Modeling of Expanding Metal Foam

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1 Modeling of Exanding Metal Foam B. Chinè 1,3 and M. Monno 2,3 1 Instituto Tecnológico de Costa Rica, Costa Rica; 2 Politecnico di Milano, Italy; 3 Laboratorio MUSP, Macchine Utensili e Sistemi di Produzione, Piacenza, Italy. Setember 17-19

2 2 Presentation overview Introduction Metal foams Bubble exansion Exanding a metal foam Modeling the disjoining ressure Conclusions

3 3 Indirect foaming via recursor: hysical henomena Foaming [1,2,3] is a comlex henomena: simultaneous mass, momentum and energy transfer mechanisms several hysical henomena on interfaces, interface motion bubble exansion, dynamics, coarsening, ruture other asects (drainage, mould filling, geometry) difficulty for exerimental measurements (foams are hot, oaque, etc.) melted Al and H 2 gas solidified metal foam

4 4 Bubble exansion: model Two Phase Flow, Level Set interface, Weakly-Comressible [4] = surface tension coefficient t = time R(t) z Liquid liquid EXT EXT (t) R Ω G G (t) t ( u) 0 u T ( u ) u [ I ( u ( u) ) t 2 ( )( u) I] F g F DV ST momentum 3 u t ( t ) G, dynamic L L viscosity G,0 continuity [ (1 ) ] G, 0 ( EXT,0 of the liquid 2 ) t R 0 3 level set Gas gas during the exansion at time t [5] n R n σ eq G 2 r AX EXT without flow at time t

5 5 Bubble exansion: simulation G, Pa, L 2.4 x10 3 kg/m 3, L 4.5 x10 3 Pa s 1.9 x10 Re m 2 /s

6 6 Exanding a metal foam: model A 2D solid region of recursor artially filling a circular mold laced horizontally inside a furnace. Comlex henomena as bubble nucleation, their location, growth, etc. simlified. Air of the cavity substituted for H 2 (only 2 fluids). A simlified model [6] may be used for metal foaming, by assuming that: mold Ste 1: heat is transferred from the furnace wall to the solid recursor ; Ste 2: H 2 starts to be released, then N H 2 bubbles are evenly generated inside the solid Al. Ste 3: The N bubbles start exanding and moving after that Al is melted. T 0 T EXT

7 7 Exanding a metal foam: model Equations (couled) (Heat transfer module [7] and level set method of the CFD module [4]): continuity Free triangular mesh on the mold wall: 2.6 x 10-3 m gas exansion rate: ( G 0 t) ex( t) G, momentum transfer interface movement (level set) heat transfer C + T C ut t ( k T ) Q DOF: Ste 1 and 2: 3.4 x 10 5 Ste 3: 1.83 x 10 6 Segregated stes for the nonlinear solver First: flow and level set variables Second: heat transfer variables TIME STEP (direct solver PARDISO): Ste 1: initial 10-6 s, final 31 s Ste 2: initial 10-2 s, final 58 s Ste 3: 10-2 s (10-5 s when bubbles are merging)

8 8 Exanding a metal foam: simulation of ste 3 merging merged merging of two central bubbles with fluid acceleration, after s the exansion is started four central bubbles have merged after s the exansion is started

9 9 Modeling the disjoining ressure The liquid metal is suctioned from the caillary films to the borders of the foam (Plateau borders) causing the interfaces to thin and bubbles to merge. G,0 L k G, 0 is the same L,2 L,1 The drainage of the thin films is slowed and revented when interactions between the film surfaces come into lay (disjoining ressure Π(h), [8]). In the model, once the film h between the bubbles became sufficiently small, we take into account the disjoining ressure Π(h) (reresenting a stabilization effect reducing the driving force for film thinning): k 1 H 2 L,2 Al k 1 R 0 L 1, G,0 L k Π(h) disjoining ressure = surface tension coefficient

10 10 Modeling by the hase field method Equations (couled) (CDF and Chemical Reaction Engineering modules): continuity momentum transfer 1. gas comressibility considered 2. flow is laminar t ( u) 0 u ( u t interface movement ( hase field ) ) u [ I ( u ( u) T 2 ) ( )( u) I] F g DV 3 gas exansion rate: ( G 0 t) ex( t) G, F ST u t 2 2 ( 2 2 f ext 1) hel variable F st G f Surface tension force 1 hydrogen hase 0 int 0.5 But when two bubbles are aroaching the middle of the interface aluminium hase External force [9] (due to the disjoining ressure) H 2 Al H 2 in Comsol: F ext f

11 11 Modeling by the hase field method in Comsol F ext f External force (due to the disjoining ressure) is a defined source of free energy c i c j to track each interface (if N=number of bubble is 1): assigning a marker c i to each bubble i and moving the marker like a secies in the system, with the same velocity field of the corresonding bubble [10] transort of diluted secies (Fick s eq. and convection term), [11] c i t Dici u ci Ri R i 0 then, if c i x c j set value 30 D i 10 m / s 2 the marker is only convected disjoining ressure is switched on

12 12 Simulations: without disjoining ressure merged without reulsive effects two central bubbles have already merged after 1.55 s the exansion is started

13 13 Simulations: with disjoining ressure, stabilization effect with reulsive effects due to the disjoining ressure volume fraction of H 2 a the same time, with the disjoining ressure setting a reulsive stabilization effect between the bubbles interfaces closer bubbles

14 14 Conclusions A modeling work by using Comsol Multihysics has been develoed for simulating a metal foam manufactured by an indirect foaming rocess via recursor. Bubble exansion, heat transfer and movement of H 2 gas bubbles in liquid Al has been modeled for a metal foam exanding in a 2D mold, driving the exansion by a secific exansion rate. Then, an exanding foam in a mold has been simulated with reulsive forces modeling the disjoining ressure by diffuse interface methods. Numerical findings verify that the comutational model, based on level set or hase field techniques, can be effective for modeling the foaming rocess of a metal. H 2 A Finally, for more comrehensive foaming models, comutational requirements should be also considered. Al H 2 H 2

15 15 References [1] J. Banhart, Manufacture, characterization and alication 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] D. Weaire D. and S. Hutzler S., The hysics of foams, Oxford University Press, Oxford (1999). [4] Comsol AB, Comsol Multihysics-CFD Module, User s Guide, Version 4.3b, (2013). [5] S.V. Gniloskurenko, A.I. Raichenko, T. Nakamura, A.V. Byakova and A.A. Raichenko, Theory of initial microcavity growth in a liquid metal around a gas-releasing article. II. Bubble initiation conditions and growth kinetics, Powder Metall. And Metal Ceramics, 41, N.1-2, (2002). [6] B. Chinè and M. Monno, Multihysics modeling of a metal foam, Proceedings of 2012 Euroean Comsol Conference, Milan, (2012). [7] Comsol AB, Comsol Multihysics-Heat Transer Module, User s Guide, Version 4.3b, (2013). [8] C. Körner, Integral Foam Molding of Light Metals, 124. Sringer-Verlag, Berlin Heidelberg Al (2008). [9] P. Yue, J.J. Feng, C. Liu and J. Shen, Diffuse-interface simulations of dro coalescence and retraction in viscoelastic fluids, Journal of Non-Newtonian A Fluid Mechanics, 129, (2005). [10] B. Chinè H 2, M. Monno, E. Reossi and M. Verani, Diffuse interface models for metal foam, Proceedings of 2013 Comsol Conference, Rotterdam, (2012). [11] Comsol AB, Comsol Multihysics-Chemical Reaction Engineering Module, User s Guide, Version 4.3b, (2013). H 2 H 2

16 16 Many thanks for your attention. We would like to also acknowledge: Vicerrectoría de Investigación y Extensión A H 2 H 2 and to the organizers of the

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