HAND CALCULATION METHOD FOR AIR SUPPLY RATES IN VESTIBULE PRESSURIZATION SMOKE CONTROL SYSTEM

Transcription

1 International Journal on ngineering Perforance-Based Fire odes, Volue, Nuber, p.7-40, 999 HAND AUATION MTHOD FO AI SUPPY ATS IN PSSUIZATION SMOK ONTO SYSTM M. Kujie Nikken Sekkei td, 4-6- Koraibashi, huo-ku, Osaka , Japan T. Matsushita Kobe University, okkodai-cho, Nada-ku, Kobe, Hyogo , Japan T. Tanaka DS, Disaster Prevention esearch Institute, Kyoto University, Gokasho, Uji, Kyoto 6-00, Japan ABSTAT While vestibule pressurization soke control systes are now popularly used in Japan in place of the soke extraction ethods prescribed in the Building Standards aw, it cannot be said that a rational ethod for deterining the air supply rates required for achieving the soke control goals has been well-established. As a result, coputer siulation odels are usually used as the eans to estiate the air supply rates. It ay not be inappropriate but it causes soe difficulties for ordinary designers to try this soke control syste. This paper proposes a practical design ethod of vestibule pressurization soke control systes. This ethod coprehensively covers the fire scenarios corresponding to every stage of evacuation, naely fire roo evacuation, fire floor evacuation and whole building evacuation. The required rates of air supply are deterined to eet all the criteria iposed to verify the safety requireents at these three stages of evacuation. The calculation procedure in this ethod consists of a set of siple forulas for pressure and opening flow rates developed based on the average pressure difference concept so it can only be followed by the use of a hand calculator. This ethod is expected to help designers and engineers easily understand what and how to do to rationally and effectively design the soke control syste and to help building officials or whoever ay concern with approval of the syste know how to check its copliance.. INTODUTION While only soke extraction ethods are prescribed in the existing governent orders associated with the Building Standards aw, the vestibule pressurization soke control ethod which directly pressurizes vestibules of staircases to prevent soke infiltration into staircases is increasingly popular in Japan, particularly for high-rise office buildings, for which protection of staircases by vestibules is required by the governent order []. This popularity sees to be attributed particularly to that the syste allows ore flexibility of floor layouts and ore rentable space than the soke extraction ethod. In addition, this soke control syste often accopanies pressurization of elevator shafts which ais at preventing soke spread through the shafts. An exaple of soke control syste of real buildings [] incorporating vestibule pressurization syste is shown in Fig.. The vestibule pressurization soke control ethod was introduced by building industries and has been applied to a significant nuber of buildings to date in Japan. However, several probles can be seen, both logically and technically, in the design procedure of this syste. They are: The target fire scenarios for the soke control syste are not clearly defined. A rational calculation ethod for estiating required air supply rates to vestibules and elevator shafts has not been well-established. onsideration for the fully-developed fire scenario is not sufficient. The theoretical bases of pressure difference criteria for soke stopping across doorways is not solid. Use of coputer odels tends to ake it extreely difficult to check if the contents of calculation are appropriate fro the side of approving bodies. 7

2 International Journal on ngineering Perforance-Based Fire odes NOTS: AI INT SMOK OUTT MANUAY-OPATD OPNING DVI FUS FI DAMP (UNSS OTHWIS STATD) FI DAMP XTATION FAN PF MVD MVD SMOK 7F OIDO OK OOM 6F VATO SD SD -5F F 9-0F VATO SHAFT VATO VATO HA VATO HA SD SD SD OFFI SD SD SD 8F VATO HA SD SD 4-7F VATO HA SD SD F VATO HA SD SD F VATO HA SD SD F NTAN HA BF VATO HA DINING OOM BF OIDO FSH BF OIDO AI PSSUIZATION SUPPY FAN VATO SHAFT PSSUIZATION SUPPY FAN Fig. : xaple of pressurization soke control syste 8

3 International Journal on ngineering Perforance-Based Fire odes In Japan, the transition fro the current prescriptive code to a perforance-based code is expected in the near future. Once this happens, the verification of safety requireents needs to be possible not only for a liited nuber of experts but also for a large nuber of ordinary engineers and building officials. So, a logically clear and technically siple ethod will be indispensable in this particular proble of designing vestibule pressurization soke control syste as well. In the ethod proposed in this paper, the scenarios of fire and evacuation of occupants to be considered and the safety criteria corresponding to the scenarios are clearly defined. Then, the procedure of calculations of the rates of air supply to vestibules and elevator shafts needed to eet the criteria are provided. The calculation procedure consists of a set of siple forulas, which is advantageous as the procedure can be followed by the use of a hand calculator.. OUTIN OF TH SYSTM In this study, we consider high-rise office buildings where special evacuation staircases (sokeproof towers) are required. Fig. illustrates a typical floor plan of such office buildings. Fig. : A typical floor plan ach floor has an office roo, a corridor, a vestibule, a passenger elevator bank, a staircase and a fire elevator bank. These spaces are identified by,,,, S and F respectively, and the outdoor space is identified by letter O in this paper. The office roo is served by the corridor, which leads to the stairway by way of a vestibule. The bank of the passenger elevator faces the corridor. The vestibule has a role to protect the staircase and the fire elevator fro soke. Mechanical pressurization is applied to the vestibule and to the shaft of the passenger elevators by separate fans. Mechanical soke extractions are equipped in the roo and the corridor, but will be shut down when the teperature of the fuse of the fire daper installed where the soke extraction duct crosses a fire wall rises to the elting point. Needless to say, floor layouts of real buildings are a little ore coplex with ultiple roos, stairs, elevator banks and so forth. Nevertheless, the key features of the layouts seen in any office buildings are retained in Fig. so that generic discussions on the pressurization soke control syste are still possible based on this siplified layout.. DFINITIONS OF SNAIOS, DSIGN FIS AND SAFTY ITIA. Scenarios orresponding to ach Stage of vacuation ike any other disasters, a fire is an event that is heavily influenced by accidental and stochastic factors. However, it is unavoidable that verification of the appropriateness of a fire safety syste is only ade under a liited nuber of selected scenarios because it is practically ipossible to consider every condition that ay take place by chance. Needless to say, it is desirable that the selected scenarios can cover as any conceivable conditions as possible, but bear in ind that abitious attepts to cover extreely rare conditions ay incur unbearable cost and technical difficulty in realizing the safety easure. The scenarios adopted here are fro such point of view as follows:.. General (a) It is assued that a fire occurs in a roo of the building. In other words, fires in the corridor, in the staircase and so forth are neglected. (b) vacuation in the roo of origin starts fairly early after the onset of fire since the occupants can directly recognize the hazardous situation. (c) vacuation fro the other roos on the floor starts soewhat later, and evacuation of the whole building follows further later on since the occupants perception of the hazard tend to be indirect. (d) The teperatures in the office roo, the corridor and the vestibule are assued to be the sae at noral tie. The outdoor teperature is different fro the teperatures in these indoor spaces. The teperatures in the stairs and the elevator shafts are in 9

4 International Journal on ngineering Perforance-Based Fire odes between the indoor and the outdoor teperatures. (e) Outdoor wind is not considered. (Note: If it is iportant, it is just easy to take into account the wind effect as long as the calculation is concerned.).. Fire roo evacuation (a) The onset of fire roo evacuation is expected to be at a fairly early stage because of the reason stated in the above. (b) It is assued that the soke control syste has not yet been activated. So, fire roo evacuation has to be copleted before the roo becoes untenable by the filling of soke layer under no soke extraction situation. (Note: In order to operate any soke control syste as early as at this stage, it will have to be activated by occupants theselves, but this is presued to be unreliable.).. Fire floor evacuation (a) Fire floor evacuation is deeed to start when the first occupant enters the corridor fro the fire roo. vacuation of the other roos begins soe tie later. (b) The corridor is designed to be free fro soke during the fire floor evacuation. (c) The corridor is deeed free fro soke until the soke layer in the fire roo descends below the height of the soffits of the openings to corridor. The soke control syste is designed to be activated before the soke layer in the roo of origin descends below the soffits of the openings. (d) After the soke control syste has been actuated, the soke is stopped at the doorway by aking up necessary pressure difference by the cobined effect of soke extraction in the fire roo and the pressurization to the vestibule and the elevator shafts. (e) The syste is so designed as not to allow air flow toward the vestibule or the elevator shaft fro the corridor for redundant safety, although theoretically, infiltration of soke is not supposed to take place if the above condition (d) is et...4 Whole building evacuation (a) Whole building evacuation is deeed to start when the first occupant gets into the staircase fro the fire floor. Soe tie later, evacuation of the occupants on the other floors follows. (b) It is assued that the fire has been fully developed so the windows in the fire roo have been broken at this stage. (Note: If the windows have not broken, the fire will not grow to a fully-developed fire, so the conditions for the soke control syste will be reduced to those in the Fire floor evacuation.) (c) After all the occupants fro the fire floor have entered the staircases, it is deeed to be sufficient to stop soke between the corridor and the vestibule, and to support fire brigade operation and evacuation in staircase. At the sae tie, soke is stopped between the corridor and the elevator shaft to prevent soke spread to other floors. (Note: It will be practically too difficult to prevent soke entering the corridor under the fullydeveloped fire situation.) (d) Both open and closed situations as illustrated in Fig. are taken into account for the fire roo doors, since the reliability of closing the doors is not always high. (Note: If they happen to be closed, the soke extraction syste is deeed to operate. If they happen to be open, the extraction fan ay be shut down but the corridor pressure becoes close to outdoor pressure. So, in any case, it is not difficult to aintain necessary pressure differences between the corridor and the vestibule, and between the corridor and the elevator shaft. Incidentally, the extraction fan is not always necessary. It can be replaced by soe other eans for the corridor pressure relief.) Fig. : Scenarios of extraction fan in corridor depending on opening condition. Design Fire.. Heat release rate The heat release rate of the design fire is assued to grow as shown in Fig. 4. 0

5 International Journal on ngineering Perforance-Based Fire odes to prevent soke fro entering the corridor, where h is the height of the doorway. In addition, the pressure differences between the vestibule and the corridor P ( z) and between the elevator shaft and the corridor P () z should satisfy: Fig. 4: Design fire in the roo of origin P ( z) > 0 and ( z) > 0 P (6) It initially increases in proportion to square of tie as: Q Q 0 t () where Q 0 is the coefficient concerning fire growth, but levels off after it reaches to the ventilation liit given as: Q, 500A O h O () where A O h is the ventilation factor of the O roo of origin... Fire plue flow rate The flow rate of fire plue is given by: 5 p 0.07Q z () where z is the height fro the fire source.. Safety riteria In this study, the safety criteria are defined for the verification of the assurance of the safety of evacuation at each stage... Fire roo evacuation The soke layer height z in the fire roo should satisfy the following condition [] until the copletion of the fire roo evacuation so that the occupants are not exposed to soke. z > H (4) where H is the ceiling height of the roo... Fire floor evacuation The pressure difference P () z across the fire roo doorway open to the corridor by the operation of the soke control syste should satisfy: () z > 0 (5) respectively, in order to prevent soke entering the vestibule and the elevator shaft should soke stopping at the fire roo doors fail... Whole building evacuation Although containation of the corridor by soke is accepted at this stage by the scenario stated in the above, in order to protect the vestibule and the elevator shaft fro soke, the pressure differences between the vestibule and the corridor P ( z) and between the elevator shaft and the corridor z should satisfy: P ( ) P ( z) > 0 and ( z) > 0 P (7) respectively, under the condition that the corridor teperature is elevated due to the entering of hot gases fro the roo of origin. 4. VIFIATION OF SAFTY AND AUATION OF AI SUPPY ATS 4. Average Pressure Difference and Approxiate Average Pressure Difference In fire situations, large differences in teperature aong different spaces ay induce large pressure difference along the height of openings, which coplicates the calculations of opening flow rates. In the ethod proposed in this paper, opening flow rates are calculated by the use of average pressure difference or further extended approxiate average pressure difference, of which the concepts are described in the appendices. The following equations are based on the average pressure difference. 4. Fire oo vacuation The soke layer height z at the tie of copletion of roo evacuation t as shown in Fig. 5 is calculated by the following forula for soke filling prediction [4].

6 International Journal on ngineering Perforance-Based Fire odes A 5 z Q t + H (8) 0 extraction rate in the fire roo respectively, and O are the flow rates fro the corridor to the fire roo and fro the fire roo to outdoor respectively. Also, regarding the heat conservation, we have: Q p p ( T T ) + h{ A + D ( H z) }( T T ) f f () Fig. 5: Soke layer height at the stage of the fire roo evacuation Hence, it follows that this z has to satisfy the criterion given by equation (4). Incidentally, calculation of the air supply rate is not involved in this safety verification because safety of the fire roo evacuation ust be assured under no soke control situation according to the above scenario. 4. Fire Floor vacuation 4.. Average pressure difference and flow rate corresponding to soke stop condition The teperatures and the air density of the corridor (), the vestibule () and the lower layer teperature of the fire roo () are distinguished fro each other in the following equations by the subscripts signifying the spaces for clarity, although they are assued the sae at the stage of fire floor evacuation. where teperatures respectively. T and T f are the soke layer and the roo A, H and D are the floor area, the ceiling height and the perieter of the roo respectively, and P and h are the specific heat of air at constant pressure and the total heat transfer coefficient. In the second ter on the right hand side of equation () expressing the heat transfer fro the soke layer to the roo boundary, the teperature rise of the boundary surface is neglected for siplicity. A sufficiently conservative estiate of the fire behavior will be obtained by this treatent since the discussion here is confined to the early stage of fire and the heat release rate is taken as the axiu during the evacuation. Using these relationships, the doorway flow rate and the average pressure difference to stop soke at the doorway can be obtained by sequentially following the procedure (4...-)-(4...-6): As a conservative assuption, a steady fire having the sae heat release rate as that at the tie of copletion of the fire floor evacuation t F is considered in the roo, that is: Q Q t (9) 0 F The soke layer height in the fire roo z ay either be lower or higher than the soffit height of the doorway h depending on the designed soke extraction rate as shown in Figs. 6a and 6b When the soke layer is lower than the doorway height ( z < h ) Based on the steady state fire assuption, the following relationship holds for the ass conservation of the roo as follows: p U (0) O where p and U are the plue flow rate at the height of the layer interface and the soke Fig. 6a: Flow patterns in the fire roo at the stage of fire floor evacuation when z < h (4...-) Arbitrarily choose the value of either soke layer height z or echanical extraction rate u provided that: U < () Q h (4...-) alculate the other that was not chosen in (4...-) using the following equations : 5 p 0.07Q z () and

7 International Journal on ngineering Perforance-Based Fire odes U p (4) (4...-) alculate the soke layer teperature T by: f T f Q T + (5) + h p p { A + D ( H z) } (4...-4) alculate the soke layer density f by: f T (6) T f (4...-5) alculate the doorway flow rate corresponding to soke stop criterion by: ( ) g( h z) z + ( h z) { } αb f (7) where fire roo and the corridor and in the corridor. B is the width of the doorway between the is the air density Fig. 6b: Flow patterns in the fire roo at the stage of fire floor evacuation when z h 4.. elationships used for the calculation of required air supply rates Fig. 7 illustrates the flow patterns expected at the stage of fire floor evacuation. The arrows in the figure show the directions of net air-flow through openings. Needless to say, these flows are induced by the pressure differences aong the spaces. (4...-6) alculate the average pressure difference across the doorway corresponding to soke stop criterion P by: P (8) ( α A) where A is the area of doorway between the fire roo and the corridor, that is A B h When the soke layer is higher than the doorway ( z h ) No soke will flow out to the corridor in this case, so the choice of the pressure difference across the doorway can be arbitrary. However, it is good to let the pressure difference satisfy: P > 0 (9) Also, if it is negative, it will often result in extracting air fro the corridor, which does not ake practical sense. The doorway flow rate due to the above pressure difference can be given by: ( A) α (0) Fig. 7: Flow patterns at the stage of fire floor evacuation 4... Pressures etting P, P, P and P be the average pressures of the fire roo, the corridor, the vestibule and the elevator shaft relative to the open air pressure at the sae height respectively, the following relationships hold for the pressures of the spaces involved. P P + () P P + () P P + () 4... Flow rates onsidering the ass conservation at steady state of each space involved, the following relationships hold for the rates of the opening flows, the soke extraction and the air supply. Fire roo (): U + (4) orridor (): + + (5) O O

8 International Journal on ngineering Perforance-Based Fire odes Vestibule (): W + + (6) levator shaft (): W + (7) where, U and W denote the rate of the opening flow, the soke extraction and the air supply respectively. The subscripts of single letter,,, O, etc., identify the space at which the echanical ventilation is applied and the subscripts of double letters, O, S, etc., signify the direction of the opening flow. 4.. alculation procedure for air supply rates Based on the above relationships, the air supply rates to the vestibule and the elevator shaft necessary to satisfy the soke stop criterion set by equation (5) can be calculated by the procedure as follows: (4..-) Deterine the soke extraction rate in the fire roo u and calculate the doorway flow rate and the average pressure difference P corresponding to the soke stop condition at the doorway between the fire roo and the corridor based on the ethod described in... (4..-) alculate the fire roo pressure as: P ( ) where O O O O ( α A) U O O ( α A) O S O F ( 0) O ( < 0) (4..-) alculate the corridor pressure by: P O (8) P + (9) (4..-4) alculate the air leak fro the corridor to the outdoor by: O ( α A) P ( P 0) O ( α A) P ( P < 0) O O (0) where ( α A) O is the effective opening area between the corridor and the outdoor. (4..-5) Deterine the flow rates fro the vestibule to the corridor and fro the elevator shaft to the corridor so as to satisfy equations () and (): + + () and O > 0 and > 0 () There is a certain degree of freedo in the choice of the values of and. Note, however, this choice eventually affects the air supply rates to the vestibule and the elevator shaft. (4..-6) alculate the average pressure differences between the vestibule and the corridor P and between the elevator shaft and the corridor P by: ( α A) and P () respectively. ( α A) (4..-7) alculate the vestibule pressure P by: P P + (4) (4..-8) alculate the air leak fro the vestibule to the staircase and to the fire elevator shaft using the vestibule pressure P, the air leak fro the vestibule to the staircase S can be calculated by: S ( αa) S ( αa) SO ( αa) + ( αa) S S S SO P + g H S O (5) where ( α A) S and ( α A) SO are the effective opening areas between the vestibule and the staircase and between the staircase and the outdoor, respectively, H S is the vertical distance between these openings. ikewise, the air leak fro the vestibule to the fire elevator can be calculated by: F F ( αa) F ( αa) FO F ( αa) F + ( αa) F FO P + g H F F (6) where ( α A) F and ( α A) FO are the effective opening areas between the vestibule and the fire S 4

9 International Journal on ngineering Perforance-Based Fire odes elevator shaft and between the fire elevator and the outdoor, respectively. H F is the vertical distance between these openings. (4..-9) alculate the required air supply rate to the vestibule W by: S W + + (7) F (4..-0) alculate the elevator shaft pressure at the level of the fire floor by: P P + (8) (4..-) alculate the air leak fro the elevator shaft to the outdoor by: O O ( αa) ( P + gh ) O O (9) where ( α A) O is the effective opening between the elevator shaft and the outdoor, H is the vertical distance of the opening between the corridor and the elevator shaft and the opening between the shaft and the outdoor. the vestibule and the corridor, and P and between the elevator shaft and the corridor are given by: 4 g h 9 ( α A) g h 4 9 g h ( α A) g h and and 4.4. elationships used for the calculation of required air supply rates (4) (4) Fig. 8 illustrates the flow patterns expected at the stage of whole building evacuation. (4..-) alculate the required air supply rate to the elevator shaft W by: W + (40) O 4.4 Whole Building vacuation 4.4. Average pressure difference and the flow rate corresponding to soke stop criterion Deterination of teperature conditions At the stage of whole building evacuation, a fullydeveloped fire is considered in the fire roo and the corridor ay be exposed to hot gases fro the fire roo. Accordingly, the teperature in the corridor is no longer the sae as that of the vestibule. At this stage, the corridor is abandoned and only the vestibule and the elevator shafts are protected fro soke. The teperatures of the fire roo and the corridor need to be first assessed to obtain the soke stop conditions at the openings fro the corridor to the vestibule and to the elevator shaft. It can be done using soe appropriate eans such as the siple forulas proposed by Tanaka et al. [5] Soke stop criteria Once the corridor teperature is given, the average pressure differences P and doorway flow rates corresponding to soke stop criteria between Fig. 8: Flow patterns at the stage of whole building evacuation The relationships which hold for the roo pressures and the flow rates are as follows: Pressures P P + (4) P P + (44) P P + (45) Flow rates Fire roo (): O (46) orridor (): + + O + U (47) Vestibule (): W + S + F (48) levator shaft (): W + (49) 4.4. alculation procedure for air supply rates Based on the above relationship, the air supply rates required to eet the soke stop criteria given O 5

10 International Journal on ngineering Perforance-Based Fire odes by equations (4) and (4) can be calculated by the following procedure: (4.4.-) Deterine the flow rates and the average pressure differences between the vestibule and the corridor, i.e. and P, and between the elevator shaft and the corridor, i.e. and P, by equations (4) and (4) according to the procedure described in (4.4.-) alculate the corridor pressure P by: P ( + U ) ( α A) O (50) where ( α A) O is the effective opening area calculated by cobining the series or parallel openings which connect the corridor to the outdoor. Note, if the corridor teperature becoes so high that the soke extraction is shut down, which ay occur when the door between the fire roo and the corridor is left open, P is calculated by letting U be 0. (4.4.-) alculate the average pressures of the vestibule Now that the pressure difference for soke stop conditions and the corridor pressure have been obtained, the pressures of the vestibule P can be obtained as : P P + (5) (4.4.-4) alculate the air leak fro the vestibule to the staircase and to the fire elevator The procedure to calculate the air leak fro the vestibule to the staircase S and to the fire elevator is exactly the sae as (4..-8). F (4.4.-5) alculate the air supply rate to the vestibule by : W + + (5) S F (4.4.-6) alculate the average pressure of the elevator shaft at the level of the fire floor P by: P P + (5) (4.4.-7) alculate the air leak fro the elevator shaft The procedure to calculate the air leak fro the elevator shaft to the outdoor is exactly the sae O as (4..-). (4.4.-8) alculate the air supply rate to the elevator shaft by: W + (54) O 4.5 Final Deterination of the Air Supply ates and Pressure elief Vents 4.5. Adjustent of the air supply rates for fire floor and whole building evacuation Since the soke stop criteria are different between fire floor evacuation and the whole building evacuation, the results of the required air supply rates are different accordingly between the two stages of evacuation. But practically, the sae fan is used in both stages, so the air supply rates should be adjusted to the sae rate to cope with any stage of evacuation. This adjustent can be done to obtain the final flow rates as follows: etting the flow rates fro the vestibule to the corridor and fro the elevator shaft to the corridor obtained for fire floor evacuation be and, respectively, and those for whole building evacuation be and, respectively, the flow rates fro the vestibule to the corridor and fro the elevator shaft to the corridor are finally deterined so as to satisfy: + + (55) and (56) Using the deterined and, calculate the air supply rates to the vestibule W and to the elevator shaft W according to the sae procedure described in 4. Fire Floor vacuation Designing of bypass pressure relief vents In the above, the condition of the doors between the vestibule and the corridor and between the vestibule and the staircase were not entioned but the air supply rates ay be calculated under the condition that all the doors are fully open in order to cope with the worst scenario for the air supply rates. As a result, the pressure rise ay becoe too high for occupants to open a door when the doors happen to be closed. Therefore, adequate pressure relief should be considered. In addition, if the corridor pressure exceeds the elevator shaft pressure, the criterion set by equation (6) is violated. So, adequate pressure relief vents ay be needed between the corridor and the vestibule and between the corridor and the outdoor. However, the details of the design of pressure relief vent is oitted in this paper. Fig. 9 illustrates the procedure for deterining the air supply rates in pressurization soke. 6

11 International Journal on ngineering Perforance-Based Fire odes Fire oo vacuation Fire Floor vacuation Whole Building vacuation flow chart for calculating the air supply rates valuate soke layer height at the tie of copletion of the fire roo evacuation. alculate the average pressure difference and the flow rate corresponding to soke stop criterion at the opening between the fire roo and the corridor. alculate the average pressure differences and and flow rates and corresponding to soke stop criteria between the vestibule and the corridor, and the elevator shaft and the corridor. opare the soke layer height with the height of safety criterion NG OK Deterine the flow rates and alculate the air supply rates to the vestibule and the elevator shaft flow chart for designing of bypasses Pressure difference between the vestibule and the corridor OK Pressure of the corridor OK NG NG Sizing pressure relief duct between the vestibule and the corridor Sizing pressure relief daper between the corridor and outdoor. nd of pressurization design Fig. 9: Procedure for deterining air supply rates in pressurization soke control syste 5. OMPAISON WITH OMPUT MOD PDITION The accuracy of the siple ethod in this paper was investigated by the coparison with the prediction by a coputer odel. The coputer odel was constructed by incorporating the function to the soke stop criteria into an existing one-layer zone ulti-roo soke oveent progra developed by Matsushita [6]. The conditions of the building for siulation are suarized below. Building Height of floor :.5 Fire floor : Second story Opening condition : : 0-story office building (The plan is referred to Figure.) Doors of the fire roo, windows of the fire roo (5% of all), doors to the vestibule and stairwell on the fire floor, ground floor door to the outside are open, and others are all closed. ach leak fro the elevator shaft and the stairwell to the outdoor is considered as an opening at the top of those shafts. Teperature: The coputer odel case was siulated with 0 o for outdoor, 0 o for roo, 8 o for corridor and 5 o for the other shafts as the initial teperatures in winter. Outdoor wind is not considered. The siple ethod case was calculated in fully-developed stage of fire with teperature 600 o for the fire roo, 00 o for corridor and 5 o for the shafts. As shown in Fig. 0, the required air supply rates calculated by the siple ethod proposed in this paper are reasonably close to the coputer prediction both for the vestibule and the elevator shaft. The errors are approxiately % for vestibule and 0% for elevator shaft. Besides, the results of the siple ethod are always larger than those of the coputer odel, that is, the siple ethod always calculates the required air supply rate for safety side. 7

12 International Journal on ngineering Perforance-Based Fire odes NOMNATU Fig. 0: oparison of the required air supply rates 6. ONUSION Although deterining the air supply rates is a very iportant process in the design of vestibule and elevator shaft pressurization soke control syste, a rational calculating ethod for the air supply rates has not yet been established in Japan. This paper intended to propose a logically clear and technically siple ethod to solve the probles. As a result, this calculation ethod has the following advantages: all the fire scenarios including evacuation at fully developed fire can be taken into account for fire safety criterion, the base of pressure difference criterion for soke stopping is logically and technically clear, and the procedures of this ethod consisting of siple forulas ake it possible to check the contents of calculation and the verification of safety requireent even for ordinary designers or building officials. The coparison between the siple ethod in this paper and the coputer odel indicates that the siple ethod is alost as accurate as the coputer odel. This calculation ethod for the air supply rates is considered to be useful in the design practice of vestibule pressurization soke control syste. AKNOWDGMNT This paper was supported by the ebers of Pressurization Soke ontrol Syste esearch oittee of the Kinki branch, the Architecture Institute of Japan. The authors gratefully acknowledge their inforative inputs. Sybols A i space area ( ) A ij opening area between space i and space j ( ) B ij width of opening between space i and space j () D i circuference length of space () g acceleration of gravity (s - ) H i ceiling height of space i () h ij height of opening between space i and space j () h heat transfer coefficient (kw - K - ) ij flow rate through the opening fro space i to space j (kgs - ) P i pressure of space i (Pa) P ij pressure difference across opening between space i and space j (Pa) Q heat release rate (kw) T i teperature of space i (K) t evacuation tie (s) U i extraction rate in space i (kgs - ) W i air supply rate to space i (kgs - ) z height of soke layer () ( αa) ij effective flow coefficient and area of opening between space i and space j ( ) i air density of space i (kg - ) ij air density difference across opening between space i and space j (kg - ) Subscripts O S F f outdoor fire roo corridor vestibule staircase elevator shaft fire elevator shaft upper layer FNS. Building ontractors Society, Trends of Fire Safety Planning on the eview of The Building etter (998) - In Japanese.. Nikken Sekkei td, Fire Safety Planning Docuents (994).. The Building enter of Japan, Sogo-boka Sekkeihou (Fire Safety Design Method of Buildings), Vol., pp (995) - In Japanese. 4. T. Tanaka, Siple topics and predicting ethods concerning soke oveent, Heating Piping & Air onditioning, pp (995) - In Japanese. 8

13 International Journal on ngineering Perforance-Based Fire odes 5. T. Tanaka et al., Siple forulas for predicting fire teperatures in the roo of origin and the connected corridor, Journal of structural and onstruction ngineering, pp. 4-4 (995) - In Japanese. 6 T. Matsushita et al., alculation Method of Air Supply ate in Vestibule Pressurization Soke ontrol Syste for Office Building (Part : alculation by oputer Model of Soke Moveent Prediction), Suaries of Technical Papers of Annual Meeting Architectural Institute of Japan (998) - In Japanese. APPNDIX : AVAG PSSU DIFFN In any building fire issues, it is necessary to consider ultiple spaces at very different teperatures, which ake it coplicated to calculate ass flow rate through openings. To avoid this coplexity, average pressure difference is used for the calculation of doorway flow rates. where h is the opening height, is the difference of air density in the spaces connected by the opening (let they be 0 and ), that is 0 and s is the ratio defined as s zn / h where z n is the neutral plane height above the lower edge of the opening. On the other hand, using the average pressure difference defined above, can also be given by: net 0 net α A (A) quating equations (A) and (A) leads to the following equation (A4), in which actual pattern of opening flow corresponding to average pressure difference P can be obtained by solving equation (A4) for s. s ( s ) gh (A4) () Definition of average pressure difference etting net be the net gas flow rate, average pressure difference is defined as: net P (A) A ( α ) This definition indicates that only the net flow rate through opening is the target of interest and intends to use the ordinary forula for orifice flow rate to calculate the net opening flow rate using regardless the conditions of teperatures and neutral plane height at an opening, that is: net α A (Aa) () Average pressure difference and flow pattern Whenever necessary, actual patterns of pressure difference and flow can be obtained fro the average pressure difference, since they are corresponding to each other as follows: etting s be the ratio of neutral plane height to opening heights, (a) when s The net opening flow rate net under different space teperatures is norally calculated by: net { s ( ) } s α B g h 0 (A) Fig. a: oncept of average pressure difference when s (b) when s < s N ikewise, fro the following equations (A5) and (A6): net and { s ( ) ( ) 0 s } net 0 α B 0 g h α A (A5) (A6) the equation which gives the relationship between P and s is obtained as follows: s ( ) ( s) 0 gh (A7) 9

14 International Journal on ngineering Perforance-Based Fire odes any cases. Taking this fact into account, the approxiate average pressure difference across an opening is defined here as the pressure difference at the height of neutral plane when the in- and outflows are balanced at the opening. This definition assures that the net gas flow rate is zero when the approxiate average pressure difference is zero. Fig. a: oncept of pressure difference when s < s N where s N is the value of s when the in- and outflows are balanced at the opening. s N + ( ) / 0 (A8) Fig. a4: oncept of approxiate average pressure difference Hence, the approxiate average pressure difference is calculated by: g h s (A0) s N Approxiate net opening flow rate is calculated using the approxiate average pressure difference as: Fig. a: Flows when the in- and out-flows are balanced at the opening ( ) Siilarly, the equations for the relationship of P and s for the cases of (c) 0 s < s and (d) s < 0 can N be developed if necessary. () Soke stop condition Substituting s into equations (A) and (A) yields required soke stop condition at the opening in ters of average pressure difference and flow rate respectively: net α A α A 0 ( s s ) N ( s < s ) N (A) The approxiate net flow rate given by equation (A) is very close to the exact net flow rate when s > and s < while the accuracy is only fair when 0 < s < except when s sn. However, the absolute value of the net flow rate is sall in the latter case, so the effect of the error on the calculation can be neglected. 4 gh 9 and net α B 0 g h (A9) APPNDIX : APPOXIMAT AVAG PSSU DIFFN It is known that the pressure difference at the iddle height of an opening is sufficiently close to the average pressure difference over the opening in 40