Fire Technology

, Volume 56, Issue 1, pp 271–286 | Cite as

Study on Fingering Pattern of Spreading Flame Over Non-charring Solid in a Narrow Space

  • Tsuneyoshi MatsuokaEmail author
  • Akihiro Yoshimasa
  • Masashi Masuda
  • Yuji Nakamura


Fingering pattern formation of flame spread over a thick solid has been observed recently. Since the oxygen-enriched atmosphere in microgravity promotes the occurrence of fingering and thus it leads to a fire in space, it is important to understand the mechanism. Motivated by this, a previous study attempted to validate a similarity to smoldering fingering. However, it remains controversial because the quantitative evaluation of the fingering pattern was not satisfactory done due to the experimental design: edges of the solid have an influence on the phenomenon. In this study, a new wind tunnel was developed, enabling experiments under the least effects of the artificial boundaries and evaluation of the pattern. A thick thermoplastic and oxygen were used as fuel and oxidizer, and a series of experiments were conducted under various channel heights and oxidizer velocities. A number of fingers, average finger width and, average flame spread rate were then quantified to estimate the scaled wavelength which characterizes the fingering pattern. The effects of the existence of flame and solid thickness are discussed and the theory for smoldering combustion was then modified accordingly to examine a correlation with the governing parameter, i.e., the modified effective Lewis number. The result shows the scaled wavelengths are well-summarized against the modified effective Lewis number. On the other hand, the data deviates from the line when the parameter becomes large, indicating a difference from the smoldering fingering. The obtained knowledge will help to develop a more rigorous risk assessment for the fire in space.


Oxygen-enhanced fire Flame spread Fingering Thick solid Diffusive-thermal instability 

List of Symbols


Specific heat (J/kg K)


Channel height (mm)


Solid thickness (mm)


Thickness of the heated layer (mm), Eq. (1)


Binary diffusion coefficient for gases (m2/s)


Activation energy (kJ/mol)


Heat transfer coefficient (W/m2 K), \(h = Nu\lambda_{g} /2d_{\text{g}}\)


Dimensionless heat transfer coefficient, \(\bar{h} = 2h\bar{\alpha }/\rho_{\text{g}} c_{\text{g}} d_{\text{g}} u_{\text{r}}^{2}\)


Lewis number, \(Le = \bar{\alpha }/D\)


Effective Lewis number, Eq. (2)


Nusselt number


Temperature (K)


Oxidizer velocity (m/s)


Oxidizer velocity relative to the flame (m/s), \(u_{\text{f}} = u + v\)


Reference velocity (m/s), \(u_{\text{r}} = u_{{{\text{r}},{\text{b}}}} \times \left( {d_{g} /d_{{{\text{g}},{\text{b}}}} } \right)^{{ - \frac{1}{2}}}\)


Dimensionless oxidizer velocity


Flame spread rate (m/s)


Finger width (mm)


Flow direction


Transverse direction

Greek Symbols


Thermal diffusivity (m2/s)

\(\bar{\alpha }\)

Weighted thermal diffusivity (m2/s), Eq. (6)


Zel’dovich number, \(\beta = E\left( {T_{\text{r}} - T_{\text{u}} } \right)/T_{\text{r}}^{2}\), Eq. (4)


Scaled dimensionless heat transfer coefficient, Eq. (5)


Thermal conductivity (W/m K)


Density (kg/m3)





Gas phase




Solid phase





This work was supported by JSPS KAKENHI Grant Numbers JP16K16365 and JP18K13967. We acknowledged their support of the Cooperative Research Facility Center at Toyohashi University of Technology to develop the wind tunnel facility. We would also like to thank Mr. Lindsay Prescott for his help on English editing.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringToyohashi University of TechnologyToyohashiJapan

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