Fire Technology

, Volume 54, Issue 6, pp 1783–1805 | Cite as

A Finite Element Model for the Simulation of the UL-94 Burning Test

  • Julio MartiEmail author
  • Sergio R. Idelsohn
  • Eugenio Oñate


The tendency of the polymers to melt and drip when they are exposed to external heat source play a very important role in the ignition and the spread of fire. Numerical simulation is a promising methodology for predicting this behaviour. In this paper, a computational procedure that aims at analyzing the combustion, melting and flame spread of polymer is presented. The method models the polymer using a Lagrangian framework adopting the particle finite element method framework while the surrounding air is solved on a fixed Eulerian mesh. This approach allows to treat naturally the polymer shape deformations and to solve the thermo-mechanical problem in a staggered fashion. The problems are coupled using an embedded Dirichlet–Neumann scheme. A simple combustion model and a radiation modeling strategy are included in the air domain. With this strategy the burning of a polypropylene specimen under UL-94 vertical test conditions is simulated. Input parameters for the modelling (density, specific heat, conductivity and viscosity) and results for the validation of the numerical model has been obtained from different literature sources and by IMDEA burning a specimen of dimensions of \(148 \times 13 \times 3.2\,{\mathrm {mm}}^3\). Temperature measurements in the polymer have been recorder by means of three thermocouples exceeding the 1000 K. Simultaneously a digital camera was used to record the burning process. In addition, thermal decomposition of the material (Arrhenius coefficient \({\mathrm {A}}=7.14 \times 10^{16}\,{\mathrm {min}}^{-1}\) and activation energy \({\mathrm {E}}=240.67\,{\mathrm {kJ/mol}}\)) as and changes in viscosity (\(\mu \)) as a function of temperature were obtained. Finally, a good agreement between the experimental and the numerical can be seen in terms of shape of the polymer as well as in the temperature evolution inside the polymer.


Dripping Melt flow UL-94 test Particle finite element method (PFEM) 

List of symbols



\(\Omega \)


\(\Gamma \)





Spacial position

\(\nabla \)








\(\mu \)


\(\rho \)



Gravity force


Heat capacity

\(\kappa \)

Thermal conductivity


Spectral intensity





\(\epsilon \)



Mass fraction

\({\mathrm {w}}_{{\mathrm {T}}}\)

Rate of production of heat

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

Radiative heat flux


Mass loss


Heat absorbed

\(\alpha \)

Absorption coefficient

\(\sigma \)

StefanBoltzmann constant


Incident radiation

\({\mathbf{q}} \)

Heat flux


Pre-exponential function


Activation energy

\({\mathrm {T}}_{{\mathrm {a}}}\)

Absolute temperature


Universal gas constant


Enthalpy of vaporization

\({\mathcal {K}}\)

Bulk modulus

\({\mathbf{F}}^{{\mathbf{D }}}\)

Drag force

\({\mathrm {C}}_{{\mathrm {D}}}\)

Drag coefficient

\({\mathrm {A}}_{{\mathrm {CS}}}\)

Cross sectional area












The authors thank to the IMDEA Materials Institute in Madrid (Spain) for providing the data of the experimental test. This work was supported by the COMETAD project of the National RTD Plan (Ref. MAT2014-60435-C2-1-R) from the Ministerio de Economía y Competitividad of Spain.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE)BarcelonaSpain
  2. 2.Department of Civil and Environmental Engineering (DECA)Universitat Politècnica de Catalunya (UPC)BarcelonaSpain

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