The effect of convective motion within liquid fuel on the mass burning rates of pool fires – A numerical study

TLDR: In this paper, a fully coupled 3D numerical formulation of liquid pool fires is proposed to directly solve convective motion in the fuel region by incorporating inhomogeneous heat feedback, and the fire dynamics is modelled using the large eddy simulation (LES) approach.

Abstract: To improve numerical simulation of liquid pool fires and remove the need for experimentally measured or empirically calculated mass burning rates as boundary conditions, a fully coupled three-dimensional (3-D) numerical formulation, which directly solves convective motion in the fuel region by incorporating inhomogeneous heat feedback, is formulated. The fire dynamics is modelled using the large eddy simulation (LES) approach. Incompressible laminar flow formation is applied to the liquid fuel region, assuming constant thermo-physical properties except for the density which follows the Boussinesq approximation. The numerical formulation of the two phases is solved using a fully coupled conjugate heat transfer approach at the pool surface. The coupled model is validated against published measurements for a thin-layer heptane pool fire and a deep methanol pool fire. The convective motion within the liquid phase is found to have important effects on the pool fire mass burning rate and its neglection would result in a fast rise and over-prediction of the mass burning rate.

Figures

Fig. 5. The predicted velocity vectors at the middle plane for the methanol fire and the maximum velocity in the fuel region.

Table 2 Liquid fuel properties.

Fig. 4. The predicted mass burning rate vs time and comparison between the predicted and measured [7] time-averaged distribution at the pool surface.

Fig. 3. Comparison between the predicted and measured gas phase time-averaged temperatures and species concentrations for the methanol fire.

Fig. 8. The predicted temperature contour and velocity vectors at the pool surface at 30 s for the heptane fire.

Fig. 7. Comparison between the predicted and measured [1] temperature profiles in the liquid at different locations for the heptane fire (z represents the vertical location from the fuel bottom).

Full text

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1
1. Title
The effect of convective motion within liquid fuel on the mass burning rates of pool fires – a
numerical study
2. Authors
Baopeng Xu, Jennifer Wen
3. Corresponding author’s COMPLETE contact information:
Jennifer Wen (Dr.)
School of Engineering
University of Warwick
Coventry CV4 7AL, UK
Phone: +44 (0)24 765 73365
Email. Jennifer.wen@warwick.ac.uk
4. Colloquium that describes the research topic
Fire research
5. Total length of paper and method of determination
Method 1
6188 words
6. List word equivalent lengths for main text, nomenclature, references, each figure with
caption, and each table determined according to the instructions that follow
Text: 3237 words
References: 507 words
Figures total: 1889 words
Figure 1: 133 words; Figure 2: 211 words; Figure 3: 484 words; Figure 4: 244 words;
Figure 5: 282 words; Figure 6: 238 words; Figure 7:163 words; Figure 8: 163 words;
Equations: 281 words;
Table 1: 76 words.
Table 2: 198 words.

2
Abstract
To improve numerical simulation of liquid pool fires and remove the need for experimentally
measured or empirically calculated mass burning rates as boundary conditions, a fully coupled
three-dimensional (3-D) numerical formulation, which directly solves convective motion in the fuel
region by incorporating inhomogeneous heat feedback, is formulated. The fire dynamics is modelled
using the large eddy simulation (LES) approach. Incompressible laminar flow formation is applied to
the liquid fuel region, assuming constant thermo-physical properties except for the density which
follows the Boussinesq approximation. The numerical formulation of the two phases is solved using
a fully coupled conjugate heat transfer approach at the pool surface. The coupled model is validated
against published measurements for a thin-layer heptane pool fire and a deep methanol pool fire. The
convective motion within the liquid phase is found to have important effects on the pool fire mass
burning rate and its neglection would result in a fast rise and over-prediction of the mass burning
rate.
Keywords
Pool fire; mass burning rate; Marangoni effect; conjugate heat transfer; large eddy simulation

3
1. Introduction
Liquid pool fires are often present in accidental fire scenarios in the process industry resulting
from fuel spills and storage tanks. The combustion of pool fires is self-driven by the closely coupled
heat and mass transfer between the flame and the liquid fuel. The heat feedback from the flame to the
liquid fuel determines the burning rate of pool fires, which sustains the flame.
Previous experimental studies have included both thin-layer [1-4] and deep pool fires [5-8]. Their
burning behaviour differs in two aspects. Firstly, the fuel level of the thin-layer pools regresses with
the progress of the combustion; while that of the deep pools remains almost constant with continuous
fresh fuel being added through the pool bottom [6]. Secondly, the burning process of thin-layer pool
fires is highly transient [9] while deep pool fires can reach a quasi-steady state after a warm-up
period [6]. Many factors can affect the burning rate, for instance the fuel type, size and depth of the
liquid pool, material and geometry of the fuel container as well as ambient conditions, etc. Because
of these complicated influencing factors, the measured burning rates often differ even for the same
pool size and fuel type during experimental investigations [10].
The heat feedback from the flame to the pool surface is in the forms of radiation and convection,
while conduction mainly contributes to the heat transfer at the container walls. The role of radiation
becomes more important for sootier fuels and larger pool sizes. It was found that heat conduction via
the container walls is only important for very small pool fires [11]. Liquid fuels are not usually
considered to be optically thin, and the in-depth radiation into the fuel region is normally absorbed
within several millimetres [2]. As the heat feedback enters the fuel, it is redistributed via conduction,
convection and in-depth radiation [12].

4
The puffing nature of pool fires creates unsteady inhomogeneous heat feedback, resulting in
transient non-uniform distribution of the mass burning rate. It was found that the burning rate can be
higher at the centre [13] or at the outer ring [14], depending on the experimental conditions. The
inhomogeneous heat feedback also creates significant surface temperature gradient, which would
lead to hydrodynamic instability through Marangoni effect [15], which induces vortex motions inside
the fuel, enhancing its heat transfer coefficient.
The development of a physics-based fully coupled numerical model to predict the burning rate
needs to consider a large number of coupled parameters associated with both the gas phase and liquid
flows. Most previous numerical studies avoided the solution of the liquid phase by directly applying
a prescribed fuel mass flow rate from experimental measurement [16] or simplified empirical
correlations [17] at the fuel inlet boundary. To truly capture the underlying physics, the liquid phase
needs to be solved along with the gas phase solver. The most popular evaporation model to predict
the burning rate in the literature is based on the ‘film theory’ where evaporation is driven by a
diffusion process and liquid-vapour equilibrium is assumed at the pool surface temperature [18, 19].
The ‘film theory’ based model is capable of capturing the transient nature of the burning processes
by allowing for the evaporation below the boiling point.
However, most previous numerical studies on the burning rate neglected the convective motion in
the liquid phase. An alternative approach to adjust the thermal conductivity to consider the internal
convection was attempted by using the convective heat transfer coefficient [18]. A faster rise of the
initial burning rate was generally predicted in these numerical studies. This is due to the neglect of
the convective motion which tends to enhance the heat transfer in the liquid fuel. Very recently,
Fukumoto et al. [20] numerically investigated the vortex motions of a steady small-scale methanol

Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, a physics-based fully coupled numerical model is proposed to predict the burning rate of pool fires. 

Q2. What is the effect of the puffing nature of pool fires?

The puffing nature of pool fires creates unsteady inhomogeneous heat feedback, resulting in transient non-uniform distribution of the mass burning rate. 

Q3. How many solid angles are used for the radiative transfer equations?

A total of 16 solid angles covering the hemisphere are used for the radiative transfer equations as a compromise between computational time and accuracy. 

Q4. What is the popular evaporation model to predict the burning rate in the literature?

The most popular evaporation model to predict the burning rate in the literature is based on the ‘film theory’ where evaporation is driven by a diffusion process and liquid-vapour equilibrium is assumed at the pool surface temperature [18, 19]. 

Q5. What is the evaporation model used in this study?

The evaporation model used in this study follows the widely used ‘film theory’ model proposedby Sikanen and Hostikka [18], which is based on the liquid-vapour equilibrium assumption. 

Q6. What is the effect of the Marangoni effect on the burning rate?

The Marangoni effect, resulting from the surface temperature gradient, is more pronounced at the heat-up stage, is expected to play a more important role for the transient burning rate. 

Q7. What is the effect of the heat feedback on the burning rate of pool fires?

the burning process of thin-layer pool fires is highly transient [9] while deep pool fires can reach a quasi-steady state after a warm-up period [6]. 

Q8. What is the popular evaporation model?

The ‘film theory’ based model is capable of capturing the transient nature of the burning processes by allowing for the evaporation below the boiling point. 

Q9. What is the LES based simulation solver for turbulent pool fire?

The turbulent pool fire is simulated by the in-house version of FireFOAM [21], the LES basedfire simulation solver within open source CFD code, OpenFOAM. 

Q10. What is the predicted convective heat flux?

The convective heat flux is much smaller than the radiative heat flux due to the relatively small flow velocity at the pool surface. 

Q11. What is the effect of the heat feedback on the pool surface?

It can also be observed that the surface Marangoni velocity is directed from the hot region to the cold region, tending to reduce the temperature gradient on the pool surface and promote more uniform distribution of the mass burning rate compared to the neglection of the convective motion. 

Q12. How is the gas flow at the pool surface resolved?

To resolve the gas flow at the pool surface, the meshes inside the burner lips are refined with a 1 mm cell size in the vertical direction, which corresponds to 𝑌+ < 1.5. 

Q13. Why are the temperature profiles at the top two locations under-predicted?

The temperature profiles at the top two locations are apparently under-predicted by the simulation without convection, and over-predicted at the bottom two locations due to the over-prediction of the mass burning rate as mentioned above. 

Q14. How long did the predicted burning rate remain constant?

From 50 s onwards, the measured burning rate remained almost constant, while the predicted value continues to increase gradually. 

Q15. How long does the burning rate remain constant?

The burning rate remains unchangedprior to 12 s during the numerical ignition process due to the relatively low radiative heat feedback, and then increase quickly to a quasi-steady value of 0.013 𝑘𝑔 (𝑚2 ∙ 𝑠)⁄ at 30 s. 

Q16. What are the common causes of pool fires?

Liquid pool fires are often present in accidental fire scenarios in the process industry resulting from fuel spills and storage tanks. 

Q17. What was the boundary condition for the transient thin-layer case?

a moving boundary was set for the pool surface to allow for the surface regression for the transient thin-layer case, while the pool surface was fixed for the steady deep pool fire during the simulations. 

Q18. How was the initial rate of the evaporation process determined?

To initiate the evaporation process, the simulations started from an initial burning rate of 0.003𝑘𝑔/(𝑚2 ∙ 𝑠) which was found to be the lowest initial rate to achieve a quick ignition. 

Q19. How did Fukumoto et al. study the vortex motions of a?

Very recently, Fukumoto et al. [20] numerically investigated the vortex motions of a steady small-scale methanolpool fire, using fully compressible description for the liquid pool. 

Q20. Why is the convective motion more significant for the methanol fire?

5. The convective motion is more significant for the heptane fire than the methanol fire due to the relatively larger radiative heat feedback. 

Q21. What might have caused the increase in the container lip height?

This might have been caused by the increase in the container lip height due to the regression of the pool surface in the experiments, which would affect the magnitude of the mass burning rate as found by Dlugogorski and Wilson [24].