Fire Technology

, Volume 56, Issue 1, pp 5–32 | Cite as

Flame Growth Around a Spherical Solid Fuel in Low Speed Forced Flow in Microgravity

  • Makoto EndoEmail author
  • James S. T’ien
  • Paul V. Ferkul
  • Sandra L. Olson
  • Michael C. Johnston


To further our understanding of flammability and quenching limit of thick solid fuels, a microgravity experiment Growth and Extinction Limits is to be conducted aboard the International Space Station with the emphasis to quantify the effect of the flame heat loss to the thermally thick solid interior by directly measuring the sub-surface temperature gradient. A precursor microgravity combustion experiment in the Burning and Suppression of Solids (BASS) project was used to assess the experimental operation and validate the accompanied numerical model. The present paper reports the development of the flame model over a solid sphere in low-speed pure convective flow (less than 100 cm/s). Computed time sequence result of one of the BASS conditions is presented. The combination of gas phase reaction rate, solid internal temperature and surface heat flux distribution reveals the effect of solid in-depth heat-up on flame growth. The experimental observations agree with the trend predicted by the model. For thick solids, flame quenching limit in low speed flow is not only a function of flow speed but also the degree of solid interior heat-up. Flammability limit can have profound implication to the current spacecraft fire protection protocol that requires turning-off of circulation flow in case of detected fire. The present and the follow-up studies will provide more quantitative estimate of the low velocity-quenching limit with heated samples. For the Polymethylmethacrylate spheres investigated, the limit is lower than 2 cm/s in air.


Thermally-thick Flammability Quenching Flame growth GEL SoFIE BASS Solid fuel 



Burning and Suppression of Solids (project)


Combustion Integrated Rack


Diffusive and Radiative Transport in Fires (project)


Growth and Extinction Limit (project)


International Space Station


Poly(methyl methacrylate)


Solid Fuel Ignition and Extinction (project)


Solid Surface Combustion Experiments (project)

Nondimensional Properties

\(\bar{\varvec{\tau }}\)

\(L {\varvec{\tau }}/(u_\infty \mu _\infty )\)


\({\dot{Q}}_R L /\lambda _s T_\infty\)


\({\dot{m}}/(\rho _\infty u_\infty )\)


Step size for gas phase calculation, CFL number times \(t /(L/u_\infty )\)


Boltzmann number\(, \rho _\infty u_\infty C_{p\infty }/(\sigma T_\infty ^3)\)


Lewis number\(, \alpha _\infty /D_\infty\)


Prandtl number\(, \mu _\infty /(\alpha _\infty \rho _\infty )\)


Reynolds number\(, \rho _\infty u_\infty L/\mu _\infty\)

\({{\bar{\lambda }}}\)

\(\lambda / \lambda _\infty\)

\({{\bar{\mu }}}\)

\(\mu /\mu _\infty\)

\({{\bar{\omega }} }\)

\(\omega /(\rho _\infty u_\infty /L)\)


\(D_i / D_\infty\)


\(H_{oc}/(C_{p\infty }T_\infty )\)


\(L_q \rho _\infty u_\infty L/ (\lambda _{s^*} T_\infty )\)


\((p-p_\infty )/(\rho _\infty u_\infty ^2)\)

\({{\bar{Q}}_{in} }\)

\(Q_{in}/( u_\infty \rho _\infty C_{p\infty } T_\infty /L )\)

\({{\bar{Q}}_{R} }\)

\(Q_R/(\sigma T_\infty ^4/L)=-\nabla \cdot {\mathbf{q_{r}}}/(\sigma T_\infty ^4/L)\)




\(t/(L^2/\alpha )\)

\({\bar{\mathbf{u}} }\)

\({\mathbf{u}}/{u_\infty }\)

Dimensional Properties


Thermal diffusivity


Absorption coefficient


Thermal conductivity




Gas phase reaction rate

\(\omega _{mol}\)

Fuel vapor consumption rate in mole/(volume\(\cdot\)time)




Stefan–Boltzmann constant


Stretch rate at the stagnation point, \(1.5u_\infty /R\)


Pre-exponential factor for gas phase reaction


Pre-exponential factor for solid fuel decomposition


Specific heat


Mass diffusivity


Activation energy of gas phase reaction


Activation energy for solid fuel decomposition


Incident radiation


Heat of combustion of fuel


Radiative intensity


Reference length, \(\sqrt{\alpha _\infty /a}\)


Latent heat of vaporization




External heat input (i.e. igniter)


Radius of curvature at stagnation point




Species mass fraction


Velocity vector


Viscous stress tensor


Burning rate of solid fuel





Reference state property. Value at the inlet except for pressure and density, former is defined at the outlet. \(\rho _\infty\) is computed by \(p_\infty\) and \(T_\infty\) using the ideal gas law


At a given wave number


Black body value


For chemical specie i


Solid phase property


Representative value of the solid fuel material



This research is supported by the National Aeronautics and Space Administration (NASA). Authors would like to thank the astronauts Don Pettit, Joe Acaba, and Suni Williams for conducting the BASS experiments. This work made use of the High Performance Computing Resource in the Core Facility for Advanced Research Computing at Case Western Reserve University and the Ohio Supercomputer Center.


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Copyright information

© This is a U.S. Government work and not under copyright protection in the US; foreign copyright protection may apply 2019

Authors and Affiliations

  1. 1.Case Western Reserve UniversityClevelandUSA
  2. 2.Universities Space Research AssociationClevelandUSA
  3. 3.NASA Glenn Research CenterClevelandUSA

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