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Numerical Simulation on Electron Beam Smelting Temperature Field of Novel Ni–Co-Based Superalloy

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Abstract

In this study, a three-dimensional (3D) transient thermal model for electron beam smelting (EBS) of a novel Ni–Co-based superalloy was developed using ANSYS FLUENT software. The model incorporated temperature-dependent material thermal-physical parameters and a rotating Gaussian body heat source. Parameters for the moving electron beam were also considered in the model as the user-defined functions (UDFs). The main objective of this research was to gain a better understanding of the thermal behavior of the molten pool during the EBS process. Experiments were conducted using the SEBM-30A EB furnace. The average surface temperature of the molten pool calculated from volatilization loss of Ni element during the EBS process was compared with the average surface temperature of the molten pool monitored by numerical simulation. The results show that the errors are 0.47 and 7.15 pct at EBS power of 10 and 14 kW, respectively. The simulation results are in good agreement with the experiment results. The temperature of molten pool rises with increasing smelting power, and its depth and width also increase. The temperature gradually rises along the z-direction, and the highest temperature occurs 2 mm below the top surface of the ingot. The relationship between average surface temperature of molten pool and smelting power was obtained. Overall, our research provides significant insights into the thermal behavior of the molten pool during the EBS process. The model can be used to optimize the EBS process to reduce costs and produce high-quality ingots, and provides the basis for modeling the preparation of large ingots from EBS.

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Data Availability

The raw/processed data required to reproduce these findings cannot be shared at this time, as the data also forms part of an ongoing study. The authors will happily share data with anyone interested upon request.

Abbreviations

EBS:

Electron beam smelting

3D:

Three-dimensional

UDFs:

User-defined functions

VIM:

Vacuum induction melting

ESR:

Electroslag remelting

VAR:

Vacuum arc remelting

EBFF:

Electron beam free forming

EBMR:

Electron beam melting and refining

EBM:

Electron beam melting

U :

Acceleration voltage

I :

Beam current

v :

Scanning speed

ρ :

Density

k :

Thermal conductivity

c p :

Specific heat capacity

H :

Mixed enthalpy

t :

Time

h(T):

Enthalpy term

L :

Latent heat of fusion

β l :

Liquid fraction

ΔH :

Latent heat of phase change

T Solidus :

Solidus temperature

T Liquidus :

Liquidus temperature

T ref :

Reference temperature

\(\mathop{n}\limits^{\rightharpoonup} \) :

Normal vector of free surface

S E :

Energy source term

Q rad :

Surface heat irradiation flux

\(\varepsilon\) :

Emissivity of the superalloy surface

\(\sigma\) :

Stephan–Boltzmann constant

\(T_{\infty }\) :

Far-field temperature

\(h_{c}\) :

Heat transfer coefficient

\(q_{m}\) :

Peak power density

r s :

Scanning radius

h :

Absolute penetration depth of the electron beam

η :

Effective power coefficient

\(r_{0}\) :

Radius of electron beam spot

\(P_{i}^{0}\) :

Saturated vapor pressure of pure component i

\(V_{i}\) :

Theoretical evaporation rate

R :

Ideal gas constant

\(\alpha_{i}\) :

Activity of component i

\(M_{i}\) :

Molar mass of the evaporating components

\(\gamma_{i}\) :

Activity coefficient

\(\chi_{i}\) :

Molar fraction

\(\Delta \overline{G}_{i}^{{{\text{ex}}}}\) :

Partial excess Gibbs energy

\(\Delta m_{ie}\) :

Mass loss of component i

\(S\) :

Melt surface evaporation area

\(V_{ie}\) :

Evaporation rate during the experiment

T :

Surface average temperature

P :

Electron beam power

R 2 :

Correlation coefficient

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Acknowledgments

The authors gratefully acknowledge financial support from the National Key R&D Program of China (Grant No. 2019YFA0705300), the Fundamental Research Funds for the Central Universities (Grant No. DUT21ZD404), the Innovation Team Project for Key Fields of Dalian (Grant No. 2019RT13). This work was also supported by Open Project of State Key Laboratory of Advanced Special Steel, Shanghai Key Laboratory of Advanced Ferrometallurgy, Shanghai University (SKLASS 2021-09) and the Science and Technology Commission of Shanghai Municipality (Nos. 19DZ2270200, 20511107700).

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Authors and Affiliations

  1. School of Materials Science and Engineering, Dalian University of Technology, No. 2 Linggong Road, Ganjingzi District, Dalian, 116024, P.R. China

    Lidan Ning, Yi Tan, Pengting Li, Xiaogang You & Xudong Wang

  2. Key Laboratory for Energy Beam Metallurgy and Advanced Materials Preparation of Liaoning Province, Dalian, 116024, P.R. China

    Lidan Ning, Yi Tan, Pengting Li & Xiaogang You

  3. School of Mechanical Engineering, Yangzhou University, Yangzhou, 225127, P.R. China

    Shutao Wen

  4. State Key Lab Adv Special Steel, Shanghai University, Shanghai, 200444, P.R. China

    Shutao Wen & Weidong Xuan

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  1. Lidan Ning
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Correspondence to Yi Tan.

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Ning, L., Tan, Y., Wen, S. et al. Numerical Simulation on Electron Beam Smelting Temperature Field of Novel Ni–Co-Based Superalloy. Metall Mater Trans B 54, 2965–2984 (2023). https://doi.org/10.1007/s11663-023-02881-7

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  • DOI: https://doi.org/10.1007/s11663-023-02881-7

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