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Journal ArticleDOI

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

01 Jan 2021-Vol. 38, Iss: 3, pp 4979-4986
TL;DR: 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.

Summary (3 min read)

1. Introduction

  • Liquid pool fires are often present in accidental fire scenarios in the process industry resulting from fuel spills and storage tanks.
  • The heat feedback from the flame to the liquid fuel determines the burning rate of pool fires, which sustains the flame.
  • 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.
  • 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.
  • Their study revealed that the Marangoni effect and the heat transfer from the sidewall had little influence on the steady burning rate; but neglecting buoyancy effect in the liquid phase surprisingly resulted in almost 64% reduction in the steady mass burning rate.

2. Numerical formulation

  • The aim of this study is to formulate a fully coupled 3-D model considering the convective motion in the liquid phase by incorporating both the Marangoni and buoyancy effects.
  • The computational domain is partitioned into a fire region and a fuel region for which different governing equations are formulated to describe the underlying physics.

2.1 Fire region

  • The turbulent pool fire is simulated by the in-house version of FireFOAM [21], the LES based fire simulation solver within open source CFD code, OpenFOAM.
  • The turbulent combustion is assumed to be mixing-controlled and modelled by the Eddy Dissipation Concept (EDC) which was modified and extended into the LES framework by Chen et al. [16].
  • Soot volume fraction is modelled by the laminar smoke point-based soot model for turbulent fires also developed by Chen et al. [16].
  • The transport equations for the radiative heat transfer are solved by the finite volume based discrete ordinate method [16].
  • More information about FireFOAM and the sub-models used can be found in [16, 21].

2.2 Fuel region

  • The fuel region exchanges mass and heat with the fire region at the phase interface.
  • The convective motion in the fuel region is in small scales and tends to gradually attenuate during the heat-up process.
  • Therefore, incompressible laminar transport is formulated by assuming constant thermo-physical properties except for the density which follows the Boussinesq approximation.
  • 𝜌𝐶𝑝 ⁄ the thermal diffusivity, and k is the thermal conductivity, 𝜌 the density, 𝐶𝑝 the specific heat at constant pressure, 𝑄𝑑𝑒𝑝 the source term of in-depth radiation, 𝒏 the normal vector of pool surface.

2.3 Evaporation model

  • The evaporation model used in this study follows the widely used ‘film theory’ model proposed by Sikanen and Hostikka [18], which is based on the liquid-vapour equilibrium assumption.
  • It assumes an existence of a fuel vapour diffusion layer, not suitable for the boiling burning stage.
  • For more information on the model please refer to the reference [18].

2.4.1 Thermal boundary condition

  • 𝑘𝑓 is the fuel thermal conductivity and 𝑘𝑔 is the gas mixture-averaged thermal conductivity.
  • The first term on the left side of Eq. (6) is the convective heat transfer.
  • Since the Reynolds number is rather small at the pool surface and there is also a mass flux at the surface, it is decided to resolve the flow adjacent to the surface.

3. Problem descriptions

  • The former produces a sooty flame while the methanol fire is soot free.
  • The fire region mesh is refined above the pool surface in the vertical direction.
  • The authors preliminary grid sensitivity study has confirmed that the adopted grid resolutions were sufficient and further refinement of the grid resolution did not improve the predictions.
  • For the soot model, the laminar smoke point height is set to 0.147m for heptane following [16].
  • Therefore, the heat conduction is neglected by setting an adiabatic boundary condition at the container walls.

4.1 The steady methanol pool fire

  • Figure 1 compares two images of the pulsating methanol pool fire.
  • Comparison between the predicted and measured time-averaged temperatures and species concentrations along the centreline are displayed in Fig. 3 for the methanol fire, demonstrating reasonably good agreement in the values, but the location of the predicted maximum temperature is higher than the measured one.
  • Overall, the predicted distribution is in good agreement with the measured profile.
  • Some discrepancies exist elsewhere and might be caused by the simplification of the boundary conditions and experimental uncertainties.
  • The convective motion is more pronounced during the heat-up stage, as evident by the maximum flow velocity also plotted in Fig.

4.2 The transient thin-layer heptane pool fire

  • Comparison between the predicted and measured mass burning rate for the heptane fire is shown in Fig.
  • The burning rate during the heat-up stage is well captured.
  • The temperature profiles at the bottom two locations are over-predicted from approximately 50 s onwards.
  • The assumption of the adiabatic bottom boundary condition is partly responsible for the over-predictions.
  • 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.

5. Concluding remarks

  • A fully coupled 3-D numerical formulation has been formulated and validated.
  • The predictions have been validated against measurements for both the gas and liquid phases achieving reasonably good agreement.
  • Counter-rotating vortices were well captured and found to apparently enhance heat transfer within the liquid fuel.
  • It was also observed that the convective motion gradually attenuated once the liquid region was heated up to a more uniform temperature distribution and the convective motion was mainly caused by the Marangoni effect.
  • Finally, the convective motion in the liquid phase was found to play an important role in the predictions of the mass burning rate.

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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

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9 citations

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TL;DR: In this paper, the radial variation of the local radiative and local net heat flux incident on the surface of 0.30 m diameter pool fires were measured using a water-cooled, nitrogen purged, narrow view-angle gauge.
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TL;DR: In this paper , a postulated enclosure fire scenario based on methanol pool ignition in a chemical cleaning facility is considered and the authors provide safety recommendations to prevent/minimize the hazard.
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TL;DR: In this article, an experimental investigation of the turbulence structure of a medium-scale methanol pool fire has been undertaken to provide further insight into the complex physical phenomena which drive mixing and entrainment and thereby control development of the fire flow field.

107 citations

Journal ArticleDOI
01 Jan 1965
TL;DR: In this paper, Hottel's theory can be applied not only to turbulent luminous combustion of liquid fuels, but also to non-luminous combustion under condistions of laminar flow.
Abstract: The rates of diffusive burning of liquid methanol, chosen as a fuel which produces a nonluminous flame, were measured in special concentric vessels having three compartments as well as in the usual single laboratory vessels The experimental results obtained include the interesting observation that the burning rate is much greater at the vessel rime (next to the flame base) than near the vessel center, and that the total burning rate in the compartments of a concentric vessel is equal to that in a single vessel of the same size These data are discussed in the light of burning-rate theories presented independently by Spalding and by Hottel, and an attempt has been made to extend the latter's theory by introducing empirical local heat-transfer coefficients The equation proposed by the authors explains successfully all the results of the present study Thus, it appears that Hottel's theory can be applied not only to the turbulent luminous combustion of liquid fuels, but also to nonluminous combustion under condistions of laminar flow

56 citations

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TL;DR: In this paper, the eddy dissipation concept is extended to the large eddy simulation (LES) framework following the same logic of the turbulent energy cascade as originally proposed by Magnussen but taking into account the distinctive roles of the sub-grid scale turbulence.

52 citations

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TL;DR: In this paper, a computational fluid dynamics model for predicting the heat release rates of liquid pool fires is presented, which makes use of the one-dimensional heat transfer solver to provide the liquid surface boundary condition for the gas phase solver.

49 citations

Journal ArticleDOI
TL;DR: In this paper, the dependence on external heat flux of ignition delay time and steady mass flux of PMMA is investigated numerically, and the importance of both gas-phase and condensed-phase radiation absorption effects are discussed.

37 citations

Frequently Asked Questions (21)
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. 

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

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

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 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. 

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. 

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]. 

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. 

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. 

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

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. 

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. 

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

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. 

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

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. 

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. 

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. 

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

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].