Study of vertical upward flame spread on charring materials—Part II: Numerical simulations

TL;DR: In this paper, an enthalpy-based pyrolysis model is used to simulate vertically upward flame spread over a charring material in a parallel plate configuration, where the mass loss rate is also considered.

Abstract: Simulation results, obtained by means of application of an enthalpy-based pyrolysis model, are presented. The ultimate focus concerns the potential of the model to be used in flame spread simulations. As an example we discuss vertically upward flame spread over a charring material in a parallel plate configuration. First, the quality of the pyrolysis model is illustrated by means of cone calorimeter results for square (9.8 cm × 9.8 cm exposed area), 1.65 cm thick, horizontally mounted MDF samples. Temperatures are compared at the front surface and inside the material, for different externally imposed heat fluxes (20, 30 and 50 kW/m2), for dry and wet samples. The mass loss rate is also considered. Afterwards, vertically upward flame spread results are reported for large particle board plates (0.025 m thick, 0.4 m wide and 2.5 m high), vertically mounted face-to-face, for different horizontal spacings between the two plates. The simulation results are compared to experimental data, indicating that, provided that a correct flame height and corresponding heat flux are applied as boundary conditions, flame spread can be predicted accordingly, using the present pyrolysis model. Copyright © 2010 John Wiley & Sons, Ltd.

Summary

1. Introduction

• By no means, it is their intention to introduce a (semi-empirical) flame spread model, to be used for other configurations than the specific one considered here.
• The only objective is to illustrate that the developed pyrolysis model is ready-to-use for such configurations and that reasonably accurate results can be obtained, provided an appropriate value for incoming heat flux onto the solid material is provided.
• This heat flux could stem from CFD (Computational Fluid Dynamics) in the gas phase, where the turbulent combustion is simulated.
• The authors do not use CFD in the present paper, as uncertainties in CFD would distract the attention from their objective as mentioned.
• The set-up is somehow a sophism, but this suffices for the sake of the present paper, as explained above.

2.1 Model description

• Pyrolysis (and evaporation) is modelled as an infinitely fast irreversible process, taking place at an infinitely thin front at 'pyrolysis' (resp. 'evaporation') temperature.
• Thus, fronts are moving through the solid material.
• As the evaporation front passes, wet virgin material becomes dry virgin material.
• In the present simulations, the water vapour and pyrolysis gases are assumed to leave the solid instantaneously.
• They are in thermal equilibrium with the solid.

INSERT TABLE 1]

• The densities were obtained by measuring the weight of wet and dry samples, along with their volume [1] .
• The other values have been taken from the literature [8] .
• Important model parameters are the heat of pyrolysis and the pyrolysis temperature [2] .
• The latter value has been adopted from [1] , where it was shown that, depending on the externally imposed heat flux, pyrolysis starts when the front surface reaches a temperature in the range of 300 -350 o C.

[INSERT TABLE 2]

• The back surface of the plate is assumed perfectly insulated and impervious.
• The burner flames heat flux is modelled as a constant heat flux '' pfr q onto the particle board over a certain height: visual observations [1] show a 'persistent flame region' of height y pfr .
• The decay constant C pfr is tuned to match the temperature measurements [1] to a reasonable extent.
• Figure 1 gives an impression of the imposed heat flux, prior to pyrolysis, along with temperature measurements after 20s for the two inter-plate distances.
• The decay constant is lower as the flame region is elongated.

As soon as T

• S =T pyr at a certain height, pyrolysis starts, with the release of volatiles.
• These volatiles burn with oxygen to form flames.
• As the set-up is in principle symmetric, the net radiative heat exchange between the plates is relatively small, but the heat loss from each surface to the surroundings is certainly reduced.
• This can be determined from the view factor for two parallel plates [9] .
• The view factor to the environment, determining the radiative losses, equals 1 minus these values.

3.1.2 Sensitivity analysis

• The effect of the flame heat flux (bottom right picture) is visible, but not dominant.
• For obvious reasons, the mass loss rate increases and the pyrolysis stage becomes shorter as the flame heat flux increases.

3.2 Vertically upward flame spread

• Figure 7 shows essentially similar results, for the smaller inter-plate distance (10.5 cm) with the honey comb burner.
• Differences between the parabola fit and the real time evolution of y f are smaller as everything evolves much faster.

4. Conclusions

• The importance of the accurate knowledge of flame height evolution in time was illustrated.
• The quality of the results indicates that, provided the flame height and corresponding heat flux are known, the present pyrolysis model can be used to simulate vertically upward flame spread in a parallel plate configuration.
• Thick line: numerical simulations; thin lines: experiments.

Figures

Table 1. Model parameters and material properties for the cone calorimeter set-up for medium density fibre (MDF) board.

Figure 3. Evolution in time of temperature (wet sample). Left: front surface temperature;

Figure 4. Evolution in time gas mass flow rate for dry samples (left) and wet samples

Table 2. Model parameters and material properties for the parallel vertical plate set-up for particle board.

Table 3. Model parameters for inter-plate distance equal to 10.5 cm or 30.5cm.

Figure 7. Temperature evolution for different heights (inter-plate distance 10.5 cm).

Figure 6. Temperature evolution for different heights (inter-plate distance 30.5 cm).

Figure 1. Imposed heat flux, prior to pyrolysis, for inter-plate distance equal to 30.5 cm (top) and 10.5 cm (bottom), along with temperature measurements.

Figure 5. Flame height evolution in time (top) and relative error of parabolic fit, compared to the experimental value (bottom). Inter-plate distance equal to 30.5 cm (left) and 10.5 cm (right).

Figure 2. Evolution in time of temperature (dry sample). Left: front surface temperature;

Full text

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This item is the archived peer-reviewed author-version of:
Study of vertical upward flame spread on charring materials-Part II: Numerical simulations
Wasan, S.R., Rauwoens, P., Vierendeels, J. and Merci, B.
In: Fire and Materials 35 (5), 261-273, 2011.
To refer to or to cite this work, please use the citation to the published version:
Wasan, S.R., Rauwoens, P., Vierendeels, J. and Merci, B (2011). Study of vertical upward
flame spread on charring materials-Part II: Numerical simulations. Fire and Materials 35 (5)
261-273.

Study of Vertical Upward Flame Spread on Charring Materials –
Part II: Numerical Simulations
S.R. Wasan, P. Rauwoens, J. Vierendeels and B. Merci
Ghent University – UGent, Department of Flow, Heat and Combustion Mechanics
Corresponding author: Bart.Merci@UGent.be

2
Abstract
Simulation results, obtained by means of application of an enthalpy based pyrolysis
model, are presented. The ultimate focus concerns the potential of the model to be used in
flame spread simulations. As an example we discuss vertically upward flame spread over
a charring material in a parallel plate configuration. Firstly, the quality of the pyrolysis
model is illustrated by means of cone calorimeter results for square (9.8 cm x 9.8 cm
exposed area), 1.65cm thick, horizontally mounted MDF samples. Temperatures are
compared at the front surface and inside the material, for different externally imposed
heat fluxes (20 kW/m
2
, 30 kW/m
2
and 50 kW/m
2
), for dry and wet samples. The mass
loss rate is also considered. Afterwards, vertically upward flame spread results are
reported for large particle board plates (0.025 m thick, 0.4 m wide and 2.5 m high),
vertically mounted face-to-face, for different horizontal spacing between the two plates.
The simulation results are compared to experimental data, indicating that, provided that a
correct flame height and corresponding heat flux are applied as boundary conditions,
flame spread can be predicted accordingly, using the present pyrolysis model.

3
1. Introduction
In part I [1], the outcome of an experimental campaign was reported. In the present paper,
we apply a simple pyrolysis and evaporation model, based on enthalpy [2], to the same
configurations.
Firstly, we discuss the one-dimensional cone calorimeter configurations.
Afterwards, vertically upward flame spread in a parallel plate configuration is considered.
By no means, it is our intention to introduce a (semi-empirical) flame spread model, to be
used for other configurations than the specific one considered here. The only objective is
to illustrate that the developed pyrolysis model is ready-to-use for such configurations
and that reasonably accurate results can be obtained, provided an appropriate value for
incoming heat flux onto the solid material is provided. This heat flux could stem from
CFD (Computational Fluid Dynamics) in the gas phase, where the turbulent combustion
is simulated. However, we do not use CFD in the present paper, as uncertainties in CFD
would distract the attention from our objective as mentioned. Rather, we use
experimental data [1] to estimate the heat fluxes that serve as boundary conditions for the
simulations. In this sense, the set-up is somehow a sophism, but this suffices for the sake
of the present paper, as explained above. The major advantage is that the strong
sensitivity of flame heat fluxes to e.g. fuel sootiness [3, 4] is avoided. To summarise,
expressions as developed in [3] for a similar set-up as the one under study in the present
paper, are not applied here, but the present paper is not intended to provide an alternative
for such relationships.

4
2. Numerical simulations set-up
2.1 Model description
In [2, 5], the model, along with the solution procedure, is extensively described and
applied to some basic configurations. The reader is referred to those references for all
details. We only recall here that the model relies on a fixed computational mesh, which
can be relatively coarse. On this mesh, the energy equation is solved numerically.
Pyrolysis (and evaporation) is modelled as an infinitely fast irreversible process, taking
place at an infinitely thin front at ‘pyrolysis’ (resp. ‘evaporation’) temperature. Thus,
fronts are moving through the solid material. As the evaporation front passes, wet virgin
material becomes dry virgin material. As the pyrolysis front passes, dry material becomes
char. In the present simulations, the water vapour and pyrolysis gases are assumed to
leave the solid instantaneously. They are in thermal equilibrium with the solid. More
advanced pyrolysis modelling (e.g. [6]) is possible, but this is beyond the scope of the
present paper.
2.2 Cone calorimeter set-up
We first discuss the results for the cone calorimeter set-up of [1]. We consider one-
dimensional heat transfer in the solid [1]. The computational mesh in the solid, with
thickness 1.65 cm, contains 33 cells. The time step size is set to 0.5s. It has been verified
that the results presented do not vary when more cells or smaller time steps are chosen.
The externally imposed heat flux
''
ext
q
equals 20 kW/m
2
, 30 kW/m
2
or 50 kW/m
2
. The
experiments were performed in open atmosphere, so that flames appear when the
volatiles are ignited with a spark ignition placed above the retainer frame. These flames
provide additional heat flux to the solid during pyrolysis. In the simulations, this is

Frequently asked questions

Q1. What are the contributions in "Study of vertical upward flame spread on charring materials-part ii: numerical simulations" ?

As an example the authors discuss vertically upward flame spread over a charring material in a parallel plate configuration. The simulation results are compared to experimental data, indicating that, provided that a correct flame height and corresponding heat flux are applied as boundary conditions, flame spread can be predicted accordingly, using the present pyrolysis model. 

Q2. What is the effect of heat on the mass flow rate?

The mass loss rate increases with decrease in the heat of pyrolysis, as the endothermic pyrolysis process consumes less energy, so that the pyrolysis front moves faster into the solid. 

Q3. How long does the flame decay after the pyrolysis?

As soon as the pyrolysis ends, i.e. as soon as the pyrolysis front reaches the back surface, the flame heat flux decays exponentially from 10 kW/m 2 , with adecay time constant equal to flame = 30 s. 

Q4. What is the effect of the set-up on the surface of the MDF board?

As the set-up is in principle symmetric, the net radiative heat exchange between the plates is relatively small, but the heat loss from each surface to the surroundings is certainly reduced. 

Q5. What is the mass loss rate in the simulations?

In all samples, the mass loss rate in the experiments, prior to the onset of pyrolysis, is related to evaporation of unbound moisture. 

Q6. What is the effect of h on the pyrolysis front?

As the material inside is then also already heated up more, the pyrolysis front moves faster during the early stages, leading to a higher first peak value in the mass loss rate. 

Q7. How is the temperature of the front surface set?

For the convective boundary condition at the front surface, the ambient temperature is set to the initial room temperature (Tamb = 300 K) until pyrolysis takes place. 

Q8. What is the reason for the small variations at the onset of pyrolysis?

The small variations at the onset of pyrolysis, after about 60 s, is due to the variation in the material properties, not due to a variation in boundary conditions (expressions (2a) and (2b)). 

Q9. What is the quality of the results?

The quality of the results indicates that, provided the flame height and corresponding heat flux are known, the present pyrolysis model can be used to simulate vertically upward flame spread in a parallel plate configuration. 

Q10. What is the temperature of the pyrolysis front?

As the surface temperature reaches the pyrolysis temperature (Tpyr = 325 o C = 598K), the temperature starts to rise more rapidly due to the additional heat flux from the flames (1b). 

Q11. How much heat flux is assumed to be absorbed by the flames?

The authors assume the heat flux from the flames, absorbed by the material, constant throughout the experiment, equal to'' 2, 10 /flame absq kW m . 

Q12. How is the heat exchange temperature at the front surface assumed to be?

From then on, until the end of pyrolysis, the surface is assumed to see flames, rather than air at approximately ambient temperature. 

Q13. What is the mass loss rate for the dry samples?

In the experiments, the total mass loss per unitarea ranges between 8.7 kg/m 2 and 9.5 kg/m 2 for the dry samples and between 9.4 kg/m 2 and 10.2 kg/m 2 for the wet samples. 

Q14. How much of the black body emissive power of the flames is the flame?

For flames of 700 o C (see below), this corresponds to a net absorption by the front surface of 20% of the black body emissive power of the flames.