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Flame Extinction of Spherical PMMA in Microgravity: Effect of Fuel Diameter and Conduction

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A series of experiments were conducted in the 3.6-s microgravity drop tower and normal gravity to investigate the effect of solid fuel curvature, conduction, and reradiation on the flame extinction of spherical polymethyl methacrylate (PMMA). In the semi-quiescent microgravity environment, flame extinction was observed if the PMMA diameter was larger than 40 mm, because of a smaller flame conductive heating in larger diameter (i.e., the curvature effect). Compared to the droplet combustion with a low evaporation point and fast heat convection in the liquid phase, the solid fuel has a high pyrolysis point and large transient heat conduction. Thus, the large surface reradiation effectively cools down the fuel surface to promote extinction. Also, as the initial burning duration increases, the conductive cooling into the solid fuel decreases, which delays or prevents the flame extinction in microgravity. The extinction criterion for microgravity flame is explained by the critical mass flux and mass-transfer number. This work helps to understand the curvature effect of solid fuel on flame extinction and the material fire safety in the microgravity spacecraft environment.

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A :

area (mm2)

B :

mass-transfer number (−).

c g :

specific heat of gas (J/kg/K).

c p :

specific heat of solid (J/kg/K).

d :

diameter (mm).

d eq :

equivalent diameter (mm).


flame stand-off ratio (df/ds).

Δhc :

heat combustion (J/kg).

Δhpy :

enthalpy of pyrolysis (J/kg).

L :

characteristic length (mm).

m :

mass (g).

\( {\overset{\cdot }{m}}^{{\prime\prime} } \) :

mass flux (g/m2/s).

k :

heat conductivity (W/m-K).

\( {\overset{\cdot }{q}}^{{\prime\prime} } \) :

conductive heat flux (kW/m2).

r :

sphere radius (mm).

t :

time (s).

t 0 :

initial burning duration (s).

T :

temperature (K).

V :

Volume (mm3)

X r :

fraction of flame radiation (−).

\( {Y}_{{\mathrm{O}}_2} \) :

mass fraction of oxygen (−).

δ :

depth (mm).

ε :

radiative emittance (−).

η :

ratio coefficient (−)

κ :

fuel curvature, 1/r (mm−1).

υ :

air to fuel stoichiometric mass ratio.

ρ :

density (kg/m3).

σ :

Stefan-Boltzmann constant (W/m2/K4).


thermocouple diameter (mm).






critical value

f :


in :

in-depth net net heat flux

py :


r :


re :


s :

solid or surface.

sh :



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This work is supported by the National Natural Science Foundation of China (No. U1738117 and 51876183), and by the Strategic Priority Research Program on Space Science, the Chinese Academy of Sciences, under grant Nos. XDA04020410 and XDA04020202-10.

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Correspondence to Xinyan Huang or Shuangfeng Wang.

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The thermal analysis was applied to the PMMA sample using PerkinElmer STA 6000 Simultaneous Thermal Analyzer. The PMMA sample was heated at the nitrogen gas environment, where the flow rate was 100 mL/min. The initial mass of PMMA sample was about 4 mg, which were heated at two constant rates of 10 and 50 K/min. Figure 9(a) shows the normalized mass-loss rate vs. temperature at both heating rates. For the pyrolysis in a larger heating rate, it needs a higher temperature to reach a certain mass-loss rate. In other words, the pyrolysis temperature increases with the heating rate. Figure 9(b) shows the temperature increase rate (or the heating rate in K/min) of the PMMA surface and in-depth during the experiment with respect to Fig. 6. Clearly, the heating rates of PMMA within the flame were significantly larger than the TG tests. Thus, 670 K is a reasonable pyrolysis temperature for such a large heating rate in the real-scale experiments.

Fig. 9
figure 9

(a) DTG curves of PMMA at the heating rates of 10 and 50 K/min, and (b) the heating rate at the surface and 2 mm beneath the surface of PMMA sphere with 10-mm and 40-mm diameters

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Wu, C., Sun, P., Wang, X. et al. Flame Extinction of Spherical PMMA in Microgravity: Effect of Fuel Diameter and Conduction. Microgravity Sci. Technol. 32, 1065–1075 (2020).

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