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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

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.
Topics: Large eddy simulation (53%), Convection (52%), Laminar flow (51%), Liquid fuel (51%), Boussinesq approximation (buoyancy) (51%)

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.
  • 𝑄𝑑𝑒𝑝 is calculated according to the Beer’s law [23]: 𝑄𝑑𝑒𝑝 = 𝑄𝑟𝑒𝑥𝑝(−𝛼 ∙ ∆𝑑𝑒𝑝) (4) where.

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 Boundary conditions

  • The numerical formulas for the fire and fuel regions need to be closed by the interface boundary conditions governing the continuity of mass, energy and momentum at the interfaces.

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.

2.4.2 Velocity boundary conditions

  • The Marangoni convection velocity at the fuel surface is related to the surface tension gradient by neglecting the shear contributions from the gas phase: 𝜇 𝜕𝑢 𝜕𝑧 = 𝜕𝜎 𝜕𝑇 𝜕𝑇 𝜕𝑥 (7) 𝜇 𝜕𝑣 𝜕𝑧 = 𝜕𝜎 𝜕𝑇 𝜕𝑇 𝜕𝑦 (8) where 𝑢 and 𝑣 are the velocity components at the pool surface, and 𝜕𝜎 𝜕𝑇 is the temperature coefficient of surface tension.
  • The vertical velocity is used for updating both the liquid phase mesh and the gas phase mesh within the container by uniformly redistributing the mesh points in the vertical direction for the transient thin-layer pool fire.

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

Citations
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01 Aug 2001-
Abstract: Abstract A series of measurements designed to investigate the heat feedback in pool fires burning liquid fuels are reported. Such measurements are essential for the development and validation of detailed models which predict the burning rate of liquid hydrocarbons and solid polymers. 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. A water-cooled, nitrogen purged, narrow view-angle gauge was developed to measure the radiative flux incident on the fuel surface. Measurements of the mass burning rate in a burner composed of annular rings was used to estimate the local heat feedback. A number of different fuels were studied, yielding flames with a wide range of heat release rates and luminosities. Consideration of the heat balance for a control volume enclosing the liquid PPOI indicated that radiation was an important component of the heat feedback for non-luminous fires and a dominant component in luminous fires.

4 citations


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Abstract: Progress in fire safety science strongly relies on the use of Computational Fluid Dynamics (CFD) to simulate a wide range of scenarios, involving complex geometries, multiple length/time scales and multi-physics (e.g., turbulence, combustion, heat transfer, soot generation, solid pyrolysis, flame spread and liquid evaporation), that could not be studied easily with analytical solutions and zone models. It has been recently well recognised in the fire community that there is need for better modelling of the physics in the near-wall region of boundary layer combustion. Within this context, heat transfer modelling is an important aspect since the fuel gasification rate for solid pyrolysis and liquid evaporation is determined by a heat feedback mechanism that depends on both convection and radiation. The paper focuses on convection and reviews the most commonly used approaches for modelling convective heat transfer with CFD using Large Eddy Simulations (LES) in the context of fire-driven flows. The considered test cases include pool fires and turbulent wall fires. The main assumptions, advantages and disadvantages of each modelling approach are outlined. Finally, a selection of numerical results from the application of the different approaches in pool fire and flame spread cases, is presented in order to demonstrate the impact that convective heat transfer modelling can have in such scenarios.

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Journal ArticleDOI
Aaron Yip1, Jan B. Haelssig1, Michael J. Pegg1Institutions (1)
Abstract: A liquid pyrolysis model was implemented into Fire Dynamics Simulator (FDS) to predict burning fluxes in multicomponent pool fires. The model was validated against steady-state pool fire data for ethanol-water, ethanol-isopropanol, and ethanol-hexane mixtures. Simulations were also compared to transient ethanol-heptane pool fire data from researchers at the State Key Laboratory of Fire Science in Hefei, China. A mesh sensitivity study on an ethanol-hexane pool fire with a user-defined burning rate showed adequate flame temperature and flame height predictions when using a 20 mm cell size and the default gas phase simulation settings in FDS. FDS simulations using the pyrolysis model reproduced the relationships between fuel composition and maximum burning rate from the steady-state experiments. However, the 20 mm mesh resolution predicted inaccurate self-extinction of ethanol-water pool fires, and a 5 mm cell size was required to model the full range of ethanol-water mixtures. FDS simulations also reproduced temporal changes in fire dynamics that occurred in the transient ethanol-heptane fire experiments. The new methodology enables the simulation of multicomponent pool fires and the evaluation of distillation effects on fire dynamics. However, the primary limitation is that the developed pyrolysis model neglects mass transfer resistances and transient heating of the pool.

Journal ArticleDOI
Xu Fang1, Xu Fang2, Xiaolei Zhang1, Richard K.K. Yuen2  +1 moreInstitutions (2)
15 Feb 2022-Fuel
Abstract: The present study provides an experimental investigation and scaling analysis of diffusion flame side sag behavior. This phenomenon happens as a result of the elevated flame (above the ground) under cross wind conditions, and manifest as the flame sinks both upstream and downstream along the burner sides. Experiments are carried out by employing four square burners of various dimensions (10, 15, 20, 25 cm) with the burner exit surface raising 0.3 m above the ground to simulate an elevated diffusion flame. Propane is used as fuel to regulate various heat release rates (HRRs). The cross winds are provided by a wind tunnel with speed in the range of 0.54 ∼ 2.77 m/s. The flame side sag lengths of the upstream (Hu) and downstream (Hd) are measured for a total of 216 test conditions. It is found that the evolution of flame side sag can be clearly distinguished as four phases and the turning points of different phases are related to the crosswind speed, burner size and HRR. Both Hu and Hd increase with the increasing of wind speed and HRR, and Hd is larger than Hu at lower wind speeds while reverse along with the increasing of wind speed. CFD simulation (FDS) is performed to interpret the flow field, from that, the flame side sag can be attributed to interaction between the induced vortex and the sinking flame. Three characteristic length scales are proposed by considering the controlling physics involved in this phenomenon. Finally, general dimensionless functions are derived based on these characteristic length scales, which correlate the experimental results of Hu and Hd well. The transition of four phases can also been quantified in these formulas.

References
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Journal ArticleDOI
Vytenis Babrauskas1Institutions (1)
01 Nov 1983-Fire Technology
TL;DR: Data for estimating the burning rate and heat output of large pool fires (diameter ≳ 0.2 m) are compiled and computational equations presented and a large scatter is noted.
Abstract: Data for estimating the burning rate and heat output of large pool fires (diameter ≳ 0.2 m) are compiled and computational equations presented. Since a large scatter in the reported data is noted, attention is also focused on areas where further research is most needed in order to improve predictability.

349 citations


Journal ArticleDOI
Suresh Menon1, Pui-Kuen Yeung1, W.-W. Kim1Institutions (1)
01 Feb 1996-Computers & Fluids
Abstract: Direct and large eddy simulations of forced and decaying isotropic turbulence have been performed to investigate the behavior of subgrid models. Various subgrid models have been analyzed (i.e. Smagorinsky's eddy viscosity model, dynamic eddy viscosity model, dynamic one-equation model for the subgrid kinetic energy and scale-similarity model). A priori analysis showed that the subgrid stress and the subgrid energy flux predicted by the scale similarity model, and subgrid kinetic energy model (with fixed coefficients) correlate reasonably well with exact data, while the Smagorinsky's eddy viscosity model showed relatively poor agreement. However, the correlation for the scale similarity model decreased much more rapidly with decrease in grid resolution when compared to the subgrid kinetic energy model. The subgrid models were then used to carry out large-eddy simulations for a range of Reynolds number. When dynamic evaluation was incorporated, the correlation improved significantly. The dynamic subgrid kinetic energy model showed, consistently, a higher correlation for a range of Reynolds number when compared to the dynamic eddy viscosity model. These results demonstrate the capabilities of the dynamic one-equation model.

246 citations


Journal ArticleDOI
Abstract: A series of measurements designed to investigate the heat feedback in pool fires burning liquid fuels are reported. Such measurements are essential for the development and validation of detailed models which predict the burning rate of liquid hydrocarbons and solid polymers. 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. A water-cooled, nitrogen purged, narrow view-angle gauge was developed to measure the radiative flux incident on the fuel surface. Measurements of the mass burning rate in a burner composed of annular rings was used to estimate the local heat feedback. A number of different fuels were studied, yielding flames with a wide range of heat release rates and luminosities. Consideration of the heat balance for a control volume enclosing the liquid PPOI indicated that radiation was an important component of the heat feedback for non-luminous fires and a dominant component in luminous fires.

149 citations


Journal ArticleDOI
D. Villers1, Jean Karl Platten1Institutions (1)
Abstract: This paper presents a study of the convection in acetone due jointly to the thermocapillary (Marangoni) and thermogravitational effects. The liquid (acetone) is submitted to a horizontal temperature difference. Experiments and numerical simulations both show the existence of three different states : monocellular steady states, multicellular steady states and spatio-temporal structures. The results are discussed and compared with the linear stability analysis of Smith & Davis (1983).

133 citations


Journal ArticleDOI
01 Feb 1991-Fire Technology
Abstract: In order to understand the combustion characteristics of crude oil pool fires, an experimental study was carried out at the Fire Research Institute (FRI) large scale test facility. The radiative output, burning rate, and the concentrations of CO, CO2, and smoke (above the flame tip) were measured during the burning of Arabian light crude oil, heptane, toluene, and kerosene floating on water. The effect of scale was studied by using steel pans ranging from 0.6 to 3 meters in diameter.

105 citations


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