# Fire in an atrium mass flow of the smoke by shv46529

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```									  Fire in an atrium: mass flow of the smoke plume
Nele Tilley
Supervisor: Bart Merci

I. INTRODUCTION                       adjacent room. Based on these experiments,
his goal was to adjust his previous formula for
When fire occurs in an adjacent room of an       the required mass flow rate in the atrium.
atrium, the smoke plume will rise and reach           The formula he proposed, based on the
the ceiling of the room. Underneath the             small-scale experiments is
ceiling, the smoke will spread in all directions
until it reaches the opening of the atrium.
M ( z ) = 0.07 (W 2Q )      ( z + Db ) + M b ,
1/ 3
There, the smoke will turn around the spill                                                            (1)
edge and become an adhered smoke plume
(Fig. 1).                                           where W is the width of the atrium.
In my work, I first repeated the experiments
M(z)                   Poreh carried out by means of Computational
Fluid Dynamics (CFD) simulations. These
simulations were carried out in the program
FDS (Fire Dynamics Simulator, developed by
z                   NIST). After repeating the experiments in the
CFD-simulations, a large-scale atrium was
Db   Mb                            also simulated, to verify whether the proposed
Q                                      formula is also valid for larger and more
Fig. 1. Smoke movement in atrium.            realistic configurations.

When this adhered plume reaches the                         II. SCALING AND SETUP
ceiling of the atrium, the smoke will
accumulate and form a smoke layer.                    In fire experiments, scaling is almost
As fire safety design, a smoke extraction        always based on the Froude number. This
system is often present in atria. The smoke is      number can be written as
extracted at the ceiling of the atrium at mass                         Q
Fr =                  .       (2)
flow rate M(z). The higher the mass flow rate,                  ρ ⋅ ∆T ⋅ c p gL5
the larger the smoke free height (z) above the
spill edge will be.                                    When scaling, temperatures should remain
Since many years, a number of authors            the same, and with them also density and heat
have tried to find a formula for the required       capacity. If the Froude-number has to stay
extraction mass flow as function of the smoke       constant, then the variation of heat release
free height and the heat release rate of the fire   rate in scaling follows the law
(Q). Most of them assume that thoroughly                     Q ~ L5/2,                         (3)
validated formulae are already available to         where L is a significant length scale.
calculate the mass flow (Mb) and thickness of          The small-scale atrium used in the
smoke layer (Db) emerging from the adjacent         experiments was 0.9 m wide. For the large-
room.                                               scale simulations, the configuration was kept,
Recently, Poreh [1] performed a series of        but scaled up to an atrium width of 7.2 m and
small-scale experiments in an atrium with
one of 4 m. The heat release rates were scaled    results, is that scaling based on Froude-
up according to Eq. 3.                            number alone might not be a correct
In the simulations, the heat release rate of    approach. Other dimensionless numbers can
the fire (Q) and the extraction velocity were     scale in a different way, and it might be
imposed. The other values (Mb, Db, z and M)       necessary to also take that into account.
were measured in the simulations.                       100

M - Mb
III. RESULTS
Firstly, the small-scale atrium was
simulated in FDS. The results of the
numerical simulations agree very well with               10
the results of the experiments. Since Eq. 1 is
based on the small-scale experiments, this
formula also agrees well with the results of
the simulations.
Afterwards, the atrium was scaled up to
sizes of width 7.2 m and 4 m. However, a                     1

difficulty arose in finding the value for the                    10          100                 1000
(W 2Q)1/3(z+Db)
smoke free height z.                              Fig. 3. Results of simulations in 4m wide atrium.
As depicted in Figure 2, the smoke free
height can only be easily defined if the smoke                        IV. CONCLUSIONS
layer is one-dimensional (the smoke layer has        The next step in this research is thus to do a
a uniform thickness under the entire ceiling).    complete dimensionless analysis, taking into
account all physics involved in this
configuration. From the results, we should be
able to conclude whether Froude-scaling is
the appropriate technique to be used when
dealing with large-scale atrium fires.
Afterwards, new formulae will have to be
developed, to also account for the more-
dimensional effect when calculating the mass
Fig. 2. Difference between a 1D (left) and a    flow in atrium buildings.
more-dimensional (right) smoke layer.
However, if the smoke layer is more-           ACKNOWLEDGEMENTS
dimensional, the smoke free height can not be
The research of Nele Tilley is funded by a
unambiguously determined. The smallest
Ph.D. grant of the Institute for the Promotion
smoke-free height present in the atrium was
of Innovation through Science and
chosen, according to the worst-case scenario.
Technology in Flanders (IWT-Vlaanderen).
The results of the simulations in the atrium
Bart Merci is Postdoctoral Fellow of the
of width 4 m are depicted in Figure 3. It is
Fund of Scientific Research – Flanders
clear that only when a one-dimensional
(FWO-Vlaanderen).
smoke layer is present in the atrium (white
dots: ○ ), the results agree well with Eq. 1.
(black line: ▬ ). The results of the more-                              REFERENCES
dimensional smoke layer (black dots: ) do         [1]   Poreh, M., Marshall, N.R., Regev, A.,
not agree with the suggested formula.                   Entrainment by adhered two-dimensional
A possible reason for the disagreement               plumes, Fire Safety Journal, 43, No. 5, 2008,
between Eq. 3 and the large-scale simulation            pp. 344-350

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