# A model of heat transfer in metal foaming

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1 A model of heat transfer in metal foaming B. Chinè 1,2, V. Mussi 2, M. Monno 3, A Rossi 2 1 Instituto Tecnológico de Costa Rica, Costa Rica; 2 Laboratorio MUSP, Macchine Utensili e Sistemi di Produzione, Piacenza, Italy; 3 Politecnico di Milano, Italy. October 14-16, 2015

2 2 Presentation overview Introduction Foaming process of a metal foam Modeling the heat transfer Mathematical model Numerical results Conclusions

3 3 Foaming process of a metal foam Metal foaming [1,2] is a complex phenomenon: melted Al and H 2 gas simultaneous mass, momentum and energy transfer mechanisms between solid, liquid and gas phases thermal gradient control the heating, the expanding process of the melted phase and the final solidification of the metal foam solidified metal foam several physical phenomena on interfaces, interface motion bubble expansion, dynamics, coarsening, rupture, etc.

4 4 Foaming process of a metal foam Heat treatment at temperatures near the melting point of the matrix material is a fundamental step. The blowing agent, decompose within the dense metallic matrix. The released gas forces the compacted precursor material to expand, thus forming its highly porous structure. The time needed for full expansion depends on temperature and the size of the precursor and ranges from a few seconds to several minutes.

5 5 Metal foaming in a furnace The heating process (convective heating process) is carried out in a furnace of dimension 3600x1400x1400 mm 3. Air is moved by three fans set on the roof (each one of 2000 W and with a diameter of 400 mm). Side inlets convey the air, heated by electric resistive elements, into the furnace volume. Fan Heater Resistenze Side inlets Metal foam

6 6 Metal foaming in a furnace With the component in the furnace, the process time (t FIN ) need to foam it completely depends on: the foaming temperature ( C) the geometry of the component the position of the foam precursor (Al alloy + foaming agent). Fan Heater Resistenze Side inlets Metal foam

7 7 Metal foaming in a furnace Electric heaters Fans

8 COMSOL CONFERENCE, 2015 GRENOBLE 8 Distance (mm) between the fans Fans

9 9 Dimensions (mm) of air inlets and component to be foamed side view air air inlets air inlet component bottom surface air inlet cross view component

10 10 Modeling the heat transfer in the furnace The 3D furnace is divided in three similar sections. The first section containing the piece is modeled. The heating process is considered transient and the air flow is assumed to be compressible and turbulent. The foaming time is 1 hr. Electric heaters are not modeled, the air temperature is set at inlet. Conductive, convective and radiative heat phenomena are considered. The material of the piece is a common structural steel. inlets The following emissivity of the structural steel, obtained experimentally [3], is used in the model: steel 0.082* exp( T( C))

11 11 Mathematical model The mathematical model is developed by coupling the equation of heat transfer to the fluid flow equations of conservation of mass and momentum (conjugate heat transfer in Comsol). In the model we use the Reynolds-averaged Navier-Stokes (RANS) equations [5, 6] equations and the transport equations for the turbulent kinetic energy and the dissipation rate, given by: Standard coefficients of the k- model used.

12 12 Boundary conditions Velocity of 4 m/s and temperature of C for the air at the inlets. Velocity of air (fan driven) set equal to 16 m/s at the. The initial temperature of the component is 40 0 C. The temperature of the wall is C. Slip condition for the air velocity at the walls. Symmetry in the vertical central plane. inlets

13 13 Numerical results: temperature in a vertical plane of the furnace inlets

14 14 Numerical results: velocity magnitude of air inlets

15 15 Numerical results: temperature and flow pattern inlet inlet inlets

16 16 Numerical results: variation of the temperature in the component ΔT inlet inlet inlets

17 17 Numerical results: variation of the temperature in the component ΔT inlet inlet inlets

18 Temperatura [ C] COMSOL CONFERENCE, 2015 GRENOBLE 18 Numerical results of temperature: comparison with experiments inlet inlet TP1 TP2 (TU02) TP3 TP4 (TD04) TP5 (TD03) TP6 (TD01) TP TP8 inlets tempo [min]

19 19 Conclusions A modeling work by using Comsol Multiphysics has been developed for simulating a heating process of a metal foam in a furnace. Air velocity and air temperature fields have been obtained by modeling the compressible turbulent flow in the furnace. An experimental value of the emissivity has been used in the modeling work to describe the radiative heat transfer of a structural steel. The temperature values compare satisfactorily with the experimental measurements obtained in the same conditions. A H 2 Al H 2 H 2 Finally, for more comprehensive transient turbulent models of metal foaming, computational requirements should be also considered.

20 20 References [1] J. Banhart, Manufacture, characterization and application of cellular metals and metal foams, Progress in Materials Science, 46, (2001). [2] J. Banhart, Light-metal foams-history of innovation and technological challenges, Advanced Engineering Materials, 15, doi: /adem (2012). [3] T. Paloposki and L. Liedquist, Steel Emissivity at high temperatures, VRT Research Notes, Espoo 2005, Finland, (2005). [4] F. Incropera, D.P. DeWitt, T.L. Bergman and A.S. Lavine, Fundamentals of Heat and Mass Transfer, 6 th ed., John Wiley and Sons, Danvers, MA, USA, (2007). [5] Comsol AB, Comsol Multiphysics-Heat Transfer Module, User s Guide, Version 5.1, (2015). [6] Comsol AB, Comsol Multiphysics-CFD Module, User s Guide, Version 5.1, (2015). [7] B. Chinè and M. Monno, Multiphysics modeling of a metal foam, Proceedings of 2012 European Comsol Conference, Milan, (2012). [8] C. Körner, Integral Foam Molding of Light Metals, 124. Springer-Verlag, Berlin Heidelberg Al (2008). H 2 A H 2 H 2

21 21 Many thanks for your attention. We would like to also acknowledge: Valerio Marra, PhD, Comsol Inc. Vicerrectoría de Investigación y Extensión A H 2 H 2 and to the organizers of the

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