# Numerical Modeling of Heat Transfer and Material Flow During Wire-Based Electron-Beam Additive Manufacturing

• A. V. Shcherbakov
• D. A. Gaponova
• R. V. Rodyakina
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)

## Abstract

The development of a mathematical model provides an analysis of heat transfer and metal flow during wire-based electron-beam additive manufacturing described. The procedure for solving the heat equation for the metal in the solid phase and the Navier–Stokes equations in the liquid phase, based on the use of the finite-difference method and the predictor–corrector procedure, is described. An algorithm for numerical approximation of the motion of the free surface of the melt, using the concept of the volume of fluid (VOF) is described. The original method for calculating the effect of surface tension forces, based on the numerical calculation of the surface curvature index, is proposed. The results of simulating the melting of a wire element localized above a substrate made of 316L steel are described. Experiments showed the predominant role of surface tension force in the formation of deposited layer and also that metal’s flow has a laminar structure. These results were obtained by simulating a short-time beam exposure (t = 0.1 s) with a power of 6 kW. Thus, even when the wire and the substrate are exposed with a more intense beam than often used in practice, the metal transfer is not characterized by the formation of intense vortex flows. This can simplify the solution of the problem of additive manufacturing modeling in the future.

## Keywords

Additive manufacturing Electron beam Melting Mathematical model Navier–Stokes equations Heat transfer Fluid flow Surface tension

## Notes

### Acknowledgements

This work was carried out in National Research University “Moscow Power Engineering Institute”; it was supported by grant from the Russian Science Foundation (Project 17-79-20015).

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© Springer Nature Switzerland AG 2020

## Authors and Affiliations

• A. V. Shcherbakov
• 1
• D. A. Gaponova
• 1
• R. V. Rodyakina
• 1
Email author
1. 1.National Research University MPEIMoscowRussia