Three-dimensional finite element modeling of the flow of a metal melt with a free surface under conditions of a moving laser source

N. I. Belozerov ; K. A. Chekhonin

Dalʹnevostočnyj matematičeskij žurnal, Tome 24 (2024) no. 1, pp. 9-21.

Résumé

Three-dimensional convective heat and mass transfer in a metal melt bath under the action of a moving laser heat source is considered. The mathematical model with a Lagrangian description is based on the Navier – Stokes equations, continuity and energy, taking into account diffusion, convective and radiative heat losses. Temperature – dependent surface effects are taken into account using surface tension (Marangoni forces) at a dynamic contact angle on a moving three-phase contact line. The numerical solution of the problem is performed by the finite element method with a divergently stable approximation of the main variables. The integration of kinematic and dynamic conditions on a free surface is performed according to the Newmark – Bassac scheme. Verification and validation of the proposed numerical algorithm is performed. The influence of the determining process parameters (laser power and scanning speed) on the geometric dimensions of the melt bath is shown.

Bibliographie

[1] Bonn D., Eggers J., “Wetting and spreading”, Reviews of Modern Physics, 81 (2009), 739–805 | DOI | MR

[2] Worner M., “Numerical modeling of multiphase flows in microfluidics and micro process engineering: a review of methods and applications”, Microfluidics and nanofluidics, 12:6 (2009), 841–886 | DOI

[3] Mukherjee T., DebRoy T., Theory and Practice of Additive Manufacturing 1st Edition, Wiley, 2023

[4] Bulgakov V. K., Chekhonin K. A., Lipanov A. M., “Zapolnenie oblasti mezhdu vertikalnymi koaksialnymi tsilindrami anomalno vyazkoi zhidkostyu v neizometricheskikh usloviyakh”, Inzhenerno-fizicheskii zhurnal, 57:4 (1989), 577–582

[5] Chekhonin K. A., Sukhinin P. A., “Dvizhenie nelineino-vyazkoplastichnoi zhidkosti so svobodnoi poverkhnostyu pri zapolnenii osesimmetrichnogo ob'ema”, Matematicheskoe modelirovanie, 13:3 (2001), 89–102 | MR | Zbl

[6] Chekhonin K. A., Sukhinin P. A., “Numerical modeling of filling axially symmetric channel with non-linearly viscoelastic fluid taking into account $\pi$ effect”, Inzhenerno-fizicheskii zhurnal, 72:5 (1999), 881–886

[7] Chekhonin K. A., Vlasenko V. D., “Modelling of capillary coaxial gap filling with viscous liquid”, Computational Continuum Mechanics, 12 (2019), 313–324 | DOI

[8] Chekhonin K. A., Vlasenko V. D., “Three-dimensional finite element model of three-phase contact line dynamics and dynamic contact angle”, WSEAS transactions on fluid mechanics, 19 (2024), 577–582 | DOI

[9] Chekhonin K. A., Vlasenko V. D., “Three-dimensional finite element model of the motion of a viscous incompressible fluid with a free surface, taking into account the surface tension”, Actual problems of continuum mechanics: experiment, theory, and applications, AIP conference proceedings, 207, 2023, 030007 | DOI

[10] Shikhmurzaev Y. D., “Solidification and dynamic wetting: a unified modeling framework”, Physics of Fluids, 33 (2021), 072101 | DOI

[11] Ruiter et al R., “Contact line arrest in solidifying spreading drops”, Phys. Rev. Fluids, 2 (2017), 043602 | DOI

[12] Herbaut et al R., “A criterion for the pinning and depinning of an advancing contact line on a cold substrate”, Euro. Phys. J. Spec. Top., 229 (2020), 043602 | DOI

[13] Gielen et al M. V., “Solidification of liquid metal drops during impact”, J. Fluid Mech., 883:A32 (2020), 20

[14] Sourais A. G., Markodimitrakis L. E., Papathanasiou A. G., “Droplet evaporation dynamics on heterogeneous surfaces: Numerical modeling of the stick–slip motion”, International Journal of Heat and Mass Transfer, 207 (2023), 123992 | DOI

[15] Bulgakov V. K., Chekhonin K. A., Osnovy teorii metoda smeshannykh konechnykh elementov, Izd-vo Khabar. politekh. instituta, Khabarovsk, 1999 | MR

[16] Rappaz M., Bullet M., Deville M., Modeling in Materials Science and Engineering, Springer Verlag, Berlin, 2003 | MR | Zbl