NBSIR 87-3607

A Catalog of Compartment Fire

Model Algorithms and Associated

Computer Subroutines

David W. Stroup

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

August 1987

J.S. DEPARTMENT OF COMMERCE

IATIONAL bureau of standards

NBSIR 87-3607

A CATALOG OF COMPARTMENT FIRE

MODEL ALGORITHMS AND ASSOCIATED

COMPUTER SUBROUTINES

David W. Stroup

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

August 1987

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

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

Page

LIST OF FIGURES iv

PREFACE v

ABSTRACT 1

I. INTRODUCTION 2 1.1. FIRE DYNAMICS 3 1.2. FIRE MODEL TYPES 4

1.3. CATALOG ORGANIZATION 6 1.4. THE VARIABLE CROSS-REFERENCING SCHEME 8 1.5. AN EXAMPLE OF USING THE CATALOG 12

1.6. REFERENCES 14

1. ALGORITHMS RELATED TO THE BURNING OBJECT ..... 1-1

2. ALGORITHMS RELATED TO CONDUCTION HEAT TRANSFER ..... 2-1

3. ALGORITHMS RELATED TO CONVECTION HEAT TRANSFER 3-1

4. ALGORITHMS RELATED TO THE HOT LAYER ........... 4-1

5. ALGORITHMS RELATED TO THE PLUME 5-1

6. ALGORITHMS RELATED TO RADIATION HEAT TRANSFER 6-1

7. ALGORITHMS RELATED TO THE VENT 7-1

8. MISCELLANEOUS ALGORITHMS 8-1

APPENDIX A. VARIABLE CROSS-REFERENCE A-l

APPENDIX B. LISTING OF ALGORITHM/SUBROUTINE WRITE-UPS B-l

iii
LIST OF FIGURES

Figure 1-

Figure 1-

Figure 1-

Figure 2-

Figure 2-

Figure 3-

Figure 4-

Figure 5-

Figure 6-

Figure 7 -

Figure 8-

Page

1. General diagram of a room fire 1-2

2. Diagram of the flame cone model 1- ANGLE -4

3. Diagram of the flame cone model 1 -HEIGHT -5

1. General diagram of a room fire 2-2

2. Schematic of heat conduction into a slab 2-TMPW01-11

1. General diagram of a room fire 3-2

1. General diagram of a room fire 4-2

1. General diagram of a room fire 5-2

1. General diagram of a room fire 6-2

1. General diagram of a room fire 7-2

1. General diagram of a room fire 8-2.

iv
PREFACE TO THE FIRST EDITION OF THE

CATALOG OF COMPARTMENT FIRE MODEL ALGORITHMS AND ASSOCIATED SUBROUTINES

The main objective of the Compartment Fire Modeling Research (CFMR) Group

of the Center for Fire Research (CFR) National Bureau of Standards is to

develop computer software for a well -documented, user-friendly, modular and

easily updated Consolidated Compartment Fire Model Computer Code, and to use

this software to implement applications of the Code which would include a benchmark or reference compartment fire model application. As part of the

documentation phase of this activity, a Catalog of Compartment Fire Submodel

Algorithms and Associated Subroutines is being compiled. The Catalog will

contain algorithms for calculating various physical/chemical fire phenomena and

associated computer subroutines, written in FORTRAN 77. The Catalog subroutine

entries are intended to be transportable and usable in compartment fire model

computer programs other than the Consolidated Compartment Fire Model Computer

Code. Modularity is the key objective in the development of this Catalog. The

document that follows represents the first edition of the Catalog.

The routines contained in this first edition of the Catalog have been

derived from the NBS/Harvard 5.N and 6.N Compartment Fire Model computer

programs. Future updates of the Catalog will include algorithms from other

fire models and newly developed ones. The Catalog is in loose-leaf form and it

is presented in a format that will allow new or revised algorithm/subroutine

entries to be issued and added conveniently.

The algorithms in this first edition of the Catalog were drawn mainly from

two sources. They are "The Physical Basis of the Harvard Fire Code" by H.E.

Mi tier and "Documentation for GFC V, the Fifth Harvard Computer Fire Code" by

H.E. Mitler and H.W. Emmons. The algorithm presentation format adopted here

was based in part on the latter of these publications. Not all of the physical

algorithms from the NBS/Harvard fire model programs have been included in this

edition of the catalog. The phenomena which have not been documented fall into

two categories: radiation heat transfer and venting. Work is underway to

complete algorithm write-ups associated with these phenomena and to include

them in a future Catalog update.

The basis of the FORTRAN subroutines for all entries of this edition of

the Catalog is the recently completed, one -room computer code, FIRST, which is a consolidation of several advanced versions of the original Harvard CFC V

code. To achieve minimum criteria of modularity, some very minor modifications

to the FIRST subroutines were required in all cases. In this sense, the

subroutine entries in this edition are untested. The subroutine modifications

included elimination of entry points , common statements and/or debug

information, all of which were peculiar to the FIRST code. The user of this

Catalog can refer to the FIRST code for an exact listing of the original

software

Considerable thought has been devoted to the development of a usable and

convenient variable cross-referencing scheme. This should allow a catalog user

to identify easily the physical input data (e.g. room dimensions, material

v
properties, etc.) and the subroutines required to calculate additional inputs

for use in a particular subroutine of interest. One desired objective was a scheme which, while assuring modularity, allowed for independence in

nomenclature from one algorithm/subroutine catalog entry to the next. The

scheme adopted consists of the common definition (in words) of a particular

physical/chemical quantity, the subroutine variable or variables used to

indicate the quantity, the equation notation used to indicate the quantity, and

the names of the subroutines in which the calculations are carried out.

Although uniformity in subroutine name and equation variable naming is

desireable, the cross-referencing scheme does not make this a strict

requirement. This method of cross-referencing variables will avoid the need to define specific common subroutine variable names and/or nomenclature. While

there is an attempt to make unambiguous the common definition of a particular

physical quantity, its meaning is clarified further from the context of the

write-ups of individual algorithms which make use of the variable. This

catalog is intended to be a dynamic publication. As suggestions for

improvements are received, they will be evaluated and incorporated into the

catalog philosophy.

Leonard Y. Cooper, Head

Compartment Fire Modeling Research

vi
A Catalog of Compartment Fire Model Algorithms

and Associated Computer Subroutines

David W. Stroup

ABSTRACT

The Compartment Fire Modeling 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 has been compiled. The catalog contains

algorithms which calculate various physical/chemical fire phenomena. The

description of each algorithm includes the input (s ) , output (s ), and

calculations performed. In addition, each algorithm has a computer subroutine

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

throughout the catalog are cross-referenced. This enables a catalog user to

determine which routines would be required to calculate a particular fire

phenomena. Updates and revisions will be issued periodically.

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

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

models; zone models.

1
I. INTRODUCTION

Many mathematical models and associated computer programs have been

developed to predict enclosure fire dynamics [ 1 - 15

]

1

. 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

.

Numbers in brackets refer to literature references listed at the

end of this section.

2
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 a form for easy inclusion in a loose-leaf binder. This will allow

for the inclusion of future catalog updates. These updates will include

improvements of old algorithms and issuing of new ones as necessary. To be

successful, this catalog will require user support and feedback which is

heartily encouraged.

1.1. 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,

3
it spreads out and forms a relatively thin, hot, sooty layer. As the 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 hot layer gases out ol

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 fe\*

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

.

1.2. 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 probabilistic 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.

4
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 combustion/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.

5
1.3. 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 a form for easy inclusion in a loose-leaf

binder. This will make it easy to update, and updates, including new and

improved algorithms, will be issued periodically. The catalog is divided into

seven sections. They are: 1 . Burning Object

2. Conduction Heat Transfer

3. Convection Heat Transfer

4. Hot Layer

5. Plume

6. Radiation Heat 1Transfer

7. Vents

8. Miscellaneous

Each section contains one or more algorithms, organized in alphabetical order,

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.

6
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 o-f the meaning of each variable. The number of output variables

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

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. The appropriate SI units are listed

next to each input variable. Variables are numbered and 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. The seventh section, labeled Prepared by .

7
lists the author (s) of the algorithm/subroutine write-up. Finally, section

eight, Computer Subroutine , presents the FORTRAN 77 computer subroutine which

implements the algorithm.

I. .4. THE VARIABLE CROSS-REFERENCING SCHEME

. A variable cross-referencing scheme has been developed to assist users in

selecting algorithms (subroutines) from the catalog. The cross-reference

enables catalog users to determine which routines are available to calculate

desired values. The user may then refer to the appropriate routines to

determine the required input information. If any of the input data are listed

as a "Calculated Value", the user may refer back to the variable crossreference to determine whether or not algorithm/subroutine write-ups are available to calculate these additional values.

The variable cross-referencing scheme consists of five parts. Each part

is separated into its own column. The first column of the cross-reference

contains an identification number. Each variable is assigned a reference

number. Whenever a variable is mentioned in the catalog, its associated

reference number is also listed. Appendix A lists the variables in the catalog

organized according to increasing reference number. The numbers are assigned

in no particular order. As the Catalog grows and updates are issued, new

variables and associated identification numbers will be added to the list.

Eventually, some variables and their identification numbers will be eliminated.

Their use in the Catalog will be updated to reflect any changes. (Any

8
variables missing from the list should be brought to the attention of the

author .

The second column contains a word definition. A common definition (in

words) has been developed for each physical/chemical quantity referenced in the

catalog. While there is an attempt to make unambiguous the common definition

of a particular physical quantity, its meaning is clarified further from the

context of the write-ups of individual algorithms which make use of the

variable. The adoption of a method of variable cross-referencing based on

common word definitions of physical/chemical quantities and associated

identification numbers avoids the need to define specific subroutine variable

names and/or nomenclature. However, uniformity in subroutine and equation

variable naming is desirable and will be maintained whenever possible.

The third part of the variable cross-reference is a column listing of the

nomenclature used in the algorithm write-ups. A list of the mathematical

equation symbols used to represent physical/chemical quantities is provided for

each common definition. There will be one or more entries in this column for

each definition. In some of the algorithm/subroutine write-ups, the

mathematical symbol for a given quantity is preceded by the mathematical

summation sign (2) . This indicates that the particular quantity is the sum of

that quantity for all objects, plumes, walls, or whatever. Its meaning should

be clear from the algorithm/subroutine write-up.

The FORTRAN subroutine variable names used to represent physical/chemical

quantities are listed in the fourth column of the variable cross-reference.

9
There will be one or more entries for each physical/chemical quantity. The

listed FORTRAN variable may be used to represent the individual quantity, the

summation of that quantity for all sources, or both. The user should check the

individual algorithm/subroutine write-ups to determine the exact meaning.

The last column in the variable cross-reference- lists the names of the

algorithm/subroutine write-ups which calculate the specified physical/chemical

quantity. Algorithm/subroutine names will be listed in all capital letters.

In some cases, more than one routine will be available to calculate a particular quantity. The user should examine the algorithm write-ups to

determine which routines are appropriate for the particular scenario being

modeled. The words "Input Data", in a combination of upper and lower case

letters, are used to indicate physical/chemical quantities which must be

obtained by the user from other sources. For the most part, these values are determined by the situation being modeled, e.g. room dimensions, object

location, type of fire, etc. In a few cases, the values are ones which cannot

be calculated given the present state of the art of fire science. Another

possible entry in this column is a dash (— )

.

The dash is used to indicate

quantities whose values are determined by the overall integrated fire model.

These quantities include current simulation time, current time step size, and

similar type of values. The final possible entry in this column is an asterisk

(*)

It is used to designate physical/chemical quantities for which one or more algorithms or subroutines are available, but they have not been written up

in a form appropriate for inclusion in the Catalog. Eventually, this categorv

will disappear.

10
The cross-reference listing is contained in Appendix A of this report.

The variables are arranged according to increasing identification number.

Appendix B lists the algorithm/subroutine names organized alphabetically for

each section heading. In addition, the inputs and output (s) are identified for

each algorithm/subroutine. The variable identification numbers are used to

identify the inputs and output (s)

Finally, the use of the variable cross-reference will be illustrated with

an example. Suppose a catalog user wants a method for calculating the rate of

addition of mass to the hot layer from a plume (V.97). The number in

parenthesis refers to the variable identification number. The user would first

refer to the cross-reference. In the cross-reference, the entry for variable

number 97 lists a common definition of "Rate at which the plume over an object

adds mass to the hot layer". The cross-reference refers the user to an

algorithm/subroutine write-up labeled TMSPLM. This routine calculates the rate

at which the plume over an object adds mass to the hot layer. Examining the

Appendix B and the algorithm write-up, the user finds that this routine

requires ten input items. Six of these inputs are classified as Input Data

(density of ambient air (V.17), specific heat of ambient air (V.112), ambient

temperature of air (V.120), the plume entrainment coefficient (V.71), pi

(V.146), and the acceleration of gravity (V.144)). The other four values are labeled as "Calculated Values". These values are the height of the plume

(V.37), the radius of the fire (V.85), the negative of the rate of chemical

energy released from the burning object (V.88), and the negative of the mass

pyrolysis rate of the object (V.61).

11
The Catalog user would refer back to the variable cross-reference and

determine whether or not routines to calculate the required "Calculated Value"

inputs were currently available in the Catalog. If routines were available,

the user would examine those routines to determine whether or not they would be

appropriate for the model being developed. If one or more of the routines were appropriate, the user would then determine what additional input data would be

required by the additional routines. If additional "Calculated Value"s were

required, the user would again examine the cross-reference to determine the

available routines and examine the algorithm/subroutine write-ups to determine

their appropriateness and required inputs. This process would be repeated

until all of the required input data could either be calculated or determined

by the user (from reference sources or whatever)

.

1.5. 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 [7,8]. 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 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 "Heat Conduction in a Slab"

(V.122). It may be used to calculate transient heat conduction in a solid

where surfaces are exposed to radiative and convective heating.

12
In the write-up of TMPW01, 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 depth of the hot layer (V.20), is already calculated by

equations in the ASET model. Inputs describing the convective flux (V.'ll) and

radiative fluxes (V.79 and V.81) being received by the material are also

required. The modeler might derive these by using 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 TMPW01 is the absorption coefficient of the

hot layer in the room (V.2). The Catalog contains an algorithm for calculating

this value. It is labeled ABSRB2 (see section 4 of this report). It assumes

the absorptivity is a constant fraction of 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 hot layer (V.44) as

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

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.

13
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.

1.6. REFERENCES

[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

14
Fire Code

M 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.W.

"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.

[15] Yang, 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.

15
'

> , n« U :* K

.

'

-

16
1. ALGORITHMS RELATED TO THE BURNING OBJECT

1-1
1-2

Figure

1-1.

General

diagram

of

a

room

fire
ANGLE - Semiapex Angle of Flame Cone

Description

This routine calculates the semiapex angle of a cone representing the

inhomogeneous, fluctuating, turbulent, flame over a burning object, figure 1

1. A description of the flame geometry is essential for flame radiation

calculations. As an approximation, the flame may be modeled as a right

circular cone, figure 1-2, of hot grey gas. The cone has a height equal to

the height of the flame above the burning object, and its radius is equal to

the radius of the fire on the burning object. The size varies with time as indicated by changing values of the semiapex angle.

Output

Semiapex angle of the cone modeling the flame

over a burning object, [degrees] (V.109)

Radius of the fire on the burning object

(Calculated Value, see Burning Object section)

[m] (V. 85)

Height of the flame above the burning object

(Calculated Value, see Burning Object section)

[m] (V. 36)

Input

R

h£

Calculation

= tan" 1 (R/hf )

1 -ANGLE -1
References

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

Technical Report No. 34, Harvard University, October 1978, p. 8.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 84-85, 89.

Subroutine Variables

PSI1 = ZRFZZ - R

ZHFZZ = hf

Prepared by

David W. Stroup

1- ANGLE -2
Computer Subroutine

SUBROUTINE ANGLE (ZRFZZ , ZHFZZ , PS II)

C

Q

'k-kk'k-k'k'k-k-k'k'k-k'k-k'k-k-k-k'k-k'k'k'k'k-k'k-k'k'k-k'k-k'kk-k-k'k-k-k-k-k-k-k'k-k-k-k'k-k-k-k-k'k-k'k-k-k'k'k'k-k'k'k-k-k'k'k-k'k c IMPLICIT DOUBLE PRECISION (A-H.O-Z)

C

C SUBROUTINE TO CALCULATE THE SEMIAPEX ANGLE OF A FLAME CONE.

e

C INPUT VARIABLES:

C ZRFZZ -- RADIUS OF FIRE

C ZHFZZ -- HEIGHT OF FLAME

C

C OUTPUT VARIABLE:

C PS II -- FLAME CONE ANGLE

C

PS II = DATAN2 (ZRFZZ, ZHFZZ)

C

RETURN

END

1- ANGLE -3
I

1- ANGLE -4
BURN - Mass Rate of Burning of the Fuel from an Object

Description

This routine calculates the mass rate of burning of the fuel released

from a pyrolyzing object. If the mass pyrolysis rate, mf

, is known, the

object's heat release rate, Q, may be obtained from

Q = X |m£ | H0 where x is the fraction of energy released in open-air burning, mf is mass

pyrolysis rate of the object (defined to be negative) , and Hc is the heat of

combustion per kilogram as obtained for complete combustion in a bomb

calorimeter. A simple (though incorrect) interpretation of the above equation

is that only the fraction x °f the pyrolyzed vapor burns and burns completely.

The object's mass burning rate ismb - x | if | As long as sufficient oxygen is available, all of the fuel will burn limited

only by the combustion efficiency of the chemical reaction.

When oxygen starvation occurs, the burning rate will decrease. The

maximum amount of fuel vapor which can burn in the presences of a known amount

of air (oxygen) is

where ma is the amount of air entrained in the part of the plume below the hot

layer and 7 is the air/fuel mass ratio in a free burn of the object. This

routine assumes no entrainment occurs above the layer interface. The quantity

of air entrained, ma

, into the plume is equal to the sum of the total mass

1 - BURN -
flow out the top of the plume, m

p

, and the mass pyrolysis rate of the fuel, m*

(this quantity is negative). At any given time, the burning rate is chosen to

be the smaller of either the combustion efficiency value or the oxygen

starvation value.

Output

“b Mass rate of burning of the fuel from an object,

[kg/s] (V . 55)

Input

X Fraction of combustion energy released in the

flame of the object (Input Data). (V.26)

7 Air/fuel mass ratio in a free burn of the object

(Input Data). (V.3)

mf (Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

m

p Rate at which the plume over the burning object

adds mass to the hot layer (Calculated Value,

see Burning Object section), [kg/s] (V.97)

Calculation

mb = min[ -xnif , (m

p +mf )/y] Burning rate, limited by combustion efficiency,

X, or by oxygen starvation.

1- BURN2
References

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

Technical Report No. 34, Harvard University, October 1978, p. 8 .

2. Mitler, H.E., and Emmons, H.W.

"Documentation for CFC V, the fifth

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, p. 89.

Subroutine Variables

TMOZB = mb CHI = X

XGAMMA = 7

TMOZZ = mf TMPZZ = m

p

Prepared by

David W. Stroup

1- BURNo

o

no

o

o

o

Computer Subroutine

SUBROUTINE BURN (CHI ,XGAMMA, ZMOZZ , TMOZZ , TMPZZ , TMOZB1)

C

C -k-k-k-k-k'k-k-kick-k-k-k-k-k'kk-k-kick-kkk-k-k-k'kk-k-k'k-k-k'k'k-k-k-k-k-k'k'k-k-kkk'k-k-k-k-k-k-k-k-k-k-k'k-k'k'k-k-k-k'k-k-k'k c IMPLICIT DOUBLE PRECISION (A-H.O-Z)

C

C CALCULATES THE MASS RATE OF BURNING OF THE FUEL FROM AN OBJECT.

INPUT PARAMETERS:

CHI -- FRACTION OF HEAT OF COMBUSTION RELEASED IN THE FLAME

OF THE OBJECT.

XGAMMA -- AIR/FUEL MASS RATIO IN A FREE BURN OF THE OBJECT.

INPUT VARIABLES:

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

C TMPZZ -- MASS FLOW INTO THE HOT LAYER FROM THE PLUME OF AN

C OBJECT.

C

C OUTPUT VARIABLE:

C TMOZB1 -- MASS RATE OF BURNING OF FUEL FROM AN OBJECT.

C

TMOZB1 = MIN (-CHI*TMOZZ, (TM'OZZ+TMPZZ) /XGAMMA)

IF (TMOZB1.LE.O.DQ) TMOZB1 = -0.01D0 * CHI * TMOZZ

RETURN

END

1- BURN4
CHEM - Energy Release Rate from a Burning Object

Description

This routine calculates the rate at which energy is released from a burning object. In general, an object's heat- release rate, Q, may be obtained

from

Q “ X m Hc where x is the fraction of energy released in open-air burning, m is mass

pyrolysis rate of the object, and Hc is the heat of combustion per kilogram ar obtained for complete combustion in a bomb calorimeter. A simple (though

incorrect) interpretation of the above equation is that only the fraction x °f

the pyrolyzed vapor burns and burns completely. The energy release is

Q

= mb Hc where mb = x | mf | In this routine, the heat of combustion, Hc , is replaced with an effective

heat of combustion. This accounts for the energy required to raise the

temperature of the object's pyrolysis gases from ambient to pyrolysis

temperature. If the layer interface is above the object's top surface, the

net power output by combustion is calculated using the effective heat of

combustion and returned as a negative value. If the layer is below the top

surface of the object, combustion is assumed to have stopped and a zero value

is returned for the heat release rate.

1-CHEM-l
Output

(Negative of the) chemical energy released from

a burning object. [W] (V.88)

Ef

Input

He

Ilk

h

P

Specific heat of ambient air (Input

Data). [J/kg-K] (V.112)

Heat of combustion of the material making up the

object (Input Data). [J/kg] (V.30)

Ambient temperature of the room containing the

object (Input Data). [K] (V.120)

Temperature at which the object begins to

pyrolyzes (Input Data). [K] (V.119)

Mass rate of burning of the fuel from the object

(Calculated Value, see Burning Object

section), [kg/sec] (V.55)

Height of the plume over an object, distance

between the object's hot surface and the layer

interface (Calculated Value, see Burning Object

section), [m] (V.37)

Calculations

H^ = Hc

- c

p (T - Ta

) Effective heat of combustion.

Jo, hp < 0

1 -mb * Hc

'

, h

p > 0

Negative of power output by combustion.

l-CHEM-2
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 = Ef CP = c

p QF = Hc ZKAZZ = Ta ZCOPY = T

p TMOZB = mb

ZHPZZ = h

p

Prepared by

David W. Stroup

l-CHEM-3
o

o

Computer Subroutine

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

)

C •k-k-kkirkirk-kk'k'k-k-k'k'k^'k-k'k'k'k'k-k'k-k-k-k^c'k^-k-k-k-k'k-k-k-k'k-k-k-k-k'k-k-k-k-k-k-k-k-k-k-k-k'k'k'k C

IMPLICIT DOUBLE PRECISION (A-H.O-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

QF -- HEAT OF COMBUSTION OF THE OBJECT AS FUEL

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 ZHPZZ -- HEIGHT OF THE OBJECT'S PLUME

C

C OUTPUT VARIABLE:

C TEOZZ -- CHEMICAL ENERGY RELEASE RATE OF THE OBJECT

C

IF (ZHPZZ .LT. 0 . DO) THEN

TEOZZ - 0.D0

ELSE

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.D0) TMB = l.D-6

TEOZZ = -TMB * TQF

END IF

C

RETURN

END

1- CHEM4
DXDPRD - Rate at which a Burning Object Produces Carbon Dioxide

Description

This routine calculates the rate at which a burning object produces

carbon dioxide. The production rate of a specific gas by a burning object

depends on the chemical composition of the material being burned. The rate of

production of carbon dioxide by a given burning material is equal to the mass

pyrolysis rate of the object multiplied by the mass fraction of the

(combustible part of the) object evolved as carbon dioxide, when it burns in

open air. The mass fraction must be obtained from fire tests of the specific

material (see Tewarsen, A., "Heat Release Rates from Burning Plastics", J

Fire and Flammability 8 (1977) for example)

Output

^02 Mass rate of evolution of carbon dioxide from

the object, [kg/s] (V.56)

Input

Mass fraction of the (combustible part of the)

object evolved as carbon dioxide, when it burns

in the open (Input Data). (V.46)

(Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

1- DXDPRD -1
Calculations

o 2

" fc o 2 mf

References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

TMOD = 1^02

FC02 = fi 02

TMOZZ = mf

Prepared by

David W. Stroup

l-DXDPRD-2
o

o

Computer Subroutine

SUBROUTINE DXDPRD (FC02 , TMOZZ , TMOD)

C

c

C SUBROUTINE TO CALCULATE THE RATE AT WHICH THE FIRE OF AN OBJECT

C PRODUCES CARBON DIOXIDE.

cC INPUT PARAMETERS:

C FC02 -- MASS FRACTION OF CARBON DIOXIDE IN THE GASES

EVOLVED FROM THE BURNING OBJECT.

C INPUT VARIABLES

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

I C

C OUTPUT VARIABLE:

C TMOD -- MASS RATE OF EVOLUTION OF CARBON DIOXIDE FROM THE

C OBJECT.

ip

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

C

TMOD = -FC02 * TMOZZ

jc

RETURN

END

1- DXDPRD -3

1

FLUX - Net Heat Flux Absorbed by the Surface of an Object,

Description

This subroutine calculates the radiation heat flux absorbed by the

surface of a burning target object. The radiation fluxes from all sources

(layer, walls, fire plume (s)) must be known. The sum of these fluxes is

modified to account for reradiation from the burning target object, the

current size of the object's fire plume, and the location of the hot layer

interface. The object is represented as a cylinder. The net radiative heat

flux incident on a burning object is equal to the sum of the incident

radiative heat fluxes from all sources minus an amount which is reradiated

away by the object. This net heat flux is the maximum which an object may

receive.

When the object is immersed or nearly immersed in the hot layer or when

the object is nearly burned out, the net heat flux which it receives must be

decreased. When the layer submerges the burning item, it is assumed that the

object continues to pyrolyze as before with no flame. If the layer were to

rise, the flame would reappear. (Warning: If care is not taken in

implementing this routine, it may lead to numerical instabilities in a model.)

The immersed surface stays at its previous temperature and pyrolyzes due to

the radiative flux it receives from the layer, and from the ceiling and walls

(0+ ). Convective heating or cooling by the layer, and reradiation from the

surface are ignored. Finally, when the object is nearly burned out, an

effective flux, 4> sff , which allows the object to burn up smoothly, is used.

1 - FLUX -
Output

<f> Net heat flux absorbed by an object. [W/m2

i

(V. 67)

Input

Hy Heat of vaporization (or pyrolysis) of the

object (Input Value). [J/kg] (V.31)

k Absorption coefficient of the flame gdses above

the burning object (Input Value), [m-1

] (V.l)

q^'o Radiative heat flux from the hot layer to the

surface of the target object (Calculated Value,

see Radiation Heat Transfer section) . [W/m2

] (V.77)

2 qp' 0 (Sum of the) radiative heat flux(es) from the

plume (s) over all burning objects to the surface

of the target object (Calculated Value, see Radiation Heat Transfer section). [W/m2

] (V,80)

2 q^' 0 (Sum of the) radiative heat flux(es) from the

hot walls and ceiling to the target object

(Calculated Value, see Radiation Heat Transfer

section). [W/m2

] (V.78)

mf Remaining mass of target object (Calculated

Value, see Burning Object section), [kg] (V.108)

R Radius of the fire on the target object

(Calculate Value, see Burning Object section).

[m] (V. 85)

1- FLUX2
7T Pi (Physical Constant). [3.141592...] (V.146)

Calculations

q-'=q”

0 +Sq-' 0+2q" 0 Radiative flux impinging on target object

from all hot sources.

qj'r =min[ 13200 , 21 700/cR] Effective reradiated flux.

*n.t - <If

- <Jr'r Net flux incident on object when flame

height not significantly reduced.

^+ ^LO + SqJo

^ef

mf ^v/^^R2

K*x = max <^n.t .*+>

Minimum flux incident on fuel surface,

when not near burnout.

Effective flux seen by (fictitious) entire

surface R

2

, when fuel is nearly

exhausted.

* ~ min^rn „.*.££> Flux incident on surface of target object.

References

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

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

Fire

1- FLUX2. Mitler, H.E., and Emmons, H.W. , "Documentation for CFC V, the Fifth

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 84-85.

Subroutine Variables

PHI = <f> QVAP - ZUFZZ = k

FQLOR = q'* 0

FQPOR = S 4p 0

FQWOR = S 4w' 0

ZMOZZ = mf ZRFZZ = R

PI = 7T

Prepared by

David W. Stroup

1- FLUX4
Computer Subroutine

SUBROUTINE FLUX ( QVAP , ZUFZZ , FQLOR , FQPOR , FQWOR , ZMOZZ , ZRFZZ , PHI 1

C -

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

SUBROUTINE TO CALCULATE THE FLUX INCIDENT ON THE SURFACE OF A

BURNING TARGET OBJECT.

INPUT PARAMETERS:

QVAP -- HEAT OF VAPORIZATION OF THE TARGET OBJECT.

ZUFZZ -- ABSORPTIVITY OF THE OBJECT.

INPUT VARIABLES:

FQLOR -- RADIATIVE FLUX FROM THE HOT LAYER TO THE SURFACE OF

THE OBJECT.

FQPOR -- SUM OF THE RADIATIVE FLUXES FROM THE PLUMES OVER ALL

BURNING OBJECTS TO THE SURFACE OF THE TARGET OBJECT.

FQWOR -- RADIATIVE FLUX FROM THE WALLS TO THE TARGET OBJECT.

ZMOZZ -- MASS OF THE TARGET OBJECT.

ZRFZZ -- RADIUS OF THE FIRE ON THE TARGET OBJECT.

OUTPUT VARIABLE:

PHI1 -- FLUX INCIDENT ON THE SURFACE OF THE TARGET OBJECT.

PARAMETER (PI = 3.1415927D0)

C

C FIND RADIATIVE FLUX IMPINGING ON TARGET OBJECT FROM ALL HOT SOURCES.

FQOO = FQPOR + FQLOR + FQWOR

C

C EFFECTIVE RERADIATIVE FLUX.

FQRR = MIN ( 13200. DO, 21700. DO*ZRFZZ*ZUFZZ)

C

C NET FLUX INCIDENT ON TARGET WHEN FLAME HEIGHT NOT SIGNIFICANTLY

C REDUCED.

FQNET = FQOO - FQRR

C

C MINIMUM FLUX INCIDENT ON TARGET WHEN NOT NEAR BURNOUT.

FQPLUS = FQLOR + FQWOR

C

FQMAX = MAX ( FQNET , FQPLUS

C

C EFFECTIVE FLUX SEEN BY (FICTITIOUS) ENTIRE SURFACE WHEN FUEL IS

C NEARLY EXHAUSTED.

IF ( ZRFZZ. GT.O. IDO) THEN

FQEFF = ZMOZZ*QVAP/(2.DO*PI*ZRFZZ**2)

ELSE

FQEFF = FQMAX

ENDIF

1- FLUXc

C FLUX INCIDENT ON SURFACE OF TARGET.

PHI1 = MIN (FQMAX, FQEFF)

C

RETURN

END

1- FLUX6
HEIGHT - Height of Flame above a Burning Object

Description

This routine calculates the height of the flame above a burning object.

The flame produced by a burning object is represented as a right circular cone

composed of hot grey gas. The tangent of the semiapex angle of this cone, at *

any given time, is equal to the fire radius (radius of the cone base) divided

by the flame height (height of the cone), figure 1-3. It is possible to

relate the time varying tangent of the semiapex angle and the mass burning

rate.

When the object burns in the presences of sufficient oxygen, its energy

release rate is limited only by its mass loss rate and combustion efficiency,

X- This is interpreted to mean that the "mass burning rate" of the fuel

produced by an object is equal to the rate of change of the object's mass

multiplied by the combustion efficiency.

=

The semi -apex angle of the flame produced by the burning object remains at

some known initial value as long as the object is burning with sufficient

oxygen. When the fire on the object becomes oxygen starved, the burning rate

and flame volume must be reduced.

Output

hf Height of the flame over the burning object, [m]

(V. 36)

1-HEIGHTInput

X

tan(V>0 )

m.

mf

R

Fraction of the theoretical combustion energy

released in the flame of the object (Input

Data). (V. 26)

Tangent of the initial value of the semiapex

angle of the flame of the object (Input Data).

(V. 118)

Mass rate of burning of the fuel from the objec

(Calculated Value, see Burning Object section),

[kg/s] (V. 55)

(Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

Radius of the fire on the burning object

(Calculated Value, see Burning Object section),

[m] (V . 85)

Calculation

h

f

R %

tan(V>Q

) x l*f

l

References

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

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344 , October 1981, pp . 84-87.

1 -HEIGHT2
Subroutine Variables

ZHFZZ = hf CHI = X

TPSIO = tan(V»0 ) TMOZB = mb TMOZZ = mf ZRFZZ = R

Prepared by

David W. Stroup

l-HEIGHT-3
Computer Subroutine

SUBROUTINE HEIGHT (CHI , TPSIO , TMOZB , TMOZZ , ZRFZZ , ZHFZZ)

•kkk’kkkk'kk^rk'k'k'k'k'k'k'k'k'k'k'k'k'kk'k'kkk'kk’k'kk'kk'k'kk'k'k'krk'kk'k-k'k'kickkkkkkkkkkkkkkkkkkk

CALCULATES THE HEIGHT OF THE FLAME OF A BURNING OBJECT.

INPUT PARAMETERS

:

CHI -- FRACTION OF THE HEAT OF COMBUSTION RELEASED IN THE

FLAME OF AN OBJECT.

TPSIO -- INITIAL VALUE FOR THE TANGENT OF THE SEMIAPEX

ANGLE OF THE FLAME OF THE OBJECT.

INPUT VARIABLES:

TMOZB -- MASS BURNING RATE OF THE FUEL OF THE OBJECT.

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

ZRFZZ -- RADIUS OF THE FIRE ON THE OBJECT.

OUTPUT VARIABLE:

ZHFZZ -- HEIGHT OF THE FLAMES OVER THE OBJECT.

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

ZHFZZ = ZRFZZ*TMOZB/(TPSIO*CHI*ABS (TMOZZ)

)

RETURN

END

l-HEIGHT-4
I

1 -HEIGHTMNXPRD - Rate at which the a Burning Object Produces Carbon Monoxide

Description

This routine calculates the rate at which a burning object produces

carbon monoxide. The production rate of a specific gas by a burning object

depends on the chemical composition of the material being burned. The rate of

production of carbon monoxide by a given burning material is equal to the mass

pyrolysis rate of the object multiplied by the mass fraction of the

(combustible part of the) object evolved as carbon monoxide, when it burns in

open air. The mass fraction must be obtained from fire tests of the specific

material (see Tewarsen, A., "Heat Release Rates from Burning Plastics", J

Fire and Flammability 8 (1977) for example)

Output

0 Mass rate of evolution of carbon monoxide from

the object, [kg/s] (V.57)

Input

Mass fraction of the (combustible part of the)

object evolved as carbon monoxide, when it burns

in the open (Input Data). (V.45)

(Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

1 -MNXPRD -1
Calculations ^ o “

'^co mf

References

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

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

TMOM - FCO - f' Q

TMOZZ - mf

Prepared by

David W. Stroup

1 -MNXPRD2
Computer Subroutine

SUBROUTINE MNXPRD ( FCO , TMOZZ , TMOM)

C

Q

•k-k-k-k'kk'k-kirkk'k-k-k-k-k'k-k-k-k-k-k-k-k-k'k-k-k-k-k'k-k-k-k-k-k-k-k-kk-k-k-k-k'kk-k-k-kk-k-k-k'k'k-k'k'k-k-k-k-k'k-k'k-k-k-k-k c

C SUBROUTINE TO CALCULATE THE RATE AT WHICH THE FIRE OF AN OBJECT

C PRODUCES CARBON MONOXIDE.

C

C INPUT PARAMETERS:

C FCO -- MASS FRACTION OF CARBON MONOXIDE IN THE GASES

C EVOLVED FROM THE BURNING OBJECT.

C

C INPUT VARIABLES:

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

C

C OUTPUT VARIABLE:

C TMOM -- MASS RATE OF EVOLUTION OF CARBON MONOXIDE FROM THE

C OBJECT.

C

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

C

TMOM - -FCO * TMOZZ

C

RETURN

. END

1 -MNXPRD -3

PFLUX - Net Heat Flux to a Potentially Pyrolyzing Object

Description

This routine calculates the net heat flux to a potentially pyrolyzing

object. This net heat flux value is the energy absorbed by the object

surface. It may be used to determine if and when the object will ignite. To

calculate the net heat flux, a heat balance is formulated for the material

surface. The net heat flux is equal to the sum of the total radiation flux

incident on the surface, the total convection heat flux to the surface, the

heat flux conducted into the material, and the heat flux reradiated by the

object surface.

Output

Net heat flux absorbed by an object. [W/m2

]

(V . 67)

Input

(Sum of all) radiation heat flux(es) incident on

the object surface (Calculated Value, see Radiation Heat Transfer section). [W/m2

] (V.82)

(Sum of all) convection heat flux(es) incident

on the object surface (Calculated Value, see Convection Heat Transfer section). [W/m2

] (V.13)

6r cond Heat flux conducted into the object (Calculated

Value, see Conduction Heat Transfer section).

[W/m2

] (V. 28)

1- PFLUXTemperature of the surface of the object

(Calculated Value, see Conduction Heat Transfer

T1 s

section). [K] (V.129)

a Stefan - Boltzmann constant (Physical Constant)

.

[5.67 x 1CT 8 W/m2 -K4

] (V.147)

Calculation

^ = 2 ^SR + 2 ^SC • ^cond _ aTS

References

No references available.

Subroutine Variables

PHI = 4> PHIR = 2 0SR

PHIC = S 0SC

COND = br , cond

ZKOZZ - Ts SIGMA = a

Prepared by

David W. Stroup

l-PFLUX-2
Computer Subroutine

SUBROUTINE PFLUX (PHIR, PHIC , COND , ZKOZZ , PHI)

SUBROUTINE TO CALCULATE THE NET HEAT FLUX TO A POTENTIALLY

PYROLYZING SURFACE.

INPUT PARAMETER:

SIGMA -- STEFAN - BOLTZMANN CONSTANT

INPUT VARIABLES:

PHIR -- RADIANT FLUX IMPINGING ON THE SURFACE OF THE OBJECT.

PHIC -- CONVECTIVE HEAT FLUX TO SURFACE.

COND -- HEAT CONDUCTION INTO SURFACE.

ZKOZZ -- SURFACE TEMPERATURE OF THE OBJECT.

OUTPUT VARIABLE:

PHI -- NET HEAT FLUX TO THE FUEL SURFACE.

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

PARAMETER (SIGMA = 5.67D-8)

C

PHI = PHIR + PHIC - COND - SIGMA * (ZK0ZZ**4)

C

RETURN

END

1- PFLUX.

.
PPYRO - Mass Pyrolysis Rate of a Burning Object

Description

This routine calculates the mass pyrolysis rate of a burning object.

This routine assumes the fire is circular or can be represented by a circle

using an equivalent radius. When not limited by fuel burnout, the total

pyrolysis rate is equal to the area of the object covered by the fire

multiplied by the pyrolysis rate per unit area. The pyrolysis rate per unit

area is equal to the net heat flux to the surface divided by the object's heat

of pyrolysis (also called heat of vaporization)

Output

mf (Negative of) mass pyrolysis rate of a burning

object, [kg/s] (V.61)

Input

Hv Heat of vaporization (or pyrolysis) of the

object (Input Data). [J/kg] (V.31)

<f> Net heat flux absorbed by the object (Calculated

Value, see Burning Object section). [W/m2

]

(V. 67)

R Radius of the fire on the burning object

(Calculated Value, see Burning Object section),

[m] (V. 85)

7r Pi (Physical Constant). [3.1415927] (V.146)

1 - PPYRO -1
Calculation

m

f

-7T 2 R <t> H

v

References

1. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V,

Harvard Computer Fire Code", U.S. Department of Commerce,

D.C., NBS-GCR-81-344, October 1981, pp . 87.

Subroutine Variables

TMOZZ = mf QVAP = Hv PI = 7T PHI = <f> ZRFZZ = R

Prepared bv

David W. Stroup

the Fifth

Washington,

1-PPYR0-2
Computer Subroutine

SUBROUTINE PPYRO (QVAP , PHI , ZRFZZ , TMOZZ)

C

Q

k-kk’k'kk’k'k'kifk-Jrk^fk-kk'kk-k'k-k'k-k-k-k'k'kk-k-k-k-k-k'k-k-k-kk'k'k-k-k-kirk'k’k-k-k-k-k-k'k’k-k-k-k-k-k-k-k-k-k-k'k-k-k c

C SUBROUTINE TO CALCULATE THE MASS PYROLYSIS RATE OF A BURNING OBJECT.

C

C INPUT PARAMETER:

C QVAP -- HEAT OF VAPORIZATION OF THE OBJECT.

C

C INPUT VARIABLES:

C PHI -- NET HEAT FLUX TO THE FUEL SURFACE.

C ZRFZZ -- RADIUS OF THE FIRE ON THE OBJECT.

C

C OUTPUT VARIABLE:

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

C

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

C

PARAMETER (PI = 3.1415927D0)

C

TMOZZ - -PI * ZRFZZ*- 2 * PHI / QVAP

C

RETURN

END

1- PPYRO.
PULRAD - Radius of a Pool Fire

Description

This routine calculates the radius of a pool fire. When the entire

(horizontal) surface of a pool of a combustible material is heated to its

ignition temperature, tig , ignition will start at a "hot spot" and spread very

rapidly over the surface. This rapid spread may introduce numerical

instabilities into a fire model. The expression used in this routine provides

for a smooth build-up to the maximum radius to improve numerical stability.

The radius is assumed to increase asymptotically from a user- specified initial

value to its user- specified maximum value. The fire is assumed to reach its

maximum size sixty seconds after ignition of the pool. This routine includes

limit statements to prevent the calculated fire radius from becoming smaller

than the initial object radius or larger than the maximum theoretical object

radius

Output

R Radius of the fire on the burning object (pool).

[m] (V. 85)

Input

R^ Augmented radius of the (pool) object, -- i.e.,

maximum equivalent possible radius of the fire

(Input Data), [m] (V.8)

Ri Initial radius of the fire on the (pool) object

(Input Data), [m] (V.39)

1 - PULRAD -
Time of ignition of the object (Calculated

Value, see Burning Object section), [s] (V.136)

Current simulation time, [s] (V.15)

t

is

t

Calculation

R = X, [1 - exp(-H(t - tt ))], 0 < t t; S SO

lx.

Limits

:

R = « R. , R < Rl

< ^tn » ^ ^

t - ti8 > 60

References

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

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS -GCR- 81- 344 , October 1981, pp . 87-88, 89.

'

Subroutine Variables

ZRFZZ = R

ZRFZM = Rm ZRFZI = Ri ZTIG - t.

i „g ZTZZZ = t

Prepared bv

David W. Stroup

1 - PULRAD - 2
Computer Subroutine

SUBROUTINE PULRAD (ZRFZM, ZRFZI , ZTIG , ZTZZZ , ZRFZZ)

C

CC

C

C

CC

C

C

C

Cc

c

'kk'kk-k'k^^ck'k'k'k'k-k'k'k'k'k'k-k-k'k'k'k'k'k'k-k'k'k'k'k'k'k'k'k'k'k'k'k-k’k'k'k-k-k'k-k'k'k'k'k'k'k-k'k'k'k'k-k'k-k'k'k'k'k

SUBROUTINE TO CALCULATE THE RADIUS OF A POOL FIRE. THE EXPRESSION

USED IN THIS ROUTINE PROVIDES FOR A SMOOTH BUILD-UP TO THE MAXIMUM

RADIUS TO IMPROVE STABILITY.

INPUT PARAMETERS:

ZRFZM -- MAXIMUM BURNING RADIUS OF THE OBJECT.

ZRFZI -- INITIAL BURNING RADIUS OF THE OBJECT.

ZTIG -- TIME OF IGNITION OF THE OBJECT.

ZTZZZ -- SIMULATION TIME.

C OUTPUT VARIABLE:

C ZRFZZ -- RADIUS OF THE POOL FIRE.

C

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

C

ZRFZZ = ZRFZM

IF ( (ZTZZZ-ZTIG) .LT. 60.) THEN

IF ((ZTZZZ-ZTIG) .GE. 0.) THEN

ZRFZZ = ZRFZM * ( 1.D0 - DEXP( - (ZTZZZ- ZTIG) /2 .DO) ) ENDIF

END IF

C

C LIMITS:

C

IF (ZRFZZ .LT. ZRFZI) THEN

ZRFZZ = ZRFZI

ELSE

IF (ZRFZZ .GT. ZRFZM) ZRFZZ = ZRFZM

END IF

C

RETURN

END

1 - PULRAD - 3
’

.
PYRO - Mass Pyrolysis Rate of a Burning Object *

.

Description

This subroutine calculates the mass pyrolysis rate of a burning

horizontal fuel slab modified to allow for smooth burn out as the fuel is used

up. 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. The pyrolysis rate

is modified to take into account the smooth cessation of pyrolysis as the fuel

nears burnout. This routine includes limits to prevent the mass pyrolysis

rate from becoming too large or too small and to set it equal to zero when the

fuel is consumed.

Output

mf (Negative of the) mass pyrolysis rate of the

object (burning slab), [kg/sec] (V.61)

Input

Heat of vaporization (or pyrolysis) of the

object (Input Data). [J/kg] (V.31)

Augmented radius of the object, -- i.e.,

maximum equivalent possible radius of the fire

(Input Data), [m] (V.8)

1 - PYRO -
0

m.

R

7T

Net heat flux absorbed'by the object (Calculated

Value, see Burning Object section). [W/m2

]

(V. 67)

Remaining mass of the object (Calculated Value,

see Burning Object section), [kg] (V.108)

Radius of the fire on the burning object

(Calculated Value), [m] (V.85)

Pi (Physical Constant). [3.141592...] (V.146)

Calculations

(~itR2 4>/hv , 4> > o

lo, t < 0

Unadjusted rate of change of fuel mass

(negative of pyrolysis rate)

.

G = mf / (2m/? )

(tr0 (l-eG

) , <f> > 0 m

p 110 , 4> < 0

Convenient definition (for m^ < 0)

Negative of pyrolysis rate, adjusted for smooth

burnout

.

Limits: mf = 0 , if mf = 0

'-6,000,000 R^/Hv , m£ < -6,000,000

mf = < 0 , mf > 0

References

1.

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

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

.

59 - 68.

2.

Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

1-PYR0-2
J

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 83 - 89.

Subroutine Variables

TMOZZ = mf QVAP = ^

ZRFZM = Rm PHI = <f> ZMOZZ = mf ZRFZZ = R

PI = 7T

Prepared by

David W. Stroup

1-PYR0-3
oooooooo

Computer Subroutine

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

Q •kkk'k'k-k'k-k-k'kkklrk'k'k'k-k'k-k'k'k-k-k'k-k-k-k'k'k'k-k'kk'k'k-kk'k'k'k'k'k'k'k-k-k'kk'k'k-k'k-k-k-k-k'k-k'k'k c IMPLICIT DOUBLE PRECISION (A-H.O-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

ZRFZM -- MAXIMUM BURNING RADIUS OF THE OBJECT

INPUT VARIABLES:

PHI -- FLUX IMPINGING ON THE SURFACE OF THE OBJECT

ZMOZZ -- REMAINING MASS OF THE OBJECT

ZRFZZ -- RADIUS OF THE FIRE ON THE OBJECT

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

C LIMITS:

IF (TMOZZ .LE. 0 . DO) THEN

BNDS - -6.D6 * ZRFZM**2 / QVAP

IF (TMOZZ .LT. BNDS) TMOZZ = BNDS

1 - PYRO -

4
ELSE

TMOZZ = O.DO

END IF

C

IF (ZMOZZ .LE. O.DO) TMOZZ = O.DO

C

RETURN

END

l-PYRO-5

SPREAD - Fire Spread Rate on Horizontal Fuel Slab

Description

' This routine calculates the spread rate of a flame on a horizontal fuel

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

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

the slab plus the sides. This equivalent maximum radius, Rm , is larger than

the radius corresponding to the top surface. The spread rate until R = 0.95^

is given by an expression which yields approximately exponential growth (as

observed in experiments). Beyond that point, the spread rate is taken to slow

down, as shown under the section "Calculations" below. The fire spread rate

equation was developed from data for polyurethane foam obtained by L. Orloff.

For additional information, the reader should refer to reference 1 below.

Output

R Rate of spread rate of a fire on an object

(horizontal fuel slab), [m/sec] (V.107)

Input

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

(V . 115)

Tf Temperature of the flaming gases, -- i.e., flame

temperature (Input Data). [K] (V.123)

Augmented radius of the object, -- i.e., maximum

1- SPREADequivalent possible radius of the fire (Input

Data) . [m] (V. 8)

R Radius of the fire on the object (pool), [m]

(V.85)

<f) Net heat flux absorbed by the object (Calculated

Value, see Burning Object section). [W/m2

]

(V. 67)

o Stefan - Boltzmann constant (Physical '

Constant). [5.67 x 10’ 8 W/m2 -K4

] (V.147)

Calculations

C = <f> / aT£ Convenient non-dimensional grouping

of terms.

fAf C(l+(C/2)+(C2 /3) ) , R < 0.95R„

R = jRate of change of fire radius.

[(Rm -R)/10, R>0.95Rm

References

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

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

61 - 67.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code", U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp. 83 - 86.

1- SPREAD2
Subroutine Variables

TRFZZ = R

AFIRE = Af T = Tf ZRFZM = Rm ZRFZZ = R

PHI = <f> SIGMA = a

Prepared bv

David W. Stroup

1- SPREAD -3
Computer Subroutine

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

Q &&-k-k-k'k-J(-k$:'k-k-k-k-k-k-Jc-k'k-k-k-k-k-k-k-k-k-k-k-k‘k-k-k-jc-k'k-k-k-k-Jt-k‘k'k,Jt

,Jc'k ,k*’k~k'krk-k*-k-k-Jc-k-k c 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

END IF

C

RETURN

END

1- SPREAD -4
SUTPRD - Rate at which a Burning Object Produces Soot

Description

This routine calculates the rate at which a burning object produces

soot. The production rate of a specific gas (or particulate like soot) by a burning object depends on the chemical composition of the material being

burned. The rate of production of soot by a given burning material is equal

to the mass pyrolysis rate of the object multiplied by the mass fraction of

the (combustible part of the) object evolved as soot, when the object burns in

open air. The mass fraction must be obtained from fire tests of the specific

material (see Tewarsen, A., "Heat Release Rates from Burning Plastics", J

Fire and Flammability 8 (1977) for example)

Output ms Mass rate of evolution of soot from the object.

[kg/s] (V. 58)

Input

fg Mass fraction of the (combustible part of the)

object evolved as soot, when the object burns in

the open (Input Data). (V.48) mf (Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

1- SUTPRD -1
Calculations

= -f' s TMf

References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

TMOS = ms FS = f'

TMOZZ = mf

Prepared by

David W. Stroup

l-SUTPRD-2
Computer Subroutine

SUBROUTINE SUTPRD (FS , TMOZZ , TMOS

C

Q

•k-k-k'k-k-k-k-k'k'k^rk-k'k'k-k-k-kirk'k'k-k'k'k-k-k'k-k'k-k-k'k'k-k'k-k-k'k-k'k'kirk'k-k-k-k-k-k-k-k-k-k-k-k-k-k-k'k'k'k-k'k-k'k'k'k'k c

C SUBROUTINE TO CALCULATE THE RATE AT WHICH THE FIRE OF AN OBJECT

C PRODUCES SOOT.

C

C INPUT PARAMETERS:

C FS -- MASS FRACTION OF SOOT IN THE GASES EVOLVED FROM THE

C BURNING OBJECT

C

C INPUT VARIABLES:

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

C

C OUTPUT VARIABLE:

C TMOS -- MASS RATE OF EVOLUTION OF SOOT FROM THE OBJECT.

C

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

C

TMOS = -FS * TMOZZ

C

RETURN

END

1- SUTPRD -3

TMGAS - Gas Flow Rate from a Gas Burner

Description

This routine computes the gas flow rate at a given time for a gas burner

with a variable flow rate. The gas flow rate is assumed to vary linearly with

time between fixed input points (time, gas flow rate). The gas flow rate

curve is entered by the user as a set of discrete points. The routine does a

linear interpolation between the appropriate points to determine the gas flow

rate at a specific time. For times of interest prior to the first input time

the gas flow rate is assumed to be zero. For times of interest exceeding the

last input time, the gas flow rate is assumed to be equal to the flow rate at

the last input time. (Note: The computer routine presented in the Computer

Subroutine section of this write-up is limited to a maximum of 100 input

points. However, the routine may be adjusted to handle any number of points.)

Output

mf (Negative of the) mass pyrolysis rate of the

object (gas flow rate at time t) . [kg/s] (V.61)

Input

t Current simulation time (time at which gas flow

rate is desired), [s] (V.15)

N

g Number of segments making up the gas flow rate

curve (Input Data). (V.69)

t* ; i — 1 , 2 , . .

. ,N +1 Array containing the times associated with the

o © input gas flow rates, m

g (Input Data), [s] (V.7)

1 - TMGAS -1
nig ; i - 1,2, . . . ,N Array containing the gas flow rates associated

g +l

with the input times, t

g (Input Data), [kg/s]

(V. 6)

Calculation

m,

0 ,

. i-i r.i

m + m

g l g

• i-ll

- m

g J

i-1

i-1

t < f

t^ ^ < t < t^ i=l,2,

g g

, N +1

g

.N +1

i V

N +1

t ^ t g

References

No references available.

Subroutine Variables

Note

:

TMOZZ

ZTZZZ

NSEG

ZTSEG(I)

TMGSEG(I)

The value

from 1 to

= t

of the index I should range from 1 to NSEG+1 while i ranges

n5+i.

Prepared bv

David W. Stroup

1 - TMGAS - 2
Computer Subroutine

SUBROUTINE TMGAS (ZTZZZ , NS EG , ZTSEG , TMGSEG , TMOZZ)

+*••JrJcJrk k-k'k-JrJck+++•Jck-k-k-k

SUBROUTINE TO COMPUTE THE GAS FLOW RATE FROM A GAS BURNER. THE GAS

FLOW RATE VARIES LINEARLY WITH TIME BETWEEN FIXED VALUE PAIRS:

TIME, GAS FLOW RATE.

NOTE: A MAXIMUM OF LOO INPUT DATA POINTS MAY BE SPECIFIED. TO CHANGE

THIS NUMBER: ALTER THE VALUE CONTAINED IN VARIABLE MAXSEG.

INPUT PARAMETERS

NSEG

ZTSEG

TMGSEG

INPUT VARIABLES

ZTZZZ

NUMBER SEGMENTS IN GAS FLOW RATE CURVE.

ARRAY CONTAINING THE TIMES ASSOCIATED WITH THE GAS

FLOW RATES CONTAINED IN ARRAY TMGSEG.

ARRAY CONTAINING THE GAS FLOW RATES ASSOCIATED WITH

THE TIME CONTAINED IN ARRAY ZTSEG.

CURRENT TIME

OUTPUT VARIABLE

TMOZZ -- GAS FLOW RATE AT ZTZZZ

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

PARAMETER (MAXSEG = 100)

DIMENSION ZTSEG (MAXSEG), TMGSEG (MAXSEG)

10

20

C

IF (ZTZZZ .GE. ZTSEG(l) ) THEN

IF (ZTZZZ .LT. ZTSEG(NSEG+1) ) THEN

DO 10 1=2 , NSEG+1

IF (ZTZZZ .LT. ZTSEG(I) ) THEN

II = I III = I - 1

GO TO 20

END IF

CONTINUE

CONTINUE

TMFGZ = TMGSEG(III)

(TMGSEG(II)

(ZTSEG(II)

- TMGSEG (II I) ) * (ZTZZZ - ZTSEG(III)) /

ZTSEG(III)

ELSE

TMFGZ = TMGSEG (NSEG+1)

1- TMGAS -3
END IF

ELSE

C

TMFGZ = O.ODO

C

ENDIF

C

TMOZZ - -TMFGZ

C

RETURN

END

l-TMGAS-4
WTRPRD - Rate at which a Burning Object Produces Water Vapor

Description

This routine calculates the rate at which a burning object produces

water vapor. The production rate of a specific gas by a burning object

depends on the chemical composition of the material being burned. The rate of

production of water vapor by a given burning material is equal to the mass

pyrolysis rate of the object multiplied by the mass fraction of the

(combustible part of the) object evolved as water vapor, when it burns in open

air. The mass fraction must be obtained from fire tests of the specific

material (see Tewarsen, A., "Heat Release Rates from Burning Plastics", J

Fire and Flammability 8 (1977) for example)

Output mH20 Mass rate of evolution of water vapor from the

object, [kg/s] (V.59)

Mass fraction of the (combustible part of the)

object evolved as water vapor, when the object

burns in the open (Input Data). (V.47)

(Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

Input

"H 2 0

mT

1-WTRPRDCalculations

m, = _ f

'

H 2 0

-l H2 0 mT

References

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

Harvard Fire Code," U.S. Department of. Commerce, Washington, D.C.,

NBS-GCR-81-344 , October 1981, pp . 128 - 131.

Subroutine Variables

TMOW = niH 2 o FH20 - f' 20

TMOZZ - mL

Prepared by

David W. Stroup

1 - WTRPRD - 2
Computer Subroutine

SUBROUTINE WTRPRD (FH20 , TMOZZ , TMOW)

'k-k~k~k‘k-k-k-k-k'k-k'k'k-k-k-kie~k-k'k'k~k-k'k'k-k-k'k-k-k'k'k-k-k'k-k'k'k'k-k'k~k'k'k-k'k'k~k'k-k~k-k'k-k'k-k'k'k-k'k-k-k‘k'k-k-k

SUBROUTINE TO CALCULATE THE RATE AT WHICH THE FIRE OF AN OBJECT

PRODUCES WATER VAPOR.

INPUT PARAMETERS:

FH20 -- MASS FRACTION OF WATER VAPOR IN THE GASES EVOLVED

EVOLVED FROM THE BURNING OBJECT.

INPUT VARIABLES:

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

OUTPUT VARIABLE:

TMOW -- MASS RATE OF EVOLUTION OF WATER VAPOR FROM THE

OBJECT.

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

TMOW = -FH20 * TMOZZ

RETURN

END

1- WTRPRD -3

2. ALGORITHMS RELATED TO CONDUCTION HEAT TRANSFER

2-1
2-2

I*

igure

2-1.

General

diagram

of

a

room

fire
TMPW01 - Heat Conduction in a Slab

Description

This algorithm calculates the time dependent temperature profile inside

a slab, figure 2-2. A slab of thickness, Tw , 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 explicitly using central differences (see for example

Holman, Heat Transfer , pp . 72-98).

This routine assumes that the slab is exposed to a fire on one side and

an ambient temperature environment on the other side. The net heat flux on

the fire exposed side of the slab is composed of convection and radiation heat

fluxes from the hot layer, radiation heat flux(es) from the flame(s) above the

burning object(s), and re-radiation from the slab surface. The unexposed side

of the slab is assumed to transfer heat, by convection and radiation, to an

ambient temperature environment. The re-radiation (on the exposed side), the

radiation (on the unexposed side)

and the resulting net heat fluxes are calculated within the routine.

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 on

the exposed side of the slab, and the convection heat flux on the unexposed

side. These fluxes may be calculated elsewhere in the user's program or

2-TMPW01-1
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 appropriately specified convection

and radiation heat flux boundary conditions.

The slab re -radiates energy (received through convection and radiation

from the hot layer and flames) through the upper layer to the lower -layer.

The lower layer is at some temperature, TD. In order to calculate the heat

flux radiated by the fire exposed slab surface, the present layer height and

the absorption coefficient of the hot layer must be specified or calculated in

some way. The layer height is usually available from most fire models.

Various methods for calculating the absorption coefficient of the hot layer

may be found in the Hot Layer section of this catalog. The unexposed side of

the slab radiates to an environment at ambient temperature, Ta. The

S tefan-Boltzmann constant must be specified for use in these radiation

calculations

.

The user must specify the time step to be used in the calculation as 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 calculation stability. If this exceeds the maximum allowable,

the maximum number of layers will be used. This method is numerically stable

for 5x > (2aAtmax ) 1 1

2

and At < Atmax , where Atmax is the maximum time step to

be used. The user must exercise care in selecting the maximum value for 5x.

2-TMPW01-2
If the value is too low, the calculation may be unstable and produce erroneous

results

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 for use in the next time step.

Output

Ti ew

; i = 1,2,...,

Temperature of the slab at each node point,

i. [K] (V.122)

Input

^lwd Convective heat flux from the hot layer inside a room to the adjacent part (interior) of the wall

or ceiling (slab) (Calculated Value, see Convective Heat Transfer section). [W/m2

] (V.ll)

^lwr Radiative heat flux from the hot layer to the

adjacent part (interior) of the wall or ceiling

(slab) (Calculated Value, see Radiation Heat

Transfer section). [W/m2

] (V.81)

2 °Ipwr (Sum of the) radiative heat flux from plume(s)

to the adjacent part (interior) of the wall or ceiling (slab) (Calculated Value, see Radiation

Heat Transfer section). [W/m2

] (V.79)

2 -TMPW01 - 3
3a WR

t

Atmax

At

Ta td

Tw

a,

or c.

and pw

a

Convective heat flux from the ambient

environment to the adjacent part (exterior) of

wall or ceiling (slab) (Calculated Value, see Convective Heat Transfer section). [W/m2

] (V.ll)

Current simulation time, [s] (V.15)

Maximum allowable time step (Input Data)-, [s]

(V. 64)

Size of current time step, [s] (V.110)

Ambient temperature of air. [K] (V.120)

Temperature of the lower layer in a room. [K]

(V. 128)

Thickness of the wall or ceiling (slab) (Input

Data) . [m] (V . 134)

Thermal conductivity of the wall or ceiling

(slab) (Input Data). [W/m-K] (V.130)

Thermal diffusivity of the wall or ceiling

(slab) (Input Data). [m2 /sec] (V.132)

Specific heat of the wall or ceiling (slab)

(Input Data). [J/kg-K] (V.lll)

Density of the wall or ceiling material (slab)

(Input Data), [kg/m3

] (V.16)

Absorption coefficient of the hot layer in a room (Calculated Value, see Hot Layer

section). [m_1

] (V.2)

Stefan-Boltzmann constant (Physical

Constant). [5.67 x 10" 8 W/m2 -K4

] (V.147)

2 -TMPW01 -4
N Maximum allowable number of layers into which

slab may be divided (Input Data). (V.63)

hL Depth of the hot layer in a room (Calculated

Value, see Hot Layer section), [m] (V.20)

T? ld

; i = 1,2,...,

Temperature of wall or ceiling (slab) at each

node point at the start of the time step

(Calculated Value. If time zero, Input Data. At

later times, solution at previous time.). [K]

(V. 121)

Calculations

The calculations below are executed once, at time t = 0. The values are returned in the calling argument list for use in future calls to this routine

‘Calculate thermal diffusivity, if

necessary.

Smallest permissible time space

increment (calculated for the

a / ( Pvt cw )

Sx. = J 2aAt i ^ m ax

N = 1 + [Tw /5xJ

f

- 1), N > Nna]t

Sx = \

TW /(N - 1), 2 < N < Nmax

l T„ , N < 2

a = 2q/(5x) 2

largest time increment to be used)

N is the number of points where the

temperature is calculated, n = 1 on

inside surface, n = N on outside

surface, (take integer part only of

term in brackets)

Space increment actually used

Computation parameter.

2-TMPW01-5
b = <5x/k Computation parameter.

The calculations below are executed each time this routine is called.

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

distribution at time t: =

^lwd + Qlwr + 2 ^PWR

4n = q^'wD

4, 1 - q" - cr(Tg ld

)

4 + exp(- KhL )aTj

h - is + < - <

T

n ew =xo Id (l. aAt )+aAt(T° ld +b^1

)

Tnew_ToLd

( 1 . aAt ) + ( aAt/2 ) (T° dd +T°J d)

Tnew_TOld(i. aAt) +aAt(T5i d -b^)

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 fo

each interior node point, i =

2,3, . .

. , Nr 1)

.

Outside surface temperature

calculation

.

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. Department of Commerce, Washington,

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

2 -TMPW01-

6
.

f

3. H.W. Emmons, "Heat Conduction Calculations for Zone Fire Modeling,"

Harvard University Home Fire Project Technical Report #44 (1980).

4. . Carslaw, H.S., and Jaeger, J.C., Conduction of Heat in Solids . Clarendon

Press, Oxford, 1959.

Subroutine Variables

ZKW(I) = 'pn e w

J'i FQLWD =

^LWD

FQLWR =

WR

FQPWR = S qf

FQAWD = ^AWD

ZTZZZ = t

DT = At

DTMAX = Atma: ZKAZZ = Ta ZKDZZ = td

- ZNWZZ = ZJWZZ = ZGWZZ = aw ZCWZZ = cw VMWZZ = pw ZULZZ = K

SIGMA = a MXLYRS = Nmax ZHLZZ = ZKWO ( I

=

•

—O

H H

; i = 1,2, . . .

,

WR

The following variables represent values which are calculated during the first

call of this routine:

DX

AW

BW

N

= <5x = a = b

= N

2-TMPW01-7
These values are retained for future use in calls to this routine. The

symbols on the right refer to the equations in the Calculations section above.

Prepared bv

David W. Stroup

2 -TMPW01 - 8
Computer Subroutine

SUBROUTINE TMPWO 1 ( ZNWZZ , ZJWZZ , ZGWZZ , ZCWZZ , VMWZZ , ZKAZZ , DTMAX

& ZKDZZ , ZKWO , ZHLZZ , ZTZZZ , DT , FQLWD , FQLWR

& FQPWR , FQAWD , DX , AW , BW , N , ZKW)

IMPLICIT DOUBLE PRECISION (A-H.O-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 PAPAMETERS:

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)

DTMAX -- MAXIMUM ALLOWABLE TIME STEP

INPUT VARIABLES:

ZKDZZ -- LOWER LAYER TEMPERATURE (EXPOSING INTERIOR

SIDE OF SLAB)

ZKWO -- PREVIOUS TIME STEP SLAB TEMPERATURE PROFILE

ZHLZZ - - SMOKE LAYER HEIGHT

ZTZZZ -- CURRENT SIMULATION TIME

DT -- CURRENT SIZE OF TIME STEP

FQLWD -- CONVECTIVE HEAT FLUX FROM LAYER TO

INTERIOR SIDE OF SLAB

FQLWR -- RADIATIVE HEAT FLUX FROM LAYER TO INTERIOR

SIDE OF SLAB

FQPWR -- RADIATIVE HEAT FLUX FROM PLUME(S) TO

INTERIOR SIDE OF SLAB

FQAWD -- CONVECTIVE HEAT FLUX FROM AMBIENT TO EXTERIOR

SIDE OF SLAB

SECONDARY OUTPUT VARIABLES:

DX -- THICKNESS OF PIECES OF SLAB USED IN FINITE

DIFFERENCE CALCULATION

AW -- CONVENIENT DEFINITION

BW -- CONVENIENT DEFINITION

N -- NUMBER OF NODES USED IN FINITE DIFFERENCE CALCULATION

OUTPUT VARIABLE:

ZKW -- TEMPERATURE PROFILE WITHIN SLAB AT NEW TIME

2 -TMPWO 1 - 9
C

PARAMETER (NON =20)

PARAMETER (SIGMA = 5.67D-8)

DIMENSION ZKWO(NON) ,ZKW(NON)

C

C INITIAL CALCULATIONS

C

IF (ZTZZZ .LE. 0.0) THEN

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

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

M = IDFIX( ZNWZZ / DXM) + 1

N = MINO (M, 20)

IF (N .LE. 1) N = 2

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

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

BW = DX / ZJWZZ

ENDIF

C

C WALL TEMPERATURE CALCULATIONS

C

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)

& • + ZKWO (1+1)

)

10 CONTINUE

C CALCULATE SLAB HEAT FLUXES

FQWA = FQLWD + FQLWR + FQPWR

FQW1 = FQWA - SIGMA * ( ZKWO ( 1

) **4 - DEXP (-ZHLZZ * & ZULZZ) * ZKDZZ**4)

FQWB = FQAWD

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

C CALCULATE INTERIOR NODE TEMPERATURE

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

C CALCULATE EXTERIOR NODE TEMPERATURE

ZKW(N) = ZKWO (N) * TEMP + AW * DT * (ZKWO(N-l) + BW * & FQW2

)

C

RETURN

END

2-TMPW01-10
2 -TMPW01- 11

3. ALGORITHMS RELATED TO CONVECTION HEAT TRANSFER

3-1
3-2

Figure

3-1.

General

diagraa

of

a

room

fire
CBLOCK - Convective Heat Flux to the Surface of a Pool

Description

This subroutine calculates the convective heat flux from the combustion

zone at flame temperature, Tf

, to the surface of a burning pool of combustible

liquid at temperature Ts

. The convection heat flux is calculated using the

equation

*conv " h(Tf

- T,).

This routine requires the user to specify a Prandtl number (V.72). The heat

transfer coefficient, h, is determined from the Nusselt number (relates

convective heat transfer effects to conduction heat transfer effects) for a horizontal heated upward facing plate with free convection. In order to

calculate the Nusselt number, the Grashof number (relates buoyancy forces to

viscous forces) must be calculated first.

Output

r Convective heat flux to the surface of a pool of c o n v

~

liquid. [W/m2

] (V.14)

Input

mf (Negative of the) mass pyrolysis rate of the

object (pool) (Calculated Value, see Burning

Object section), [kg/s] (V.61)

R Radius of the fire on the burning object (pool)

3- BLOCK(Calculated Value, see Burning Object section),

[m] (V. 85)

Ts Temperature of the surface of the object (Input

Data). [K] (V.129)

g Acceleration of gravity (Input Data) . [m/s 2

]

(V . 144)

7r Pi (Physical Constant). [3.141592...] (V.146)

c

p Specific heat of ambient air (Input Data)

.

[J/kg-K] (V.112)

Tf Temperature of the flaming gases, -- i.e. flame

temperature (Input Data). [K] (V.123)

Pr Prandtl number (Input Data). (V.72)

Calculations

k = 2.72(10“ 7 )((Ts -Tf )/2) 4/5

i/ = 7.18(10' 10 )((Ts +Tf )/2)

7/A

d = 2R

Gr = gd3 [(Tf -Ts )/(i/2 Tf )]

Nu = 0 . 012 (GrPr) 1 1

3

Thermal conductivity of the air layer

between flame and pool surface.

Kinematic viscosity of the air layer

between flame and pool surface.

Pool diameter.

Grashof number for flame - surface area. Nusselt number calculation.

z

rii_ c 4

f p

7r d Nu k

Dimensionless blowing factor.

<f> conv

Nu [ 3 ] <VV z Convective heat flux to the surface of

the pool.

3 - CBLOCK2
References

1. Holman, J.P., Heat Transfer . McGraw-Hill Book Company, 1981, pp . 265

292.

Subroutine Variables

PHIC = ~ c o n v ZRFZZ = R

TMOZZ = mf TS = Ts PI = 7T G = g

CP = c

p TG = Tf PR = Pr

Prepared by

David W. Stroup

3 - CBLOCKo

o

Computer Subroutine

SUBROUTINE CBLOCK (PR , TG , TMOZZ , ZRFZZ , TS , PHIC)

'k-k-k-kk-k'k-k'k-k'k'k'k'k-k-k-k-k-k-k-k-k-k'k-k'k-k-k-k-k-k-k-k-k-kick-k'k'k'k-k-k-k-k-k-k-k-k-kkk-k-k-k-k-k'k-k'k'k'k'k-k-kk'k-k'k

THIS ROUTINE CALCULATES THE CONVECTION HEAT FLUX TO THE SURFACE

OF A BURNING POOL OF COMBUSTIBLE LIQUID.

INPUT PARAMETERS:

PR -- PRANDTL NUMBER.

TG -- FLAME TEMPERATURE.

INPUT VARIABLES:

C TMOZZ -- MASS PYROLYSIS RATE OF THE POOL.

C ZRFZZ -- RADIUS OF POOL.

C TS -- SURFACE TEMPERATURE OF POOL.

C

C OUTPUT VARIABLE:

C PHIC -- CONVECTIVE HEAT FLUX TO THE POOL SURFACE.

C

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

C

PARAMETER (PI-3 . 141592654 , G=9 . 8 , CP=1004.)

C

C CALCULATE TEMPERATURE DEPENDENT THERMAL CONDUCTIVITY AND

C KINEMATIC VISCOSITY OF AIR AT POOL SURFACE.

FK = 2.72D-7*((TS+TG)/2.)**(4./5.)

VISKIN = 7.18D-10*((TS+TG)/2.)**(7./4.)

C

C CALCULATE POOL DIAMETER.

D = 2 . *ZRFZZ

C

C CALCULATE GRASHOF AND NUSSELT NUMBERS.

GR = G*D**3.*(TG-TS)/(VISKIN**2*TG)

NU - 0.012*(GR*PR)**(l./3.)

C

C CALCULATE THE DIMENSIONLESS BLOWING FACTOR.

IF (-TMOZZ .LT. l.D-5) TMOZZ = -l.D-5

Z = -TM0ZZ*CP*4./(PI*D*NU*FK)

C

C CALCULATE THE CONVECTIVE HEAT FLUX TO THE POOL SURFACE.

IF (Z .LT. -30.) THEN

PHIC = NU*(FK/D)*(TG-TS)

ELSE

PHIC = 0.

IF (Z .LT. 30.) PHIC = NU*(FK/D)*(TG-TS)*Z/(DEXP(Z) - 1.)

ENDIF

C

RETURN

3 - CBLOCK-4
END

_

.

3 - CBLOCK'
CNVF - Convection Heat Flux from Floor to Lower Layer

Description

This routine calculates the convection heat transfer from an elevated

temperature floor to the cooler lower layer above it. The floor is heated by

radiation from the flames and from the hot layer. The floor in turn will heat

the (cool) lower layer of gas above it by convection. This analysis uses the

convection heat transfer equation. The flow above the floor may be laminar or

turbulent, and the lower layer thermal conductivity and kinematic viscosity

may vary with temperature. This routine requires data for the floor

temperature, lower layer temperature, and floor dimensions.

Output

1 o o r Convective heat flux from the lower layer to the

floor. [W/m2

] (V . 12)

Input

Temperature of the lower layer in the room

(Calculated Value, see Hot Layer section). [K]

(V.128)

Tfloor Temperature of the floor in the room (Calculated

Value, see Radiation Heat Transfer section). [K]

(V.125)

Dimension of the room in the x-direction (Input

Data) . [m] (V . 21)

3-CNVF-l
Ly Dimension of the room in the y- direction (Input

Data), [m] (V. 22)

Pr Prandtl number (Input Data). (V.72)

g Acceleration of gravity (Input Data). (V.144)

Calculations

T = (TD +T£loot )/2 Film temperature..

i/=13 . 7 (10" 6 r T

i [-392.56 -I

-273.16- -119.4+TViscosity of the film (assumed to be air)

r0 . 26262Tb

k=2 . 829 ( 10" 3 )+

L 3080+T J Thermal conductivity of the film (air)

.

f L* Lx < Ly

1 ly , ly < Lx

Determine the smallest dimension of the

floor for use in Grashof number

calculation.

Gr - (9 . 8d3 /V2 )((Tfi00r -TD )/TD )

Ra = Pr Gr

Grashof number (relates buoyancy forces t viscosity forces)

.

Rayleigh number.

[ 0 . 1 , Nu=^0.6236Ra1/4

[0.145Ra1/3

,

Ra < 1

1 < Ra < 4(10 7

) Ra > 4(107

)

Nusselt number (relates convection to

conduction)

.

h = (k Nu)/d

^floor^^D'^floor^

Convective heat transfer coefficient.

Convective heat flux from the lower layer

to the floor.

’’ -CNVF-2
References

1. Kolman, J.P., Heat Transfer . McGraw-Hill Book Company, 1981, pp . 265

282.

Subroutine Variables

FQDFD = 0floor

ZKDZZ = Tl ZKFLO = Tfloor

ZLRZX = L*

ZLRZY = Ly

PR = Pr

G = g

Prepared bv

David W. Stroup

3-CNVF-3
oooooooooo

Conrputer Subroutine

SUBROUTINE CNVF ( ZKDZZ , ZKFLO , ZKRZX , ZKRZY , PR , FQDFD

)

Q k'k-k-kkk'k'kk'kk'kkk'k-k'kk'kkkkk-k'k-k'kkk'k'k'k'k'k'k'k'kkkkk'k'kk'kkk'k'k'k'k'k'k'k'k-J''rk'kkk-kkk-k'kk c

C THIS SUBROUTINE CALCULATES THE CONVECTION HEAT FLUX FROM THE ROOM

FLOOR TO THE LOWER LAYER.

INPUT PARAMETERS:

ZLRZX -- DIMENSION OF THE ROOM IN THE X- DIRECTION.

ZLRZY -- DIMENSION OF THE ROOM IN THE Y- DIRECTION.

PR -- PRANDTL NUMBER

INPUT VARIABLES:

ZKDZZ -- LOWER LAYER TEMPERATURE IN ROOM.

ZKFLO -- FLOOR TEMPERATURE IN ROOM.

C

C OUTPUT VARIABLE:

C FQDFD -- CONVECTIVE HEAT FLUX FROM THE LOWER LAYER TO THE

C FLOOR

.

C

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

DOUBLE PRECISION HBAR , K , NU

C

PARAMETER (G = 9.8)

C

C CALCULATE FILM TEMPERATURE

.

TBAR = 0 . 5* (ZKDZZ + ZKFLO)

C

C CALCULATE THE THERMAL CONDUCTIVITY AND KINEMATIC VISCOSITY OF THE

C FILM.

THERM = 0.002829 + (0.26262 -TBAR) /( 3080 .

0

+ TBAR)

VISC = 13.7E-6 * ( (TBAR/273 . 16 ) ** 2.5) *

& (392.56/(119.4 + TBAR))

C

C DETERMINE THE SHORTEST DIMENSION OF FLOOR.

IF (ZLRZX .LE. ZLRZY) THEN

D = ZLRZX

ELSE

D = ZLRZY

ENDIF

C

C CALCULATE THE GRASHOF NUMBER.

GR = (G*D**3/VISC**2)*DABS(( ZKFLO- ZKDZZ) /ZKDZZ)

C

C CALCULATE THE RAYLEIGH NUMBER.

RA = PR * GR

C

C CALCULATE THE NUSSELT NUMBER.

3 -CNVF -4
IF (RA .LT. 1.0) THEN

NU = 0.1

ELSEIF ((RA .GE. 1.0) .AND. (RA . LT . 4.0D7)) THEN

NU = 0.6236 * RA**(0.25)

ELSE

NU = 0.145 * RA**(l./3.)

ENDIF

C

C CALCULATE THE HEAT TRANSFER COEFFICIENT.

HBAR = THERM * NU / D

C

C CALCULATE THE CONVECTIVE HEAT FLUX FROM THE LOWER LAYER TO THE FLOOR.

FQDFD = HBAR * (ZKDZZ - ZKFLO

C

RETURN

END

3-CNVF-5
.
CNVL - Convection Heat Loss from the Hot Layer

Description

This subroutine calculates the convective heat loss rate from the hot

layer (to the extended ceiling) . The hot layer is located in a room

surrounded by a uniform ambient environment. The hot layer is assumed to be

at a uniform temperature as are the surfaces of the walls and ceiling in

contact with the hot layer. The routine also assumes only one "wall" per

room, and that side two of the "wall" is in contact with the outside -- i.e.,

with quiescent ambient air. The decrease in wall area in contact with the hot

layer due to vents is also considered in this routine.

Output

Eld Rate of increase of the energy of the hot layer,

by convection, from the walls in a room --

generally negative. [W] (V.86)

Input

L*

Ly

hL

El

Dimension of room in x-direction (Input Data)

[m] (V . 21)

Dimension of room in y-direction (Input Data)

[m] (V . 22)

Depth of the hot layer in room (Calculated

Value, see Hot Layer section), [m] (V.20)

Net rate of change of the energy of the hot

3- CNVLlayer in a room (Calculated Value, see Hot Layer

section). [W] (V.68)

el Energy contained in the hot layer in a room

(Calculated Value, see Hot Layer section). [J]

(V.25)

^LWD Convective heat flux from the hot layer inside a room to the adjacent part of the wall/ceiling

(Calculated Value, see Convection Heat Transfer

section). [W/m2

] (V.ll)

Jo ^LWD^AWD )

<^ t Total energy stored in a unit area of the hot

wall due to convection (Calculated Value, see Convection Heat Transfer section) . [W/m2 ]

(V. 138)

(Sum of the) area(s) of the vent(s) covered by

the hot layer (Calculated Value, see Vent

section) . [m] (V . 5

)

^vL (Sum of the) width(s) of vent(s) which intersect

the interface between the hot and cold layers

(Calculated Value, see Vent section), [m]

(V . 141)

Calculations

-^(L^. +Ly ) hL Area of heated (vertical) wall.

A = ^+Ly Lx - L Area of heated part of wall and ceiling which is

not covered by vents

.

3-CNVL-2
f'^LWD ’ EL EL < 0

I’^LWD "\^vL ) t/o (^LWD+^AWD ) ] ^L /^L » ^L ^L — *“*

References

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

Harvard University, Home Fire Project Technical Report No. 34, October

1978, pp. 49 - 51.

2. Mitler, H.E., and Emmons, H.W.

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS -GCR- 81- 344 , October 1981, pg. 113.

Subroutine Variables

TELZD = Eld

AQ =

It (4£wD +i

AVLSM = 2 Avi

WVLS = ^ wvL

ZLRZX = L* ZLRZY = Ly

ZHLZZ = hL ZELZZ = El TELZZ = El

FQLWD =

^LWD

Prenared bv

David W. Stroup

3-CNVL-3
o

o

Computer Subroutine

SUBROUTINE CNVL ( ZLRZX , ZLRZY , AQ , AVLSM , FQLWD , WVLS , TELZZ

,

& ZELZZ , ZHLZZ , TELZD

)

C

•k-k-k-k-k-kk-k-k-k-k-k-k-k-k'k-k-k-k-k-k-k-k-k'k-kk-k-k'kk-k-k-k-k-k-k'k-k-k-k-k-k'k-k-k-k-k-k'k'k-k-k-k-k'k-k k-kk-kkk

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

FINDS THE RATE OF LOSS OF ENERGY FROM THE HOT LAYER IN

A ROOM DUE TO CONVECTIVE HEATING OF THE WALLS AND CEILING

INPUT PARAMETERS:

ZLRZX -- LENGTH OF THE ROOM ALONG THE X-AXIS.

ZLRZY -- LENGTH OF THE ROOM ALONG THE Y-AXIS.

INPUT VARIABLES:

AQ

AVLSM

FQLWD

WVLS

TELZZ

ZELZZ

ZHLZZ

CONVECTIVE ENERGY STORED IN A UNIT AREA OF HOT WALL.

TOTAL AREA OF THE VENTS COVERED BY THE HOT LAYER.

CONVECTIVE HEAT FLUX FROM THE LAYER TO THE ADJACENT

WALL.

TOTAL WIDTH OF VENTS WHICH INTERSECTS THE INTERFACE

BETWEEN THE HOT AND COLD LAYERS (I.E. THE AMOUNT BY

WHICH THE PERIMETER OF THE WALLS IS DECREASED BY THE

VENT HOLES AT THE INTERFACE.)

TIME RATE OF CHANGE OF TOTAL ENERGY OF THE HOT LAYER,

TOTAL ENERGY OF THE HOT LAYER.

DEPTH OF THE HOT LAYER.

OUTPUT VARIABLE:

TELZD -- RATE OF CHANGE OF LAYER ENERGY DUE TO CONVECTIVE

HEATING OF THE WALLS.

AWO = 2.0D0 * ( ZLRZX + ZLRZY ) * ZHLZZ

A = AWO + ZLRZY*ZLRZX - AVLSM

TELZD = -A * FQLWD

IF ( TELZZ * ZELZZ .GT. 0 . DO ) THEN

TELZD = TELZD - 0 . 5DO*(AWO-WVLS*ZHLZZ)*AQ*TELZZ

1 / ZELZZ

ENDIF

RETURN

END

3 -CNVL4
CNVW01 - Convective Heat Flux from Hot Layer to Walls and Ceiling

Description

This routine computes the convective heat transfer rate per unit area

from an adjacent hot layer to one side of a wall (or ceiling) . The hot layer

is assumed to have the same temperature throughout and likewise the surface of

the walls and/or ceiling are assumed to have a uniform temperature where they

are in contact with the hot layer. The standard form of the convection heat

transfer equation is used for these calculations. The minimum and maximum

heat transfer coefficients for the hot layer gases are assumed to be known.

Studies are still being conducted to determine the appropriate values for

these coefficients. Reference [2] suggests values of 10 and 50 W/m2 K.

As the fire grows, the convection currents increase, and the interior

heat transfer coefficient should increase. In this routine, the increase is

assumed to be linear in the difference between the layer temperature and

ambient temperature over a 100 degree rise in temperature.

Output

q£ w

Convective heat flux from the hot layer in a room to the adjacent part of the wall/ceiling.

[W/m2

] (V.ll)

Input

Tw Temperature of the surface of the wall and/or

ceiling (Calculated Value, see Conduction Heat

Transfer section). [K] (V.126)

3 - CNVW01 -
Temperature of the hot layer in a room

(Calculated Value, see Hot Layer section), [m]

(V. 127)

Ta Temperature of ambient air (Input Data) . [K]

(V . 120)

b Minimum heat transfer coefficient of hot layer

gases in the room (Input Data). [W/m2

] (V.66)

a Maximum heat transfer coefficient of hot layer

gases in the room (Input Data). [W/m2

] (V.62)

Calculations

h = min(a, [b+(a-b) [ (TL -Ta )/100] ] Inside heat transfer coefficient,

q^wo = h (Tl

- Tw ) Heat flux to inside wall surface.

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 48 -

49.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pg. 112.

Subroutine Variables

FQLWD = q£ w d ZKWZZ = Tw ZKLZZ = Tl ZKAZZ = Ta

3-CNVW01-2
ZOLZZ = b

ZOLZM = a

Prepared by

David W. Stroup

'

3-CNVW01-3
Computer Subroutine

SUBROUTINE CNVW01 ( ZOLZM , ZOLZN , ZKLZZ , ZKAZZ , ZKWZZ , FQLWD)

•k&-k-k'k‘kmk"k'k‘k'k'k'k'k'k'k’k'k'k'k$:-k'k’kmk'k'k‘k,k-k‘k'k‘k‘k‘k-k'k-k-k-k’k‘k,k'k,k‘k'k'k'k‘k'k'k,k'k'k'k‘k ,k-k-k'k-k'k'k'k~k'k-k~k

CALCULATES THE CONVECTIVE HEAT TRANSFER FROM THE ADJACENT HOT LAYER

TO ONE SIDE OF A WALL.

INPUT PARAMETERS:

ZOLZM -- MAXIMUM HEAT TRANSFER COEFFICIENT.

ZOLZN -- MINIMUM HEAT TRANSFER COEFFICIENT.

INPUT VARIABLES:

ZKLZZ -- TEMPERATURE OF THE HOT LAYER.

ZKAZZ -- TEMPERATURE OF AMBIENT AIR (LOWER, COOL LAYER).

ZKWZZ -- TEMPERATURE OF THE WALL ADJACENT TO THE HOT LAYER.

OUTPUT VARIABLE:

FQLWD -- CONVECTIVE HEAT FLUX TO THE HOT LAYER FROM THE

SURROUNDING WALLS.

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

C

c

C HEAT TRANSFER COEFFICIENT.

H - DMIN1 ( ZOLZM, ZOLZN + (ZOLZM -ZOLZN)* (ZKLZZ -ZKAZZ) /100 . DO)

C

C CALCULATE THE CONVECTIVE HEAT FLUX.

FQLWD = H * ( ZKLZZ - ZKWZZ ) C

RETURN

END

3-CNVW01-4
4. ALGORITHMS RELATED TO THE HOT LAYER

4-1
4-2

Figure

4-1.

General

diagram

of

a

room

fire
ABSRB2 - Absorption Coefficient 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 fraction (by mass) of smoke (particulates,

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

proportionality 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 fraction calculated in a standard run of

NBS/Harvard 5.

Output

k. Absorption coefficient of the hot layer in a

room, [m" 1

] (V. 2)

Input

Ys Mass fraction of soot (particulates, mainly C,

and condensed hydrocarbons) in the hot layer in

a room (Calculated Value, see Hot Layer

section), [grams of soot/grams of hot layer gas]

(V . 44)

4- ABSRB2 -
Calculation

k - 265 * Ys

References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.-,

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

Subroutine Variables

ZULZZ = k

ZYLSZ = Ys

Prepared by

David W. Stroup

4- ABSRB2 - 2
Computer Subroutine

SUBROUTINE ABSRB2 (ZYLSZ , ZULZZ)

Q'k'k'k'k'k-k-k'k-k'k-k-k'k'k'k'k'k-k-k-k'k-k'k'k-k‘k-k-k'k'k'k-k'k-k-k-k-k-k'k‘k'k'k c IMPLICIT DOUBLE PRECISION (A-H,0-Z)

C

C THIS SUBROUTINE CALCULATES THE INFRA-RED ABSORPTIVITY OF THE

C HOT LAYER. WE ASSUME THE ABSORPTION COEFFICIENT IS IN FACT GRAY/

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

C PROPORTIONALITY CONSTANT USED IN THE EQUATION BELOW WAS

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

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

C SMOKE FRACTION CALCULATION CALCULATED BY LAYR03 IN A

C STANDARD RUN OF HARVARD 5.0.

I C

C INPUT VARIABLES:

C ZYLSZ -- MASS FRACTION 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

C LIMITS:

C ZULZZ = DMAX1 (ZULZZ, 0.0005D0)

C

RETURN

END

i

4-ABSRB2 - 3
.

'

4-ABSRB2 -4
DXDCNC - Mass Fraction of Carbon Dioxide in Hot Layer

Description

This routine calculates the mass fraction of carbon dioxide in the hot

layer in a room. The mass fraction of carbon dioxide in the hot layer is

equal to the ratio of the mass of carbon dioxide in the hot layer to the total

mass of the hot layer. The initial mass fraction of carbon dioxide in the hot

layer is assumed to be the same as the fraction of carbon dioxide in ambient

air , i . e .

500 ppm.

Output

YC02 Mass fraction of carbon dioxide (C02

) in the hot

layer in a room. (V.41)

Input

mC02 Mass of carbon dioxide in the hot layer in the

room (Calculated Value, see Hot Layer section),

[kg] (V.49) mL Mass of the hot layer in a room (Calculated

Value, see Hot Layer section), [kg] (V.54)

Calculations

f 0 2 /mL » 0 2 — mL ^ mL ^

YC02 = Mass fraction of carbon dioxide.

[ 0.0005, otherwise

4- DXDCNC -1
References

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

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

ZYLDZ - YC02

ZMDL = mCQ2

ZMLZZ = mL

Prepared by

David W. Stroup

4-DXDCNC2
o

o

Computer Subroutine

SUBROUTINE DXDCNC ( ZMDL , ZMLZZ , ZYLDZ

C •k'kk-k-k'k-k'k'k-k-k-k-k-k-k-k-k-k-k-k-k-k-k'k-k'kk-k-k'k'k'k-k'k'kk-k-k-k-k-k-k-k-k-k-k-k-k-k'k-k-k-k-k'k-k’k-k'k c

C SUBROUTINE TO CALCULATE THE MASS FRACTION OF CARBON DIOXIDE

C IN THE HOT LAYER.

C

C INPUT VARIABLES:

C ZMDL -- MASS OF CARBON DIOXIDE IN THE HOT LAYER.

C ZMLZZ -- TOTAL MASS OF THE HOT LAYER.

C

C OUTPUT VARIABLE:

C ZYLDZ -- MASS FRACTION OF CARBON DIOXIDE IN THE

HOT LAYER.

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

1

PARAMETER (YC02 = 5.D-4)

C

IF ((ZMDL .GE. 0 . DO) .AND. (ZMLZZ .GT. 0.D0)) THEN

IF (ZMDL .LE. ZMLZZ) THEN

ZYLDZ = ZMDL / ZMLZZ

ELSE

ZYLDZ = YC02

END IF

ELSE

ZYLDZ = YC02

END IF

C

RETURN

END

4 -DXDCNC -3
.

'

4-DXDCNC-4
LAYDPT - Depth of the' Hot Layer in a Room

Description

This routine calculates the depth of the hot layer in a room containing

at least one burning object. The depth of the hot layer may be determined if

the internal energy of the layer and the pressure are known. The energy

contained in the upper, hot layer is a function of its mass, temperature, and

heat capacity (specific heat). In this routine, the heat capacity of the hot

layer is assumed to be the same as that of ambient air. Thus

The hot layer mass is equal to its volume multiplied by its density. Ignoring

the small change in molecular weight due to fuel (combusted and uncombusted)

I the layer density is

P "

and its mass is (assuming the room is a parallelpiped)

m = pLx LyhL

These three equations may be combined and solved for the depth of the hot

layer

hL - EL / (LxLyCpTa p a )

4-LAYDPT-l
This is the equation used to 'determine the depth of the hot layer.

Output

hL Depth of the hot layer in a room, [m] (V.20)

Input

Ta

A

EL

Specific heat of ambient air (Input Data)

.

[J/kg-K] (V.112)

Density of ambient air (Input Data) . [kg/m3

] (V.17)

Height of the room (Input Data), [m] (V.33)

Ambient temperature in the room (Input Data).

[K] (V.120)

Dimension of the room in the x-direction (Input

Data), [m] (V.21)

Dimension of the room in the y-direction (Input

Data), [m] (V. 22)

Energy contained in the hot layer in the room

(Calculated Value, see Hot Layer section). [J]

(V.25)

Calculation

hL - EL / (Lx L, c

p Ta p a )

4-LAYDPT-2
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

18.

2. Mitler, H.E., and Emmons, H.W.

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981.

Subroutine Variables

ZHLZZ - hL CP = c

P VMAZZ = p a ZHRZZ = hR ZKAZZ - Ta ZLRZX = Lx ZLRZY = Ly

ZELZZ = El

Prepared by

David W. Stroup

4-LAYDPTComputer Subroutine

SUBROUTINE LAYDPT ( CP , VMAZZ , ZHRZZ , ZKAZZ , ZLRZX , ZLRZY , ZELZZ , ZHLZZ

)

k'k’k’k'k'kk'k'k-k'k'krk'k'k-k-Jrk'Jckrk-k-k'k'k'k-k'k'k'k'k-k-k'k-k'kirk'k’k'k-k'k’kirk-k-k-k'k'krk-kic^ckk'kk-kk'k-k’k'kk-kkk

SUBROUTINE TO CALCULATE THE DEPTH OF THE LAYER IN A ROOM.

INPUT PARAMETERS:

CP -- SPECIFIC HEAT OF AMBIENT AIR.

VMAZZ -- DENSITY OF AMBIENT AIR.

ZHRZZ -- HEIGHT OF THE ROOM.

ZKAZZ -- AMBIENT TEMPERATURE IN THE ROOM.

ZLRZX -- LENGTH OF THE ROOM ALONG THE X-AXIS.

ZLRZY -- LENGTH OF THE ROOM ALONG THE Y-AXIS.

INPUT VARIABLES:

ZELZZ -- TOTAL ENERGY OF THE LAYER.

OUTPUT VARIABLE:

ZHLZZ -- DEPTH OF THE LAYER.

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

ZHLZZ = ZELZZ / (ZLRZX * ZLRZY * CP * ZKAZZ * VMAZZ)

IF (ZHLZZ .GT. ZHRZZ) ZHLZZ = ZHRZZ

RETURN

END

4 -LAYDPT -4
MNXCNC - Mass Fraction of Carbon Monoxide in Hot Layer

Description

This routine calculates the mass fraction of carbon monoxide in the hot

layer in a room. The mass fraction of carbon monoxide in the hot layer is

equal to the ratio of the mass of carbon monoxide in the hot layer to the

total mass of the hot layer. The mass fraction of carbon monoxide in the hot

layer at the start of the fire is assumed to be zero.

Output

Yco Mass fraction of carbon monoxide (CO) in the hot

layer in the room. (V.40)

Input

n^Q Mass of carbon monoxide in the hot layer in the

room (Calculated Value, see Hot Layer section),

[kg] (V . 49

mL Mass of the hot layer in the room (Calculated

Value, see Hot Layer section), [kg] (V.54)

Calculations

co

^

0

/

mL »

> 0 . 0 ,

mCQ < mL & mL /0

otherwise

Mass fraction of carbon monoxide.

4- MNXCNC -1
References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

ZYLMZ = Yco ZMML = ZMLZZ = mL

Prepared bv

David W. Stroup

4-MNXCNC-2
Computer Subroutine

SUBROUTINE MNXCNC ( ZMML , ZMLZZ , ZYLMZ

k-k-kkk'kmk-kmk-kk'k'k'k'k'k-k'k'k'kkk-k'k'k-k'k'kk'k'k'kkkk'k'k'k'k'k'k'k'kk'kk~k~k'k-k-k'k'k'kk'k‘k-k-kk'k'kk'k'k

SUBROUTINE TO CALCULATE THE MASS FRACTION OF CARBON MONOXIDE

IN THE HOT LAYER.

INPUT VARIABLES:

ZMML -- MASS OF CARBON MONOXIDE IN THE HOT LAYER.

ZMLZZ -- TOTAL MASS OF THE HOT LAYER.

OUTPUT VARIABLE:

ZYLMZ -- MASS FRACTION OF CARBON MONOXIDE IN THE

HOT LAYER.

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

PARAMETER (YCO = 0.D0)

IF ((ZMML .GE. 0 . DO) .AND. (ZMLZZ . GT . 0.D0)) THEN

IF (ZMML .LE. ZMLZZ) THEN

ZYLMZ = ZMML / ZMLZZ

ELSE

ZYLMZ = YCO

ENDIF

ELSE

ZYLMZ = YCO

END IF

RETURN

END

4 -MNXCNC -3
.
OXYCNC - Mass Fraction of Oxygen in Hot Layer

Description

This routine calculates the mass fraction of oxygen in the hot layer in

a room. The mass fraction of oxygen in the hot layer is equal to the ratio of

the mass of oxygen in the hot layer to the total mass of the hot layer. The

initial mass fraction of oxygen in the hot layer is assumed to be the same as

the fraction of oxygen in ambient air (0.2318).

Output

Y,02 Mass fraction of oxygen (02

) in the hot layer in

the room. (V.43)

Input

H^O 2 Mass of oxygen in the hot layer in the room

(Calculated Value, see Hot Layer section), [kg]

(V.52)

Mass of the hot layer in the room (Calculated

Value, see Hot Layer section), [kg] (V.54)

Calculations

mo 2 /mL , < mL & mL ^0

0.2318, otherwise

Mass fraction of oxygen.

4- OXYCNC -1
References

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

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

ZYLOZ = Y02

ZMOL = 11^2 ZMLZZ = mL

Prepared bv

David W. Stroup

4-0XYCNC-2
o

o

Computer Subroutine

SUBROUTINE OXYCNC (ZMOL, ZMLZZ , ZYLOZ)

C

Q kkkkkkkkkk'kk'k'k'k'k'k'k'kk'k'kk'kkk'k'k'k'k'k'k'k'kkk'k'k'k'kkkkk'k'k'kk'k'k'k-k'k-k'kk'krkk'k'k-k-k-k-k'k-k-k'k c

C SUBROUTINE TO CALCULATE THE MASS FRACTION OF OXYGEN IN THE

C HOT LAYER.

C

C INPUT VARIABLES:

C ZMOL -- MASS OF OXYGEN THE HOT LAYER.

C ZMLZZ -- TOTAL MASS OF THE HOT LAYER.

C

OUTPUT VARIABLE:

ZYLOZ -- MASS FRACTION OF OXYGEN IN THE HOT LAYER.

C

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

C

PARAMETER (Y02 = .2318D0)

C

IF ((ZMOL .GE. 0 . DO) .AND. (ZMLZZ .GT. 0.D0)) THEN

IF (ZMOL .LE. ZMLZZ) THEN

ZYLOZ = ZMOL / ZMLZZ

ELSE

ZYLOZ = Y02

ENDIF

ELSE

ZYLOZ = 0.D0

ENDIF

C

RETURN

END

4 -OXYCNC -3
,v ..

.
POWL - Rate of Change of the Energy in the Hot Layer

Description

The routine calculates the rate of change of the energy contained in the

hot layer. The rate of change of the energy in the layer in a room is a function of the rate of convective heat transfer to the hot layer from the

walls in the room, rate of radiative heat transfer to the layer from all

sources, the total convective energy output of the plumes in the room, and the

total convective outflow through the vents in the room from the layer.

Output

E. Total rate of change of internal energy of the

hot layer in the room. [W] (V.68)

Input

Er

D Rate of increase of energy of the hot layer by

convection from the walls in the room --

generally negative (Calculated Value, see Convection Heat Transfer section). [W] (V.89)

Et r Rate of change of energy in the hot layer by

radiation from all hot sources in the room

(Calculated Value, see Radiation Heat Transfer

section). [ W ] (V.86)

2 E

p (Sum of the) convective enthalpy flows out the

top of the plumes in the room into the hot layer

(Calculated Value, see Plume section). [W] (V. 9)

4- POWL2 Ev (Sum of the) convective enthalpy outflow from

the hot layer through the vents in the room

(Calculated Value, see Vent section). [W] (V.10)

Calculation

= ^ D + ^LR

References

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

Harvard University, Home Fire Project Technical Report No. 34, pg. 17.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 128 - 131.

Subroutine Variables

TELZZ = El TELZD = Eld

TELZR = Q

TEPSM =ZEp TEUSM = 2 Ev

Prepared bv

David W. Stroup

4-P0WL-2
Computer Subroutine

SUBROUTINE POWL (TELZD , TELZR, TEPSM, TEUSM, TELZZ)

C

C

C

C

C

C

C

C

C

c

c

c

cc

c

c

c

c

c

k'k-k'k'k'k^rk-k-k^rk-k-k'k-k-k-k-k'k'k-k-k'k'k-k'k'k-k^rk'k-k'k-k-k-k'k-k'k'k'k'k'k'k-k-k-k-k-k'k'k'k'k-k-k'k'k-k'k'k 'k'k-k'k-k-k~kk

SUBROUTINE TO CALCULATE THE RATE OF CHANGE OF THE ENERGY OF THE HOT

LAYER.

INPUT VARIABLES:

TELZD -- RATE OF CONVECTIVE HEAT TRANSFER TO THE HOT LAYER

FROM THE WALLS IN THE SAME ROOM.

TELZR -- RATE OF RADIATIVE HEAT TRANSFER TO THE HOT LAYER

FROM ALL HOT SOURCES IN THE SAME ROOM.

TEPSM -- TOTAL CONVECTIVE ENERGY OUTPUT OF THE PLUMES IN

THE ROOM.

TEUSM -- TOTAL CONVECTIVE ENERGY OUTFLOW THROUGH THE VENTS

IN THE ROOM FROM THE HOT LAYER.

OUTPUT VARIABLE:

TELZZ -- RATE OF INCREASE OF ENERGY OF THE LAYER.

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

C

TELZZ = TEPSM - TEUSM + TELZD + TELZR

C

RETURN

END

4 -POWL’

’

4-P0WL-4
SUTCNC - Mass Fraction of Soot in Hot Layer

Description

This routine calculates the mass fraction of soot in the hot layer in a

room. The mass fraction of soot in the hot layer is equal to the ratio of the

mass of soot in the hot layer to the total mass of the hot layer. The mass

fraction of soot in the hot layer at the start of the fire is assumed to be

zero.

Output

Ys Mass fraction of soot in the hot layer in the

room. (V.44)

Input ms Mass of soot in the hot layer in the room

(Calculated Value, see Hot Layer section), [kg]

(V . 53

mL Mass of the hot layer in the room (Calculated

Value, see Hot Layer section), [kg] (V.54)

Calculations

f ms/mL , ms < mL & mL ^0

Ys = 4 Mass fraction of soot.

[ 0.0, otherwise

4- SUTCNC -1
References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS-GCR-81-344 , October 1981, pp . 128 - 131.

Subroutine Variables

ZYLSZ = Ys ZMSL - ms ZMLZZ = mL

Prepared by

David W. Stroup

4- SUTCNC2
Computer Subroutine

SUBROUTINE SUTCNC (ZMSL, ZMLZZ , ZYLSZ)

C

c

C SUBROUTINE TO CALCULATE THE MASS FRACTION OF SOOT IN THE

C HOT LAYER.

C

C INPUT VARIABLES:

C ZMSL -- MASS OF SOOT IN THE HOT LAYER.

C ZMLZZ -- TOTAL MASS OF THE HOT LAYER.

C

C OUTPUT VARIABLE:

C ZYLSZ -- MASS FRACTION OF SOOT IN THE HOT LAYER.

C

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

C

PARAMETER (YS = 0.D0)

C

IF ((ZMSL .GE. 0 . DO) .AND. (ZMLZZ .GT. 0.D0)) THEN

IF (ZMSL .LE. ZMLZZ) THEN

ZYLSZ = ZMSL / ZMLZZ

ELSE

ZYLSZ = YS

ENDIF

ELSE

ZYLSZ = 0.D0

END IF

RETURN

END

4 -SUTCNC -3
. -

.
TC02M - Rate of Change of Mass of Carbon Dioxide in the Hot Layer

Description

This routine calculates the rate of increase of carbon dioxide in the

hot layer. The upper layer gains carbon dioxide from entrainment of ambient

air into the plume and from production by burning objects. The layer loses

carbon dioxide through flow of gases out the vents in the roonj. A mass

balance relating the rates of gain and loss of carbon dioxide in the layer

provides the equation necessary for this algorithm.

Output

Rate of increase of mass of carbon dioxide in

the hot layer, [kg/s] (V.90)

Input

(Sum of the) mass rates of evolution of carbon

dioxide from all objects (Calculated Value, see Burning Object section), [kg/s] (V. 56)

2 m.f (Sum of the) (negative of the) mass pyrolysis

rates of all objects in the room (Calculated

Value, see Burning Object section), [kg/s]

(V.61)

2 m,p (Sum of the) rate(s) at which the plume (s) above

burning objects in the room add mass to the hot

layer (Calculated Value, see Hot Layer section).

[kg/s] (V . 97)

4-TC02M2 m^Q 2 Rate at which carbon dioxide flows out through

all the vents in the rooms (Calculated Value,

see Vents section), [kg/s] (V.98)

Calculation

TMc 02 = 0.0005 (2 ^ + mf

) + 2 ^51“ - 2

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16 -

17.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS -GCR- 81 - 344 , October 1981, pp 128 - 131.

Subroutine Variables

TMDL = 1^02

TM0DS = 2

TM0SM - 2 mf TMPSM = 2 m

p TMDZF = 2

Prepared bv

David W. Stroup

4-TC02M2
Computer Subroutine

SUBROUTINE TC02M (TMODS , TMOSM, TMPSM, TMDZF, TMDL)

k-k-k-k'k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k-k’k-k^^rk'k-k-k-k-k-k-k-k'k-k-k-k-k-k-k'k-k-k-k-k-k-k-k-kick'k'k-kirk-kk'k'k-k-k-kkk-k

SUBROUTINE TO CALCULATE THE RATE OF CHANGE OF MASS OF CARBON

DIOXIDE IN THE HOT LAYER.

INPUT PARAMETERS:

YC02 -- MASS FRACTION OF CARBON DIOXIDE IN AMBIENT AIR.

INPUT VARIABLES:

TMODS -- RATE AT WHICH THE OBJECTS IN A ROOM PRODUCE

CARBON DIOXIDE.

TMOSM -- NEGATIVE OF THE SUM OF THE MASS PYROLYSIS RATES

OF ALL OBJECTS IN THE ROOM.

TMPSM -- RATE AT WHICH THE PLUMES OVER ALL THE OBJECTS IN

THE ROOM ADD MASS TO THE HOT LAYER.

TMDZF -- RATE AT WHICH CARBON DIOXIDE FLOWS OUT OF THE ROOM

THROUGH ALL THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMDL -- RATE OF INCREASE OF MASS OF CARBON DIOXIDE

IN THE LAYER.

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

PARAMETER (YC02 = 5.D-4)

C

TMDL = YC02 * (TMPSM + TMOSM) + TMODS -TMDZF

C

RETURN

END

4-TC02M1
TH20M - Rate of Increase of Mass of Water Vapor in the Hot Layer

Description

This routine calculates the rate of increase of water vapor in the hot

layer. The upper layer gains water vapor from the burning of hydrogencontaining fuels, hydrocarbons in particular. The layer loses water vapor

through the flow of hot gases out the vents in the room. A mass balance

including the rates of gain and loss of water vapor in the layer yields the

rate of change.

Output

Rate of increase of mass of water vapor in the

hot layer, [kg/s] (V.95)

Input

(Sum of the) mass rates of evolution of water

vapor from all objects (Calculated Value, see Burning Object section), [kg/s] (V.59)

(Sum of the) rates at which water vapor flows

out through all vents in the room (Calculated

Value, see Vents section), [kg/s] (V.102)

4-TH20MCalculation

m = y Iprod _ y 'vent

H 2 0 ^ mH2 0 ^ mH2 0

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16

17.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp 128 - 131.

Subroutine Variables

TMWL = mH 2 o TMOWS = 2 m]?!2 d TMWZF = 2 m^ ® o

Prepared bv

David W. Stroup

4-TH20M-2
o

o

Computer Subroutine

SUBROUTINE TH20M (TMOWS , TMWZF , TMWL)

•kick'k'kkk'k'kk'k-k'kk'k'k'k'k'kk'kk-k'kick'k'kkk'k’k’k'k'k'kk'k'k'k-k'kk'kk’k'k'k'kick'kk'kk'k'k-k'kkickkkkk'k-k

SUBROUTINE TO CALCULATE THE RATE OF INCREASE OF MASS OF WATER VAPOR

IN THE HOT LAYER.

INPUT VARIABLES

TMOWS

TMWZF

TOTAL RATE AT WHICH OBJECTS IN THE ROOM PRODUCE

WATER VAPOR.

RATE OF MASS OUTFLOW OF WATER VAPOR THROUGH ALL

THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMWL -- RATE OF INCREASE OF MASS OF WATER VAPOR IN THE

C HOT LAYER

C

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

C

TMWL = TMOWS - TMWZF

C

RETURN

END

4-TH20M" J -
TMNXM - Rate of Change of Mass of Carbon Monoxide in the Hot Layer

Description

This routine calculates the rate of increase of carbon monoxide in the

hot layer. The upper layer gains carbon monoxide from production by burning

objects. The layer loses carbon monoxide through the flow of hot gases out

the vents in the room. The rate of change is found from a mass balance.

Output

Rate of increase of mass of carbon monoxide in

the hot layer, [kg/s] (V.91)

Input

(Sum of the) mass rates of evolution of carbon

monoxide from all objects (Calculated Value, se Burning Object section), [kg/s] (V.57)

(Sum of the) rates at which carbon monoxide

flows out through all vents in the room

(Calculated Value, see Vents section), [kg/s]

(V. 99)

4 - TMNXMCalculation

tt» = y ‘prod _ y'vent

“co 24 “co 24 “co

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16

17.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp 128 - 131.

Subroutine Variables

TMML = mco TMOMS = Z mP£ od

TMMZF = Z m£® nt

Prepared by

David W. Stroup

4-TMNXM2
Computer Subroutine

SUBROUTINE TMNXM (TMOMS , TMMZF , TMML)

•k-kie'k'Jt'/c^c'krk'k-k'k’k-k'Jrk^e'kic-Jrk-k-k-k-k'k'kic'k'k-k'k-k-k-k-kirkick-k-kicJrk-Jrk-Jrk'k'k’k'kieifk********5!: -jrkii'k

SUBROUTINE TO CALCULATE THE RATE OF INCREASE OF MASS OF CARBON

MONOXIDE IN THE HOT LAYER.

INPUT VARIABLES:

TMOMS -- TOTAL RATE AT WHICH OBJECTS IN THE ROOM PRODUCE

CARBON MONOXIDE.

TMMZF -- RATE OF MASS OUTFLOW OF CARBON MONOXIDE THROUGH ALL

THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMML -- RATE OF INCREASE OF MASS OF CARBON MONOXIDE IN THE

HOT LAYER.

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

TMML = TMOMS - TMMZF

- RETURN

END

4 -TMNXMTMPL - Temperature of the Hot Layer

Description

This routine calculates the temperature of the hot upper layer in a room

with a fire. The energy contained in the upper layer at any given time is a function of the layer mass, the layer temperature, and the specific heat (or

heat capacity) . If the layer mass and energy content are known, the layer

temperature may be calculated. The layer specific heat is assumed to be the

same as that of ambient air at 25° C.

Output

Tl Temperature of the hot layer in the room. [K]

(V. 127)

Temperature of ambient air (Input Data) . [K]

(V . 120)

Specific heat of ambient air (Input Data)

[J/kg-K] (V.112)

Energy contained in the hot layer in the room

(Calculated Value, see Hot Layer section). [J]

(V.25)

Mass of the hot layer in the room (Calculated

Value, see Hot Layer section), [kg] (V.54)

Input

Ta

El

mL

4-TMPL-l
Calculation

/ ( C

p mL ) ’

v »

mL t 0

mL = 0

References

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

Harvard University, Home Fire Project Technical Report No. 34, pg. 18.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp 128 - 131.

Subroutine Variables

ZKLZZ = Tl ZKAZZ = Ta CP = c

p ZELZZ = El ZMLZZ = mL

Prepared bv

David W. Stroup

4-TMPL-2
Computer Subroutine

SUBROUTINE TMPL (ZKAZZ , CP , ZELZZ , ZMLZZ , ZKLZZ)

C

Q

it-k-k-k'k'k'k-k'k-k-k-k-k’k-k'k'k'k'k'k'k'k’k-k'k'k-k'k'k'k'k'k'k'k'k'k'k'k'k'k-k-k-k'k-k-k'k-k-k'k-k-k-k'k'k-k'k-k-k-k-k-k'k-k-k'k-k-k-k c

C SUBROUTINE TO CALCULATE THE TEMPERATURE OF THE HOT LAYER IN A ROOM.

C

C INPUT PARAMETERS:

C ZKAZZ -- AMBIENT TEMPERATURE IN THE ROOM.

C CP -- SPECIFIC HEAT OF AIR.

C

C INPUT VARIABLES:

C ZELZZ -- ENERGY CONTAINED IN THE LAYER.

C ZMLZZ -- MASS OF THE LAYER.

C

C OUTPUT VARIABLE:

C ZKLZZ -- TEMPERATURE OF THE LAYER.

C

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

C

IF (ZMLZZ .EQ. 0 . DO) THEN

ZKLZZ = ZKAZZ

ELSE

ZKLZZ = ZELZZ / ( CP * ZMLZZ ) END IF

C

RETURN

END

4 -TMPL.
TMSL - Rate of Change of Mass of the Hot Layer

Description

This routine calculates the rate of change of the mass of the hot layer.

The upper layer gains mass from the plumes above the burning objects in a room

while losing mass through flow of hot gases out vents in the room. A mass

balance relating the gain and loss of mass in the layer to the rate of change

provides the equation necessary for this algorithm.

Output

mT Rate of increase of mass of the hot layer in the

room, [kg/s] (V.93)

(Sum of the) rates at which the plumes over the

objects in the room add mass to the hot layer

(Calculated Value, see Plume section), [kg/s]

(V. 97)

(Sum of the) rates of mass outflow from the hot

layer through all the vents in the room

(Calculated Value, see Vent section), [kg/s]

(V. 106)

Input

2 m_

2

4-TMSL-l
Calculation

mT = 2 %

" 2 nv

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16

17. .

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS -GCR- 81 - 344 , October 1981, pp 128 - 131.

Subroutine Variables

TMLZZ = mL TMPSM =2 m

p TMUSM = 2 ii^

Prepared bv

David W. Stroup

4-TMSL-2
Computer Subroutine

C

C

C

C

C

C

C

C

C

C

C

C

C

C

C

SUBROUTINE TMSL (TMPSM, TMUSM, TMLZZ)

kkk-k-k-k-k-k^^-k^-k-k-kitit'k-k-k-k-k-k-kkkk-k-k-k-k-kk'k-k-k'k^-k-k-k-k'k-k-k-k-k-k-k-k-k-k-k-k'k-k'k-k-k-k-k-kk-k-k-k-k-k-k

SUBROUTINE TO CALCULATE THE RATE OF CHANGE OF MASS OF THE HOT LAYER.

INPUT VARIABLES:

TMPSM -- TOTAL MASS OUTFLOW FROM THE PLUMES IN THE ROOM

INTO THE HOT LAYER.

TMUSM -- TOTAL MASS OUTFLOW FROM THE HOT LAYER THROUGH ALL

THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMLZZ -- RATE OF CHANGE OF MASS OF THE LAYER.

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

TMLZZ = TMPSM - TMUSM

RETURN

END

4-TMSL*

4-TMSL-4
TOXYM - Rate of Change of Mass of Oxygen in the Hot Layer

Description

This routine calculates the rate of increase of oxygen in the hot layer.

The upper layer gains oxygen from entrainment of ambient air into the plume,

which then "delivers whatever oxygen remains after combustion, to the hot

layer. The layer loses oxygen through flow of hot gases out the vents of the

room. The rate of change is found via a mass balance.

Output

mL0 2

Input

2 m£| e (Sum of the) rates at which the objects in the

room burn oxygen (Calculated Value, see Hot

Layer section), [kg/s] (V.103)

2 mf (Sum of the) (negative of the) mass pyrolysis

rates of all objects in the room (Calculated

Value, see Burning Object section), [kg/s]

(V.61)

2 nip (Sum of the) rates at which the plumes over all

objects in the room add mass to the hot layer

(Calculated Value, see Hot Layer section).

[kg/s] (V. 97)

Rate of increase of mass of oxygen in the hot

layer, [kg/s] (V.94)

4-TOXYM(Sum of the) rates at which oxygen flows out

through all the vents in the rooms (Calculated

Value, see Vents section), [kg/s] (V.100)

2 mg- t

Calculation

mL02 = 0.2318(2 m

p + 2 mf

)

- 2 mg- - 2 iigf

nt

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16 -

17.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp 128 - 131.

Subroutine Variables

TMOL = mLQ2

BOXYS = 2 mg —

TMOSM = 2 mf TMPSM = 2 m

p TMOZF - 2 mgj nt

Prepared bv

David W. Stroup

4-TOXYM2
oo

Computer Subroutine

SUBROUTINE TOXYM (BOXYS , TMOSM , TMPSM , TMOZF , TMOL)

•k'kk'k-k’kk-kk-k-k'k-k-k-k-k-k'k'k'k'k'k-k'k'k-k-k-kk-k'k'k'k’k'k'k-k-k-k-kick-k'k'k-k'k-k-k-k-k'kk-k-k-k'k-k'k-k'k-k-k-k'k-k'k'k-k

SUBROUTINE TO CALCULATE THE RATE OF CHANGE OF MASS OF OXYGEN IN

THE HOT LAYER.

INPUT PARAMETERS:

Y02 -- MASS FRACTION OF OXYGEN IN THE AMBIENT AIR.

INPUT VARIABLES:

BOXYS -- RATE AT WHICH ALL OBJECTS IN THE ROOM BURN OXYGEN.

TMOSM -- NEGATIVE OF THE SUM OF THE MASS PYROLYSIS RATES

OF ALL OBJECTS IN THE ROOM.

TMPSM -- RATE AT WHICH THE PLUMES OVER ALL THE OBJECTS IN

THE ROOM ADD MASS TO THE HOT LAYER.

TMOZF -- MASS RATE OF OUTFLOW OF OXYGEN FROM THE HOT LAYER

THROUGH ALL THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMOL -- RATE OF INCREASE OF MASS OF OXYGEN IN THE LAYER.

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

PARAMETER (Y02 = .2318D0)

TMOL = Y02 * (TMPSM +' TMOSM) - BOXYS -TMOZF

RETURN

END

4 -TOXYM.

_
TSUTM - Rate of Change of Mass of Soot in the Hot Layer

Description

This routine calculates the rate of increase of soot in the hot layer.

The upper layer gains soot from production by burning objects. The layer

loses soot through flow of hot gases out the vents in the room. " The rate of

change is found via a mass balance.

Output

H^OOT Rate of increase of mass of soot in the hot

layer, [kg/s] (V.92)

Input

2 m? r 0 d ^ mS 0 0 T

y mvent

S 0 0 T

Calculation

(Sum of the) mass rates of evolution of soot

from all Objects (Calculated Value, see Burning

Object section), [kg/s] (V.58)

(Sum of the) rates at which soot flows out

through all the vents in the room (Calculated

Value, see Vent section), [kg/s] (V.101)

HIS 0 0 T ^ SOOT r\ r\ t y 'vent ^ ulS 0 0 T

4-TSUTMReferences

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 16

17.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp 128 - 131.

Subroutine Variables

TMSL = niS00T

TMOSS = 2

TMSZF = 2 m

Prepared bv

David W. Stroup

4-TSUTM2
Computer Subroutine

SUBROUTINE TSUTM (TMOSS , TMSZF , TMSL)

kkick-kickk'k-kk'k'kk'k'k'kk'k-k'k'k-kk-klck-k'k'k'k-k-k-kkick'k-k-kk'k'k'k'k'k'k-k'k'k'k'k'k-k'k'kk-klrk-k'k'k-k-k'k'k'k-k

SUBROUTINE TO CALCULATE THE RATE OF CHANGE OF MASS OF SOOT IN THE

HOT LAYER.

INPUT VARIABLES:

TMOSS -- TOTAL RATE AT WHICH ALL OBJECTS IN THE ROOM

PRODUCE SOOT.

TMSZF -- MASS RATE OF OUTFLOW OF SOOT FROM THE HOT LAYER

THROUGH ALL THE VENTS IN THE ROOM.

OUTPUT VARIABLE:

TMSL -- PATE OF INCREASE OF MASS OF SOOT IN THE LAYER.

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

TMSL = TMOSS - TMSZF

RETURN

END

4- TSUTM4-TSUTM-4
WTRCNC - Mass Fraction of Water Vapor in Hot Layer

Description

This routine calculates the mass fraction of water vapor in the hot

layer in a room. The mass fraction of water vapor in the hot layer is equal

to the ratio of the mass of water vapor in the hot layer to the total mass of

the hot layer. The mass fraction of water vapor in the hot layer at the start

of the fire is assumed to be zero.

Output

Mass fraction of water vapor in the hot layer in

the room. (V.42)

Input

Mass of water vapor in the hot layer in the room

(Calculated Value, see Hot Layer section), [kg]

(V.51)

Mass of the hot layer in the room (Calculated

Value, see Hot Layer section), [kg] (V.54)

CalculationsmH2o/mL » mH 2 0 — mL ^ mL 7^

0.0, otherwise

Mass fraction of water vapor.

4- WTRCNC -1
References

1. Mitler, H.E. and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Fire Code," U.S. Department of Commerce, Washington, D.C.,

NBS -GCR- 81- 344 , October 1981, pp . 128 - 131.

Subroutine Variables

ZYLWZ = YH20

ZMWL = mH 2 o ZMLZZ = mL

Prepared by

David W. Stroup

4-WTRCNC-2
oo

Computer Subroutine

SUBROUTINE WTRCNC (ZMWL, ZMLZZ , ZYLWZ)

C

Q •kk-kk'kk-k'k-k'kkk'k'k'k'k'k'k'k'k'k'k'k-k-k'k'k'k'k'kk'k-k-k'k'k'k'k-k'k'kk'k'k'k-k'k'k-k'k'k-k'k'k'k-k-k'k'k'k'k'k'k-k-k-k'k'k'k c

C SUBROUTINE TO CALCULATE THE MASS FRACTION OF WATER VAPOR

C IN THE HOT LAYER.

C

C INPUT VARIABLES:

C ZMWL. -- MASS OF WATER VAPOR IN THE HOT LAYER.

C ZMLZZ -- TOTAL MASS OF THE HOT LAYER.

C

OUTPUT VARIABLE:

ZYLWZ -- MASS FRACTION OF WATER VAPOR IN THE

C HOT LAYER.

C

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

C

PARAMETER (YW = 0.D0)

C

IF ((ZMWL .GE. 0 . DO) .AND. (ZMLZZ .GT. 0.D0)) THEN

IF (ZMWL .LE. ZMLZZ) THEN

ZYLWZ = ZMWL / ZMLZZ

ELSE

ZYLWZ = YW

END IF

ELSE

ZYLWZ = 0.D0

ENDIF

C

RETURN

END

4 -WTRCNC -3

5. ALGORITHMS RELATED TO THE PLUME

5-1
5-2

Figure

5-1.

General

diagram

of

a

room

fire
OXYBRN - Mass Rate of Oxygen Burning in the Plume of an Object

Description

This routine calculates the mass rate of oxygen burning in the plume of

an object. The rate of oxygen consumption by a burning object is a function

of the mass rate of burning the object and the amount of oxygen required for

combustion. The stoichiometric air/fuel ratio is a measure of the amount of

oxygen required for combustion of a certain fuel item. This value can be

determined for each fuel item from numerous texts on the chemical reaction of

materials. The mass burning rate is calculated by other routines in this

catalog

.

Output

mQ2 Mass rate of oxygen burning in the plume of an

object, [kg/s] (V. 60)

Input

Yq 2 Mass concentration of oxygen in ambient air

| (Input Data). (V.43)

7S Stoichiometric air/fuel mass ratio for the

object (Input Data). (V.116) mb Mass rate of burning of the fuel from the object

(Calculated Value, see Burning Object section),

[kg/s] (V. 55)

5- OXYBRN -1
Calculation

^2 ^02 Is mb

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 59

67.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS -GCR- 81 - 344 , October 1981, pp . 83 - 91.

Subroutine Variables

BOXY = m02

XGAMAS = 7 s Y02 = Yq 2 TMOZB = mb

Prepared bv

David W. Stroup

5 - OXYBRN - 2
Computer Subroutine

SUBROUTINE OXYBRN (XGAMAS , TMOZB , BOXY)

-klck'k-Jrk'k•k-k'k-frk-klrk-k'k-Jc'k'k

SUBROUTINE TO CALCULATE THE MASS RATE OF OXYGEN BURNING IN THE

PLUME OF AN OBJECT.

INPUT PARAMETERS:

XGAMAS -- STOICHIOMETRIC AIR/FUEL MASS RATIO FOR THE OBJECT

Y02 -- MASS CONCENTRATION OF OXYGEN IN AMBIENT AIR.

INPUT VARIABLES:

TMOZB -- MASS RATE OF BURNING OF FUEL FROM THE OBJECT.

OUTPUT VARIABLE:

BOXY -- MASS RATE OF OXYGEN BURNING IN THE PLUME OF THE

OBJECT.

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

PARAMETER (Y02 = .2318D0)

BOXY = Y02 * XGAMAS * TMOZB

RETURN

END

3 - OXYBRN3
'

.

.

5 - OXYBRN -

4
PLMHT - Height of the Plume over an Object

Description

This routine calculates the height of the plume above a burning object.

Specifically, the height calculated is the length of the plume as measured

from the top of the object to the bottom of the hot layer. The height of the

plume may be determined from the room height, the object height, and the smoke

layer depth. The height of the object and the height of the room above floor

level are input values. The depth of the hot layer is a calculated value.

Output

Input

h°

hr hL

Calculation

h_ = h - h - hT p r o L

References

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

Height of the plume over an object, [m] (V. 37)

Height of the surface of an object above the

floor (Input Data), [m] (V.38)

Height of the room (Input Data), [m] (V.33)

Depth of the hot layer in the room (Calculated

Value, see Hot Layer section), [m] (V.20)

5- PLMHT1
Harvard University, Home Fire Project Technical Report No. 34, pp . 10

13.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 136 - 137.

Subroutine Variables

ZHPZZ - h

p ZHOZZ = ho ZHRZZ = hr ZHLZZ = hL

Prepared by

David W. Stroup

5-PLMHT-2
Computer Subroutine

SUBROUTINE PLMHT (ZHOZZ , ZHRZZ , ZHLZZ , ZHPZZ)

C

Q

'k-k'k-k'k-kk-k-kk-k-k-k-k'k-k-k'k-k-k-k-k-k-k'k-kirk-k-k-k-k-k-k-k-k-k-k-k-k'k-k-k'k-k-k-k'k-k-k'k-k'k-kk'k-k-k-k-k-k-k-k'k-k'k-k'k'k c

C SUBROUTINE TO CALCULATE THE HEIGHT OF THE PLUME OVER AN OBJECT.

C

C INPUT PARAMETERS:

C . ZHOZZ -- HEIGHT OF THE OBJECT.

C ZHRZZ -- HEIGHT OF THE ROOM CONTAINING THE OBJECT.

C

C INPUT VARIABLES:

C ZHLZZ -- DEPTH OF THE HOT LAYER IN THE ROOM CONTAINING THE

C OBJECT.

C

C OUTPUT VARIABLE:

C ZHPZZ -- HEIGHT OF THE PLUME OVER THE OBJECT.

C

ZHPZZ = ZHRZZ - ZHOZZ - ZHLZZ

c RETURN

END

5 -PLMHT3
.

5-PLMHT-4
TENPLM - Rate of Addition of Energy to the Hot Layer from the Plume

Description

This routine calculates the rate at which the plume over an object adds

energy to the hot layer. The rate at which energy is convected into the hot

layer is determined from a plume energy balance. The object's flame is

included as part of the plume. When an object burns, it produces energy at a

rate Ef

. Some of this energy is lost by radiation from the flame, EpR . Another portion of the energy produced by the burning object is used to

maintain the object at pyrolysis temperature. Any energy left over from the

combustion of the object plus the energy in the air entrained into the plume

is carried into the hot layer.

Output

E Rate at which the plume over a burning object

adds energy to the hot layer. [W] (V.96)

Input

Ta Ambient temperature in the room containing the

plume (Input Data). [K] (V.120)

T

p Temperature at which an object begins to

pyrolyze (Input Data). [K] (V.119)

cD Specific heat of ambient air (Input Data)

.

[J/kg-K] (V.112)

Ef (Negative of the) rate of chemical energy

5- TENPLM -1
released from a burning object (Calculated

Value, see Burning Object section). [W] (V.88)

EpR Heat loss rate from the flame of the object

(Calculated Value, see Radiation Heat Transfer

section). [W] (V.29)

mf (Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

m

p Rate at which the plume over an object adds mass

to the hot layer (Calculated Value, see Plume

section), [kg/s] (V.97)

Calculation

E

p = -Ef + (mp + mf

) c

p Ta

- EpR - mf c

p Tp

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 10 -

13.

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 136 - 137.

Subroutine Variables

TEPZZ = E

p ZKAZZ = Ta ZKOPY = T

p

5 -TENPLM-2
TEOZZ = Ef CP = c

p TEPZR = EpR

TMOZZ = mf TMPZZ = iiip

Prepared bv

David W. Stroup

5 -TENPLM3
o

o

oo

oo

o

Computer Subroutine

SUBROUTINE TENPLM (ZKAZZ , ZCOPY, TEOZZ , TEPZR, TMOZZ , TMPZZ , TEPZZ)

C

c

C SUBROUTINE TO CALCULATE THE RATE AT WHICH THE PLUME OVER AN OBJECT

C ADDS ENERGY TO THE HOT LAYER.

C

C INPUT PARAMETERS:

ZKAZZ -- AMBIENT TEMPERATURE IN THE ROOM CONTAINING THE PLUME

ZKOPY -- PYROLYSIS TEMPERATURE OF THE OBJECT.

INPUT VARIABLES:

TEOZZ -- RATE OF CHEMICAL ENERGY PRODUCTION IN THE COMBUSTION

C TMOZZ

C TMPZZ

C

c

C OUTPUT VARIABLE:

C TEPZZ

C

C

TEPZZ

OF THE OBJECT.

HEAT LOSS RATE FROM THE FLAME OF THE OBJECT.

NEGATIVE OF MASS PYROLYSIS RATE OF THE OBJECT.

RATE AT WHICH THE PLUME OVER THE OBJECT ADDS MASS

TO THE HOT LAYER.

RATE AT WHICH THE PLUME ADDS ENERGY TO THE HOT

LAYER.

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

C

PARAMETER (CP = 1004. DO)

C

TEPZZ = -TEOZZ + (TMPZZ + TMOZZ) * CP * ZKAZZ - TEPZR

= - TMOZZ * CP * ZKOPY

C

RETURN

END

5 -TENPLM-4
TMSPLM - Rate of. Addition of Mass to the Hot Layer from a Plume

Description

This routine calculates the rate at which the plume over an object adds mass to the hot layer. The density and velocity profiles are assumed to be

Gaussian, and the equations are essentially the same as those found by Morton,

Taylor, and Turner (ref. 3 below), for a point source of heat. This

formulation assumes an area source of heat of given radius by taking a virtual

point source at an appropriate distance below the base of the fire, and

subtracting from the resulting mass flux the amount of air which would have

been entrained between the vertex and the base of the fire. The plume is

assumed to stop at the interface. The entrainment coefficient, a, is assumed

to be constant. The equations are discussed in detail in reference 1 listed

below.

Output

Rate at which the plume over an object adds mass

to the hot layer, [kg/s] (V.97)

Input

* a

Pa

Plume entrainment coefficient (Input Data)

.

(V.71)

Density of ambient air in the room containing

the plume (Input Data), [kg/s] (V.17)

Ambient temperature in the room containing the

plume (Input Data). [K] (V.120)

5-TMSPLM-l
Ef

mf

h

p

R

7T

g

(Negative of the) rate of chemical energy

released from a burning object (Calculated

Value, see Burning Object section). [W] (V.88)

(Negative of the) mass pyrolysis rate of the

object (Calculated Value, see Burning Object

section), [kg/s] (V.61)

Height of the plume over the object (Calculated

Value, see Plume section), [m] (V.37)

Radius of the fire on the object (Calculated

Value, see Burning Object section), [m] (V.85)

Pi (Physical Constant). [3.1415927...] (V.146)

Acceleration of gravity (Physical Constant)

.

[m/s 2

] (V.144)

Specific heat of ambient air (Input Data)

.

[J/kg-K] (V.112)

Calculations

x = R / (1.2 a)

b

p 1.2 a hpx

25gE

f

c

' «

^ 48a 7rc T p

p a a

U = (C' / h ) 1/3

v p

' px y

Distance of virtual point source below base of

fire

.

Height of augmented plume -- i.e. distance

between virtual point source and layer.

Plume radius at layer.

Convenient coefficient.

Axial velocity of plume gases at top of plume.

5-TMSPLM-2
u£ - (C^ / x) 1 ' 3

m

p - P a ^r(bpU-R2 Uf )

Axial velocity of plume gases at fire base.

Net mass flow into layer (augmented by pyrolysis

fuel mass)

mf

References

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

Harvard University, Home Fire Project Technical Report No. 34, pp . 10 -

13.

2. Mitler, H.E., and Emmons, H.W.

,

"Documentation for CFC V, the Fifth

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 136 - 137.

3. Morton, B.R., Taylor G.I., and Turner, J.S., "Turbulent Gravitational

Convection from Maintained and Instantaneous Sources", Proc. of Royal

Soc. (London) A234 (1956), 1.

Subroutine Variables

TMPZZ = m

p ALPHA = a VMAZZ = p a ZKAZZ = Ta TEOZZ = E f TMOZZ = mf ZHPZZ = h

p ZRFZZ = R

PI = 7T G = g

CP = c

p

Preoared bv

David W. Stroup

5 -TMSPLM3
o

o

o

o

o

Computer Subroutine

SUBROUTINE TMSPLM (ALPHA , VMAZZ , ZKAZZ , TEOZZ , TMOZZ , ZHPZZ

,

& ZRFZZ , TMPZZ)

C

c

C SUBROUTINE TO CALCULATE THE RATE AT WHICH THE PLUME OVER AN OBJECT

C ADDS MASS TO THE HOT LAYER.

INPUT PARAMETERS

ALPHA

VMAZZ

ZKAZZ

INPUT VARIABLES

TEOZZ

TMOZZ

ZHPZZ

ZRFZZ

PLUME ENTRAINMENT COEFFICIENT.

DENSITY OF AMBIENT AIR IN THE ROOM CONTAINING THE

PLUME.

AMBIENT TEMPERATURE IN THE ROOM CONTAINING THE

PLUME.

NEGATIVE OF THE RATE OF CHEMICAL ENERGY RELEASE

THE COMBUSTION OF THE OBJECT.

NEGATIVE OF MASS PYROLYSIS RATE OF THE OBJECT.

HEIGHT OF THE PLUME OF THE OBJECT.

RADIUS OF THE FIRE ON THE OBJECT.

IN

OUTPUT VARIABLES:

TMPZZ -- RATE AT WHICH THE PLUME OVER THE OBJECT ADDS MASS TO

THE HOT LAYER.

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

PARAMETER (PI = 3.1415927D0, G = 9.8D0, CP = 1004. DO)

IF (ZHPZZ .LT. 0 . DO) THEN

TMPZZ = -TMOZZ

ELSE

X = ZRFZZ / (1.2D0 * ALPHA)

HPX - ZHPZZ + X

BP = 1.2D0 * ALPHA * HPX

TMP = ( -2 5. DO * G * TEOZZ ) /

& ( 48. DO * ALPHA*ALPHA * PI * CP * ZKAZZ * VMAZZ)

C PROVIDE SAFETY AGAINST FLUCTUATIONS:

IF (TMP .LE. 0 . DO) THEN

TMPZZ = -TMOZZ

ELSE

U = ( TMP / HPX ) ** ( 1.D0 / 3. DO ) UF = ( TMP / X ) ** ( 1 . DO / 3 . DO ) TMPZZ = VMAZZ * PI * ( BP*BP * U - ZRFZZ*ZRFZZ * UF) - TMOZZ

ENDIF

ENDIF

RETURN

END

5 -TMSPLM-4
6. ALGORITHMS RELATED TO RADIATION HEAT TRANSFER

6-1
H

zm

6-2

Figure

6-1.

General

diagram

of

a

room

fire
7. ALGORITHMS RELATED TO THE VENT

7-1
7-2

Figure

7-1.

General

diagram

of

a

room

fire
CVWID - Width of the Segment of a Vent which Intersects the Layer

Description

This algorithm calculates the width of the segment of a given vent which

is intersected by the interface between the hot and cold layers. Thus, if the

layer interface intersects the vent, the routine returns a value equal to the

user- specified width of the vent. .If the interface does not intersect the

vent, the routine returns a value of zero. When the interface is very close

to the top or bottom of the vent, an intermediate width is calculated in order

to maintain continuity.

Output

W,vL Width of the vent which intersects the interface

between the hot and cold layers, [m] (V.141)

Input

B Width of the vent (Input Data), [m] (V.140)

h.

t Distance of the top of the vent below the

ceiling, --i.e. transom height (Input Data), [m]

(V. 23)

h.V Height of the vent (Input Data), [m] (V.34)

Depth of the hot layer in the room (Calculated

Value, see Hot Layer section), [m] (V.20)

Calculations

Intermediate computation

7 -CVWID1
0.0, ^ < 0 .0

Bhi/( £

CM 0.0 < V CM B, •2hv < A OO Ef*<C -BOC•hv )/(.2hv ), •8hv < h' * hV 0.0, > hv

References

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

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

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 113 - 114.

Subroutine Variables

WVL = WvL

ZBVZZ = B

ZHTZZ = ht ZHVZZ = hv ZHLZZ = hL

Prepared bv

David W. Stroup

7-CVWID-2
Computer Subroutine

SUBROUTINE CVWID ( ZBVZZ , ZHTZZ , ZHVZZ , ZHLZZ , WVL)

C

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

C

C THIS SUBROUTINE CALCULATES THE WIDTH OF THE SEGMENT OF A GIVEN

C VENT WHICH INTERSECTS THE INTERFACE BETWEEN THE HOT AND COLD

C LAYERS. THUS, IF THE LAYER INTERFACE INTERSECTS THE VENT, THE

C SUBROUTINE RETURNS ZBVZZ, AND IF THE INTERFACE DOES NOT INTERSECT

C THE VENT THE SUBROUTINE RETURNS 0. WHEN THE INTERFACE IS VERY

C CLOSE TO THE TOP OF THE VENT, THE SUBROUTINE RETURNS AN INTER

C MEDIATE VALUE IN ORDER TO MAINTAIN CONTINUITY.

C

C INPUT PARAMETERS

:

C ZBVZZ -- WIDTH OF THE VENT.

C ZHTZZ -- DISTANCE FROM THE CEILING TO THE TRANSOM OF THE VENT.

C ZHVZZ -- HEIGHT OF THE VENT.

C

C INPUT VARIABLES

:

C ZHLZZ -- DEPTH OF THE HOT LAYER.

I C

C OUTPUT VARIABLE:

•

C WVL -- LENGTH OF THE INTERSECTION OF THE VENT ‘WITH THE

| C INTERFACE

.

C

HV = ZHLZZ - ZHTZZ

TOP = . 2D0*ZHVZZ

BOTTOM = . 8D0-ZHVZZ

IF (HV.LT.O.DO .OR. HV . GT . ZHVZZ) THEN

WVL = 0.D0

ELSE IF (HV.GE.O.DO .AND. HV.LT.TOP) THEN

WVL = ZBVZ.Z*HV/TOP

ELSE IF (HV.GE.TOP .AND. HV . LT . BOTTOM) THEN

WVL = ZBVZZ

ELSE IF (HV.GE. BOTTOM .AND. HV.LE. ZHVZZ) THEN

WVL = - ZBVZZ/TOP* ( HV - ZHVZZ

)

END IF

RETURN

END

7 -CVWID -3
'

7 - CVWID-4
VNTCVR - Area of a Vent Covered by the Hot Layer

Description

This algorithm calculates the area of the part of a vent covered by the

hot layer. When the layer interface is above the top of the vent, this

routine returns a value of zero. When the layer interface is below the vent,

it returns a value equal to the total area of the vent. If the layer

interface is located somewhere between the top and bottom of the vent, this

algorithm calculates how far down the layer extends below the top of the vent

and multiplied by the (user- specified) vent width to obtain the area of the

vent covered by the hot layer.

Output

Avl Area of the vent covered by the hot layer, [m2

]

(V . 5)

Input

B Width of the vent (Input Data), [m] (V.140)

h,

t Distance of the top of vent below the ceiling,

- i.e. transom height (Input Data), [m] (V.23)

h.V Height of the vent (Input Data), [m] (V.34)

h.L Depth of the hot layer in the room (Calculated

Value, see Hot Layer section), [m] (V.20)

7 -VNTCVR1
Calculations

\i - K B

hL

- ht < 0 .

0

0.0 < hL

- ht < hv hL ht > bv

References

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

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

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

Harvard Computer Fire Code," U.S. Department of Commerce, Washington,

D.C., NBS-GCR-81-344, October 1981, pp . 113 - 114.

Subroutine Variables

AVL1 = A, l ZBVZZ = B

ZHTZZ = ht ZHVZZ = hv ZHLZZ = hL

Prepared by

David W. Stroup

7 -VNTCVR2
o

o

Computer Subroutine

SUBROUTINE VNTCVR ( ZBVZZ , ZHTZZ , ZHVZZ , ZHLZZ , AVL1

)

•k’k^rk’frkJrk'k'k•JcJrJck'k'k c IMPLICIT DOUBLE PRECISION (A-H.O-Z)

C

C SUBROUTINE TO CALCULATE THE AREA OF A VENT COVERED BY THE HOT

C LAYER.

C

C INPUT PARAMETERS:

C ZBVZZ -- WIDTH OF THE VENT.

C ZHTZZ -- DISTANCE FROM THE CEILING TO THE TRANSOM

C OF THE VENT.

C ZHVZZ -- HEIGHT OF THE VENT.

C

C INPUT VARIABLES:

C ZHLZZ -- DEPTH OF THE LAYER IN THE ROOM CONTAINING THE VENT

C

C OUTPUT VARIABLE:

C AVL1 -- AREA OF THE VENT COVERED BY THE HOT LAYER.

C

HV - ZHLZZ - ZHTZZ

IF ( HV .LT. 0 . DO ) THEN

HV = 0 . DO

ELSE IF (HV .GT. ZHVZZ ) THEN

HV = ZHVZZ

END IF

AVL1 = HV * ZBVZZ

RETURN

END

7 -VNTCVR3
7 -VNTCVR-4
8. MISCELLANEOUS ALGORITHMS

8-1
8-2

Figure

8-1.

General

diagram

of

a

room

fire
APPENDIX A

VARIABLE CROSS-REFERENCE

A1
a o

3 S

ja

a) ui jz

u S

O <*-i

<0 a) -u C

C u

% %

e js

•H 03 -H

t

2

-H M

oj a)c

C M

o a o ,Q

a) a)

4-> M

C -H

(13 <4-1 E

oo a) 3 JS < 4J

A2

a 5

o ~

u

<M 60c

X -4 3 -I

V.20

Depth

of

the

hot

layer

in

a

room

(in

m).

h.

ZHLZZ

LAYDPT
V.

41

Mass

concentration

of

C02

in

the

hot

layer

in

a

room

(in

kg/kg).

Y

C02

ZYLDZ

DXDCNC
a o <0 <0 z

u zu Q Q

>• Eh 43 43 X O 3 3 o C/3 ftC

l-l

ftCM

SI S3 O C/3 ft ft X >1

SI S3

o

eP O

#= <P F i

1

T3ON T3 MO o O^J MO M S

Qg_> 0^/3

T3 TJ~ H~

0 O

M C3

O O

• E

*h £ C so

T3

IS ft

oS3

ft

Ss <M ft o

1/3 T3

I! £

O E

J-l 73

<4-1 (D>

OCNJ SC

S S s

A4

V.

61

(Negative

of

the)

mass

pyrolysis

rate

of

an

object

(in

W).

TMDZZ

PPYRO,

PYRO,

TMGAS
S'

40

43 a

CM <44 C3 CM ©

s 0 © 6

© •*o pG S 0 2 CO pO 2 0 40

34 o G

CM_ c © c G ©

xx 6 •H 40 43 *f4 © C3 © © C © © 40 f4 2 £ o so <44 •r) O D

(

o

E *4 34 40 O 73 40 © a 0 2 C 40 © O © C3 *H O •H Oh 40 © © 40 ©

so M C 34 •r) O © CJ •*7) C •H 0 © -Q © © 73 •H M © © CO O <44 40 ©

t-4 •H cu -Q <44 4 pG CM

•^4 © c E © 0 3 O 0 © £

o o CM © CO 40

CO 0 40 - CM © SO 40 2 40 CO 34 • E <44 © E G

34 © 73 © ZD © 0 o •H o ZD o © CO © © • CM i-4 40 o c 40 •fH -H © -4 <44 © 34 34

f-4 -G SO 34 w II C3 o 3 E

^4 £ -*4 © © © 43 © pG o ©

© © 34 © <44 co ^ <44 0 u © 34 > © © 40 34 SO © © —4 ©

© 34 4 CO <44 3 73 <H4 <0 4J © >N 3 © 0 o CO 34 © H © o - so 40 >-4 CO © © i-4 P f-4 © •p4 G > © CO o 03 o 4J CM © O © © 40 pG © •f4 o 73

73 (0 0 £ 4J 40 O E o O 40 <J CO © ,C o © 34 © o © <0 O •H 34 -4 34 •*o O 34 © © G 40 U &

© © <44 Oh pG 43 O E E ~ •H C3 0 © X6 c © 2 •4 0 © ©CM ©

4J CO 40 •H x: O <+4 G o 34 (0 f-4 p-4 £ 34 40 i-4 o -4 © © © f-4 44 ^ <44 \ © ^ pG

•H G <44 <4-1 <44 34 G • >> t-4 1-<M^ — z >*CM 0 O O 4-3 <44 34 CO 0 ^ © © E © E

(0 C3 O CO O G © CM f-4 £ © ^ © G f-4 -— c

34 4-3 4J © © O O pG <H E E 2 E -h ©

© © c c >% so SO f-4 43 40 O ^ 40 40 3 3 ^ 40 >> N © © ,g SO -X <44 o o o ^4 C •-4 O G c

(0 •«H •H *4 o 34 © e pC 43 .C pC Oh -4 Gh 40 0= -4 o

t-4 (0 <0 © © G 40 © Oh CO E G O

*H ~H c G a pC c 3 © *«4 © © © © © © 40

<44 CU VI <4-4 © © 3 © 40 4 <44 -r) f-4 ' pC pG x: so fG pC so G

o © <4-1 <44 0 <44 40 43 40 c 40 02 40 c ©

4-) © © >> © so 40 o <44 (0 •H O fH 73

(0 o O •G x: G <0 -•4 0 pC •G *4 E C E E E *-4 E E -i 0 o (0 4J -«4 © <44 40 43 0 o O o O -H O 40 0 -H CO •§ © 73 pX <44 34 © © CO 34 -i4 34 34 34 © 34 © u a> G

E *4 M © <44 © -Q © © 04 Oh *4 <44 40 <44 <44 <44 O <44 SO <t-l u •pH 3 •H © © .g o E O O 40 pG (3 34 C 4-3 <4-4 <44 34 <0 C © © E-» X © X X X M X © X l-i X

(0 (0 o © co G © © © 3 U 3 3 3 O 3 40 D o 3

a) © G c CO SO 40 © 40 (j 34 34 »-4 © f-4 f-4 f-4 t-4 ^4 f-4 f-4 © © XX c G c <44 <44 • <44 40 <44 <44 <44 f-4 <44 © <44 i-4 <44 SX pG 34 u © © © <44 © © ^ G f-4 »-4 <0 <0 4J 4J E 0 34 pC 40 G G E 40 -f4 40 43 40 © 40 <44 40 © 40 s $ X O so © 40 a © © © © © © 5 © o © 5 ©

o o 4J 4-3 3 © CO *t4 pQ © © © G © © © © © © © ©

^4 ^4 © © f-4 <44 CO CO © 1= 40 »-4 £ E *4 -C E pG x: pG © pG © .G © pC —1 73 © © <44 O 34 3 © © © pG C3 x: © © © x: pC <44 40 C > C G i © f-4 © © ~ © 40 © © © 40 c

- T3 4-3 © O G © -»4 o O i > <44 > ><np- > > <H > o

£ *H £ E E © 40 i-4 © i-4 U 3 •H •4 f4 1 •f4 E ~H <44 •H 34 f4 <44 2 > © © 34 © 40 3 C 40 43 ,c 40 © 40 40 40 o 40 D 40 o 40 E *H x: 34 © •H © 73 (0 © © © 43 © E © © z © © (0 © ©

•H 73 •H •H -9 40 E G (0 **4 *4 eo •^4 © -4 43 f4 f4 40 •H X X c e 4-3 40 1=

•*4 3 © © 34 73 73 G 73 r-4 73 73 G 73 34 73 © 73 34 73

<3 © (0 2 2

© © 3 G r-4 34 34 -H © © © © <44 © © -pH © © © pG © © © £ -Q 2 z z Z h4 &4 04 04 © CC 06 ^ 0$ ^ 06 06 ^ 06 Oh 06 -*0 z a 06

cn -T vn CD CD O) O H CM CO M* m CD co O) O rH CM

CD CO CD CD CD CD CD r>. r>. r>. rv fS

rv rv CO CO 00 > > > > > > > > > > > > > > > > > > > >

A5

u

5

£cu

CO

CO CO 4J 4J

CO CO Q Q

S3§S3S

S3

S3§S3 H

Q

S3

S3

S3

S3<S3 ' Cn

CJ

a ^

- £

SI

S ^

4J<

c? "w

nj ^

0) U£ A •

<D c

d» ~H CO ? 2

a c

jJ -H

(0 c

*j e

A7

V.

123

Temperature

of

the

flaming

gases

--

i.e.

flame

temperature

(in

°K)

.

TxTG

Input

Data
3HHHM

Z

is

4Jo

0)

•*“) 42o

c

O

<DO

cfl CMM

3

(0

(0 42

4-) CMO

cuu

a

4J

(0M

0

§•

<u H

00C

0)u

M

o

(0 CMO*4J•H>

•H

4JO

3

T3C

o

u

E E

E C O

-H o

.C E

O <1) a) js

•«-) 4J 43O CM

CM M

O CO>%

CD (0

42

4jT3 ^

O T3 O M

o o

m cd CM <N

oo

CM CM > >

a>

eg>

o

CO

rH>

eg

co

rH>

CO

coH

>

->r m

CO CO > >

CD

CO

rH>

f.

ro> > >

A8

V.

143

Y

coordinate

of

an

object

in

a

room,

with

respect

to

the

local

y

Q

ZYOZZ

Input

Data

coordinate

system

of

the

room

(in

m)

.
V.

144

Acceleration

of

gravity

(g

03 (0 4J 4J

<3 03 Q Q

0

b

1

HM

Z

S3c

00

O)

II

u

03 4Jc

0)

CV] O)

co

II

•H

CL.

CNS2

co

i o

X

COm

b

-oC

03 4J

U3c

oo

s

o

-•H 4J•HT3

03M

03

4-10) -OCO

A9

APPENDIX B

LISTING OF ALGORITHM/SUBROUTINE WRITE-UPS

B-l
1. Algorithms Related to the Burning Object

Subroutine

Name Output ( s ) Input (s)

ANGLE V . 109 V. 85 , V. 36

BURN V . 55 V. 26 , V. 3 , V. 61 , V. 97

CHEM V. 88 V.112,V.30,V.120,V.119,V.55,V.37

DXDPRD V . 56 V. 46 , V. 61

FLUX V . 67 V.31,V.1,V.77,V.80,V.78,V.108,V.85,

V . 146

HEIGHT V . 36 V.26,V.118,V.55,V.61,V.85

MNXPRD V . 57 V.45 , V. 61

PFLUX V . 67 V.82,V.13,V.28,V.129,V. 147

PPYRO V. 61 V . 31 , V. 67 , V . 85 , V . 146

PULRAD V . 85 V. 8 ,V. 39 ,V. 136 ,V. 15

PYRO V. 61 V.31,V.8,V.67,V.108,V.85,V. 146

SPREAD V. 107 V.115,V.123,V.8,V.85,V.67,V. 147

SUTPRD V. 58 V . 48 , V . 61

TMGAS V . 61 V. 15 , V. 69 , V. 7 , V. 6-

WTRPRD V. 59 V . 47 , V . 61

2 . Algorithms related to Conduction Heat Transfer

Subroutine

Name Output (s) Input ( s ) TMPW01 V . 122 V.11,V.81,V.79,V.11,V.15,V.64,

V. 110, V. 120, V. 128, V. 134, V. 130,

V.132,V.111,V.16,V.2,V. 147

,

V. 63 , V. 20 , V. 121

B-2
3 . Algorithms related to Convection Heat Transfer

Subroutine

Name Output ( s ) Input (s')

CBLOCK V. 14 V.61,V.85,V.129,V. 144 , V. 146 , V . 112

,

V. 123 ,V. 72

CNVF V . 12 V.128,V.125,V.21,V.22,V.72,V. 144

CNVL V. 86 V.21,V.22,V.20,V.68,V.25,V.ll,

V. 138 , V. 5 , V. 141

CNVW01 V.ll V.126,V.127,V.120,V.66,V.62

4. Algorithms related to the Hot Layer

Subroutine

Name Output (s) Input (s')

ABSRB2 V. 2 V . 44

DXDCNC V . 41 V . 49 , V . 54

'LAYDPT V . 20 V . 112 , V . 17 , V . 33 , V . 120 , V . 21 , V . 22 , V . 25

MNXCNC V: 40 V . 49 , V . 54

OXYCNC V . 43 V . 52 , V . 54

POWL V. 68 V. 89 ,V. 86 ,V. 9 ,V. 10

SUTCNC V . 44 V . 53 , V . 54

TC02M V. 90 V.56,V.61,V.97,V.98 -

TH20M V . 95 V. 59 , V. 102

TMNXM V . 91 V. 57 , V. 99

TMPL V.127 V. 120 , V. 112 , V. 25 , V. 54

TMSL V . 93 V. 97 , V. 106

TOXYM V . 94 V.103,V.61,V.97,V. 100

TSUTM V.92 V . 58 , V . 101

WTRCNC V . 42 V. 51 , V. 54

B-3
5 . Algorithms related to the Plume

Subroutine

Name Output (s) Input (s)

OXYBRN V . 60 V. 43 , V. 116 , V. 55

PLMHT V . 37 V. 38 ,V. 33 , V. 20

TENPLM V. 96 V. 120 , V. 119 , V. 112 , V. 88 , V. 29 , V. 61

,

V . 97

TMSPLM V . 97 V. 71, 7.17,7.120,7.88,7.61,7. 37,

V. 85 ,V. 146 ,V. 144, V. 112 *

7 . Algorithms related to the Vent

Subroutine

Name Output (s') Input (s')

CVWID V. 141 7 . 140 ,V.23,V.34,V.20

VNTCVR V. 5 V. 140,7.23,7.34,7. 20

B-4
NBS-114A (wev. 2«ac) U.S. DEPT. OF COMM. 1. PUBLICATION OR 2. Performing Organ. Report NoJ 3. Publication Date BIBLIOGRAPHIC DATA

REPORT NO.

SHEET (See instructions)

A -PI-PI C Akin Cl IDTITI e NBSIR-87/3607 August 1987

^ Catalog of Compartment Fire Model Algorithms and Associated Computer

Subroutines

5. AUTHOR(S)

David W. Stroup

6. PERFORMING ORGANIZATION (If joint or other than N AS, see instructions)

national bureau of standards

repartufmt flF rnuiiFDrP

Gaithersburg, MD 20899

7. Contract/Grant No.

S. Type of Report & Period Covered

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

10. supplementary notes

program; SF-185, FIPS Software Su mmary, is attached. U* ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant bibliography or literature survey, mention it here) 6

The Compartment Fire Modeling Research group of the Center for Fire Research,

National Bureau of Standards has been charged with the development of a

M benchmark ,r compartment fire model. As part of this activity, a catalog of available fire

model algorithms has been compiled. The catalog contains algorithms which

calculate various physical/chemical fire phenomena. The description of each

algorithm includes the input(s), output(s), and calculations performed. In

addition, each algorithm has a computer subroutine written for it in FORTRAN 77.

The variables used as input and output throughout the catalog are cross-referenced.

This enables a catalog user to determine which routines would be required to

calculate a particular fire phenomena. Updates and revisions will be issued

periodically.

2. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

algorithms; building fires; cataloging; combustion physics; compartment fires;

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

3. AVAILABILITY

Kx\ Unlimited

I I For Official Distribution. Do Not Release to NTIS

Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Joel Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

235

15. Price

$24.95

USCOMM-OC 8043-P80
,

.