Three-Jet Powder Flow and Laser–Powder Interaction in Laser Melting Deposition: Modelling Versus Experimental Correlations
Abstract
:1. Introduction
2. Mathematical Modelling
2.1. Powder Stream Distribution in the LMD Process
- The gravitational effect, during the powder particle flow, is neglected. This assumption is reasonable as the time of flight of powder particles across the laser beam interaction zone is very short, equivalent to 25% of standoff distance [19].
- All the powder particles are spherical. Moreover, their normalized size distribution is considered in the modelling.
- There are two types of collisions mainly involved in the LMD process: (i) Powder debits with the powder feeder’s walls and (ii) among the powder particles. If such collisions are taken into account, various factors, including elastic motion, damping effects, friction forces due to sliding effects, powder particles’ velocity, reiterated powder flow rate, and powder debits overlapping, must be considered. It will result in a tremendous number of unknown variables and a complex system of equations, which requires a considerable amount of calculation time, iteratively. Besides, the powder debits are microparticles. It means that one should carry out investigations at the microscale to monitor the quantities mentioned above. It will result in a tedious and challenging system of equations. Moreover, there are studies [20,21,22] that show that if such collisions are ignored, the resultant flow rate will make a difference within the range of no more than 9–12%. Based on the above findings and to develop a simplified dynamic system, it is reasonable to ignore the collision between powder particles. Hence, the overlapping and all sort of collisions have been ignored throughout the deposition process.
2.2. Temperature Distribution within the Substrate in the LMD Process after Powder Addition
2.2.1. Powder Particles Heating: Inflight and within Melt-Pool
2.2.2. Powder Particles’ within Melt-Pool Heating
3. Materials and Methods
3.1. Analytical Computations
3.2. Experimentation
4. Results and Discussion
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
List of Symbols
: | Area of powder particle |
: | Laser beam area |
cpp: | Powder particle’s specific heat |
cps: | Substrate’s specific heat |
dl: | Distance between the center of the laser beam and powder nozzle |
: | Thermal gas diffusivity |
Lfp: | Powder particle’s latent heat of fusion |
Lfs: | Substrate’s latent heat of fusion |
: | Powder particles’ flow rate |
: | Normal distribution of powder debits |
Nu: | Nusselt number |
: | Gaussian powder flow |
Pr: | Peclét number |
rs: | Radius of powder nozzle |
: | Radius of the mean powder particle |
Tpboil: | Powder particle’s boiling temperature |
Tpm: | Powder particle’s melting temperature |
Tpsol: | Powder particle’s solidus temperature |
tiph: | Laser–powder particles interaction time needed to initiate the vaporization |
Tsboil: | Substrate’s boiling temperature |
Tsm: | Substrate’s melting temperature |
Tssol: | Substrate’s solidus temperature |
Tsli: | Laser–substrate interaction time needed to initiate the vaporization |
: | Ambient temperature |
: | The volumetric flow rate of gases |
: | The velocity of powder particles |
: | The laser scanning speed |
: | The velocity of gas |
: | Powder particles’ density |
: | Density of gas |
: | Viscosity of gas |
: | Laser beam attenuation ratio |
: | Powder efficiency |
: | Powder particles’ cloud density |
: | Substrate’s thermal diffusivity |
: | Substrate’s laser absorptivity |
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Parameter Name | Value (Units) |
Thermal coefficient for radiation | 5.67 × 10−8 (W/m2. °C4) |
Heat transfer coefficient | 24 (W/m2. °C) |
Room temperature | 25 (°C) |
Liquidus temperature | 1654.85 (°C) |
Solidus temperature | 1604.85 (°C) |
Thermal conductivity | 0.067 (W/m. °C) |
Specific heat capacity | 526 (J/kg. °C) |
Density | 4420 (kg/m3) |
Viscosity | 4.0 × 10-3 (kg/m.s) |
Latent heat | 2.0 × 105 (J/kg) |
Powder particles’ laser absorption coefficient | 0.70 |
Laser spot size | 800 (µm) |
Powder efficiency | 0.40 |
Standoff distance | 17 (mm) |
Powder particles’ diameter in the normalized distribution | 43–106 (µm) |
Parameter Name (Units) | For Numerical Simulations: Fe-TiC Depositions on the Carbon Steel Substrate [34] | For Numerical Simulations: 12Cr Ni2 Alloy Steel Powder Depositions 45 Steel Substrate [35] | For Experimental Analysis: Ti6Al4V Titanium Alloy Powder Deposition on Ti6Al4V Titanium Alloy Substrate [36] |
Laser power (W) | 885 | 1800 | 400 |
Scanning speed (mm/s) | 2.0 | 5.0 | 6.67 |
Powder feeding rate (g/min) | 4.0 | 11.0 | 2.5 |
Powder jet radius (m) | 1.30 × 10−3 | 1.60 × 10−3 | 1.70 × 10−3 |
Laser beam radius (m) | 1.25 × 10−3 | 1.50 × 10−3 | 1.05 × 10−3 |
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Mahmood, M.A.; Popescu, A.C.; Oane, M.; Ristoscu, C.; Chioibasu, D.; Mihai, S.; Mihailescu, I.N. Three-Jet Powder Flow and Laser–Powder Interaction in Laser Melting Deposition: Modelling Versus Experimental Correlations. Metals 2020, 10, 1113. https://doi.org/10.3390/met10091113
Mahmood MA, Popescu AC, Oane M, Ristoscu C, Chioibasu D, Mihai S, Mihailescu IN. Three-Jet Powder Flow and Laser–Powder Interaction in Laser Melting Deposition: Modelling Versus Experimental Correlations. Metals. 2020; 10(9):1113. https://doi.org/10.3390/met10091113
Chicago/Turabian StyleMahmood, Muhammad Arif, Andrei C. Popescu, Mihai Oane, Carmen Ristoscu, Diana Chioibasu, Sabin Mihai, and Ion N. Mihailescu. 2020. "Three-Jet Powder Flow and Laser–Powder Interaction in Laser Melting Deposition: Modelling Versus Experimental Correlations" Metals 10, no. 9: 1113. https://doi.org/10.3390/met10091113