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The Establishment of A Catalog of

Compartment Fire Model

Algorithms and Associated

Computer Subroutines

Reference

NBS

PUBLICATIONS

David W. Stroup

U S DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1 985

v« O *

U S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
\
NBSIR 85-3263

THE ESTABLISHMENT OF A CATALOG OF

COMPARTMENT FIRE MODEL

ALGORITHMS AND ASSOCIATED

COMPUTER SUBROUTINES

NATIONAL BUREAU OF STANDARDS

LIBRARY

6

i

David W Stroup

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1985

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
TABLE OF CONTENTS

Page

Abstract 1

The Establishment of a Catalog of

Compartment Fire Model Algorithms and

Associated Computer Subroutines 2

APPENDIX A: CATALOG INTRODUCTION 4

APPENDIX B: CATALOG TABLE OF CONTENTS 13

APPENDIX C: CATALOG ENTRIES 19

APPENDIX D: REFERENCES 45

ii
The Establishment of a Catalog of Compartment Fire Model

Algorithms and Associated Computer Subroutines

David W. Stroup

ABSTRACT

The Compartment Fire Model Research group of the Center for Fire

Research, National Bureau of Standards has been charged with the development of

a "benchmark" compartment fire model. As part of this activity, a catalog of

available fire model algorithms is being compiled. This paper presents a proposal for the organizat ion , format, and use of the catalog. Appendix A of

this report is a copy of the proposed introductory text for the catalog.

Appendix B presents the Table of Contents for the first edition of the catalog,

and Appendix C contains several examples of catalog algorithm write-ups.

Finally, Appendix D lists the references used in Appendix A.

Keywords: algorithms; building fires; cataloging; combustion physics;

compartment fires; computer programs; fire chemistry; fire models; mathematical

models; zone models.

1
The Compartment Fire Model Research group of the Center for Fire

Research, National Bureau of Standards has been charged with the development of

a "benchmark" compartment fire model. As part of this activity, a catalog of

available fire model algorithms is being compiled. The catalog will contain

algorithms which calculate various physical/chemical fire phenomena.

The description of each algorithm will include the input(s), output(s),

and calculations performed. In addition, each algorithm will have a computer

subroutine written for it in FORTRAN 77. The variables used as input and

output throughout the catalog will be cross-referenced. This will enable a

catalog user to easily determine which routines would be required to calculate

a particular fire phenomena.

Appendix A is a draft of the introductory text of the catalog. It begins

with a brief discussion of the purpose of the catalog. Following these

remarks, there is a description of fire dynamics and fire models. Appendix A

details how the catalog will be published and updated. It outlines the format

used to present each algorithm as well as describing the method used to

cross-reference variables. Through the use of an example, the utility of the

catalog for upgrading and enhancing existing fire models is illustrated.

Appendix B is a tentative List of Algorithms for the first release of the

catalog. It shows the major catalog divisions and the many algorithms to be

included under each heading. The majority of these algorithms in the first

2
edition are derived from the NBS/Harvard 5.N and 6.N Compartment Fire Model

computer programs.

Appendix C presents several algorithm write-ups including those

referenced in the example discussed in Appendix A. These write-ups are shown

as they would appear in the actual catalog. Appendix D lists the references

that are used in Appendix A (the catalog introduction).

In summary, the Appendices to this paper illustrate the proposed format

for the Compartment Fire Model Algorithm Catalog. Comments on the text and

ideas presented are heartily solicited.

3
APPENDIX A.

Compartment Fire Model Algorithm Catalog
1. INTRODUCTION

Many mathematical models and associated computer programs have been

developed to predict enclosure fire dynamics [1-15]^. These models differ in

many respects. They differ in the number and complexity of fire compartments

which may be analyzed; the amounts of computer time and memory required; the

number and detail of individual physical phenomena accounted for; the amount

of documentation available; and the degree of "user-friendliness". Regardless

of the many differences, all of these models attempt to describe the same basic

fire phenomena. It is possible to break existing fire models up into

"elemental" pieces. These "elemental" pieces describe the physical/chemical

effects associated with the fire phenomena.

It is the purpose of this catalog to present the available

physical/chemical algorithms and corresponding subroutines in a form which may

be used by fire researchers who wish to develop or improve fire modeling

computer programs. Researchers may use routines from the catalog according to

their needs and take advantage of the progress made by others. The catalog

contains descriptions of the methodologies used to calculate each of the

fire related physical/chemical phenomena. In addition, a FORTRAN 77 computer

subroutine which implements the method is included with each algorithm

write-up

1 Numbers in brackets refer to references listed in

Appendix D.

5
This catalog provides fire researchers with convenient access to each

others' work. It eliminates the need for researchers to continually redevelop

the same algorithms. For the most part, only the most accurate and efficient

algorithms and subroutines are included in the catalog. The catalog is

published in loose-leaf form so that old algorithms may be improved and new

ones added as necessary. Finally, to be successful, this catalog will require

user support and feedback which is heartily encouraged.

2. FIRE DYNAMICS

The physical and chemical processes simulated by the algorithms and

subroutines in this catalog are relevant to compartment fire-generated

phenomena. The generic fire scenario of interest can be briefly described as

follows. An unwanted ignition is assumed to occur within an enclosed space.

The fire may start in a couch, for example, or stacked commodities in a

warehouse. Regardless of the method and location of ignition, the applicable

physical/chemical phenomena discussed below will be the same.

Heat from the initial flame pyrolyzes the material of fire origin. The

resulting vapors rise into the flame zone, ignite, and maintain the flame. The

elevated temperature products of combustion are driven out of the combustion

zone by buoyancy. In this way, a plume of upward moving elevated temperature

gases is formed above the fire. The gas entrains some of the surrounding

air and the mixture rises to the ceiling. When the plume impinges on the

ceiling, it spreads out and forms a relatively thin, hot, sooty layer. As the

6
fire grows, this layer will thicken and. the relatively sharp interface between

it and the cool ambient air layer below will continuously drop. Eventually,

the layer falls below the top of the highest vent, whereupon buoyancy-generated

cross-vent pressure differentials will drive some of the layer gases out of the

room. In addition to energy losses from the flow of hot gases out of the

vent(s), the layer also loses energy by radiation and convection to the

floor, ceiling, walls, and other objects within the room.

Due to heating from the elevated room temperature environment,

combustible objects in the room remote from the fire, may eventually reach

their ignition temperature, and ignite. If such ignitions begin to occur, they

may follow one another very rapidly, until all combustible objects within the

room are burning. This transition period between ignition of the first "target

item" and full room involvement is called "flashover." It generally only lasts

a few seconds. Following flashover, the fire may spread from the room of

origin to other parts of the building, thus presenting a severe danger to

life and property.

3. FIRE MODEL TYPES

Many attempts have been made to model the above fire phenomena

mathematically. Fire models may be divided into two main groups. The first

group is composed of probabalistic models. Models in this group "calculate"

fire development based on the probability of one event following another.

Routines from these models will not be discussed in this catalog.

/
The other group consists of deterministic models. In general, these

models solve differential and/or algebraic equations to determine the

time-varying fire characteristics. The deterministic models may be further

sub-divided into categories which describe the assumptions used to solve the

problem. The first of these groups is "field" models. Field fire models

describe events within an enclosure volume by a set of coupled partial

differential equations, which are applicable throughout the volume, and which

stipulate boundary conditions at the surfaces of the volume. Field models are

generally very complex and require large amounts of computer time and memory.

The other group consists of the "zone" models. The zone type fire models

divide the room into zones, usually three. The three zones are an upper zone

which includes the smoke layer, a lower zone which contains relatively cool and

uncontaminated air, and a combust ion/plume zone which transports the smoke from

the fire below to the upper smoke layer. Models developed using the zone

concept range from very simple to very complex.

The focus of attention of this catalog is on the physical/ chemical

algorithms which would be used in zone-type models and, possibly, in hybrid

models which combine both zone-type and field-type descriptions of the

fire-generated compartment environment.

8
4. CATALOG ORGANIZATION

This catalog of compartment fire model algorithms is intended to be used

as a reference by persons desiring to develop their own fire models or enhance

existing ones. Each algorithm write-up, contained in the catalog explains the

methodology for calculating a fire related parameter. The format, used to

present each algorithm, has been chosen to be as "user-friendly" as possible.

The catalog is being issued in loose-leaf form. This will make it easy to

update, and updates, including new and improved algorithms, will be issued

periodically. The catalog is divided into eight sections. They are: Burning

Object, Conductive Heat Transfer, Convective Heat Transfer, Hot Layer, Plume,

Radiative Heat Transfer, Room Conservation, and Vents. Each section contains

one or more algorithms which calculate result(s) related to that section

heading. An individual algorithm is only described once. However, if the

algorithm could logically be expected to be found under two or more headings,

reference to the complete algorithm description may be found under each

appropriate heading.

Each algorithm is described individually. The algorithm's name and brief

title appears at the top of each page. The first section. Description ,

describes the methodology used in the algorithm. In addition, the major

limitations of the algorithm are listed as are any other details which may be

important to someone wishing to incorporate the algorithm into a fire model.

The second section, Output , lists the output variable(s), with a brief

description of the meaning of each variable. The number of output variables

from a given subroutine are generally limited to one. This enables a catalog

9
user to build a complete fire model using relatively small pieces of the

phenomena. It also makes it possible to include alternate algorithms for

modeling the same phenomena. The third section. Input , includes a list of the

required input variables along with a brief description of each variable. Each

input variable is identified as to whether it is a physical constant, input

data, or calculated physical variable. Input variables are cross-referenced so

the user can easily find required input which is calculated by routines

elsewhere in the catalog.

A fourth section, Calculations , presents the step-by-step procedure or

algorithm used to calculate the result. The meaning of each calculation is

briefly described next to the calculation. The fifth section, References , is a

listing of reference sources where the user may obtain more information

about the theory used to develop the algorithm, its limitations, and/or its

implementation in other fire models. Section six, Subroutine Variables ,

relates the variables used in the output, input, and calculations sections to

the associated FORTRAN variables. Finally, section seven, Computer Subroutine ,

presents the FORTRAN 77 computer subroutine which implements the algorithm.

5. AN EXAMPLE OF USING THE CATALOG

Suppose a fire researcher wishes to improve the modeling capabilities of

the ASET (Available Safe Egress Time) computer code[7,8j. A likely improvement

would involve use of a more fundamental means of estimating heat transfer to

the compartment ceiling. This improvement would require an algorithm for

calculating the transient heat conduction through the depth of the ceiling

10
material. Such an algorithm and its associated subroutine can be found in the

section on Conduction Heat Transfer in the Catalog. In that section, there is

an algorithm named TMPW01 (see Appendix C of this report). It may be used to

calculate the transient heat conduction through a surface exposed to radiative

and convective heating.

In the vrite-up of this algorithm, there is a listing of the required

inputs. Many of these deal with characteristics of the wall or ceiling material

and may be obtained from published data on thermophysical properties of

materials. Another input, the layer height, is already calculated in the ASET

model. Inputs describing the convective and radiative fluxes being received by

the material are also required. For these, the modeler might use the simple

assumptions already used in the ASET model. (In the ASET model the total rate

of heat transfer to bounding surfaces of the compartment is represented as a

constant fraction of the instantaneous fire heat release rate.) The

alternative would be to compute these inputs using algorithms and subroutines

referenced elsewhere in the catalog and to incorporate these subroutines into

the ASET model.

The final input required by this routine is the infra-red absorptivity of

the hot layer. The Catalog contains several algorithms useful for calculating

this value. The simplest is ABSRB2 (see Appendix C of this report). It

assumes the absorptivity is a constant fraction cf the mass concentration of

the soot in the hot layer. If this routine is selected, another input is

required. This input represents the mass concentration of soot in the layer as

a function of time. In this case, a simple way to represent this value would

11
be to use the product of combustion calculation capability of the ASET model.

The soot concentration could be modeled as either a constant fraction of

the heat release rate or as input data from fire tests.

Using these two subroutines, TMPW01 and ABSRB2 , it would be possible to

incorporate heating of a slab (ceiling, floor, or wall) into the ASET model.

This would be the first step in developing an improved method of calculating

the fraction of heat lost to the bounding surfaces of the room from elementary

principles. The modeler would have to find a way to control the calling of

these subroutines, but the subroutines themselves would not have to be

developed again.

12
APPENDIX B.

List of Algorithms in the Catalog

13
1. Burning Object

ANGLE Calculates the angle of the flame cone based on radius of fire and

height of flame.

BURN Calculates the rate of burning, on a mass basis, of the vapors

released by a combustible object.

CHEM Calculates the rate at which chemical energy is released from a burning object.

FLUX Calculates the heat fluxes from the hot layer, plume(s), and walls,

incident on the surface of a burning object.

HEIGHT Calculates the height of the flame of a burning object.

PFLUX Calculates the net heat flux from user determined sources to a potentially pyrolyzing surface.

PULRAD Calculates the radius of a pool fire.

PYRO Calculates the mass pyrolysis rate of a burning horizontal fuel

slab

SPREAD Calculates the rate of spread of a fire on a horizontal fuel slab.

TANPSI Calculates the tangent of the angle of the flame cone based on constant volumetric heating (open air burning).

TMGAS Calculates the gas flow rate, at a given time, from a burner with a variable gas flow rate.

2. Conduction Heat Transfer

CONDUC Calculates the heat conduction from the surface into the interior

of a pyrolyzing fuel item.

TMPOOl Calculates the temperature of an object by a "shortcut" method when

the object is heating or pyrolyzing.

TMPO02 Calculates the temperature profile within an object using a discrete grid.

TMPW01 Calculates the temperature profile within a wall (slab) using a discrete grid.

14
3. Convection Heat Transfer

CBLOCK Calculates the convective heat flux from the flame above to the

surface of a burning pool.

CNVF Calculates the convective heat flux from the lower layer to the

floor assuming that radiation (from the flames and from the hot

layer) heats the floor, and that in turn will heat the (cool) lower

layer of gas above it by convection.

CNVL Calculates the convective heat loss rate from the hot layer to the

extended ceiling.

CNVL1 Calculates the rate of loss of energy from the hot layer in a room

due to convective heating of the walls and ceiling.

CNW01 Calculates the convective heat flux to one side of a wall from the

adjacent hot layer.

THERM Calculates the thermal conductivity of air as a function of

temperature (required by CNVF).

vise Calculates the kinematic viscosity of air as a function of

temperature (required by CNVF).

4. Hot Layer

ABSRB2 Calculates the infra-red absorptivity of the hot layer.

ABSRB3 Calculates the infra-red absorptivity of the hot layer (requires

EMSVTY and associated routines).

ASYMP Calculates the asymptotic expansion for the penta-gamma function

(required by PENTA )

CHEBY Calculates the value of the Chebyshev polynomial of order N and

argument x (required by SCRTH).

DLECK Calculates the 2.7 and 15 micrometer overlap correction for

mixtures of CC>2 and H 2 O (required by EGAS).

DXDCNC Calculates the mass concentration of carbon dioxide in the hot

layer

DXDPRD Calculates the rate at which the fire of an object produces carbon

dioxide

EGAS Calculates the emissivity of a given path of a mixture of carbon

dioxide and water vapor at temperature t (required by EMSVTY).

15
EMSVTY Calculates the emissivities of the isothermal and homogeneous

mixtures of soot, carbon dioxide, and water vapor at a total

pressure of one atmosphere (required by ABSRB3).

LAYDPT Calculates the depth of the hot layer.

MNXCNC Calculates the mass concentration of carbon monoxide in the hot

layer

MNXPRD Calculates the rate at which the fire of an object produces carbon

monoxide

OXYCNC Calculates the mass concentration of oxygen in the hot layer.

PENTA Calculates the value of the penta-gamma function of argument x.

POWL Calculates the rate of change of the energy of the hot layer.

RBLOCK Calculates the absorption of radiant flux directed toward the fuel

surface as a result of a layer of cool, absorbing fuel gas close to

the pyrolyzing surface.

SCRTH Calculates the chebyshev polynomials for carbon dioxide and water

vapor (required by EGAS).

SOOT Calculates the transmissivity of the path of soot to a blackbody

radiation source at a given temperature (required by EMSVTY).

SUTCNC Calculates the mass concentration of soot in the hot layer.

SUTPRD Calculates the rate at which the fire of an object produces soot.

TC02M Calculates the rate of change of mass of carbon dioxide in the hot

layer

TH20M Calculates the rate of increase of mass of water vapor in the hot

layer

TMNXM Calculates the rate of increase of mass of carbon monoxide in the

hot layer.

TMPL Calculates the temperature of the hot layer.

TMSL Calculates the rate of change of the mass of the hot layer.

TOXYM Calculates the rate of change of mass of oxygen in the hot layer.

TSUTM Calculates the rate of change of mass of soot in the hot layer.

WTRCNC Calculates the mass concentration of water vapor in the hot layer.

16
WTRPRD Calculates the rate at which the fire from an object produces water

vapor

5 . Plume

DPLUM Calculates the rate of change of the mass of a fire plume

(Delichatsios model).

ENTPL Calculates the rate of entrainment of the layer gases into the

upper part of the plume over an object (inside hot layer).

HPLUM Calculates the rate of change of the mass of a fire plume (modified

Hasemi model).

MPLUM Calculates the rate of change of the mass of a fire plume

(McCaffrey model).

OXYBRN Calculates the mass rate of oxygen burning in the plume of an object.

PLMHT Calculates the height of the plume over an object.

PLUM Calculates the dimensions and rate of change of mass and energy of

a fire plume (virtual point source).

PTPLUM Calculates the dimensions of and throughput of mass and energy in a plume above an object (point-source).

TENPLM Calculates the rate at which the plume over an object adds energy

to the hot layer.

TMSPLM Calculates the rate at which the plume over an object adds mass to

the hot layer.

ZPLUM Calculates the rate of entrainment of mass in a fire plume

(Cetegen, Zukoski, Kubota model).

6. Radiation Heat Transfer

PWRPLR Calculates the power (energy) absorbed by the layer due to

radiation from the fire plume of a burning object.

RADFW Calculates the radiative flux from the fire plume of a burning

object to the walls of the room.

RADLW Calculates the radiative flux from the hot layer to the portion of

the walls and ceiling covered by the hot layer.

RDNL Calculates the energy losses and gains of the hot layer via

radiation (using an empirical value of optical depth).

17
RDNP

RDNW

RNFF02

RNLH

RNLV

RNP001

RNW002

NEWMAS

CVWID

FLOW

ROUND

SPECFL

VNTCVR

Calculates the total radiative heat loss from the flame of a burning object. [The flame is assumed to be a cone or conical

shell .

Calculates the radiative heat transfer to the portion of the walls

and ceiling contiguous to the hot layer, from the flame(s) and the

hot layer. [The layer is approximated by a cylinder, with the fire

centrally located and itself further approximated by a point source at the centroid.]

Calculates the energy absorbed by a flame due to radiation from

another flame which may be shaded by a fuel slab.

Calculates the radiative flux to the horizontal surface of an object from the layer via a cylinder approximation (even if the

object is burning).

Calculates the radiative flux from the layer to the surface of a vertical object via a cylinder approximation (even if the object is

burning )

Calculates the sum of the radiative fluxes from flames to objects.

Calculates the radiative flux from the walls and ceiling in a room

to the top surface of an object (even if the object is burning).

7. Room Conservation of Mass

Check for conservation of mass in a room.

8. Vents

Calculates the width of the segment of a given vent which

intersects the interface between the hot and cold layers.

Calculates the energy and mass flow through a vent.

Linear for large values of x and rounds out the Vx singularity at

small values of x (used by FLOW).

Calculates the mass flow rate of each of the gaseous species

through a vent.

Calculates the area of a vent covered by the hot layer.

18
APPENDIX C.

Catalog Entries

19
CHEM - Chemical Energy Release Rate from a Burning Object

Description

This routine calculates the rate at which chemical energy is released from

a burning object. The energy release rate of an object is a function of the

object's rate of burning and its heat of combustion. In this routine, an

effective heat of combustion is used. This accounts for the energy required to

raise the object’s temperature from ambient to its pyrolysis temperature.

The power output by combustion is then calculated using this effective heat of

combustion and returned as a negative value.

Output

Rate of chemical energy release from a

burning object. [W]

Input

C

P Specific heat of ambient air (Input

Data). [J/kg-K]

H,c Heat of combustion of the object as

fuel (Input Data). [J/kg]

20
Ta Ambient temperature of the room containing

the object (Input Data). [K]

T

P Temperature of object at onset of pyrolysis

( Input Data) . [K]

TMb Burning rate of object (Calculated Value,

see Burning Object section), [kg/sec]

Calculations

H' = H„ - Cn (T„ - T a ) Effective heat of combustion. L L, P P ^

Ef = -m^ * Negative of power output by combustion.

References

1. Mitler, H.E., "The Physical Basis of the Harvard Fire Codes," Home Fire

Project Technical Report No. 34, Harvard University, October 1978.

Subroutine Variables

TEOZZ = E f

21
CP = c

p

QF = Hc ZKAZZ = TCL ZCOPY = T

p

TMOZB = mb

22
oo

Computer Subroutine

SUBROUTINE CHEM ( CP , QF , ZKAZZ , ZCOPY , TMOZB , TEOZZ

)

Vc s’« -,’c ;'c * -,V * * * V: * Vc >'< * V; v\- * * * * * >'< >'< * -c * * >'{ >'< * Vc * ** >'»• * * V; *

IMPLICIT DOUBLE PRECISION (A-H,0-Z)

C

C SUBROUTINE TO CALCULATE THE RATE AT WHICH CHEMICAL ENERGY IS

C RELEASED FROM A BURNING OBJECT.

C

C INPUT PARAMETERS:

C CP -- SPECIFIC HEAT OF AMBIENT AIR

C QF -- HEAT OF COMBUSTION OF THE OBJECT AS FUEL

C ZKAZZ -- AMBIENT TEMPERATURE OF THE ROOM CONTAINING THE

C OBJECT

C ZKOPY -- TEMPERATURE OF THE ONSET OF PYROLYSIS OF THE

C OBJECT

C

C INPUT VARIABLES:

C TMOZB -- MASS BURNING RATE OF OBJECT

C

C OUTPUT VARIABLE:

C TEOZZ -- CHEMICAL ENERGY RELEASE RATE OF THE OBJECT

C

TQF = QF - CP * (ZKOPY - ZKAZZ)

C PATCH TO PREVENT TEOZZ FROM STAYING AT 0. AFTER AN OBJECT MOVES

C OUT OF THE HOT LAYER.

TMB = TMOZB

IF (TMOZB .LE. 0 . DO ) TMB = l.D-6

TEOZZ = -TMB * TQF

10 CONTINUE

C

RETURN

END

23
PYRO - Mass Pyrolysis Rate of Burning Object

Description

This subroutine calculates the mass pyrolysis rate of a burning

horizontal fuel slab. The pyrolysis rate is taken to be proportional to the

net heat flux to the surface and to the (instantaneous) burning area. The net

heat flux is the radiation incident from all sources (principally the flame)

plus the convective heating from the flame, minus the reradiation. For

small flames convective heating is substantial, but rapidly falls in importance

as the flame grows. Theoretical expressions for it exist, but they are very

complex. In this algorithm, the reradiation is simply cut down for small

flames in such a way that the observed growth rate of pyrolysis is followed.

This ad hoc procedure turns out to be very simple. The energy loss by

diffusion into the slab is ignored. The pyrolysis rate is also modified (in an

arbitrary way) to take into account the smooth cessation of pyrolysis as the

fuel nears burnout.

Output

mf Mass pyrolysis rate of burning

slab, [kg/sec]

24
Input

Hv

R

TT

Heat of vaporization of the object (Input

Data). [J/kg]

Flux impinging on the surface of the object

(Calculated Value, see Burning Object

section) . [W/m z

]

Remaining mass of object (Calculated Value,

see Burning Object section), [kg]

Radius of fire on object (Calculated

Value) . [m]

Pi (Physical Constant). [3.141592...]

Calculations

m(3~

-itR 2 (J)/Hv , d > 0

0, d S 0

G = mf / (2mp)

mf = mp(l-eG

), d > 0

0, d S 0

Unadjusted rate of change of fuel

mass (negative of pyrolysis rate).

Convenient definition (for m^ < 0

)

Negative of pyrolysis rate,

adjusted for smooth burnout.

25
References

1. Mitler, H.E., "The Physical Basis for the Harvard Fire Codes," Home Fire

Project Technical Report No. 34, Harvard University, October 1978.

Subroutine Variables

TMOZZ = mf

QVAP = Hv

PHI =

ZMOZZ = mf

ZRFZZ = R

PI = u

26
o

n

Computer Subroutine

SUBROUTINE PYRO ( QVAP , PHI , ZMOZZ , ZRFZZ , TMOZZ

)

vV * * * * * * V; * V; * * * * * V; * * * Vc ** >V * ?< *** * * *** * 'A* >’c A- A A* A A A A A A A AA A A A A A A A

IMPLICIT DOUBLE PRECISION (A-H,0-Z)

C

C SUBROUTINE TO CALCULATE THE MASS PYROLYSIS RATE OF A BURNING

C OBJECT.

C

C INPUT PARAMETERS:

C QVAP -- HEAT OF VAPORIZATION OF THE OBJECT

C

C INPUT VARIABLES:

C PHI -- FLUX IMPINGING ON THE SURFACE OF THE OBJECT

C ZMOZZ -- REMAINING MASS OF THE OBJECT

C ZRFZZ -- RADIUS OF THE FIRE ON THE OBJECT

C

C OUTPUT VARIABLE:

C TMOZZ -- NEGATIVE OF MASS PYROLYSIS RATE OF THE OBJECT

C

PARAMETER (PI = 3.1415927D0)

C

TMOZZA = TMOZZ

C

IF (PHI .GT. 0 . DO ) THEN

TMO = -PI * ZRFZZ**2 * PHI / QVAP

C

C THE FOLLOWING LINES PRODUCE A SMOOTH CUT-OFF OF BURNING AT

C FUEL EXHAUSTION.

C

IF (TMO .NE. 0 . DO ) THEN

G = ZMOZZ / (2. DO * TMO)

IF ( ABS(G) .LT. 30. DO) THEN

TMOZZ = TMO * ( 1 . DO - DEXP(G))

ELSE

TMOZZ = TMO

ENDIF

ELSE

TMOZZ = 0.D0

ENDIF

ELSE

TMOZZ = 0.D0

ENDIF

C

RETURN

END

27
SPREAD - Fire Spread Rate on Horizontal Fuel Slab

Description

This routine calculates the spread rate of a fire on a horizontal fuel

slab, ignited at the center of its top surface. The fire grows slowly until

the entire surface (including the sides) is burning. The fire radius grows

until it reaches a maximum such that the resulting area is the area of the top

plus sides of the slab. This equivalent maximum radius, Rj^, is of course

larger than the radius corresponding to the top surface. The spread rate until

R = O.QSR^ is given by an expression which yields approximately exponential

growth (as observed). Beyond that point, the spread rate is taken to slow

down, as shown under the section "Calculations" below.

Output

R Spread rate of a fire on a horizontal fuel

slab, [m/sec]

28
Input

A

T f

Rm

R

<D

a

Spread rate parameter (Input Data), [m/sec]

Flame temperature (Input Data). [K]

Maximum burning radius of the object (Input

Data), [m]

Current radius of the fire on the object

(Calculated Value, see Burning Object

section), [m]

Flux incident on the surface of the

object (Calculated Value, see Burning

Object section). [W/m z

]

Stefan - Boltzmann constant (Physical

Constant). [5.67 x 10~® W/m‘-K u

]

Calculations

C = © / oT£ Convenient non-dimensional grouping of

terms

.

29
Rate of change of fire radius.

j AC(l+| + ^), R $ .95Rm

R =

( (Rm

-R)/10, R > . 95Rm

References

1. Mitler, H.E., "The Physical Basis for the Harvard Fire Codes," Home Fire

Project Technical Report No. 34, Harvard University, October 1978.

Subroutine Variables

TRFZZ = R

A = A

T = T f

ZRFZM = Rm

ZRFZZ = R

PHI = d>

SIGMA = o

30
o

o

Computer Subroutine

SUBROUTINE SPREAD ( A , T , ZRFZM , PHI , ZRFZZ , TRFZZ

)

IMPLICIT DOUBLE PRECISION (A-H.O-Z)

C

C SUBROUTINE TO CALCULATE THE SPREAD RATE OF THE FIRE ON AN

C OBJECT.

C

C INPUT PARAMETERS:

C A

- - FIRE SPREAD PARAMETER

C T -- FLAME TEMPERATURE

C ZRFZM -- MAXIMUM BURNING RADIUS OF THE OBJECT

C

C INPUT VARIABLES:

C PHI -- FLUX INCIDENT ON THE SURFACE OF THE OBJECT

C ZRFZZ -- RADIUS OF THE FIRE ON THE OBJECT

C

C OUTPUT VARIABLE:

C TRFZZ -- SPREAD RATE OF THE FIRE ON THE OBJECT

C

PARAMETER (SIGMA = 5.67D-8)

C

ZRFZZA = ZRFZZ

C

C = PHI / (SIGMA * T**4)

IF (ZRFZZ .LE. 0.95D0*ZRFZM) THEN

TRFZZ = A * C * ( 1 . DO + C/2. DO + C*C/3.D0)

ELSE

TRFZZ = (ZRFZM - ZRFZZ) / 10. DO

ENDIF

C

RETURN

END

31
TMPW01 - Heat Conduction in a Slab

Description

This algorithm calculates the time dependent temperature profile inside a

slab. A slab of thickness, 6, is exposed to radiative and convective heat

fluxes on its front and back surfaces. The temperature profile through the

slab is calculated numerically by cutting the slab into pieces (parallel to its

front surface), and solving the one-dimensional heat diffusion equation by

finite differences (see for example Holman, Heat Transfer , pp. 72-98).

To calculate the slab temperature profile, the slab thermal properties

(conductivity, diffusivity, specific heat, and density) and its thickness must

be known. It is also necessary to know the convective and radiative fluxes to

which the slab is exposed. These may be calculated elsewhere in the user's

program or appropriate routines may be inserted directly into this subroutine.

Of course, the user will have to make sure the necessary input data is

available to the routine when needed. This routine may be used to calculate

temperature profiles in walls, ceilings, or floors with the appropriately

specified boundary conditions.

This algorithm requires that the present layer height be specified. This

is usually available from most fire models. The absorption coefficient of the

hot layer must also be specified or calculated in some way. Various methods

for calculating this value may be found in the Hot Layer section of this

catalog. The user must specify the time step to be used in the calculation as

32
well as the maximum number of layers into which the slab may be divided. The

method outlined below will automatically calculate the number of layers

required for stable calculations. If this exceeds the maximum allowable, the

maximum number of layers will be used. The Stef an-Boltzmann constant must be

specified for use in the radiation calculations.

Finally, the slab temperature profile at the end of the previous time

step must be known. Initially, the entire slab is assumed to be at ambient

temperature. After a calculation is completed, the new temperature profile

must be stored and later returned as input for use in the calculation at the

next time step.

This routine assumes that the interior part of the slab radiates to an

environment at some temperature, Tp, while the exterior part of the slab

radiates to an environment at ambient temperature, Ta

.

Output

Thew

; i = 1,2,...,N Slab temperature profile. [K]

Input

• (I q^D Convective heat flux from layer to interior

side of slab (Calculated Value, see Convective

Heat Transfer section). [W/m 2

]

33
^LWR

• 1 f ^PWR

• M ^AWD

^AWR

# II QPR

At

Radiative heat flux from layer to interior side

of slab (Calculated Value, see Radiation Heat

Transfer section). [W/m 2

]

Radiative heat flux from plume(s) to interior

side of slab (Calculated Value, see Radiation

Heat Transfer section). [W/m*]

Convective heat flux from layer to exterior side

of slab (Calculated Value, see Convective Heat

Transfer section). [W/m*]

Radiative heat flux from layer to exterior side

of slab (Calculated Value, see Radiation Heat

Transfer section). [W/m‘]

Radiative heat flux from plume(s) to exterior

side of slab (Calculated Value, see Radiative

Heat Transfer section). [W/m 2

]

Size of current time step (calculated within

routine), [sec]

Ambient temperature of air. [K]

Temperature of lower layer. [K]
e Slab thickness (Input Data), [m]

k Slab thermal conductivity (Input Data). [W/m-K]

a Slab thermal diffusivity (Input Data). [nWsec]

or C

p

Slab specific heat (Input Data). [J/kg-K]

and o Slab material density (Input Data). [kg/m3

]

< Infra-red absorptivity of the hot layer in the

room (Calculated Value, see ABSRB routines in Hot

Layer section), [m -3

]

o Stef an-Boltzmann constant (Physical

Constant). [5.67 x 10~ 3 W/irr-K4

]

Nmax Maximum allowable number of layers into which

slab may be divided (Input Data).

hj_ Smoke layer height (Calculated Value, see Hot

Layer section), [m]

jpld; ^ = i f 2,...,N Temperature profile of slab at start of tine step

35
(Input Data. At time zero, ambient temperature.). [K]

Calculations

a = k/( pCp

)

6x^ = V2aAt

N 1 +

6

h X;

Calculate thermal diffusivity, if necessary.

Smallest permissible time space increment

(calculated for the largest time increment to be

used )

.

N is the number of points where the temperature

is calculated, i = 1 on inside surface, i = N on

outside surface, (take integer part only of

term in brackets)

( e/(N-l), 1 < N ^ Nmax

6x =< 9/(Nmax -l), N > Nmax Space increment actually used.

\ 9 , N = 1

a = 2a/(6x) 2 Computation parameter.

b = 6x/k Computation parameter.

36
The calculation of the temperature distribution at time t + At given the

distribution at time t:

II tl It II 1l

= ^LWD + ^LWR + ^WR

II II II II ^N

= ^AWD + ^AWR + ^PR

4>i =

q i - 0T3 + e

_,<h LoT^

(t>N =

°lN + oTa

‘ oTN

T^t+At) = T x (t) (1-aAt)

+ aAt (T 7 ( t Hbd-^

)

T

i Ct+At) = Tilt) (1-aAt)

+ [T

i

_

1 (t)+T i+1 (t

T

N (t+At) = T^( t ) (1-aAt)

+ aAt (TN _i(t)-bbN

)

Heat flux to side 1 (inside).

Heat flux to side N (outside).

Net flux to inside of wall after re-radiation.

Net flux to outside of slab.

Inside surface temperature

calculation

.

Interior node temperature calculation.

] (repeat calculation for each interior node,

i = 2 , 3 , . .

. ,N- 1

)

Outside surface temperature

calculation

.

37
References

1. Mitler, H.E., "The Physical Basis of the Harvard Computer Fire Codes,"

Harvard University, Home Fire Project Technical Report No. 34, pp . 51 -

59.

2. Mitler, H.E., and Emmons, H.W. , "Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. National Bureau of Standards,

Washington, D.C., NBS-GCR-81-344 , October 1981, pg. 114.

Subroutine Variables

ZKW = rpnew

i FQLWD(l) =

. < i ^LWD

FQLWR( 1

)

=

• 1* ^LWR

FQPWR(l) =

• II 9PWR

FQLWD( 2) =

• H 9AWD

FQLWR( 2

)

=

• II 9AWR

FQPWR( 2

)

=

. ii ^R

DT = At

ZKAZZ = Ta ZKDZZ = td

ZNWZZ = 6

ZJWZZ = k

ZGWZZ = a

ZCWZZ = S

38
VMWZZ = P

ZULZZ = K

SIGMA = 0

MXLYRS “ ^max

ZHLZZ = hL

ZKWO = T° ld

; i = 1,2 N

39
oononooonononooonoooononooonnonooooo

on

Computer Subroutine

SUBROUTINE TMPW01 ( ZNWZZ , ZJWZZ , ZGWZZ , ZCWZZ , VMWZZ , ZKAZZ

,

& ZKDZZ , ZKWO , ZHLZZ , MXLYRS , FQLWD , FQLWR , FQPWR , DT , ZKW

)

i< * * >'c * * * **V; * V; * V; >'< * * * *>'< * ** * * * >'< >'< * * * * V; *V; *V; ***>'c * ***** * * * * * * * *** *

IMPLICIT DOUBLE PRECISION (A-H,0-Z)

SUBROUTINE TO CALCULATE THE TEMPERATURE PROFILE WITHIN A SLAB

USING A DISCRETE GRID. THE SLAB IS HEATED OR COOLED ON EACH

SIDE BY CONVECTION AND RADIATION AND THE HEAT DIFFUSES

THROUGH IT BY CONDUCTION.

INPUT PARAMETERS:

ZNWZZ -- SLAB THICKNESS

ZJWZZ -- SLAB THERMAL CONDUCTIVITY

ZGWZZ -- SLAB THERMAL DIFFUSIVITY

ZCWZZ -- SLAB MATERIAL SPECIFIC HEAT

VMWZZ -- SLAB MATERIAL DENSITY

ZKAZZ -- AMBIENT AIR TEMPERATURE (EXPOSING EXTERIOR

SIDE OF SLAB)

INPUT VARIABLES:

ZKDZZ

ZKWO

ZHLZZ

MXLYRS

FQLWD ( 1 ) --

FQLWR(l) --

FQPWR(l) --

FQLWD(2) --

FQLWR( 2) --

FQPWR ( 2 ) --

DT

LOWER LAYER TEMPERATURE (EXPOSING INTERIOR

SIDE OF SLAB)

PREVIOUS TIME STEP SLAB TEMPERATURE PROFILE

SMOKE LAYER HEIGHT

MAXIMUM NUMBER OF LAYERS INTO WHICH THE SLAB

MAY BE DIVIDED

CONVECTIVE HEAT FLUX FROM LAYER TO

INTERIOR SIDE OF SLAB

RADIATIVE HEAT FLUX FROM LAYER TO INTERIOR

SIDE OF SLAB

RADIATIVE HEAT FLUX FROM PLUME(S) TO

INTERIOR SIDE OF SLAB

CONVECTIVE HEAT FLUX FROM LAYER TO EXTERIOR

SIDE OF SLAB

RADIATIVE HEAT FLUX FROM LAYER TO EXTERIOR

SIDE OF SLAB

RADIATIVE HEAT FLUX FROM PLUME(S) TO

EXTERIOR SIDE OF SLAB

SIZE OF TIME STEP

C OUTPUT VARIABLE:

C ZKW -- TEMPERATURE PROFILE WITHIN SLAB AT NEW TIME

C

PARAMETER (SIGMA = 5.67D-8)

C

C INITIAL CALCULATIONS

C

IF (ZGWZZ .LE. 0.0) ZGWZZ = ZJWZZ / (VMWZZ * ZCWZZ)

AO
non

DXM = DSQRT (2. DO * ZGWZZ * DT)

M = IFIX( ZNWZZ / DXM) + 1 N = MINO (M.MXLYRS)

IF (N .LE. 1) N = 2

DX = ZNWZZ / ( FLOAT ( N - 1 ))

AW = 2. DO * ZGWZZ / (DX * DX)

BW = DX / ZJWZZ

WALL TEMPERATURE CALCULATIONS

TEMP = 1 . DO - AW * DT

NM1 = N - 1 C CALCULATE INTERIOR NODE TEMPERATURES

DO 10 I = 2 , NM1

ZKW ( I ) = ZKWO(I) * TEMP + AW * (DT / 2. DO) * ( ZKWO(I-l)

& + ZKW0(I+1)

)

10 CONTINUE

C CALCULATE SLAB HEAT FLUXES

FQWA = FQLWD(l) + FQLWR(l) + FQPWR(l)

FQW1 = FQWA - SIGMA * (ZKW0(1)**4 - DEXP (-ZHLZZ *

& ZULZZ * ZKDZZ**4 ) FQWB = FQLWD(2) + FQLWR(2) + FQPWR(2)

FQW2 = FQWB + SIGMA * (ZKAZZ**4 - ZKW0(N)**4)

C CALCULATE INTERIOR NODE TEMPERATURE

ZKW ( 1 ) = ZKW0(1) * TEMP + AW * DT * (ZKW0(2) + BW *FQW1

)

C CALCULATE EXTERIOR NODE TEMPERATURE

ZKW(N) = ZKWO(N) * TEMP + AW * DT * (ZKWO(N-l) + BW *

& FQW2

)

C

RETURN

END

41
ABSRB2 - Infra-red Absorptivity of the Hot Layer

Description

This routine calculates the infra-red absorptivity of the hot layer. In

this routine, the absorption coefficient is assumed to be gray and due mostly

to the smoke concentration in the layer. Therefore, it is modeled as being a

constant multiple, 265, of the concentration (by mass) of smoke (particulates,

mainly C, and condensed hydrocarbons) in the hot layer in a room. The

proport ionality constant used in the equation below was obtained by comparing

the infra-red absorptivity as measured in the July 6, 1977 full-scale fire test

(channel 126), with the smoke concentration calculated in a standard run of

NBS/Harvard 5.

Output

K Infra-red absorptivity of the hot layer, [m

Input

Y s Mass concentration of smoke in the hot layer

(Calculated Value, see Hot Layer section). [ gms

of smoke/gms of hot layer gas]

42
Calculation

< = 265 * Y s

References

1. Mitler, H.E. and Emmons, H.W., "Documentation for CFC

Harvard Fire Code," U.S. National Bureau of Standards,

NBS-GCR-81-344, October 1981, pg. 132.

Subroutine Variables

ZYKZZ = <

ZYLSZ = Y s

V, the Fifth

Washington, D.C.

43
nononnooooo

on

Computer Subroutine

SUBROUTINE ABSRB2 ( ZYLSZ , ZULZZ

)

IMPLICIT DOUBLE PRECISION (A-H.O-Z)

THIS SUBROUTINE CALCULATES THE INFRA-RED ABSORPTIVITY OF THE

HOT LAYER. WE ASSUME THE ABSORPTION COEFFICIENT IS IN FACT

AND DUE MOSTLY TO THE SMOKE CONCENTRATION IN THE LAYER. THE

PROPORTIONALITY CONSTANT USED IN THE EQUATION BELOW WAS

OBTAINED BY COMPARING THE I.R. ABSORPTIVITY AS MEASURED IN

THE JULY 6, 1977 FULL-SCALE FIRE TEST (SEE CHANNEL 126), WITH

SMOKE CONCENTRATION CALCULATION CALCULATED BY LAYR03 IN A

STANDARD RUN OF HARVARD 5.0.

INPUT VARIABLES:

C ZYLSZ -- MASS CONCENTRATION OF SMOKE IN THE HOT LAYER

C

C OUTPUT VARIABLE:

C ZULZZ -- INFRA-RED ABSORPTIVITY OF THE HOT LAYER

C

ZULZZ = 265. DO * ZYLSZ

C

RETURN

END

44
APPENDIX D.

References

45
1. Tanaka, T. , "A Model of Multiroom Fire Spread," NBSIR 83-2718, National

Bureau of Standards, 1983.

2. Zukoski, E.E. and Kubota, T. , "Two- layer Modeling of Smoke Movement in

Building Fires," Fire and Materials , 4 (1) (1980) 17 - 27.

3. Zukoski, E.E. and Kubota, T. , "A Computer Model for Fluid Dynamic Aspects

of a Transient Fire in a Two Room Structure," C.I.T. Report prepared for

the U.S. National Bureau of Standards, 1978.

4. Quintiere, J. , Steckler, K. , and McCaffrey, B. , "A Model to Predict the

Conditions in a Room Subject to Crib Fires," presented at the First

Specialists Meeting of the Combustion Institute, Bordeaux, Talence,

France, published by the U.S. National Bureau of Standards, 1981.

5. Steckler, K. , "A Calculation of Wall Fire Spread in an Enclosure," NBSIR

83-2765, U.S. National Bureau of Standards, 1983.

6. Cooper, L.Y., "A Concept for Estimating Available Safe Egress Time in

Fires," Fire Safety Journal , 5 (,1983) 135 - 144.

7. Cooper, L.Y., "A Mathematical Model for Estimating Available Safe Egress

Time in Fires," Fire and Materials , 6 (3/4) (1982) 135 - 144.

8. Cooper, L.Y. and Stroup, D.W., "ASET - A Computer Program for Calculating

Available Safe Egress Time," Fire Safety Journal , 9 (1985) 29.

9. Babrauskas, V., "C0MPF2 - A Program for Calculating Post-Flashover Fire

Temperatures," NBS TN991, U.S. National Bureau of Standards, 1979.

10. Mitler, H.E. and Emmons, H.W., "Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. National Bureau of Standards, Washington, D.C.,

NBS-GCR-81-344, October 1981.

11. Pape, R. , Waterman, T.E. and Eichler, T.V., "Development of a Fire in a Room from Ignition to Full Room Involvement - RFIRES," IITRI Report

NBS-GCR-81 -301 for U.S. National Bureau of Standards, 1981.

12. Jones, W.A., "A Model for the Transport of Fire, Smoke, and Toxic Gases

(FAST)," U.S. National Bureau of Standards report NBSIR 84-2934 (1984).

13. Siu, N.O., "COMPBRN - A Computer Code for Modeling Compartment Fires,"

University of California at Los Angeles report UCLA-ENG-8257 (1982) and

U.S. Nuclear Regulatory Commission Report NUREG/CR- 3239 (1983).

14. MacArthur, C.D., "Dayton Aircraft Cabin Fire Model - Version 3: Vol. 1 - Physical Description," University of Dayton Research Institute, May,

1981.

46
15. Vang, K.T. and Liu, V.K., "UNDSAFE - II: A Computer Code for Buoyant

Turbulent Flow in an Enclosure with Thermal Radiation," University of

Notre Dame report TR-79002-78-3 , July 1978.

47
NBS-114A (REV. 2-80

U.S. DEPT. OF COMM.

4 .

1 . BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR 2 REPORT NO.

NBSIR 85/3263

. Performing Organ. Report NoJ 3.

TITLE AND SUBTITLE

Publication Date November 1985

The Establishment of a Catalog of Compartment Fire Model Algorithms

and Associated Computer Subroutines

5. AUTHOR(S) TT _ David W. Stroup

6. PERFORMING ORGANIZATION (If joint or other than NBS. see in struction s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS _

DEPARTMENT OF COMMERCE 8 Gaithersburg, "MD 20899

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State. ZIP)

. Type of Report & Period Covered

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl lography or literature survey, mention it here) The Compartment Fire Model Research group of the Center for Fire Research,

National Bureau of Standards, has been charged with the development of a "benchmark" compartment fire model. As part of this activity, a catalog

of available fire model algorithms is being compiled. This paper presents

a proposal for the organization, format, and use of the catalog. Appendix A

of this report is a copy of the proposed introductory text for the

catalog. Appendix B presents the Table of Contents for the first edition

of the catalog, and Appendix C contains several examples of catalog

algorithm write-ups. Finally, Appendix D lists the references used in

Appendix A.

12. KEY WORDS (Six to twelve entries ; alphabetical order; capitalize only proper names; and separate key words by semicolon s) algorithms; building fires; cataloging; combustion physics; compartment fires;

computer programs; fire chemistry; fire models; mathematical models; zone models

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

iX Unlimited

| For Official Distribution. Do Not Release to NTIS

i Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

' 20402.

51

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