a mass injection rate for input to the code as in the first example.

The first method for estimating the quantity of material made airborne by

aerodynamic entrainment is to apply the "per cent airborne" and "resuspension

flux" data measured by Mishima and Schwendiman.1 8 F'or -example, they measured

entrainment of uranium dioxide powder and uranium nitrate solution at different

air velocities. The application of these data will require engineering judgement.

A second method for estimating entrainment is to use the results developed

by Singer et al. 2 1 ' 22 to estimate coal dust entrainment. These results are

19 discussed by Sutter as well. Finally, the analyst may use the resuspension

rate concept introduced by Sehmel and Lloyd. 2 3 Resuspension rate is defined

as fraction of initial mass resuspended per second:

209
S -GAt'A

where S = resuspension rate, fraction/s;

A =mass su.spended and flowing horizontally

through a given cross-sectional area, g;

G = ground source mass, g; and

At = duration of sampling, s.

Measurements of S obtained during a number of atmospheric field tests are tabulated in Sutter's paper.

The procedure and equations used with option (2), calculated aerodynamic

entrainment of dry powder from thick beds, will be discussed in detail. This

technique is modeled in the code. It has the advantage of calculating entrainment automatically for the user. As with the three methods discussed in the

second example above, our objective is to provide the material convection module

with an estimate of the quantity of particulate material that can be entrained

from a contaminated surface as a result of accident-induced transient flow conditions. However, the previous three methods are not suitable for use in the

code because they are based on steady-state measurements for specific conditions. Except.for Singer.'s work with coal dust,21 they fail to couple unsteady flow (changing velocity) conditions to the amount of material entrained.

In addition tolocal flow characteristics, the previous methods fail to account

for material or surface characteristics in a systematic way. Thus, the resuspension factor, resuspension rate, and per cent airborne would have to be measured for innumerable cases to encompass accident conditions.

The analytical method used in the code for calculating aerodynamic entrainment was proposed and illustrated in a fuel cycle facility application in

Ref. 5. To estimate the quantity of material entrained, this method considers

the following questions. (1) When does the surface material begin to 'move?

(2) What criterion determines when material will be suspended? (3) How much

material becomes suspended? A valid answer to (1) implies that-particle, surface, and flow characteristics have'been taken into account. Some account also

must be made for the forces acting, namely, aerodynamic, interparticle (cohesion), and surface to particle (adhesion) forces. This procedure is similar to

210
the approach taken by Travis,24 who developed a computer model to preIdict reentrainment and redistribution of soil contaminants as a result of eolian effects.

The first question we must answer is: When does material begin to move

Before particle motion can occur, a threshold air speed must be equalled or exceeded so that the aerodynamic forces will be sufficient to overcome restraining

forces. To relate threshold air speed to surface effects, we introduce the

friction speed

: u ,k = ./. . , ( C -5 )

where - = mean shear stress at the surface, and

p = fluid density.

Experimental measurements of threshold friction speed, u*t, obtained at the

onset of material movement are available for a wide range of material sizes and

densities.

These measurements are fitted25 to the following semi-empirical equations.

A = (0.108 + 0.0323/B- 0.00173/B2 ) (C-6a)

x (1 0.055/p gD2 ) + ppg 1 12

where A = u*t/ (Pp - p)gD pp 112

B = u tDplv,

D = average particle diameter,.

p

pp = particle density,

g = gravitational acceleration, and

v = PI/p = fluid kinematic viscosity.

211
Equation (C-6a) holds for 0.22 < B < 10. The variable A is the threshold

coefficient. The variable B is the particle friction Reynolds number.

For the range B < 0.22 Eq. (C-6b) applies:

A = 0.266(1 + 0.055/ppgD)21/ 2 . (C-6b)

x (1 + 2.123B)- 11 2

Equations (C-6) collapse the threshold friction speed data in the appropriate

range of B onto a single curve with D and Pp as parameters. Given a particular aerosol size and density we can calculate u*t from Eqs. (C-6). An iterative technique is used to solve for u*t in Eqs. (C-6) because'this variable

appears implicitly on both sides of the equations. The value of v was assumed

to be constant at v = 0.1454 cm2/s, corresponding to standard atmospheric conditions.

In u*t we have a measure of when particle motion will occur and, therefore, when entrainment is possible. Under given flow and surface conditions, a

value of the friction velocity exceeding the threshold friction velocity can

produce entrainment. That is, entrainment can occur only when u, > u*t. We

may relate u, to the corresponding velocity at the turbulent boundary layer

edge using one of the following two equations. For a smooth surface with a laminar sublayer, 5

u(y)/u, = (1/0.41) In (yu,/v) + 5.0 . (C-7)

For a rough surface with no laminar sublayer, 2 6

u(y)/u, = (1/k) ln (yly0 ) , (C-8)

212
where y = distance from surface,

k = 0.4 = Von Karman constant,

Yo = R/30 = roughness length, and

R = average surface roughness height,

and where the velocity u(y) is calculated by the gas dynamics module of the

code. For a duct with fully developed turbulent airflow conditions, the centerline velocity or velocity at the boundary layer edge may be 25 times higher than

the average or bulk velocity. This version of the code uses Eq. (C-8) for a

rough surface with an assumed boundary layer thickness of y = 10 cm and a roughness length of y0 = 0.0104 cm (a moderately rough surface). Our use of Eq. (C-8)

will lead to higher values of u, for the same values of u(y) and y than Eq. (C-7).

Because entrainment is known to depend on the difference (u, - u*t), our choice

of Eq. (C-8) will lead to conservative estimates of entrained material.

The next question is: What determines whether particles go into suspension That is, of all the particles, how do we divide those that could become

airborne from those that remain close to the surface Iversen et al. 2 7 have

shown that, for particles smaller than 52 pm, suspension occurs as soon as the

threshold speed is reached. The criterion assumed here was that suspension will

occur for those particles for which u su. = 1 and u, > u~t, where us is the particle fall or terminal speed. The friction speed u, is of the same order of

magnitude as the vertical component of turbulence in a boundary layer. Values

of D < 50 pm for suspension are in agreement with measurements using soils. 2 4

P

We have assumed that all of the particles are subject to suspension.

How much material becomes suspended Travis 2 4 has suggested the following expression for qv, the mass of particles per unit area per unit time-that

go into suspension:

v= h (Cvl/utch) (u,/U~t)PI 3 - 1 (C-g)

213
where P..= mass percentage of suspendable particles, and

Cs, Ch. empirical constants (2 x. 10 and 10C6 respectively).

In Eq. (C-9), qh is the mass of material moving horiz6ntally• through a''vertical plane perpendicular to the surface per unit.width per unit time and may

be determined from2 4

= 2.61(p./g)(u, + u*t)Z(u. U*t) - . (C-10)

The calculated aerodynamic entrainmrent'in the material transport module is

a model that uses Eqs. (C-6) through (C-40). The steps can be summarized as

follows. At a given time, the gas dynamics module of the codet'calculates the

velocity u(y) for every Volume with material .subject to aerodynamic entrainment.

This value of u(y) and the turbulent boundary layer velocity profile [Eq. (C-8)]

are Used to compute a surface friction veloCity u,. A characteristic Value of

threshold friction velocity u~t for the input material --characteristics is obtained from Eqs. (C-6). If u,< u no entrainment occurs. [See Eq. (C-10).]

If u, > u*t, then the semi-empirical entrainment Eqs. (C-9) and (C-10) are used

to estimate the vertical flux of suspendable material qv. Knowing'-q and the

v v

floor area over which the contaminant is uniformly distributed A, we c-an compute the source term

Mp= qvA. (C-Il)

which has the units kilograms per second. As a source term, Eq. (C-11).

represents a-positive contribution to'the."M."' term on the right-hand side of

p

Eq. C-29. The floor area A is assumed to be flat and free of obstacles or

protuberances.

The question of how heavily a surface must be loaded before equations like

Eqs. (C-6), (C-9), and (C-10) are applicable is debatable. For the realistic

types-of loadings such as we expect to find in many locations of. a fuel cycle

214
facility,. the empirical constant in Eq., (C-1O) may not be satisfactory because

it was.obtained for relatively thick.powder beds. Furthermore, the empirical

coefficients in Eq.. (C-9) are':suspect.because;they were obtained from experiments with soil particles.

We believe-the recent experimental and theoretical work underlying

Eqs. (C-6) and (C-10) is the best available. 2 5 ' 2 7' 28 Thus, the basis for

predicting u~t u'sing Eq. (C-6) is sound; however, theýdata base to which

Eq. (C-6) was fit is sparse for small, heavy particles. In principle,-these

uncertainties could be checked and reduced with appropriate experimentation.

V. CONVECTIVE TRANSPORT

A. Assumptions

The usual mathematical formulation for the motion of a multiphase, multicomponent material system is based on the concept of continuum mechanics with

29

some pertinent qualifications. We can obtain a set of partial differential

equations for some macroscopic parameters.with a few phenomenological descriptions of the stress, heat flux, and diffusion, plus other formulations for the

physical andchemical interactions among phases andecomponents and with the

boundary. Some of the relationships are either incomplete or not yet known.

Depending on the range of interest, an extensive simplification is necessary.

The following assumptions are made to reduce the complexity of the problem but

still allow us to meet our simple objective, namely, the capability of handling

material transport without disturbing the main gas flow to any significant degree.

We define the material as any pneumatically transportable substance in a

ventilation system. The material can be solid, liquid, or gas other than the

main gas stream. The individual, material is assumed to be quite small in size

if it is in the condensed phase. A material cloud is an ensemble of material.

Throughout the ventilation system, the main body of the gas and the material

cloud form a mixture; the description of the flow systemis based on the continuum point of view. We will neglect all chemical reactions and physical processes (deposition, entrainment, coalescence, material break-up, evaporation,

and condensation). The material generation rate is a prescribed quantity; when

the material cloud is formed and mixed with the main gas stream, our attention

will be on the movement of the material.

215
Even for a dusty cloud, the volume occupied by the material is quite small

compared with the gas volume, and we will assume this is the case and refer to

it as the disperse condition. A consequence of this is that the material mot~ion

is dominated by the aerodynamic forces (mainly drag) but not by the inter-material forces. Furthermore, the material size we most often encounter in a ventilation system falls into the micron range, and the aerodynamic relaxation time

is quite small compared with the typical residence time. This means the material can respond quickly to the variation of gas velocity, and most of the time

the material velocity would be nearly identical to that of the gas at any location and time. Thus, we have obtained the dynamic equilibrium condition between

the gas and the material cloud, and the only equation needed to find out the

material flow rate is the material continuity equation. We can add one more

equilibrium condition (that is, the material temperature is assumed to be the

same as the gas), and we have a homogeneous equilibrium model for the gas and

material cloud mixture. This mixture can be treated as a simple gas with proper

thermodynamic and transport properties.

In principle, we could proceed to solve the set of gas dynamic equations

for the mixture; however, the mixture transport properties are not easy to'

determine. On the other hand, we still can obtain governing equations for the

main gas stream and for the material cloud separately. Some of these equations

will contain terms that express the effect of interaction between the gas stream

and the material. A closer examination of these terms reveals that if the material mass fraction is quite small compared with that of the gas, the effect

of the interaction on the gas phase flow is negligible. This is the disperse

condition for the material cloud relative to the gas mass, and we will assume

this is the case. At this point, we have achieved the complete separation of

the gas-phase flow dynamics from the material cloud. The gas dynamic aspect of

the material transport problem can be solved first; then the continuity relation

of the material will be used to determine the material flow. A more complete

presentation of various multiphase, multicomponent flow problems is given in the

literature. 2 9 -31 All the above assumptions and steps leading to the final

simplification of the material transport problem are based on those references.

216
B. Continuity Equation

In a volume V, a part of it is occupied by the material with massM Pand

volume V and the rest by the gas of mass M and volume V g; obviously

p g .

V=V +V

P g

We define a volume fraction of the material by

V

ap = V "

and the densities of the material and gas based on the mixture volume,

* (C-12)

(C-13)

(C-14) M

p V and

M

g V

which differ from the densities based on the volume of the individual phase,

Pp-- Mp Vp and

M

P g I V g (C-15)

Only pg

state.

is related to the pressure and temperature through the equation of

The mass fraction of the material is defined as

Mp

p + g M (C-16)

217
We can express the mass fraction in terms of volume fraction through the.

following, relation:

i+ u pg-i

= 1+ 1ap A C-7

pa p •p pp -

Because the material-phase density, of a liquid or solid is usually so much

larger than the gas-phase density, the disperse condition (p <<1) does not

imply the dilute condition (Y <<1) unless

p

p

•p << Pg(C-18)

pp

which is a more stringent condition. We shall assume this is the case in the

current material convection model.

The velocity of a mixture is defined as

rp U p;'u (C-19)

U= p p g

with

'=~n+ 'i (c-2o) ;P =.Pp P (C20

p is the density of the mixture, and jj, Up, MUg represent the mixture velocity,

material velocity, and gas velocity; they are vector quantities. Using the

mass fraction Yp, we have

= p)A p + 1-Y p Mg (C-21)

218
If u and u are of the same order of magnitude and for the dilute condition• p . .g

(Y << 1),

p

a JUg. ,(C-22)

The mixture velocity is dominated by the gas velocity. ,Also from Eq. (C-20),

the mixture density is roughly the same as the gas density. We expect this

should be the case for a light loading situation., From now on, we shall drop

the subscript g for all quantities associated with the gas phase.

The continuity equation for any phase or component in a mixture is 3 1

p1 dV = - ' . M(C-23) _dtV P S O" pp

The time~derivative term on the left-hand side represents the change of the

amount of material inside a control volume V:. The first term on the right-hand

side is.the material flow through the boundary S of thevolume V, and the last

term is the material source. Assuming that p is uniform over the control

volume and using the same representation we have for the gas continuity,.equation, Eq. (C-23) becomes

Vd = - p . upi A + Mp .(C-24)

Vdt i Ppi pi i p

Here we drop the vector notion for the velocity but add subscript i to indicate

the flow path connecting to that volume. A. is the flow area and u is the

.p1

flow velocity normal to the area. The positiveness of the flux term is referred

to as the flow into the volume. Again, we introduce Y into Eq. (C-24):

p

dt LipPi p= P u pu Ai + Mp (C-25)

219
or

dYp

dt p

Y . P. u .A. +M -Y Vd p

i Y P i 1i p p dt (C-26)

The last term in Eq. (C-26) is the gas density change and is determined by the

gas continuity equation.

Under the dynamic equilibrium condition, the material velocity is almost

identical to the gas velocity everywhere and at any instance, namely,

upi =u . (C-27)

u. 1 represents the gas. velocity in the pathway i. Substituting that into

Eq. (C-26) and recalling that the gas mass flow in branch i is

mi = i u1i Ai '1(C-28)

we obtain,

(C-29)

dY dY 1 Ypmi +M -Y p

v -- =di +• p

Equation (C-29) is a differential equation for the unknown Y . Once the gasdynamic quantities (p, mi) are known, Eq. (C-29) can be integrated to obtain

Y at a new time. The advantage of using Y instead of pp as unknown is that

p . p

Y is not subject to the effect of compressibility as is pp. Once Y is calcu- p h m

lated, the material density can be obtained through

p =Ypp (C-30)

220
The quantity mass fraction (or molar fraction) has been used extensively in-:

fluid flow with chemical reaction.

Finally, we must emphasize again that the assumptions we have made about

the dilute condition of material enable us to solve the gas dynamic problem

independently. The validity of the assumptions depends on the individual case

we are facing, but we do believe this simple model covers a broad range of problems related to. actual nuclear fuel facilities.

VI. MATERIAL DEPLETION

As the flow Reynolds number based on the enclosure or duct hydraulic diameter and fluid bulk velocity will be greater than about 2100 for:most cases of

interest here, the flow will be assumed to be turbulent. We will assume that

all flows are developed fully so that boundary layer or duct velocity profile

shapes are constant with distance. This will be approximately true .sufficiently

far from inlets (20 to 50 hydraulic diameters) so that entrance effects are

unimportant in. our calculations.

Under these conditions, not all of the material that is made airborne at

the location of material transport initiation will survive convective transport

to the filtration systems or facility boundary. Depending on the aerosol aerodynamic characteristics and passage geometry, there may be a sizable reduction

in aerosol concentration. As such, an enclosure or duct acts as an aerosol filter.

A number of processes that can cause aerosol depletion, and hence contribute to a material transport sink term, should be considered. Particles that

come sufficiently close to surfaces can be intercepted mechanically and' stick.

Particles with enough inertia can deviate from the flow streamlines, impact, and

stick to roughness elements, obstacles, or bends. Particles withi sizes less

than about 1 om can be transported to surfaces by both turbulent (eddy) and

molecular (Brownian) diffusion. Particles with sizes greater than about 1 um

and being transported parallel to surfaces can be deposited because of the fluctuating velocity components normal to the surface (turbulent inertial deposition). Also, particles moving through passages that are horizontal (or not

exactly vertical) will deposit through gravitational sedimentation. Lower flow

velocities enhance deposition caused by molecular diffusion and sedimentation.

22-1
Unless the surfaces are sticky, the net rate of deposition will depend on the

relative rates of transport and reentrainment. Except for fibrous particles or

very light particles, interception may be neglected because particles large

enough to be intercepted will most likely deposit as a result of inertial effects or sedimentation.

Under certain conditions other effects may become important for the smallest particles. These effects include thermophoresis, diffusiophoresis, and

electrical migration. The latter three effects are discussed in Ref. 26 and

Ref. 32. They are believed to be relatively unimportant compared with other

effects.

The current version of the code is restricted to gravitational sedimentation. The particle flux J resulting from gravitational sedimentation is26

J= Usn (C-31)

where the units of J are particles per unit area per unit time, us is the

terminalsettling velocity, and n is the uniform local aerosol number

concentration in particles per unit volume. If we multiply both sides of

Eq. (C-31) by the homogeneous particulate mass m then

= uspp , (C-32)

where the units of J' are mass per unit area per unit time and Pp = nmp

is the aerosol mass concentration per unit volume. Theterminal settling

velocity is calculated from

us =ppDpgC/18p , (C-33)

where

Pp = aerosol density,

Dp = aerosol diameter,

222
g = gravitational acceleration,

C = Cunningham slip correction factor, and

= fluid dynamic viscosity.

The code input variables for material depletion are p and D These variables may be assumed or selected to be aerodynamic diameter with unit density

or Stokes diameter with the material bulk density. This selection was discussed

in Sec. A above. To calculate the slip correction factor, the code uses26

C = 1 + (2L/Dp)(A 1 + A2 exp(- A3 Dp/L)) , (C-34)

where L is the molecular mean free path and the A's are dimensionless constants

based on experimental measurements of small particle drag. The code uses

L = 0.065 um,

A1 1.257,

A = 0.400,

A 3 0.550,

2

g = 981 cm/s2, and

= 0.0001781 g/cm s,

where L, u, and g are taken at standard sea level conditions.

We know pp from the material transport mass balance calculation for-the

previous time step for each node (volume or duct). Then, knowing us and the

projected floor area. for sedimentation A, we can compute the sink term using

Eq. (C-32):

M = - J'A = - UpA . (C-35)

223
Because aerosol depletion is a sink term, we have used a minus sign in

Eq. (C-35). This equation represents a negative contribution to the M term

p

on the right hand side of Eq. C-29 in Sec. V. above. Aerosol depletion by

sedimentation may be selected for all volumes and ducts and is calculated in

the same manner.

VII. FILTER MODEL

A. Introduction

33 Experimental evidence indicates that the pressure drop across a filter

commonly used for air cleaning in chemical and nuclear industries increases nonlinearly at high-speed flow, in contrast to the linear relation applicable to 1

the low-speed flow region for normal or near normal application. We can take

an entirely experimental approach to determine all the influence coefficients

on filter and flow properties, or we can model the filter flow based on the

principle of flow through porous media and determine the relationship between

the flow rate and the pressure drop with most if not all pertinent parameters

explicitly included. Even so, some empirical constants still are needed; for

practical purposes, we can combine some filter properties into these constants

and determine them by experimental means. We will review some theoretical works

and then present a model that is suitable for our needs.

The purpose of using an air filter in a ventilator system is to remove airborne material in the stream to prevent harmful elements from getting into the

environment. Experience shows that the accumulation of material, usually in

the condensed phase, will cause the pressure drop to increase for the same flow

rate, thus causing degradation in system performance. In the case of fire, rapid flow resistance increases as the result of large amounts of material caught

by the filter, which is known as filter plugging or clogging. Following the

same analytical works in filter modeling, we will review the filter plugging

phenomena briefly, but a semi-emperical formulation eventually is proposed to

describe this condition.

B. Filter Model

The pioneer work of D'Arcy34 established the foundation of the principles

of fluid flow through porous media; his experimental results led to an understanding of the linear relationship between the flow rate and the pressure drop

224
through an empirical constant, permeability. This parallels quite well the conclusion of fully-developed laminar flow through pipe made by Hagen-Poiseille. 3 5

It is not surprising to find that many theoretical models on flow through porous

media are based on that concept with different qualificat'ions, among them the

most successful one is the Kozeny model. 3 6 According to his theory, the porous medium is represented by an assemblage of channels with various crosssections and a definite length. The flow through the channels is determined by

the Navier-Stokes equations, and the permeability is expressed in terms of viscosity and the porous medium properties. However, an empirical constant is

needed to include the effect of the tortuous characteristic of the medium; a

modification of the Kozeny model by Carman37 defines the constant, known as

tortuosity, in a more explicit way. This new model still requires an empirical

coeffic~ient'to account for the uncertainty of determining various porous medium

properties.

Another point of view on pressure drop with flow through a porous medium.

is based on the drag theory; the dragging obstacles can be particles or fibers.

A model 3 8 using the fiber as porous medium leads to a permeability that is

weakly'dependent on flow rate. As a result of the actual complexity of themedium, some empirical adjustment is needed for this model.

So far we have discussed the D'Arcy law and its derivatives, which are adequate only when the flow velocity is low; the pressure drop is proportional to

the viscous dissipation by the porous medium. For the channel flow, as the flow

velocity increases, the dissipation mechanism changes from viscous effect to

turbulence, and the pressure drop is proportional to the Kinetic energy of the

stream. 3 5 Following the reasoning of Kozeny in modeling porous media as channels, a quadratic relation3 9 is established between the pressure drop and flow

rate at high velocity. Again, an empirical coefficient equivalent to the resistance factor in pipe flow under turbulence conditions is introduced. The

summation of viscous effect and turbulent dissipation leads to an equation

proposed by Ergun: 4 0

pu150 2 um (1-C) PUre2 (C-36)

d; + 1.75--IdT 1d

p p

225
with

. pressure drop,

: = bed l engt h,

g,= gravitational constant,,

=.void fraction,

u = viscosity,

dp= effective porous medium particle s~ize,.

p

p = fluid density, and

um = superficial, velocity.

Superficial velocity is the flow velocity approaching the packed bed, not, the

average flow velocity, in the interstitial region. Equation (C-36) also can be

expressed in a different form:

2i

Ap=KL~A +7L KTP 2 (C-37)

A XA

where Q and A represent volume flow rate and the frontal area of the packed

column.. It can be easily identified that

u =Q (C-38)

o 2 A112" :

L 3 A 2 (C-39)

p

and

(1-c) I C40

KT = 1.75 - (C-40)

TS

226
We can see that KL and KT are dimensionless and are dependent on the properties of the porous media. Equation (C-37) is identical to the expression of

Reynolds41 on pipe flow in laminar and turbulent regions.

As we discussed earlier, no matter what theoretical model we choose to use,

some empiricalcoefficients must be included to account for thec.complexity and

uncertainty of the porous medium. Obviously, it does not matter if we obtain

KL and KT first from Eqs. (C-39) and (C-40) and add.experimental correction

later or if we go ahead to determine the effective KL and KT directly from

experiment.. The task is no more difficult than finding the correction factors

alone because there are only two unknowns involved as presented in Eq. (C-37).

From now.on, we will use Eq. (C-37) as the foundation of our filter model

regardless of what filtration media we use as long as we can determine the two

coefficients through experiment or analytical means.

C. Filter Plugging

The physical phenomena'involving the capture of suspended particulate in a

stream by some filtration medium are quite complicated.42 The porous material

provides.various sites for material retention: resting on the surface of the

bed grain, wedged in a crevice, stopped at a constriction, and contained in a

pore cavity. The normal pressure of the fluid, friction, interparticulate force

and chemical, bonding force give the required means of holding the particulate

on the site. The mechanisms for the suspended material reaching the retention

site include gravity, inertia, hydrodynamic force, interception, and Brownian

motion. Attempting to relate the overall filter efficiency with the aforementioned sites, forces, and mechanisms without.any experimental coefficient is

almost impossible and impractical. -A more useful approach is a phenomenological

one; namely, we assume some form of dependence of filter efficiency on the total

amount of retention; experiments indicate a small increase in the efficiency for

increasing retention. For all practical purposes, we assume the filter efficiency remains constant in any flow condition.

The same conclusion cannot be made about the flow resistance of the filter

for the increasing amount of material gathered. The increase in resistance can

be quite substantial and should be dealt with properly. The plugging is related

to material .size, shape, and phase; the filter structure; and the quantity of

captured material. Using the filter model of Carman-Kozeny, 37 the material

227
retention reduces the specific surface, defined as the total surface of the bed

grain per unit filter volume, and thus increases the effective resistance. We

can express the general relation as..

ap =•;'fM )(C-41)

where (Ap) is the pressure drop for a clean filter, shown in.Eq. (C-37), and

0

f is a monotonically increasing function of material mass Ma on the filter.

Clearly f(M = o) = 1. For light loading condition, f is a linear function

a

of M: *a

f(M) = 1 +M , (C-42)

where a is a coefficient dependent on filter-and material properties and has

ý43 the unit of the reciprocal of mass. More recent work of Berýman using-the

32 fiberous drag model of Da:.ies concludes that a depends on the fiber volume

fraction, fiber size anddparticle size. However, the foundation of Davies' model *is still empirical. For the time being, we shall postulate the phenomenological relation of Eq. (C-42) with a being determined by experiment. As future data warrant, Weshall modify the equation with more explicit relations

included.

228
APPENDIX D

BLOWER MODEL

Blowers or fans are approximated by a model that describes the interaction

of the gas (or air) in the system with the blower. Specifically, the model calculates the volumetric flow rate through the blower as a function of the differential pressure across the blower and the gas density at the inlet to the

blower.

The blower module depends on the measured constant speed performance curve

of the Fan. These data usually are reported by the manufacturer in the form of

a curve.

Ap(Po) - f(Q) (D-1)

where AP is the static pressure difference across the blower and Q is the

volumetric flow rate through the blower. This curve applies at a given density

(p = Po) and fan speed and may be obtained from the manufacturer's literature.

During a fire transient, the gas density at the fan may vary a great deal,

and the curve Eq. (D-1) must be modified to take into account the density

variation from standard conditions. Similarity analysis and experimental

measurements show4 4 that it is possible to correlate the blower performance

at any density, p, if the performance at a given density (p = Po) is measured.

Specifically, the result is of the form

Ap(p) = O AP(Po) . (D-2)

Because Ap(Po) is known, Eq. (D-1), we have

Ap(P) of(Q) f "(D-3)

229
Therefore, the blower head-flow characteristic curve is known at all densities.

In the solution procedure for the gas dynamics it is necessary to have an

expression for the flow rate as a function of the differential pressure; thus

Eq. (D-3) must be inverted. The solution is of the form

•'Q =. g(- Po Ap) . (D-4)

This inversion can be performed only if the function, f, is single valued.

Therefore, as discussed, in Sec. II-.A.4, certain manufacturer's curves may not

be modeled exactly but must be distorted slightly.

The actual user input to the code is a number of points on the blower

characteristic curve. The curve then is approximated by a series of straightline segments as shown in Fig. 1.. If all of the segments have a negative slope,

there will be no problem in obtaining the inverse function represented by

Eq. (D-4).

230
APPENDIX E

CONTROL DAM4PER MODEL

In many ventilation systems, control dampers are used.to maintain a pressure in a room automatically. For this reason an option for modeling.dampers

that open or close based on the pressure in a given room. In the initial version there are three types of dampers with the ability to add more damper types

as data become available.

The dampers initially modeled in FIRAC are 2-ft by 2-ft opposed-blade

light-duty dampers,.opposed-blade medium-duty dampers, and parallel-blade

light-duty dampers. The dampers were manufactured by American Warming. and

Ventilation, Inc. Figure E-1 shows the configurations of .these dampers.,.,

25. 4 cm

-Bl1ades

Control

-Linkage

rBlades

Control

-Linkage

FLO14

FLOW

E

2x 0

0

.Parallel Blade

Damper

Opposed Blade

Damper

Side views

Fig. E-l.

of the opposed-blade and the parallel-blade dampers.

231
The damper models are based on experimental data relating flow rate through a

damper and the pressure drop across a damper. In FIRAC pressure drop and flow

rate across a damper are related using the equation P = R x Q2 where R is a

resistance coefficient. The resistance coefficients for these damper types

were determined experimentally in reference to different damper angles. Using

this information, a least-squares polynomial fit was made to the data. The

resulting equations are quartics of the following general form.

R= a + b(theta) + c(theta) 2 + d(theta) 3 + e(theta) 4

The coefficients of theseequations should be calculated-with theunits of R

being kPa/[(m 3/s) 2] and theta being in degrees.

Adding more damper types can be done by simple modifications to the subroutine damper. The first step in adding a damer type.is to increase the array

size of the coefficients in subroutine damper to the total number of damper

types.available, including the one being added. The second step is to add the

coefficients for the new damper type to the end of the data statements that define the coefficients. After these two changes have been made, the damper can

be modeled by specifying a damper type on the control damper card that corresponds to the array location:of the coefficients in sub routine damper.

A control damper is modeled in FIRAC by changing the resistance coefficient

of-a damper-to correspond with the opening and closing of the damper. A damper

can be made to open or close based on the pressure in any room in the system.

This is done by specifying a minimum and a maximum pressure in the room, the

damper type, the amount the damper opens or closes at one response time, and

the time between responses. If the damper closes at pressures above pmax then

dthata (the amount the damper opens at pressures above pmax) should be a negative number.

232
APPENDIX F

MODELING DUCTS AND VALVES

Ducts and valves are modeled in FIRAC based on resistance coeffecients

relating the pressure, drop across a duct to the volumetric flow irate through

the duct., The.equation showing this relationship is

dP RC Q2 (F-I)

Reasonable values for ..these resistance coefficients can be calculated based on

ambient condit.ions,.flow..:-.rate though the duct or valve, and the.configuration

of the duct or valve. The pressures throughout the system can be approximated

based on these resistance coefficients.

To calculate the resistance coefficient (RC) for a component using this

method, a dimensionless coefficient or k value for the component first must be

computed. Some of the-,morecommon values-for this coefficeint.are given in

Fig. F-i. A more complete list of values can be found in Ref. 45. Using this

dimensionless k value, the resistnace coefficient can be calculated using the

equation

RC - k x Pambient

2 X A2 x Rair x T

where k is the crane k value, Pambient is the ambient pressure,-A is the

flow area of the duct,.Rair 'is .the gas constant for air, and T is the ambient

temperature. A value for R that wi.ll allow you to input temperature in OR,

area in ft 2 , and ambient pressure in psia is

Rair = 222.64 x ft 2 psia

min 2 in. wg. OR

233
ENTRANCE

K =.5

K =.78

.EXIT

K=1

LOSS DUE TO LENGTH OF DUCT

K=f-L/D

T

D

I

L

WHERE f IS THE MOODY FRICTION FACTOR

EXAMPLE

I

K =.78 • K=f'L/D

TOTALK=.78+(f -L/D)+1.

Fig. F-I.

Typical K values.

K=1. -r

234
Using this value for Rair produces resistance coefficients with the units of

inches water gauge per cubic foot per minute squared, which are the units

needed for FIRAC input. The pressure drop across a duct can then be

calculated using Eq. (E-I).

235
APPENDIX G

SAiMLE OUTPUT

(1) Sample Problem 1 system response (FOUT) output file.

(2) Sample Problem 1 fire compartment effects (PRINT 1) output file.

(3) Sample Problem 1 radioactive source term (RST) output file.

S236
(1) Sample Problem 1 system response (FOUT) output file.

executed on -84/06/11 time ;21:56:02

table no. ¶

l i s t of Input data

10 20 30 40 50 60 70 80

12345678901234567890123456789012345678901234567890123456789012345678901234567890

1S

2S Sample problem ¶

3$# run control card 1

4$ at 1. 999.0

55# print / plot control card

6S all 2 1 1 2 5

7$ 1 1 1

8$ 2 I 1

9$ 3 1 1

10$ to 1 1

11$ 13 1 I

12$# plot frame description card

13$ 4 2 3 4 5

14$ 4 4 14 15 17

15$ 4 2 3 13 15

16$ 4 2 3 .8 15

17$ 4 2 3 4 5

Is$ 4 9 14 16 17

19$ 4 2 3 '13 14

.20S 4 2 3 13 14

ý21$ 4 2 3 13 14

22$ 4 2 3 13 14

23$ 4 2 3 13 14

24$ 4 2 3 13 14

25$ 4 2 3 13 14

26$ 4 2 3 13 14

•$7 4 2 3 13 14

28$ 4 2 3 13 14

29$# run control card 2 "tfirin"

30S t 0 0 ,;<%13

31S# boundary control card

32$ 0 4 56.

1635#geometry and component control card

34S M 18 14 1 1

355# branch description data cards

36$ 1 1 2 1200. 4.6944 .25 v .06

37$

38$ 2 2 3 1200. 4.6944 .25 d .14

39%9.5000e-08

40$ 3 ..>4 5 1200. 4.6944 3.2 d .02

41$ 1.389e-08 2.1666 6.9333

*42S 2.167 27.77 1. .25 .3 .3 26.2 489. .12 56.

-,43$ 4 5 6 1200. 4.6944 3.2 d .02

.44$ 2.1666 6.9333 t

45S 2.167 27.77 1 .25 3 .3 26.2 489. .12 56.

*46S 5- 6 7 1200. 4.6944 3.2 d ý02

47S .2.1666 6.9333

48$ 2.167 27.77 1 .25 .3 .3 26.2 489. '.12 56.

49$ 6 7 8 1200. 4.6944 3.2 d .02

50S 2.1666 6.9333 1

51$ 2.167 27.77 1 .25 .3 .3 26.2 489. .12 56.

52.% 7 8 9 1200. 4.6944 3.2 !d .02
00

eexecuted on : 84/06/11 time ;21:56:02

table no. I (page 2)

l st of Inpu t d a t a

10 20 30 40 50 60 70 80

1234567890123456789012345678901234567890123456789Oi23456789O12345678901234567890

53$ 2.1666 6.9333 1

54$ 2.167 27.77 1 .25 .3 .3 26.2 489. .12 56.

55$ 8 9 10 1200. 4.6944, 3.2 d .02

56$ 2.1666 6.9333 1

57$ 2.167 27.77 1 .25 " .3 .3 26.2 489. .12 56.

58$ 9 10 11 1200. 4.6944 3.2 d .02

59$ 2.1666 6.9333 1

60$ 2.167 27.77 1 .25 .3 .3 26.2 489. .12 56.

61$ 10 11 12 1200. 4.6944 3.2 d .02

62$- 2.1666 6.9333 1

63$ 2.167 27.77 1 .25 .3 ..3 26.2 489. .12 56.

64S 11 12 13 1200. 4.6944 3.2 d .02

65$ 2.1666 .6.9333

66$ 2.167 27.77 1 .25 .3 .3 26.2 489. .12 56.

67$ 12 13 14 1200. 4.6944 3.2 d .02

68$ 2.1666 6.9333 1

69$ 2.167 27.77 1 .25 .3 .3 26.2 489. .12 56.

70$ 13 14 15 1200. .7854 f .965

71. 1

72$ 14 15 16 1200. .7854 25. d .2

73$ 2. 75. 1

74$ 1. 78.5 1 .0625 .3 .3 26.2 489. .12 56.

75$ 15 16 17 1200. .7854 b -1.4 1

76$

77$ 16 17 18 1200. .7854 0.5 v .2

78S

79$#

80$

81$

82$

83$

84$

85$

86$

87$

88$

89$

90$

91$

92$

93$#

94$

95$

96$

97$

98$5/

.99$

100$ 101$

102$

103$

104$

i.Oe-07

particulate spncie.data cards

I smoke 100.

2 total rad part 20.

3 red part .1 .1

4 rad part .2 .2

5 rad part .4 .4

6 mad part .6 .6

7 rad part .8 .8

8 rad part 1. 1.

9 rad part 1.5 1.5

10 rid part 1.9 1.9

II rid part 8. a. 12 rad part iS. 15.

13 rad part 20. 20.

boundary node data

1 0 0. 56.

1.

1.

1.

1.

1.

1.

1.

1..

1.

1.

1.

1.

1.

31 0.

4 .0. 18 0 0.

room data

2 1.0

4.6944

5 13.636

4.6944

6 13.636

4. 6944

56.

56.

56.
executed on 84/06/11 ttme.;21:56:02

table no. I (page 3)

s t of input da t a

10 20 ,30 40 50 60 70 80

1234567890123456789012345678901234567890123456789o123456789012345678901234567890

105$ , 7 13.636

106S 4.6944

107$ 8 13.636

108$ 4.6944

1095 9 13.636

I10$ 4.6944.

t11$ 10 13.636

112$ 4.6944

113$ 11 13.636

114$ 4.6944

115$ 12 13.636

116$ 4.6944.

117$ 13 13.636

t.18$ 4.6944

119$ 14 Q3.636

120$ 4.6944

121$ 15 13.636

122$ .7854

123$ 16 . 9.8

124$ .7854

125$ 17 9.8

126$ .7854

127$# blower curve cards

128$ 1 4

129S-80OO. 8. 0. 1.8 1200. 1.5278

130S6000. 0.

131$# filter data

132$ 1 .9995 1.

133$# temperature data

134S 56. 56. 56. 56. 56.

135$ 56. 56. 56. 56. 56.

136$ 56. 56. 56. 56, 56.

137$ 56. 56. 56.

138$# fire scenario control specifications liflow3"

139$ 110O. 100 2

140S 1 0.0 0 0.0 0 0

141$# fire compartment initial condittons and noding

142$ 56.0 -. 20.-

143$ 2 '3 1.084 2.166

144$ 3 4 11.76 2.166

145$# fuel type, mass',and burn area

146$ 0.0 0.0 0.0 0.0' 0.0 0.0 5.750 0.0 0.0

147$ 0.0 0.0 0.0 0.0 0.0 0.0 2.150 0.0 0.0

148$ 0.0 0.0 0.0 0.0 0.0 0.0 4.0 0.0 0.0

149$ 0.0 0.0 0.0 0.0 0.0 .0.0 2.0 0.0 0.0

t50$# fire compartment dimensions and materials

151$ 20.0 17.0 15.0 0.492 0.492 3.281 0.492

152$ 9 8 9

153$# combustible identifier card (required If Ignite >. 0)

154$ 2 2 2 '2 2 2 1 2 2

155$5 radioactive source term Input

1'56$ 0 1 1 0 0 0 0

t0
40C:

exec

157$

1581

159$

160$

161$

162S

163$

=uted on ; 84/06/11 time ;21:56:02

table no. I (page 4)

list of i nput data

10 20- 30 40 50 60 70 80

123456789012345678901234567890 1234567890 1234567890123456789012345678901234567890

1 7 1 2

.22050

2 0.1653

.# time step cards

.001 3.0 1.0

.01 10.0 1.0

.05 999.0 50.0
table no. ii

summary of control information and diagnostics

-- warning -- the number of particulate species must be between 0 and 5 nspeces 13

boundary nodes = 4

pressure functions = 0

energy functions = 0

temperature functions = 0

mass addition functions = 0

particulate addition functions =

gas addition functions = 0

branches = 16

nodes = IS

rooms = 14

number of blower curves.- 1.

number of filter types'- I

buoyancy effects will not be con!

0

sidered

-%a
table no. iii

summary of problem control parameters

maximum iterations per time step

convergence criteria

problem type ss/trans

0.0000

80.0000

160.0000

240.0000

320.0000

400.0000

480.0000

560.0000

640.0000

720.0000

800.0000

880.0000

960.0000

10.0000

90.0000

170.0000

250.0000

330.0000

410.0000

490.0000

570.0000

650.0000

730.0000

810.0000

890.0000

970.0000

times for line pr

20.0000 30.0000

100.0000 110.0000

180.0000 190.0000

260.0000 270.0000

340.0000 350.0000

420.0000 430.0000

500.0000 510.0000

580.0000 590.0000

660.0000 670.0000

740.0000 750.0000

820.0000 830.0000

900.0000 910.0000

980.0000 990.0000

inter plots

40.0000

120.0000

200.0000

280.0000

360.0000

440.0000

520.0000

600.0000

680.0000

760.0000

840.0000

920.0000

50.0000

130.0000

210.0000

290.0000

370.0000

450.0000

530.0000

610.0000

690.0000

770.0000

850.0000

930.0000

1000

1.00e-04

60.0000

140.0000

220.0000

300.0000

380.0000

460.0000

540.0000

620.0000

700.0000

780.0000

860.0000

940.0000

70.0000

150.0000

230.0000

310.0000

390.0000

470.0000

550.0000

630.0000

710.0000

790.0000

870.0000

950.0000

p-ambient= 14.7000 psia

boundary data

t-ambient= 56.000 f number of boundary nodes= 4

node

no.

18

initial

pressure

0.00

0.00

p fn

no.

0

0

initial

temp.

56.00

56.00

t fn

no.

0

0

node initial p fn initial

no. pressure no. temp.

3 0.00 0 56.00

t fn

no.

0

node initial p fn

no. pressure no.

4 0.00 0

initial

temp.

56.00

t fn

no.

0

geometry and component data

number

number

number

of

of

of

branches= 16

blowers =

rooms = 14

number of nodes (boundary+ ordinary)= 18

number of blower curves= I
table no. Iv

summary of model control parameters

branch data

no.

2

3

4

5

6

7

8

9

10

I I

12

13

14

15

16

in

node1

2

4

5

6

7

8

9

10

11

12

13

14

15

16

17

out.

node

2

3

5

6

7

a

9

t0

11

12

13

14

15

16

17

Is

initial

f low

1. 200e+03

1. 200e+03

. 200e+03

1 200e+03

. 200e+03

. 200e+03

. 200e+03

. 200e+03

1. 200e+03

. 200e+03

1 200e+03

. 200e+03

. 200e+03

. 200e+03

. 200e+03

. 200e+03

flow

area

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

4.694e+00

7. 854e-01

7.854e-01

7.854e-01

7.854e-01

comp

type

valv

duct

duct

duct

duct

duct

duct

duct

duct

duct

duct

duct

duct

blwr

valv

cu

exp resist intercept

rve q

2.0 4.t67e-08

2.0 9.500e-08

2.0 1.389e-OE

2.0 1.389e-08

2.0 1.389e-08

2.0 1.389e-08

2.0 1.389e-08

2.0 1.389e-08 .2.0 1.389e-08

2.0 1.389e-O0

2.0 t.389e-08

2.0 1.389e-08

1.0 8.042e-04

2.0 l.389e-07

I 1.0-4.409P*03 7.94e+03

2.0 1.000e-07

initial

del ta-p

61 OOOe-02

6.000e-02

2.000e-02

2.000e-02

2. 000e -02

2.O00e-02

2.000e-02

2.000e-02

2. O00e- 02

2.O00e-02

2. 000e-02

2. 000e-02

9.650e-0t

2.000e-01

I. 400e+00

3. 500e-02

Inertia

5.325e-02

5.325e-02

6.817e-O0

6.817e-01

6.817e-0i

6.817e-01

6.817e-01

6. 81 7e-OI

6.817e-01

6.8 17e-0I

6.817e-01

6.817e-O0

0.

3. 183e+01

0.

6.366e-01

rev resist

4.167e-08

9.500e-08

1.389e-08

1.389e-08

1.389e-08

1.389e-08

1.389e-08

i.389e-08

1.389e-08

1.389e-08

1.389e-08

1.389e-08

B.042e-04

1.389e-07

0.

1.000e-07

heat transfer data

branch nodes htarea diameter delta-x emmlsivity absorbtivity

initial

k rho cp temperature

3

4

5

6

7

8

9

10

12

14

.1 2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

2.78e+01

7.85e+01

2.17e+00

2.17e+00

2.17e+00

2.17e+00

2. 17e+00

2.17e+00

2.17e+00

2. t7e+00

2•'17e+00

2.1,7e+00

I. 00e+00

2. SOe-01

2.50e-01

2.50e-01

2.50e-01

2.50e-01

2.50e-01

2;50e-01

2.50e-01

2.50e-01

2.50e-01

6.25e-02

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300

.300 .300

.300

.300

.300

.300

.300

2.62e÷01

2.62e+01

2.62e+01

2.62e+01

2.62e+Of

2.62e+01

2.62e+01

2.62e+01

2.62e+01

2.62e+01

2.62e+01

4. 89e+02

4.89e+02

4. 89e+02

4.89e+02

4. 89e+02

4.89e+02

4.89e+02

4. 89e+02

4. 89e+02

4.89e+02

4.89e+02

1. 20e-01

1. 20e-01

1.20e-01

1. 20e-01

1. 20e-01

1.20e-01

1.20e-01

1.20e-01

1.20e-01

1.20e-01

1.20e-01

56.00

56.00

56.00

56.00

56.00

56.00

56.00

56.00

56.00

56.00

56.00

room

I.

5

9

13

node vol. area

2 1.000e+00 .4.694e+00

8 1.364e+0i 4.694e+00

12 1.364e+01 4.694e+00

16 9.800e+00 7.854e-01

room data

room node vol. area

2 5 1.364e+01. 4.694e+00

6 9 1.364e0O+ 4.694e+00

10 13 1.364e+01 4.694e+00

14 . 17 9.800e+00 7.854e-01

room node vol. area. 3--- 6..36-- ----...... ---- 3 6 1.3648+01 4.694e;+00

7 10 1.364e+01 4.694e+00

11 14 1.364@+01 4.694e+00

room node vol.

4 7 1.364e+0I

8 11 1.364e+01

12 15 1.364e+01

area

4.694e+00

4.694e+00

7..854e-01

r%)

CA. blower curve data coefficlents
N)

:::> .' 44•!t•~~l••:.:}''

.4;4.-• 4• 44

444~

4.4 -

-A'

4'

4 4

''4

4 -~

44

44 4

4'

.4•444 (4 "4 44~ ;~

44 "~4 44 4444

4' "< i4~44

444 44

44.444 444 4 4' 4>4

4 4'

r -" 4 .o 44d . '

"'2

I•' . 40e -0 7

6700:•,4 3 -

types i . ' ,. .

. 4!•i• 44 :•!'i>, i: : :,!i•

ght boud~f low

• •2 4•

4- •4 '4)

44~~

44.4

4' 4

a b

* ~t:' v-4(4< -•

~ 

,* *,. 4-* I'

4 ' ''-.4 4

4 A

4 4'

4)f

A'

no.

/e'4fo. segment left' bolund(flow) ri

)44I -8.000e+03'

i'2 0., .3 , i.200e+03,

. filterdaa

theotal< nube o f44er-i

the total number of filersa fislteter branch filter • filter

-no. - type, effri~ciency

1l IS 1, 99950e-01

.3226e+03 -1.2903e+034

* 9353e+03 -4. 4085e+03

.0000e+03 -32141e+03 '...

44 kplugging

factor

1.00' : .. 4 . . ....44 i~ •,•

4 A,

4 4• 4.- ¢ .

4' ,4

- 4 :. , ,: , 4:{ .

- akt

0.

o.,,•

• ::..!!

44~ -.. ' •44

4 4 4' -.4

'.4

4 444

4 4

4 4 4 4

~44

44'-

4 4

4. 4 44 -4 4 444

4 4 4 '44 '44 ~4 ~'4

4 ~44 4'. ' '4•4 4 •4 4 4•444'~.4 44. 44 4~4

4• 4

44'•

4~4 4-

44 44 44 4 4

,~4'. ~ 4.4 4 4

.4~4 44"' -. 44 •44 4•44.4 44 4444 4 44'4444 4

4 4'' 4

4 .• 4

444.4

44 4'

• A44'4,44 44

44

4' '444•

44 44. '~44 444

4'4'

4444

4•4444'
table no. v

summary of node type, initial pressure and branch connections

node

no.

2

3

4

5

6

7

a

9

10

i1

12

13

14

15

16

17

l8

node(-,for boundary

type(+,room no+i000) pressure

-1 0.

1001 -6.00Oe-02

-1 0.

-1 0.

1002 -2.0000e-02

1003 -4.0000e-02

1004 -6.0000e-02

1005. -- 8.0000e-02

1006 - 1.OOOe-01

1007 -1.2000e-01

I0O8 -1.4000e-0t

1009 -1.6000e-01

1010 -t.800e-01

1011 -2.00OOe-0t

1012 -1.1650e+00

1013 -1.3650e+00

1014 3.5000e-02

-1 0.

associated branches

1 2

3

4

5

6

7

B

10

1213

14

15

4

5

6

7

a

9

10

II

12

13

14

15

16

N)

LnI
table no. vi

dimensionless resistance factors and critical mach numbers

branch no.

.I

2

3

4

5

6

7

a

9

10

.11

12

13

14

15

16

up. node

I

2

4,

5

6

7

8

9

10

11

12

13

14

15

16

17

dn. node

2

3

5

6

7

8

10

11

12

13

14

15

16

17

18

fwd rf

I 435e+01

3. 172e+Oi

4. 784e+00

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e÷00

4. 783e+00

4. 783e+00

4.783e+00

0.

1.339e+00

0.

-3.596e-02

rev rf

. 335e+01

3. 272e+01

3. 784e+0O

4 783e+00

4. 783e400

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e+00

4. 783e+00

4 .783e+00

-6. 934e-01

1.339e+00

0.

9.640e-01

fwd mach

.20108

.4159

.31 58 .31159

.31159

.31159

.31 59

.31159

.31 159

.31159 .31159

.31159

1. 00000

•47051

AIM000

t. 00(000

rev mach

.20735

.13959

.33899

.31159

.31159

.31159

.31159

.31159

.31159

.31159

.31159

31159

1 .00000

.47051

S.00000

.51353
time 1 0. dolt = 0. nstep = 0 ktotr = 0 Igtot = 0 iptot = 0 cPu time 8.10e-01

branch data

branch vol. flow mass flow velocity

(m**3/s) (kg/s) (m/s)

i $.663e-01 6.98Be-Oi 1.299e+00

2 5.663e-01 6.987e-Oi 1.299e+00

3 5.663e-01 6.988e-Oi i.299e+00

4 5.663e-0i 6.988e-01 1.299e+00

5 5.663e-01 6.988e-01 1.299e+00

6 5.663e-01 6.987e-0i 1;299e+00

7 5.663e-0i 6.987e-O1 1.299e+00

8 5.663e-01 6.987e-01 1.299e+00

9 5.663e-01 6.9860-01 1.299e+00

1O 5.663e-01 6.986e-01 1.299e+00

ii 5.663e-01 6.986e-01 1.299e+00

12 5.663e-01- 6.98se-01 i.299e+00,

13 5.663e-01 6.983e-01 7 762e+00

14 5.663e-01 6,.969e-01 7.762e+00

15 5.663e-01 6'.965e-0t 7.762e400

16 5.663e-Oi 6.989e-01 7.762e+00

node data

node p t rho

(pa) (k) (kg/m**3)

I t.0135e+05 2.865e*02 1.234e+00

2 i.0134e*05 2.865e*02 i.234e+00

3 i.0135e4 05 2.865e+02 1.234e+00

4 i.0135e+05 2.865e+02 1.234e+00

5 1.0135e+05 2.865e+02 1.234e+00

6 t.0134e+05 2.865e÷02 1.234e+00

7 l.0134e+05* 2.865e+02-. i.234e÷00

8 1.0133e+05 2.865e+02 1.234e+00

9 i.0133e+05 2.865e+02 1.234e+00

10 1.0132e+05 2.865e+02 1.234e+00

11 i.0132e+05 2.865e+02 1.234e+00

12 t.0t31e+05 2.865e+02 1.233e+00

13 i.013ie405 2.865e+02 1.233e+00

14 I.0130e+05 2.865e+02 1.233e+00

15 1.0106e+05 2.865e+02 1.230e+00

16 1.0101e+05 2.865e+02 1.230e+00

17 1.0136e+05 2.865e402 1.234e+00

18 1.0135e+05 2.865e+02 1.234e+00

heat transfer information

branch tavg qqq hco qco qro hci qci qri rvn

3 2.865e+02 0. 0. 0. 0. 0. 0. 0. 0.
Co wall temperatures (k) 2.B65e+02

branch tavg hco

4 2.865e+02

wall temperatures

branch tavg

5 2.865e+02

wall temperatures

branch tavg

6 2.865e+02

wall temperatures

branch tavg

7 2.865e+02

wall temperatures

branch tavg

a 2.865e+02

wall temperatures

branch tavg

9 2.865e+02

wall temperatures

branch . tavg

10 2.865e+02

wall temperatures

branch tavg

ti 2.865e+02

wall temperatures

branch tavg

12 2.865e+02

wall temperatures

branch tavg

14 2.865e+02

wall temperatures

qqq qco qro hcI qct qrf ryn

0.

(k)

O.

(k)

0.

(k)

0.

(k)

0.

(k)

0..

(k)

0.

(k)

0.

(k)

0.

(k)

0.

(k)

0.

2.865e+02•

qqq hco

0.

2.865e+02

qqq hco

:0.

2.865e+02

qqq hco

0.

2.865e+02

qqq hco

0.

2.865e+02

qqq hco

0.

2.865e+02

qqq hco

.0.

2.865e+02

qqq -hco

0. 0. 0. 0. 0. 0.

qco qro hc I

0. 0. 0. 0.

qc 

i

qe 

i

qr I

0.

ryn

0.

qco qro hcl qrI ryn

0. 0. 0. 0. 0. 0.

qco qro hci qc 

i ryn

0. 0. 0. 0. 0. 0.

qco qro hc 

I qc 

I qr 

l ryn

0. 0. 0. 0. 0. 0.

qco qro hc 

f qc i qrf ryn

0. 0. 0. 0. 0. 0.

qco qro hc 

I qc 

I qri ryn

0. 0. 0. 0. 0. 0.

qco qro hc 

I qcl qri ryn

qqq

0.,

2.8865e+02

hco

0.,

2.865e+02

hco

0.

2.865e+02

0. 0. 0. 0. 0.

qco qro hci

0.

qc 

I qrl ryn

0. 0. 0. 0. 0. 0.

qqq qco qro hcl qc 

I qrt ryn

0. 0. 0. 0. 0. 0.
**..**.*.**********.$.***.*.*.*.**.****** particulate specie data

species no. I smoke

* * ** * * *** * * &* #0**0 * * ** * * * * * *#** *. * *#**** *.* * * * * *.***

specie nodal mass fraction

frac. 0. 0.

0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

0. 0.

0. 0.

specie branch flux (kg/sec)

dfl1ux 0. 0.

0. 0.

specie integrated branch flux (kg)

int.mass 0. 0.

*0. 0.

front filter mass (kg)

fil:mass 0.

back filter mass (kg),

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 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.

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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

total specie airborn mass ; 0.

specie mass on duct wall (kg)

mass 0 0.

0. 0.

deposition rate at each' branch (kg/9)

rate 0. 0.

0. 0.

entrainment rate at each branch (kg/s)

rate 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 species no. 2 total rad part
specie nodal mass fraction

C, frac. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.* 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. .. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

species no. 3 rad part 

.

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
specie nodal concentration (kg/m**3)

conc.. 0. O 0.

0. . 0.

0. O.

specie branch flux (kg/sec)

dflux 0. 0.

0.. 0.,

specie integrated branch flux (kg)

int.mass 0. 0.

0. 0.

front filter mass (kg)

fil.mass 0.

back fi-lter mass (kg)

f il.mass "0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0.

0. 'O.

0. 0.

total specie airborn mass 0.

,specie mass on duct wall (kg)

mass :0. 0.

0. 0.

deposition rate at each branch (kg/s)

rate 0. 0.

0. 0.

entrainment'rate at each, branch (kg/s)

rate 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.

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.

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.

species no. 4 rad part .2

specie nodal mass fraction

frac. 0. 0.

0. - 0.,

0.ý 0.1

specie nodal concentration (kg/m**3)"

conc. 0. 0.

01 0. 0. ,-1

-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.

N)

C'" specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

Int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 5 rad part .4

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.
0. 0.. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fl.mass- 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0., 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 6 rad part .6

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kgim**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. .0.

specie branch flux (kg/sec)

dflUx 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

Int.mass 0. 0. 0. 0. 0. 0. 0. 0.

c.)
N)

0"1 4ý:

0.

.0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

.fil.mass .0.

total specie mass on filters.: 0.

airborn mass (kg)

air mass 0. 0. • O. 0

0. 

0

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 

0

0. 

0

0.

0.

deposition rate at each branch (kg/s)

rate 0. 0.

0. 0.

entrainment rate at each branch (kg/s)

rate 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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 

7 rad part .8

specie nodal mass fraction

frac. 0. 0.

0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

.0. 0.

0. 0.

specie branch flux (kg/sec)

dflux O, 0.0.

•O. 0.

specie Integrated branch flux (kg)

int.,mass, 0.. 0.

0. 0.

front filter mass (kg)

fil.mass 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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.
back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. .0. 0. 0. 0. 0. 0.

.0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0O.0.. 0. 0. 0.

O. .0. .0. 0. :0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0.. 0. 0. 0. 0. 0. 0.

0. "0. 0. 0. 0. 0., 0. 0.

entrainment rate at each branch (kg/s)

rate 0. . 0 . 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0,. 0.

species no. 8 rad part i..

specie nodal mass fraction

frac. 0. 1 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. .0. 0. 0. 0. 0.

0. 0.. 0.

specie nodal concentration (kg/ma*3)

conc. . 0. .0. 0. 0. 0. 0. 0..

0. 0. 0. 0. 0... 0. 0.

0.-. 0

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

-0. 0.. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (1'g)

fil.mass 0.

back filter mass (kg)

fil.mass 0. (71
1`10 total specie mass on filters ; 0.

U,

ON• airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 9 rad part 1.5

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. . 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux .(kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

ffl.mass 0.

total specie mass on filters 0.

atrborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0.
0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass .. 0. 0. 0. 0.. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0.. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 10 rad part 1.9

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. O 0.

0. 0. 0. 0., 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. .0. 0. 0. 0.

0. 0." 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.- 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

Int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mnss (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

(C71 total specie airborn mass 0. ,,,
r%) specie mass on duct wall (kg) U,

00 mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. .0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

species no. ii rad part 8.

specie modal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 00.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

afrborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.
deposition rate at each branch (kg/s)

rate 0. 0.

.0.

entrainment rate at each branch (kg/s)

rate 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.

species no. 12 rad part 15.

specie nodal-mass fraction

frac. 0. 0.

0. 0. 0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

,0. 0.

0. 0.

specie branch f-lux (kg/sec)

dflux . .0. 0.

0. 0.

specie Integrated branch flux (kg)

tnt.mass 0. 0.

0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 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.

0.0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.Oo

0;.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

total specie airborn mass ; 0.

specie mass on duct wall (kg)

mass 0. 0.

0. 0.

deposition rate at each branch (kg/s)

rate 0. 0.

0. 0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

N, 0.
r.3

0%C) entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

species no. 13 rad part 20.

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0- 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

filmass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

total specie airborn mass o.

specie mass on duct wall (kg)

mass 0. 0. .0. '0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0O.0. 0. . 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
new time domaeIin reached -

delt = i.00e-03 tend = 3,O0e+00 edint 1-.OOe+O0 Orfint = 0.

steady state results . *• •• *.***$$**,.f$••e$$t•$$$$$$• $$tti$$$tt$$$$$ $$$$$•$•

time =,0. delt = .O0e-03 note ,- i-" :ktotr 144 .- igtot 0 iptot " = 0ý cpu time 1.96e+0Q

branch dat

branch vol. flow mass flow

(m*t3/s), (kg/s)

velocity '(mis).

1

2

3

4

5

6

7

8

9

10

ii

12

13

14

15

i6

5. 296e-Oi

5. 296e-Oi

S. 296e -.0 1

S. 286e7,01

S. 286e ýO,Ir

5.287@-01

5.290e.-01

5 , 294e-.0I

5.;9861-01-

5.30,16-0l

5.302e-01z

5.299e-01

5. 299eý01

5. 292eý-Ol

G. 5351870.1 A. 214e+00,,

6.535e-01 '1.214 ,e+00

6,5 32e -.01 1. 21i4e+00-

6.521e-01.. i.212e0+60

6.520e-Ot i.2;2e400

6.1522e-01 1.2 2e+00ý

-6.52644-01-., i.213e+00..

6.5306-01 1.2146+00.

6.535e-Oi 1. 215e4t100

6-.53Be-01 1;.I*2 15e+00-

6ý. I539e-0i 1V. 2i6p+0OQ_

6.536ei-.i 1.2,15e+00

6.*516e-Of 7:ý262e+c03

6.*508e-01i 7 ' 253e+00

6.502e-01 7.220e+00

node data

node

2

3

4

5

6

7.

8

9

10

tf

12

13

14

15

16

17

Is

P't.

(pa) .(k)

i .0135e+05 2.865e*02

i.0134e+05 2.8,65e*02

1.0131e+05 2. 865e+02

i.0Olie+Q5 2.8656+02.

I.Oi~ie+05 2.865e+02

1. 1 03ie+05 2.8656+02

1.0131.e*05 2.865e+02

i .013.iC+05ý, 2.:865etb2

1.013ie*05 2.865e+62

1". 013iet05 . 2.865e+02,

i.01i3e+05 .2.865e402 ..0130e4 05 -Z.865e+02

I. .O3Oe465 ý2. 9.65e4O02

i.0130e40S.- 2.865e402

1.0i05e*05 2.865.P402

i..00539e+05 2.865e+02

1.0139e+05 2.865e'02

i.0135e*05 2.865e+02

* rho

(kg/me*i3)

1.234e+00

.1. 234e+00

1.233e+00

1 . 233e+00 I . 234e+00

1-. 2346+00

1. 234e+00

1. 234e+00

1. 234e+00

I. 2 33e+00.

1. 233e+00.ý'

i. 233e4+00

1.233e+06

1. 233e$-00.

I.:230e+00

* '230P+00:

1.234e+00

i . 23'e400. ON
heat transfer Information

branch tavg

3 ,2.,865e+02

wall temperatures

branch tavg

4 2.865e+02

wall temperatures

branch tavg

5 2.865e÷02

wall temperatures

branch tavg

6 2.865e+02

wall temperatures

branch tavg

7 2.865e+02

wall temperatures

branch'. tavg

8 2.1165e+02

wall temperatures

branch, tavg

9 2.865e+02

wall temperatures

branch tavg

to 2.865e+02

wal.l temperatures

branch tavg

Ii 2.865e+02

wall temperatures

branch tavg

qQq hco

i.393e-02 75.943e-03

ý(k) 2.8 65e+02

qqq hco

2.571e-Oi -i.226e-02

(k) 2.865e+02

qqq hco

3.963e-01 -1.366e-02

(k) 2.865e+02

qqq hco

*3.906e-Oi -i.360e-02

(k) 2.865e+02

qqq hco

3.393e-01 -1.311e-02

(Sc) 2.85e,+02

qqq ý.hca

2.815e-OI -1.249e-02

(k) 2.865e+02

-qqqhc

2.257e-01 -i. ilie-02

(k) 2.865e+02

qco qro hcI qcI qrI ryn

5.592e+00 1.057e-02 3.363e-03 5.499e+04 0. 0.

qco qro hcI

5.578e+00

qc I qri ryn

0. 0. 1.949e-Oi 6.217e-02 5. 481e+04

qco qro hcI qci qri ryn

0. 0. 5.577e+00 3.OO4e-0i 9.584e-02 5.481eO44

qco qro hc I qc I

5.578e+00 2.962e-01

qri ryn

0. 0. 9.446e-02 5.482e+04

qco qro hcI

5.581 e+00

* qci -qrI ryn

0. 0. 2.572e-Oi 8.202e-02 6.485e+04

qco

0. 0.

qco

qro hci qc. qri" rypn

5.54e+00 2.135e-01 6.803e-02 5.489e+04

qro hci qcI qrt ryn

5.586e+00 i.712e-01 5.452e-02 5.492e+04

qro hci qci qrI ryn

5.588e+00 i.308e-01 4.163e-02 5.495e+04

0. 0.

qqq

i.724e-O0

(k)

hco

-I. 103e-02

2.865e+02

qco

0. 0.

i.21i2e-0-I -1.Oi~e-02

(k) 2.865e+02

qco qro **hcl qci *qri, ryn

0. 0. 5-588e +00 g..196e-02 2.928e-02 5.495e+04

qqq hco qco

0. 0.

qro hc I qcI qri ryn

12 2.865e+02 7.2.35e7O2 -8.908e-03 12 .85e02 .25e02-.9~e035.586e+00 5.487e-02 1.74SP-02 5.492e*04
wall temperatures (k) 2.86,5e+02

branch tavg qqq hco

14 2.865e+03 2.848e'+00 -2.974e-02 0.

wall temperatures (k) 2.865e+02

qco qro

0.

hci qci qri ryn

2.7i7e+0i 2.673e+00 1.751e-01 1.509e+05

**tt.**t*******t*******..******.*.**.*t. * particulate specie data

species no. I smoke

specie nodal mass fraction

.frac. 0.

0.

specie nodal concentration

conce 0.

0.

specie •branch flux (kg/sec)

dflux :0.- "

0.

0.

0.

(kg/rn.*3)

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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.ý

0.

:0 .

0.. . 0.

specie integrated branch flux (kg)

int.mass 0. 0.

0. 0.

front filter:-Mass (kg)

fit.mass +0.

back filter mass (kg)

fIl.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. .. 0.

0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0.

0. 0.

deposition rate at each branch (kg/s)

rate 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. 0. 0.

0. 0. 0. 0.

0. 0.

0. 0.
entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 2 total -ad part

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.
species no. 3 rad part .

specie nodal mass fraction

frac. 0. 0.

0. 0.

O. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0.

01. 0.

specie Integrated branch flux (kg)

int.mass 0. 0.

0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0.

0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0.

0. 0.

deposition rate at each branch (kg/s)

rate 0. 0.

0. 0.

entrainment rate at each branch (kg/s)

0r 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.

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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 4 , -ad part .2
rPa specie nodal mass fraction C71

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.,

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0.. 0. 0. 0. 0. 0.

0. O. 0;. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.. 0. 0. 0. 0. 0. 0.

species no. 5 rad part .4

specie nodal mass fraction

frac. 0. 0 0.• 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.
specie nodal concentration (kg/m**3)

conc. 0.0 . O. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. i0, 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

int.mass 0.. 0. 0.O 0. 0O. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)-

fI.mass 0."

back filter mass (kg)

fil~mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0'. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.ý

total specie airborn mass 0.

specie mass on duct wall (kg.)

mass, 0.o 0. 0.. 0. 0. 0. 0.

,00. . 0. 0.- 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0 . 0. 0. 0 .

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 6 rad part .6

specie nodal mass fraction

frac. 0. 0 0 0. O O. 0. O. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m" 3)

cone. 0. 0. 0. 0. 0.. 0. 00. .

0. 0. 0. 0. 0. 0. 0. 0. -.1
0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie Integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. t0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 7 rad part .8

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m.*3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.
A A V. 0. 0. 0. 0. 0. U. U.

specie integrated branch flux (kg)

0n~as . 0. 0. 0. 0.-- 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg).

air mass 0. 0. 0. O. 0. 0. 0. O.

0. 0. 0.. 0O.0 . 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. b.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. .0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 8 rad part I.

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

.0. 0O.0 . 0. 0. 0. 0.

0. 0.

specie nodal concentration (kg/m**3)

cnnc. 0 0. 0. 0. 0. O. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux fkq/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

0, int.masq 0. 0. 0. 0. 0. 0. 0. 0.
ro 0. 0. . 0. 0. 0. . 0.

C:) front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

species no. 9 rad part 1.5

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie nodal concentration (kg/m**3).

conc. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.

specie branch flux (kg/sec)

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

spdcie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.
back filter mass (kg)

fil.mass 0.

total specie mass on filters :'0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

-0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate .. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 10 rad part 1.9

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0..

specie nodal concentration (kg/m**3)

conc. 0. .0. 0. 0. 0. 0., 0. 0.

.. 0. 0. 0. 0. 0. 0. 0.

' "0. " • 0. 

;

specie branch flux (kg/sec)

dflux 0. 0. O,0. 0. 0. 0..- 0; 0.

0. 0. 0. 0. 0. 0. 0. 0.

-specie integrated branch flux (kg)

Int;mCss 0. " 0. 0. 0. 0. 0. 0. ' 

0

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

-.I fil.mass 0.

..:.,.i 

:
total specie mass on filters ; 0.

airborn mass (kg)

air mass 0. 0.

0.

0.

0.

0.

0.

0.

0.

0.

total specie airborn mass ; 0.

specie mass on duct wall (kg)

mass 0.. 0.

0. 0.

deposition rate at each branch (kg/a)

rate . 0. 0.

0. 0.

entrainment rate at each branch (kg/s)

rate 0. 0.

0. 0.

0.

0.

0.

0.

O.

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.

0.

0.

0.

0.

0.-

0.

0.

0.

0.

species no. Ii rad part 8.

specie nodal mass fraction

frac. 0. 0.

0. 0.

0. 0.

specie nodal concentration (kg/m-*3)

conc. 0. 0.

0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0.

0. 0..

specie Integrated branch flux (kg)

int.mass 0. 0.

0. 0.

front filter mass (kg)

Mil.ass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 01.- 0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

.0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0. 1 0. 0. 0." 0. 0.
0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

ettrainment rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

species no. 12 rad part 15.

specie nodal mass fraction

frac. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0.. 0. 0. 0. 0. 0. 0.

0. 0..

specie nodal concentration (kg/m**3)

conc. 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

specie branch flux (kg/sec)*

dflux 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

specie integrated branch flux (kg)

int.mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

0. 0.

total specie airborn mass ; 0.
specie mass on duct wall (kg)

mass 0.

0.

0.

0.

deposition rate at each branch (kg/s)

rate 0. 0.

0. 0.

entrainment rate at each branch (kq/s)

rate 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.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 13 rad part 20.

specie nodal mass fraction

frac. 0.

0.

0.

0.

0.

0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

0. 0.

0. 0.

specie branch flux (kg/sec)

dflux 0. 0.

0. 0.

specie integrated branch flux (kg)

tnt.mass 0. 0.

0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

airborn mass (kg)

air mass 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.

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. C

0. C

total specie airborn mass ; 0.

specie mass on duct wall (kg)

masS 0. C

0o. .

).

0.

0.

0.

0.

p. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.
deposition rate at each branch (kg/s)

rate 0. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. 0. 0.

entrainment rate at each branch (kg/s)

rate 0.. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. 0. 0. 0. O 0.

***************************** ...... *************** * ......... .. *..... .* * * * ** * *** ********* ***************.**.****************

end of time step cards reached -- normal. exit

time = 9.9905e+02 delt = 5.00e-02 ns tep =23481 ktotr =27086 igtot = 0 iptot = 298699 cpu time = 1.47e+03

branch data

branch vol. flow- mass flow velocity

(mr*3/s) (kg/s) (m/s)

i 4.732e-01 5.839e-01 i.085e+00

2 4.732e-01 5.83ge-01 1.085e+00

3 4.951e-01 5.559e-0i i.t35e+00

4 4.947e-Ol 5.558e-01 i.134e+00

5 4.941e-Oi 5.557e-01: 1.i33e+00

6 4.935e-0i., 5. 556e-0 1, i.i32e+00

7 4.929e-0l 5.555e-0t 1.130e+O0

a 4.923e-Oi 5.554e-0i 1.129e+00

.9 4.916e-01 5.554e-01 1.127e+00

I0 4.910e-0i 5.553e-0 1.126e+00

li 4.904e-O0 5.552e-Oi 1.124e600

12 4.898e-01 - 5.552e-01 i.123e+00

13 d.897e-01 5.551e-0 6.7tle400

14 4.935e-01 5.549e-O0 6.763e+00

15 4.949e-01 5.547e-01 6.782e+00

16 4.931e-0i 5.546e-01 6.758e+00

node date

node p t rho

(pa) (k) (kg/m**3)

I i.0135e÷05 2.865e*02 1.234e4o00

2 i.Ot34e+05- 2.865e+02 1.234e+00

3 1.0132e+05 3.151e+02 1.i2:1e+00

4 l.0132e405 3.151e+02 1.121e+00

5 t.0131e405 3.148e+02 I.i23e+00

6 i.0131e+05 3.145e+02 i.124e+00

7 i.013ie÷05 3.141e+02 l.125e+00

8 i.0t30e+05 3.138e+02 1.I26e+00

.9 1.0130e+05 3. 134em02 1. i27e+00

10 1..0130e05,,:, 3.13ie*02 l.129e+00

Ii 1.0129e405 3. t27e+02 *.130e+00

12 f.O29e+05 3. 123e402 t.131e400,

1J3 .0129p+05.- 3. 1204P+02 I . 137,+00

Ul
N) 14

15

16

17

18

¶ .0;26e4 05

, .0105+05 I .0olie+05

i .0138e+05

i .0135e+05

3.116:+02

3.1 6e 402

3. 143e+02

3. 144e+02

2. 865e+02

1. 134e+00

1. 13le+00

i. 12 ie+00

1. 125e+00

i. 234e+00

heat transfer information

branch tavg qqq

3 3.149e÷02 -2.315e+02

wall temperatures (k)

branch tavg qqq

4 3.146e÷02 -2.352e+02

wall temperatures (k)

branch tavg qqq

5 3.143e+02 -2.387e+02

wall temperatures (k)

branch tavg qqq

6 3.139e+02 -2.4t7e+02

wall temperatures (k)

branch tavg qqq

7 3. 136e+02 -2.440e+02

wall temperatures (k)

branch tavg qqq

8 3.t32e+02 -2.444e+02

wall temperatures (k)

branch .tavg qqq

9 3.128e+02 -2.459e+02

wall temperatures (k)

branch tavg qqq

10 3.125e+02 -2.470e+02

wall temperatures (k)

branch tavg qqq

11 '3.12ie+02 -2.47Re÷02

hco

3.055e+00

3.025e+02

hco

3.030e+00

3.020e÷02

hco

3.004e+00

3.0 5e402

hco

2.978e+00

3. 009e.02

hco

2.953e+00

3.004e+02

hco

2.933e+00

3.000e.02

hco

2. 909e+00

2.996e÷02

hco

2. 885e+00

2.99 1e+02

qco qro

-i;266e÷02 -7.205e÷01

qco qro

-1.213e+02 -6.941e+0i

qco qro

-1.160e+02 -6.677e÷01

qco qro

-1.110e+02 -6.426e+01

qco qro

-1.062e+02 -6.187e÷01

qco qro

-t.025e+02 -5.999e+01

hc f qcl

5.017e400 -1.603e+02

hci qcI

5.Ci8e400 -i.631e402

hci qci

5.016e400 -i.657e402

hcI qct

5.014e+00 -1.680e+02

hci qci

5.012e+00 -1.698e+02

hcI qcI

5.610e+00 -'i.703e402

qr i

-7. 118e÷01

qr t

-7.210e+01

qrl

-7.299e+01

qr i

-7.368e+01

qrl

-7.422e+01

qri

-7.4 16e401

qri

-7.442e+01

qri

-7.458e+01

qri

-7.463e÷0t

ryn

4.366e+04

ryn

4.37 1e+04

ryn

4. 374e+04

ryn

4.377e+04

ryn

4.379e+04

ryn

4.382e+04

ryn

4.385e+04

ryn

4. 388e+04

ryn

4. 392e÷04

qco qro hcl qcl

-9.821e+0i -5.781e+01 5.008e+00 -1.715e+02

qco qro hcl qci

-9.408e+01 -5.572e.01 5.006e÷00 -1.725e+02

hco qco qro hct qci

2.861e400 -9.014e*Oi -5.371e+01 5.005e*00 -1.732e402
wall temperatures (k)

branch tavg qqq

12 3.117e+02 -2.482e+02

wall temperatures (k)

branch tavg qqq

14 3.129ge02 1.454e+03

wall temperatures (k)

2.987e+02

hco qco qro

2.837e+00 -8.640e+Oi -5. 17ge+Oi

2.983e+02

hco qco. qro

4.414e*00 -1.Ogie+03 -4.7i3e+02

3.204e+02

hc I qc I.qri

5.003e+660 -i.736e+02. -7.456e+Oi

ryn

4. 395e+04

hci qci qrf ryn

2.439e÷O 1.323e+03 i.304e*02 1.206e+05

****..* ..... *.. *...*....* s.****particulate specie data ********.***** ***********.

species no. smoke

specie nodal mass fraction

frac. 0. 0.

4.586891e-05 3.08097e-05

3.i39i5e-09 0.

specie nodal concentration (kg/m**3)

conc. 0. 0. 5. 17094e-05 3.47719e-05

3.51087e-09 0.

specie branch flux (kg/sec)

dflux 0.1 0.

1.71108e-05 1.14860e-05

specie integrated branch flux (kg)

int.mass -3.60396e-06 -3. 17228e-06

2.42867e-02 1.62485e-02

front filter mass (kg)

fil.mass 4.80655e-03

back filter mass (kg)

f1l.mass 0.

total specie mass.on filters 4.807e-03

airborn mass (kg)

air mass 0. 0.

i.99665e-05 i.34264e-05

9.79835e-10 0.

total specie airborn mass i.038e-03

specie mass on duct wal I (kg)

mass 0. 0.

8.-03806e-03 5.39854e-03

3.32871.-Od 3.3287ie-C4 2.2416ge-04

2.0684le-O5 i.38789e-05 9.30777e-06

3.73297e-04 3.73287e-04 2.51637e-04 .2. 33705e-05 i .56994e-05 i .05409e-OS

1.85049e-04 1. 24590e-04 8. 38438e-05

7.70627e-06 5.16764e-06 3..46312e-06

2.59534e-O1 1.7578ge-O1 i. iBlSe-Oi

1 .08497e-02 7.2311i7@-03 4.890895@-03

i.50882e-04 1.01504e-04

6.23883e-06 3.12745e-09

1.69545e-04 1.14180e-04

7.07348e-06 3.53708e-09

5.63958e-05 3.79147e-05

1.73537e-09 i.73815e-09

8.01375e-02 5.39381e-02

2.40382e-06 2.40320e-06

6.82509e-05

3.1333ge-09

7.68578e-05

3.51248e-09

2.5477ie-05

1.74095e-09

3.62299e-02

2.40225e-06

3.73287e-04 3.73287e-04 9.71643.-05 6.54662e-05 4.40883e-05 2.96770e-05

9.0240ie-06 6.06t98e-06 4.07009e-06 2.73127e-06 i.36577e-09 9.7473ie-iO

8.37i7ge-02 5.698t6e-02 3.86803e-02 2.62003e-02 1.77084e-02 i.19343le-02

3.6,1835e-03 2.42034e-01 0. 3.77453e-11 0. 0.
deposition rate at each branch (kg/s)

rate 0. 06.07779e-05 .

5.65410e-06 3.79927e-06 2.55i6ie-06

entrainment rate at each branch (kg/s)

rate 0., 0. 0.

0. 0. 0.

species no. 2

4.0964Be-0S 2.75945e-05 i.85793e-05 i.25033e-05 8.410i9e-06

i.71278e-06 0. 7.54906e-10 0. 0.

0.

0.

0.

0.

0.

7. 55023e- 10

0.

0.

0.

0.

total rad part

specie-nodal mass fraction

frac. 0. 0.

0. 0. 0..

specie nodal concentration (kg/m**3)

conc. 0., 0.

0. 0.

0. -. 0.

specie branch flux (kg/sec)

dflux 0. 0.

0. 0.

specie integrated branch flux (kg)

Int.mass 0. o. 0. 0.

front filter mass (kg)

fil.mass 0.

back filter mass (kg)

fil.mass 0.

total specie mass on filters 0.

alrborn mass (kg)

air mass 0. 0.

0. 0. 0. 0.

total specie airborn mass 0.

specie mass on duct wall (kg)

.mass 0. 0.

0. 0.

deposition rate at each branch (kg/s)

rate 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.

0.

0.

0.

0.

*

0.

0.

0.

0.

0.

0.

0.

0.

0. 0. 0. 0.

0. 0. 0. 0.

0.

0.
entrainipent rate at each branch (kg/u)

rate 0. .0.

0. 0. 0.

0..

0.

0. 0.

0.

0.

0.

0.

0. 0.

.0.

species no. 3 red part .,

specie nodal mass fraction

frac. 0. 0.

9.77434e-08 9.76277"-0B

4.R4327e-1t 0.

specie nodal concentration (kg/m**3)

conc. 0 0. .. O1i9le-07 1. 10183e-07

5.44765e-1i 0.

specie branch flux (kg/sec)

dflux 0. 0.

5.42197e-08 5:;41487e-08

specie integrated branch flux (kg)

int.mass -8.9iO80e-12 -7.84346e-i2

8.55795e-06 8.51403e-06

front filter mass (kg)

fil.mass 8.37762e-06

back filter mass (kg)

fil.mass 0.

total specie mass on filters 8.378e-06

airborn mass (kg)

air mass 0 0. 0.

4.25479e-08 4.25448e-08

i.5i175e-1t 0.

total specie airborn mass : 6.460e-07

specie mass on duct wall (kg)

mass 0 0.

9.95230e-i2 9.92752e-12

deposition rate at each branch.(kg/s)

rate 0. 0.:

6.20542e-i4 6.20500e-14

entrainment rate at each branch (kq/s)

rate 0. 0.

0. 0.

9.831 OOe-08

9.751 12e-08

1. 10246e-07

1. 16176e-07

5.46522e-08

5.40778e-08

8.82546e-06

8. 47026e-06

1. 10246e-07

4. 25420e-08

1.00902e- 11

9.9022 e- 12

6.20898e- 14

6. 20460e- 14

9.83100e0-08

9.73938e-08

1.10246e-07

1. 1O169e-07.

5.45775e-08

5.4007le-08

8.77966e-06

8.42662e-06

1.10246e-07

4.25392e-08

9.81983e-08 9.80857e-08

9.72756e-08 9.7t565e-08

9.79724e-08 9 *78583e-08

4.85186~e-ii 4;84758e-ii

1.W1208e-07 1. 10199e-07

5.48735e-ii 5.43406e-ii

1.10231e-07

1.10162e-07

5.45055e-08

5.39306e-08

8.73508e-06

8.3818Ie-06

4.25634e-08

4.25365e-08

1.10219e-07

l.10i54e-07

5.44338e-08

2.69221e@-1

8.69060e-06

4.16849e-09

4.25586e-08

4.25337e-08

5.43623e-08

2:68905e-ii

5.42909e-08

2.68605e-ti

8.64624e-06 8.60202e-06

4. 15237e-09 4. 13626e-09

4.25545e-08

2.1 882e-11

4.255IOe-08

i.50798e-ii

1.00683e-il i.00460e-ii 1.00233e-i 1.00002e-11 9.97655e-12

9.87635e-12 0. 6.92048e-i5 0. 0.

6.20812e-14

6.2042ie-14

6.20742e-i4 6.20682e-14 6.20631e-i4 6.20587e-14

0. 4.37591e-17 0. . 0.

N-I 0.

0.

0.

0. 0.

0.

0.

0.

0.

0. 0.

0.
species no. 4 rad part .2

specie nodal mass fraction

frac. 0- 0.

8.96453e-08 8.95284e-08

4.4379le-ii 0.

specie nodal concentration (kg/m**3)

conc. 0. 0.

i.01062e-07 1.01042e-07

4.99170e-1l 0.

specie branch flux (kg/sec)

dflux 0. 0.

4.97216e-08 4.96504e-08

specie integrated branch flux (kg)

int.mass -4.00986e-i2 -3.52956e-12

7.19954e-06 7.i5867e-06

front filter mass (kg)

fil.mass 7.03258e-06

back filter mass (kg)

fil.mass 0.

total specie mass on filters 7.033e-06

airborn mass (kg),

air mass 0. 0.

3.90228e-08 3.90153e-O8

1.38522e-il 0.,

total specie airborn mass : 5.926e-07

specie mass on duct wall (kg)

mass 0. 0.

2.185i6e-li 2.t7806e-11

deposition rate at each branch (kg/s)

rate 0. 0.

i.4857te-13 1.48543e-13

entrainment rate at each branch (kg/s)

rate 0. 0.

0. 0.

9.02179e-08

8.94106e-08

9.02179e-08 9.010SOe-08

8.92920e-08 8.91725e-08

1.01172e-07 1.01i72e-07 l.01146e-07

1.01023e-07 1.01004e-07 1.00985e-07

5.01537e-08 5.00794e-08 5.00075e-08

4.95793e-08 4.95083e-08 4.94320e-08

7.44874e-06 7.40615e-06 7.36455e-06

7.11795e-06 7.07738e-06 7.03609e-06

8.99913e-08 8.98768e-08

8.90522e-08 4.44659e-il

1.0i123e-07 i.OllOie-07

1.00966e-07 5.02899e-ii

4.99358e-08 4.98643e-08

2.46734e-ii 2.4642ie-11

7.32308e-06 7.28175e-06

3.49745e-09 3.48265e-09

8.97615e-08

4.44226e-ii

f.01081e-07

4.97970e-Ii

4.97929e-08

2.46i24e-t1

7.24057e-06

3.46790e-09

1.01i72e-07

3.90079e-08

1.Oi172e-07 3.90554e-08

3.90006e-08 3.89932e-08

3.90464e-08 3.90381e-08 3.90303e-08

3.89858e-08 1.94184e-il 1.38189e-i1

2.22586e-ii 2.21924e-1i 2.21258e-11

2.17085e-1i 2.16355e-il 0.

i.48762e-13 i.48724e-i3 1.48690e-13

i.48515e-i3 i.48487e-i3 0.

2.20586e-il 2.19906e-li

1.5140ge-14 0.

1.48658e-13 i.48628e-13

1.04704e-16 0.

2.19217e-il

0. -

1.48600e-13

0.P . ,

0.

0i*

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 5 rad part .4
specie nodal mass fraction

frac. 0. 0.

5.12010e-08 5.1i337e-08

2.53456e-ll 0.

specie nodal concentration (kg/m**3)

conc.- 0. , 0.

5.77215e-08 5.77098e-08

2.85083e-1.1,, 0.

5.15304e-08 5.15304e-08 5.146540-08 5.14OO0e-08 5.13341e-08 5. i2675e-OB

5.i0660e-08 5.0 9 978e-08 5.09291e-08 5.08599e-08 2.53954e-ii 2.53704e-ii

5.77869e-08. 5.77869e-08 5.77718e-08 5.775BOe-08

5.76983e-08 5. 7 6 870e-08 5.76756e-08 5.76640e-08

specie branch flux (kg/sec)

dflux 0. .0.

2.83983e-08 2.83573e-08

specie integrated branch flux (kg)

int.mass -2.22770e-12 -i.96087e-12

4. 10223e-06 4.07885e-06

front filter mass (kg)

fIl.maSS 4.00675e.06

back filter mass (kg)

fil.mass 0.

total specie mass on filters 4.007e-06

airborn mass (kg)

air mass 0. -0.

2.22879e-08 '2.22834e-08

7.9112te-12 0.

total specie airborn mass ; 3.385e-07

specie mass on duct wall (kg)

mass 0. 0.

3.77325e-1i 3.76088e-li

deposition rate at each branch (kg/s)

rate 0 0. 0.

2.57i59e-13 2.57108e-i3

entrainment rate at each brainch (kg/s)

rate 0. 0.

.0. 0.

2.86466e-08 2.86039e-08

2.83i65e-08 2.82756e-08

2.85626e-08

2.82318e-08

2.85214e-08

1.40915e-ii

5.77451e-08 5.77330e-08

2.87217e-ii 2.84399e-il

2.84803e-08 2.84392e-08

i.40735e-li 1.40565e-li

4.i4925e-06 4.12570e-06

1.98414e-09 1.97572e-09 4.24477e-06

4.05556e-06

4.2204ie-06

4.03236e-06

4.19662e-06 4.17289e-06

4.00875e-06 1.9926te-09

5.77869e-08 5.77869e-08 2.23073e-08 2.23020e-08 2.2297le-08 2.22924e-08

2.227904-08 2.22746e-08 2.22702e-08 2.22657e-08 1.10903e-it 7.89221e-12

3.84417e-li 3.83263e-Il 3.82103e-1i

3.74833e-li 3.73561e-lt 0.

2.57503e-13 2.57436e-13 2.57374e-13

2.5705.e-13 2.57007e-13 0.

3.80931e-il 3.79746.-il

2.61413e-14 0.

2.57317e-i3 2.57263e-13

1.81222e-i6 0.

3.78545e-tl

0.

2.5721te-13

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 6

qpecie nodal mass fraction

Frc. 0 0. " 3.23457.-OS

3.21422e-08 3.21007e-08 3.20589e-OS

1.59139e-il 0.

rad part .6

3.23457e-08 3.23056e-08 3.22652e-08 3.22245.-O 3.21835e..08

3.20167e7OR 3.19743e-08 3.19316e-08 i.59446e-ii .I.59291e-11
I%3

specie nodal concentration (kg/m*03)

conc. 0. 0.

3:.62356e-08 3.62290e-08

i..78997e-ii 0.

specie branch flux (kg/sec)

dflux 0. 0.

i.78278e-08 .1.78025e-08

specie integrated branch flux (kg)

int.mass -1.782i6e-12 -1.56869e-12

2.63505e-06 2.6204ie-06

front filter mass (kg)

flf.mass 2..57515e-06

back filter mass (kg)

fil.mass 0.,

total specie mass on filters 2.575e-06

airborn mass (kg)

air mass 0. 0. 1.399t6e-08 i.39891e-08

4.96726e-12 0.

total specie airborn mass 2.125e-07

specie mass on duct wall (kg)

mass 0. 0.

4.9i334e-ft 4.892fe-ff

deposition rate at each branch (kg/s)

rate 0. 0.

3.27235e-i3 3.27177e-13

entrainment rate at each branch (kg/s)

rate 0. 0.

0. 0.

3.62730e-08

3.62226e-08

I .798Iie-08

i. 77773e-08

2.72434e-06

2.6058le-06

3.62730e-08

S.39866e-08

4.99955e-i i

4.88284e- if

3. 27632e- 13

3.27120e- 13

3.62730e-08

3.62163e-08

1.79551e-08

1.77520e-08

2.70908e-06

2,59127e-06

3.62730e-08

t.39841e-O8

3.62642e*0S 3.62563eO08 3.6248ge-08 3.62421e-08

3.62099e-08 3.62035e-08 1.80331e-ti 1.78563e-li

1.79295e-08 1.79040e-08 1.78786e-08 1.78532e-08

i.77249e-08 8.84742e-12 8.83620e-12 8.82574e-12

2.694i8e-06

2.57644e-06

2.67932e-06 2.6645ie-06 2.64976e-06

t.28084e-Og 1.27551e-09 1.27022e-O9

1.40026e-0. i.39996e-08 1.39967e-08 1.39941e-08

1.39817e-08 1.39792e-08 6.9630Se-12 4.95521e-12

4.98558e-ii 4.97152e-i1 4.95729e-li 4.94287e-i1 4.92824e-il

4.86724e-ii 0. 3.407fge-i4 0. 0.

3.27553e- 13

3.27063e- 13

0.

0.

3.2748le-i3 3.27415e-13 3.27353e-13 3.27294e-13

0. 2.30633e-i6 0. 0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

species no. 7

specie nodal mass fraction

frac. 0. 0. 3.20275e-08

3.t1832e-08 3. 17694e-08 3.17254e-08

1.57412e-11 ,0.

specie nodal concentration (kg/m**3)

conc ' 0. 0. 3.59i61e-08

3.58646e-08 3.5855ie-08 3.58458e-OR

rad part .8

3.20275e-08 3.19852e-08 3.19426e-08 3.18998e-O8 3.18566e-08

3.i6SiOe-08 3.10363e-08 3.159t4e-08 i.57736e-ii 1.575 7 1e-I1

.,3.59161e-08 3.59046e-08 3.59938.-08 3.58837.-OS 3.58740e-08

3.58365e-08 3.58272e-08 3.58177e-08 1.7R53GP-i i.76635e-il
t.77055e-1ff 0. specIe hranrh flux Ikg/sec)

dflux 0. 0. f.764396108 4 .76173e-69

specie integrated branch flux (kg)

fnt.mass -8.91OSOe-f3 -7.84346e-13 2.471--89e-06- 2.45724e-06

front filter-mass (kg)

fIl 'ma-ss 2."41 217e6 -06.

back filter mass (kg)

rI .mass 0.

total §pecie mass on filters 2.4i2e-06

airborn mass (kg)

air mass 0. i.38B43e.08 .0. 1|'35447.-OS

4.91336e-12 0.

total specie airborn mass-, 2. 1O3e-07

specie mass on duct walI (kg)

mass 0. ' 0. 7.75086e-it 7.72305@-li

deposition rate at each branch (kg/s)'

rate 0. 0. 5.44736e-13 5.44595e-13

entrainment rate at each branch (kg/s)

rate 0. 0. 0. 0.

1.78O46e-Oil 1.77770e-08 I.77503e-O9, l.77236e-OB l.76970e.08 1'.76704e-08

f.J5 904e -08 1.756 4 tl,- 08 .75361e-08, 8.7525-le- 12 8.740796- 12,, .7 29gRe -12.'

2.56123e-06 2.54597e-06 2,S3105e-06 2.51618e-06 2.50136e-06 2.48660e-016

2.44265e-06 2-.42812e-06- 2.4133e-06 f. 19938eo-09 1. l94O~e-09 1. 18885e-09

3.5916ie-08

i.38375e-OB

3T.59J6 .384 e-OS 1 e-08

7.git49e-If

7.69492e-11

1.38638e-0O

1.38339e-08 1.38g~eO8 .38557e-08 1.39520e-Og 'l.3R883Og2e-008 15.B8931e-12 4.4Oi7le-i2

7.66644e-11 0., 7. Il .227e'- I t 5.3623e- 14 0. ,-7.,77835.- I"

5.4563e-13 5.45488e-t3 5.44453e-i3 5.453256-13 5.443i2e-13 0. 5.4517Oe-3 5.45023e-13 3.83767e--16 5.4480e-13 0. 0.

0.

0. 0.

0. 0.

0. 0.

0. 0.

0. 0:

0.

species specie no. 8 nodal mass fraction " frac. 0. 0. i.92172e-08 f.93438e-O8 -i.91914e-O0 ".5 1.91654e-O8 lIm-12 0.

sp•cie nodal conrentratIon (kg/eOt3)

ronc. 0. 0. 2. 16645e-08 2.16924e-08 2. 16595e:O8 I ,0690e- 2. .6546e-08 t 0 , 

sperIe branch Flux (kg/sec.)

t0 

0.I0 f.07535e-OR

red part I

i.348-0 .93,18se-OB 1.9!937e-OS 1.92684e-7O8 t.92429e-OS t.9t1392e-OS 1;91t29e-0B 1..90963.-OSa 9.53029ep-12 9.52045e-i2

2,.16924e-08

2. A6496e-OS

t. 07372e-Ol1

2. 16861e-O8 2. 16447e-08 2. M6R02e.-OR

2. 16397e,- OS

.2.16747P-O8 2,16695e t.07786e-I OS f i.06723e-ill

l.0721e-. iO7OSi~e -OR 1. O659lRo-flR 1.06741e-OS
1.06584e-08 i.06427e-08 i.06270e-08 1.06114e-08 1.05946e-OS 5.28820e-12 5.28ilte-12 5.27484e-12 O' ~ ~ ~ ~ ~ ~ ;,1)•:; ~ ~ ~ ~ ,;-~• ~ ~ •":..•••; ~ ~~ ~ ~ ~ 2 ~ ;£•,•O: ~ ~ ~ 0 •• ',•k'• 1) 1 i(r C"U ;•:. 1 6•3 t

specie integrated branch flux (kg)

Int.mass -8.9i080e-13 -7.84346e-13 1.60198e-06 I.59279e-06

A '545fg:17."-06; I.53935e-06 1.53055e-06 1.52179e-06

'ront f I I ter mass (kg) - ' Ci Oh C

back filter mass (kg) "

tfitmass i 0e t ,5!2e i 9 0 H, j -lI 

-jtbt a v sI-pe Ici1- mas s on Ii fTilters i.Si2e-06

A. 583800-06

1 .5i2S5e-06

"4',4 O3

I .574A~e-06 I .565920-06

7.52027e-10 7.48807e-10

1.55703e-06

7.45646e-tO

I ~ o. )C.i:~ li~~* C C~ ij;

airborn mass (kg)

air mass 0. 0.

8.36530e-09 8.36335e-09

t t l p c 2.96876e- 12ý 0 . 0

total specie airborn mass 1.270e-07

specie mass on duct wall (kg)

'mass 0. 0"0.

7.32845e-ii 7.30452e-1i

deposition rate at each branch (kg/s)

, te i . C) 0.

4.96694e-i3 4.9658ie-13

entrainment rate at each branch (kg/s) I '1 .i: v.-I.'3

2.16924e-08

8.36144e-09

(I

2. 16924e-08

8. 35954e-09ii

8 1l736le-09

6~.35764e-09

0

8.37136e-09

8.3557 le-09

3A O

O

8. 36924e-09 8. 36723e-09

4.C6191e-12 2.96i61e-12

Tz"At t S7 4-1 12 7,"'4ý4 j2 7 1 1 7 b5e-1i1

7.28024e-1i 7.25562e-11 0.

39Soi, go I i~ 7'? 1 y 14e.- 8 1-4" iý65iý 32O 11 

5.07759e-14.- 0. 0.

0~74'496-1321 ) iýg33iiu"§7e~3 7 0 4 3 ~ 69 2 5 e'1 3 '41A68'00-i 3

4.96468e-13 4.96355e-i3 0. 3.49983e-16 0. 0.,

rate 0.- 0.

0.

0.

0.

:3 "d .C7-OP

0.

0.

JAI 1 A01

0.

~0. _0

08

0.

0.

0.

0.

.3 '12-i. 83Oill

!;"'.::ý:ý' w4aý_, !Vf!L species no. 9 rad part 1.5

r AV 0f . 0. 6.45323e-08 6.45323e-08 6.44459@-08

6.40949e-08 6.40057e-08 6.39160e-08 6.38256e-08 6.37347e-08

isp46,ie nodal c6nd iifrýAt ion (kg/m**3)

6.43590e-08 6.42715e-08 6.41835e-08

6.36432e-08 3.17789e-it 3.17438e-ii

6c6nc- 6":,. 0. 7.23675e-08

7.22574e-08 7.22372e-08 7.22172e-08 • ' " :> ~~3 -,"567'O3e 'i. 1 :• 0 ;! ' '•~ •; •7 ' • •; :y e ;i ;IiO. . .10 .

specie branch flux (kq/sec)

dflisx 0. 0. 3.58746e-08

specie integrated branch flux (kg)

Int.mas .3.l17Re-i2 -2.74521e-i2 5.36713e-06

7.23675e-08 7.23429e-08

7.21974e-08 7.21775e-08

..'i:i.;,iA._\':'0 C' 031 I0;.' . 1 • 5

7. 23200e-08

7.21575e-08

I 4 C k3 C-Ai)(

7.22983e-08 7.22775e-08

3.59412e-it 3.55843e-it

C)il I ' , ''12 0 0 0

3.58183e-08 3.57638e-08 3.57095e.-O 3.56552e-08 3.56011P-08

I5u.336e-06 '5.30595e-0 I R.-5I'0 5.24609-06 54.215e- Al

5.3361Se-06 5.30595e-06 5.27582?e-06 5.24579P-06 5.21587@-06
S.iB86Oe06em 5.15637e-06 S. 1267_9e-06 -5.0973,ie-06 5.06732e-06 2.51894e-,09 .2.5080 1e-09 2.49747e-09ý

front fl1ter mass (kq)

f I I.mass: 7" 5.06478e-06

back filter mass- (kg)"'

fi-l'•..mas•s 0.;

total-specie mass on filters 5.065e-06

airborn mass Ak"g) ( :.

air mass 0.0 . 7.23675e-08

2.79667e-08 2.78928e-08 2:.7885ie-08

9.89870e-.i2 0.

total specie airborn-mass 4.237e-O7

specie-mass 6nr-'duct-wallI-(kg),

mass 0. 0. -536370e-iO

5.26478e-10 5.2475te-10,,5.23000e-10

deposit-ion rate at.-each branch-.(kg/s)

rate : 0 .- ."i 0 .A;v-.- w 3T55899e-12"

3.55258e-t2 3-.55160e- 12 3-:55062e- 12.

-. entrainment rate at each brinch (kg/s)

rate 0. 0 0..

0.- . 0.

species no. 10

specie,-nodal mass.fraction:

frac. 0.. 1"'Y. 0:.• .0972lle07

I.08947e-07 i.08789e-07T 1-.08630e-07 5°. 3B855e-1 0 .-

specie nodal concentration (kg/m-*3)

conc. 0.- 0. V:- .23043e-07 - I.2282ie-07 i.22780e.07 1.22739e-07

.-. : -. ~- 6.06096e-i i 0.

snece. branch-flux fkg/sec) -

df lux O- 0:- . 0 6.09957e-08,

6.0418,47-08 6.03233e-08 6.02283e.-08

%sPCrIP Infecrated brantch flut'x (kg) .

*Int masq 5 4Ae-2-4.70i§000-i2 si.13227e-06

. -,+ 06. _214e R..7,7043e-06,: :871965P-06

* f ront .4f i I ter mas, (kqr):"

j fIi-raq Ai200

7:23675e-08 '2_79.3374-08_2.79248.-OS 2.79164e-08 ?,790a4e-OS2.7,8175e-08, 2:7116980-08 2:78621e-0B i.73,77ge-li 9.ý8746jqiz12

5. 3476 1e-10.

5. 21224e-10

3; 55778e- 12

3.54964e-t2:

0.

0.

5.331446-iO-- 5z3i510e-iO oie-10 5.!9857e-i0 5.'2o0. 3".64760e-13 0. 0. -

3%55665e12

0.

0.

3.55558e-12. 3.55456e`12

2.150274e-15 0..

0. 0.

0. 0.

3. 55357e-12

0.

-0. : _ .- .•..

0 .

rad part 1.9

1.09721e-07

1.0847.1e707

1.23043e-07

. 22698e-07

6.08966e-08

6.013.14e-08

9.07914e-06

8 .66907P-06

I .0966e-07 I .094d-0 O5-07ge 

1.08V310e07 1.08148~e-07: 5. 400 le,-AI.

i'.09i36-07

5. 39.37ge- I.

i.22994e-07. I.221945e-07 61.,212.9704 4i--r0171 '1.202 866 2ee- 01 i.22658e.-07. i.226i7e-07 .04.Il 643ei

6,08006e-08 .6.07048P-0Pl: 6.06092eý-OA 6.517.O

6.00322e-OR 2., 9646e~-,i 2.99204e-1129i56eI

9:.02-724P.-70f R: W55OP 06 9.92395eý-06 8.87258P-06

8_6t7.59e-06 4:211I 179P0O19 4.;26486e-09 4.J24695ie-09eý

200 "LU,
back, fill ter mass,

total specie -mass on,,f1.jlters R;: 1,~3e-06 ý3

airborn mass (kcjg

air mass 0. 0. 1. 23043e-07 4.r7•2A8e.08 ,,,4 .740880e7OB 4 . 73931e•08

•;• ,I- t.68i95e-lI j0. 01ý), O g?;"';ý 0-ji

,to~taI. spec,~ej a born,,mss- 7. 203e-07

specie mass on duqojVL2wahl-j(kg)p:l

mass 1. (0. 0 .43395e!Q9

Si. 40708e-09 i. 40239e-09 .3-'764e-09

deposition rate at each branch (kg/s)

rate ".o~ 0 ';:• 0 "I .opp p . .9 • 5,'68e •>t2

9.48737e-i2 ý9.48422e-12 9.9••48,lfot!ý.2

ehitratainment eratte; a~t eachit)ranch (kg/s)

rate 0. 0. . LE C)

0. 0. 0.

CA~7 I~ (-~ A,~ j w ~ Cij ..... '.C

1.23043e-07 4.,74915e-.08 4.74738e-08 4.74569e-08 4.744606-08

0 0 a i2 l) qO 0'.4"10i0e10t id.7, 0ý) 3 5eoB c~ 2.520- Q~ ")'-1 i i

v * 4723A 0) A ) 03A .A3IQ G .ICA I iI . -

1 25,18 ec7,ePD9 1 17!519m-Q9 4O,99 -42O 1 i.4165e70 1 4j )-,ep0 9

1.39282e-09 0. 9.74659e-13 0. 0.

19 c50192et,ý112 j9ý50038e0-12 A9o,49700eý-!ý2 p 9 ,49.7-4ej-i-2 p ~95Oj2

M c,417794e r) .2 !O,.) a.ap e :3i . 46of682&i5e:1,j5Opp'-, o

0. b.A:g • ): 0.

0. 0.

0.

0.

0.

0.

0.

0.

0. species no. I1 C) rad part 8):-

spec tIe ýnoda I ;,•ras') f rac~iti onu ,,., fl.lt '10;

frac. -0, J

-. *•3:8076e.-08 -1.79600e-08

i.85556e-ii 0.

specie nodal concentration (kg/m**3)

i : 4 A- 9E; - 10 2 * .. 1). 

cone. 0 . 0.

4.29607e-08 4.284d8e-08 E.•;: • '• . A &:: d,(L • 2 y 0 8 7 "(i te-,.1i 0

l: 0.O

d f l u x • . i oS:t•eJ "00 O b .

specie Integrated'branch flux (kg)

AInt.mass -2 ,22790e-12 -1.96104e-t2

.3-8B1230-08

4. 27233e-08

'3.:9Sd67e-,08 G3.869B8e-08 P3-'.15509eý08 03.8403ie-08 '3.82554e-08

:3.,.--&I647e-08 .33.P75I!i:e-08 :332.A736g6eý0B .3 U286601-e-:1 I 1iCB;5-7.34eýý I

e 3A) e(.- 1AC 3 C 0

FAS."356330-08 -(4 3a,140Be-08 24.4333i9Se-08 QC)'A1992e-08 2C40,796eý;08

4.2605ie-08 4.24870e-O8 4.23690e-08 2.11042e-ii 2.09205e-ti

2. 5956e-08 2. 15084m-OS 2.14225e-08 2.13369m-OS. 2. i25i6a-0B 2. ii666e-08

2.09i3-Z!;' .- 82de0b -16 a2~Im~ 'I ý03!42e-ý14 I i1303030e- ii i02009e-3 V) 1 A Of )CP)'-A 00' aA'. 4C~ v G '013C0 A (CAiC

3.-28554e-06 3.25874e-06 3.23248@-06 3.20636e-06 3. 1038e-06 3.1i5456e-06

3.07803e-06 3.05283e-'06 3.02738e-06 1.50505e-09 1.49318e-09 1.4870te-09

frr'dni"761ter mass (kq)

f ~~s.....3.052586ie-06

a

4

ck f Vftpr mass~j~C

2 V e. (11 C 0 j)CPAO '2' Z)~Y E.3A a S P 0134A~). 6--10 ý DA 35 7,( 3 ~a 0aV- ?0V0)0 0~a. :5 A.YO
ale-born mass ikg),- 01'J' Vz )

awir" mass;! 0-, 0 s4 4,3S3oO~ 35633e 4 ,Oe--8' t 1 -6 -773ie.O8ou I .67269o.ýO8 k)t i. SISSOe-Oi 541.64es0

1'.6583eS3-08 1.65424g.-OS -.64967.-OS I.645i0e-06. 1.645054e-OS 1.463599.-OS 8.14894e- 12 5.77778e-i2

j.jc (,5179te4e-I2 0.

SpeC-ioe~kiS s on- duc;t via I (kg)

ma.", 0. 8.5813ie-O9. S'.53545e-09 S.'48954e-09j 8.44346e-09 B..39717e-09 8.350654-09

S.3030Oe-09' 9.25565e-09 8.20930e-09 8.46i66e-Og 0- 5..69S42e-i2 0. 0.

dpos It;n rate at each'branch (kg/s)

-~~ ý 0. 0. 5. G006e -l1 I 5.58481e-ii 5.5692te-ii 5.55373e-111 S.533.i .20.

ra~te" .0 .0. 0.35-- 0. 0.S. 520.S0. 

0r0te. 0. <.0 0O.. 54;4 0.: 444 0.

0 ,ý4W 6.4)36C), 0* 44'j. 0 3454A 1-44,O. A t4jj.46V.0) q - ) A::3V 4444 I P 4 .- tŽ3 i3* G.(4.5. .. 44I

6 4i.34.44.4~4 5 4.0<'~ 4.404'4 species no. 12 rad. 'part IS.

specie nodal masas 4 rý,ý4iN ,... . .)4 6(' 04 0)444 343d56- 3 43

;.46- ý 144 q 4 

(444 Oe JA,5 It"!04 !,7 -) 0 (-I;; 5(54444 E. (3aa i~

0P.: 3 .Wi1e~S ti,~b"3.91 '16LibS8(3"3.i 47 9 ýJ ;'0 '-3-. 399di-68 '3.8b1 d 3. 1

'3.72310 le-08 3.,68522e-OS -3.64733e-OS 3.60975.-OS 3..572480-OS 3.5355te-OS 1.76552e-il- 1.76392e,-.i

spec I, nodalI concintr'a'4i~{h(k/M.3

0o&'o 01 '4 .1ý5tbloe 8ýz4 .39501 0S()ý14.3547d.-16i 14. 14W4~-8 .2S4O r26.4-a

4.1i9759e-08 4.115915@-68 4.12103e-08 4.08323e-OS 4.04572e-O8 4.008S0e-08 1.99677e-ii 1.97733e-i1

specie branch flux (kg/sec) wo~42(. 3 , .( .•6 (

dfIux 0. 0. 2,17873e-08 2.1561ie-08 2.13381e-08 2.it117le-08

.2.,04667e-08 2.02539e-08 2.00431e-08 1.98343e-0 1.962530-08 9.79659e-12

5 - 0 -0 -,) 0 A 4 3 .-

specie Integratedbranch flux(4kg) 0'- ( 0 0

In t3..mass.44C.4'( * 3..2566lfe•.12P'-2,1466531-, .1 2 3,46152e-06 3.4120le-06 3.36349e-06 3.31552eý06

3.17499e-06 3.12926e.06 3,08409e-06 3.03946e-06 2.99492e-06 1.48930e-09

43,4d:3 ".- 4(. 4 'r 44 , iO 4) 4. ", 4 4,6.' 44'', 43" 44(.54,44462• *G ;,4 - 4" 5 .464\4

frontt filter mass -kg) ._ .

f 14b 5ma-5 S .. .19347e -" .-

back V i 1tee- mass 0, q '44. v0 0 905(.4 N, t4PE 4 W1 54 W3 5 1,1.64 OR4.5. 4. )

IFIlI.ma'ss 0.4

total specie mnss; on f Itetr~s 2.993.P-06

airborn mass (kq) ..

2.08983e-O0

9.78485e-112

43 0

0'

3.26812e-06

1.48343e 09

i4 -:-,

(4" )50)4

2.06815e-08

9.7737 Ie- 12

0'

3. 22127i-06

1.47757e-09 C)

W4 4 4 ý1' .44444e

40 '7 44

4744 .5 dd4'0'4~-42~4 3~ 44,4445(4546-434)

0.0 ,(446(e).4 (544444..1i0TO 44A. 90l 5D-4. 8149'OR4I.66l1'O -. 41.0.6.S-4 4 637701O' 5

air mars
i I 62081e-08 1.60597e-08, t.5925e'-08 1.57665e-08 1.56217e-08 i.54-780e-08 -7.71010e-12 5.4872de-i2

5.50079e-12z 0.

total specie airborn mass 2.493e-07

specie mass on duct wall (kg)

mass 0. 0. .3.13663e-08 3.10093e.-08 3.06544e-08 3.03015e-08 .2.99504e-08 2.96009e-08

:2.92529e-08 2.89065e-O8 2.85617e-08 2.82187e-08 0. 6.29737e-15 0. 0;

deposition rate at each branch (kg/s)

rate 0. 0. 1.96154e-10 ".94356e-1O .1.92576e-O i.90814e-"O 1.89068e-10 1.87338e-t0

i.8562ie-10 1.839g9e-10 1.82231e710- 1.80556e-I0 0. I.25947e-13 0.- 0 .

entrainment rate at-.each branch .(kg/s)

rate O. 0. 0. 0. 0. 0. 0. 0.

0. 0. 0. O: 0. i.25936e-i3 0. 0.

15

specie nodal mass-fraction,.

frac. . 0.

6.81548e-08 6.69972e-08

J3. 11915e-f'I, 1 0.

specie nodal concentration (kg/m**3)

conc-. 0. 0.

7.658344e-08 7.56134e-08

3.50838e-11 0.

specie branch flux I(kg/sec)

dflux 0. 0.

3.-72084e-08 3.657i.-O08

specie Integrated branch-flux (kg)

intemass -I.256166e-ii'-I.I3211e-II

6.67525e-06 6.5376ie-06

front filter mass (kg)

fil mass 6. 13507e-06

back filter mass (kg)

fil.mass. 0~O.

total speciewmass on filters ;6.135e-06

airborn mass (kg)

air mass 0 0.

2.96680P-0R 2.,91965e-08 -.- 9.73594e 12 0.

total specie airborn mass 4.(Iie-07

pecies no. 13

7. 42 179e6-08

6. 5A5174e-08

8 .32290e7-08

7.44108e-08

4. 12590e-08

3. 59440e-08

7. 55564e-06

6.40244e-06

rad part

7.42i79e-08-

6. 47350e-08

8. 32290e-OS

7.3226 le-08

4.05546e-08

3.5327 ie-08

7.40159e-06

6.26971e-06

20.

7.29677e-08

6. 36298e-08

S. IqOqqe-.OS

7.20588e-08

3.98635e-08

3.47163e-08

7.25 11e-06

6.13814e-06

7.t7366e-08

6.254 17e-08

8,:06101e-08

7.09066e-O0

3.91835e-08

1.73336e-1I1

7.10335e-06

3.05471e-09

7;05242e-08

3. 12383e-il

7.933i9e-0S

3.53299e- i

3.85144e-08

1.73156e- i

6.95810e-06

3.04435e-09

6.93304e-08

3. 12150e-11

7.80735e-08

3.49915e-it

3.7856ie-08

1.72987e-ii

6.8t540e-06

3.03395e-09

8.32290e-08. 8.32290e-O8 3.-1627Ie-08 3.11259P-08 3.06323e.08. 3.01464.-OS

2.87321e-08 2.82747P-08 2.78240e-08 2.73798e-O 1.364i9r-11 q.71033e-t2
specie mass on duct'wall (kg)

mass 0. 0..

1...08698e-07 1.06766e-07

deposition rate at eachbrailch (kg/s)

rate 0. 0.

5.96212e-1O 5.86723e-10

entrainment rate at each branch'(kg/s)...

rate 0. 0.

0. -0.

i.20748e-07 1.1,7683e-07 1.1664le-07

1.04857e-07 1.02969e-07- 0.

6.56298e-10 6.45884e- 1O 6.35636e-10

5.77376e-10 5.68166e-10 0.

1.14622e-07 i.12626e-07 1.10651e-07

t.96574e-14 0. 0.

6.2555te-i0 6.i5622e-10 6.05845e-10

3.93148e-13 0. 0.

0..

0.

0. 0. 0.

0. 0. 1 1 0. 3.93119e-ý13, 0.

0.0.

00

%0
iCo

table no. vii

summary'of solution parameters

sample problem i

executed on 84/06/11 time.:21:56:02

run type = st

convergence criterion - 1.00e-04

total problem run time = 999e÷02 ( O

- •.**_ r j1 4

ttotaikgasp:dynamics iterations for problem = 27086

!.týabg~ Pec iesý \i~t~ A tin s f tr,,(pr~otjm,- 0!e

4) (2 el~4 k ý C 42 40 10,3ýC)ýC 40, r 1C, C (D 44 01 e (L - 04 total number of particulate species iterations for problem'= 298699

total nu6mber of time steps = 23481

44C-. P4 GU -4~ 4 0 C.1.1 C G4 - t,ý , :

table no. viii

archival list of output parameters
(2) Sample , • oi`. Problem a" o.J 1 , ', fire compartment.effects ) I .fL .O '. ,'. 0,;,v i - " " .% ý ".0, (PRINT - , ou 1)1,

.1 1' outputif;on compartment effect.si-,- compartment histonyo

L-o J- ,ý,.; ch: q3 , s, A 1- 1Ž3333: •• ,,< " 3'•• '33)) .3 ",:'{J )5 • '33 .3 ;2'. 3 '~

.t:S~tep pcomp'.' 1M02 i0.:, zrhtI:3"\ vif,, o.3 vof PŽ:03

('Jsec,)' ( atmA.)<3( fract lono) (".m-;) (B*3/,S.J) Vs (M**3/S J) '4,"J,, +{• bd~ , i) " ''Ž" ) , .' ,,i2• ' ' ' •: 3• ; 1•

v i'2 .00 39998, .2100 0.0000 .5296 -. 5091

,'.,7" to 1:0004; 2100 -.0143 -. 162f - :5766

3.2.20 1:0006 .2,10 "1.0290 -. 4-7.43 -. *5lt7,5

0"2. '.30 1:000 .2t00 • .0431. - ;5592- - .5941,

u'2.40 1.00081 .2 100) .0584 -. 5948,) -. 5662

,3.2.5" 1.0009 .100. :. .'0731t -:6268 -:5839

'260 1:0009 .2, I00; 3.08:7.7 -. 6362, -. 597.5

2.:7-0.' I .,00091; .'2,100. 3: 1.022. -:647,9 %5834 -. 42,.'80 1'.00100 3,1166 - .6495. - 6090;

J,!Z.'2'90 1 .OO09 :24100i :. 1310 " .:6512 - :5865

"3.00 1 .0009i .'21,00 3."1454' -..'6504 - .608;7

1 3A.'99' 1 . 0008 .:2,00, 3:28.33 - .6107 -. 5851

S. 000,7 :" 2:1,00, Ž.4:5'1: - .552.21 - .516.6,

4 5'.,99' 1 .0006, .31f00i ::5398 - .4-908 -.. 5696

.1:00061 1.6.99 .'2.100', n.6578& - .4:3.1,3 -. v5638 •

7'ý.' -993 1 .0005! T2,1006 6 7.6971 .-3698: -.. 56423

318:'.99 1.0004) .21000). .473.875 - .31.53 - .'562,2

" 1399 I .00041 :2100) ':".,9;76,4, - .2629, -:5O60

'' ,1195' , 1 .00021: .,2,1,0M 1 . 280.71 .2.7.06' -.. '56'4

,19M.'95' 1 .0001) .,2,1003 13.520' .3"309' - .5502

",4 95 1: 1 .000413 .2,1.00• t1.209, .3.!56,•1% .5354,

.2,9i.'957 I .000413 .2,100M 11.8898 .3:73"7.8) - 5267, :,34,!95 M 1 .00001 .'2,100, 2;. 0332. .3(970 .,52169

:,39. 953 1.0000, .201.00, 2 155,74 AI;120G 4513

-44;.'953 I.00001 .2,100) 2. 261. .4254; -:5,167t

Ž493.95! 1..0000, :2,1f0)3.- 2.35418 .,4:36,7j -.. 559

:5.4.'95, 1.00001 .'2:100a 2.4,3044 .,4460 -. 5'153!

:59.9.5'5 1.00001 .'2•100) 2:49883 .453M7 -. 5149.

:64!.9&' 1.0000, :21t00) 21.5586 A4599' - .545:

'69.95' .9999t .'2400 2:.'6013•. .4651) - .:51411

474i. 95' .:9999 . 2100M 2':. 65.70. .4.694) -.. 5:113?:

.79-.95! .29999, .2100. 2.6 7,T .4,730 -. 5133

:,8*43.9, .9999% .2:100, 21'7335' A476•10 -. 512%

A893.95? .19999, .2,100' 2i. 7.652 .4,7.86' . .'126•

94. 95' .99991 .'2100 2.. 7934* .4809. -. 51:22,

:99T.95' .9999, ., 2.100,, 23. 8.185' . 48a&8; --. 51)18'

104. 95' .9999 .2100Y 2. 8408 - .4845,,. - .:5115!

1091.95 .99999 .'2,1003) 2.: 8600 .Z4859 -. 5.11

1,t43. 953 .. 9999i .2,1003) 2.:878k,7 .A48172 -.:51,08;

131.9'.95) .'99993 . 2100) 23. 89,42 .4884, - .'5't051

1f24.L'95) .99991 .'2A,100 2Ž. 908q3 . 48943 -. .'102'

1'29). 95? ;9999) .:2400 2. 9210) A4.903, -:.5099,

1'34;. 95' .9999T .'2100) 23.'9325i .49063 -:.53102.

1:39i. 95i .99994 .2,1007, 2i; 9A441 .'4903; --.'5'1023

13443.95! .9999" .2)100) 2).9557. .4898! --.51102,

14'.9ý. 953 .. 99993 .24100) 2l.'96731 .48931 --. 54100.

1.54J. 95' .99993 ..2,1003 23i. 97931.9 .-48R8 -. 5099)

159. 953 .99q9; .22100) 23. 9909' .48R4ý3 -. 509.7!

163 ~' .99993 .7,100." 331.0079) ..:489303 506

169'f; . 99' .9999" .2:100) 33. 0148 ."484763 -- 50cJ

174.. 9.5 .9999; .2,100) 3i. 0268& .4837313 -. 5093'

.17T.95? .999q) .2100) 33.0389W ."4867 --. 509A1Ž

1:843.9! .999'V .252100' 3'051. Oa48643 - 50R19

1R8 9.9'1 - : .99 .9 9:1 . .Zlc0i 3i. 063'T .4862 , . --.90883

'19•. 95. 99993) .2100.- 33.079551 ,.:495, -5.086?

204 Q9 9999 .2100 3. 1001 .4855 -. 50R3

output file.

t h lIuc,; a

C1:• "A 0/

:55 67.00

223 2095

23t.4592

235:5993

238.2493

240.' 1,369

241t:57.59

242.7 1T2.9

24,3:6421'

244:41,42

245:06,76

248: .38&36,

24,9:355:71

249. 4A6Q

24.9.' 2310

248'. 7T405,

248a. tt26,

247,7. 3,998; 227Ž., 7:8B1.4!

215). 24",39

2 06"9.033

2,01,. 0574,

1+,•4j 1,04.

1 890,124%5

l,8•.' 7373 1:8

1•8'?.::. 12,7,43

58r.8S03,9,

1!8,4:. 7-3O0

1183.:0798)

1:83. 1f92,9

182:. 64,91I 1:82.i 22,1t,?Ž

1;8,,t,. 651-0.6 -18: 1, .'-7,6.8Ž

18:1,. 36•2,3;

18:1t." 3009,9

A18,, 809, 18;12.-29621

t831:. 3.4 16,

181-.+4Ž1.3,1

IS133 50937. 18,1Ž.'623+2)

18311. 7:4.93'

18'&. 8a 65;

182,.34.16,

182 5,14Z7. I•R2Ž. 69237Ž

182,'. o68,7 I 2.8%7,-,5731

183,. 24•.00Ž

I t3,. 422Ž,,7

1R3. 7877

., ......
'209.95 .9999 .2100 3.1124 .4851 -. 5083 183.9729

-2.14.95 .9999 .2100 3.1249 .4848 -. 5081 184.1646

219.95 9999 .2100 3.1373 .4846 -. 5079 184.3536

224.95 .9999 .2100 3.1498 .4845 -. 5077 184.5398

-229.95 9999 .2100 3.1623 .4843 -. 5076 184.7234

234:95 .9999 .2100 3.1748 4842 -. 5074 184.9047

239.95 .9999 .2100 3.1874 4840 -. 5073 185.0837

244.95 .'9999 .2100 3.2000 .4839 -. 5071 185.2607

249.95 .9999 -. 2100 3.2126 .4835 -. 5071 185.4480

254..95 .9999 .2100 3.2253 .4833 -. 5069 185.6318

259.95 .9999 .2100 3.2380 .4832 -. 5067 185.8119

264.95 .9999 .. 2100 3.2507 .4831 -. 5066 185.9885

269.95 .9999 2100 .3.2635 .4829 -. 5065 186.1620

274.95 .9999 .2,100 3.2763 .4828 -. 5064 1863327.

2.79.95 .9999 .2100 3.2890 .4827 -. 5062 186.5009

284.95 .9999 .2100 3.3019 .4824 -. 5062 186.6777

289.95 .9999 2:100 3.3147 .4822 -. :5060 186.8533

294.95 .9999 .2-100 3.3276 .4821 -. 5059 187.0249

299.95 .9999 .2100 33405 .4820. -. 5058 187.1928

304.95 .9999 .'2,100 3.,3534- .4819. -. 5056 187.3573

309.95 .9999 2100 3.3664 .48-18 -. 5055 187.5189.

314.95 .9999 .2,100 3.3793 .4817 -. 5054 187.6777

319.95 .9999 2100 3.3923 .4814 -. 5055 187.8445

324.95 .9999 2100 3.4054 .4812 -. 5053 188.0118

329.95 .9999 2100 3.4t84 .4811 -. 5051 188.1748

334.95 .9999 2100 3.4315 .4810 -. 5050 188.3341

339.95 .9999 2100 3.4446 .4810 -. 5049 188.4900

344.-95 9999 .. 2100 3.4577- .4809 -. 5048 188.6428

349.95 .9999 2100 3.4708 .4808 -. 5047 188.7930

354.95 .9999 2100 3.4839 .4804 -. 5048 J188.95.16

-359.95 .9999 2.100 3.497A1 .4803 -. 5046 189.1108

364.-95 .9999 .2100.: 3.5103 .4802 -. 5044 189.2659 -369.95 .9999 .2100 3.5235. .4802 -. 5043 189.4172

374.95 .9999 221,00 3.5367 .4801 -. 5042 189.5651

379.95 .9999 .2100 3:5500 .4800 -. 5041 189.7.100

384.95 A9999 .2100 3.-5632 .4800 -. 5040 189.8523

389.95 .9999 .2100 3.5765 .4796 -. 504.1 190'0047

394.95 .9999 .2.100 3.5899 .4795 -. 5039 190.1565

399.95 .9999. .2.100 3.6032 .4794 -. 5038 190.3042

404.95 " .9999 .2100 3.-6.166 .4793 -. 5037 190.4482

409.95 g9999 .2,100 3.6299 .4793 -. 5036 190.5889

414.95 .9999 '.2100 3.6433 .4793 -. 5035 190.7267

419.-95 .9999 .2100 3.6567 A4792 -. 5034 190.861.9

424.95 .9999 .2100 3.6701 .4788 -. 5035 19-1.0100

429.95 .9999 -2-100 3.6815 .4787 -. 5033 191.t550

434.95 .9999 .2100 3.6970 .. 4786 -. 5032 191.2959

439.95 .9999 .2100 3.7105 A4786 -. 5031 191.4332

444..95 .9999 -. 2100 3.7240 , .4786 -. 5030 191.5673

449.95 .9999 .2.100 3.7375 .4785 -. 5029 191.6986

-454.95 09999 .2100 3.75 10 .4783 -. 5032 191.8301

459.95 .9999 .2100 3.1645 .4.781 -. 5029- 191.9728

464.95 .9999 .2100 3.7781 .4780 -. 5028 192.1114

469.95 .9999 .2100 3.7917 .4779 -:5027 192.2461

474.95 .9999 .2100 3.8053 .4779 -. 5026 192.3773

479.95 .9999 .2100 3.8189 .4779 -. 5025 192.5054

484.95 .9999 .2100 3.,832-5 .4779 -. 5024 .192.6308

49q95 .9999 .2100 3.8461 .4776 -. 5026 192.76.11.

494.95 .9999 .2100 3.8598 .4774 -. 5024 192.8978

499 95 .9999 . .. .. 2100 3..8735 .4773 -. 5023 193.0306 " 04. .99qq 2100 3.8872 -.4773 -. 5022 193. 1595

509.95 .999c9 .2100 3.9009 .4773 - .5021- 193.2850

514.95 .191149 .210.) 3.9146 .477:1 - .5020 193.4076

519.95 .29,99 2100 3:.284 .4772 - .5020 193. 5276

524.99 .999.9 .2100 3.9424 .4768 -. 5021 193.6582
529.95

534.95

539.95

544.95

549.95

554.95

559.95

564.95

569.95

574.95

579.95

584.95

589.95

594.95

.599.95

604 95

:614,95 com bus t tbl!e type

:-6)39 .95

24, 95

A529 :95 ,_634 ,:95

S6_9 .95

,;6•9:95

,6.84:95

,6.94 !195.

:6.9 .'95

.,!721' •9ý5 6729.i,95

78394.95

ý744"',95

I-7SC,95 .7,69.,,95

764 !-95

769.95

774.95

allI combtistibie

7130.00, .

7t85.0r0o

7n5. 00

8079.9

8754 .05

•~8.15.00o 7920.00

N)O', 827 5.00

t00"0

80)0

.9999

.9999

.9999

.9999

.9999

.9999

.9999

:9999

.9999

.9999

".9999

.9999

.9999

.9999

.9999

• •99,99

.:999.9

.9999

1 ..0002

I .:002

i q:oQo.9

1 0 0 .02

I, ..OOQ,• I I 1..000.A .*•1Q

I ý_QQQI

I .0.-0.3

1 . .0001

I (OOQý_I

I .OQC..Ol

1 :.001,

1- .ý0,1

i•. _0001

t.0001

i.000,1

I .-OOOA

1 .O00il

1..000i

r .•ooo,1

I .ooot)

1.000t1

1 .0Pa Is

materials

.9996

.9q95

gqq5

.9996

.99r6

9qlQ7

.9q97

.9997

9199R

99911

.2100 3.9559

.2100 3.9697

.2100 3.9835

.2100. 3.9973

.2100 4.0111

.2100 4.0249

.2100 4.0388

.2100 4.0527

.2100 4.0666

.2100 ) 4.0805

.2100 4.0944

.2100, -4;1083

.2100 4.1223

.2100 .4.1362

.2100 4.1502

.,2400 2.21 ,IZIIp 9oo _ A • ,4j4 .7220 2O.8•,, ;n I tietdjt t ime;, <69.

1936H A 57.20

-+ 9..+, 4 •57,20 .4j!92 .•4 -q57•20

• ,i,9.1. ,4 T57,20 . I d4;IvI4 57,20

•.!I9I A;.1 • -57,20

M,1806 ; .5720

.-A 4,8 4 .57,20

". 18683 ~.4 :i57:20

; 18,0 .4 .5.7,20

. i8•70 ,\4 5.7,20 .1 13685 A.4-:A6720

.j

1

8

5; 3 

.tl80 .q4-:,ý20 14,.45720

.J954 A4:•5720

4i88 ,4.5,720

184.5 .'4 ,'-5,72.0

.1842 4.5720

.1840 4.5720

.1837 4.5720

were consumed by; 77

.4767

.4767

.4767

.4767

.4767

;4765

,4762

.4761

.4761,

.4761

.4761

.4761

.4758

.4756

.4756

147.56

.- 47,56

8000 .semc .'4 ý ý .

-.+3,9J5.2

..42,55.0

•.23 .6,58 ,?2,•A8

-.13318,

?329 1

. 4.30 116. -.ý.,r7,0.

.3628

.. ,2.5,2

.33Q88

• ;33•57

.- 1339,8 . 134_65

.,3,49_1

'3.53.3

.3594

..:_.357,6

.3586

1..704 .736914

;:361 t8

36272

.3625

.3628

.3630

.3631

77.9000 sec

.6459

.7280

*.7046

.6763

.6507 .6290

.6106

.5948

.511

.5696

- .5019

-. 50t8

-. 5017

-. 5016 - .5016 - .5019 - .5016 - .5015 - .5014

-. 5013 - .5012

-. 5012

-. 5014 - .5012 - .5010

-- .4 ,50!t

-,500,

_-P .13p, - ;.,6,7)

-•,5 1,5

-. 5164.

-.3209

.- .i%,95

1'598

•- 5.,•,8

.- .+,51.8,

•--.5. )7,9

.. .51,I7,2

-5. 68 --,5.16,7 - -1,5 66

-- 51,65 - 5164

- .5163 - .5162

-. 43209

-. 4459 - .4656 - .4690

-, .4709 - . 4734 - . 4756

-. 4775 - 47q2 - .4809

193.7894

193. 9 165

194.0400

194. 1603

194.2777

194.3950

194.5247

194.6505

194.7724

194.8908

195.0062.

095. 1190

195. 2391

195.3637

195.4843

1'95 A6090

I ý+ 6"0,oo ,200 -17,31

t 83

j20 2!59725

f706 .",77, +212 , t7.90

22 1,5 .a3725

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•228 •9,3,523

,22.76Q,3s%

,27.8 :,4,9.,7

129 -L?,9q9

2•3,2.+4,52.4

433 6 2,. 16 (2 3 3 .1099

234 .95834

230.17. 9.3

+236 .0,44

+23.6 .+8,850

•237,;87,58

238.63409

238. 7996

239. 2206

233:9694

221.0477

209..7719,

200. 0444

191 .5945

184. 1 942

1 77. 6634

17 1,.8608

166.6"73R

162.011.5

1838

1647

1855

1862

1869

1R75

18841

I RRF.7

IR92

1897

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.45720

4.5720

4.5720
hQ

830.00

835:.00

840.00.

845.00

850.00

855i 00

-860.00

865.00

870.00.

875:00

880.00

885.00

890.00

895.. 00

900.00

905.00

910.00

9.15.00

920" 00

925.00

930.00

935.00

940.00

945.00

950.00

955.00

960.00 965.00

9"70.00

975.00

980.00

985:.00

990.00

995.00

.9998

.9998

.9998.

.9998ý..•

.9998,

.9999

9999

9999..

.9999

.9999

.9999

.9999;

.9999

9999

.9999

.9999

;9999

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.9999

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.9999

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.9999

.9999

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.1902

.,1906

19.1.1

.19.15.

1919

1923

1926

1930

.1933

.1937.3

1940.

1943

1946

1949

1952 .1955

1958

1960

1963

1966

1968

1971-

1973

1975

1978

1980

19S2

1984

1986

1988

.1990

.1992

.1994

.1996

4 5720

4.5720

4.5720

4.5,720.

4:*5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4C5720

4.5720

4.5720

4.5720

4. 5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4.5720

4 .5720

4'.5720

4.5720

4.5720

4.5720

.5597

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.5434

S5366:

.5303

-. 5247

.5196

.5152

.5.113

.5079

25049

.5022

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.4975

.4954

.4933

.49 14.

.4896

.4879

.4864

.4849

.4836

.4824

.4813"

.4802

.4792

.4783

.47.4

.4767

.4759

-47.53

:4747

.4741

.4.736

--. 4826

-. 4840 - .4853

-. 4864:

-. 4870

-. 4874

-. 4878

-. 488,1

-. 4884

-. 4888

-. 4891

-. 4894

-. 4897

-. 4901

-. 4905 - 4908

-. ,49 11

-. 4914

-. 4917

-. 4920

-. 4922 - .4925

-. 4927

-. 4930

-. 4932

-. 4934

-. 4937.

-. 4939.

-. 4941 - .4943

-. 4944

-. 4946

-. 4948

-. 4950

157.79.987

153.9748

150.4892

147. 2996

144-; 3704

141.6716.

139.1764

136.8613,

134. 7061

132.6935

130.8086

129,037.7

127. 3718"

125.8033

124. 3269,.

122. 9377

121.6302

120.3985

119.2370

118.1402

117.1038

116.1238

115.1964,

114.3180

113.4858

112.6969,

1 1.9487

111: 2384

110.5636

109.9219

109.3111

108.7292

108. 1742.

107.6445.
(3) Sample PrOblem 1 radioactive source term (RST) output file. . . .. 0. ý0 1315' : 17 0., 962e7 o7+

209.95 '0. 0. ' 0. 0. 0.1 019 020 3-- 13e-07. -10 .6 e 7 21.495 2 0.- 0 0 - 0. 0 0. .0. 0.. .93.-fO .f36e-07 .619e-07 .9630-07

-224.95 219.9 '5 2.0. 2o0. 0, 0 0 0 '0. -03. 0. 0: 0: .1930-10 1366-07 .820e-r07 .965,-,07 0. . 0. 0. 0. 0. .193e-10. .136e-07 .822e.-07, .967e-07

229.95 2 0. 0.. .0. 0. 0 0. 0. 0. . 1,94e-10 . 1364-07, .023e-07 .968e-07, . 234.95 ý20: 0 0. 0., 0. 0. 0. 0. .194e- 10 .137e-07, .524e-07 .970e,-07 239:.95 '2 o -0. -0. 0. 0. 0. - 0. 0. .194e-10 .1376-07 .926e-07. .971e-07 2 9 2000 0. 0: . 0. .195e,mI0: . 137e,07. 27e-07. .973e-07 244:.95 2 0. 0. 0. ' 0;- 0. 0. 0. 0. ".195e-lO .137,-07 .928e-07 .97- 07P .254.95 2 0. :0. " 0 0.- o. -0 .0 .15-0 .17-7 .3o0 -... 6.0. 254.95 2 0.. . 0 0- .0. - 0. . 0. , .196e- 10 _139o-07 .- 30-07 .979e-r07

:264.95 69.95 2 2 0. 0. 0 0. - "'0-' 0 " " 0;•. 0. "-0•:.'. 0. 0 0 " . 0"" 0. . :-0".- 0.. " ".196e0-10 .2968-O .139eo-07. .1. 39-07 .9320-07 .934.-Ot .979e-07• .991?0 " .4.95 2 0. 0 0. 0. - 7.35-0 0. .. 0 0. 0 0. .1960-10 138e:07 .92,-07 279.95 2 0. 0,0. 0 0. 0. 0. .195e,-10. 1.39e-07- .836-0"i .98.40207

294.95 2 0. . 0 0. 0. 0. . 0 0. 0:.- :197e-16 .139e-07 .8316-67 .985e-.07 259.95 0 0 0. 0. 020. 0. 0. - O 0 .19.7-e10 . 139e-07 .A39e-0 .99eo-.07 294.95 .2 . . 0 39o:07 .040'-07 .9590-07

299.95 2 0. 0. 0. 0. 0. 0. o. 0. .196-e10 .1390-07 .842-O07 .9900-07 304.95 .2 0. 0. 0o. 0" . 0. 0. 0 .9e-0 .140e-07 .8435e-07 _-.992e07. 309.95 2 0. 0. 0.. 0: 0. 0. 0. 0 .199e-i0 . 140o07, .944e07 .9930-07 314.95 .20. 0. 0.. 0. 0 ,0. 0. 0. " .199e-0-- .. 140e-07 .8345-e07 .994e'-07: 39.95 200. 0. 0". 0 0. 0. 0. 01 , 7 e - 10 .:140e-07 .;471.-07 .99r6,-07 324.95 2.0. 0. 0. 0. 0. 0 0 0 . .2000-10 .1-0O-07. ."49oe07 .9950-07 329.95 -o2 0. 0. 9 0. 0. 0. 0 0. 0 .2007e-0 t1,1ge-07 .8349e-07 .999-07 3342.95, 2 0. 0. 0. 0. o. 0 . o . 0 o. .200.-1,.1410-07 ".500, _ .9i6e,:06 -339.95 .,2.0.- .... - 0. -. .0. o. 0. 0. 0 .2000-,0 .. 141 0 -.. 852e-07 .9 ,06 344.95 .2 0. 0. 0. 0. 0. 0., . 0 -201e.-10- .ol'e-07 .. 53,-07,.-10006. 349.95 20- - . 0. 0. 0. '0. 0. - 0..8 e.201i0 :14.10-07" .854e.-al 9..i0-06" 354.95 2 0. 0. 0. 0 0. 0. 0- 0. .. . 0..-7201-i0 07 .. 5o07. .101.-S06,. "0359.95 2:0: 0 0 0. 0. 0. 0 - 0 . .202 I .142.0 - .0 .. 8 7e-07. . -6,01 364.95 2 0. 0. 0 . 0. .0. 0 202e10 .1 4 2-o 07 .95-07 ,.101. . ,"0 369.95 .2.0. 0. 0.- 0. 0o. 0. - 0 0 202e-0 .. 142".0 59-07, -101-0, 314.95 2 0. ,0 0. 0. 0. 0. 0. 0 .92020- 10 .- 143e-07 .860-07 . 107e06 37/9.q95 2 0. 0. 0-. 0. 0. 0. 0. o0. .-20309-10 .. :.43.ýe-07. .862e07 . o01 706

394 .95 20. 0 0. OO. 0. .0. 0.: 0. .2030- 10 143~.07 .9630-07 .101-06 329.95 2 0. .0. 0. 0. 0.- 0. 0. .20030e-r10 .1430e07 .864e-07 §.e1027-

394.95-2,0. 0 0. 00 0. 0 .2040e-10 143.e:o07 .865e-07ý .b02e906',- 32,9.95-20. 0. 0. 0. 0 0.- .20400-10 .144e07 .8660-07 .102e-06

404.95 2 "0. 0. 0. .0." 0. O. 0 . 0 0 O .204~0-10 , 44eo 0 .968o•07 . . l0o~e.06 + 409.95 2 0.. 0. 0. 0 . 0'. 0. 0.• " 0' .2040-1t0 .144e-07 - .969o-07 " 1020-06"" 414.95 2,0. . 0. 0. 0. 0. 0. 0. .205i010 .1440-07 .850e07- .102.e-O

419.95 20. 0. 0. . .0. 00 0 .12050-A0. .. 144e-07 .81"-07i .026oý.06 342495 2 0.. . 0 0. . 0. 0. • - 0. .2050 10- .144e-07 .872e-07 .03e-06: .429.95 20. 0 0 0. 0. 0 0. .206'-10 .145e-07 .573e-07' .l03-06"" 434.495 2 0. 0 . 0.0. .0 0: 0 .206i- 10 .145 .8"5e-07'. 8507 103o•06'.

49.5.. 0 0. 0. 0. 0 0 0 206e'-I0 .45e:07- .- 76:07- . 103e-e06' 444.95 .2 0. - 0.:: "0; .L" - :,0. + 0. 0: 0. 0. " .206o- 10: 145e-07 .977T-07 .103e-06

449.95:.. 2 0. 0 . " 0: 0 . - 0. .o 0._ 0. - 2o7e~to.. . 145e•o07 ., 79e-07- .10o30-0o6.- 454.95 2 0.. 0. 0. 0 0. 0 0 0 - :2070-10- . 7-846t,07 79n-07. I03.06W .

459.95 2'0:. 0. Oa. - .. o. 0. " 0" 0; .207e0' 10' .146o-07• .9800-07: . 104e"-06":• 464.95 

'469:95 2 2.0. 0. 0. . 0 

0.. . 0. 0. 0 0. 00.207.-b 0 0. .2090-10 .Vile,07ý •146e-07 .9830-07, Btq2-07. ..104e-06 - 3474.95 '20. . 0. 0. 0.. 0. 0. 0 .-200e-10 ,.146e-07- .,04e.-07 ".104e':'06

479.95 2 0. 0:. 0. 0. -0. - 0. 0. 0. .2090;-10 , 14."/-07 ".9l5o-O7 l+ I0e-0S-: 434,95 20. 0 0. 0 .0 0. 0 0. :.209-,0 0 .04. -0 :96o-O? .104e-06 439.95 2 0 -. 0- 00 0 0. 0. 0 0... .209.-10 -1 47e-07: 153e0'07 .i04e-06 4 000 0 :"209.- .14 7 e-0 7 .0.le-07 -. 105-06 "49 49 2 0-. "0 0. 0. 0- . 0 -0.- " 0 -: . : • ,20910 ,47 0-07 90-07 05'-06 -

389 .9.5 2" 0...' . -, .: -0 0:' -0;': :,"3"." to

91.5r)::.5 53q.§5 -2.0. 2. . ; . . 0. . - .0+ 0 -. :-0 0 -. - 0.. 0. '0, -0 " . ' 0: 0.''• . .2.10 .210e- -0.- 10 .14e.-07 .:- 14R.-07 .5Rllez07 .992e-07 ...W205-Or 105.-OS .549. 2 0.. 0 . 00. 0. 0 . O. 2104 O- 10 .. 14dP-07 .- 636-07 .105e. -06

404.95 20. 0 0. 0 0. 0. -0 - 0 . .204ý .I0 .14R (07 .RBG4e-07 .o10rei-06 . 4'24.95 2 0. 0. 00 O, .0. 0.- 0-. . •2.1 i.. 0 14Re.07. . R95e-07 .10.4Yo06 .. 4 2(" " 0. 0. 21 4 , ,/ 

0. 0. 0. 1' +0 ,.
output for radioactive source terms

time jact mass rate (g/sec) accordlngto size distribution (microns) (sec) (<.I) (.1-.3) C'.3-.5) (.57.7) 11. 7- CO (.A -I. ) (1r.,1-2) - - ) total

(6-10) (10r20) (>20)

-2ý.002 10

2.20

2.30

2.40

2.50

2.60

2.70

2 80

21.90

3.00

3.49

4.99

5.99

6:99

7.99

8.99-

9.99"

14.95"

19.95

24.95

29.95

341.95

39.95

44.95

49.95.

54.95

59.95

64.95

69.95

74.95

79.95

. 84..95

89.95

94.95

99.95

104.95

109.95

1t4.95

119.95

124.95

129.95

134.95

139.95

144.95

149.95

154. 95

159.95

164.95

S69. -95

174.95

I 19. 95

194.91r

iR1 .115

194 ,95

199.95

204 . 95

0 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0. 2 0.

2 0.

2 0.

2-0.

2 0.

2 0.

2 0.

2 0.

2' 0.

2 0. 2 O.

2 0.

2 0. 20.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0..

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

2 0.

20.

2 0.

2 0.

2 0:

2 0.

2 0.

2 0

2 0.

2 0.

2 0.

2 0..

2 0.

2 0.

2 0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

O;

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

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0.

0.

0.

0.

0.

0.

0.

0.

0.

0.

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0.

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0.

0.

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0.

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0.

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0.

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0.

0.

0.

0.

0.

0.

.0.

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0.

0.

0.

0.

0.

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0.

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0.

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0.

0.

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0. 0. 0. 0 O:

:2368- to .-248e-10

.254e- 10

.258e- 10

*26le-iO

.264e-10

.266e-'10

.267e- 10

.268e-10

;269e- 10

.275e- 10 .. 277eý10

.277e'10

.277e- 10

.276e- 10

.275e- 10

.274e- 1o

.243e- 10

.226e-10

.2 I5e- 10

.208e- 10

.203e- t0.

.igge- 10

.196e- to

.t94e- 10

192e- 10 .Igle-.lO,

.1890-10

loge- 10 .1880-10

.188e-10

.187e-10.

.187- 10

.187.- 10

.1870-10

.I 7e- 0

.187.- 10

is.?. - to .Iase-lO

.M8e- 10

.1n9.-tO loge- 10

Iose- 10

.f18e- 10

189e- tO

.. 189e- i0

. 189e- tO

.190'-10

gOp - 10

19(1p- 10

1.90.- 10

l91p- 10

.191C.-I0

.191p- 10,

192e- 10

192e- 10

.166e-07

.174P-07

.179e-07

.82e-07

.- 184e-07

;'186@-07

187e-07

.188e-07

.189e-07

190e-07

194e-07

195e-07

195e-07

195e-07

194e-07

194P-07

193e -07

171e-07

159e-07

Is51e-07

146e-07

143e-07

.140P-07

.138e-07

.136e-07

.135e-07

..134e-07

.134e-07

.133e-07

.133e-07

132e-07

.132e-07

.132e-07

.132e-67

.132e-07

.132e-07

.132e-07

132e-07

.132e-07

132e-07

.132e-07

.132e-07

.t32e-07

.133e07

.133e,07

.. 133e-07

.133e-07

.- 133P-07

134P-07

14•407

.134-07

134P 07

135eP07

135e-07

135-w07

135e-07

.. 100e-06

I ose-06

108-e06 .1100~-•06 :I1 ie'06

.i t2e-06

:1 13e-06

1 13e-06

.114e-06

I 14e-06

I 17e-06

.1180-06

:I ISe-06

118@-06

I 17e-06

.1176e-Os

11. I -06

.1030-06

.9590-07

.914oe-07

.883e-07

:"16 le-07

.845e-.07

. 133e -07

7824.e07

• 817e:07

.81 Ie-07

.807e-07

.803e-07

.800e-07

.798e-07

..797e-07

.796e-07

.7950-07

* 795e-07

* 795e -07

.795.-07

.796e-07

.796e-07

.797e-07

.798e-07

.799e -07

.800e007

* ROle-07

.802e-07

.803e-07

.R04e-07

.RO5e-07

..807P- 07

R809P 07

.8 II "-07 A 120 -07

. A C le - 07

,li~e-07 .815--07

.816.-07

A ise-06

.124e-06

127e-06

129e-06

;131e-06

132e-06

.133eo-06

.134e-06

.134-e06

.135e-06

.138e-06

.138e-06

.139e-06

.138e-06

.138-06

.137e-06

.137P-06

.1229 06

.A 13e-06

.to~e os

.04 e-06

.995e-07

.980e-07

.969e-07

.96 1e-07

.954e-07 .949.-o7?

.945e-07

.942P-07

.939e-0a

.938e-07

.936P-07

.936e-07

.935e-07

.935e-07

.936e-07

.936e-07

.937e-07

-938e-q7

.939e-07

.940e-07

.941e-07

.942P-07

,.943e-07

.945p-.07

.946e-07

..94Re-07

.949P-07

.951P-07

_952e-07

.954P-07

_.955P-07

.957e-07

.959P-07

.Qrf).-07
529.95 2 0. 0. 0. 0. 0. 0. 0. 0. .21te-tO .48e-07 .896e-07 t05e-06.

534.95 2 0. 0. 0. 0. 0. 0. 0. 0:. .211e-10 .49e,07 .897e-07 106e-06

539.95 2 0. 0. 0. "0. 0. 0. 0. 0. .21le-10 .149e-07 .898e.-07, i06e-06

544.95 2 0. 0. 0. 0. 0. 0.' 0. 0. .212e-I 0. .. 49e-07 .900e-07* .106e-06

549.95 2 0. 0. 0. 0. 0 . 0. 0. 0. .2 1.-tO .149e-07 .90Ie-07: 106e.-06

554.95 2 0. 0. 0. 0. 0. 0: O. 0.'' .212e-I0 .149e-07 .902e-07. . 106e406

559.95 2 0. 0. 0. 0. 0. 0. 0. 0. .212e-10 .150e-07 .903e-07 .106e-06

564.95 2 0. 0. 0. 0: 0. 0. 0." 0. .213.-IO .150-07 .904P-07 .106:-06

569.95 20. 0. 0. 0. 0. 0. 0. 0. .213e-,tO tSoe-07 .905e-07 .106e-06.-

574.95) 2 0. 0. 0. 0: 0. 0. 0. 0. .213e-tO A500-07 .906e-07:. .107e-06

579.95 2 0. 0. 0. 0. 0. 0. 0. 0.. .213p- 0 .1500-07 .9070-07. 107e-06-,

594.95 2 0. 0. 0. 0. 0. 0. • Ot 0. .2140-10 .150.-07. .908e-07. f07e-06,

589.95 2 0. 0. 0. 0. 0. 0. 0. 0. .214e-A0 .151e-'07 .909e-07 ".107-06

594.95 2 0. -0. 0. 0. 0. Ox 0. 0. .214e-10 .151e-07 .910e-07. 107e-06,

599.95 2 0-. 0. 0.. 0. 0. 0. 0. 0. .214e-I0 .151e-07 .912e-07 107e606.

604.95 .2 0. 0. 0. 0. 0. 0 . 0. O0 .215e-,0 .151e-07 .913e-07, .107e-040,.

609.95 2 0. 0. 0. 0. 0.. 0. 0. 0.O. .215e-10 .iSle-07, .914e-07 107e-06

614.95 .20. 0. . 0. 0. 01.. 0. 0. 0. .215e-tO .152e-07. .915e-07 .108e-06

combustible type 7 has Ignited at ti we; 619.8000 sec

619.95. 1 .. 222e-04 ..997e-05 .554e-O0 .443e-05 .222e-'05 .222e-OS .776e-05 .133e-04 .554e-05 .776e-05 .299e-04 .Ifle-03

619.95 2 0. .0. 0. 0: 0. 0. 0. 0. .216e-10 .152e-07 .916e-07 .i08oe-06

624.95 I .222e-04ý .998e-05 .555e-05 .444e-05 .222e-05 .222e-05 .776e-05 .133e-04 .555e-05 .776e-05 .299e-04 . I1e-03

624.95 "2 0. 0. 0." 0. : 0. 0.- 0 0.; .221e-lO, .155e-07 .938e-07. . 10i-06

629..95 1 .234e-04 .105e04 .. 594e-05 .467e-O5 .234e-05 .234eý05 .818.-05 .140e-04' .594-O0S Afge-05 .315e-04 .t,7e-03-

629.95 2 0. 0. 0. 0. 0 .. 0 0. .643e-10 .452e-07 .273P 06, .321e-06

634.95 1.,. 234e-04 .,105e-04 .586e-05 .4684-05 .234e-05 .234e-05 .620e005 .141e04 .586e-05 .820e-05 .316-e04 .117e-03

634.95 20. . O. 0. O. 0. 0. 0. 0: .673e-10 .474e-07 .2866-06 .336e-06:

639.95 1 .215e04+ . 106e-04 .587e-05 .470e-05 .235e-05 .235Be05 .822e-05 .141e-04 .587er05 .822e-05 .317P-04 . .117e-03

639.95 20. 0. 0. 0. 0.- 0. 0" . 0. -, .700e-10 .493e-07 .298e-06 .350e006

644.95 1 .235e-04 .10i6e-O4 .588e-OS .470e-O5 ..235e"05 .235e005 .823e- 05 .141.-04 .589e-05 .823e-05 .3,19-04 .l18e-03

644.95 2 0. 0. 0. .- .0. 0, O0. 0 0. .726e-t0 .511e-07 .308e-06,. 363e-06

649.95 I .236e-04. .o06e-04 .589e,-05 .471e-05 .0236e-05 .236e-05 .825e-05 .141e 04- .589e-OS-: .8256-05 .318e-04. I.g8e-03.

649.95 20. . 0.'. 0. . 0 . ,. .:' 0. O .7496-1O .527e-07 .318e-06 .375e -06

654.95 1 .236e-04' .. 106e-0)di .590e-05 .472e-05 .236e-05 .236e-05" .826e-05 142e-04 .590P-05 -. 8260-05 .319e-04 .118e.-03

654 95 2 0. 0. 0. , .0. 0. 0. 0. 0.. .770e-10. .542e-07 .3276-06. .385Q-06

659.95 f .236e-04 .106e-04 .591e-05 .473e-05 .2360e05 .236e-05 .827e-05 :.142e 04 .591e-05 .827e-05 .319e-,04 . Ioe;03.-

659.95 2 0. . 0 0. o0. , 0. 0- - 0. 0. 0 .7900ýtO .556e-07 .336e-06-- .395e-06

664.95 I .237e-04 .106e-04 .5920-OS .473e-05 OS 237e05 O .237e-05 .828e.05 9 142, 04 :5922e05 .828e-OS .319e-04 . I18e,03

664.95 2 0. 0. 0. 0. . 0. 0." 0. 0 ,-,10 .569Se-07 .343e-06 .404e-06

669.95 1 .237e-04 .. 107e-04 .592.-OS .474e.05 .237e-05 .237e-O5 .929e-05 .1426-04 .5920--O .829e-05 .320e-04 .119e-03

669.95 2 0. 0. 0. .0. 01. 0. 0 0 .824e-10 .5800-07 .350e0-06- .412e-06, 674.95 :237e-04 ".107-04S .593.-OS .474e-,05+ ý237,)-05 .237-O 930e- 05 .142e-04. .593e-05 -.8300-05- .-3200e04 .Il9e.-03

674.95 20. 0'. " 0.. " 0. 0. 0. 0 .839e-t0 .59 0e07 .357e-06 .420e-06

679..95 1 .2370-04 .,107e-04 .593e-OS .470eý05.-OS'.237e-05 .237e-05 .831.-05 .142e-04 .593e-05 .831e05 .3200-04 .119e-03

679.95 2 0 0. 0. . 0. -0. 0. 0: .853e-10 .601e-07 .363e-06 .427e-06

684.95 1 .238e-04 .107e-04 .594e-05 .475e-05 .238e-05 .238e-O5 .831e-O5. 143,-04, .594e-05 ;831e-05 .321e-04 . 19e-03.

684.95 2 0., .0 . 0. . .. 0. 0. 0. 0.- 0., .866e-t0 .610e-07 .368e-06 .433e-06

689.95 1 .2380-04 .107e-04 .594-OS -.- . 4756-05' :238.-05 .238.-OS .832e-05 143 04', .5 9 4 e-05 .832e-05, .3210-04, . 1I9e-03t.

6R9.95 2 0. 0. 0. 6 . o.- o. 0.. 0. 08 7.e'10 .618e-07 .373e-06, .

4 3 9 eO06'

694.95 1 .238e-04 .. 107e0-04 .595e-05 .476e-O5" .238e-O5 .238eo05 .832.-05 .143e004 .595--05 .832eý05 .321e.04. . I19ge03

694.95. 2 0. 0. 0. 0. 0. 0. 0. 0. .-89e-10 ..626e-07 .37ge-06- .445e-062

699.95 1 23o-04" .1074-04 .595e-05 .476e-05 .238e-O -. 238e-O5 .833e-05 .143e-04- .595e-05 .833Be05- .32 le-04 .11t9er03

69 .i95 2 0. 0.. 0 00 00. 0. 0 . .899e-10 :633e-07 .3820-06' .450e-06-

704 .-9% I .2710+04 . 107e-04 .5959-05 .476e-'05 238't-05 .238e05 .833.-OS' 143 -04 O 595-05 .833e'05 .321e-04 .AIge,-03

704 .95 2 0. 0.. 0 0. 0. 0. 0. -) 0 .909,- tO .640e-07 .396e;-06. .455e-06

7 09.,.15 I .219e-04 107P-04 .595+-05. .476e.-OS .. 219e05 .238e-05- .834--05 143P O' .595e-O5 .,14.05 32.04 .S19,-03

709.q15 20 0. - 0. 0.0. 0. 0. 0:. .9114- 10 .647.%07 .390P-.06 .459e: 06

114 95 I 236e 04 .,1074-04 .596e-05 .477e-05 .238e-'05 2:-38,-O5 3 .834M051,..143e,-4 .596-'05 .. 34P-05 322e-04 619.-03 .

714. 95 ,,.2 0.. 0. 0. 0. 0: 0. O. 0. .9.' 10 .653, -0 . 3q4P-&0 i .464 -06fi

7 95 210e-04 .107e-04 .596e.-OS ".-477e-05 .2389.-05' :2389 -OS' .834.-OS e f43e.-04' .596-05v .,934P.05 .322e-04 . 1qP.-03,- S • 0.. . 0. . .- - . , a . . O. 0 .. 0 .659, 07 - 98 9 06' . 46. Of'-

724 99 I .2391 04 .1•704 7 5-id , '6-05 .477e-05 .2180-O5 2IR .05 9.634a+0' 1431-04 .59q6o 05 .934P-05 .322P-041 119 e03

724 9q 7,0. . 0'00 00 0. .0. 0. -:.94310-10 .6641.-07 .401P-06 472P. 06;

17N) m : :0 

ý' . . . " "+j.+ . . . " " + . + " :- •
00 729.95 i .238P-04 .107e-04 .596e-05 .477e-05 .. 238e-05 .238e-05..835e-05 .143e-04 .596e-05 .835e-05 .322e-04 119e703

729.95 2 0. 0 0.. 0.Q 0. 0. 0.. 0. 95"e-10 .669e-07 .404P-06 .475e-06

734-95 1 .23e,-04 .107e-04 .596e-05 .477.-05 .239e-05 .239:-OS .835e-05 .I43eýOd .596e-05 :835e-05 .322e-04 .119e-03

734.95 2 0. 0. 0. 0. 0. 00. '. 95Ae-t0 ...675'-07 .4070706 .479e-06

739.95 1 .239e-04 .107e-04 .597e-05 A477e-05 .239o-05 .23ge-05 .835e-05 t43e;04 .597e-05 .835e-O5 .322e-04 ltge-03-

739.95 2 .0 . 0:ý 0: 0'. 0. 0. 0. 0. . -:.965e-10 .679e-07 .410e-06 .483e-06 .. 744.95 .239e-G4 .107e-04 .597e-05 .477e-05, .239e-05 .239e-65 '835e-05 .. f43e-04 .:597e-05 .835e-05 .322e-04 Itge-03 "744.95 2 0. 0. • 0. 0. • 0. 0"O . 0. ':972e-10 .684e-07 .413e-06 -496e!06

'749.95 1 .239e-04 .107e-04. .597e-05 .477e-05 .239e-05 '239e-05 A835e-05 .143e-04 .597e-05 1835e-05 .322e-04 119e-03

7,49.95_ 2 .. _ 0. . 0.. 0. - . 0. 0.". ,0. 0. .978e-AO .689e-07 .416e-06 .489e-06. 754.95 1 .'239e-04 .107e-04 .597e-05 .478e-05. '239e-05 .239e.-05 O83650-05 .143e-04d .597e-05 .836e-05 .322e-04 .. 1i9e-03

754.95 0 0. 0. - 0 . 0. 0. 0. 0. 0O-. .985e-'fO ;693e-07 .4fee%06 -492e-06

759.95 1 .239e-b4 .107,-04 .597e-05 .478:-05 .239e-05 .239@-05 .836e:05 .143e-04 .597e-OS .836e-05 .322e-04 .119e-03

759.95 2 0. 0 "0. 0.7 0., . 1 O -. '0. 0. ".99,le-10 .698e&07 .42le-06 .495e-06

764.95 t .239e-04 .. t0 7 e-04 .597e-05 ..78-05 .239e-05 .239g-05 -:836e-05 .143e-04 .597P-05. :836e-05 .322e-04 .119e-03

:764.195. 2 0. . 0. . 0. 0. , 0.. 0. 0. . .997e-1O .702e-07 .424e'-06 .498e-06

J69.95 I ..239e-0d .107e-04 .5970-OS .476e-05 -239e-05 .239e705 .8 36405 .143e-04 .597e`05 ý836e-05 .322e-04 .119e-03 6 6995. 2,0.-. 0 0. 0. 0. 0. 0. . O0e-09 .706e-07 .426e-06 .501e,06

774.95 1 .239e-'4 .108e-04 .597e-05 .478e-05 .23.e-05 .239e-05 .836e-05 .143e-'04 .597e'-05 .836e-05 .323e,04 .1l9e-03

774".95 2. 20. 0 0. 0. 0 . 0. 0. -. tOle-09 .710e-07 .429e;06 .504e-06 all combustiblemateiawls were consumed by; 777.9000 sec 2

.780.00 I. .135e-03 . 126e-03 7.20e-04 .45e-04 - "450e-04 - 270 -04 90e -04 .153@e03 .540e-04 .540e-04 .990e:04 :900e-03

7AO.00 2 0 0.;. 0. " 0. 0. 0. 0 0. :966e-10 .680e-07 .410e-06 .483e,06

m' "mmm785."00 78500 5. 2 1 0' 1.3560-06 O.. .126e-03 "'. 0. .720.-04 0' .450e-04 . 1-'-'0. :450G-04 .0:O .270.*04 . 900.e-04 . "0 .153e-03 

. "' .540.04 !1 0 -0 .540e-04 .06 07 .990e-04 .3660-06 .900e-03 .4 0 -06

790.00 I .1,35e-03 1l26e-03 -720.e-0 L450e-O4":.450e-04 .270e-04 900e-04 .153e-03 .540e-04 ;540e-04 :990e-04 .900e:03

795.00 20.. 0. ', . 0. 0. 0. 0-o 0. .7750-10 .546e-07 .32e-06 .388e:-06

795.00 1 .5-03 . 03 .720e-04 .450e-04 .450e-04 2700ý04 .900e;04 .1153e.03 4540:-04 .540e-04 .990e-04 -90Oe;03

795.00 2 0. . 0.. 0. 0. - O. 0. 0. 0. .707e-10 .498e-07 .300e-06 .353o-06

I00.00 I .135e-03 .126e-03 .720e-04 .450e-04 .450e-04 .270e-04 " 900e-04 1 153e-03 .540e-04. .540e-04 .990eý04 .900e-03 800.00 2 0. . O..0. 0. 0. 0 -0. 0. 0 0..65le-.10 .458e-07 .277e-06 .325e-06

805.00 I .135e-03 .126,e03 .720e-04 .'450e-d04., 450e-04 .270.-04 ;900e-04 0153e-03 .540e-04 :540e-04 .990oe-04 .900e-03

805.00 2 0. 0. 0. 0. 0'. 0. 0. " 0. .604e-tO .426e-07 .257e.-06 .302e-06

810.00 i .135e-03 .126e-03 .720e-040 450-04. .450e-04 .2700-04 .90e04 -O .53e-03 .540e-04 ..-540e-04 .990e-04 .900e-03

8e10.00 2 0. 0.' 0. 0 . 0., 0. 0. 0. S6Sert .398.-7. .240e-06 .213e-06

.15. . 00 1 *.135e-03 .1•.26e-03 .7 2 0 . 45004 450e-04 .450.e-04 :. 270e-04 -: 900--04 .153e-03 .:540e-G .540e-0d .990:-Gd .900e-03

815.00 2 0.. " 0. 0.- 0. . 0 0. " 0. .533e-10 .375e-07 .226e-06 .266e-06

.820.00 1 .135e-03 .t26e-03 .720e-04 .450e-04 .450e-04 .270.-04 .900e-04 .1530-03 .540.-04 :540e704 .990e-04 .900e-03

820.00 2 0. 0. 0. 0- 0. 0. .0. 0.. . .504e-10 .355e-07 .214e-06 .252e-O6

825.00 . 135e-03 .126e-03 .720e-04 .450.-04 .450e-G4d'.270.-O4 '.900e-04 :.153e-03 .540e-04 .540e-04 .990e-04 .900e-03

825.00 2 0. 0.... . 0. 0. .. 0. . .490e-10 .338e-07 .204eý06 .240eG06

810.00 1 .135e-'03 .126e-03 .?72be 04 .450e-04 .450e-04 .270-04d. .900e-04 .153e-03 .540e-04 .540e-04 .990e.04 .900e-03

830.00 2.0.. 0O. 0 . 0. :0. .459e-10 .323e-O7 .195e-06 .229e-06

835.00 .. 135e-03 .126e-03 .720e-04 .450e-04 .450e-04 .270e-04 .900e-04 .153e-03 .540e-04 .540e-04 .9909e04 .900e-03

835.00 2 0. O. 0. 0. 0. .. O. 0. .440e-10 .3100-07 .187e-06 .220e-06

840.00 1 .35e-03 . f26e-03 .720e-04 .450.'04 -. 450e-04 .270.-04 .900e-04 . 153e-03 .540e-04 .540.-04 .990e-04 .900e-03

840.00 2 0. 0. 0. 0. 00. 0. 0. .423e-1 .298e-07 .180e-06 .212e-06

845.00 1 .135e-03 126e-03 .720e-04 .450e-04 .450e-04 .270e-04 .900e-04 .153e.03 .540e-04 .540e-04 .990.-04 .900e-03

845.00 20. 0. 0. 0. 0. 0. 0. 0. .409e-10 .2889e-07 .1740-06 .204e-06

11850600 1 A35e-03 .126e-03 .720e-04 .450e-04 .450e-04 .270e-04 G .900e-04 .153e-03 .540e-04 .540e-04 .990e-04 .900e.-03

850.00 2 0. 0. . . 0. 0. 0 . 0.O. .396e-10 .279e-07 .168-06 .198e.-.06 855.00 I .135e-03 .126e-03 .720.-04 .450.-04 .450e-04 .270.-04 .900.-0d 1539-03 .540e-04 .540e-04 .990.-04 .900e-03

855.00 2 0. 0. 0. 0. 0. 0. 0. 0.. -.384e-.10 .270e-07 .163e-06 .192e-06

860:00 1 .135e-03 .126e-03 .720e-04 .450e-04 .450e-04 .270e-04 .900e-04 .153e-03 :540e-04 .540e-04 g9900-04 .900e-03

860.00 2 0. 0. 0. 0. 0. 0. 0. 0. .373e-10 .263e-07 .159e06 .187.-06

865:0 0 f f35e-O .126e-03 .720e-04 .450e-04 .,450e-04 .270e-04, .900e-04. .153e-03 .540e-04 .540e-04 .990,-04 .900e-03

865.00 2 G. 0. 0 0. 0. 0. O0. O. .363e-10 .. 256e-07. .154e-06 .182e-06

8R70.00 1s. 135e-03 .126e-03 .720e-04 .450e-04 .4SOP-04 .270e-04 :900e-04 153e-03 .540e-04 .540P-04 .990e-04 .qO0e-03

'70.00 2 0. 0. 0. 0. 0. 0. 0. 0! .355e-fO .250. 07 .151-06 .1I7e-06

R75.00 1 .35e-03 .126e-03 .720e-04 .450e-04 .450e-04 .270.-04 .900i-04 .153e-03 .540,-04 .540e.04 .990e-04 .900e:03

875.00 2 0. 0. 0. IO 0. 0. O. 0. .346.-tO .2244e:07 f4147e7O6 .1 73f.-G6

8R8.00 1. . 135e-O . 126P-01 .720P-04, .4O 0-04 .450e-04 .270e-04 -. 900e-04 153e-03 .540r-04 .540-04 .q9GOe-4 ..900 e03

R890 00 9 0. 0. O. . O. 0. 0. . .:1:3P. 1(0 .219P:07 .144P-06 . 170"-GO
8g5.00 1. t35e-03 .126e-03 .720e-041 .4500-04 _.450e.04 .2700-04 .900e-ad .153e-03 .540e-04 .540e-04 .990e-04 .9000-03

885.00- 2 0. 0. 0. 0. .O 0. 0. 0.. .332e-t0 .234e-07 . idle706 . 166.-06

890.00 1 .135e-03 .126e-03 .720e-04 .450e-04 450e-.04 .270.-04 .900"-04 .153e-03 .540e-04 .540e-04 .990e-O4. .900e-03

.0 2.0. . 0. 0. 0. 0. 0. 0. .326e-10 '.229e-07 .13ge-06 .i63e-06

995.00 . 135e-03 . 126e-03 .720e-04 .450e-04 .450e-04 .270.-04 .900.-04 153e-03 .540.-04 .540e-04 .990e-04 .900e-03

.895-00 2-0. 0. 0. 0. 0. 0. 0. 0. .320e-10 -. 225e-07 .136e-06 .160e-06

900.00 1 135e-03 .126e-03 .720e-04 .450e-04- .450.ý04 270.-04 .900e-04 .153e-03 .540e-04 .540e-04- .990e-04 .900e.03

900 00 2 0. 0. 0. 0. 0. 0 . 0. 0. - .314e-10 .221e-07 .. 134e-06 .157e-06

905.00 1 135e-03 .126e-03 .720e-04 .450e-04 .4500.04 . 270.-04 .A0o0.04 .1536-03 .540e-04 .540e-04 :990e-04 .900e-03

905;00 2 0. 0. 0. 0. O. 0. 0: 0. 0. .309e1i0 .218e-07 . 13ie-06 .155e-06

910.00 1 .135e-03 .1264-03 .720e-04 .456-04.- .450.-04 .270e-04 .900e.04 .153e-03 .540e-04 .540e-04 .990e-04 .900e-03

910::00 2 0. 0. 0. .0.. . . 0. 0. .305e-.10 .214e-07 .129e.-06 .152e-06

915.00 I .135e-03 .'126e-03 .720e-04 .450e-04 .450e-04 .270e-04 .9000-04 153e-03 .540e-04 .540C-04 .990e-04 .AOOe-03

915.00 2 0. a. 0. 0. 0. 0. 0. .300e-10 -. 2111-07 -. 128e-06 .150e-06

920.00 . 135e-03 f26e-03 .720.-04 .450e-04 .450e-04 .270e-04 .900e-04 153o-013 .540e-a4 .540e-04, .990e-04 .900e-03

920.00 2 0. 0. 0. O.. a a....0.- 1 0. 0. .296e-10 -. 208e-07 .126e-06 .d14e-06

925.00 1 .135e-03- .1 26s-03 .720e-04 .450e-04 .450e-04 .270e-04 .9000-04 1534-03 .540e-04 .540e-a4 .990e-a4 .900e-03

.925.00 2,0. 0. 0. 0. 0. 0. 0. 10. .292-710 .206e-07 .1244-06 ,146e-06

930.00 1 . 135.e03 . 126e-03 .720e-04 .450e-04 . 450e-04 .270-a04 .9004-04. 153e-03 .5404-04 '.5404-04 .9900-04 . 900e-03

930.00 2 0.. 0. 0. 0. 0. 0. 0. 0. .289e-la .203e-07 .423e-06 .144e-06

935.00 1 .135e-03 .126e-03 .720e-04 .450e-O4 .450e.04 .270e-04 .9000-04 .1530-03 :.540e-04 .540e-d 04 .990e-04 .900e-03

.935.00 20. a. a. a. O. a! 0. 0. .285e-I0 .20ie-07 .121e06 ,+143e-06

940.00 f .135e0-03 .126e-03 . 720e-04 .4504-04 .450"-04 .270e-04 .900e-04 1530-03 .540e-04 .540@-04 .990e;04 .900e-03

940.00 2-0. 0.. .0. 0. .0. 0.. 0. " .0. .282e-10 .199e-07 . 120e-06 , 14l.e-06

.945:.00 1 , 135e-03 .126@-03 .720e-04 .450e-04 .450e;04 .270e-04 .900e-04- .153@703 .540e-04 .540e-04 .990e.-04 .9000-03

945.00 .2 0. 0. - . 0. 0. 0'. 0. .2790-10 .197e-07 .1 9ge-06 .140e-06

950.00- 1 .135e-03 .I26e-03 .720@-04 .450-a04 .4500-04 .270e-04 .900.-04 .153e-03 :540e-04 .540e-04 .990e-04 .o00e-03

950.00 20. O. 0. 0. 0; 0. 0 0. 0. .276e-10 .,195e-07 .117e-06 .138eý06

955.00 1- . t35e-03 .126e-03 .720e-04 '450@-04 .450e-04 .2700-04 .900-04a .153e-03 .540P.-04 .540e-04 .990e-04 .900e-03

955.00 2 0. 0. :0. 0. ,0. 0. 0. 0. ..274e7-0a .193e-07 .1164-06 .137e-06.

960.00 -1 .,135e-03 .126e-03 .7200-04 .450e-04 .450e-04 .2706-04 .900e-ad4 .53e-03-,.540e-04 .. 540e-04 .990e-04 .900e-03

960.00 2 0. 0.. 0. 0. I 0. 0. 0. 0. .271- I0 .19le-07 .115e-06,. 136de-06

965.,00 I .135e-03 .126e-03 .720e-04 .4506-04 .450e-04 .2700-04 .900.-04 A53e-03 -. 540e-04 .540e-0e .9900-04 .,900e:-03:, 965.00 20. 0. - . 0. 0. O... - : O. 0. -2690-10 . .199e-07 - .114e-06 e135e-06

970.00, 1 I3Se-03 .A26e-03 -. 720e-04 .450e-04- .450e-04 .2706-04 .900-04d .153e-03 :540-04- .540.-04" .990e-04 .9OOe-03

970.00 2 0. 0. 0 0. 0. 0. 0. 0. *'267e., 10 .. 188e-07 .113e-06 .133e-06

975.00 I 135e-03 ý.26e-03" .720e-04 .450e-04 .4500-04 .270e-04: .900e-04 .. 153e-03 .5406664 .54eo-04-. .990e-04 .900e-03

975.001. 2 0. . 0.. 0- 0. 0. 0.- 0. .265e-tO .186e-07 .113e-06 ,.132e-06

9800- 1 .135e-03 .126e-03 .720.-04 .450e-a04 .450e-04 .270.-04 .900-a04 .153e-03 .540e-04 .540e-04 .990e-04 .900e-03

980;00 2 0; . . 0. 0. - 0. 0. -0. - O. " .263e-tO .185e-07 -. 112e-06 .131e-06

985.0 0 - .135e-03 126e-03 .720e-04 .450e-04 .450e-04 .2700-04 .9000-04 153e-03 .540L-04 .540e-04 .994p-04 .900e-03 985.00 2 0. 0. 0. 0. - O. .(O O. - 0 .261e-I0 .l84e-07 4 1tife-06 .130 -06

990:.00•1 : 135e-03 .126e-03 .720e-04': 450e-04 .2 4500-04. .2706-04 .900.-d4 .1530-03 ,.540 -.:-a .540e-04 .9909-04 .900e-03

990.00 20.. 0. 0. 00 0. 0. .. o. .259.e-a %.182P07 . f- fO-06 . r30,-06.

995:00 1 . 135e'03 . 126r-03 .720e-04 .450e-04 .450e-04 .270e-04 .9000-04 153e'-03 .540e4O44 .540e-04 .990e-04 .900eP-03

995.00 0. 0. 0. . 0. 0. 0. .25ae-t0 .181e-07 . m9e*-6 .129e-06-

1.0
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302
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ITLE AND SUBTITLE 4 RECIPIENTS ACCESSION NUMBER

IRAC User's Manual: A Computer Code to Simulate

ire Accidents in Nuclear Facilities 5 DATE REPORT COMPLETED

MONTH 1YEAR

__February 1986

UTHOR(S) 7 DATE REPORT ISSUED

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SUPPLEMENTARY NOTES

ABSTRACT (200 words or lessi

This user's manual supports the fire accident analysis computer code FIRAC. FIRAC is

lesigned to estimate radioactive and nonradioactive source terms and to predict fireinduced flows and thermal and material transport within the ventilation systems of nuclear

Fuel cycle facilities. FIRAC has been expanded and modified to include the capabilities

)f the zone-type compartment fire model computer code FIRIN developed by'Battelle Pacific

4orthwestfLaboratories. The two codes have been coupled to provide an improved simulation

)f a fire-induced transient within a facility. The basic material transport capability

)f FIRAC has been retained and includes estimates of entrainment, convection, deposition,

ind filtration of material. Also, the interrelated effects of filter plugging, heat

transfer, gas dynamics, material transport, and fire and radioactive source terms are

3imulated.

This report summarizes, the physical models that describe the gas dynamic, material

transport, heat transfer, and source term processes and illustrates how a typical

facility is modeled using the code. The modifications required to couple the code to

FIRIN also are presented. Finally, the input and code-calculated output for several

sample problems that illustrate some of the capabilities of the code are described.

KEY WORDS AND DOCUMENT ANALYSIS 15b DESCRIPTORS

FIRAC computer code

FIRIN computer code

fire accident

source term

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