s i

wedeity o

Pre-ashoverHeat transfer

el foo haratus asulaandp. I

literature and the heat release rates were provided from the experiments. The re temperature pre-

x effecbeenely bore s

ers harocedu

solved as a function of the heat release rate at a particular time step

ver res, derivedresented here ismay be assumedal inertia is con-re with uniformr layer re tem-dary structure as

functions of time for given heat release rates varying with time.

Contents lists available at ScienceDirect

.el

Fire Safety

Fire Safety Journal 72 (2015) 7786http://dx.doi.org/10.1016/j.resaf.2015.02.0082. Method

Based on simple heat and mass balance of re enclosures,Wickstrm has developed a general approach to calculate

0379-7112/& 2015 Elsevier Ltd. All rights reserved.

* Corresponding author.E-mail addresses: franz.evegren@sp.se (F. Evegren),

ulf.wickstrom@ltu.se (U. Wickstrm).often claimed that the relationship is applicable to steady-state aswell as transient re growths [13]. However, the temperature istemperature. Commonly used simple methods for pre-ashoverre temperature approximations are often based on [1] the cor-relation developed by McCaffrey, Quintiere, and Harkleroad [2],the so called MQH relationship. It builds on a simplied energybalance and regression correlation with data from numerous testres.

Whilst the MQH relationship is simple to use it has many lim-itations which are seldom properly considered. It is for example

This paper shows a clear and understandabmodel for estimating temperatures in pre-ashobased on well-known re physics. The model plimited to re enclosures where the boundariesto have lumped heat capacity, i.e. where thermcentrated to one layer of the boundary structutemperature. It may be used to predict the uppeperature as well as the temperatures in the bounsessments of the severity of a compartment re before ashover isthe temperature of the upper hot layer, here referred to as the re

bounded enclosures, similar to the ones studied here, but thegeneral limitations of the empirical correlation remain.

le enclosure reCompartment re

1. Introduction

To model the many and complesophisticated computer models havedecades; they are now used routinscientic community and in applieddesire for quick approximate answvated the development of simple pdictions of the model matched very well with experimental data. So did the FDS predictions while theoriginal MQH relationship gave unrealistic results for the problems studied. Major benets of using themodel in comparison with CFD modeling are its readiness and simplicity as well as the negligiblecomputation times needed. An Excel application of the presented pre-ashover re model is available onrequest from the author.

& 2015 Elsevier Ltd. All rights reserved.

ts of res, increasinglydeveloped the last fewth in the re researchafety engineering. Thes, however, also moti-res. A key value in as-

and takes no account to the re growth history (e.g. slow or con-stant). The applicability in case of a growing heat release rate istherefore questionable. Furthermore, it has not been generally un-derstood that the original MQH relationship is inappropriate whensurrounding boundaries are thin and highly conductive [cf. 1,3]. Tomanage this shortcoming, Peatross and Beyler developed a mod-ied expression for the heat transfer coefcient in the MQH re-lationship [4]. It gave improved correlation with tests in steel-Fire temperatureZone modelNew approach to estimate temperatureres: Lumped heat case

Franz Evegren a,*, Ulf Wickstrmb

a Fire Research, SP Technical Research Institute of Sweden, Box 857, SE-501 15 Bors, Sb Department of Civil, Environmental and Natural Resources Engineering, Lule Univers

a r t i c l e i n f o

Article history:Received 25 June 2014Received in revised form12 January 2015Accepted 1 February 2015Available online 14 February 2015

Keywords:Temperature prediction

a b s t r a c t

This paper presents a modboundaries are assumed tlayer with uniform temperesistance. The model yieldpredict temperatures in inwith full scale experimentsso called MQH relationshi

journal homepage: wwwn pre-ashover

nf Technology, SE-971 87 Lule, Sweden

r estimating temperatures in pre-ashover res where the re enclosureve lumped heat capacity. That is, thermal inertia is concentrated to onere and insulating materials are considered purely by their heat transfergood understanding of the heat balance in a re enclosure and was used toted and non-insulated steel-bounded enclosures. Comparisons were madewith other predictive methods, including CFD modeling with FDS and the

nput parameter values to the model were then taken from well-knownsevier.com/locate/firesaf

Journal

L air replacement

R radiationr radiations surfacetot totalult ultimateW walls

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 778678temperatures in enclosure res by simple, often analytical, meth-ods. For ventilation controlled res it was presented [5] assuminga one-zone model, similar to the models by Magnusson and The-

Nomenclature

A area [m2]c specic heat capacity

[J/(kg K)]d core thickness [m]H opening height [m]h heat transfer coefcient

[W/(m2 K)]L ame height [m]l thickness of insulation [m]m mass ow rate of gases [kg/s]R heat resistance [m2 K/W]T temperature [K]t time [s]q heat ux [W/m2]

Greek symbols

constant [kg/(s m2.5)] emissivity [dimensionless] temperature difference [K] core density [kg/m3]s StefanBoltzmann constant

[W/(m2 K4)] coefcient of proportionality

[dimensionless]landersson [6] and the parametric curves in Eurocode 1, EN1991-1-2 [7]. In this paper a pre-ashover model is derived with thesame approach but based on a two-zone assumption and expres-sions of the heat transfer through the re enclosure boundaries.The upper layer re temperature and temperatures throughout theboundary structure may thereby be predicted as functions of timefor given heat release rate histories. The model presented in thispaper applies only to enclosure boundaries for which lumped heatcapacity may be assumed. Different insulation alternatives can beconsidered and the heat capacity of the insulation can either beneglected or numerically added to the core of the boundaries. Tovalidate the model, which was derived straight from re physics,comparisons were made with two large scale experiments per-formed in a steel container with and without insulation [8].Comparisons were also made with FDS simulations [9] and cal-culations based on the MQH relationship [2]. FDS simulations wereperformed as they were expected to yield the most accurate the-oretical predictions, in particular in comparisons with the moreapproximate two-zone models.

2.1. New simple pre-ashover re model

The heat released by combustion in an enclosure is lost indifferent ways, as illustrated in Fig. 1. By setting up a heat balance,the heat loss at enclosure boundaries qW

can be derived. It equalsthe heat ux into the boundary structures q"i which heats up and isconducted through the structure [10] depending on itscomposition.

The heat transfer through the boundaries was modeled as-suming that surrounding structures have lumped heat capacity,which was described in three parts. Together with the descriptionO openingo outsidep at constant air pressurekofneexp

1.2.3.4.

corcorcorcantembettemobsisfol

2.1

Figbouconduction

i inside

h boundary heat transfer

g gasSuperscripts

* pre-ashover model. per unit time per unit area

Subscripts

1 ambientC combustionc convectioncore core of structuref rethe heat ux into the boundary structure the derivation of thew simple pre-ashover model may thus be described by fourressions, accounting for:

the enclosure heat balance;the boundary conditions at the inside of the core;the core's response to heating; andthe boundary conditions at the outside of the core.

The model was expressed in electric analogy by identifying thee as a capacitor and the boundary conditions at each side of thee as well as heat losses in the enclosure as heat resistances. Thee is thereby the only component of the boundary structure thatstore heat. Temperatures therefore vary linearly between theperature in the enclosure and the core temperature as well asween the core temperature and the ambient temperature. Theperature rises of the re and of the boundary surfaces are

tained as weighted averages depending on the thermal re-tances. This is illustrated in Fig. 2 and further described in thelowing subsections where the model is derived.

.1. Enclosure heat balance (1)The temperature in a re enclosure can be estimated based on

. 1. Heat balance components of a re enclosure and an illustration of thendary structure assumed.

boundary as in Eq. (1), analogy is attained with a description of theheat ux to a surface. In re safety engineering this is generally

written as ( ) ( )q T T h T TW s r s g s4 4 = + . The parameters includedin this expression can be identied in analogy with Eq. (1), wherecorresponding parameters are A A/s O tot f = , T Tr

4 4 = , h mc A/p tot = ,and T q mc/ = . Thus, the q mc/ term can be recognized as the

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 7786 79conservation of energy. The enclosure is then a control volume inan open system where energy is released by combustion, andwhere energy and mass are exchanged in balance with the sur-roundings. The heat released by combustion qC is an input para-meter which in the pre-ashover stage is assumed independent ofthe access to oxygen in the enclosure. The heat is lost in a numberof ways, as illustrated in Fig. 1 [6]: by radiation out throughopenings qR, by replacement of hot gases with air of ambienttemperature qL and by radiation and convection to the enclosureboundary surfaces qW . Omitting the relatively small amount en-ergy stored in the enclosure gas volume, the energy balance can besummarized as q q q qC W L R = + + .

The heat loss by replacement of gases can be expressed as

( )q mc T TL p f = and the heat loss by radiation through theopening as ( )q A T TR O f f4 4 = , where m is the mass ow of gasesout through the opening, cp is the specic heat for air, Tf is the re(gas) temperature, T is the ambient temperature, AO is theopening area, f is the emissivity of the elements emitting radia-tion inside the enclosure, and is the StefanBoltzmann constant.The radiation out through the opening, from ames, smoke layerand enclosure surfaces, is thereby calculated assuming a ctitiousemissivity f and a uniform internal temperature equal the retemperature Tf . Using these expressions and assuming that theheat is spread evenly to all surrounding surfaces allow expressingthe mean heat ux to the boundaries as in Eq. (1).

( )q AA T T

mc

A

q

mc (1)W

O

totf f

p

tot

C

pf

4 4 = +

where Atot is the total internal enclosure surface area (i.e. ex-cluding the opening area) and f is the temperature rise T Tf .

When expressing the heat transfer to the surrounding

Fig. 2. Electric analogy of the new pre-ashover re model assuming lumped heat.g C p c p

ultimate temperature rise, here denoted ult . This is generally thehighest temperature possible to obtain in a re enclosure, reachedif the heat losses by transfer to the surrounding surfaces qW and byradiation out through the openings qR are negligible. Then all theenergy released by combustion qC is used to heat the air owingthrough the enclosure (m). In practice this temperature could beobtained in for example a furnace. Furthermore, the term A mc/tot pwas recognized as an articial convective heat transfer resistance(the inverse of the heat transfer coefcient). It is here denoted Rc

and the convection part of Eq. (1) hence becomes ( )R1/ c ult f .The radiative part of the equation may also be expressed as afunction of a temperature difference. By an algebraic operation(linearization) an articial radiative heat transfer resistance Rr

wasderived as Eq. (2).

( )( )RAA

T T T T1

(2)rO

totf f f

2 2 = + +

Using these new terms gives the simplied expression of theheat transfer to the surfaces in the enclosure in Eq. (3).

q R R R R

1 1( )

1 1( )

(3)W rf

cult f

r cmax f = + = +

Eq. (3) can be expressed in an electric analogy, as illustrated inFig. 3. It shows how the heat ux depends on the resistances re-lated to convection and radiation as well as the ultimate tem-perature rise, the re temperature rise, and the ambient tem-perature rise (i.e. zero). The relation can be further simplied byintroducing the equivalent resistance Rf

and the equivalent tem-perature difference max (cf. electric potential difference). Hence,the latter represents the maximum temperature rise possible toreach when the enclosure boundaries are adiabatic, i.e. cannotabsorb any heat. Indifference of the ultimate temperature rise, themaximum temperature rise includes heat losses due to radiationout through openings and will therefore be lower. The new termsgive a simple description of the heat exposure of surfaces and willallow simple linear descriptions of the heat transfer throughboundaries (see Fig. 2).

2.1.2. Boundary conditions at the inside of the core (1)At the inside surfaces of the enclosure, a boundary condition of

the third kind is applicable. In other words, the heat ux to thesurface depends on convection, driven by the temperature differ-ence between the surface and the gas, and on radiation, driven bythe difference between the incident and emitted radiation. This isexpressed in Eq. (4).

( ) ( )q T T R T T1

(4)is i f s i

c if s i,

4,4

,, = +

The heat transfer by radiation can be linearized as a function ofthe difference between the re and surface temperatures,Fig. 3. Electric analogy of Eq. (3).

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 778680( )T Tf s i, . A radiative heat transfer resistance Rr i, may then be de-rived as Eq. (5). The boundary condition at the inside surfaces canthereby be simplied and expressed in analogy with the heattransfer by convection, as shown in Eq. (6). A new heat transferresistance for the inside surface of the boundary structure Rh i, ,which includes both convection and radiation, can thereby bedened as Eq. (7).

( )( )R T T T T1

(5)r is i f s i f s i

,,

2,2

, = + +

( ) ( )qR

T TR

T T1 1

(6)i r if s i

c if s i

,,

,, = +

R R R1 1 1

(7)h i c i r i, , ,= +

If no insulation is provided at the inside of the construction, thetemperature of the inside surfaces equals the temperature of thecore, i.e. T Ts i core, = . However, in case the construction includesinsulation, as illustrated in Fig. 2, the conduction heat resistancethrough the insulation must be considered in order to nd thecore temperature. Since no inertia was assumed for the insulation,the conduction heat resistance may be added to the combinedconvection and radiation heat transfer resistance, R R Ri h i k i, ,= + .This totals the heat resistance at the inside (re exposed side) ofthe core. It gives the simplied expression of the heat transfer tothe surrounding surfaces as a function of the temperature differ-ence between the core and the re, as expressed in Eq. (8). Herethe temperatures are also expressed as differences in relation tothe same initial temperature, generally assumed to be the ambienttemperature. Note that q qi W = .

( )qR

T TR

1 1( )

(8)i if core

if core = =

2.1.3. Lumped heat at the core (4)For this paper, all inertias were assumed lumped into the core

of the structure, which in electric analogy is represented by a ca-pacitor, as illustrated in Fig. 2. If such a structure is exposed toheating, its temperature may be estimated by Eq. (9). As the heatbalance of the core yields q q qcore i o = the increase in the coretemperature over a time step may be derived as Eq. (10).

q c ddTdt (9)corecore =

( )T T tc d

q q" "(10)core

icorei

i o1

= +

2.1.4. Boundary conditions at the outside (3)The heat lost at the outside surfaces of the structure can also be

expressed with the third kind of boundary condition, as expressedin Eq. (11).

( ) ( )q T T R T T1

(11)os o s o

c os o, ,

4 4

,, = +

Similar to above, the heat transfer by radiation can be ex-pressed as a function of the temperature difference ( )T Tf s o, ifexpressing the radiation heat transfer resistance in analogy withEq. (5). A total heat transfer resistance for radiation and convectioncombined at the unexposed side of the core can then be dened inanalogy with Eq. (7).

If there is no insulation at the unexposed side of the core, the

outside surface temperature equals the temperature of the core,i.e. T Ts o core, = . In case the construction includes insulation at theoutside, the heat resistance of the insulation may be added to theheat transfer resistance by convection and radiation, i.e.R R Rh o k o o, ,+ = . This gives the concluding expression in Eq. (12) forthe heat losses from the core at the unexposed side.

qR

T TR

1( )

1(12)o o

coreo

core = =

2.1.5. Constructing the pre-ashover re modelBy combining the equations derived in Sections 2.1.12.1.4 it is

possible to calculate the re temperature and temperatures in theboundary construction depending on the heat release rate (and anexpression for the mass ow). Knowing that the heat ux to theenclosure boundaries q W is equal to the heat ux to the core q iallows deriving a new expression for the incoming heat ow.Solving Eq. (8) for f and inserting it into Eq. (3) gives an expres-sion which can be rearranged into Eq. (13). The core temperatureas a function of time can now be derived by inserting Eqs. (13) and(12) for the incoming and outgoing heat ows into Eq. (10), re-sulting in Eq. (14).

q

R RR RR

RR RR R

1 1

(13)

o

i ci c

r

ult

ir c

r c

core =+ * +

**

* +

* + ** *

tc d

R RR RR

RR RR R

R

1

1 1

(14)

corei

corei

i ci c

r

ult

ir c

r c

ocorei

1

= +

+ * +*

*

*

+

* + ** *

+

+

where corei is the core temperature rise at the time increment i,

t is the length of the time step, c and are the specic heatcapacity and the density of the core material, respectively and d isthe core thickness. R is heat resistance with subscripts indicatingradiative, convective, or conductive at the inside or outside of thecore. The core temperature of time increment (i1) is hence cal-culated by determining the parameters on the right hand side ofEq. (14) at time increment i. This may be determined only from thecurrent heat release rate and known constants, as shown in Sec-tion 2.3.

Based on the core temperature, the re temperature and tem-peratures throughout the boundary structure may be calculateddepending on the various thermal resistances according to the lawof proportion (see Fig. 2). The calculation procedure is demon-strated step by step in Appendix A.

Eq. (14) is expressed in terms of the ultimate temperature,which may be the easiest for calculation purposes. Alternativelythe maximum temperature rise max , dened according to Eq. (15),may be used to express the core temperature as in Eq. (16). Thisexpression may also be derived directly from Fig. 2.

R R1( )

1( ) 0ult max max +

(15)c r

( )tc dR

R R

R RR

RR R

R R

1

1

(16)

corei

corei

fr i c i

r i c ik i

max corei

k or o c o

r o c o

corei

1

, ,

, ,,

,, ,

, ,

= +

* ++

+*

+

+

+

A similar simple model can be developed if the boundarystructures are assumed semi-innite with constant thermalproperties, which has been demonstrated for post-ashover res[5]. For other types of boundary structures the same approach formodeling the re may be applied but more laborious numericalprocedures are then needed to solve for the re temperature.

2.2. Full-scale experimental arrangements

The model was validated by comparisons with full-scale experi-ments performed in a standard 20 ft. steel dry cargo container withpanels of corrugated steel. The gables and roof panels were 2.0 mm

measured with thin type K thermocouples (0.25 mm) mounted inthree trees with six thermocouples in each. The measuring heightswere 0.6 m, 0.9 m, 1.2 m, 1.5 m, 1.8 m, and 2.1 m from the oor andthe trees were positioned along the centreline of the container, asillustrated in Fig. 5. As the thermocouples were thin and placedeither in a relatively homogeneous thermal environment insidethe re enclosure or in the opening with high gas velosities, thethermocouple measurements were not corrected for radiationerror but interpreted to yield true gas/re temperatures [cf. 12].The steel core temperature was measured with thermocoupleswelded to the walls at 0.9 m, 1.5 m, and 2.1 m from the oor nextto the thermocouple trees and re source, as shown in Fig. 5. In theexperiments with insulated boundaries, thermocouples were alsoplaced in the middle of and on the outer side of the insulation inthe corresponding locations.

2.3. Setup of the pre-ashover re model

To model the experimental conditions with the pre-ashoverre model, input parameters must be specied. No insulation wasprovided at the inside (re exposed side) of the enclosureboundaries and therefore Rh i, is the only heat resistance at theinside of the enclosure boundaries, i.e. R 0k i, = and R Rh i i, = . In the

and

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 7786 81thick and side walls 1.6 mm. The inner measurements of the con-tainer were (LWH) 5.902.352.39 m3. One of the containergables had a 12 m2 opening constructed, as illustrated in Fig. 4.

Two different experimental set-ups were used. In the rst ex-periment the container had no insulation while in the second theoutside walls and roof were covered with nominally 95 mm thickrock wool (Rockwool FlexiBattss), as shown in Fig. 4. The oor ofthe container was in both tests covered with calciumsilica boards.

The re source was a heptane pool in a tray with a diameter of0.89 m, standing on supports with the fuel surface 0.60 m abovethe oor level. It was placed 2.95 m from the opening, just beyondthe center of the container oor, as illustrated in Fig. 5. Theoreti-cally this re source gives a maximum heat release rate of about1200 kW [11].

The heat release rate as a function of time was recorded bymeasuring the oxygen consumption with a large scale so calledIndustry Calorimeter. Gas temperatures in the container were

Fig. 4. Dimensions of the test enclosureFig. 5. Position of thermocouple tretests with insulation added on the outside boundaries, the heatresistance at the outside is expressed as R R Ro h o k o, ,= + . Similarly,for the non-insulated case, R Ro h o,= since R 0k o, = .

A number of constants must be dened related to the geo-metrical and material properties. The thicknesses of the corru-gated steel panels were assumed to be 1.8 mm, close to aweighted average of the exposed roof and wall panels. Thespecic heat capacity of the insulation may vary with tem-perature increase but was here assumed to be constant in MQHand FDS calculations. The conductivity of the insulation was inFDS described as a function of the temperature in C,k T T T( ) 3 10 10 0.033 W/(m K)7 2 4= + + , based on SP FireResearch internal tests on similar rock wool products. In cal-culations with the new model and the MQH relationship aconstant insulation conductivity of 0.09 W/(m K) was assumed,representing the conductivity at 300 C. The conductivity ofsteel in the FDS and MQH calculations was set to 45 W/(m K),

a photo of the insulated test enclosure.es and surface measurements.

also representing a value at 300 C. Densities were assumed asat room temperature. In the new model the conductivity of thesteel was assumed innite (lumped heat capacity) and insula-tion density and specic heat are assumed negligible andtherefore not required information.

The elements emitting radiation through the opening wererepresented by a blackbody surface having the re temperature atthe opening, i.e. 1f = . The emissivities of the inside and outsidesurfaces of the boundary structure were set to 0.7, based onEurocode 3, EN1993-1-2 for steel [12]. A slightly higher value maybe motivated as most used building materials have a surfaceemissivity of 0.80.9. The choice has, however, very little inuenceon the calculated re temperatures. The convective heat transfercoefcients at the inside (re exposed) and outside surfaces wereset to 25 W/(m2 K) and 4 W/(m2 K), respectively, according toEurocode 1, EN1991-1-2 [13]. The value for the re exposed sur-faces is strictly speaking meant for fully developed res but as ithas limited inuence on the nal results it was used in absence ofany obvious alternative. The derived heat transfer resistances arespecied in Table 1 along with the other input parameters used in

proximately 0.67 in the experiments, which was adopted.

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 778682the models.As outlined in Section 2.1.1, the re heat transfer resistance Rf

as well as the ultimate temperature difference ult depend on themass ow rate of gases out through the opening. According totwo-zone models the mass ow rates in and out through theopening and into the re plume must be equal. It is here denotedm. The re plume may be seen as a pump. Equating expressions forthe three mass ow rates will give solutions to all the unknowns(the smoke layer height, the height of the neutral layer, and themass ow) since the re temperature is solved by the pre-ash-over re model. The mass ow rate was obtained by an iterationprocedure, which was coded as a macro in Excel.

Alternatively the mass ow rate can be approximated withoutiterations from re plume ow predictions, e.g. those of Zukoskiet al., Thomas or Heskestad (see e.g. [13] for a review). To de-monstrate this procedure the Heskestad re plume ow correla-tion [13] was used in parallel with the iterations. Fire plume owpredictions require, however, input on the smoke layer height,which is not easily determined and is at the same time a verysensitive parameter to the calculation of the re temperature. Inthis paper the smoke layer height was derived based on a sim-plied correlation derived by Johansson and van Hees [14] be-tween the mass ow rate through the opening and the smoke

Table 1Input parameters to the models and correlations.

Parameter Value Unit

Ho 2 mAo 2 m2

Atot 65.33 m2

T1 293 Kcp (air) 1012 J/(kg K)kcore (steel) 45 W/(m K) (steel) 7820 kg/m3

c (steel) 460 J/(kg K)d (steel thickness) 1.8 mmk (insulation) 0.09 W/(m K)ins (insulation) 30 kg/m3

cins (insulation) 800 J/(kg K)l (insulation thickness) 95 mmf 1 dimensionlesss,i 0.7 dimensionlessRc,i 0.04 m2 K/Ws,o 0.7 dimensionlessRc,o 0.25 m2 K/W 0.684 dimensionlessc 0.67 dimensionless2.4. FDS simulations

For comparison, the experiments were modeled in FDS, FireDynamics Simulator, version 5.5.3 [9]. The heat release rate re-corded in the experiments was used as input to the simulations.Since circular objects cannot be specied in FDS, a square resource with the same surface area was assumed, placed at thesame height as in the experiments. Heptane was used as fuel inFDS and the soot yield was set to 0.037 [15]. The walls and roof ofcorrugated were assumed plane in the FDS model. The walls, oor,and ceiling of the construction were given material properties forsteel or steel and insulation, as presented in Table 1. The oor wasnot insulated in any of the simulations, as it was never insulated inthe experiments. Neither was any consideration taken to theconcrete oor on which the container was placed. The size of thegrid cells was set to 50 mm cubes, which gives a D*/x value of 16after about 50 s in the simulations (a value of at least 416 is re-commendable to adequately resolve re plume dynamics [9]). Amesh sensitivity study was performed, which showed grid in-dependent results.

For comparison, output devices were specied in FDS whichpredict temperatures as the 0.25 mm thick thermocouples used inthe experiments. The core (wall) temperatures were derived di-rectly from the model.

3. Results

Two full scale experiments were performed. The measured heatrelease rates were input to the calculation models. Then themeasured core and re temperatures were compared with thecorresponding temperatures predicted by the models.

3.1. Observations and heat release rates from experiments

Flames reached the ceiling 10 s after ignition and thereafter theres grew quickly, reaching a heat release rate of 700 kW in about1 min. In the non-insulated enclosure the re grew slower than inthe insulated, reaching about 950 kW after 500 s. The re wasextinguished after 960 s. In the experiment with insulatedboundaries, small ames emerged at the opening already after375 s. After 465 s the re was considered to have reached ash-over and was extinguished. The walls were then glowing red.

The measured heat release rates from the experiments werelayer height. The correlation was optimized for a ratio between there temperature and the ambient temperature of T T/ 1.7f = , giv-ing the coefcient a value of 0.684, and is given in Eq. (17). As thecorrelation is independent of the neutral layer height it may besolved for the smoke layer height, z. The result was at each timestep inserted into the Heskestad re plume ow correlation, seeEq. (18), for a less uncertain approximation of the mass ow ratem.

m A H

zH

1(17)

O OO

=

m L q H A H0.0056

1

(18)c C O O O

1

= +

The Heskestad re plume ow correlation includes the con-vective proportion of the total heat release rate qC . The averageconvective part of the heat release rate c was measured to ap-directly input to the new pre-ashover re model and to the MQH

relationship. However, for the FDS simulations the data wereevened out, as shown in Fig. 6. The peaks at the end of the graphsare due to extinguishment.

3.2. Core temperature comparison

The new pre-ashover re model yields the temperature of thecore of the surrounding structure, from which the re (gas) tem-perature is calculated by the law of proportion. The MQH re-lationship predicts only a re temperature. From experiments andFDS simulations on the other hand, distributions of both tem-peratures were obtained. To represent the overall temperature ofthe core, steel temperature data was collected from the threedifferent distances from the opening (each with thermocouples atthree different heights) in experiments and FDS. Arithmeticaverages were calculated from these nine measuring points andwere compared with the core temperatures calculated from thepre-ashover re model, as illustrated in Figs. 7 and 8 for the in-sulated and non-insulated enclosure, respectively.

In the insulated case the core temperature estimated by thenew model was generally less than 60 K lower than measured. FDSgave similar results. The nal temperatures were particularly closeto the experimental values. For the non-insulated case the newmodel predicted a core temperature which was generally less than50 K lower than measured. This difference decreased throughoutthe test and in the second half it was less than 20 K. The FDSpredicted temperatures were constantly 3035 K below the

measured.

3.3. Fire temperature comparison

To compare predicted re temperatures with values measuredin experiments there are several different data reduction ap-proaches, of which Weaver [16] provides a good review. In thiscase a simple arithmetic average of the re temperature was cal-culated from data inside the smoke layer in the enclosure, both forexperiments and FDS simulations. The smoke layer height wascalculated from the pre-ashover re model and was consistentwith video observations. In the insulated enclosure the smoke

throughout the test. Thus, data from thermocouples at the heights1.2 m, 1.5 m, 1.8 m, and 2.1 m were used from the two thermo-

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 7786 83Fig. 6. Heat release rate histories used as inputs to the different models.

Fig. 7. Comparison of the measured and estimated core temperatures in the in-sulated container.

Fig. 8. Comparison of the measured and estimated core temperatures in the non-

insulated container.couple trees inside the insulated as well as the non-insulatedenclosure to estimate re temperatures. The temperature in theupper layer is also deemed well represented by the temperature ofthe smoke exiting through the opening as they have been mixingwith the rest of the enclosure before exiting. An arithmetic averagewas therefore calculated also from the thermocouples in thesmoke exiting the enclosure. Measured temperatures from 1.2 mabove the oor and below were here excluded since they were notin the smoke layer at the opening. Hence, only data from 1.5 m and1.8 m were used to calculate the re temperature from the hotgases exiting the opening. The average temperatures from mea-surements were compared with predictions from the pre-ash-over re model, as shown in Fig. 9 for the insulated and non-in-sulated enclosures. Figs. 10 and 11 includes comparisons withpredictions by FDS simulations as well as calculations based on theMQH relationsship.

The calculated re temperatures by the new model matchedvery well with the experimental results for the insulated en-closure. FDS gave a delayed response at the start and then 2045 Klower predictions than measurement, a difference which increasedthroughout the test. The MQH relationship gave unrealistic results.

For the non-insulated enclosure the new model predicted retemperatures well, although constantly about 30 K above themeasured. FDS gave results similar to those from the experimentin the rst half of the test. The re temperature predictions dif-fered the most, about 30 K. In the second half of the test FDS gaveunder predictions of 2060 K. The original MQH relationship gaveagain unrealistic results. However, the modied relationship witha corrected heat transfer coefcient as suggested by Peatross andBeyler [4] predicted the experiments well.

4. Discussion

Comparisons with experiments and FDS simulations showed

Fig. 9. Fire temperatures estimated by the new pre-ashover re model in com-layer height was calculated to about 1.0 m, descending to about0.8 m at the end of the test. In the non-insulated enclosure thesmoke layer was at the same average height but varied lessparison with experiments for the insulated and non-insulated cases.

unrealistic results for the problems studied. The expression for theeffective heat transfer coefcient by Peatross and Beyler [4] im-

ments and FDS shows that the pre-ashover re model gives ac-curate results.

Fig

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 778684that the new model predicts core and re temperatures well, bothfor insulated and non-insulated steel enclosures. The new modeland FDS gave similarly good predictions for the steel core tem-perature. Both models under predicted these temperatures onlyslightly up until the end of the tests. The new model predicted there temperature in the insulated case well but over predictedslightly in the non-insulated case.

When comparing temperatures calculated by the new modelwith measurements and FDS predictions, arithmetic averagetemperatures were used which is an uncertainty of thecomparison.

The calculations with new model include a number of simpli-

Fig. 11. Estimated re temperatures in the non-insulated container by differentmodels compared with measurements.camo

com

. 10. Estimated re temperatures in the insulated container by different modelspared with measurements.tions and assumptions of which the following are deemed thest signicant:

A two-zone model was assumed for calculation of mass owrates.As an alternative, mass ow rates were for comparison alsocalculated based on the Heskestad re plume ow correlation[13] and the Johansson and van Hees [14] simplication. Asensitivity study showed insignicant effects on the resultsfrom using these correlations in the studied cases.Heat ux to the enclosure boundaries was assumed uniform toall surrounding surfaces, including the oor. This assumption isjustied by the fact that radiation is the dominant mode of heattransfer at high temperatures.The compartment boundary structure was modeled assuminglumped heat, i.e. the thermal inertia is concentrated to a corepossibly insulated on either side. The heat capacity of the in-sulation material is neglected and the conductivity of the coreis assumed to be innite.Effects of the corrugation of panels were disregarded.Input data for calculations were obtained from measurementsand where relevant with reference to Eurocodes [7,17]. Theonly exceptions are the insulation properties which were pro-vided by the manufacturer and the emissivity at the enclosureopening which was assumed to be 1.

The great strengths of the new pre-ashover re model are its

gramme under Grant agreement no. 233980 and two competencecenters at SP Technical Research Institute of Sweden, Novel De-

signs at Sea: Shipping and Offshore and Zero EmissionBuildings.

Appendix A. Calculation procedure

This appendix describes step by step a calculation procedure ofthe above presented model. An Excel application of the model isavailable on request from the author.

A.1. Input data and the core equation

Initially two columns are set up with the heat release rateversus time input data. With this information and temperaturesThe new model adds to the understanding of the physics inpre-ashover enclosure res. It is simple and requires very shortcomputation times. Hence, the model is a powerful tool for sen-sitivity and uncertainty studies.

Lumped heat capacity was assumed in this paper but the ap-proach may as well be used in combination with other enclosureboundaries. Particularly, simple temperature expressions can bederived when boundaries are assumed semi-innite with constantproperties, to be demonstrated in future work. In other cases theheat transfer may be modeled using general nite element codesas has been demonstrated for a one-zone model by Wickstrmand Bystrm [5].

An Excel document with the pre-ashover re model wasmade available alongside the electronic version of this paper at theElsevier and ScienceDirect websites and may also be obtainedfrom the corresponding author.

Acknowledgments

The authors are grateful to associate professor Johan Andersonat SP Fire Research for support in FDS simulations. Thanks are alsoextended to Anna Back for managing the re tests. The tests werenanced by the European Community's Seventh Framework Pro-proved, however, the results for the non-insulated caseconsiderably.

5. Conclusions and future work

This paper presents a new enclosure re model to estimatetemperatures in pre-ashover res based on thermal physics. It isapplicable to enclosures where the heat capacity is lumped intothe core of the surrounding structure. Comparison with experi-simplicity and speed of computation. Results are obtained withinthe second by an Excel application while the alternative of CFDmodeling may require several hours. The readiness is particularlyuseful in preliminary evaluations, when evaluating multiple rescenarios or when performing sensitivity assessments. The modelalso opens up for more detailed analyses with use of input dis-tributions to better describe effects of uncertainties in inputparameters on the end result, for example by Monte Carlosimulations.

Finally it is worth mentioning that the MQH relationship gavecalculated in the previous time step the core temperature can be

F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 7786 85transiently solved according to Eq. (14), here reproduced as Eq.(A1). Thereafter the re temperature and temperatures through-out the boundary structure may be calculated depending on thenew core temperature. First, however, the mass ow rate must beestimated.

tc d

R RR RR

RR RR R

R

1

1 1

(A1)

corei

corei

i ci c

r

ult

ir c

r c

ocorei

1

= +

+ * +*

*

*

+

* + ** *

+

+

A.2. Estimate the mass ow rate

There are several ways to estimate the mass ow rate. The massow rates in and out through the opening are assumed equal tothe plume ow and may be estimated directly from a re plumeow correlation. An alternative is to estimate the mass ow rate byiterating the original equations for the mass ow rates in and outthrough the opening [6] and a re plume ow correlation [13](possible with information from the previous time step). As a thirdalternative a simplied correlation between the mass ow ratesthrough the opening and the smoke layer height [14] may be usedinstead of the original mass ow equations. For example, togetherwith the Heskestad re plume ow correlation the mass ow canthen be calculated from Eq. (A2).

m L q H A H0.0056

1

(A2)c C O O O

1

= +

A.3. Calculate the ultimate temperature rise

The ultimate temperature rise is calculated according to Eq.(A3).

q

mc (A3)ultC

p =

A.4. Calculate heat resistances

All four heat resistances in Eq. (A1) must be calculated. Thearticial convective and radiative heat transfer resistances in there enclosure are calculated according to Eqs. (A4) and (A5), re-spectively.

RAmc (A4)

ctot

p=

( )( )R

AA

T T T T(A5)

rO

totf f f

2 21

= + +

The heat resistance at the inside (re exposed side) of the coreRi depends on convection and radiation heat transfer resistances atthe surface and on conductive heat resistance of potential coveringmaterial, as shown in Eq. (A6). The latter is zero if the inside of thecore is not covered. The radiation heat transfer resistance at theinside surface may be calculated in a separate column according toEq. (A7), where the re and inside surface temperatures are taken

from the previous time step.

R R R R

1 1

(A6)i

c i r ik i

, ,

1

,= + +

( )( )R T T T T1

(A7)r is i f s i f s i

,,

2,2

, = + +

Similarly, the heat resistance at the outside (unexposed side) ofthe core Ro may be calculated by Eq. (A8). If the outside or the coreis not covered, the conductive heat resistance is zero. The radiationheat transfer resistance at the outside surface is calculated ac-cording to Eq. (A9).

R R R R

1 1

(A8)o

c o r ok o

, ,

1

,= + +

( )( )R T T T T1

(A9)r os o f s o f s o

,,

2,2

, = + +

A.5. Determine heat uxes and temperatures

The core temperature as a function of time in Eq. (A1) can nowbe solved. Thereby the incorporated heat uxes to and from thecore can also be solved according to Eqs. (A10) and (A11), re-spectively.

q

R RR RR

RR RR R

q1 1

(A10)

i

i ci c

r

ult

ir c

r c

core W =+ * +

**

* +

* + ** *

=

qR

T TR

1( )

1(A11)o o

coreo

core = =

The re temperature and temperatures throughout theboundary structure are then calculated by the rule of pro-portionality, as indicated by Fig. 2 and exemplied in Eqs. (A12)and (A13).

qR

R q1( )

(A12)i if core f core i i = = +

qR

R q1

( )(A13)i k o

core s o s o core k o i,

, , , = =

References

[1] W.D. Walton, P.H. Thomas, Estimating temperatures in compartment res, in:P.J. DiNenno (Ed.), The SFPE Handbook of Fire Protection Engineering, third ed.,NFPA, Quincy, MA, USA, 2002, pp. 3-1713-188.

[2] B. McCaffrey, J. Quintiere, M. Harkleroad, Estimating room temperatures andthe likelihood of ashover using re test data correlations, Fire Technol. 17 (2)(1981) 98119.

[3] B. Karlsson, J.G. Quintiere, Enclosure Fire Dynamics, CRC Press, Boca Raton,2000.

[4] M.J. Peatross, C.L. Beyler, Thermal environmental prediction in steel-boundedpreashover compartment res, in: Proceedings of the Fourth InternationalSymposium on Fire Safety Science. International Association for Fire SafetyScience, Boston, 1994, pp. 205216.

[5] U. Wickstrm, A. Bystrm, Compartment re temperature a new simplecalculation method, in: Proceedings of the Eleventh International Symposiumon Paper Presented at the Fire Safety Science. Christchurch, New Zeeland,2014.

[6] S.E. Magnusson, S. Thelandersson, Temperature-time curves of completeprocess of re development: theoretical study of wood fuel res in enclosedspaces, Civ. Eng. Build. Constr. Ser. 65 (1970), pp. 181.

[7] CEN, EN 1991-1-2, Eurocode 1: Actions on Structures Part 12: GeneralActions Actions on Structures Exposed to Fire. European Committee forStandardisation, 2002.

[8] A. Back, Fire Development in Insulated Compartments: Effects from Improved

Thermal Insulation, Department of Fire Safety Engineering and Systems Safety,

Lund, 2000.[9] K. McGrattan, B. Klein, S. Hostikka, J. Floyd, Fire Dynamics Simulator (Version

5) User Guide, National Institute of Standards and Technology, USA, 2008.[10] O. Pettersson, K. deen, Brandteknisk Dimensionering: Principer, Underlag,

Exempel. 1978.[11] V. Babrauskas, Heat release rates, in: P.J. DiNenno, D. Drysdale, C.L. Beyler,

et al., (Eds.), The SFPE Handbook of Fire Protection Engineering, fourth ed.,National Fire Protection Association, Quincy, MA, USA, 2008, pp. 3-13-59.

[12] S. Welch, A. Jowsey, S. Deeny, R. Morgan, J.L. Torero, BRE large compartmentre tests-characterising post-ashover res for model validation, Fire Saf. J. 42(8) (2007) 548567. http://dx.doi.org/10.1016/j.resaf.2007.04.002.

[13] G. Heskestad, Fire plumes, ame height, and air entrainment, in: P.J. DiNenno,D. Drysdale, C.L. Beyler, et al., (Eds.), The SFPE Handbook of Fire ProtectionEngineering, fourth ed.,National Fire Protection Association, Quincy, MA, USA,2008, pp. 2-12-20.

[14] J. Johansson, P. Van Hees, A simplied relation between hot layer height andopening mass ow, in: Proceedings of the Eleventh International Symposiumon Paper Presented at the Fire Safety Science. Christchurch, New Zeeland,2014.

[15] A. Tewarson, Generation of heat and chemical compounds in res, in: P.J. DiNenno, D. Drysdale, C.L. Beyler, et al., (Eds.), The SFPE Handbook of FireProtection Engineering, third ed.,National Fire Protection Association, Quincy,MA, USA, 2002, pp. 3-8283-161.

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F. Evegren, U. Wickstrm / Fire Safety Journal 72 (2015) 778686

New approach to estimate temperatures in pre-flashover fires: Lumped heat caseIntroductionMethodNew simple pre-flashover fire modelEnclosure heat balance (1)Boundary conditions at the inside of the core (1)Lumped heat at the core (4)Boundary conditions at the outside (3)Constructing the pre-flashover fire model

Full-scale experimental arrangementsSetup of the pre-flashover fire modelFDS simulations

ResultsObservations and heat release rates from experimentsCore temperature comparisonFire temperature comparison

DiscussionConclusions and future workAcknowledgmentsCalculation procedureA.1. Input data and the core equationA.2. Estimate the mass flow rateA.3. Calculate the ultimate temperature riseA.4. Calculate heat resistancesA.5. Determine heat fluxes and temperatures

References