[SY-J4] Micro-Scale Model of Thermomechanics in Solidifying Saturated Porous Media
In the contribution, we discuss the model of solidification of melt occupying pores of the porous medium with grains intact but participating in the heat transfer. The research motivation is given by development of advanced materials as well as by climate changes. The model is based on coupled heat conduction equation and the phase-field. We present the model and several computational studies.
Solidiffication inside the porous medium is accompanied by complex processes affected by the material composition, micro-scale interfaces between phases within the medium, bulk properties of the presented phases, and ambient physical conditions. Volumetric changes of the liquid presented in pores subjected to phase change conditions is one of crucial phenomena. Due to the generic inhomogeneity of volume occupied by the solidifying porous medium, we focus on treating the phase transition at microscale. We have developed a micro-scale model describing mechanical, thermal, and phase change processes within a small sample of a porous medium. The phase change is described in the Lagrangian framework by means of the energy, Navier, and phase-field equations. A coupling of multi-physics and multiple phases is introduced. The model provides spatio-temporal dependencies of primary variables, the resulting forces exerted on grain surfaces by the change in specific volume due to phase transition, and possibly, the mean values of the key quantities useful for upscaling. The role of the model is demonstrated on several computational studies which follow recently published results [1-2].
[1] Žák A., Beneš M. and Illangasekare T.H. Analysis of Model of Soil Freezing and Thawing, IAENG International Journal of Applied Mathematics, Volume 43, Issue 3, pp. 127--134, September 2013
[2] Žák A., Beneš M., Illangasekare T. H., Trautz A. Mathematical Model of Porous Medium Freezing at Micro-Scale, to appear in Communications in Computational Physics, 2018
Solidiffication inside the porous medium is accompanied by complex processes affected by the material composition, micro-scale interfaces between phases within the medium, bulk properties of the presented phases, and ambient physical conditions. Volumetric changes of the liquid presented in pores subjected to phase change conditions is one of crucial phenomena. Due to the generic inhomogeneity of volume occupied by the solidifying porous medium, we focus on treating the phase transition at microscale. We have developed a micro-scale model describing mechanical, thermal, and phase change processes within a small sample of a porous medium. The phase change is described in the Lagrangian framework by means of the energy, Navier, and phase-field equations. A coupling of multi-physics and multiple phases is introduced. The model provides spatio-temporal dependencies of primary variables, the resulting forces exerted on grain surfaces by the change in specific volume due to phase transition, and possibly, the mean values of the key quantities useful for upscaling. The role of the model is demonstrated on several computational studies which follow recently published results [1-2].
[1] Žák A., Beneš M. and Illangasekare T.H. Analysis of Model of Soil Freezing and Thawing, IAENG International Journal of Applied Mathematics, Volume 43, Issue 3, pp. 127--134, September 2013
[2] Žák A., Beneš M., Illangasekare T. H., Trautz A. Mathematical Model of Porous Medium Freezing at Micro-Scale, to appear in Communications in Computational Physics, 2018