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Computation of Heat Transfer in Micro-channel Flow using Direct Simulation Monte Carlo Method
1

B. Farouk, G. W. Mulholland*, K. B. McGrattan* and T. G. Cleary*

Department of Mechanical Engineering and Mechanics, Drexel University
Philadelphia, PA
*Building and Fire Research Laboratory, National Institute of Standards and
Technology, Gaithersburg, MD
Simulation of Smoke Transport and Coagulation for a Standard Test Fire

Abstract
Large eddy simulations of a standard test fire (EN 54-9, TF4) were carried out. The
development of the large-scale air movements and temperature fields generated by the
enclosure fires are calculated. In addition, the smoke transport and time evolution of the
size distribution of smoke aerosol due to coagulation are also predicted. The mass and
number densities of smoke particles are computed at a detector location, as specified in
the standard test fire procedure. Recent measurements of the number and mass densities
of smoke using electrical aerosol spectrometry compared favorably with the model
predictions.

Introduction
Smoke detector response is sensitive to both the concentration of smoke within the
sensing volume and the size distribution of the aerosol in a fire scenario. The object of
the simulation is to compute the local smoke characteristics given the burning rate of
the fire, the yield of smoke and its initial size distribution, and the geometric properties
of the enclosure. Once the smoke characteristics are known at the detector location the
response of the smoke detector can be computed.

Generally the ionization detectors are found to be more sensitive to the number density
of the smoke. As a class, smoke detectors using the ionization principle provide
somewhat faster response to high energy (open flaming) fires, since these fires produce
larger numbers of the smaller smoke particles. On the other hand, photoelectric smoke 2
detectors respond to the volume (mass) density of the smoke particles rather than the
number density.

Prediction of smoke transport and coagulation has been attempted in the past [1, 2]
where the evolution of size distribution of smoke aerosol under the influence of
coagulation as well as the large scale fluid motion and temperature fields were studied.
Specifically, Lagrangian particles or thermal elements were used to model the burning
of fuel in the fire plume. Each thermal element (blob) represents a given mass of smoke
(containing many smoke particles), which is proportional to the instantaneous heat
release rate. The transport of the thermal elements is also used to model smoke
movement (without smoke coagulation) in a Lagrangian sense. The evolution of the size
distribution in space was calculated deterministically from the solution to the
Smoluchowski equation.

A promising methodology for the prediction of large-scale gas movement, temperature
field and smoke movement in fire plumes and enclosure fires has been recently
introduced [3]. The model and computational methodology have reproduced mean
temperature and buoyant velocity correlations for large fire plumes [4]. In this paper,
we present numerical results for the velocity and temperature fields induced by a
standard test fire (EN 54 part 9) [5] by applying the above model, which incorporates
large eddy simulation techniques. The simulations reported here are for the test fire TF4
(open plastic fire)

[5]. The smoke particles are again represented by a large number of
the thermal elements - continuously introduced at the burning surface, while the fuel is
being consumed. Based on prescribed rates of smoke yield (Y kg/kg of fuel consumed),
the smoke transport within the enclosure is reported. While the ionization detectors are
found to be more sensitive to the local number density of the smoke, the photoelectric
detectors are more sensitive to the mass density. Hence it is necessary to determine both
the mass and the number densities of the aerosol reaching a detector. A smoke
coagulation sub-model based on the Smoluchowski equation

[6]

is incorporated to track
the mean number density of smoke particles in each blob with time. The mean size of
the smoke particles in each thermal element increases with time due to coagulation. The
smoke mass and number densities at a specified detector location are computed directly 3
from the number of thermal elements and the corresponding number densities of smoke
particles in each thermal element (blob), present at the detector location. The time
evolution of the mass and number densities of smoke at the detector location are
compared with the recent measurements reported by Mirme et al. [7]. The model
predictions for smoke coagulation compare favorably with the reported measurements.

Problem description
The test fire TF4 in EN 54-9 [4] is an open plastic fire, which is allowed to burn freely
with no restriction of air supply in an enclosure. The overall enclosure dimensions and
the detector location are specified in the test procedure. For the present simulations, a
9.5 m x 6.3 m x 4.0 enclosure was considered (see Figure 1 below). A small vent is
considered at a bottom corner of the enclosure to allow for constant pressure condition
during the combustion process. The fire source is located at the center of the enclosure
(0.5 m x 0.5 m) on a 0.25 m high pedestal. The walls, floor and ceiling are considered to
be thermally insulated. The rate of heat release
)
(t
q! for the TF4 fire is estimated from
the measurements reported by Ahonen and Sysio [8].

Model description
A fire plume is a three-dimensional transient buoyant flow that can be modeled by the
motion of a thermally expandable ideal gas [8]. The Navier-Stokes equations are solved
for such a fluid driven by a prescribed heat source Following Rehm and Baum [9] the
pressure is decomposed into three components, a background (average) pressure, a
hydrostatic contribution, and a perturbation to the hydrostatic pressure. High-frequency
acoustic oscillations are eliminated while large temperature and density variations
typically found in fires are retained. The resulting equations are thus referred to as
weakly compressible and are valid for low Mach number flows. Constant pressure
specific heat of the gas is considered in the formulation. An elliptic partial differential
equation for pressure perturbation is formulated by taking the divergence of the
momentum equation. Further details of the mathematical formulation can be obtained in
[3]. 4
Figure 1. Schematic of the test fire laboratory

Large eddy simulation technique
The application of the large eddy simulation (LES) techniques to fire is aimed at
extracting greater temporal and spatial fidelity from simulations of fire performed on
the more finely meshed grids allowed by modern fast computers. The small-scale eddy
motion is modeled via a sub-grid description. One such representation is the
Smagorinsky model [10]. There have been numerous refinements of the original
Smagorinsky model but it is difficult to assess the improvements offered by the newer
schemes. In this study, we have used the Smagorinsky model, which produces
satisfactory results for most large-scale applications where boundary layers are not
important [3].
Combustion model
A sub-grid thermal element model (TEM) is formulated to represent the fire. A large
number of Lagrangian elements (blobs) are introduced into the plume, releasing heat as
they are convected by the thermally induced motion [3]. The combustion and
hydrodynamics are coupled here since the fluid motion determines where the heat is
released, while the heat release determines the motion. The overall heat release rate q! (t)
from the fire is discretized as thermal elements that represent pyrolized fuel. At a
specified surface, such as the fuel bed, thermal elements are ejected at a rate of "
n! blobs
per unit time per unit area. The heat release rate of a single thermal element j is given
by
(1)






1
"
n
)
(t
"
q


0
,
b
j
p
t
q
!
!
!
=

C e n te r
D e te c to r
P o ly u re th a n e
F o a m M a ts
R o o m
V e n t
9 .5 m
4 .0 m
6 .3 m
3 m 5
where "
q! (t
0
) is the instantaneous heat release rate per unit area of the fuel bed and t
b
is
the burnout time (t t
0
< t
b
) of the thermal element and t
0
is the time the element is
ejected from the burning surface. The burnout time is obtained from the plume
correlations of Baum and McCaffrey [4].
Smoke transport model
A specified percentage of the fuel consumed (smoke yield, Y kg/kg of fuel