Diffuse Interface Models for Metal Foams

Transcription

1 Diffuse Interface Models for Metal Foams B. Chinè 1,3, M. Monno 2,3, E. Reossi 3, M. Verani 3 1 Instituto Tecnològico de Costa Rica, Costa Rica; 2 Politecnico di Milano, Italy; 3 Laboratorio MUSP, Macchine Utensili e Sistemi di Produzione, Piacenza, Italy. bchine@itcr.ac.cr October 23-25

2 2 Presentation overview Introduction Metal foams with foaming agents in the melt Physical model Governing equations Simulations by Comsol Multihysics Results Conclusions

3 4 Decomosition of foaming agents in the melt 2 cm Foaming rocess (ALPORAS) for aluminium: - base metal melting - temerature stabilization - viscosity raising adding 1-2% Ca - aggressive stirring - adding of foaming agent owder - short stirring - withdrawing of the stirring system

4 5 Decomosition of foaming agents in the melt 2 cm - crucible sealing - foam formation controlled by adjusting overressure, temerature and time - cooling of foamed aluminium - withdrawing. bubble Al metal foam: melted Al and gas Al (or Al alloy)

5 6 Decomosition of foaming agents in the melt: hysical henomena Foaming is a comlex henomena: simultaneous mass, momentum and energy transfer mechanisms several hysical henomena on interfaces: surface tension effects, disjoining ressure, interface motion bubble dynamics, coarsening, coalescence, ruture other asects (drainage, mould filling, geometry) difficulty for exerimental measurements (foams are hot, oaque, etc.)

6 7 Physical model wall A 2D rectangular cavity where melted Al and gas bubbles are flowing inside during the foaming rocess. inlet wall Al Al outlet Isothermal rocess, mass diffusion is not considered and gravity is absent (cavity is set horizontally). wall The gas follows the ideal gas law, the liquid is considered an incomressible Newtonian fluid, the two fluids are immiscible. wall The bubbles have the same radius and ressure, the gas-liquid interface is a free surface with uniform surface tension coefficient. With system at rest, the stress balance at the surface of a circular bubble is given by the Lalace s equation (caillary ressure): G,0 L k Al k 1 R 0 L

7 8 Physical model 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: these effects are reresented by a ressure, the disjoining ressure Π(h) (attractive and reulsive molecular forces in the thin film). k 1 L,2 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 suressing the driving force for film thinning): Al k 1 R 0 L1, G,0 L k Π(h) disjoining ressure

8 9 Simulations by Comsol Multihysics 4.3b Equations (couled) continuity t ( u) 0 (CDF and Chemical Reaction Engineering modules): momentum transfer u ( u ) u [ I ( u ( u) t 1. gas comressibility neglected 2. flow is laminar T )] F st F ext F interface movement ( hase field ) u t f ext ( 1) hel variable F st f G Surface tension force in Comsol: F ext f 1 int 0 hydrogen hase But when two bubbles are aroaching: 1 int the middle of the interface aluminium hase External force (due to the disjoining ressure) Al

9 10 Simulations by Comsol Multihysics 4.3b Yue et al. 2005: 2 Π( ) ( 2 0 1) 4 2 in Comsol F ext f External force (due to the disjoining ressure) is a defined source of free energy ci c j to track each interface: 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 transort of diluted secies (Fick s eq. and convection term) c i t Dic i u ci Ri R i 0 if c i xc j set value 30 2 D i 10 m / s the marker is only convected disjoining ressure is switched on

10 12 Exerimental results: without disjoining ressure, bubbles merge volume fraction of in a metal foam flowing in a cavity after t =0.06 s with disjoining ressure equal to zero volume fraction of in a metal foam flowing in a cavity after t =0.12 s with disjoining ressure equal to zero

11 13 Exerimental results: with disjoining ressure, stabilization effect volume fraction of a t =0.12 s when the disjoining ressure sets a reulsive stabilization effect between the bubbles interfaces body force due to the disjoining ressure at t =0.12 s giving reulsive forces between the bubbles interfaces

12 14 Exerimental results: ressure field without reulsive effects with reulsive effects due to the disjoining ressure ressure field in a metal foam flowing in a cavity after t =0.12 s with disjoining ressure equal to zero ressure field in a metal foam flowing in a cavity after t =0.12 s when the disjoining ressure sets a reulsive stabilization effect

13 15 Conclusions A metal foam reresented by gas bubbles and liquid aluminium moving in a laminar flow has been modeled and simulated. Surface tension effects have been considered and reulsive forces between neighboring bubbles have been exressed through the disjoining ressure. The model uses a formulation of the disjoining ressure in the framework of the hase field method. Fundamental mechanisms due to surface tension effects and disjoining ressure have been reroduced. A The numerical results show that diffuse interface methods are effective to model this kind of comlex henomena. Al The above results are encouraging for our under way researches in the modeling of metal foaming rocesses.

14 17 Many thanks for your attention. Thanks also to the organizers of A