The effect of convective motion within liquid fuel on the mass burning rates of pool fires – A numerical study
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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Frequently Asked Questions (21)
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].