A11107 S'lOflVo

NBSIR 84-2934

A Model for the Transport of Fire,

Smoke and Toxic Gases (FAST)

Walter W. Jones

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

September 1984

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Director

100

.1156

34-2934

NBSIR 84-2934

A MODEL FOR THE TRANSPORT OF FIRE,

SMOKE AND TOXIC GASES (FAST)

Walter W. Jones

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

September 1984

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

NATIONAL BUREAU OF STANDARDS. EmMt Ambler, Director
r " .r .\ • - : r -• y* - :- v: £
TABLE OF CONTENTS

Page

LIST OF FIGURES iv

1. INTRODUCTION . 1

2. STRUCTURE OF THE MODEL 2

3. DERIVATION OF THE CONSERVATION EQUATIONS 8

3.1 Fluid Transport 9

4. SOURCE TERMS 11

4.1 Source Terms: Radiation 12

4.2 Source Terms: Convective Heating 16

4.3 Source Terms: Plumes 17

4.4 Source Terms: Door Jets 19

4.5 Source Terms: Fire 21

4.6 Source Terms: Conduction 22

5. NUMERICAL INTEGRATION 25

6. COMPARISON WITH EXPERIMENTAL DATA 29

7. STABILITY AND COMPLETENESS 31

8. CONCLUSIONS 32

9. ACKNOWLEDGMENTS 33

10. REFERENCES 33

APPENDIX A: Notation 35

APPENDIX B: Input /Output Format 38

APPENDIX C: BUILD 41

APPENDIX D: FASTPLOT 44

-iii-
LIST OF FIGURES

Page

Figure 1. A schematic of one compartment in the zone model concept.

Two layers u,l) and a single vent are shown 50

Figure 2. Radiation transport scheme. Shown is the view factor

calculation of surface "i" as seen by surface "j",

transmitted through both layers 51

Figure 3. Possible upper/lower mixing mechanisms which occur at

vent jets 52

Figure 4. Comparison of experimental and calculated temperature

profiles for the upper layer in the burn room and

corridor in the "Nike Site" experiments (Table I) 53

Figure 5. Comparison of experimental and calculated interface

height in the corridor of the "Nike Site" experiments

(Table I). See ref. Qulntiere et al . (1984) and

Cooper et al. (1981) for an explanation of the

criteria (10%, 20%) used to determine the experimental

interface height 54

Figure 6. Comparison of experimental and calculated upper layer

temperature in the corridor of "B205" experiments

(Table I) 55

Figure 7. Comparison of experimental and calculated interface

height in the "B205" experiment (Table I) 56

Figure 8. An example of the upper layer separation which occurs

in actual flows 57

Figure 9. An example of fire size specification through mass loss

data 58

Figure 10. Sample output from "FASTPLOT". Shown is one of the

100 kW calculations for the "B205" experiments in the

three compartment configurations 59

-iv-
A. MODEL FOR THE TRANSPORT OF FIRE, SMOKE AND TOXIC GASES (FAST)

1 . INTRODUCTION

In recent years there has been considerable research in the area of the

spread of fire and smoke from a room of fire origin to connected compartments. The work is motivated by a need to understand and be able to predict

the environmental conditions which occur as a fire develops and spreads. Much

of the attention has focused on the development of numerical models which are

able to make a reasonably accurate assessment of the environment from ignition. The motivation is two-fold. Being able to correlate laboratory scale

experiments with full-scale tests is desirable from a cost standpoint. More

important, however, from a life-safety and operational standpoint, the ability

to make accurate predictions of the spread of fire, smoke and toxic gases

opens up many possibilities for combating these problems, as well as taking

effective preventive measures. The ability to prevent the hazards from developing becomes especially important as new and exotic materials become available.

This paper describes a model which allows one to predict the evolution of

a fire in a room and the subsequent transport of the smoke and toxic gases

which evolve from this fire . The numerical implementation improves on

previous work, for a review see Jones (1983), in particular by retaining the

conservation laws in their full differential form and solving them as a set of

coupled ordinary differential equations (ODE's). Such a formulation takes

advantage of the effort which has gone into solving such systems of equations.

The result is a numerical scheme which is considerably faster and much more

"rugged" than previous models.

- 1 -
The model is assumed to be in a world of uniform temperature T

a and

reference pressure P a

, with the outside of a wall at T

£ which may not be the

same as the ambient. The discussion is broken down into the basic structure

and fundamental assumptions which go into the model, followed by a derivation

of the predictive equations, a discussion of the source terms, the numerical

implementation and some calculations and comparisons with experimental data.

The notation is given in Appendix A. The numerical implementation of the

model is modular and straightforward. It is designed to be transportable.

2. STRUCTURE OF THE MODEL

The primary element of the model is a compartment. The primary interest

lies in the composition of the gas layers in each of these compartments. As

such, the model is structured around fluid transport phenomena. In this

context, the predictive equations for the gas layers in each compartment

result from conservation of mass, momentum and energy together with an equation-of-state for each compartment. The actual physical phenomena which drive

the transport are then couched as source terms. Such a formulation allows the

greatest flexibility in adding, modifying or deleting terms which are appropriate to the problem being solved.

Each compartment is subdivided into one or more "control volumes." These

control volumes will be of sufficient size that we will require only a few to

describe any system of interest. The choice is based on the premise that the

details which occur within such a volume do not concern us (at present), but

their mutual interaction does. Each of these control volumes is called a

zone. The rationale for such a choice arises from the experimental observa-

-2 -
tion that when a fire spreads, the gas layers in the compartments actually

stratify into two distinct zones. This is a compromise between a network

model and a finite difference model. The former is computationally fast but

yields no information on the internal structure whereas the latter yields a

great deal of information but requires more computational resources than is

warranted. The two zones are referred to as "upper" and "lower", respectively. The basic equations describe the mass, momentum and energy transfer from

zone to zone in a fire driven environment. A schematic is shown in figure 1.

In considering dynamic systems, it is necessary to solve a problem selfconsistently. If such is not done, then some of the dynamics may be obscured

or even lost. In particular, discussion of movement of the zone interfaces

must be consistent.

The conservation equations for mass and energy can be written in the form

dm „ . dF

- l

m

i (l)

for mass and from the first law of thermodynamics we have

If (ev) +

p If = q + h ( 2 )

together with an equation of state

P = pRT ( 3 )

which closes the set of equations, and with the definitions

-3-
E = Cv

p(T-TR

)

h = c Z m. , (T - T_

p t i,in'- R

) - c Em. (t - T

' p i,out v R ) +

f

h

l,o(

TJ

Q

=

Qi: + Q0 + Q

= net energy input

r K c

i = index of other compartments (i 4 volume of interest).

The term h^ 0 (T^) is relative to the temperature from which this mass parcel,

mdt, came. It includes enthalpy of formation. The equation of state for an

ideal gas is usually used for closure of the system. More correctly it should

be written

P = P (p,T,{i}), {i} = set of species (4)

especially for applications to fire problems which are not ideal gas problems.

However, for the case of an ideal gas, the derivations and discussion are

simplified, and generalizations can be discussed later. The sign convention

is that positive fluxes on the right hand side of an equation will increase

the quantity being calculated on the left hand side, that is, transfer into a

volume is indicated by a positive flux on the right hand side.

The general form of the model is to divide each compartment into two

zones: an upper zone which contains a hot layer, and a lower layer which is

relatively cool. There may exist one or more fires and plumes in each

compartment and these can usually be considered to be part of the upper zone.

Mass and energy transfer between the zones is provided by the plumes, mixing

-4-
at the vents, radiation between layers and flow along the walls. In general a

plume, once created, simply transfers mass and energy from one zone to

another. Another set of equations could be written for the plume, but as long

as it is in quasi-steady equilibrium, considering it to be part of the upper

zone is sufficient. Another way of the looking at the plume Is to consider it

so small in mass, energy content and volume that it can be ignored except as a

transfer mechanism. For some problems, however, the plume must be considered

a separate zone along with the concomitant conservation equations. An example

would be when the rise time of the plume is of interest or when the actual

size and composition of the plume is important.

Since the conservation equations are written in terms of the volumes of

these entities, a relationship between the height and the volume is needed,

such as

hr

V - / ZA (Z) dz (5)

to calculate the layer depths. This removes the usual restriction that the

compartments be rectangular parallelepipeds, and allows calculations for

circular crosssections (aircraft) and trapezoids (atria).

The radiation transport scheme used is fairly simple and derives from the

work of Siegel and Howell [1981]. The view factors which are used In the

calculation of solid angles are concomitant with surfaces which are planes or

discs. The relationship is shown schematically in figure 2. The simplification used here and discussed in more detail by Jones (1983) is retained, but

the actual areas are used, and the exact view factors are used wherever

- 5-
possible, Kusada (1976). For example, in calculating the area of the upper

wall, allowance is made for any vents which exist by subtracting their area

from the total wall area. In addition, ceiling and upper wall, lower wall and

floor are treated separately (as pairs). This is necessitated by the possible

use of different materials for the respective surfaces which may have different radiative properties, as well as the different types of convective flow

which occur over each of these surfaces. More correctly, we should consider

three surfaces, ceiling, wall and floor. This is under development. A

problem arises in treating vertical convection as the layer depth tends to

zero.

Actual closure of the model is obtained by assuming that the size of the

compartment is fixed so that

V = V + V 0 u a

( 6 )

and that there is a single reference pressure

P = P„ u i (7)

at the boundary (interface) of the zones.

The set of equations which is necessary to describe fully such a physical

system can be reduced by considering the physical impact of some of the terms.

In particular, the pressure should be a general function of position,

P (X,Y,Z), in the compartment, which would require us to include a differential equation for the conservation of momentum explicitly. A general form for

the perturbed pressure might be

-6 -
( 8 )

Z

P (x >y ,t) = P(t) - / p(t)dz + 6P (X,Y,Z,t)

o

where P is a reference pressure and is usually the pressure at the base of the

compartment. In the spirit of the "control volume" formulation

<SP -*• 0.

This implies that acoustic waves are filtered out and that internal

momentum need not be calculated. The hydrostatic term is small in absolute

value in comparison with the reference pressure, so it is not necessary to

carry this calculation through the equation of state. Finally, the time

dependent portion of the hydrostatic term deals with the movement of the

interface, and thus can be ignored if we limit ourselves to problems where the

momentum associated with the discontinuity (alternatively the velocity) is not

significant. Dropping the momentum equation for internal waves increases the

computational time step a great deal since we are not limited by the Courant

time step criterion (time step a grid size/speed of sound). This prohibits us

from considering problems such as deflagration waves and explosions. With

these considerations in mind, we will assume

Pu

- P

Jt = P - (9)

The pressure in eqn. (9) is the reference pressure at the floor. This

simplification is carried through the conservation equations and greatly

simplifies the resulting predictive equations. However, it is necessary to

retain the hydrostatic term for the flow field calculations at vents. As we

are considering only small changes in the absolute pressure, differences of

these terms will be comparable to the hydrostatic pressure change, eqn. (8).

-7 -
For example, for eqn. (22)

6P ~ 1 - 1000 pa

whereas

/ (pjTj - p2

T

2

) dz ~ 100 pa

where the integration is over a vent opening. So the flow can be dominated by

the hydrostatic term whereas the 6P/P < 1%.

3. DERIVATION OF THE CONSERVATION EQUATIONS

A zone model describes a physical situation in terms of integrals of

extensive physical quantities. Thus we deal with total mass rather than mass

density, total energy rather than energy density but temperature is used as

before (an intensive quantity). The integrals are volume integrals whose

boundary surfaces enclose the Euclidean space of interest. The space with

which we are concerned usually is a compartment with zones including a hot

upper gas, a cool (relatively) lower layer, objects, plumes and fires. The

connections occur at the boundary of these zones. Examples of possible

connections are the vents connecting compartments, the radiation from a fire

to the compartment walls, etc. With this basis we can mold the conservation

equations into a form which describes a fire in terms of the quantities which

are appropriate to the control volume approach, intuitively understandable and

lend themselves to measurement.

-8 -
3.1 Fluid Transport

The conservation equations for each compartment of a two layer model are

dm

udt

I m , m

L u,i u

dm

j

dt

— • • l in* , > m n L A,i i

if {c m (T - Tp )} dt 1 v u

v u R' 1 - V

dP

\ u dt u

Qu

+ h

( 10 )

(ID

( 12 )

c m

v i

dP

l dt (13)

In writing these equations, we will make two assumptions. First, that the

fire will not feed mass directly into the lower layer. Second, we will write

the upper layer equation as if there is only one fire. If more than one fire

exists, then a sum over such sources is necessary and if none are present,

then this term vanishes. The source term Q includes all energy transfers due

to radiation and convection and h includes the enthalpy flow. We can rewrite

the energy conservation equations as predictive equations for temperature, in

which case they become

dT dP

m c u dm

u p dt

V -rr- = Q + h - cT .. u dt ^u u p u dtu dm+ c Tv R dt

-» Eu

and

(14)

dT dp o

• dm,

-j—— - V„ -r~— = Q n + h - c T„ t-1 l p dt l dt x

l l p i dt

dm

+ c T

v R dt

+• E,

(15)

-9 -
The right hand side of eqn. (14, 15) can be rewritten in a simpler form. The

reference temperature (TR

) is chosen arbitrarily. If the only phase change

occurs in pyrolysis of the fuel, then we can set the reference pressure to

zero and include the pyrolysis energy as a sink term in the energy release

rate. As T -* 0 we obtain

K

(16)

and

(17)

The equations and assumptions necessary to close this set are

P = pRT (18)

(19)

with

m PV ( 20 )

and V = V + V. = constant,

u l

( 21 )

- 10-
The energy source terms {e , E } are shown schematically in eqns. (16,

X u

17) but can be much more complex and depend upon the configuration. Combining

eqns. ( 10— 11) and (14-17), together with the closure relations, we obtain

dP

=

s d t (6-l)V

dVi (M(i i

dl " 6 IpV

u j\ u (B-l)V

dt

dVu

dt

i/M U +

0 vpv^ J l * ( 3-i )v ,

—

\

(cmT + E s P6 \ p u u u V I

where

c m T +

p u u

C

PV* + E +

u

and 6 = c /R = y/(Y~1)

P

( 22 )

(23)

(24)

(25)

(26)

(27)

It should be pointed out that the equations are written in this form for

the sake of clarity and simplicity. In a numerical implementation there are

better ways to express the source terms which minimize the problem of the

small difference of large numbers.

4. SOURCE TERMS

Equations (22-25) are written so that physical phenomena which affect the

environment are source terms and appear on the right-hand-side. Sources which

appear directly are:

-ll-
1. radiation between the gas layers and walls, fires and other objects,

2. convective heating,

3. flow in plumes,

4. flow in vent jets,

5. mixing at vents.

Phenomena which are included but do not show up explicitly are:

1. radiation between objects,

2. conduction through walls and objects.

4.1 Source Terms: Radiation

In order to calculate the radiation absorbed in a zone, a heat balance

must be done which includes all objects which radiate to the zone. Clearly,

in order for this calculation to be done in a time comensurate with the other

sources, some approximations are necessary.

The terms which contribute heat to an absorbing layer are the same (in

form) for all layers. Essentially we assume that all zones in these models

are similar, so we can discuss them in terms of a general layer contribution.

Radiation can leave a layer by going to another layer, to the walls,

exiting through a vent, heating up an object or changing the pyrolysis rate of

the fuel source. Similarly a layer can be heated by absorption of radiation

from these surfaces and objects as well as from the fire itself. The

formalism which we will employ for the geometry is that used by Siegel and

- 12 -
Howell (1981) and Is shown in figure 2. The radiative transfer can be done

with a great deal of generality; however, as with most models we assume that

zones and surfaces radiate and absorb like a grey-body with some constant

emissivity (e<_l).

A further assumption consonant with the stratified zone assumption is

that emission and absorption are constant throughout a gas layer. In application to a growing fire, a further assumption is made that the lower layer is

mostly diathermous. Although not a necessary assumption, this reduces the

computation time for this term by 50%. For smoke propagation some distance

from the fire(s) such an assumption will not be valid, but the temperature

will be so low that radiation will not be the dominant mechanism for heat

loss. Flames, plumes, fires, objects and bounding surfaces have some average

shape from which the view factors can be calculated. The walls of compartments are usually flat and rectangular. The gas layers are spheres with an

equivalent radius of

L = 4V/A (28)

and an effective emissivity of

£ = 1 - exp(-oiL).

o (29)

- 13-
The terms which contribute to heating of a layer are:

1 . fires and plumes

2. walls,

3. other layers,

4. vents (radiation from other compartments),

5. nonbuming objects.

The radiation balance of items 2-5 can be dealt with using the following

notation:

a

a

L

£

g

- geometrical view factor of surface (j) by surface (k) —ft ) lx - Stephen-Boltzman constant = 5.67x 10 W/m K

- absorption coefficient of the upper gas layer m

^

- mean beam length of the equivalent sphere (m) , defined in eqn.

- emissivity of the upper/lower walls

- emissivity of the upper gas layer

(28)

Using the formalism of Siegal and Howell (1981) we have

D ' f1 ' U- eu

)(l- Eg

>uu } (1 - (l-^u) O0a)

- {(l-e )(l-e )(l-e ) 2

F F

u' v }

g

J u£ Jlu

"u

" tfl - (1-gjF.J {1 -

- {(l-eJ(l- Eg ) 2

F

uJtF

ta H^ (30b)

- ' I 1 +

- 14-
(30c)

A

Aw

Finally

Q(upper) = A e II /D u u u

Q( lower) = A^e^H^/D.

To this must be added the energy radiated by the fire. A heat transfer

balance with the fire is not necessary simply because the amount of heat

radiated by the fire is usually much greater than that absorbed by the fire.

In order to investigate flashover, however, this calculation must be generalized to include the fire and lower layer absorption in the radiative heat

balance equation rather than relying on the postulate that superposition of

the terms is sufficient.

A simple example of the results can be given for the case

for which we have

- 15-
where Ad area of the upper/lower layer discontinuity

A

uv

= area of vents which the gas layer "sees"

A

u

= area of the upper wall (including ceiling)

Ff = fraction of the fire which radiates times its view factor for

the gas layer.

A " Au + Ad

4.2 Source Terms: Convective Heating

Convection is the mechanism by which the gas layers lose (or gain) energy

to walls or other objects. Conduction is a process which is intimately

associated with convection but as it does not show up directly as a term for

heat gain or loss, it will be discussed here.

Convective heat flow is energy transfer across a thin boundary layer.

The thickness of this layer is determined by the relative temperature between

the gas zone and the wall or object surface, Schlichting (1955) and Turner

(1973). We can write the heat flux term as

where the transfer coefficient can be written as

h

c

- I

cv(Gr • Pr > 1/3

-

(32)

- 16 -
The terms are:

Gr

Pr

k

l

C„

N

=» area of wall(s) in contact with the zone

3 2 “ Grashoff number = g£ | T — T j

/

v T

O ” O = Prandtl number » 0.7

_7 /T + T \4/5

= thermal conductivity of the gas = 2.7 x 10 ( ® ^—

—J

= length scale - /a~

= coefficient which depends on orientation, Turner (1973)

= Nusselt number

/T + T \7/4

= 7.18 x

10" 10

( S- - 2

-

For the cases of interest

Orientation Coefficient Condition

Vertical 0.130 Gr x Pr > 10

Horizontal 0.210 > Ttt g w

Horizontal 0.012 T_ < T

g w

The coefficients for horizontal surfaces apply to a slab over the zone. For

the inverse of this situation the coefficients should be reversed.

4.3 Source Terms: Plumes

A fire generates a plume which transports mass and energy from the fire

into the upper layer. In addition, the plume entrains mass from the lower

layer and transports it into the upper layer. The former generally increases

the upper zone internal energy whereas the latter will have a cooling effect.

For a fire which is consuming mass at a rate m^ , heat addition will be

- 17 -
q

; • h

c

.

Some fraction, x^» will exit the fire as radiation and the remainder will be

left to drive the plume. We can emperically devide the heat transfer into

actual combustion and simple gasification. The former, denoted by x

c

» is the

relative fraction of pyrolysate which participates in the combustion. Also,

once combustion occurs, a fraction of the energy leaves the fire as radiation

(x^Q) and convective energy ({1-x^K})* The former is a function of such

external effects as radiation, e.g., other fires, and vitiation. The latter

efficiencies relate to sootiness and Froude number. The mass flow in a plume

comes from a correlation of experimental data given by McCaffrey (1983). This

correlation divides the flame/plume into three regions:

flaming: m

p = 0.011 Q (Z/q

2/5

) 0 * 566

Z/Q

2/5

< 0.08

intermittent: m

p = 0.026 Q (Z/Q

2/5

) 0 * 909

0.08 _< Z/Q

2/5

< 0.20

j

(33)

plume: m = 0.124 Q (Z /q

2 / 5

)

1 * 895 0.20 < Z/Q2 ^ 5

. p —

Entrainment in the intermittent region agrees with the work of Cetegen et

al. (1982) but yields greater entrainment in the other two regimes. This

difference is particularly important for the initial fire as the upper layer

is far removed from the fire. In this formulation, the total mass flow in the

plume is given by the above correlation and the fuel pyrolysis is related to

it by

m + ft = f (mz, Q)

p v

* x

given above.

( 34 )

- 18 -
4.4 Source Terms: Door Jets

V

Flow at vents is governed by the pressure difference across a vent. In

the control volume approximation the general momentum equation for the zones

is not solved. Instead, the momentum transfer at the zone boundaries is

included by using Bernoulli’s solution for forced flow. This solution is

augmented for restricted openings by using "flow coefficients." The modification deals with the problem of constriction of velocity streamlines at an

orifice.

There are two cases which apply to these models. The first, and most

usually thought of in fire problems, is for air or smoke which is driven from

a compartment by buoyancy. The second type of flow is due to a piston effect

which is particularly important in the early stages of a fire. Rather than

depending on density difference between two gases, the flow is forced, for

example, by volumetric expansion when combustion occurs.

The results used for this model are those of Bodart and Jones (1984) and

will not be duplicated here. The notation used is:

S = smoke

A - air

ij * flow from compartment (i) to (j)

P = floor pressure (reference)

-19-
The order of the letters indicate the type of atmosphere from which the fluid

is coming and to which it is going. As many as three neutral planes can exist

for such flows. Two mixing phenomena which occur at vents are similar to

entrainment by plumes. For the case when hot gas leaves a compartment and is

driven by buoyancy into the upper layer of a second compartment, a door jet

exists which is analogous to a normal plume. Mixing of this type occurs for

flow

> 0

and is discussed in detail by Zukoski (1982) and Tanaka (1980). The other is

much like an inverse plume and causes contamination of the lower layer as cold

gas from a compartment flows through a hot layer in a second compartment and

is driven by buoyancy (negative) into the lower layer. Quintiere et al.

(1981) discuss this phenomena for the case of crib fires in a single room and

deduce the relation

sa

1 (u->-jO/as

^ 1 (36)

This term is predicated on the Kelvin-Helmholz shear flow instability and

requires shear flow between two separate fluids. The instability is enhanced

if the fluids are of different density since the equilibration distance is

proportional to Vp. A schematic of this type of flow is shown in figure 3.

As can be seen, mixing into the lower layer of a room occurs under the same

conditions for which the "door—jet" mixing to the upper layer occurs.

-20-
4.5 Source Terms: Fire

Currently we can deal with two types of fires. The first is a specified

fire. Then the mass pyrolysis rate is specified and the heat release rate

becomes

q

£ = h>f - cp

(Tu

- T

f

) *

f * Qp4f (37)

whereas the mass loss rate, m^, is related to the pyrolysis rate by

*

v

- i>f = (1 -

Xf)

As the burning efficiency becomes 100%, all of the volatiles are burned, and

nothing remains for sooting. The heat release goes into radiation and

enthalpy flux

QR

(fir e) = XrQj

Q

c (fire) - (1 - XR ) Q

f

.

The term Q^Cfire) then becomes the driving term in the plume flow equation

(see eqns. (33, 34)).

This approach is extended for a pool fire. A pool fire is basically the

same except that it is driven self-consistently by reradiation from the

compartment and the flame itself. From Rockett (1983) we have

- 21 -
( 38 ) conv

where Q = external radiation to the fuel source R

= radiation from the flame back to the fuel

Q

= fuel surface reradiation

KK

Q

conv

= enthalpy flux away from the fire

Qcond

= conductive heat loss from the fuel to the surroundings

4.6 Source Terms: Conduction

Conduction of heat through solids is not a source term in the sense

mentioned earlier. That is, loss or gain of energy from solids occurs by

convective heating, which in turn is influenced by subsequent gain or loss

through the solids. However, as much of the net heat loss from a compartment

occurs through loss to the walls, as well as heating of interior objects, the

form of heat propagation in solids will be discussed here.

The equation which governs the heat transfer in solids is

and is a linear parabolic equation. As such, it must be solved by a different

technique than is used for the ordinary differential equations which describe

mass and enthalpy flux. In order to couple these systems in a reasonable way,

we appeal to the principle of time splitting. Simply stated, we have two

systems of equations which are decoupled as long as the time step used is

short compared to the characteristic time scale for either set of equations.

(39)

-22-
Wall temperatures change and the characteristic time for energy flux through a

solid is characteristically on the order of minutes. By using a time step of

no more than one second the applicability of time splitting is assured.

Currently the model assumes two walls, the upper wall (and ceiling) which

is in contact with the upper layer, and the lower wall (and floor) which is in

contact with the lower layer. A refinement will be to separate the ceiling

and upper wall, and the lower wall and floor. This will be useful since walls

are generally constructed of materials whose thermal properties are different

than the ceiling and floor. A further assumption is that conduction is one

dimensional only. That is, the heat equation is

9T

3t

k_ jfc

PC

3x

2

(40)

and the solid behaves as an infinite slab in the other two space dimensions.

A corollary to this is that the wall in contact with the gas layer changes

temperature instantaneously as the layer interface moves up and down. Such a

formulation is not entirely satisfactory as there is a finite equilibriation

time for the solid. An additional refinement will be to extend this equation

to two dimensions to track the layer as it moves up and down. So far, the

only zone model to attempt to include this effect is discussed by Jones (1983)

and Mitler and Emmons (1981). Even in this case the attempt was made only to

include heat loss from the upper layer as it moves down and comes in contact

with cool lower walls. However, the phenomenon is important, as is discussed

by Quintiere et al (1983), especially as the thermocline in the wall will

influence the direction in which the wall boundary flow propagates.

-23-
Conduction through solids occurs in two places: the compartment walls

and interior objects. The technique used is the same in both cases, although

the boundary conditions on the equation may be different. Generally a slab is

cut into N intermediate slices (N+l nodes). Then eqn. (40) is solved for each

slice. The actual finite difference used is a time centered, implicit scheme

which is symmetric about the nodes. For the interior nodes we have

q[l+nl - j

[T' +1 + T'.J + {t± + |

[T 1+1 - + T^jll (41a)

where

At k_

Ax pc

and for the edge nodes

(41b)

The temperature at the starting time at node "i" is T^ and at time t+6t it

is T^. The number of nodes is chosen to reduce the residual error to some

reasonable value, say less than 1%. Use of N > 20 will improve precision with

no concomitant increase in accuracy. This technique would allow one to use

different constituents for each slab, although such is not done in the current

implementation. Each time step requires both an initial condition and one

boundary condition. We start with the internal temperatures in each case, and

the flux on the "hot" side. The usual scheme is to set the far side boundary

condition to zero heat flux (which allows heat build up in the interior) or to

approximate the far side exterior as a constant temperature bath. Either

-24-
technique is satisfactory unless this far side happens to be the interior

boundary for another compartment.

5 . NUMERICAL INTEGRATION

The problem of the spread of fire, smoke, etc. has been formulated as a

set of differential equations. These equations are derived from the conservation of mass and energy. As a result, most of the equations are non-linear

and first order ordinary differential equations (ODE). The exception to this

rule is the heat conduction equation which is a linear parabolic equation, in

one or two dimensions. The former can be solved using implicit predictorcorrector methods, Conte (1965), and the latter successive over-relaxation

(SOR), Mitchell and Griffiths (1980).

In the numerical implementation, we have relied on the validity of a

technique called time splitting. Simply stated, we have decoupled equations

which have greatly differing relaxation times , that is

1_ dn

n dt n

where varies by more than an order of magnitude for each process. Except

for the driving program which invokes the hydrodynamics, species transport and

thermal conductivity, the various modules which incorporate the physical

processes are exercised separately and interact as source terms. This

splitting technique is standard but the inherent assumptions should be checked

when implementing a new numerical model. In addition, a check should be made

at each time step to insure that the relevant stability criterion (similar to

a Courant condition for fluid flow) is not violated.

- 25-
For both types of equations the solution at each time step is found by an

implicit scheme. The implicit method allows us to implement the numerical

solution as a time centered algorithm. This insures reversibility in the

physical phenomenon, at least for non-diffusive systems. A test of this

assertion is to exclude thermal conduction, integrate from an initial condition to some final time, and subsequently, by changing the sign of the time

step, we should be able to return to the starting position. A time reversal

calculation is an important step in assuring ourselves that the integration

scheme itself is not dissipative and thus will not relax to an incorrect final

state. This is a real property in non-dissipative physical systems and should

be mirrored as closely as possible in a numerical model. When conductivity is

included, such reversibility ceases to be strictly valid, of course.

An additional virtue of the time centered scheme is avoiding the

bifurcation which can occur in pure leapfrog schemes. The disadvantage is the

one additional source calculation required at each time step. This time

appears to be short, however, in comparison with the "corrector" phase of the

implicit scheme.

The order of the integrations is as follows

(1) Estimate the values for pressure, etc. at t + 6t.

(2) Find the source terms for eqns. (22-25) based on the time centered

values (tQ + 1/2 6t).

-26-
(3)

Integrate eqna. (22-25) using the source terms defined at the time

centered positions.

(4) Repeat steps (2) and (3) until convergence is reached.

(5) Integrate the conduction equation using the SOR technique.

The following illustration shows where each of these time-step points is,

in relation to steps (1-5):

(1) tQ

> tQ + St

(2) tQ >X< > tQ + St

(3) tQ > tQ

+ 6t/2 > tQ + St

(4) tQ > tQ + St

(5) t 0

> tQ + St

estimate values at (tQ + St)

find sources at (tQ + St)

integrate from (tQ) to (tQ + 5t/2)

repeat steps (2) and (3)

integrate conduction equation

Since each step is of at least second order accuracy, the overall scheme

3 will also be second order accurate (0(6t )). The relative error allowed at

-3

each time step is ~ 10 . Thus the precision is greater than the precision of

the computer being used (at least as long as these calculations are being done

in single precision).

As for the integration scheme itself, it is derived from an Adam-Bashf ord

backwards difference scheme, Conte (1965), of order k=l. This yields a single

step predictor and second order corrector, 0(6t ). These equations become

"stiff" if the individual source terms are large, which leads to a short time

step, yet the total source function may be tightly coupled if the solution is

-27 -
being approached asymptotically. Another possibility is that the source terms

for the various equations differ by more than an order of magnitude. In

either case, the usual time step criterion would require a time step which is

prohibitively short. It is possible to modify the Taylor expansion used in

obtaining the predictor-corrector scheme to use the asymptotic nature of the

equations to enhance the speed of the solver. Young and Boris (1977).

The general form of an equation is

dn

dt q “ Jin = f.

Using the notation n(0), q(0), £(0), f(0) are the initial values at time (to),

and n(l), q(l), £(1), and f(l) are the values at the new time (tQ + 6t) , we

obtain first for the normal equations

predictor n(l) = n(0) + f(0) (42a)

corrector n(l) = n(0) + (f(0) + f ( 1 ) ) (42b)

and for the stiff equations

predictor n(l) n(0) + ~ 6tJl(0) (43a)

corrector n(l) = n(0) + i+ 6t {jt(oT+ji(T)

' }

' ( f(0)+9( 1 >~A(l)n(0) } . (43b)

-28-
The corrector must be iterated until some specified error criterion i9

reached. If the specified error can not be reached in a small number of

iterations, say two or three, then the time step must be reduced. It turns

out to be advantageous to half the time step for each instance that a reduction is required, and increase it by only 10% for each subinterval that the

error criterion is satisfied.

One technique which has been used in previous work to reduce the solution

time for these equations is to convert them to an algebraic form. The

conversion is done by noting that the final state of the equations at each

timestep is a pseudo equilibrium. Thus the transient term can be dropped.

For a number of reasons, simultaneous ODE’s are generally easier to solve than

the corresponding algebriac equations unless one is exceedingly close to the

solution. Such an assertion is difficult to prove in the general case but two

examples should suffice to indicate the difference in the nature of the root

finding procedure. One of the simplest nonlinear algebraic equation is

A B = C

with A, B, and C being integers. Until recently this nonlinear decomposition

was thought to be unsolvable (in finite time) for an arbitrary value of C.

Also, a straight comparison of this method (embodied in a model) with other

models using the algebraic scheme, has shown a reduction by at least a factor

of ten in the time required for a given calculation. A detailed timing

comparison of several models is given elsewhere, Jones (1982).

-29 -
6. COMPARISON WITH EXPERIMENTAL DATA

The series of tests which serve as a data-base for this analysis are

based on a two-room fire scenario by Cooper et al. (1981) and an ongoing

series of full scale validation tests at the National Bureau of Standards.

The former was a two-room configuration, consisting of a burn (or fire) room

and a corridor. It is referred to as the "Nike Site" in later discussions.

The latter is a three room configuration with the additional room being a

target room for testing high density occupancy, referred to as "Building

205." The geometry of each of these configurations is shown in Table I.

Comparisons between the model and experimental data are for fires of

100 kW. Figures 4 and 5 show the comparison for the Nike Site tests for the

upper layer temperatures in the bum room and corridor, and the interface

height in the corridor. Figures 6 and 7 show a similar comparison to the

current experiments in B205, a full scale facility at NBS. It is apparent

from a comparison of Fig. 4-7 that plume entrainment is estimated very well

but that the door jet entrainment is underestimated. We can see this from the

good agreement between experiment and theory in any compartment which contains

a primary plume whereas in other compartments the predicted temperature is too

high and the layer depth too small in comparison with experimental values.

This underestimation occurs in the regions which McCaffrey (1983) calls the

flaming and far field regions. In the intermittent region, where the results

of McCaffrey (1983) and Cetegen et al. (1982) agree, the entrainment rate

appears to be correct.

-30-
Another factor which gives rise to disparity between theory and

experiment is the assumption, in the model, of known and uniform wall

materials. In the experiments, walls consist of several materials in a

composite such as calcium-silicate board over gypsum. Allowing for these

factors, the agreement seems quite good. As research continues, these

discrepancies will be resolved.

Table I.

Burn Vent Corridor Vent

Depth** 4.3 — 11.1-20.2 — Nike Width 3.3 1.07 2.4 0.95

Site Height 2.3 2.00 2.3 0.15

Area 14.2 2.14 26.6-48.4 0.14

Volume 32.2 - 61.2-112.3 -

Burn Vent Corridor Vent* Target

Depth 2.3 «. 12.2 2.3

Bldg. Width 2.3 1.0 2.4 1. 0/1.0 2.3

205 Height 2.2 1.9 2.4 1. 9/2.0 2.2

Area 5.5 1.9 29.7 1. 9/2.0 5.5

Volume 11.8 - 72.6 - 11.8

Note 1: VI /V2: VI is from corridor

the ambient.

to target room and V2 is from corridor to

Note 2: Lengths are in meters , areas meters.

in square meters and volumes in cubic

-31 -
7. STABILITY AND COMPLETENESS

There are a number of phenomena which are either not included or need

additional work. They are:

1. Wall effect - two dimensional, unsteady heat flow

2. Separation of flow - vents

3. Ceiling jet - transit time

The first refers to the finite thermal inertia of the wall as the hot

layer moves down (or possibly up). There will be a two dimensional thermocline in the wall which differs from that in the compartment. Although this

has only a small direct effect, it can lead to flow along the walls which can

subsequently contribute to contamination of the lower layer. Such effects

become particularly important as the smoke travels further from the fire

source and temperature differentials become small.

The second problem is quite important for asymptotic predictions,

especially near the room of fire origin. Currently we assume that hot gas

mixes with hot gas or cold with cold gas as it traverses a vent. This was a

reasonable approximation while the lower layer was assumed to be ambient. Now

that we calculate the lower layer temperature, we find that the recirculating

gas may have a temperature on the order of the lower layer of the room into

which it enters. A particular example will demonstrate the effect. In a two

compartment calculation, Jones and Quintiere (1983) found that the layer

outside of the burn room is lower than that in the compartment of fire origin.

As there is no source of heat in this second compartment and cooling occurs

-32 -
due to mixing, the upper layer in this adjacent space is cool relative to the

upper layer in the fire room, and even comparable in temperature with the

lower layer. Currently we assume all of the hot gas in the adjacent room,

which flows into the fire room, will be deposited in the fire room upper

layer. As can be seen in figure 8, Evans (1983) this assumption leads to

discrepancies in prediction versus experiment. A better approach is to divide

the incoming flow into two components: for flow into compartment (i) from

compartment (j), we have a component into the upper layer =

' "ui

with the remainder going into the lower layer. This occurs only after' an

interface discontinuity has been established.

T

u1 - T*1

T , - T„, | “j+i *

The third problem will only be important for very long corridors (20 m)

or very tall compartments or shafts. Also, it is only a transient phenomenon.

For purposes of siting smoke detectors, for example, this transient may be

important.

8. CONCLUSIONS

The fire and smoke transport model, as described in this paper, is quite

detailed and complete as far as our current understanding of fire phenomenology is concerned. It draws on a great deal of the research into fires which

have occurred over the past ten years, pulling together much of the best work

which has been done in the field. The numerical implementation is of particular interest because it is extremely durable. The problems discussed in the

section "Stability and Completeness" need to be addressed if we are to carry

this work further, such as to fires in high rise hotels or on aircraft

carriers.

- 33-
9. ACKNOWLEDGMENTS

Two NBS cooperative students, Alicia Fadell and Charles DeWitt have

contributed to this effort. Ms. Fadell was instrumental in implementating the

"BUILD" program which generates the configuration and description files for

the "FAST" model. Mr. DeWitt is responsible for "FASTPLOT", a routine which

enables one to analyze rather easily the extensive output available from

"FAST."

A machine readable copy of the model is available through NTIS. The tape

includes the data file listed in the appendices.

10. REFERENCES

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

University Press, London (1959).

Cooper, L.Y., Harkleroad, M. , Quintiere, J. and Rinkinen, W. (1981), An

Experimental Study of Hot Layer Stratification in Full Scale Multiroom Fire

Scenarios, ASME 81-HT-9, Milwaukee.

Cetegen, B.M. , Zukoski, E.E. and Kubota, T., Entrainment and Flame Geometry of

Fire Plumes, Ph.D. Thesis of Cetegen, Cal. Tech. (1982).

Conte, S.D., Elementary Numerical Analysis, McGraw-Hill, New York (1965).

Evans, D., private communication (1983).

Jones, W.W. , An Improved Numerical Method for Fire Models, Fall Technical

Meeting of the Eastern Section of the Combustion Institute, Atlantic City

(1982).

Jones, W.W., A Review of Compartment Fire Models, National Bureau of Standards

(USA) IR 83-2684 (1983).

Jones, W.W. and Fadell, A., A Device Independent Graphics Kernal , to be

published as an NBSIR.

Jones, W.W. and Quintiere, J.G., Prediction of Corridor Smoke Filling by Zone

Models, Comb. Sci and Tech 1

, 111 (1983).

-34-
Kusada, T., NBSLD, The Computer Program for Heating and Cooling Loads in

Buildings, National Bureau of Standards (USA) BSS 69 (1976).

McCaffrey, B.J., Momentum Implications for Buoyant Diffusion Flames, Comb, and

Flame 52., 149 (1983).

Mitchell, A.R. and Griffiths, P.F., The Finite Difference Method in Partial

Differential Equations, J. Wiley & Sons, New York (1980).

Mitler, H.E. and Emmons, H.W. , Documentation for CFC V, The Fifth Harvard

Computer Fire Code, Home Fire Project Tech. Rep. #45, Harvard University

(1981).

Quintiere, J.G., Steckler, K. and Corley, D. , An Assessment of Fire Induced

Flows in a Compartment, submitted for publication in Fire Science and

Technology (1984 )

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

Conditions in a Room Subject to Crib Fires, First Specialists Meeting

(International) of the Combustion Institute, Talence, France (1981).

Rockett, J.A., Experimental Determination of the Heat Flux to a Burning

Surface, to be published in Fire Science and Technology.

Schlichting, H., Boundary Layer Theory, Pergammon Press, New York (1955),

translated by Kestin, J,

Siegal, R. and Howell, J.R., Thermal Radiation Heat Transfer, McGraw Hill Book

Co., New York (1981).

Steckler, K.D., Quintiere, J.G. and Rinkinen, W.J. , Flow Induced by Fire in a Compartment, Nineteenth Symposium (International) on Combustion (1982).

Tanaka, T., A Model of Multiroom Fire Spread, National Bureau of Standards

(USA) IR 83-2718 (1983).

Tanaka, T. , A Model of Fire Spread in Small Scale Buildings, Building Research

Institute (Japan) RP #84 (1980).

Turner, J.S., Buoyancy Effects in Fluids, Cambridge University Press (1973).

Yokoi, S., Study on the Prevention of Fire Spread Caused by Hot Upward

Currents, Kenchiku Hokoku No. 34 (1960).

Young, T.R. and Boris, J.P., A Numerical Technique for Solving Stiff Ordinary

Differential Equations Associated with the Chemical Kinetics of Reactive

Flow Problems, J. Phys. Chem. 81, 2424 (1977).

-35 -
Appendix A - Notation

O A area (m ); A , A^, A^ are the upper and lower compartment surface areas

in contact with the upper and lower gas layer, fig. (1), respectively.

A^ is the interface area between the upper and lower layers. In

section 4.4, "A" is used as a variable in the flow equations to

indicate air.

B width of a vent (m)

C, C' flow coefficient = 0.6-0. 7 for both smoke and air

c specific heat - Cp, cv

(J/kg/K)

E energy release rate (J/s)

E internal energy of the gases - see eqn. (2)

F^j view factor - relative area of "i" as seen by "j" (dimensionless)

o g acceleration of gravity (9.8 m/ s )

H height (m), H

u , H^, are the upper and lower limits of a vent - fig. (1)

h enthalpy (J/kg/K)

h

c heat of combustion - theoretical (J/kg)

i,j compartment indices

k thermal conductivity (J/s/K)

L mean beam length (m) equivalent opaque sphere

m mass (kg)

m mass flow (kg/s): m^ - rate of release of volatiles

m^ - entrained into a plume

m_ - fuel burning rate = y m

f e v

m^j - mass entering room "i" from room "j"

m - flow rate in plume fm = m + m ) p

v p v e

J N height of the neutral plane (m)

P pressure (pa): P - P - floor reference pressure

P

a - outside ambient pressure

36
rate heat is added or lost (J/s):

Q

- upper, lower zones, respectively

Q- - fire (h m ) c v

•Q

q - objects

Q

- radiation

K

Q

c - convection by walls

Q

- radiation added to upper gas laye

§

- radiation from surface "k"

Q - combustion energy lost by

^ formation of volatiles

gas constant for specific mixture

smoke - section 4.4

time (s)

temperture (k) : T

a - ambient

T

c - external wall

Tu

- upper wall

- lower wall

- reference temperature for enthalphy flow

T - upper zone temperature

oTv

- pyrolysis temperature

O volume (m )

layer thickness (m) - = interface height in compartment (i)

absorption coefficient of upper gas layer (m

-

^), thermal dlffusivity

(m2/ s)

ratio of specific heat (Cp/c

v

)
e emissivity (dimensionless): - surface "i"

e - upper gas layer

S - upper compartment surface

- lower compartment surface

p^ - density of the lower layer in

compartment (i)

O p mass density (kg/m )

< thermal conductivity (j/msK)

6. . Kronecker delta =0 i ^ i J-3 = l i = j

At time step (s)

Ax spatial discretization

Subscripts - In general "u" and "l" Indicate upper and lower gas layer,

respectively. For area and emissivity variables, reference is to

the compartment Itself.
Appendix B

Shown in Table II is a sample Input for FAST. The organization is that

control is at the beginning, followed by component information, connections,

wall properties, a description of the fire, species generation information and

finally file descriptors for graphics and the dump file.

In general, the first word in each line is a key word and must be

included. The explanation of this file will be by example:

Line

12

3

4

5

6

7-10

11-16

17

18-27

28

29

30

31

32

Meaning

version and title

time step information

600 •* number of seconds for the calculation

120 •> print interval

120 •* dump interval (requires files)

l graphics Interval (requires files)

0 hard copy counter

Number of floors - not used with this version,

but retained for compatibility

Total number of compartments

Maximum number of openings between compartments

ambient temperature,

compartment geometry, W x L x H x Floor

(1 -»• NROOM)

connection configuration (outside is compartment

NROOM + 1)

1 number of walls used in the calculation

thermophysical properties of the upper and lower

walls respectively (units are SI except

energy (kj) and power (kW)).

which compartment the fire is in

type of fire (currently only a gas burner is

allowed)

number of intervals for production rate^

interior position of the fire to establish

entrainment rate (l + center)

fuel properties necessary for partial combustion

1.0 fraction of pyrolysis which burns

0.0 -* fraction of water in the fuel

0.750 fraction of carbon in fuel by weight

0.25 fraction of hydrogen in fuel by weight

0.00 + fraction of oxygen in fuel by weight

49758 heat release rate (kj/kg)

300. fuel inlet temperature

0.0 fraction of heat which exits the fire plume

in the lower layer as radiation

^Currently an upper and lower wall are used. This will change shortly to four

walls to reflect the physical difference among the ceiling, walls and floor.

o Figure 9 shows a sample fire production curve.

39
33 mass loss rate at each end point (kg/s),

LFMAX + l e 34 area of the fire at each end point (mz

) 35 height of the base of the flame (m)

36 duration of each time interval (LFMAX)

37-40 fractional production rate of species 3, 7, 9 & 10 J first number is species (1 -* 12)

second number is a conversion factor

third through LFMAX + 3 are fractional production

rates 4

41 termination label (required)

42-44 file descriptors

DISFG = plan view^

CONFG = layer information^

DUMPR = dump file for FASTPLOT

There are two primary output files for the model. The first is binary

(UNIT =9) and is used by the routine "FASTPLOT" described in appendix D. The

other is an ASCII file (UNIT = 6) and usually is displayed on the printer.

Units are SI (MKS) except for energy which is in kJ. The meanings of the

symbols, in the order which they appear, are:

Initial

Timestep Output

TIME

U. TEMP

L. TEMP

U. VOLUM

U. DEPTH

C. TEMP

F. TEMP

EMS

EMP

ADS

QF

QR

QC

Pres mass

reiterate the input parameter, generally in the order

of input

simulated time (s)

upper layer temperature (K)

lower layer temperature (K)

upper layer volume (m^)

vertical thickness of the upper layer (m)

ceiling temperature at the surface (K)

floor temperature (K)

flow into the upper layer from the plume (kg/s)

pyrolysis rate (kg/s) area of the fire (m^)

enthalpy release rate of the fire (kW) to the upper

and lower layer

total radiant energy to the upper and lower

layers (kW)

total convective heating of the upper and lower

layers (kW)

floor reference pressure (pa)

vent flow from i j (kg/s) - sec (section 4.4)

^Species 1-12 are N

2

, O

2

, CO2

, CO, HCN, HCL, ThHC, ^0, smoke density, total %

LC^q, smoke number density and HCL number density.

^Fraction of the mass burning rate at the corresponding endpoint (see line 33

and figure 9).

“’Format for the graphics files is given in the NBSIR by Jones and Fadell.

40
Species concentrations listed by species

mass M/V

PPM

PPM-M

total mass of that species in the layer (kg) mass per unit volume multiplied by the conversion

factor shown in line 37-40 of the input fuel.

Unity leaves this value in (kg/mJ ).

parts per million of the total molecules present

dosage which is an integral of (PPM) over time

(PPM - minutes)

Table II

1 - 2 - 3

- 4

- 5 - 6

78

9

• 10

1112 • 13

14

15167

.81920

l

24

25

262728

2930

3132

33

34

3536

37

38

3940

4142

4344

VERSION 15 Tlraesteps NFLOR

NROOM

NMXOP TAMS HI/F WIDTH

DEPTH HEIGH

HVENT

HVENT

HVENT HVENT

HVENT

HVENT

• WALLS

- COND SPHT

- DNSTY THICK

- EMISS

- COND

- SPHT

- DNSTY

- THICK

- EMISS

- LFBO

- LFBT

- UMAX

- LFPOS

Toxic hazard evaluation

600 120 120 1 0

1 NUMBER OF FLOORS IN THE CALCULATON

5 TOTAL NUMBER OF ROOMS

l 300.0.0 0.0 0.0

3.3 2.4 2.9

4.3 18.8 9.9

2.3 2.3 2.3

l

0.0

2.4

18.8

2.3

23

64

6

5

0.0

2.4 9.9

2.3

1.07 1.07 0.95

1.07

.95 1.07

0.0

3.3 4.3

2.3 2.0

2.0

.15 2.0

.10 2.0

2

3

24

2

2.0012 .0012 .0012 .0012

.840 .840 .840 .840

2000. 2000. 2000. 2000. 0.50 0.50 0.50 0.50

0.8 0.8 0.8 0.8

.0012 .0012 .0012 .0012

.840 .840 *840 .840 2000. 2000. 2000. 2000. 2000. 0.50 0.50 0.50 0.50

0.8 0.8 0.8 0.8

1 ROOM OF FIRE ORIGIN

l TYPE OF FIRE (GAS BURNER)

6 NUMBER OF INTERVALS FO FIRE GROWTH

l POSITION OF THE FIRE (CENTER)

0.0

0.0

0.0

0.0 0.0

0.0

.0012 .840 2000.0.50

0.8

1.0 - FMASS .002

- FAREA .5

- FH1GH .0 - FTIME 60. - SPECI 3 1.0

- SPECI 7 1.0 - SPECI 9 3500.

- SPECI 10 31.2

- ENDSP

- DISFG NIKE 13A. DAT

- CONFG NIKE13B.DAT

- DUMPR TOXIC. DMP

0.0

.002

.5.0 60.

1.0.025

.02

1.0

.750

.002

.5.0

.250

.002

.5.0 60. 60.

1.0.025 .02 1.0

1.0.025

.02

1.0

.0012

.840

0.50

0.8

.00 .002

.5

.0 60.

1.0.025

.02 1.0

49758

.002

.5

.0

60.

1. 0

.025

.02 1.0

300. .002

.5

.0

1.0.025

.02 1.0

.0

1.0.025

.02

1.0

^This conversion factor allows the user to

density, LC^q or whatever.

convert this output to an optical

41
Appendix C

The program BUILD is used to construct data files for configuration

display. These files can then be used by FAST to display a decision tree

either interactively or as a graphics streaming file. Both the configuration

file for display as well as information on position and type of display for

the decision tree are built by this program. The commands are:

ADD [VERTEX, EDGE, POLYGON] (default = VERTEX)

add vertex - create vertices by specifying three (x, y, z) coordinates;

add vertices to the work file

add edge - create edges by specifying two vertices; add edges to work

file

add polygon - create polygons by correcting vertices. A minimum of three

vertices are required to define a polygon, and there is an internal maximum specified by NPVERT.

DELETE [VERTEX, EDGE, POLYGON] (default = VERTEX)

delete vertex - delete vertices and any edges or polygons which are connected to the deleted vertices

delete edge - delete edges

delete polygon - delete polygons

DISPLAY [ALL, VERTEX, EDGE, POLYGON] (default = ALL)

display all - display all edges and polygons in graphics mode

display vertex - display all vertices and their line numbers in graphics

mode .

display edge - display all edges in graphics mode

display polygon - display all polygons in graphics mode

DUPLICATE

Duplicate a polygon at another location - askes for a displacement vector.

END

End the program.

ERASE

Erase the display screen.

42
GET [filename] (default = INFILE)

Open an existing file and assign the filename to INFILE; the elements of

this file make up the new work file.

HELP

List all the BUILD commands, their corresponding options, and the default

values.

LIST [VERTEX, EDGE, POLYGON] (default = VERTEX)

list vertex - list the world coordinates, window coordinates, and the

vertices of the work file on the display screen

list edge - list the edges of the work file on the display

list polygon - screen list work file's polygons on the display screen

MOVE [VERTEX, POLYGON] (default = VERTEX)

move vertex - move a vertex from its present location to a new

location - asks for a displacement vector

move polygon - move a polygon from its present location to a new

location - asks for a displacement vector

PRINT [ALL, VERTEX, EDGE, POLYGON] (default = ALL)

print all - list the work file's world and window coordinates,

vertices, edges, and polygons on the printer

print vertex - list the world coordinates, window coordinates, and

vertices of the work file on the printer

print edge - list the work file's edges on the printer

print polygon - list the polygons of the work file on the printer

SAVE [filename] (default = OUTFILE)

Save the current file under the specified filename; assign the filename to

OUTFILE.

STATUS

List the filenames stored in INFILE and OUTFILE; indicate the current

number of vertices, edges, and polygons and the maximum number of each

element allowed.

WINDOW

Create the work file's window space by specifying minimum and maximum x and y coordinates for display. Defaults to WORLD.

43
WORLD

Create the work file's three-dimensional world space by specifying x, y,

and z coordinates. All structures must be contained in this cartesian

coordinate system.

44
Appendix D

' 4 HV

FASTPLOT is a data analysis program which runs in conjunction with

"FAST." The results for "FAST" are dumped to a data file after each

prescribed desired time step. FASTPLOT has the capability to form a list of

variables, read in their values at each time interval, list out the values in

tabular form, graph the values (hard copy or screen), and save the variables

in a file for future reference.

The FAST model models a fire in one of several compartments, or rooms,

and follows smoke and toxic gases from one compartment to another. We are concerned with variables in both the upper and lower layers.

The list of variables presently available through FASTPLOT are:

AREA burning area of the fire (m )

CONCENTRATION species density in parts per million

CONVECTIVE heat loss from layer to solid surface due to

convection (kw/mz

)

DOORJET bouyant mass flow through a vent (kg/sec)

DOSE species concentration integrated over time

(ppra-min)

ENTRAINED mass entrained by a plume (from lower layer to

the upper layer)

INTERFACE height of the two-zone discontinuity (m)

MASS mass density in a layer (kg/m )

MDOTFIRE mass loss rate of the fire source (kg/sec)

NEUTRAL n

NEUTRAL 2> neutral planes (maximum of three) for each vent

NEUTRAL 3)

PLUME total mass flow into the plume (kg/sec)

PRESSURE reference pressure at the floor of the

compartment (pa)

QC total convective heat gain by a layer

QF total enthalpy increase from the fire source

QR total radiative heat gain by a layer

RADIATION heat loss from layer due to radiation (kw/m^)

TEMPERATURE temperature of the layer (C)

45
VENTFLOW mass flow through a vent (kg/sec) - bidirectional

O VOLUME volume of the upper zone (m )

WALLTEMP temperature of the wall (C)

The CONCENTRATION, DOSE, and MASS also have associated with them a species number.

The main control of the program is carried out in the subroutine

WHICHONE. It does the actual building of a list and the processing of the

options. The possible options available to the user are:

ADD

CHANGE

CLEAR

DEFAULT

DELETE us* END

HELP

LIST

PLOT

REVIEW

SAVE

Upon running the program, the first input encountered will be that of the

dump file generated by FAST. Most of them will be of the form:

f ilename .DMP

Next, the user will be asked to input the option which he wishes to have

performed. The following is a description of each of the options available.

They are in the order that they usually will be encountered. However, some may be executed before the others without any problems. The minimum number of

characters required to recognize an option is enclosed in the parenthesis at

the beginning of each word.

1. (DE) FAULT

This enables the user to set his own default parameters for the

following

COMPARTMENT #

VENTFLOW DESTINATION

LAYER

SPECIES #

CHARACTER SET FOR PLOTTING

This option may be done at any time and if it is not done the defaults

are set to "l, 2, upper, 9, and 4", respectively. The purpose of this option

is to change the defaults available for other commands and data input.

46
2.

(VA)RIABLES

The purpose of this option is to allow the user to recall the possible

variables that are available for use. They will be listed on the screen.

3.

(AD)D

This command is used to build a list of variables. When an option is

requested ADD may be entered by itself or together with a list of variables

that are to be added. If it is entered alone a message will be printed asking

for the variables that are to be added to the list. For example:

> ADD

- INPUT VARIABLES TO BE ADDED > or

> ADD TEMP, PRES,

For each variable selected there is a series of questions that will be

asked as to the type of that variable wanted. Questions asked about all

variables are:

WHICH COMPARTMENT? -> WHICH LAYER? ->

If VENTFLOW is chosen the compartment origin and destination will be

requested; if CONCENTRATION, MASS, or DOSE are selected the species number of

each will be requested.

The maximum number of variables allowed on the list at any one time is

25. If the list is full or the variable is presently on the list the addition

will be disallowed and another option requested.

4.

(DEL)ETE

When this option is entered the present list of variables will be printed

out to the screen and the user will be asked to input the variables to delete

by the number associated with them on the list. They must be entered on a single line separated by commas or blanks.

If the variable number that is input does not correspond to one that is

currently on the list it will be skipped. After the deletions have been

processed a new list is presented and another option requested. If the list

is presently empty then that fact will be stated in an error message.

5.

(HE)LP

This command may be input at any time that the user is asked for an option. It's purpose is to simply list out to the console a list of the

available commands and a brief explanation after which another option will be

asked for.

47
6.

(RE)VIEW

At times the user may wish to see what is presently on his list before

entering a command. This may be done with the REVIEW command. It will print

out the current list along with the compartment number, species, and layer of

each of the variables. After the printing of the entire list the option

request is again displayed.

7. (LI)ST

After variables have been added to the list and their data values read

in, the user may list out the values of any of the variables on the list to

either the printer or the console. The user will input the device number

(5 = CONSOLE, 6 = PRINTER), and the list of variables presently on the list

will be displayed. He will then be asked to input the corresponding number(s)

of the variable(s) to be listed out. They must be entered on a single line

separated by commas or blanks. The maximum number of variables able to be

listed at one time is 8 for the printer and 5 for the console.

8. (PL)OT

This option is central to the data analysis. After entering this command

the current list of variables will be displayed along with their numbers. The user will be asked to input the number of the variable(s) to be plotted from

the list. They should be entered in a string separated by a comma or a blank

space. For example:

ENTER VARIABLES TO BE PLOTTED -> l, 2, 3,

or ENTER VARIABLES TO BE PLOTTED ->1234

After entering the variable numbers, the number of the device which the

graph is to be plotted on will be asked for.

The possible devices are:

1 . CALCOMP

2. PRINTER

3. LEXIDATA

4. SCREEN

The maximum number of plots per call to PLOT is limited to 4. They will

be printed in the following order on the device depending on the number of

graphs per page:

l 2 1 2 3 4 3

FOUR THREE

48
l 1 2

TWO ONE

If more than 4 variables are input only the first four will be accepted

and the remaining ones disregarded. If a variable number not on the list is

entered, an error message will appear, the list will be reprinted and the

input will be asked for again. This will continue until all variables entered

are currently on the list.

Before the graphing is done the user is given the opportunity to change

the range of the X and Y axes. The maximum and minimum values of the X and Y axes will be displayed, followed by a request for a change in each, which will

be of the form:

CHANGE (X or Y) AXIS TO? ->

If no change is desired simply enter a <RETURN> and the next axis change

will be displayed. If a change is made the value will be entered and the same change request will be made again. This will be repeated until a <RETURN> is

entered.

When all the changes have been made, if any, the graph of that particular

variable will be plotted. After it has been completed the next variable's

maximum and minimum will appear and their changes input as before.

After the final graph has been completed the option request will be

displayed and a new option may be entered.

9. (SA)VE

This option allows the user to save the values of the variables on the

list in a file. The format used will make the data compatible with an experimental data processing program designed for handling of data in the Center for

Fire Research.

The user will be asked for the name to be used for the file. A check

will be made to see whether that file presently exists or not. If it does the

user will be asked if he wants to write over the old file with this new data.

If his answer is NO, nothing will be placed in the file and another option

requested. If, however, he does want the file rewritten, or the file does not

already exist, the new file will be created and the data stored in it.

Each variable on the list will be dumped with the following format at the

beginning of each block of data:

16 , 16 ,A6 , * COMMENT

The first 16 will be for the number of data points for that variable, tie- next 16 is for the number given to that variable on the list, and the A6 Is for the actual variable name. Everything after the * is a comment block and

will be filled with information relevant to that particular variable, such

49
things as species number, compartment number, layer, etc. The actual

numerical data will be dumped using the format 7E11.5.

10. (CL)EAR

The input of this command empties the variable list.

1L. (CH)ANGE

This option restarts the program by asking for a new file and resetting

all variable lists.

12. (EN)D

This function terminates the execution of the FASTPLOT program.

50
Surface

1

51
52
H3H Z

(0

53
TEMPERATURE

(

K)

Nike site 100 kW

TIME (s)

54
INTERFACE

HEIGHT

(m)

55
205

Corridor

100

kW

o o o

o o

CM t-

(Oo) 3UniVH3dlAI31 H3AV1 H3ddD

56

900

1800

TIME

(s)
(W) 1H9I3H 30Vdy31NI

57

TIME

(s)
140

120

100

80

60

40

20

0

—Expt.

Model

50 kW Steady Fire

10 20 30

TIME (min)

58
1x10“*- A

sample

fire

interval

(1^

-I5)

production

curve

which

requires

six

end

points

(E-|-Eg)

/VSee

Appendix B

TIME

(s)
O*) 3UniVU3dN3I U3ddD

60

TIME

(s)
hbs-m *a;. ?ev. «.»qi

2. Performing Organ. ReportNo^ i. Publication Date September 1984

U.8. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBSIR-84-2934

4 . TITLE AND SUBTITLE

A Model for the Transport of Smoke, Fire and Toxic Gases (FAST)

5. AUTHOR(S)

Walter W. Jones

6. PERFORMING ORGANIZATION (If joint or other than NBS. see instructions)

national bureau of standards

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8 . Type of Report & Period Covered

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

10. SUPPLEMENTARY NOTES

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

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

bibliography or literature survey, mention it here) a. numerical implementation of a zone model which

will transport fire, smoke and toxic gases in a multi-compartment structure is

described. The areas covered are the equations which are solved, the numerical

technique for the solution of these equations, species transport and the other

relevant physical phenomena which govern fire growth and spread, and the transport

of smoke. Also included in the model are the calculations necessary for a toxic

hazard evaluation of a structure with a specific material loading. Forced ventilation is not yet included (version 15)

.

A machine readable copy of the model (FAST) is available through NTIS. The tape

includes the data file listed in the appendices of this report.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semico on-.

Fire growth; mathematical models; smoke spread; toxic hazard; zone models.

13. AVAILABILITY

QX] Unlimited

| | For Official Distribution. Do Not Release to NTIS

[~j Order From Superintendent of Documents, U.S. Government Printing Office. Washington, D.C.

20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

15. Pr.c«

j ICOuu- • 04 »