NATL INST OF STAND & TECH

A 11 ID 7 3^0131

NBS

PUBLICATIONS

NBSIR 83-2737

Computer Analysis of A Pressurized

Stairwell

U S DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

August 1 983

-GO

100

.1156

83-2737

198:>

U S DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

C.2

NATIONAL BUREAU OF STANDARDS

LIBRARY SEP 1 5 1983

NBSIR 83-2737

l • « COMPUTER ANALYSIS OF A PRESSURIZED

STAIRWELL

John H. Klote

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Fire Research

Washington, DC 20234

and

Xavier Bodart

Service Securite - Feu

Station de Recherche

Centre Scientifique et Technique du Batiment

Champs Sur Marne, France

August 1 983

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director
01 1 III ! 1

•• • i AM
TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES v

Abstract 1

1 . INTRODUCTION 2

2. NBS COMPUTER PROGRAM 3

3. TEST SERIES 6

4. FLOW MODEL 7

5. COMPUTER SIMULATION 9

6. REEVALUATION OF FLOW EXPONENTS IN SMOKE CONTROL DESIGN 10

7. CONCLUSIONS 11

8. REFERENCES 12

APPENDIX A. Calculations of Flow Factors 21

APPENDIX B. Notation 29

APPENDIX C. Unit Conversions..... 30

-iii-
LIST OF FIGURES

Page

Figure 1. Idealized flow model for CSTB tower 20

Figure A1 . Duct connection between floors of CSTB tower 27

Figure A2. Floor plan of ground floor of CSTB tower 28

-iv-
LIST OF TABLES

Page

Table 1. Flow factors and flow exponents between the building

and the outside obtained by regression analysis 14

Table 2. Flow factors 15

Table 3. Test schedule including supply and exhaust air flow

rates 16

Table 4. Comparison of measured and calculated pressure

differences 17

Table 5. Flow factors from building to the outside based on a flow

exponent of 1/2 18

Table 6. Comparison of calculated pressure differences for a flow

exponent of the exterior wall, of 1/2 and greater

than 1/2 19

-v-

COMPUTER ANALYSIS OF A PRESSURIZED STAIRWELL

John H. Klote and Xavier Bodart

Abstract

In recent years pressurized stairwells have been

incorporated in buildings in an effort to provide smoke

free exits during building fires. This paper compares

the results of tests conducted in a pressurized stairwell

at Champs Sur Marne, France, with computer analysis using

a computer code developed at the National Bureau of

Standards (NBS). A second paper is planned which will

compare the NBS program with the Centre Scientifique et

Technique du Batiment (CSTB) program for the same series

of tests. Agreement between the NBS computer simulation

and the test data was good for all tests analyzed. The

appropriateness of using exclusively a flow exponent of

1/2 for smoke control design is reevaluated, and is found

to have only a slight effect on the results of a computer

simulation.

Keywords: Air movement; computer programs; egress;

elevator shafts; escape means; modeling; pressurization;

simulation; smoke control; stairwells.

- 1 -
1 . INTRODUCTION

The concept of stairwell pressurization has been developed in recent

years as a means to provide a smoke free exit during building fires. Ideally,

a pressurized stairwell maintains a positive pressure with respect to the rest

of the building which prevents smoke infiltration into the stairwell when the

stairwell doors are closed.

The work reported on herein is part of an investigation of pressurized

stairwells undertaken jointly by the National Bureau of Standards (NBS) in the

United States and the Centre Scientifique et Technique du Batiment (CSTB) in

France. The objective of this paper is to compare the results of tests on a

pressurized stairwell at Champs Sur Marne, France, with results calculated by

computer analysis using the NBS program for analysis of pressurized stairwells

[1]. In addition, the appropriateness of exclusively using flow exponents of

1/2 for smoke control design is reevaluated. A second paper is planned which

will compare results calculated by the NBS program with those of the CSTB

program [2] for the same series of tests. This report is not intended as a

design guideline, however design information is available from Klote and

Fothergill [3].

The National Research Council (NRC) of Canada [4-9] has performed a

number of tests on buildings to evaluate the effectiveness of various

approaches to smoke control by measuring levels of pressurization produced by

these systems. These tests and others [10,11] by the NRC have also provided

considerable information concerning leakage areas for walls and floors of

commercial buildings. Cresci [12] has performed a computer analysis of tests

-2 -
on a 22-story pressurized stairwell located in New York City. He also used a

scale model to investigate air flow and friction losses due to vertical air

flow through the stair shaft.

The tests described in this paper differ from these earlier ones in that

the flow network throughout the building was carefully analyzed and controlled

and the characteristics of the flow paths were determined throughout the

building. This flow network and the characteristics of the flow paths were

then used in the computer analysis to determine the level of agreement between

the computer program and test data.

2. NBS COMPUTER PROGRAM

The NBS program [1] was specifically written for the analysis of pressurized stairwells and pressurized elevators. Data input has been designed to

minimize the quantity of required data and still maintain a high level of

generality in the computer model. In this program a building is represented

by a network of spaces or nodes, each at a specific pressure and temperature. Stairwells and other shafts are modeled by a vertical series of spaces,

one for each floor.

Air flows through flow paths from spaces of high pressure to spaces of

lower pressure. The principle flow paths are doors and windows which may be

opened or closed. Air flow can also occur through cracks in partitions,

floors, exterior walls and roofs. Such air flow can be empirically described

by the flow equation

-3 -
m = K(AP)

n

where m = mass flow rate of air through the path

K = flow factor

AP = pressure difference across the flow path

n = flow exponent

The flow factor, K, depends on the shape and cross sectional area of the

flow path. The flow exponent, n, can vary between 1/2 and 1. Large openings

and all but extremely narrow cracks have a flow exponent of 1/2.

In the NBS computer model, air from outside the building can be introduced by a pressurization system into any level of a shaft or even into other

building spaces. This allows simulation of stairwell pressurization. The

steady state pressures and flows throughout the building are obtained by

solving the air flow network, including the driving forces (i.e., wind,

pressurization system, inside/outside temperature difference, etc.).

The assumptions upon which the program was developed are:

1. Each space is considered to be at one specific pressure and one

specific temperature.

2. The flows and flow paths are assumed to occur at mid-height of

each level (or floor).

-4 -
3. The net air supplied by the air handling system or by the

pressurization system is assumed to be constant and independent

of building pressure.

4. The outside air temperature is assumed constant.

5. The outside static air pressure at ground level is assumed to

be 101,325 Pa, standard atmospheric pressure. (This can be

changed by modifying the program. However, this was not

necessary for the analysis discussed in this paper.)

Computer input consists of:

1. outside air temperature,

2. air temperatures throughout the building,

3. outside wind velocity, and

4. description of network including flow factors and flow

exponents for all connections.

Computer output consists of steady state flows and pressures

throughout the entire building network.

- 5 -
3. TEST SERIES

The stairwell pressurization tests were performed in a tower located at

the CSTB Research Station, Champs Sur Marne, France. The top story of the

nine story building was not connected to the stairwell, so that the stairwell

was effectively eight stories.

The tests, described in detail by Hognon [13], were divided into three

groups:

1. six tests without overpressure relief,

2. seven tests with a non-powered exhaust duct for overpressure

relief, and

3. twenty-one tests with a barometric damper for overpressure

relief

The concept of overpressure relief is to prevent excessive stairwell

pressures when all stairwell doors are closed by relieving some of the stairwell supply air to either the building or to the outside. This concept is

discussed in more detail by Klote [14,15].

Extensive modifications were made to the tower, including installation of

a pressurization system along with the two means of overpressure relief. A

variable speed supply air fan was used so that the stairwell could be pressurized at several different air flow rates.

- 6 -
Pressure differences, pressurization air flow rates, wind speed and

direction, and temperatures were recorded on strip chart recorders.

Temperatures were recorded continuously throughout the test series. The

pressure differences and flow rates were recorded sequentially during each

test on the same recorder. The period of time required to record the data for

a single test was approximately 90 seconds. The wind speed and direction

fluctuated throughout the tests. During all of the tests, the temperature

difference between the building and the outside was insignificantly small.

Even though the wind data were recorded continuously, the wind data were

not cross referenced with the other data so that specific wind data is not

available for the tests. During the tests without overpressure relief, the

maximum wind speed was 18 km h”^. During the tests with the non-powered

exhaust, the maximum wind speed was 23 km h

-

^ . The performance of the barometric damper was found to be highly dependent on wind velocity, and accordingly these tests could not be analyzed by the NBS computer program. The wind

was also a significant factor for two of the tests with the non-powered

exhaust duct, rendering these tests unsuitable for analyses.

4. FLOW MODEL

Considerable effort was extended in modifying the tower so that the air

flow network of the tower would be represented by the idealized flow model

illustrated in figure 1. This was done to facilitate the evaluation of the

air flow paths.

- 7 -
Transom windows were located in the exterior tower walls. For the case

where the transom windows closed, the flow factors, KgQ^, and flow exponents,

n Boi> between the building and the outside at any level i were obtained by

regression analysis of pressure difference and flow data provided by Hognon

[13] and are listed in table 1. For the rest of the flow paths in the

building the flow areas were relatively large, and therefore a flow exponent

of 1/2 was used. A summary listing of these flow factors is provided in table

2 and detailed descriptions, areas and calculations of the flow paths are

provided in Appendix A.

For a flow exponent of 1/2, the flow equation becomes the orifice equation.

m = AC t/ 2pAP

where A = flow area

C = flow coefficient

p = density of air in the flow path

The flow coefficient is generally in the range of 0.6 to 0.7 for cracks

in buildings, the actual value being dependent on the geometry of the flow

path. For an open door of a pressurized stairwell, Cresci [12] found that the

flow coefficient was half or less than that which would have been anticipated. This was attributed to the complex flow patterns that existed near the

open doors. In fact, Cresci observed stationary vortices on various floor

landings of a scale model of the stairwell he analyzed. Based on Cresci'

observation, a flow coefficient C = 0.30 was chosen for this test series for

-8 -
the open stairwell doors where the air flows were relatively high. This

occurred when the ground floor door was open or when another stairwell door

was open and the transom window on that floor was also open. When the transom

window was closed on the floor with an open stairwell door, the resulting flow

through the stairwell doorway was much lower. In this case it was expected

that the flow patterns in the vicinity of the open doorway would be less

complex and accordingly larger flow coefficients were used.

The ducted supply system for the stairwell had four injection points, one

located between the ground floor and the 1st floor and the others at the 2nd,

4th, and 6th floors, and the ducted exhaust system had three inlets, one each

on the 1st, 3rd, and 5th floors. Before the tests, the supply system was

balanced so that the supply air was approximately evenly divided between the

injection points, and the exhaust system was also balanced so that the exhaust

air was approximately evenly divided between the exhaust inlets. Accordingly,

for the computer analysis the total measured air flow rates were evenly

divided amoung injection points or the exhaust inlets, as appropriate.

5. COMPUTER SIMULATION

Eleven of the stairwell pressurization tests conducted at the CSTB

Research Station were analyzed by the NBS computer program. Because of the

lack of specific wind data for each test (see section 3), the tests analyzed

were limited to those tests for which the wind effects were minor. This

comparative analysis includes all the tests without overpressure relief and

five of the seven tests with the non-powered exhaust duct but none of the

tests with the barometric damper.

- 9 -
Table 3 is a schedule of the tests analyzed by the NBS program including

measured air supply and exhaust rates. Table 4 is a comparison of measured

and calculated pressure differences for these tests.

It is apparent that the results of the computer simulation are in good

agreement with the test data.

An attempt was made to simulate one of the tests where wind was a significant factor. The variation in wind velocity with height above the ground

was modeled by the power law as provided in the NBS program. Unfortunately,

the results were less than satisfactory. Possibly this was due to local wind

effects near the ground. Further research is needed with regard to the

effects of wind on such pressurization systems.

6. REEVALUATION OF FLOW EXPONENTS IN SMOKE CONTROL DESIGN

The values of the flow factors and flow exponents between the building

and the outside were obtained by regression analysis (table 1). All of these

flow exponents are greater than 1/2.

However, for smoke control design a flow exponent of 1/2 is commonly used

for all flow paths. This simplifies calculations both in itself and by

allowing the use of equivalent flow areas for systems of flow paths in series,

parallel or both.

The NBS computer program was used to reevaluate the 1/2 exponent. Table

5 lists flow factors between the building and the outside which are based on a

-10-
flow exponent of 1/2. These flow factors were evaluated at flows and

pressures that were calculated in the computer analysis of test 1 with the

flow factors and exponents listed in table 1. Therefore, the computer simulation of test 1 with the flow exponent of 1/2 was esentially identical to that

where the flow exponents were obtained by regression anlaysis.

Table 6 is a comparison of calculated pressure differences for tests 3

and 5 with flow exponents of 1/2 and flow exponents obtained by regression

analysis. It is apparent that the change in the flow exponent causes only a

slight change in the results of the computer simulation.

7. CONCLUSIONS

1. The good agreement between the pressure differences calculated by the NBS

computer program and the test data indicate that the assumptions of the

NBS computer program are reasonable for an analysis of a pressurized

stairwell under circumstances similar to the tests described in this paper

when wind is not a significant factor.

2. In situations where wind is a significant factor, the NBS computer program

was not capable of performing a satisfactory simulation. Further research

is needed with regard to wind effects.

3. An analysis with all flow exponents at 1/2 yields acceptable results for

design purposes. However, for experimental research more accurate evaluation of flow exponents may be appropriate for very narrow cracks.

- 11 -
4. The use of a relatively low flow coefficient (C = 0.30) for open stairwell

doors with large flow rates yielded computer simulations in good agreement

with measurements.

8. REFERENCES

[1] Klote, J.H., A Computer Program for Analysis of Pressurized Stairwells

and Pressurized Elevator Shafts, Nat. Bur. Stand. (U.S.), NBSIR 80-2157,

Jan. 1981.

[2] Rilling, J. , Smoke Study, 3rd Phase, Method of Calculating the Smoke

Movement Between Building Spaces, Centre Scientifique et Technique du

Batiment (CSTB), Champs Sur Marne, France, Sept. 1978.

[3] Klote, J.H. and Fothergill, J.W., Design of Smoke Control Systems for

Buildings, Nat. Bur. Stand. (U.S.), NBS-Handbook 141, June 1983.

[4] Tamura, G.T., Experimental Studies on Pressurized Escape Routes, ASHRAE

Transactions 1974, Vol. 80, Part 2, pp. 224-237, 1974.

[5] Tamura, G.T. and Shaw, C.Y., Experimental Studies of Mechanical Venting

for Smoke Control in Tall Office Buildings, ASHRAE Transactions 1978,

Vol. 86, Part 1, pp. 54-71, 1978.

[6] Tamura, G.T., Experimental Studies on Exterior Wall Venting for Smoke

Control in Tall Buildings, ASHRAE Transactions 1978, Vol. 84, Part 2,

pp. 204-215, 1978.

[7] Tamura, G.T., Exterior Wall Venting for Smoke Control in Tall Office

Buildings, ASHRAE Journal, Vol. 20, No. 8, pp. 43-48, August 1978.

[8] Tamura, G.T., A Smoke Control System for High-Rise Office Buildings,

ASHRAE Journal, Vol. 24, No. 5, pp. 29-32, May 1982.

[9] Tamura, G.T., The Performance of a Vestibule Pressurization System for

the Protection of Escape Routes of a 17-Story Hotel, ASHRAE Transactions

1980, Vol. 86, Part 1, pp. 593-603, 1980.

[10] Tamura, G.T. and Shaw, C.Y., Air Leakage Data for the Design of Elevator

and Stair Shaft Pressurization Systems, ASHRAE Transactions 1976,

Vol. 82, Part 2, pp. 179-190, 1976.

[11] Tamura, G.T. and Shaw, C.Y. , Studies on Exterior Wall Air Tightness and

Air Infiltration of Tall Buildings, ASHRAE Transactions 1976, Vol. 86,

Part 1, pp. 122-134, 1976.

-12 -
[ 12 ] Cresci, R.J., Smoke and Fire Control in High-Rise Office Buildings - Part II: Analysis of Stair Pressurization Systems, Symposium on

Experience and Applications on Smoke and Fire Control at the ASHRAE

Annual Meeting, June 1973, Louisville, Kentucky, ASHRAE, Atlanta, GA,

pp. 16-23, 1973.

[13] Hognon, B., Prevention of Smoke Build-Up in the Stairwells of High-Rise

Buildings by Pressurization, Centre Scientifique et Technique du

Batiment (CSTB), Champs Sur Marne, France, Aug. 1981.

[14] Klote, J.H., Stairwell Pressurization, ASHRAE Transactions 1980,

Vol. 86, Part 1, American Society of Heating, Refrigerating and AirConditioning Engineers, Inc., New York, NY, 1980.

[15] Klote, J.H. , Smoke Control by Stairwell Pressurization, Engineering

Applications of Fire Technology Workshop, Society of Fire Protection

Engineers, Boston, MA, to be published.

[16] Edel'chik, I.E., Handbook of Hydrolic Resistance - Coefficients of Local

Resistance and of Friction, U.S. AEC, 1966.

- 13-
Table 1. Flow factors and flow exponents between the building

and the outside obtained by regression analysis

Floor (i)

KBOi

(kg s -1Pa

_1 ^ nBOi

nB0i

0.55

Correlation

Coefficient

1 0.0104 0.99

2 0.00684 0.64 0.94

3 0.00720 0.59 0.98

4 0.00468 0.68 0.96

5 0.0132 0.58 0.99

6 0.00312 0.77 0.99

7 0.00456 0.70 0.97

14
Table 2. Flow factors

Flow Factor

Symbol (kg s

1 Pa Rema rks

SBi» for i = 0 to 7 0.0252 stairwell door closed

SBi * for i = 1 to 7 1.48 stairwell door open when

transom on floor i is closed

SBi* for i = 1 to 7 0.739 stairwell door open when

transom on floor i is open

SBO* ground floor 0.628 stairwell door open

BOi * for i = 1 to 7 0.310 transom window open

SOi* for i = 0 to 8 0.00344

Fi* for i 2 to 7 0.0123

BOO* ground floor 2.50

Notes :

1. Calculations of these flow factors are provided in Appendix A.

2. For definition of symbols, see Appendix B.

15
Table

3.

Test

schedule

including

supply

and

exhaust

air

flow

rates

4-J oa CM sjm o

i£>

m r"- cr> o 4-1 1 l 1 1 1 1 • • • • •

CO | l 1 1 | 1 CM rH CM o rH 3

CO .3Xw

r

J

-1 | TO CD

0)Vj GO 3 -X 4-1 CD w o

CO 3

cy 3 Q 00 v3O -0- CT> CM CM

m

O CO co S O 00 CO cr> o CM O' -O’ r-» vO 00 00

rH rO • • • • • • • • • • • i—1 Ph rH pH <N CM CM rH CM <r CM CM

CO

a

u Vj a- £3 3

C/D —s c e

CO CX

Ph Vj Vw/ o O o o o o o o o o o rH TO m m m m m m CM CO CM CM a 0) r-» r» r-- r^. o- hT a> in ON o\

cx <u 3 CX

C/D C/D

rH •—4 c

<u Vj Vj

u Vj Vj cx E o o

CD CD 3 3

(Uco 33O<U3O

OO

iH

14H

OO

»H

MH 33O 3O

Oo

rH

>44

<u3O

OO

rH

>44

OO

rH

Mh

cOO • i ptH c 3 3 TO TO 3 3 T3 3 TO TO W vj

r i /— Vj Vj Vj VJ Vj

V-H •H CO CO CO CO CO

Vj Vj

;airwell

Dors

Open

VJO Vj Vj Vj

OO

rH Vj Vj

OO

iH

none o

i-H <44

OO

1—t OO

rH

OO

rH

144 T3 3H

(11

Oo

rH

OO

rH

Mh

TO

TO3H

144 TO

144

4-1

MH

TO

Vj CO

O3

Vho3

>44

T3

MH

TO

Vj co

wJo Vj CD Vj <4> Vj Vj <-3

C/D

Q

w

vj co rH CO

4-1 co CO

4J GO CD CD -J i—H

4J

CD

H CM CO <r

m vO 00 cr.

O *—H

0) *—H

r—H

H •

16

air

flows

are

average

values

of

supply

and

exhaust

that

were

recorded

for

each

test
Table

4.

Comparison

of

measured

and

calculated

pressure

differences I

<D T3

fa o

•u X. to c c <u •H >

X) <U

C/D 3P0

rH lHo 3 O

PQ rH

fa oH ,C

rHC

rH <U

cy > £ <D In C/D

<da o 2 * uO fa

rHH

0) *H S fa

>H

X>

<u

X)

<D3

COCO

<3

xj

Q)U3

vOm ocoON

CO

<rm

com o m • •

r-H

O

<r

r^co o

<r

co<r

<f cr> • • rH <f

<rm CO

v£> CM o•

CSI in om.

Hfm

CM coCM

00CO

00 I CO I I rH | mm

XD

CDU3

00 I CM I I rH |

VO rH • • O' o oo

rH • • <r

CO rH

O oo

X>

<Uu3cn

«d X

'Clin

CM

St

<r

rH CM • • oo m

<Dto

cdu

Q)>

cd

T3

0)

lH3

17

Calculated

pressure

differences

were

obtained

by

the

NBS

computer

program

with

the

flow

factors

and

flow

exponents

listed

in

tables 1

and 2
Table 5 Flow factors from building to the outside based

on a flow exponent of 1/2

Floor (i)

1

2

3

4

3

6

7

K

BOi

(kg s~

1 Pa~*^)

0.0133

0.0137

0.0113

0.0114

0.0196

0.0119

0.0122

18
Table

6.

Comparison

of

calculated

pressure

differences

for

a

flow

exponent

of

the

exterior

wall,

ngg^,

of

1/2

and

greater

than

1/2

<U rH H i—

i

0>

m

u

w

<u H

a

4_) C/5

19
Symbols:

Kgoi = flow factor between building

and outside on floor I.

Kr = flow factor between floor I and floor i-1.

Ksb, = flow factor between stairwell

and building on floor I.

KgQj = floor factor between stairwell

and outside on floor i.

Figure 1. Idealized flow model for CSTB tower.

20
APPENDIX A. CALCULATION OF FLOW FACTORS

This appendix consists of the calculations of the flow factors that were

used in the simulations presented in this report. For convenience, a summary

of these flow factors is listed in table 2.

As stated in section 2, the air flow through a flow path can be expressed

as

m = K ( AP) n

When n = 1/2, the mass flow rate of air can be expressed by the orifice

equation as:

m = AC/2pAP

where A = flow area

C = flow coefficient

p = density of air in the flow path

Therefore the flow factor can be expressed as

K = AC/2p

and for the flow in kg/s at 21°C and 1 atmosphere pressure the flow factor is,

K = 1.55 AC

21
In the following calculations, the areas were all measured values and the

flow coefficients were generally based upon experience. However, the flow

coefficient for the open transom windows was based on flow data obtained from

Idel'chik [15]. The flow coefficients used for open doors are discussed in

section 4.

1. Calculate the flow factor, Kgg^, between the stairwell and the building

with the doors closed on floors i = 0 to 7. The stairwell doors were tightly

gasketed and when the doors were closed, virtually all the leakage was through

a hole cut in the center of each door.

AgBi = 0.025 m^; C = 0.65

K

S Bi = 0.0252

2. Calculate the flow factor, Kggi* when the stairwell door is open on the

floors i = 1 to 7.

ASBi = 1,59 “

2

When the transom window is closed on the floor with the closed stairwell door,

the flow through the open doorway is relatively low.

C = 0.60

KgBi = 1«48 when transom window on floor i is closed

22
When the transom window on floor i is open, the flow through the open doorway

is much larger. In such a case, a flow coefficient of C = 0.30 is used as

explained in section 4.

Kggi = 0.739 when transom window on floor i is open

3. Calculate the flow factor, KggQ, from the stairwell to the building on the

ground floor when the door is open. Because there is considerable area for

leakage from the building to the outside, the flow through the open doorway is

relatively large, and therefore a flow coefficient of C = 0.30 is used.

a

sbo

= 1,35 m2

KSB0 = 0,628

4. Calculate the flow factor, Kg0^ , with the transom window in the exterior

wall open.

Afioi = 0.40 m^

Because the transom window is open at a 45° angle, the flow coefficient is

chosen as C = 0.50.

KB0i

“ 0.310

23
5. Calculate the flow factor, Kg oi , between the stairwell and the outside for

i = 0 to 8. This calculation is based on Hognon's calibration of the leakage

This is distributed over the height of the stairwell so that,

KSOi

= °* 00344

6. Calculate the flow factor, Kp^ , for the flow path in floor i where i = 2

to 7. The leakage between floors is through an arrangement of flexible duct

and wood boxes as illustrated in figure A1 . This arrangement was installed to

achieve a calculated flow factor between floors. Other leakage paths between

the floors were sealed. The friction loss in the duct was determined to be

negligible and the flow factor was expressed as,

where = flow factor through the adjustable opening

K

2 = flow factor through the inlet (or outlet) of the duct.

The flow coefficient for Kj is C = 0.60 and the flow coefficient for K£ is

C = 0.80.

O from the stairwell to the outside at AC = 0.020 m for the entire stairwell

K.Fi

2_

-1/2

k

2 K

2 J

A^ = 0.021 m

2

K

x = 0.0195

A

2 = 0.0314 m

2

K2 = 0.0398 m

2

K

pi = 0.0123

24
7. Calculate the flow factor, KgQQ, between the building and the outside on

the ground floor. The connections are shown in figure A2 with the following

O flow areas (in m ):

Aj = A2 = 0.80 x 1.93 = 1.544

A

3 = 0.80 x 1.97 = 1.576

A4 = 1.05 x 1.75 = 1.838

A

5 = 1.05 x 1.96 = 2.058

A

6 = 0.67 x 1.97 = 1.320

A7 = 0.70 x 2.00 = 1.400

Ag = 0.90 x 2.23 = 2.007

A9 = 0.87 x 1.98 = 1.723

A

10

= 0.70 x 2.20 = 1.540

A

11 = 0.87 x 1.82 = 1.583

A

1

= 4(1.10 x 0.90) = 3.960

A13

= 1.10 x 0.90 = 0.990

A14

= 2.0 approximate area

A1

= 1.10 x 0.90 = 0.990

A16

= 0.70 x 2.00 = 1.400

open doors

open door

open door

open door

open door

open door

open door

open door

open door

open door

4 transom windows

1 transom window

holes in corridor wall

1 transom window

open door

2 The approach is to calculate the equivalent area, A

g (in m ), of the system as

follows

A

l,2,3,4

1

(Ai + A

2

) 2 + 1.116

A

14,15

0.887

25
5, 6, 7,

1 + 1 + 1 + 1 2 >2 .2 .2 Ar A

^

A-j A

L 5 8

- 1/2

= 0.798

11,13,16

1 + i^ +1 T -1/2

2 2 2 A A A

11 13 16 J

= 0.720

5-13,16

1 1 1 - 1/2

L

(A5,6,7,8

+ A

9

) (A

10 + A

12 ) (A11,13,16 )

A

e “ A

1 ,2,3,4 + A

14, 15 + A5-13,16 " 2,69

For C = 0.60

KBOO “ 2,50

0.687

26
27

Figure

A-1.

Duct

connection

between

floors

of

CSTB

tower.
o

in

E

o

CO

c

CO

28

Figure

A-2.

Floor

plan

of

ground

floor

of

CSTB

tower.
APPENDIX B. NOTATION

A flow area

C flow coefficient

K flow factor

m mass flow rate

n flow exponent

AP pressure difference across flow path

P density

Subscripts

B building

F floor

0 outside

S stairwell

i floor level

0 ground floor

29
APPENDIX C. UNIT CONVERSIONS

1 m = 3.28 ft

1 Pa = 0.00402 in H

2 0

1 kg = 0.454 lb mass

1 km h~^ = 0.621 mph

1 m/s = 197 ft/mln

30
U.S. DEPT. OF COMM. 1. BIBLIOGRAPHIC DATA

SHEET (See instructions)

PUBLICATION OR

REPORT NO.

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

NBSIR 83-2737 August 1983

4. TITLE AND SUBTITLE

Computer Analysis of a Pressurized Stairwell

5. AUTHOR(S)

John H. Klote and Xavier Bodart

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

national BUREAU OF standards and Centre Scientifique et

7. Contract/Grant No.

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

Technique du Batiment

Station de Recherche

Champs Sur Marne, France

8. Type of Report & Period Covered

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

10.

SUPPLEMENTARY NOTES

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

11.

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

bibliography or literature survey, mention it here) recent years pressurized stariwells have been

incorporated in buildings in a effort to provide smoke free exits during building

fires. This paper compares the results of tests conducted in a pressurized stairwell at Champs Sur Marne, France, with computer analysis using a computer code

developed at the National Bureau of Standards (NBS) . A second paper is planned

which will compare the NBS program with the Centre Scientifique et Technique du

Batiment (CSTB) program for the same series of tests. Agreement between the

NBS computer simulation and the test data was good for all tests analyzed. The

appropriateness of using exclusively a flow exponent of ^ for smoke control design

is reevaluated, and is found to have only a slight effect on the results of a computer simulation.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon s) Air movement; computer programs; egress; elevator shafts;

pressurization; simulation; smoke control; stairwells.

13. AVAILABILITY

escape means; modeling;

14. NO. OF

PRINTED PAGES

^Unl imited

| | For Official Distribution. Do Not Release to NTIS

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

20402.

34

15. Price

X Order From National Technical Information Service (NTIS), Springfield, VA. 22161 $ 8.50

USCOMM-DC 6043-P80