ELEVENTH JOINT PANEL 

MEETING OF THE UJNR 

PANEL ON FIRE 

RESEARCH AND SAM 

Nora H. Jason 

Deborah M. Cramer 

Editors 

U.S. DEPARTMENT OF COMMERCE 

Natlonal Institute of Standards 

and Technology 

Natlonal Englnemlng Laboratory 

Center for Flre Research 

Gaithersburg, MD 20899 

October 1990 

U.S. DEPARTMENT OF COMMERCE 

Robert A. Mosbacher, Secretary 

NATIONAL INSTITUTE OF STANDARDS 

AND TECHNOLOGY 

John W. Lyons, Mrector 
A SMOKE CONTROL CALCULATION FOR PRESSURIZED ELEVATOR SHAFT 

Takayuki MATSUSHITA 

Building Research Lnstitute 

Ministry of Construction 

1 Tatehara,Tsukuba-shi,Ibar&i-ken 

Japan 

1. INTRODUCTION 

The possibility of using pressurized elevator for the evacuation of the 

handicapped is being explored by Klote,Tamura and othersll]. In this paper, it 

is shown that the computer smoke transport model developed by the author et 

al.(4] is successfully applicable for the case where a building has a shaft 

with a moving cage, and the effects of multiple air supply inlets on the smoke 

control of pressurized elevator shaft are investigated. 

2 -MATHEMATICAL FORMULATION 

Klote and Tamura made the experiments and theoretical analyses on the air 

flow in a pressurized elevator shaft with a moving cage[2,3], however, it will 

be difficult to apply their analytical method to the conditions which change as 

a fire develops in a building. The advantage of using a computer model is that 

it can be flexibly applied to such transient conditions. Unlike usual one zone 

models for smoke transport in buildings, the change of node(space) volume with 

respect to time cannot be ignored when a cage moves in a shaft. Accordingly, 

the basic equations for the smoke transport in a building are given as follows: 

{ 1 ) Mass conservation 

where V,&w and W stand for node volume[m 3 J, gas density[kg/m 3 1, net flow rate 

at opening[kg/s] and mass generation rate[kg/s], respectively. Symbols {I stand 

for vector of nodes and {I stand for vector of openings, and [I] is the 

incidence matrix(41. Note that dV/dtfO at a node in the elevator shaft. when the 

cage is moving in the node. 

(2) Energy conservation 

eTV dP dV 

P dt dt 

(C--- --)+{C,PT--~+[IJ(E}={Q~ (2) 

where Cp)P,T,E and Q stand for specific heat of gas [kJ/kgK], absolute 

pressuretPa] temperature [K] ) net energy flow at an opening[kJ/s] and heat 

release rate(kW1, respectively. When temperature is the same at all the nodes, 

Equation (2) becomes as follows: 

dV 

dt 

CCppT--}+CpTII] (w}=(Q) 
(3) Equation of state of ideal gas 

(4) Flow rate through an opening 

Flow rate through an opening is calculated using Bernoulli’s equation for 

orifice flow as a function of pressure difference, temperature and opening 

conditions. 

(5) Change of node volume 

The difference of this system of equations from that of existing one is 

that dV/dt term is added in the equations for mass and energy conservations. 

The change of the volume with time of a node in which an elevator cage is 

passing is given as 

dV 

dt 

---=ACv (4) 

where A, and v stand for the horizontal section area 

the cage [m], respectively. 

[m2] and the velocity of 

3.CALCULATION OF SMORE CONTROL IN THE ELEVATOR SHAFT 

The experiments by Klote et a1.[3] were conducted under room temperature 

condition. For the smoke transport calculation at constant temperatures, Eqns. 

(2’),(,3) and (4) are the only equations to be used. 

The test building is modeled as shown by the graph in Figure 1. The input 

property data are given in Table 1. The velocity of the elevator cage is 

modeled as shown in Figure 2. 

In this calculation method, the elevator shaft is divided at each floor 

height so that each segment space is taken as a node. The pressure loss AP due 

to flow friction of the elevator shaft can be calculated by the following 

equation, which has been established for circular ducts. 

where h,L,D stand for friction coefficient, length [m] ‘and diameter of the duct 

[m], respectively. Substituting the real dimensions of the shaft in the 

experiment by Klote and Tamura into D and L, and an established data for 

concrete duct into A, we have the value corresponding to the flow coefficient 

for the length of a floor height as follows: 

(D/ L) ’/‘=5.0 (6) 

As for the flow coefficient d’ for the space between the cage and the 

shaft wall, Klote et al. obtained the value of 0.83. The value of d’ was 

calculated using the following equation assuming that the volume flow rate 

through the space is equal to the shaft section area multiplied by the cage 

veloci t y . 

where A and Af stand for the section area of the shaft and the space between 

the shaft wall and the cage, respectively. 

On the other hand, in this calculation method, it is considered to be more 

appropriate to use the cage section area A, instead of A, in Eq.(7) for 

defining the flow coefficient a, then using the data of Klote’s experiment, 

CA becomes as follows. 

189 
In Figure 3, comparisons of the pressure between the analysis by Klote et 

al. and this computing method are shown. A good agreement is seen between the 

two in case of d=O. 6. 

The comparison of the pressure between the experiments by Klote and Tamura 

for a pressurized elevator shaft with a moving cage and the results of the 

calculations by the computer smoke transport model are shown in Figure 4 and 5 

respectively for the cases, when the cage ascends and in Figure 5 when the cage 

descends. These results show a good agreement between the experiments and the 

calculations. 

4.EFFECT OF AIR SUPPLY PATTERNS ON SHAFT PRESSURE 

In order to investigate the effects of different air supply patterns on 

the smoke control efficacy of a pressurized elevator shaft, the calculations 

were made for the following three typical supply patterns. 

(1) air supply at two positions; on the 1st and the 15th floors 

(2) air supply at three positions; on the lst,8th and 15th floors 

(3) uniform air supply; on each of the floors 

The total air supply rate is fixed at the same value which is uniformly 

distributed to the air supply positions in each case. 

The calculation results of pressure at the levels of lst, 8th and 15th 

floors in each of the above mentioned cases are shown in Figs.6-8. Although 

these results are given only for the cases when the cage ascends, the results 

for the cases when the cage descends can be obtained just by exchanging the 

pressures of 1st and 15th floors. 

In these figures, it can be seen that the pressure drop at the 1st floor 

due to the cage passing is the smallest when air supply is given to 1st and 

15th floors and the shaft pressure is stable. In case of uniform air supply, 

the pressure change at the 1st floor is large, although the pressure difference 

between above and below the cage is kept constant. 

5. CONCLUDING REMARKS 

(1) In case of a pressurized elevator shaft with a moving cage, the computer 

model of smoke transport developed earlier by the author et al. can be used 

by a slight modification that dV/dt#O at a divided node in the elevator 

shaft . (2) In this calculation method, the value of 0.6 which is modified from 

experimental data of Klote and Tamura to the flow coefficient for the space 

between the cage and the shaft wall gives an acceptable agreement with the 

experiment . (3) The effects of different air supply patterns in a pressurized elevator 

shaft is investigated by using the computer model of smoke transport. Such 

flexibility of the computer model will be useful when we need close 

consideration on the availability of pressurized elevator shafts for the 

evacuation of the handicapped. 

REFERENCE 

[l] Klote;NBSIR82-2507,1982.5 

[Z] Klote,Tamura;ASHRAE Transactions,Vol.93,2217-2228,1987 

[3] Klote,Tamura;Fire Safety Journal,Vo1.11,227-233,1986 

[4] Matsushita,Fukai,Terai;lst Fire Safety Science,1123-1132,1986 

190 
1rr 

13f 

121 

llf 

10f 

9f 

8f 

If 

6f 

5f 

lr 

If 

2f 

If 

Supply rate of air 

Cross-sectional shaft area 

Area around elevator car 

HEVATOR lOBlY ROOH OUTSlDf 

SHAFT 

fipure-1. GtaDh of buildinp for analysis 

I 

Comments i 

8.05[kg/s] Exp. condition by KLOTE 

1 

5.515 [d] ditto 

1.947 [d] ditto I 

Values 

i 

I 0 

0 esc 

n 

z 

- tx~etiacntr BY larurr ci tl.121 ! 

1 Area between shaft and lobby 1 0.131 [ I' 1 1 Used value by KLOTE ~~ ~~~ 1 Area between lobby and building 1 0.0901[$] 1 dltto 

1 Area between building and outside I 0.450 [ m'l 1 ditto ~ ~~~ ~ I Flow coefficient for opening ~ 1 0.65 1 ditto(est1mated) 

Flow coefficient for flow around 0.83 

elevator car 1 0.60 1 tA:Isied value I 

I 

-04 w 

0 10 20 

TIHE[secl 

Figure-2. Tire schedule of a 

roving cage in a elevator 

OO 

L 

10 20 

TlHE (SKI 

Figure - 3. Corparison between the analytical 

results by Klote and Tarura and the calculation 

by the corputing method when a cage ascends in 

a oressurired elevator shaft 

TIHf [SKI IIHt ISXI IIHt [Sic] 

Figure-4. Corparison betweer: the experiments 

by Klote and Tarura and the calculation by 

the corwting rethod when a cage ascends In 

a pressurized elevator shaft 

70 1 i 1 I 1 1 

- exoeriaants by laaura (I ~1.[21 

I . . . ... . . . ~al~ult~ion~ for 0-0.6 

t t 

Figure-5. Coroarison between the experiaenrs 

by Klote and Tarura and the calculation by 

the corouting method when a cage descends in 

a pressurized elevator shaft 

191 
Figure - 6, Calculation results figure - 7. Calculation results figure-8. Calculation results 

when air SUDDIY on 1st and 15th vhcn air suooly on lst,8th and 

floors and a cage ascends 15th floors and a cage ascends 

when air suo~ly on each of the 

floors and a cage ascends