Elsevier

Combustion and Flame

Volume 156, Issue 9, September 2009, Pages 1828-1833
Combustion and Flame

Modeling a fire whirl generated over a 5-cm-diameter methanol pool fire

https://doi.org/10.1016/j.combustflame.2009.06.010Get rights and content

Abstract

We conducted a series of laboratory-scale fire whirl experiments spinning 5-cm-diameter methanol pool fires and observed elongated flame height compared with the pool fire without spin. A simple scaling analysis was conducted to obtain dependency of the axial flame height on the momentum-controlled circulation and the effect of buoyancy. To obtain a specific functional relationship for the parameters obtained by the scaling analysis, we developed an analytical model consisting of coupled species and energy equations and Burgers vortex for circulation generated by a fire whirl. The solution of the coupling equations shows that the average rate of heat transfer from the flame to the fuel surface is a function of the vortex core radius; a smaller vortex core radius provides more heat to the fuel surface enhancing evaporation thereby producing the longer flame height. This new model predicts both flame height and flame shape. The flame height prediction compare favorably with results from the scaling analysis and experiment.

Introduction

A fire whirl is a phenomenon that can be generated by the interaction of fires with spinning flow. A number of fire whirl studies, both theoretical and experimental, have been conducted [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]. Especially, worth mentioning is the pioneer study by Emmons and Ying [6] that involved experiments using a spinning cage with burning a 10-cm-diameter acetone pool at its center and the development of a theoretical model to predict the average temperature along the axis. Other researchers have conducted computational studies [12], [13], [14], [15], [16], [17] to visualize the detailed fire whirl structure. Experimental studies include laboratory-scale models [6], [7], [8], [12], [16] as well as relatively large-scale open-field [1], [10], wind-tunnel [2], [9], [11], and laboratory tests [10], [15], [18].

These studies suggest that our understanding of the mechanism of fire whirls is still incomplete. Previously Chuah and Kushida [17] developed a simple analytical model for a fire whirl created by spinning a 5-cm-diameter methanol pool fire. Their model [17] consists of two regions separated by an imaginary boundary: the inner region is described by a Burgers vortex and the outer region by an ideal vortex. Their model, however, includes no heat-feedback mechanism from the flame to the fuel surface, which are important for the 5-cm-diameter methanol pool fire. To satisfy the mass balance, this small pool fire entrains airflow through its flame base driven by momentum conservation [19], while for a 1-cm-diameter methane–air co-flow diffusion flame, diffusion controls the airflow entrainment [20]. The present study discusses a newly developed simple model for fire whirls generated over a 5-cm-diameter methanol (non-luminous) pool fire, which includes the heat-feedback mechanism from the flame to the fuel surface and the buoyancy effect. The new model predicts flame heights and flame shapes which compare favorably with our laboratory experiments.

Section snippets

Scaling analysis

A simple scaling analysis can help obtain parametric relationships (as demonstrated by Emori and Saito [11] and Kuwana et al. [2]) that govern the fire whirl. To find the relationship between the flame height and fuel flow rate for small non-luminous and non-rotating diffusion flames, we can reason as follows. For a 5-cm-diameter non-luminous methanol pool fire, the following relationship between the axial flame height, zf, and the volumetric fuel supply rate, Q can be obtained [17], [21]:zfrpQ

Formulation

This section presents an analytical model of small-scale fire whirls. We employed the following assumptions to develop an analytical model that can predict the flame shape in the fire whirl:

  • (a)

    the system is axisymmetric and steady,

  • (b)

    the Lewis number, Le (=α/D), is unity,

  • (c)

    the gas properties are constant, including density,

  • (d)

    the combustion reaction, [Fuel] + νO[Oxidizer] → [Product], is irreversible and infinitely fast,

  • (e)

    species diffusion and thermal conduction in the axial direction are negligible compared

Conclusions

We conducted a scaling analysis to obtain major parameters that control fire whirls and parametric relationships among these parameters. Consistent with these results, we developed a new fire whirl model incorporating a heat-feedback mechanism from the flame to the fuel surface and diffusion–momentum–buoyancy effects, obtaining an analytical solution for the flame height and flame shape as a function of vortex core radius.

The appeal of this new model is its simplicity. Despite the absence of a

Acknowledgments

This research was supported by Kentucky Science and Engineering Foundation, NASA Grant (NAG3-2567), and Japan’s Grant-in-Aid for Scientific Research (19860021). We wish to thank Professor Forman Williams who has provided us with a series of valuable comments by reading the manuscript and carefully checking the equations.

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    Present address: Department of Chemistry and Chemical Engineering, Yamagata University Yonezawa-Shi, Yamagata 992-8510, Japan.

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