FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Numerical simulation of the growth of a sessile drop of metal melt on a horizontal substrate under direct feeding of laser energy and powder |
Chekhonin K. A. |
2024, issue 2, P. 286-299 DOI: https://doi.org/10.47910/FEMJ202426 |
Abstract |
| The paper proposes a new method for studying the dynamics of non-isothermal processes in laser direct additive manufacturing (L-DED) technologies of metal products by growing a sessile drop. Its growth is performed with stationary laser radiation acting on the substrate and metal powder, which is supplied by a jet of inert gas to the focusing area of the laser beam. Heat and mass transfer of a metal melt with Newtonian rheology is considered laminar with a temperature-independent density. The heated powder is instantly melted on the surface of the bath and added as a continuous mass flow through the free surface of the growing droplet with a given distribution. Dynamic conditions on its free surface depend on the value of surface tension, Marangoni shear stress and normal pressure from the action of a jet of gas with powder. Modeling of wetting of solid surfaces by the melt is performed within the framework of the modified Voinov model. The numerical solution of the problem is performed in three-dimensional and axisymmetric formulations by the mixed finite element method using the ALE free surface tracking algorithm. The features of heat and mass transfer in a growing droplet and the evolution of its free surface are investigated. A significant effect of the gas flow and the mass flow rate of the powder on the structure of melt convection in the droplet and the evolution of the free surface with the formation of a crater is shown. |
Keywords: laser (L-DED) additive technology, convective heat and mass transfer, growing droplet, mixed finite element method, free surface, Marangoni effect, contact wetting angle. |
Download the article (PDF-file) |
References |
| [1] Rudsko? V. K. [i dr.], Additivnye tekhnologii. Materialy i tekhnologicheskie prot?sessy, Politekh – Press, SPb, 2021, 515 s. [2] Mukherjee T., DebRoy T., Theory and Practice of Additive Manufacturing 1st Edition, Wiley, 2023, 522 pp. [3] Liu T. S., Chen P., Qiu F., Yang H., Tan N. Y. J., Chew Y., Wang D., Li R., Jiang Q.-C., Tan Ch., “Review on laser directed energy deposited aluminum alloys”, International Journal of Extreme Manufacturing, 6:2, (2024), 022004. [4] Bayat M., Dong W., Thorborg J., To A. C., Hattel J. H., “A review of multi-scale and multiphysics simulations of metal additive manufacturing processes with focus on modelling strategies”, Additive Manufacturing, 47, (2021), 102278. [5] Yu T., Zhao J., “Quantitative simulation of selective laser melting of metals enabled by new high-fidelity multiphase, multiphysics computational tool”, Comput. Methods Appl. Mech. Eng., 399, (2022), 115422. [6] Russell M. A., Souto-Iglesias A., Zohdi T. I., “ Numerical simulation of Laser Fusion Additive Manufacturing processes using the SPH method”, Comput. Methods Appl. Mech. Eng., 341, (2018), 163–187. [7] Kovalev O., Bedenko D., Zaitsev A., “Development and application of laser cladding modelling technique: From coaxial powder feeding to surface deposition and bead formation”, Appl. Math., 57, (2018), 339–359. [8] Yu J., Lin Y., Wang J., Chen J., Huang W., “ Mechanics and energy analysis on molten pool spreading during laser solid forming”, Applied Surface Science, 256:14, (2010), 4612–4620. [9] Shikhmurzaev Y. D., “Solidification and dynamic wetting: a unified modeling framework”, Physics of Fluids, 33, (2021), 072101. [10] 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. [11] Gielen et al M. V., “Solidification of liquid metal drops during impact”, J. Fluid Mech., 883:A32, (2020), 20. [12] 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. [13] 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”, AIP conference proceedings. Actual problems of continuum mechanics: experiment, theory, and applications, 207, (2023), 030007. [14] Belozerov N. I., CHekhonin K. A., “Trekhmernoe konechno-?lementnoe modelirovanie techeniia rasplava metalla so svobodno? poverkhnost?iu v usloviiakh dvizhushchegosia lazernogo istochnika” , Dal?nevost. matem. zhurn., 1, (2024), 9–21. [15] Bulgakov V. K., CHekhonin K. A., Lipanov A. M., “Zapolnenie oblasti mezhdu vertikal?nymi koaksial?nymi t?silindrami anomal?no viazko? zhidkost?iu v neizometricheskikh usloviiakh”, Inzhenerno-fizicheski? zhurnal, 57:4, (1989), 577–582. [16] Chekhonin K. A., Vlasenko V. D., “Modelling of capillary coaxial gap filling with viscous liquid”, Computational Continuum Mechanics, 12, (2019), 313–324. [17] Belozerov N. I., CHekhonin K. A., “Rol? poverkhnostnogo natiazheniia i smachivaniia pri vyrashchivanii metalloizdeli? v priamykh lazernykh tekhnologiiakh 3D-pechati”, Dal?nevost. matem. zhurn., 2, (2024), 157–169. [18] DebRoy T., Wei H. L., Zuback J. S., Mukherjee T., Elmer J. W., Milewski J. O., Beese A. M., Wilson-Heid A., De A., Zhang W., “Additive manufacturing of metallic components – Process, structure and properties” , Prog. Mater. Sci., 92, (2018), 112–224. [19] Bax B., Rajput R., Kellet R., “Systematic evaluation of process parameter maps for laser cladding and directed energy deposition”, Additive Manufacturing, 21, (2018), 487–494. [20] Malikov A. G., Golyshev A. A., Vitoshkin I. E., “ Sovremennye tendent?sii lazerno? svarki i additivnykh tekhnologi? (obzor)” , Prikl. mekh. tekhn. fiz., 64:1, (2023), 36–59. [21] Voinov O. V., “Gidrodinamika smachivaniia” , Izv. AN SSSR. MZHG, 5, (1976), 76–84. [22] Bulgakov V. K., CHekhonin K. A., Osnovy teorii metoda smeshannykh konechnykh ?lementov, Izd-vo KHabar. politekh. instituta, KHabarovsk, 1999. |