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

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Abstract

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.

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Notes

  1. This assumption becomes satisfactory for higher temperatures and regarding a narrow range of shear rates like those experienced in the UL-94 test [30].

  2. Assuming constant values for the Schmidt (\(\mathrm {Sc=1}\)) and Prandtl (\(\mathrm {Pr=1}\)) numbers simplified composition and temperature dependent transport properties thus \(\rho {\mathrm {D}}= \kappa /{\mathrm {C}}\).

Abbreviations

3D:

Three-dimensional

\(\Omega \) :

Domain

\(\Gamma \) :

Boundary

t:

Time

\({\mathbf{x}}\) :

Spacial position

\(\nabla \) :

Nabla

\({\mathbf{v}}\) :

Velocity

p:

Pressure

T:

Temperature

\(\mu \) :

Viscosity

\(\rho \) :

Density

\({\mathbf{f}}\) :

Gravity force

C:

Heat capacity

\(\kappa \) :

Thermal conductivity

I:

Spectral intensity

s:

Direction

c:

Speed

\(\epsilon \) :

Emissivity

Y:

Mass fraction

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

Rate of production of heat

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

Radiative heat flux

\(\epsilon_v\) :

Mass loss

\(Q_v\) :

Heat absorbed

\(\alpha \) :

Absorption coefficient

\(\sigma \) :

StefanBoltzmann constant

G:

Incident radiation

\({\mathbf{q}} \) :

Heat flux

A:

Pre-exponential function

E:

Activation energy

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

Absolute temperature

R:

Universal gas constant

H:

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

a:

Air

p:

Polymer

F:

Fuel

O:

Oxygen

References

  1. Stoliarov SI, Lyon RE (2008) Thermo-kinetic model of burning for pyrolyzing materials. Fire Saf Sci 9:1141-1152

    Article  Google Scholar 

  2. Lautenberger C, Fernndez-Pello C (2009) Generalized pyrolysis model for combustible solids. Fire Saf 44:819

    Article  Google Scholar 

  3. Lautenberger C (2014) Gpyro3d: A three dimensional generalized pyrolysis model. Fire Saf Sci 11:193–207

    Article  Google Scholar 

  4. Firefoam code. http://www.fmglobal.com/modeling

  5. McGrattan K, McDermott R, Weinschenk C, Forney G (2013) Fire dynamics simulator (version 6), technical reference guide

  6. Stoliarov Stanislav I, Leventon Isaac T, Lyon Richard E (2013) Two dimensional model of burning for pyrolyzable solids. Fire Mater 38(3):391–408

    Article  Google Scholar 

  7. Lautenberger C, Fernandez-Pello C (2009) A model for the oxidative pyrolysis of wood. Combust Flame 156(8):1503–1513

    Article  Google Scholar 

  8. Lautenberger C, Rein G, Fernandez-Pello C (2006) The application of a genetic algorithm to estimate material properties for fire modeling from bench-scale fire test data. Fire Saf J 41(3):204–214

    Article  Google Scholar 

  9. Chaos M, Khan M, Krishnamoorthy N, de Ris J, Dorofeev S (2011) Evaluation of optimization schemes and determination of solid fuel properties for cfd fire models using bench-scale pyrolysis tests. Proc Combust Inst 33(2):2599–2606

    Article  Google Scholar 

  10. Ramroth WT, Krysl P, Asaro RJ (2006) Sensitivity and uncertainty analyses for FE thermal model of FRP panel exposed to fire. Compos A 37:1082-1091

    Article  Google Scholar 

  11. Linteris GT (2011) Numerical simulations of polymer pyrolysis rate: effect of property variations. Fire Mater 35:463480

    Article  Google Scholar 

  12. Stoliarov SI, Safronava N, Lyon RE (2009) The effect of variation in polymer properties on the rate of burning. Fire Mater 33:257271

    Article  Google Scholar 

  13. Bal N, Rein G (2013) Relevant model complexity for non-charring polymer pyrolysis. Fire Saf J 61:36–44

    Article  Google Scholar 

  14. Blasi C, Crescitelli S, Russo G, Cinque G (1991) Numerical model of ignition processes of polymeric materials including gas-phase absorption of radiation. Combust Flame 83(3):333–344

    Article  Google Scholar 

  15. Tsai T, Li M, Shih I, Jih R, Wong S (2001) Experimental and numerical study of autoignition and pilot ignition of pmma plates in a cone calorimeter. Combust Flame 124(3):466–480

    Article  Google Scholar 

  16. Wu K, Fan W, Chen C, Liou T, Pan I (2003) Downward flame spread over a thick pmma slab in an opposed flow environment: experiment and modeling. Combust Flame 132(4):697–707

    Article  Google Scholar 

  17. Gotoda H, Manzello S, Saso Y, Kashiwagi T (2006) Effects of sample orientation on nonpiloted ignition of thin poly(methyl methacrylate) sheets by a laser: 2. Experimental results. Combust Flame 145(4):820–835

    Article  Google Scholar 

  18. Kempel F, Schartel B, Marti J, Butler K, Rossi R, Idelsohn SR, Oñate E, Hofmann A (2015) Modelling the vertical ul 94 test: competition and collaboration between melt dripping, gasification and combustion. Fire Mater 39(6):570–584 FAM-14-012

    Article  Google Scholar 

  19. Wang Y, Jow J, Su K, Zhang J (2012) Development of the unsteady upward fire model to simulate polymer burning under ul 94 vertical test conditions. Fire Saf J 54:1–13 Part of special issue: Large Outdoor Fires

    Article  Google Scholar 

  20. Matzen M, Marti J, Oñate E, Idelsohn S, Schartel B (2017) Advanced experiments and particle finite element modelling on dripping v–0 polypropylene, fire and materials 2017. In: 15th International conference, San Francisco, CA, USA

  21. Li J, Stoliarov SI (2013) Measurement of kinetics and thermodynamics of the thermal degradation for non- charring polymers. Combust Flame 160:1287–1297

    Article  Google Scholar 

  22. Stoliarov SI, Safronava N, Lyon RE (2009) The effect of variation in polymer properties on the rate of burning. Fire Mater 33:257–271

    Article  Google Scholar 

  23. Marti J, Ryzhakov P, Idelsohn S, Oñate E (2010) Combined eulerian-pfem approach for analysis of polymers in fire situations. Int J Numer Methods Eng 92:782–801

    Article  MathSciNet  Google Scholar 

  24. Oñate E, Marti J, Ryzhakov P, Rossi R, Idelsohn S (2013) Analysis of the melting, burning and flame spread of polymers with the particle finite element method. Comput Assist Methods Eng Sci 20:165–184

    MathSciNet  Google Scholar 

  25. Idelsohn S, Oñate E, Del Pin F (2004) The Particle Finite Element Method: a powerful tool to solve incompressible flows with free-surfaces and breaking waves. Int J Numer Methods Eng 61:964–989

    Article  MathSciNet  Google Scholar 

  26. Oliver X, Agelet de Saracibar C (2017) In continuum mechanics for engineers. Theory and problems

  27. Holzapfel G (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New York

    MATH  Google Scholar 

  28. Cox G (ed) (1995) Combustion fundamentals of fire. Academic Press, New York

    Google Scholar 

  29. Modest MF (2003) Radiative heat transfer. Academic Press, New York

    Book  Google Scholar 

  30. Oñate E, Rossi R, Idelsohn SR, Butler K (2009) Melting and spread of polymers in fire with the particle finite element method. Int J Numer Methods Eng 81:1046–1072

    MATH  Google Scholar 

  31. Codina R, Vazquez M, Zienkiewizc OC (1998) A general algorithm for compressible and incompressible flows. Int J Numer Methods Fluids 27:13–32

    Article  Google Scholar 

  32. Fiveland W (1991) The selection of discrete ordinate quadrature sets for anisotropic scattering . ASME Fundam Radiat Heat Transf 160:89–96

    Google Scholar 

  33. Sousa Pessoa De Amorim MT, Comel C, Vermande P (1982) Pyrolysis of polypropylene. J Anal Appl Pyrolysis 4(1):73–81

    Article  Google Scholar 

  34. Xie W, DesJardin P (2009) An embedded upward flame spread model using 2d direct numerical simulations. Combust Flame 156(2):522–530

    Article  Google Scholar 

  35. Idelsohn SR, Marti J, Limache A, Oñate E (2008) Unified lagrangian formulation for elastic solids and incompressible fluids: Application to fluidstructure interaction problems via the pfem. Comput Methods Appl Mech Eng 197(19):1762–1776(Computational Methods in Fluid Structure Interaction)

    Article  Google Scholar 

  36. Delaunay B (1934) Sur la sphre vide. izvestia akademii nauk sssr. Otdelenie Matematicheskikh i Estestvennykh Nauk 7:793–800

    Google Scholar 

  37. Idelsohn SR, Marti J, Souto-Iglesias A, Oñate E (2008) Interaction between an elastic structure and free-surface flows: experimental versus numerical comparisons using the pfem. Comput Mech 43(1):125–132

    Article  Google Scholar 

  38. Idelsohn SR, Mier-Torrecilla M, Marti J, Oñate E (2011) The particle finite element method for multi-fluid flows. In: Eugenio O, Roger O (eds) Particle-based methods: fundamentals and applications. Springer, Dordrecht, pp 135–158

    Chapter  Google Scholar 

  39. Oñate E, Idelsohn SR, Celigueta MA, Rossi R, Marti J, Carbonell JM, Ryzhakov P, Suárez B (2011) Advances in the particle finite element method (PFEM) for solving coupled problems in engineering. In: Eugenio O, Roger O (eds) Particle-based methods: fundamentals and applications. Springer, Dordrecht, pp 1–49

    Chapter  Google Scholar 

  40. Kundu PK, Cohen IM (2002) Fluid mechanics. Academic Press, New York

    Google Scholar 

  41. Hughes TJR (1989) The finite element method: Linear static and dynamic finite element analysis. Comput Aided Civil Infrastruct Eng 4(3):245–246

    Google Scholar 

  42. Idelsohn SR, Nigro N, Gimenez JM, Rossi R, Marti J (2013) A fast and accurate method to solve the incompressible navier-stokes equations. Eng Comput 30(2):197–222

    Article  Google Scholar 

  43. Ryzhakov PB, Marti J, Idelsohn SR, Oñate E (2017) Fast fluidstructure interaction simulations using a displacement-based finite element model equipped with an explicit streamline integration prediction. Comput Methods Appl Mech Eng 315:1080–1097

    Article  Google Scholar 

  44. Donea J, Huerta A (2003) Finite element method for flow problems. Wiley, New York

    Book  Google Scholar 

  45. Lohner R (2008) Applied CFD techniques, 2nd edn. Wiley, New York

    MATH  Google Scholar 

  46. Codina R (2001) A stabilized finite element method for generalized stationary incompressible flows. Comput Methods Appl Mech Eng 190(20–21):2681–2706

    Article  MathSciNet  Google Scholar 

  47. Guermond JL, Minev P, Shen J (2006) An overview of projection methods for incompressible flows. Comput Methods Appl Mech Eng 195:6011–6045

    Article  MathSciNet  Google Scholar 

  48. Temam R (1969) Sur lapproximation de la solution des equations de navier-stokes par la methode des pase fractionaires. Arch Ration Mech Anal 32:135–153

    Article  Google Scholar 

  49. Chorin AJ (1967) A numerical method for solving incompressible viscous problems. J Comput Phys 2:12–26

    Article  Google Scholar 

  50. Ryzhakov P (2017) A modified fractional step method for fluid-structure interaction problems. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 33(1–2):58–64

    Article  MathSciNet  Google Scholar 

  51. Ryzhakov P, Marti J (2018) A semi-explicit multi-step method for solving incompressible Navier–Stokes equations. Appl Sci 8(1):119

    Article  Google Scholar 

  52. Ryzhakov P, Rossi R, Oñate E (2012) An algorithm for the simulation of thermally coupled low speed flow problems. Int J Numer Methods Fluids 70(1):1–19

    Article  MathSciNet  Google Scholar 

  53. Dadvand P, Rossi R, Oñate E (2010) An object-oriented environment for developing finite element codes for multi-disciplinary applications. Arch Comput Methods Eng 17(3):253–297

    Article  Google Scholar 

  54. Repsol pp isplen 045 g1e. http://www.repsol.com/en/products-and-services/chemicals

  55. Kissinger H (1956) Variation of peak temperature with heating rate in differential thermal analysis. J Res Natl Bureau Stand 57(4):217–221

    Article  Google Scholar 

  56. Flynn J, Wall L (1966) A quick, direct method for the determination of activation energy from thermogravimetric data. J Polym Sci B Polym Lett 4(5):323–328

    Article  Google Scholar 

  57. Ozawa T (1965) A new method of analyzing thermogravimetric data. Bull Chem Soc Jpn 38:1881–1886

    Article  Google Scholar 

  58. Thermal properties. http://www.engineeringtoolbox.com/

  59. Tc direct. http://www.tcdirect.es/

  60. Selected thermal properties. http://pslc.ws/fire/howwhy/thermalp.htm

  61. Wang Y, Zhang J, Jow J, Su K (2009) Analysis and modeling of ignitability of polymers in the ul-94 vertical burning test condition. J Fire Sci 27:561–581

    Article  Google Scholar 

  62. Wang Y, Zhang F, Jiao C, Jin Y, Zhang J (2010) Convective heat transfer of the bunsen flame in the ul94 vertical burning test for polymers. J Fire Sci 28:337–356

    Article  Google Scholar 

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Acknowledgements

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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Authors and Affiliations

  1. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Barcelona, Spain

    Julio Marti, Sergio R. Idelsohn & Eugenio Oñate

  2. Department of Civil and Environmental Engineering (DECA), Universitat Politècnica de Catalunya (UPC), 08034, Barcelona, Spain

    Julio Marti & Eugenio Oñate

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  1. Julio Marti
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Correspondence to Julio Marti.

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Marti, J., Idelsohn, S.R. & Oñate, E. A Finite Element Model for the Simulation of the UL-94 Burning Test. Fire Technol 54, 1783–1805 (2018). https://doi.org/10.1007/s10694-018-0769-0

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