NBSIR 87-3657

A Computer Mode! of Smoke

Movement by Air Conditioning

Systems (SMACS)

John H. Klote

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1987

Sponsored by:

General Services Administration

Public Buildings Service

Office of Real Property Development

Buildings Technology and Standards Division

Washington, DC 20405

NBSIR 87-3657

A COMPUTER MODEL OF SMOKE

MOVEMENT BY AIR CONDITIONING

SYSTEMS (SMACS)

John H. Klote

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Gaithersburg, MD 20899

November 1987

Sponsored by:

General Services Administration

Public Buildings Service

Office of Real Property Development

Buildings Technology and Standards Division

Washington, DC 20405

U.S. DEPARTMENT OF COMMERCE, C. William Verity, Acting Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

LIST OF FIGURES iv

1. INTRODUCTION 1

2. AIR CONDITIONING SYSTEMS 2

3. CONCEPT OF SMACS ..... 6

4. TOTAL MASS FLOW 8

5. SMOKE TRANSPORT 9

6. FAN FLOW 10

7. EFFECTIVE RESISTANCES 11

8. STRAIGHT DUCTS 12

9. OTHER RESISTANCES 13

10. JUNCTIONS 14

11. SMACS LOGIC 16

12. FUTURE DIRECTION 16

13. REFERENCES 18

14. NOMENCLATURE 19

iii
LIST OF FIGURES

Figure 1. Residential Air conditioning system 3

Figure 2. Constant volumetric flow, single control zone system 3

Figure 3. Constant volumetric flow system with terminal reheat 4

Figure 4. Variable air volumetric (VAV) flow system 4

Figure 5. Dual -duct system 5

Figure 6. Network representation of residential system 5

Figure 7. Diagrams of converging and diverging junctions 15

Figure 8. Flow chart of SMACS model 17
A COMPUTER MODEL OF SMOKE MOVEMENT BY AIR CONDITIONING SYSTEMS (SMACS)

John H. Klote

Abstract

A computer model for simulation of smoke movement through air

conditioning systems is described. A brief overview of air conditioning

systems is presented. The methods of calculation of mass flow, smoke

transport, fan flow and duct and fitting resistances are presented along with

a general description of the program logic.

Key words: air conditioning, computer models, duct, fans, smoke

control, smoke movement.

1 . INTRODUCTION

There is much concern within the fire protection community regarding the

hazards of smoke transported through air conditioning systems. These system

are capable of moving smoke to locations remote from a fire and thereby

endangering life. The Center for Fire Research (CFR) of the National Bureau

of Standards is developing a computer model to predict the quantity of smoke

transported by an air conditioning system which will help in evaluating the

hazards due to smoke distributed by these systems and should be useful in

evaluating the impact of the air conditioning system on fire growth and

development. In similar models, Greuer [1] has developed a model simulating

smoke transport by mine ventilation systems, and Bolstad, et al. [2] have

developed another model particularly for nuclear facilities. However, an unique feature of the code under development at CFR is that it is intended to

be a part of a larger model predicting smoke movement throughout a building.

The code is called the model of Smoke Movement by Air Conditioning Systems

(SMACS). The term 'air conditioning' is used in the broadest sense to include

heating, ventilating and cooling. SMACS is modular in that it has been

developed with the idea that it could be incorporated into any multi-room fire

1
model, and it can be run by itself without a fire model. It is planned that

SMACS will be incorporated into a future version of the FAST model [3].

Further, the model can be used to simulate the flow of any airborne

contaminate through an air conditioning system. Thus it could have

application in the area of indoor air quality.

2. AIR CONDITIONING SYSTEMS

It is to the credit of the air conditioning industry that most people can take

their systems for granted. For this reason, a brief overview of these systems

is provided for background information. More detailed information about these

systems is available from the American Society of Heating, Refrigerating and

Air-Conditioning Engineers (ASHRAE) [4]

.

The industry classifies air

conditioning systems into three types: all water systems, air and water

systems and all air systems. The all water systems are not of much concern

with regard to smoke transport. In most cases, the air portion of air and

water systems can be regarded as all air systems for purposes of smoke

transport analysis. Thus, the all air systems are of primary concern in the

context of this paper. Figure 1 is a representation of a residential system.

In this example return air from the living quarters is drawn in at one location, flows through filter, fan and coils, and is distributed at several

locations throughout the residence.

Residential systems do not have the capability of providing fresh outside air

needed for ventilation, and traditionally it has been considered that

residences get sufficient outside air by infiltration through leakage paths in

walls and cracks around windows and doors. The system illustrated in figure 2 for commercial buildings is probably the simplest system capable of providing

ventilation air. All the spaces served by this system can be thought of as a single control zone because one thermostat (possibly in combination with a humidistat) control the temperature (and humidity) of the air supplied to the

zone. Figure 3 shows a system which has a reheat coil arrangement to allow

control for several zones. The energy conserving system of figure 4 has a

2
Cooling

Coil

Heating

Coil

I I I I

Supply Air

Return 1

Air

Fan Filter

Figure 1. Residential Air conditioning system

3
Exhaust

Figure 3. Constant volumetric flow system with terminal reheat

Figure 4. Variable air volumetric (VAV) flow system

4
Figure 5. Dual-duct system

R6

Figure 6. Network representation of residential system

5
variable flow rate fan arrangement which allows for multiple control zones. The system illustrated in figure 5 has both hot and cold air ducts, and mixing

boxes provide the required flow rates to maintain conditions in many zones.

The systems addressed here are all general categories, and for each there are almost limitless variations of added, deleted or rearranged components. A

common arrangement is to have one or more all air systems serving the building

interior, and to have all water or air and water system serve the perimeter

spaces of the building. In addition, different spaces like theaters, shops,

offices and kitchens have different needs. Thus, many buildings have more

than one air conditioning system.

It is obvious that an air conditioning model should be capable a simulating an almost limitless number of systems, and of simulating one or many systems in a building. The model described in the paper is modular and has the flexibility

to accomplish this.

3. CONCEPT OF SMACS

The air conditioning system is represented as a network of nodes each at a specific temperature and pressure. The nodes may be connected by fans, ducts,

fittings and other components. Except for fans, air flows through these

components from nodes of higher pressure to nodes of lower pressure. For

example, the residential system illustrated in figure 1. is represented in

figure 6 as a network of six resistances and a fan. These resistances

incorporate all the resistance to flow between nodes. For instance, the

equivalent resistance, R1

, between nodes 1 and 2 accounts for resistances of

the inlet, duct, filter and connection to the fan. For a given (short) time

interval, pressures at the exterior nodes (nodes 1, 6, 7 and 8) are all

supplied to SMACS by the main program. Because node 1 is an inlet to the air

conditioning system, the temperature and concentrations of gases at this node

are supplied by the main program. The model SMACS solves for the pressures at

the interior nodes (nodes 2, 3, 4 and 5) and then calculates the mass flows,

temperatures and concentrations throughout the air conditioning system.

6
The SMACS model is based on the following assumptions:

• the total mass flow through the system is quasi - steady

,

• smoke movement within a duct behaves like plug flow,

• heat transfer to air conditioning components is

insignificant with respect to the heat of the fire,

• the duct system is assumed to be perfectly insulated.

It is believed that the total mass flow through an air conditioning system is

generally a very weak function of the pressures produced in a building fire.

The considerable extent of leakage areas in residential and commercial

construction is well known, and therefore, the pressures due to the expansion

of gases in fires is not a concern for such construction. For a residential

system, the pressure across the fan is on the order of a 500 Pa, the

volumetric flow is on the order of 1 m

3 /s , and the slope of the fan curve is

about 1000 Pa per m

3 /s . Thus it would seem that the pressure difference due

to buoyancy of hot fire gases of about 20 Pa would have a maximum effect on

the total flow rate of the system of about 2 %. Typically, air conditioning

systems in commercial buildings operate at larger flow rates and pressure

differences, therefore, these systems are effected by fire produced pressures

less than residential systems. This supports the quasi-steady assumption for

air conditioning systems that serve a large area such as an entire residence

or a commercial building. Of course, research is needed to determine the

actual extent of applicability of the quasi-steady assumption. Obviously,

this assumption is not appropriate for small fan powered systems serving only

one tightly constructed space in which there is a fire. Another model is

being developed for this application.

In this paper, the term "smoke" is used in accordance with the ASTM [5] and

NFPA [6] definition which states that smoke consists of the airborne solid and

liquid particulates and gases evolved when a material undergoes pyrolysis or combustion. All the gases and particulates entering a section of duct flow

through it like a plug and leave the duct after some time has passed. The air

conditioning system is divided into control volumes, one for each effective

resistance and fan. Even though the total mass flow rate is considered quasi7
steady, transient calculations of temperatures and concentrations are made for

each control volume.

Neglecting heat transfer to the air conditioning system components is

appropriate for this model, because temperature differences due to the air

conditioning system are on the order of 20 °C, while those of interest in a fire are at least an order of magnitude greater. Simulating perfectly

insulated duct systems is supported by the fact that almost all ducts in

commercial buildings are very well insulated for energy conservation. In the

future the model may be extended to include uninsulated duct.

4. TOTAL MASS FLOW

The mass flow rate, mi ^

, to node i from node j can be expressed as a function

of the difference in pressure , Pj -Pi, between the two nodes.

mij - mij < P

j

- P i> < 1)

The form of the function depends on the type of connection between the two

nodes as will be discussed later in detail. The conservation of mass equation

for node i can be written as

2 mij =0 ( 2 )

j

By substitution of eq. (1) into eq. (2) and expressing in terms of pressure, a system of equations can be obtained for all n nodes.

8
fi(Pi,P2 , , pn ) =0

fi (P 1 ,P2

, ... , pi( ... , pn ) = 0 (3)

fn(Pl-P2

. ••• • *n> = 0

Thus the air conditioning system pressures, P k to Pn , are solved

simultaneously by solving n number of mass balance equations. The number of

pressures included in each equation fA = 0 are only P k and those of the nodes

directly connected to node i. Because the form of the functions m^CP^ - P k

)

are nonlinear, a Newton-Raphson method was employed for solution.

5. SMOKE TRANSPORT

Each section of duct is considered a control volume. Air enters a control

volume at time, t, and leaves at time, t + td , where td is the travel time.

The concentration of gas in the air leaving at time, t + td , equals the

concentration that entered at time, t. This is expressed as

Cko (t + td ) = Cki (t) (4)

where Cko and Ck

are the concentrations of gas k at the control volume outlet

and inlet respectively. For a control volume of uniform cross section, the

travel time is L/V where L is the duct length and V is the average velocity

9
through the duct. The average velocity is defined as V = m/pA where m is the

total mass flow rate through the duct, p is the density of the gas in the duct

and A is the cross sectional area of the duct. For a control volume made of

sections of ducts of various sizes, the total travel time is the sum of the

travel times for each duct (td = X /Vk for k = 1 to number of ducts). For

perfectly insulated duct, temperatures are handled in the same manner as

concentrations. This is similar to the approach that Greuer uses to model

smoke transport in his mine ventilation model.

6 . FAN FLOW

Fan manufacturers routinely provide typical data of volumetric flow rates

through fans at various pressure heads across the fan. This data is either in

tabular or graphical form. As indicated by Jorgensen [7], the use of a

polynomial form of fan curve is common within the industry. The SMACS model

simulates fan flow by the polynomial

Q

= B0 + B x X + B2 X

2 + . . . + Bn X

n (5)

where Q is the volumetric flow rate and X is the pressure difference or

pressure head across the fan. The coefficients can be entered as data or

calculated by least squares regression from flow and pressure data. For

incompressible fluids, eq . (5) is independent of temperature and pressure.

For fan data at 20 ° C, compressibility effects amount to an error of about 6

% at a temperature of 200 °C. For this first order model compressibility is

neglected

.

10
7. EFFECTIVE RESISTANCES

The resistance, R, of a flow element can be defined as

rap

R = — (6) m

where AP is the pressure loss through the element corresponding to a mass flow

rate, m. To reduce computation time, the conductance, G, is used in the SMACS

model (G = R~ 1 and m = G (AP) % ). The effective resistance between two nodes

is always positive, however, sometimes one of the resistances between nodes

can be negative as will be explained later. To account for this, R = K* is

substituted into eq. (6) to give AP = Km2

. The total pressure loss, APt ,

from one node to the next is the sum of the losses, AP, , through each flow

element, i, between the nodes.

APt = S AP, (7)

i

The effective value, Ke

, relates the total pressure loss to the mass flow rate

as APt = Ke m

2

, and K, relates the pressure loss through element i as AP, =

K, m

2

. These pressure losses can be substituted into eq. (7), and canceling

like terms yields

Ke = S K, (8)

i

Values of K, are calculated for each element using equations developed later

11
in the paper, and K0 is calculated by eq. (8). The effective conductance is

calculated byJ G = K e e

8 . STRAIGHT DUCTS

For a straight section of duct with constant cross sectional area, the

Bernoulli equation incorporating pressure loss, APf , due to friction is

commonly written

p i “ p2 = APf + P S(Z2

- Z i> (9)

where the subscripts 1 and 2 refer to the duct inlet and outlet respectively,

P is pressure, Z is elevation, g is the acceleration due to gravity, and p is

the density of the gas. The pressure los due to friction is expressed by the

Darcy equation,

L pV2 AP f = f (10)

D e 2

where f is the friction factor, L is the duct length and De is the effective

diameter of the duct. The commonly used hydraulic diameter concept is not

used because more accurate relations have been developed specifically for

rectangular duct by Huebscher [8] and for oval duct by Heyt and Diaz [9].

Using the definition of V, equations (9) and (10) can be expressed in terms of

a duct conductance, G, as

12
- p t + pg(Z. - zt

) ( 11 )

and

2pD,A2 K = G' 2 =

f L

( 12 )

where A is the cross sectional area of the duct. The friction factor can be

evaluated by the Colebrook equation

1

2 L°g10

€ +

3.7 De

2.51

(13)

where Re is the Reynolds number (VDe /u where u is the kinematic viscosity) and

e is the roughness of the inside surface of the duct. The ASHRAE handbook of

fundamentals [10] lists values of e for common duct materials and

constructions. Equation (13) can be solved for f by the Newton-Raphson

method.

9. OTHER RESISTANCES

The pressure loss, AP, through many other elements can be expressed as pV

AP = C_ (14)

13
where VQ is the average velocity at cross section o within the element, and C o

is a local loss coefficient. This equation is commonly used for inlets,

outlets, duct contractions and expansions, heating and cooling coils, dampers,

bends and many filters. For a large number of these elements, values of CG have been empirically determined and are tabulated frequently as functions of

geometry in handbooks [10 - 12]. Manufacturers literature also contains some

values of C o

. Equation (14) and the definition of V can be used to obtain the

following expression of K:

(15)

where A0 is the area at cross section o.

10. JUNCTIONS

Junctions may be either converging or diverging as illustrated in figure 7.

For network representation, a node is located at cross section c of a

junction. The pressure losses in the main section depends on the flow in it

and on the flow in branch, and the loss in the branch depends on both the flow

in it and in the main. The pressure loss in the branch is expressed as

P

b (16)

and the pressure loss in the main is

PS (17)

14
Main Main

Converging Junction Diverging Junction

Figure 7. Diagrams of converging and diverging junctions

where C c b and C c are local loss coefficients, P, p, and V are pressure,

density and average velocity at cross sections b, c and s as illustrated in

figure 7. Local loss coefficients for many junctions have been experimentally

evaluated, and they are tabulated as functions of geometry and various flow

ratios in handbooks along with values of Co

. Converging junctions may have

negative local loss coefficients. For example when the flow in the main is

much greater than that in the branch, the gas in the branch is pulled by the

greater flow similar to the operation of a carburetor. As was done for the

other elements, an expression for K in the branch is

K

Pr. Cc c , b

2Pb

2 \

Pb\

l PcK

P s Vs A

Pc\ A

( 18 )

15
and for the main is

rp c Cc f p A , s s Pb ^b ^ K + (19)

11. SMACS LOGIC

Figure 8 is a flow chart of the SMACS model. The first time through SMACS,

data describing the air conditioning network is read, and arrays are set up

and temperature and concentrations are initialized. The effective

conductance, Ge , for each resistive connection between nodes is calculated

using rough estimates of the flows. The system of equations (3) is solved

using the approximate values of G0

. Because the initial values of flow are

rough, multiple iterations are required to solve the system. The improved

flows are calculated from the solution pressures . The process of calculating

G 0

'

s

and solving the system of equations is repeated until two or less

iterations are needed to solve the system. These flows are then used to

calculate concentrations and temperatures.

A users manual and a program manual for the SMACS need to be developed.

Experiments will be conducted to evaluate the smoke transport predictions of

the model. Further, the need has been identified for a model of Smoke

Movement through Air-Fan Systems (SMAFS) . SMAFS would be a model of a system

12 . FUTURE DIRECTION

16
Figure 8. Flow chart of SMACS model

17
consisting of only one fan and one effective resistance. This simple system

is used extensively in buildings, and SMAFS would be developed to simulate it

with computational efficiency beyond the capability of SMACS . These

subroutines will be used within fire models to study the interaction between

air conditioning systems and smoke movement.

13. REFERENCES

[1] Greuer, R. E., Modeling the Movement of Smoke and the Effect of

Ventilation Systems in Mine Shaft Fires, Fire Safety Journal, Vol. 9, 1985,

pp . 81-87.

[2] Bolstad, J. W. , Krause, P. K. , Tang, P. K. , Andrae , R. W. , Martin, R. A.

and Gregory, W. S., FIRAC - A Computer Code to Predict Fire Accident Effects

in Nuclear Facilities, Proceedings of the CSNI Specialist Meeting on Interaction of Fire and Explosion with Ventilation Systems in Nuclear

Facilities, Los Alamos National Laboratory, Los Alamos, NM, Oct 1983, pp . 211-

230.

[3] Jones, W. W. , A Model for the transport of fire, smoke and toxic gases

(FAST), Nat. Bur. Stand. (U. S.), NBSIR 84-2934, 1984.

[4] ASHRAE Handbook - 1984 Systems, American Society of Heating,

Refrigerating and Air-Conditioning Engineers, Atlanta, GA, 1984.

[5] Annual Book of ASTM Standards, Part 18, ASTM E176-80, American Society of

Testing and Materials, Philadelphia, PA, 1980.

[6] Standard for the Installation of Air Conditioning and Ventilating

Systems, NFPA 90A-1985, National Fire protection Association, Inc., Quincy,

MA, 1985.

[7] Jorgensen, R. , Fan Engineering - An Engineering Handbook, Buffalo Forge

Co.

,

Buffalo, NY, 1983.

[8] Huebscher, R. G., Friction Equivalents for Round, Square and Rectangular

Ducts, ASHVE Transactions (renamed ASHRAE Transactions), Vol. 54, 1948, pp

101-144.

[9] Heyt, J. W. and Diez, J. M. , Pressure Drop in Flat-Oval Spiral Air Duct,

ASHRAE Transactions, Vol. 81, Part 2, 1975, p 221.

[10] ASHRAE Handbook - 1985 Fundamentals, Chapter 33 Duct Design, American

Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA,

1985.

18
[11] HVAC Duct System Design, Sheet Metal and Air Conditioning Contractors'

Association, Inc., Vienna, VA, 1981.

[12] Bevirt, W. D., Environmental Systems Technology, Chapter 6 Air

Distribution Systems, National Environmental Balancing Bureau, Vienna, VA,

1984.

14 . NOMENCLATURE

A area

C local loss coefficient

D effective diameter e f friction factor

G duct conductance

g gravitational acceleration

K square of duct resistance

m mass flow rate

P pressure

Q volumetric flow rate

R duct resistance

T temperature

V average velocity

Z elevation

AP pressure loss

e roughness of interior duct walls

p density

Subscripts

b section b

c section c

e effective

f friction

o section o

s section s

19
NBS-114A (rev. 2 -ac) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See instructions) NBSIR-87/ 3657 November 1987

4. TITLE AND SUBTITLE

A Computer Model of Smoke Movement by Air Conditioning Systems (SMACS)

5. AUTHOR(S)

John H. Klote

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

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

i. Type of Report & Period Covered

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

General Services Administration

Public Buildings Service

Office of Real Property Development

Buildings Technology and Standards Division Washington, DC 20405

10. SUPPLEMENTARY NOTES

f | 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 computer model for simulation of smoke movement through air conditioning systems

is described. A brief overview of air conditioning systems is presented. The

methods of calculation of mass flow, smoke transport, fan flow and duct and fitting

resistances are presented along with a general description of the program logic.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

air conditioning; air movement; computer models; ducts; fans; smoke movement;

ventilation systems

13. AVAILABILITY 14. NO. OF

PRINTED PAGES

[j^J Unlimited

| | For Official Distribution. Do Not Release to NTIS

[~l Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

24

15. Price

$9,95

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

U S COMM* DC 6043-P80