A Posteriori Modelling of the Growth Phase of Dalmarnock Fire Test One

7/24/2019 A Posteriori Modelling of the Growth Phase of Dalmarnock Fire Test One

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et al.[14]found temperature proles, smoke layer heights and gas

species concentrations in a 10 10 5 m compartment predictedby FDSv4 to be in good agreement with experimental data for the

burning of pool res (heptane or toluene) and single cribs (PMMA

or wood). The measured mass loss rate of the fuel was used to

calculate the HRR, which was then input into the model.

Theevaluationof the entire process ofre modelling, in which the

mathematical model is only a component, is an important taskfor the

advancement ofre safety engineering. The state of the art of re

modelling is reected not only in the mathematical models capa-

bilities, but also on how it is implemented throughout the different

stages ofre modelling[9].The assumptions made by the user, the

collection of data for input and the selection of the parameter valuesare crucialcomponents leading to the creation of the inputle.Thisis

particularly important when advanced and complex computational

tools areused (e.g. CFDand evacuationmodelling). Under the current

state of the art, there are many ill-dened and uncertain parameters

within the models which cannot be rigorously and uniquely deter-

mined. Thus, there is plenty of space for uncertainty and doubt to

unravel, and for curvetting and arbitrary parameter value selection

to take place. This is summarised best in the words attributed to the

German scientist Carl Friedrich Gauss (1777e1855): Give me four

parameters, and I will draw anelephant for you; withveI willhave him

raise and lower his trunk and his tail.

This paper reports a series of CFD simulations (with FDSv4) con-

ducted a posteriori to reproduce the large-scale Dalmarnock Fire Test

One thatinvolved several real burningitems leading to a complex respread process. The HRR of the growth phase was not measured. But

because the compartment was densely instrumented, it provides

a veryrich set ofdata thatcouldbe usedto aid dening the HRR of the

re source and uncertain parameters to reproduce the main features

of the re. A key difference between previous modelling studies of

large-scale tests and the present work is that the heavily instru-

mented full-scale Dalmarnock Fire Tests provides for the rst time

measurements at sufcient spatial resolution to be suitable for

comparison witheld models at the grid size level.

2. Dalmarnock Fire Test One

Detailed information about the experimental set-up and the

chain of events that occurred during the Test One can be found

elsewhere[15,16], but a short summary is given here. Test One was

held in a two-bedroom single family at, with the living room

set-up as the main experimental compartment. This compartment

was 3.50 m by 4.75 m wide and 2.45 m high and made of concrete

walls. It had two-pane windows as shown inFig. 1. While the main

source of fuel was a two-seat sofa stuffed with exible poly-

urethane foam, the compartments also contained two ofce work

desks with computers, each with its own foam-padded chair, three

tall wooden bookcases, a short plastic cabinet, three small wooden

coffee tables, a range of paper items and two tall plastic lamps. A

plastic waste paper basket lled with crumpled newspaper and

300e500 ml of heptane was the ignition source. The re spread to

a blanket on the sofa hanging into the basket, igniting the seatingarea of the sofa. After about 275 s the bookshelf next to the sofa

ignitedand was rapidly engulfed in re. Within 25 s afterignition of

the bookshelf the compartment reached ashover conditions (see

Table 1for a time line of the events).

Fig. 2shows the HRR, the average temperature of the hot layer

and the vertical distribution of temperatures along one specic

thermocouple rack measured in Test One. A detailed presentation

of the data can be found in[15,16]. The HRR in the re tests was

estimated by the principle of oxygen depletion, using the

measurements from the gas velocity probes at all the ventilation

openings and assuming total O2 consumption[16]. An estimation

for the post-ashover re results in about 3 MW before the rst

window breakage, and about 5 MW after the second breakage as

shown inFig. 2. During the growth phase the assumption of totalO2 consumption does not hold, as the re is not ventilation

controlled, thus the evolution of the HRR during re growth is

unknown.

Fig. 1. Room layout with location of furniture and sensors [15,16].

Table 1

Time line of main events during Dalmarnock Test One [15,16].

Event Time from ignition (s)

Ignition 0

Cushions ignite 9

Bookcase ignites 275

Fire engulfs bookcase (ashover) 300

Compartment window breakage (NW Pane) 800

Compartment window breakage (SW Pane) 1100

Extinction 1140

W. Jahn et al. / Building and Environment 46 (2011) 1065e10731066


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Prior to Test One, laboratory experiments were conducted in

order to determine the HRR curves for the sofa and the book-

shelves inside the furniture calorimeter (using an exact replica of

those used in Test One) [15]. A second series of laboratory

experiments was conducted after Test One in order to analyse

variations to the ignition protocol[17]. These two sets of experi-

ments were the only direct source of information on the HRR in

Test One.

Fig. 3shows the evolution of the HRR of the sofa and the effect of

variations to the ignition source. The experiment conducted prior to

Test One (referred to as Set 1) consisted of a sofa with two cushions,

and a waste paper basket located next to the sofa. Accelerant was

poured into the paper basket and the basket was ignited. The re

then spread over the armrest to the sofa and was stopped about

800 s after ignition when approximately one third of the sofa had

been burnt. In the experiments conducted after Test One (referred to

as Set 2), the exact ignition protocol of Dalmarnock Test One was

replicated, which was like Set 1 but including a blanket that had

been placed over the armrest of the sofa, and the accelerant

distributed between basket and blanket. The presence of the blanket

in Set 2 allowed the re to bypass the armrest re barrier and led to

a faster growth rate involving the cushions. The re growth rate for

Set 2 is equivalent to a t-squared re with growth constant 1.6 W/s2

(a mediumre [18]).The constantin Set 1 is 0.5 W/s2 (corresponding

to a slow re[18]). The two tests show that the uncertainty in the

growth rate of the sofa re during the early stages is signicant and

varies between a slow and a medium re.

Fig. 3suggests two patterns in the burning behaviour; an initial

peak that rapidly decreases is followed by a growing re that

resembles a t-squared curve. A similarbehaviour can be seen forSet

2. It is conjectured that the initial peak corresponds to the waste

paper basket, accelerant and the blanket (in the case of Set 2), while

the t-squared re corresponds to the sofa itself.

By measuring ame heights from visual recordings, it can be

established that the sofas HRR in Set 1 grew slower than the

observed re in Test One. Flashover in Test One occurred at 300 s.

According to Set 1, this is only 100 s after the period when the basket

re dominated the HRR. Comparison of the re development using

the video available of both resconrms this. At the initial laboratory

experiment no blanket was used, so that the re could not spread

across thearmrest to the cushions as fast. The re in Dalmarnock Test

One spread quickly from the basket over the armrest to the sofa,

whereas in Set 1, the ames took considerably longer to spread over

the armrest.

3. A priori vs. a posteriori modelling

Before the Dalmarnock Tests were carried out, a round-robin

study of blind predictions [9] was conducted in order to explore the

a priori predictive capabilities ofre modelling in realistic scenarios.

The aim of the exercise was to forecast the re development as

accurately as possible and compare the results. Comparison of the

modelling results showed a large scatter and considerable disparity

among the predictions, and between predictions and experimental

measurements. Thescatter of the simulations was much largerthan

the error and variability expected in the experiments. The studyemphasized on the inherent difculty of modelling re dynamics in

complex re scenarios like Dalmarnock, and showed that the

accuracy of blind prediction ofre growth (i.e. evolution of the heat

release rate) is poor.

The present work revisits the modelling of the Dalmarnock Fire

Test One, this time using the large set of measurements available.

That is, the work is conducted a posteriori. Many different simula-

tions are conducted and many parameters are adjusted and read-

justed until acceptable agreement is reached. Work is focused only

on the growth phase of the Dalmarnock Fire Test One.

a b c

Fig. 2. Measurements from the Dalmarnock Test One: a) estimated HRR (using oxygen consumption), b) average temperature of the hot layer in the main compartment (corrected

for radiation) and c) vertical temperature distribution in front of the compartment door at 600 s[15,16](rack 4, seeFig. 1).

a b

Fig. 3. Measured HRR for variations to the ignition source and equivalent t-squared res: a) measured in the laboratory prior to Test One including sofa and waste basket (Set 1);

and b) after Test One including the sofa, waste basket and blanket (Set 2).

W. Jahn et al. / Building and Environment 46 (2011) 1065e1073 1067


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As mentioned before, during the growth phase of Test One

the evolution of the HRR is unknown. Moreover, the laboratory

experiments of the sofa and similar ignition sources show signi-

cant uncertainty. Indeed, this is one of the most important issues

addressed in this article. The challenge is to be able to reproduce

the HRR such that the re environment (temperature and smoke)

is simulated correctly. The work solves a large and complex inverse

problem by trial and error.

4. Computational model

The code Fire Dynamics Simulator v4.07 [19,20], one of the most

commonly used re CFD codes, is used here. FDS solves a form of

the NaviereStokes equations adequate for low-speed thermally

driven ows. While large eddies are solved directly, turbulences at

subgrid scale are modelled using Smagorinskys approach[21].

FDS is a tool still under active development, and improved

versions are released with some frequency. At the time this paper

goes to press, FDSv5 had been released and FDSv6 is expected

soon. But research has a characteristic time that seems to be longer

that the time between version releases of FDS. This means that by

the time a research project has been completed and conclusionshave been reached, newest versions might be available. While not

all of the ne results of this paper might apply directly to FDSv5 or

FDSv6, the merit of the study is that the bulk of the conclusions

relate to the signicant amount of papers in the technical litera-

ture where FDSv4 was used, and to current re safety engineering.

This last is particularly important for infrastructure designed,

approved and built, and to forensic ndings agreed on with the aid

of FDSv4.

The computational domain used reproduces in detail the main

Dalmarnock compartment (Fig. 4) and includes the vent openings

(two-pane windows to the exterior), the nearby kitchen (with

another window to the exterior) and the hallway connecting to

the apartment entry. It was considered that the other rooms of

the apartment did not contribute signicantly to the re dynamics

and therefore were not included. The fuel load in the main

compartment was reduced to the fuel elements involved in the

growth phase; the sofa, the ignition source and two bookshelves in

the corner behind the sofa. The other fuel items, the computers,

coffee table, chairs and desks contributed to the re only after

ashover, and therefore are outside the scope of this work.

The compartment walls and ceiling were modelled as 10 cm

thick concrete, and the compartment ooras covered with a carpet.

Open boundary conditions were used at the exterior of the

compartment at some distance from the building facades.

FDS models combustion based on a mixture fraction approach

[19] with a single-step instantaneous reaction chemistry. While the

Dalmarnock Fire Test One contained several dozen different

fuels burning at the same time, FDSv4 only allows for one single

fuel. Thus, as an overall representative, propane was assumed as

fuel (FDS default fuel) with combustion reaction:

C3H8 5O2/3CO2 4H2O (1)The time variation of the HRR is imposed as a ramp of the fuel

injection, while there area is assumed constant at 2/3 of theseating

area of the sofa. Because there area affects the air entrainment into

the ame, in principle, it should be changed in time as well. This has

been shown in previous sensitivity studies with FDSv4 [22].However, the uncertainty in the actual rate of change of the re area

is large. Therefore, it has not been considered here for the sake of

simplicity but its effects can be investigated in future studies

together with other uncertain combustion, turbulence and radiation

parameters within FDS.

The grid size is one of the most critical parameters in numerical

simulations.In the scope of this work a large number of simulations

had to be run in order to converge toward good agreement with the

measured data and it was therefore necessary to use a sufciently

coarse grid allowing for an efcient use of computational resources.

However, too coarse a grid could induce signicant numerical

errors in the solution. It has been proposed[23,24]that to resolve

the re plume properly, the ratio between the characteristic re

diameter, D*, and the gridsize shouldbe atleast5 to10, where D* is

dened as:

Fig. 4. Computational domain and fuel items used in the FDS simulations.



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D*

Q$

rN

cpTNffiffiffigp

2=5: (2)

During the growth phase, the peak of the HRR is 300 kW, and

the characteristic diameter of the sofa is around 0.6 m. Hence the

grid size should be smaller than 11 cm for an adequate plume

resolution. This value is used as an order of magnitude reference. In

order to select an adequate grid size, simulation were run with

a wide range of different grid sizes: 5 cm, 10 cm, 15 cm and 20 cm

edge cubes. The 10 cm grid size resulted in 120,000 cells, and the

number of cells in other grids scales with the inverse of the cube of

the grid size. The HRR was prescribed according to the laboratory

experiment Set 1.

Fig. 5 shows the temperature vs. height distribution at two

different locations in the experimental compartment, one near the

burning sofa, and one near the window away from there. See Fig.1

for rack locations. The time of comparison is 140 s, and data are

averaged in time (10 s) in order tolterout inconsistent uctuations.

The simulations using coarser grids (15 and 20 cm) actually showed

better agreement when compared to the measured data, both

qualitatively and quantitatively than the ner grids (5 and 10 cm).

Near the re (Fig. 5a), the 20 cm and 15 cm grids are in agreement

between them and reproduce well the lower zone temperatures andthe smoke layer height, but overpredict the temperatures of the

smoke layer by 17%. The 10 cm grid underpredicts the smoke layer

height by around 15%, but is in good agreement regarding the smoke

layer temperature. The 5 cm grid underpredicts the measurements

by more than 35% at all heights. Away from the re (Fig. 5b), the 10,

15 and 20 cm grids are in reasonable agreement to the measure-

ments, while the 5 cm grid shows divergence both quantitatively

(>30%) and qualitatively.

Based on this grid dependency study, the 10 cm grid was chosen

because it showed good comparison to the experiments, allowed

for fast computations and complied with the recommendation

associated to the characteristic re diameter [23,24]. Given the

present results, there are no good reasons to choosea different grid,

but most validation studies by the FDS developers had been con-ducted with similar grid sizes to this.

We cannot explain why the coarser grids in this case provide

lower global errors. While it is generally accepted for numerical

integration that a smaller grid yields more accurate results, FDS

results are known to dependsignicantly onthe size of thenumerical

grid due to the LES approximation[25,24]. A possible explanation is

that the LES Smagorinsky constant used by default in FDS was cali-

brated to predict smoke movement in a very large enclosure and

away from the ames [26]. This is a very different scenario to theDalmarnock Test One and the constant might need recalibration.

All other parameters not discussed here were left with the

default values in FDSv4.

5. Hot layer average temperatures

Two distinct levels of detail are analysed. This section predicts

the average hot layer temperature while the next section looks at

the distribution of local eld temperature and wall heat uxes.

Comparison at detailed level requires a good agreement at aver-

aged level rst.

As seen in the Set 1 and Set 2 experiments, the blanket signi-

cantly modies the HRR. A possible HRR of the blanket alone can

be estimated assuming quadratic growth and decay phases. Theblanket, made of cotton, weighed 1 kg, hence the total combustible

energystored in the blanket including 100 ml of accelerant can be

estimated to be around 21 MJ [22], assuming a heat of combustion

of 16.5 MJ/kg for the cotton. The resulting peak HRR would be

150 kW. This is not negligible compared to the measured HRR of

the sofa in the early stages, and should therefore be included

in the input HRR for the model. Fig. 6shows the reconstructed HRR

of the blanket alone and its addition to the HRR of Set 1. The

a b

Fig. 5. Comparison of results with different grid sizes at 140 s: a) distribution at the north wall next to the bookshelf (rack 1); and b) distribution near the window (rack 17).

Fig. 6. Addition of the blanket to the HRR measured in Set 1 (Measured sofare) to

obtain Set 1b (combined re).



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resulting HRR is referred to as Set 1b. Note that here the data is

shifted by 150 s compared to Fig. 3, sothat the ignitionoccurs at0 s.

The predicted hot layer average temperature using different

HRR and comparison to measurements are shown in Fig. 7.For the

Set 1 (Fig. 7a), the simulated hot layer temperature rise agrees with

the measurements during the rst 100 s. The predicted average

temperatures after t 100 s are lower that measured (up to 50%error). For Set 1b (Fig. 7b), the simulated hot layer temperatures are

in good agreement with the measured temperatures (within theinstrumental uncertainty) until 200 s into the re. After that, the

simulated temperature decreases in contrast to the measured

temperature which rises continually until ashover. For Set 2

(Fig. 7c), the average hot layer temperature is overpredicted by

about 50% between 25 s and 100 s, and by about 35% between 150 s

and 250 s.

Overall, it is seen that Set 1 results in unrealistically low average

temperatures for the hot layer, but Set 1b and Set 2 provide predic-

tions closer to the measurements. Thus, it is concluded that Set 1b

provides a lower bound to the HRR curve during the growth phase,

while Set 2 is an upper bound. This range captures the intrinsic

uncertainty ofre growth in real complex scenarios and alsoincludes

experimental variability. The uncertainty in the average temperature

predictions using these HRRbounds is between0 and50%. It conrms

that to predict temperatures with reasonable agreement, the HRR

must be well characterized.

6. Comparison of local measurements

The density of measurements in Test One presents an oppor-

tunity to assess eld level simulations.Fig. 8shows the tempera-

ture vs. height distributions at different locations (three vertical

thermocouple racks) in the experimental compartment using the

two bounding HRR curves Set 1b and Set 2. Two different times,

150 s (HRR plateau) and 200 s (rapid HRR rise), are chosen arbi-

trarily for illustration purposes. In general the simulations are inreasonable agreement with the measurements, although it can be

seen that the further away from the burning sofa the better the

agreement between measurements and simulations.

As expected the lower and upper HHR bounds result in upper and

lower bounds for the smoke temperatures. It is observed that the

thickness of the hot layer is not signicantly affected by the HRR

within the bounds, but the upper HHR leads to higher temperatures

in smoke. Within the cold layer, the simulations underpredict the

temperature even for the upper HHR bound. This indicates that the

Dalmarnock FireTest had a less well dened hot layer thanpredicted.

At thermocouple rack 7, roughly 1.5 m from the re, the

temperatures are underpredicted by 20e200% at 150 s (Fig. 8a)

when using both the lower HRR bound (Set 1b) or the upper HRR

bound (Set 2). At rack 11, near the centre of the compartment, and

150 s into the re (Fig. 8b) the simulations with both input HRR

curves are in good agreement with the measured data lying within

Fig. 7. Predicted average hot layer temperatures; a) Set 1; b) Set 1b and c) Set 2.

Fig. 8. Temperature vs. height distribution at different locations in the compartment at 150 s (a, b and c) and 200 s (d, e and f). Thermocouple rack 7 (a, d) is located near the re,

rack 11 (b, e) is located near the centre of the compartment, and rack 19 (c, f) is located near the window. See Fig. 1for rack location.



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the experimental error in the hot layer, but underpredicting the

temperatures in the cold layer by about 40%. At rack 19, near the

window, and 150 s (Fig. 8c), the lower HRR bound produces

temperatures that lie within the experimental error in the hotlayer,

while the upper HRR bound results in overprediction by about 30%.At 200 s the hot layer temperatures at rack 7 are slightly over-

estimated (although close to the experimental error, Fig. 8d) when

using the upper HRR bound, and underestimated by around 35%

when using the lower HRR bound. The cold layer temperatures are

underestimated by 50e100% for both input HRR curves. At rack 11

temperatures simulated with the lower HRR bound are under-

predicted by less than 20% in the hot layer (Fig. 8e), having similar

shape to the measured distribution. With the upper HRR bound as

input, the temperatures are overpredicted by about 25% in the hot

layer, but underpredicted by about 35% in the cold layer, thus indi-

cating higher temperature differences between hot and cold layer.

Near the window, at rack 19 (Fig. 8f), the temperatures (specially in

the hot layer) are in good agreement with the lower HRR bound as

input, although the predicted hot layer height is around 0.5 mhigher than that observed. But the upper HHR bound overpredicts

the hot layer temperature by 40%, which is in accordance to the

overprediction by around 40% of the hot layer average temperature

resulting from the upper HRR bound at 200 s (Fig. 7c).

In addition to gas phase temperatures, the simulated wall

temperatures and wall heat uxes are compared to the measure-

ments in Fig.9 at two different times. Theux for both measurement

and predictions is the total incident heat arriving to the location.

Using the lower HRR bound, the wall temperature is underpredicted

by about 20% at 150 s, and within (or very close to) the experimental

error range at 200 s. For the upper HRR bound, the simulated wall

temperature lieswithin the experimental error at both times. Butthis

apparently best agreement of the upper HRR bound for wall

temperatures contradicts the corresponding results for the wall heat

uxes. While the lower HRR bound produces heat uxes in the hot

layer close to the experimental error at 150 s, the upper HRR bound

overpredicts heatuxes in the hot layer by20% and the cold layer by

100%. Fig. 9 shows that at 200 s the predicted wall heatux with the

lower HRR bound is in reasonable agreement with the measure-ments, both qualitatively and quantitatively. The upper HRR bound

overpredicts of the heat uxes by 60e150%.

Fig. 10shows the comparison of the distribution of heat uxes

on the ceiling along two perpendicular directions at two different

times. The simulated heat ux to the ceiling agrees with the

measured heat ux when using the lower HRR bound (within 20%

error). Using the upper HRRbound, the heat uxes tothe ceiling are

consistently overpredicted (20e100%). The betterpredictions of the

ceiling heat ux compared to the wall heat ux (seeFig. 9) for the

lower HRR bound could be explained by the fact that the radiation

from the ame to the ceiling is reduced by the presence of the

smoke layer. The inaccuracies when modelling the ame could

have a smaller effect on the ceiling heat ux.

The difculty of modelling the near eld of the re on one hand,and the relatively good agreement of the results away from there

on the other, is consistent throughout this paper and with previous

work[9].

7. Conclusions

This work presents a detailed account of the a posteriori

modelling of Dalmarnock Test One. A very large pool of scenario

descriptions and measurements is used together with possible

HRR curves. Simulations were then compared against detailed

measurements, and uncertain input parameters were adjusted in

order to t the results. It was shown that even with full access to

the measurements, it is not easy to satisfactorily reproduce the

course of the

re. Although averaged quantities were in reasonable

Fig. 9. Wall temperature vs. height (a and c) and Heat ux vs. height (b and d) distribution on the wall of the re compartment against the kitchen at times 150 s (a and b) and 200 s

(c and d).



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A Posteriori Modelling of the Growth Phase of Dalmarnock Fire Test One

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