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Applied Thermal Engineering 31 (2011) 2992e2999

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

On the front velocity of buoyancy-driven transient ceiling jet in a horizontalcorridor: Comparison of correlations with measurements

D. Yang a,*, R. Huo b, X.L. Zhang b, X.Y. Zhao b

a Faculty of Urban Construction and Environmental Engineering, Chongqing University, Chongqing 400045, Chinab State Key Laboratory of Fire Science, University of Science and Technology of China, Hefei, Anhui 230026, China

a r t i c l e i n f o

Article history:Received 30 November 2010Accepted 21 May 2011Available online 27 May 2011

Keywords:Corridor fireTransient ceiling jetFront velocityBuoyancy

* Corresponding author. Tel.: þ(86) 23 65120750; fE-mail addresses: yangd8210@gmail.com, yangdon

1359-4311/$ e see front matter � 2011 Elsevier Ltd.doi:10.1016/j.applthermaleng.2011.05.031

a b s t r a c t

Front velocity of transient ceiling jet is a major concern for building fire safety. This work concentrates onthe front velocity of transient ceiling jet in corridor fires. Experiments with both steady fire sources anda developing fire source are performed to evaluate the applicability of existing theoretical correlations fora relatively long corridor. To account for the conditions with significant heat loss from smoke flow, somemodifications for these correlations are proposed by this work. Results show that the classical Hinkley’scorrelation without consideration of the heat loss can significantly over-predict the front velocity oftransient ceiling jet at the remote locations with relatively low temperatures (e.g., less than 80 �C). Jones’model, Benjamin’s model and CFAST’s model also over-predict the front velocity at these low temper-atures, but with much smaller deviations in relation to Hinkley’s correlation. The modified Hinkley’scorrelation, with consideration of the heat loss from smoke flow, produces more acceptable predictionsfor both steady and growing fires.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

When a fire occurs in a corridor or the fire smoke spreads intoa corridor from its adjacent rooms, the development of thebuoyancy-driven flow can be generally divided into three stages: (I)over the fire source, the flow rises vertically in the form of buoyantplume; (Ⅱ) after the impingement of the buoyant flow on theceiling, it propagates horizontally to the locations remote from thefire region in the form of gravitational current (see Fig. 1). This stageis usually called as a “transient ceiling jet” in previous literatures[1]; (Ⅲ) while the ceiling jet front arrives at the end of the corridor,a smoke layer is formed.

There have been numerous studies conducted for the first stage,i.e., fire plume, and many quantitative models have been developedfor this stage [2,3,4]. For the last stage of a corridor/tunnel fire, i.e.,steady smoke layer, there are also some studies describing thedistributions of fire-related parameters [5,6]. However, ascompared with the above two stages, there seems to be much fewstudies that are concerned with the second stage, transient ceilingjet, especially for a corridor fire. This may be due to the complexityof quantification of a transient ceiling jet, as indicated by Evans [7].It has been reported that fire-induced toxic smoke is responsible for

ax: þ(86) 23 65120773.g@cqu.edu.cn (D. Yang).

All rights reserved.

most of the casualties in building fires [8]. Therefore, the time takenfor the smoke to overtake the escaping people, or the front velocityof transient ceiling jet, becomes one of the important consider-ations for building fire safety. For a corridor-like structure, it willprovide an effective route for smoke spread, which increases thedangerous levels for the evacuating people. Tunnel is another typeof long and narrow structure, and its side entrances are usuallyused as the fire emergency exits, which would be far away from thefire origin. Therefore, it is very important to gain the information onthe front velocity of transient ceiling jet in a long corridor ora tunnel, for the concern of human safety in such buildingconfigurations.

In the previous studies about the front velocity of the transientceiling jet, the correlation developed by Hinkley is a well-knownone [9]. Hinkley’s formula, i.e., U ¼ 0:8ðgQf T=CpraT

2aWÞ1=3, with

T denoting the absolute temperature of the smoke flow and Qf

denoting the fire heat release rate, was reported to get encourageagreementwith the results of a fire test [9]. However, as declared byHinkley, more experimental work is required to establish theirvalidity [9]. In 1998, Kim conducted experiments to further eval-uate Hinkley’s correlation by using laser-assisted visualizationtechnology [10]. It was found that the front velocity calculated fromHinkley’s formula was 20% greater than the measured one. It isnoted that, Hinkley assumed that smoke goes only in one direction,but the smoke flow propagates to both two directions in Kim’sexperiment. So, He [11] introduced a factor of 0.5 into the term of

Nomenclature

Cp specific heat of air at constant pressure (kJ/kg K)cvent vent coefficient W width of corridor (m)d channel height (m)Fr Froude numberFr0 Froude number of smoke flowg gravitational acceleration (m/s2)g0 gravitational acceleration with variable density (m/s2)h ceiling jet depth (m)Q fire heat release rate (kW)S longitudinal distance (m)t time (s)T ceiling jet temperature (K)Ta ambient temperature (K)u local horizontal velocity (m/s)U front velocity of transient ceiling jet (m/s)

_V volumetric flow rate of ceiling jet (m3/s)W width of corridor (m)z height (m)

Greek symbols6 difference between variablesa fire size growth rate (s�2)r ceiling jet density (kg/m3)ra density of ambient air (kg/m3)

Subscriptsa ambientb bottomc characteristiccv convective1 inflow boundary

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e2999 2993

fire heat release rate to improve Hinkley’s correlation, i.e.,U ¼ 0:8ð0:5gQT=CpraT2aWÞ1=3. A much better agreement betweenthe result of Kim’s experiment and this improved formula wasobtained.

However, the applicability of Hinkley’s correlation remainsquestionable. The main reason is that the experimental corridorused by Kim was only 11.83 m long and thus the heat losses fromsmoke flow to bounded walls were neglected when comparingHinkley’s prediction with the measurement [10]. However, fora long corridor or a tunnel, the heat transfer between smoke flowand bounded walls could play an important role, and the heat lossleads to an obvious decrease in heat flow rate of smoke flowand thedeceleration of smoke spread as well. Hinkley’s correlation needs tobe modified for such conditions. This is one of the motivations ofthis work. Another reason is that previous validation experiments(e.g., the ones conducted by Kim) used pool fire as the fire source, inwhich the heat release rates appreciably vary with time at theinitial stage. As seen from Kim’s data [10], the transient ceiling jetcould have arrived at the end of the corridor before the fire heatrelease rate reached the quasi-steady state. Since the heat flow rateis an important input parameter for Hinkley’s correlation, usinga constant fire source seems to be necessary for validation purpose.

On the other hand, there are also some other correlations ormodels predicting the front velocity of transient ceiling jet. Asmentioned above, the transient ceiling jet in a corridor can betreated as a buoyancy-driven gravitational current. In the funda-mental hydrodynamics area, Benjamin [12] performed pioneeringtheoretical studies on the two-dimensional gravitational flow andestablished a correlation for its front velocity. Jones [13,14] alsoestablished empirical correlations for the velocity of corridor jetflow, some of which have already been used as sub-models fora classical two-zone fire model, CFAST [14]. Despite these theoret-ical studies, further experimental investigations are required toevaluate these correlations or models. This is another motivation ofthis work. In this work, experiments were performed in a reduced-

Fig. 1. Schematic of transport of transien

scale corridor to investigate the front velocities of transient ceilingjets at different fire sizes. The predictions obtained from bothexisting correlations and the modified correlations were comparedagainst the measurements.

2. Reviews on previous correlations and modifications

Benjamin [12] theoretically studied the gravitational currentwith a constant density in a two-dimensional channel. Usinga reference frame moving with the same velocity as that of thecavity tip (shown in Fig. 2), the transient current can be treated asa steady gravity front. The following formula is established byBenjamin [12]:

U2 ¼ ghðd� hÞð2d� hÞdðdþ hÞ (1)

where U denotes the front velocity of gravitational current ata stationary coordinate (shown in Fig. 2), h is the thickness ofgravitational current and d is the height of the channel.

Benjamin recommended that all the equations are applicable togravitational currents with variable density by replacing g withg0 ¼ gðra � rÞ=ra. On the basis of Benjamin’s theory, Hinkleyimproved the formula of Froude number to represent the fire-induced buoyant flows [9]:

Fr0 ¼�U3CpraT

2aW=gQf T

�1=2 ¼ ðU=UcÞ3=2 (2)

Uc ¼�gQf T=CpraT

2a

�1=3(3)

where U is the front velocity of the transient ceiling jet, Cp is thespecific heat of air at constant pressure, ra is the air density atambient temperature, Ta is the ambient temperature, W is thewidth of a corridor, g is gravitational acceleration constant, Qf is

t ceiling jet in a horizontal corridor.

Fig. 2. Arrested cavity front as viewed in a moving frame with the same velocity offront (Benjamin’s theoretical framework).

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e29992994

heat release rate of fire source, T is the absolute temperature ofsmoke gases and Uc represents the characteristic velocity of the hotsmoke flow.

By extracting one series of data from an experimental corridorfire, a linear relationship between the front velocity of transientceiling jet, U, and the characteristic velocity, Uc, is established byHinkley [9]:

U=Uc ¼ 0:8 (4)

The linear relationship between U and Uc suggests that theFroude number of transient ceiling jet (see Eq. (2)) is a constant. Itshould be noted that, for a fire environment with appreciableamount of heat loss from smoke flow to bounded walls, the actualheat flow rate of smoke flow could be smaller than the convectiveheat released from the fire origin. In such conditions, Hinkley’scorrelation should be modified by substituting the actual heat flowrate of ceiling jet, Qcv, for the fire heat release rate, Qf :

U=�gQcvT=CpraT

2aW

�1=3 ¼ 0:8 (5)

Eq. (5) is named as the modified Hinkley’s correlation in thefollowing sections. The volumetric flow rate, _V , is assumed to beconstant along the corridor, which is equal to the one at the inflowboundary, _V1. The convective heat flow rate of transient ceiling jetcan then be calculated by:

Fig. 3. Measurement system and

Qcv ¼ DT _mCp ¼ DT _V1raTaCp=T (6)

where DT is the average temperature rise of transient ceiling jet.In 1992, Jones developed amodel for prediction of the depth and

front velocity of transient ceiling jet [13]:

h ¼�32

�2=3�2Drgr

��1=3� _V1

W

�2=3

(7)

U ¼ 2$3�2=3�Drg _V1rW

�1=3

(8)

The term of density can be transformed to be that of absolutetemperature by using ideal gas law. This model is named as Jones’model in the following sections. It is derived from Eqs. (7) and (8)that the Froude number of Jones’ model is not a constant, butvaries with smoke gas temperature:

Fr0 ¼ Uffiffiffiffiffiffigh

p fDT1=2 (9)

In Jones’ model, the Froude number decreases as the ceiling jettravels along the corridor because of the longitudinal decay intemperature [5,15]. This indicates that there are inherent discrep-ancies between Jones’ model and Hinkley’s model.

Jones also proposed another empirical correlation as a sub-model for the classical fire zone model, CFAST [14]. A simpleformulawas established using an integrated form of Bernoulli’s law.The pressure drop at the bottom of the ceiling jet is Pb ¼ 0, thepressure drop at the top is Pt ¼ ghðr� raÞ, and using a vent coef-ficient cvent of 0.74, it gives

U ¼ cvent

ffiffiffi8

p

31ffiffiffir

p Pt þffiffiffiffiffiffiffiffiffiPtPb

p þ PbPt þ Pb

z0:7

ffiffiffiffiffiffiffiffiffiffiffiffigh

DTTa

s(10)

layout of corridor fire test.

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e2999 2995

This model is named as CFAST’s model. In the following sections,comparisons will be made between the predictions of correlations(Eqs. (1), (4), (5), (8) and (10)) and the measurements.

3. Experimental

3.1. Apparatus and measurements

Experiments were conducted in a reduced-scale horizontalcorridor with internal dimensions of 66.0 m long � 1.5 mwide� 1.3m high. The schematic viewof the experimental corridoris shown in Fig. 3. The ceiling and the side walls of the corridor aremade of fire-resistant glass with thickness of 12 mm. The corridorfloor is made of steel plate with thickness of 3 mm. During the testsof this work, the smoke can flow out of the corridor through bothsides.

A propane gas burner, rather than a pool fire, was used tosimulate the fire source. The dimensions of the gas burner was0.86 m � 2.16 m, which was located at 9 m away from one end ofthe corridor (see Fig. 3). The fuel supply rates can be controlled andmonitored by a gas flow-meter, and the corresponding heat releaserates were determined from calorimeter measurements in prior tothe formal tests. Seven series of tests were included in this work. InTest1eTest6, the heat release rates were controlled to be constant,e.g., for Test5, the heat release rate only cost about 13 s to reach itsquasi-steady state after the ignition time (see Fig. 4), while the

0 5 2 0 0 2 0 5 1 0 0 1 0 5 0 0

0 2

0 4

0 6

0 8

0 0 1

0 2 1

0 4 1 Ignition time in

calorimeter measurement

Hea

t rel

ease

rate

(kW

)

) s ( e m i T

R R H

s 3 1

Ignition time

10 0 1 0 8 0 6 0 4 0 2 0 0

0 1

0 2

0 3

0 4

0 5

0 6

0 7

0 8

CO

vol

ume

conc

entra

tion

(ppm

)

mi T

A B C D E

113s 12s

Fig. 4. Variation of heat release rate, temperature and c

transient ceiling jet had just arrived at the first measurement point.The test conditions for Test1eTest6 were summarized in Table 1. Toevaluate the applicability of these correlations in developing fires,a t-squared firewith growth rate of 0.02 andmaximumheat releaserate of 220 kW was designed in Test7. The fires in the experimentsof this work are all well-ventilated.

The arrival time of the transient ceiling jet was detected at fivelocations: 9m (Location A),17m (Location B), 23m (Location C) and31 m (Location D) and 45 m (Location E). Both the temperature andCO volume concentrationwere monitored at these five locations, asshown in Fig. 3. The gas temperatures were measured by K-typeshielded thermocouples with diameter 1 mm. The measurementaccuracy was �1 �C and the response time was on the order of 1 s.Each thermocouple tree was consisted of 12 thermocouples withvertical interval of 0.1 m. The CO volume concentrations weremeasured by a multi-channel gas analysis system (Testo, Co. Ltd.,Model 350XL). The sample gases were drawn through a stainlesssteel pipe and a flexible hose by a pump with volume flow rate of1.0 L/min, then passed through filters to remove moisture and sootparticles, and were finally directed into the analytic models. Themeasurement uncertainty of dry CO volume concentrationwas lessthan 5%. The sampling interval of CO volume concentration was settobe1 s. TheCOprobeswerefixedat the same longitudinal distancesas those of thermocouple trees, andwere all installed at theheight of1.08m.Another four thermocouple treeswere installedbetween theneighboring measurement points, which were installed at the

0 4 2 0 2 2 0 0 2 0 8 1 0 6 1 0 4 1 0 2 1 0 0 1 0 8 0 6 0 4 0 2 0 0

0 1

0 2

0 3

0 4

0 5

0 6

0 7

0 8

0 9

0 0 1

Tem

pera

ture

) s ( e m i T

A B C D E

Ignition time

15s 13s 11s

0 4 2 0 2 2 0 0 2 0 8 1 0 6 1 0 4 1 0 2

47s

) s ( e

6s

arbon monoxide concentration with time for Test5.

05 5 4 0 4 5 3 0 3 5 2 0 2 5 1 0 1 5

0 . 0

1 . 0

2 . 0

3 . 0

4 . 0

5 . 0

6 . 0

7 . 0

8 . 0

9 . 0

0 . 1

1 . 1

No

rm

alize

d c

on

ve

ctiv

e h

ea

t flo

w r

ate

) m ( e c r u o s e r i f m o r f e c n a t s i d l a n i d u t i g n o L

1 t s e T 3 t s e T 5 t s e T

Fig. 5. Normalized convective heat flow rates of transient ceiling jet at differentlongitudinal distances.

Table 1Test conditions and depths of transient ceiling jet for steady fires.

Test no. Ambient temperature (�C) HRR (kW) _V1a (m3/s) Depth of ceiling jetb (m)

9 m 17 m 23 m 31 m 45 m

M P M P M P M P M P

Test1 16 218 0.60 0.31 0.35 0.32 0.40 0.40 0.45 0.42 0.52 0.62 0.78Test2 18 191 0.58 0.35 0.36 0.36 0.40 0.43 0.45 0.48 0.48 0.60 0.73Test3 17 149 0.54 0.36 0.36 0.36 0.40 0.42 0.45 0.49 0.52 0.57 0.73Test4 18 129 0.48 0.35 0.35 0.38 0.40 0.44 0.44 0.52 0.50 0.55 0.70Test5 23 83 0.44 0.40 0.36 0.42 0.39 0.42 0.43 0.48 0.49 0.53 0.71Test6 19 58 0.39 0.38 0.36 0.42 0.40 0.48 0.44 0.51 0.50 0.52 0.69

a _V1 is the volume rate of smoke flow at the first measurement point (i.e., 9 m away from the fire source).b M denotes measurements and P denotes predictions by Jones’ model.

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e29992996

distance of 13 m, 20 m, 27 m and 38 m, respectively. These fourthermocouple trees were used to detect the temperatures of ceilingjet at corresponding distances. To obtain the volume flow rate of theceiling jet, a multichannel-anemometer (KANOMAX Model 1560)was used to measure the vertical velocity profile.

In order to record the development process of the flowparameters, the measurement systems of temperature, CO volumeconcentration and flow velocity were all activated before theignition of gas burner. Temperature measurements were in oper-ation until the ends of the tests, and the duration time were about450 s. CO measurements were in operation until the transientceiling jet arrives at the end of the corridor.

To record the depths of the transient ceiling jet, a laser sheetwith thickness of 5 mm was used to assistant the smoke flowvisualization. The laser sheet was positioned at the remote side ofcorridor (see Fig. 3). Since the combustion of propane yields fewsmoke particles at well-ventilated conditions, an artificial smokesource was placed over the gas burner to simulate the smokeparticles. Rulers with resolution of 1 cm were positioned atdifferent locations of the corridor for measurement of the depths ofthe transient ceiling jet.

3.2. Data reduction

The arrival of smoke front at each measurement point can beidentified by the sudden increase in fire-related parameters fromtheir individual ambient values. As seen in Fig. 4, the signal oftemperature and that of CO volume concentration experiencesudden increase at different instants, e.g., for each measurementpoint of Test5 (see Fig. 4), the time of abrupt change in temperatureis about 17 s earlier than that of CO volume concentration. This isbecause the response time of COmeasurement system is about 17 slater than that of thermocouple. However, the traveling time overthe corresponding distance (e.g., the distance between the neigh-boring measurement points) identified by temperature signal isnearly the same as that by CO volume concentration, as shown inFig. 4. This indicates that the traveling time can be identified byboth these two signals. At the remote locations (e.g., at Location E inTest5), it may be difficult to identify the abrupt change in temper-ature, as shown in Fig. 4. Therefore, the sudden increase in COvolume concentration was used to identify the arrival of transientceiling jet in this work.

The front velocity over the neighboring measurement points iscalculated by:

U ¼ DSDt

(11)

where DS is the longitudinal distance over the neighboringmeasurement points, Dt is its corresponding traveling time.

The temperatures detected by the thermocouple trees installedbetween the neighboring measurement points were used as the

input parameters for the correlations. These input temperatureswere all integral average ones, which are calculated through theintegral ratio method [16]. The maximum deviation between theaverage temperature of the middle thermocouple tree and the onesof its neighboring thermocouple trees was about 40%, which wouldresult in an uncertainty of front velocity prediction of about 11%.Smoke average temperatures could also be obtained from spatiallyintegrating the vertical temperature profiles within the smoke flow.The relative deviations between these two methods were less than15% for this work, and resulted in an uncertainty of front velocityprediction of about 5%. The total uncertainty due to input param-eter was estimated to be 12%.

The volume flow rate of the ceiling jet at the initial measure-ment point (Location A) is calculated from the following equation:

_V1 ¼Zh

uWd (12)

where u is the local horizontal velocity measured by the velocityprobe.

4. Results and discussion

4.1. Actual heat flow rate of transient ceiling jet

The driving force of transient ceiling jet, buoyancy, dependsupon both the convective heat release rate from the fire source andthe heat loss to bounded walls. The heat flow rates of transientceiling jet can be quantified by Eq. (6). Fig. 5 shows the normalized

7 . 0 8 . 0 9 . 0 0 . 1 1 . 1 2 . 1 3 . 1 4 . 1

fron

t vel

ocity

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e2999 2997

heat flow rate of transient ceiling jetQ*cv, for Test1, Test3 and Test5,

respectively. The actual heat flow rates are normalized by the onesat the initial measurement point, i.e., Qcv/Qcv,1. It is shown that thenormalized heat flow rate of transient ceiling jet experiences a fastdecay in the longitudinal direction. This indicates that the amountof heat loss of smoke flow become significant when the smoketravels a relatively long distance. This also indicates that modifi-cations on Hinkley’s correlation (i.e., substituting Qcv for Qf ) wouldbe necessary for a relatively long corridor.

4. 1 3 . 1 2 . 1 1 . 1 0 . 1 9 . 0 8 . 0 7 . 0 6 . 0 5 . 0 4 . 0 3 . 0 2 . 0 1 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0

Q 2 / 1 h t i w y e l k n i H f Q h t i w y e l k n i H v c

Pred

icte

d

y t i c o l e v t n o r f d e r u s a e M

Fig. 7. Comparison of predicted front velocities obtained from Hinkley’s model andmodified Hinkley’s model with measured front velocity.

4.2. Depth of transient ceiling jet

The flow depth is an important input variable for the correla-tions that are utilized for predicting the front velocity of the tran-sient ceiling jet. The depths of the transient ceiling jet can bevisualized by the assistance of a laser sheet (see Fig. 3). Table 1illustrates the depths of the transient ceiling jet upstream theflow front. The smoke flow depths obtained from Jones’model (i.e.,Eq. (7)) are also illustrated in Table 1 for comparison. It is shownthat the measurements and the predictions of Jones’model were ingood agreements at the distances of 9 m, 17 m, 23 m and 31 m. Ata remote location (e.g., 45 m), the predictions of Jones’ model wereabout 20% higher than the measurements.

05 5 4 0 4 5 3 0 3 5 2 0 2 5 1 0 1 5 0 . 0

2 . 0

4 . 0

6 . 0

8 . 0

0 . 1

2 . 1

4

a

b

. 1

6 . 1

Fron

t vel

ocity

(m/s

)

) m ( e c n a t s i d l a n i d u t i g n o L

t n e m e r u s a e M Q 2 / 1 h t i w y e l k n i H f

Q h t i w y e l k n i H v c

T S A F C s e n o J

n i m a j e B

Test 1

05540453035202510150.0

2.0

4.0

6.0

8.0

0.1

2.1 Test 4

Fron

t vel

ocity

(m/s

)

)m(ecnatsidlanidutignoL

tnemerusaeMQ2/1htiwyelkniH f

QhtiwyelkniH vcTSAFC

senoJnimajeB

4tseT

1 t s e T

Fig. 6. Longitudinal distributions of front velocity of transient ceiling jet.

4.3. Front velocity of transient ceiling jet

Fig. 6 shows the longitudinal distributions of measured frontvelocity and the ones predicted by different correlations for Test1and Test4. The measured ceiling jet depths and the instantaneoustemperatures obtained from integral ratio methodwere used as theinput parameters of the correlations.

Since the smoke propagates to both two directions, a factor of0.5 was introduced into the fire heat release rate term of Hinkley’scorrelation (i.e., He’s correlation as discussed in Section 1). For thepredictions of Hinkley’s correlation, there are few variations infront velocity along the longitudinal direction. This results ina significant over-prediction of front velocity at the locationsremote from the fire source. The reason is that the actual heat flowrates at the remote locations become much smaller than those atthe near-fire locations, as demonstrated in Section 4.1. It is shownthat the modified Hinkley correlation (i.e., Eq. (5)) produces muchbetter predictions at these remote locations. The other threecorrelations (CFAST’s model, Jones’ model and Benjamin’s model)also predict the longitudinal variation trend of front velocity well,as compared with those obtained from Hinkley’s correlation.

4. 1 3 . 1 2 . 1 1 . 1 0 . 1 9 . 0 8 . 0 7 . 0 6 . 0 5 . 0 4 . 0 3 . 0 2 . 0 1 . 0 1 . 0 2 . 0 3 . 0 4 . 0 5 . 0 6 . 0 7 . 0 8 . 0 9 . 0 0 . 1 1 . 1 2 . 1 3 . 1 4 . 1

T S A F C s e n o J

n i m a j e B

Pred

icte

d fro

nt v

eloc

ity

y t i c o l e v t n o r f d e r u s a e M

Fig. 8. Comparison of predicted front velocities obtained from CFAST’s model, Jones’model and Benjamin’s model with measured front velocity.

08 1 0 6 1 0 4 1 0 2 1 0 0 1 0 8 0 6 0 4 0 2 0 0

0 5

0 0 1

0 5 1

0 0 2

0 5 a

b

2

Fire

siz

e (k

W)

) s ( e m i T

t 2 h α = 0.02 t i w e r i f R R H e r i f d e r u s a e M

05540453035202510150.0

2.0

4.0

6.0RRHydaetS

Fron

t vel

ocity

(m/s

)

)m(ecnatsidlanidutignoL

QhtiwyelkniH vcTSAFC

senoJ nimajeBtnemerusaeM

RRHgnipoleveD

yticolevtnorF

e v r u c e z i s e r i F

Fig. 9. Fire size curve and front velocities of transient ceiling jet for a growing fire.

D. Yang et al. / Applied Thermal Engineering 31 (2011) 2992e29992998

Fig. 7 compares the predictions of Hinkley’s correlation and themodified Hinkley correlation against the measured front velocity.The data of Test1e6 were all included in this figure. It is shown thatHinkley’s correlation generally over-predicts the front velocity. Atrelatively smaller velocities (e.g. less than 0.4m/s), the prediction ofHinkley’s correlation can be higher than the measured data to theextent of 180%. It is also noted that the data predicted by Hinkleyshow considerable scatter. At the velocities higher than 1.0 m/s, themodified Hinkley’s correlation can under-predict its value withthe deviation of about 25%. However, at the velocities lower than0.8m/s, the predictions of modified Hinkley’s correlation agreewellwith the measurements. As compared with Hinkley’s correlation,the predictions obtained from the modified Hinkley’s correlationshow more satisfactory collapse.

Fig. 8 compares the predictions obtained from CFAST’s model,Jones’ model and Benjamin’s model against the measured ones. Ata relatively higher velocity (e.g., the ones higher than 1.0 m/s),Jones’ correlation predicts its valuewell, but both Benjamin’s modeland CFAST’s model under-predict its value with the deviation ofabout 20% and 37%, respectively. At a relatively smaller velocity(e.g., the ones lower than 0.8 m/s), Jones’ correlation and Benja-min’s correlation over-predict its value with the maximum devia-tion of about 100% and 74%, respectively. This may be due to thatboth these two correlations neglect the viscous force between the

hot flow and the surroundings. At relatively lower temperatures,the effects of viscosity could become more significant, and thusincreases the resistance on the transient ceiling jet. Reasonableresults are obtained from CFAST’s model when the velocity issmaller than 0.6 m/s.

4.4. Application to a growing fire

In the above sections, the previous correlations and the modi-fied correlations were evaluated by using steady fires. The resultsshow that Hinkley’s correlation could significantly over-predict thefront velocity, while the modified Hinkley’s correlation, CFAST’smodel, Jones’ model and Benjamin’s model can produce muchmore reasonable predictions. However, in real fires, the initial firedevelopment is always accelerating, and a suitable way to describethis is to use the t-squared fire (i.e.,Qf ¼ at2) [17]. In Test7, a t-squared fire with growth rate of 0.02 and maximum heat releaserate of 220 kW was provided by the gas burner, for the purpose ofevaluating the applicability of these correlations in developingfires. The profile of fire heat release rate is presented in Fig. 9(a).Both the measured front velocity and those predicted from themodified Hinkley’s correlation, CFAST’s model, Jones’ model andBenjamin’s model are presented in Fig. 9(b). As compared with theones in a constant fire source, the transient ceiling jet front velocityin a developing fire experience a slower decay in the longitudinaldirection. It is shown that all the correlations over-predict the frontvelocity at the developing fire stage but with acceptable deviations.The maximum deviation between the measurements and those ofJones’ model is about 42%, and the maximum deviation betweenthe measurements and those of the modified Hinkley’s correlationis only about 15%.

5. Conclusions

Reduced-scale experiments were performed to investigate thefront velocity of transient ceiling jet in corridor fires. The predic-tions obtained from previous correlations (including Hinkley’scorrelation, Jones’ model, Benjamin’s model, and CFAST’s model)and the ones obtained from themodified Hinkley’s model proposedby this workwere compared against themeasurements. The resultsshowed that Hinkley’s correlation significantly over-predict thefront velocity at the locations far away from the fire source. Jones’correlation, Benjamin’s correlation and CFAST’s model could alsoover-predict the front velocity at the remote locations, but thepredictions become much better in relation to those of Hinkley’scorrelation. As compared with those previous correlations ormodels, the modified Hinkley’s model with substituting the actualheat flow rate of ceiling jet for the fire heat release rate, can producebetter results for such a long corridor. The conclusions formulatedabove were demonstrated to be also suitable for developing fires.

Acknowledgements

This work is a part of Project No. CDJZR11210010 Supported bythe Fundamental Research Funds for the Central Universities.

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