# Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Melt Flow Description

_{x}, directed along the direction of movement of the laser, is much greater than the transverse velocities V

_{y}and V

_{z}. In the case of a steady-state process, the Navier–Stokes fluid motion equation can be written as:

_{s}is the maximum surface temperature, while T

_{m}and T

_{b}are the melting and evaporation temperatures, respectively. Assuming that the law oftemperature drop to the tail of the melt pool is linear , then we can write:

_{x}. Here, it is necessary to take into account that the density of the mass flow j(x) incident on the melt surface is determined by a gas–powder jet. Then the continuity equation for the flow will be written as follows:

#### 2.2. Influence of the Powder Jet on the Heat Transfer in the Deposited Wall

_{0}is the initial temperature of the substrate.

_{p}, we can use a well-known analytical solution to the problem of temperature distribution in a homogeneous ball of radius R with an initial temperature T

_{0}for the case when a constant heat flow q

_{p}is fed into the ball through its surface [16,17]:

_{n}are the positive roots of the equation $tg\left(R\mu \right)=R\mu $; and t is the heating time, which is determined for each particle as the time of flight through the laser radiation zone before it enters the melt pool. Knowing the density of the powder flow in the gas–powder jet, the trajectory of the particles, their size, and the amount that got into the melt pool—for example, from [18]—it is possible to obtain the temperature distribution T

_{p}(x) in the gas-–powder jet at the time of meeting with the melt surface.

_{w}is the residual temperature of the previous layer when applying the bead, determined by the product construction strategy.

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

L | Melt pool length, mm |

H | Melt pool depth, mm |

b | Melt pool half-width, mm |

R | Curvature radius of a bead profile |

V | Laser beam motion speed, mm/s |

V_{m}(x,y,z) | Liquid metal flow velocity, mm/s |

V_{x}, V_{y}, V_{z} | X, Y, and Z components of the liquid metal flow velocity, mm/s |

c | Heat capacity, J/(kg·K) |

λ | Heat conductivity, W/(m·K) |

χ | Thermal diffusivity, m^{2}/s |

ρ | Density, kg/m^{3} |

ν | Kinematic viscosity of the liquid melt, m^{2}/s |

η | Dynamic viscosity of the liquid melt, Pa·s |

α, β, γ | Coefficients of the parabolic equation of the melt velocity X component |

σ, σ* | Surface tension, N/m |

T_{0} | Initial temperature, environment temperature, K |

T_{m} | Melting point, K |

T_{b} | Boiling point, K |

T_{s} | Maximum surface temperature, K |

T_{w} | Residual temperature of the previous deposited bead, K |

p | Pressure, Pa |

p_{add} | Additional pressure over change of the longitudinal curvature radius, Pa |

j(x) | Powder mass flow density, kg/(s·m^{2}) |

q(x) | Distribution of the total energy flux on the melt pool surface, W/m |

I(x) | Intensity of the laser beam radiation, W/m |

A | Light energy absorption coefficient |

T_{i}(r,t) | Temperature of a particle at co-ordinate r and heating time t, K |

T_{p}(x) | Temperature distribution in the powder jet along the X axis, K |

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**Figure 2.**Melt pool top surface profile for 316 L steel for different powder feed rates (

**a**) and motion speeds (

**b**); laser beam radius on the surface was 2.5 mm, beam power was 2000 W, and powder jet diameter was 3 mm.

**Figure 3.**Melt pool top surface profiles for Inconel718, VT6, and 316 L steel in comparison with one another. Motion speed was 20 mm/s, laser beam power was 2000 W, laser beam radius on the surface was 2.5 mm, powder jet diameter was 3 mm, and powder feed rate was 2 kg/h.

**Figure 4.**Temperature distribution along the melt pool length. Laser power was 2000 W, motion speed was 20 mm/s, laser beam radius on the surface was 2.5 mm, powder jet diameter was 3 mm, and powder feed rate was 2 kg/h.

**Figure 5.**Melt pool shape. Laser power was 2000 W, motion speed was 20 mm/s, laser beam radius on the surface was 2.5 mm, powder jet diameter was 3 mm, and powder feed rate was 2 kg/h.

Properties | Inconel 718 | VT6 | 316 L |
---|---|---|---|

Heat capacity, J/(G·K) | 0.435 | 0.546 | 0.45 |

Heat conductivity W/(m·K) | 8.9 | 26 | 30 |

Density, kg/m^{3} | 8190 | 4430 | 7800 |

Melting point, K | 1600 | 1920 | 1710 |

Reflectivity for 1.06 μm, % | 77 | 61 | 68 |

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**MDPI and ACS Style**

Turichin, G.A.; Valdaytseva, E.A.; Stankevich, S.L.; Udin, I.N. Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology. *Materials* **2021**, *14*, 4141.
https://doi.org/10.3390/ma14154141

**AMA Style**

Turichin GA, Valdaytseva EA, Stankevich SL, Udin IN. Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology. *Materials*. 2021; 14(15):4141.
https://doi.org/10.3390/ma14154141

**Chicago/Turabian Style**

Turichin, Gleb A., Ekaterina A. Valdaytseva, Stanislav L. Stankevich, and Ilya N. Udin. 2021. "Computer Simulation of Hydrodynamic and Thermal Processes in DLD Technology" *Materials* 14, no. 15: 4141.
https://doi.org/10.3390/ma14154141