To improve the agglomeration of powder in a coaxial powder feeding nozzle used in the frame of a laser energy deposition technique, the influence of several parameters must be carefully assessed. In the present study the problem is addressed by means of numerical simulations based on a DEM-CFD (Discrete Element Method and Discrete Element Method) coupled model. The influence of the powder flow concentration, powder flow focal length and the amount of powder at the nozzle outlet on the rate of convergence of the powder flow is considered. The role played by the nozzle outlet width, the angle between the inner and outer walls and the powder incident angle in determining the powder flow concentration is also considered. The results show that, with increasing of nozzle outlet width, the powder flow concentration per unit volume at the nozzle focal point undergoes a non-monotonic behaviour (it first increases and then decreases). When the nozzle outlet width

Laser energy deposition is a newly formed technology that has developed rapidly in recent years. Computer-aided design, digital control and laser rapid prototyping are used to enable component forming that can considerably shorten the manufacturing cycle [

Scholars have researched powder transport characteristics and the trends of different nozzle structural parameters. Kovalenko et al. [

Current research on the influence of the nozzle structure on powder flow agglomeration has mainly focused on air flow field models in CFD [

In the calculation process of a coupled model of gas-solid two-phase flow based on a Euler model, the conservation equation of particles is calculated by the DEM model. The DEM model transfers the volume fraction, position and velocity of the particles to the CFD model. The CFD model introduces the force of the fluid on the particles into the coupled solver. The CFD model combines the data transmitted by the DEM model to calculate the force acting on the particle surface and transfers it to the DEM model. The DEM model analyses the position and velocity information of the particles under the force in the new calculation step and passes the information to CFD for the next iteration. The process is repeated until the simulation analysis converges.

To simulate the particle flow state effectively, the equivalent diameter of an equal volume sphere is adopted to describe the powder particles [

where _{ev} is the equivalent diameter of a ball of equal volume and _{dt,ij} is the tangential contact force of particle _{ct,ij} is the tangential contact force of particle _{dn,ij} is the normal contact force of particle _{cn,ij} is the normal contact force of particle _{i} and _{j} are the angular velocities of particle _{i} and _{j} are the velocities of particle _{i} and _{j} are the gravitational acceleration of particle _{n}, spring _{n}, and slider

When two spherical particles make contact and collide in space with radii _{1} and _{2}, respectively, the normal contact force _{n} can be expressed as

where

The tangential contact force _{t} can be obtained as follows:

where _{t} is the tangential overlap amount when the particles collide and _{t} is the tangential contact stiffness, which is shown in

where

The tangential damping force _{t} between two particles is shown in

where _{t}^{rel} is the relative tangential velocity when the particle collides.

The basic governing equations of the gas phase include the mass, momentum and energy conservation equations [

where

where _{D} is the interaction between the gas and the particles; and

The turbulent energy equation can be represented as

The turbulent dissipation rate equation can be written as follows:

where _{0} + _{t} (_{0} is the molecular viscosity; _{t} is the turbulent viscosity). _{k} represents the turbulent kinetic energy generated by the average velocity gradient; _{b} represents the turbulent kinetic energy generated by buoyancy; _{t} is the turbulent Prandtl number, and the correction coefficient can be obtained according to the standard k-ε turbulence model. _{k} = 1.0, _{s} = 1.0, _{1} = 1.0, and _{2} = 1.0.

The calculation domain of the coaxial nozzle simulation model is mainly divided into three parts. The upper part is a circular powder channel, the middle part is a funnel-shaped channel with different inclination angles, and the lower part is a cylindrical calculation domain of powder distribution. As shown in

To describe the geometric characteristics of the calculation domain of the coaxial powder feeding nozzle, the main parameters are set as shown in _{1} and _{2} are the heights of the funnel-shaped tapered ring and annular powder flow channels, respectively;

Parameter | _{1}/mm |
_{2}/mm |
|||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Numerical value | 10 | 60 | 1 | 5 | 5 | 4 | 6 | 10 | 5 | 20 | 15 | 5 | 4 |

ICEM grid preprocessing software is adopted to mesh the nozzle and the calculation domain. A hexahedral structured grid is selected to improve the quality and efficiency of the computing grid. Due to the different powder concentrations caused by different nozzle locations and the calculation domain, the key component grid should be refined, and the remaining grid should be appropriately divided into sparse structure grids on the premise of meeting the calculation requirements. The mesh sizes of the nozzle inlet, the cylindrical domain and the nozzle ring channel calculation domain are set as 0.8 mm, 0.75 mm and 1.5 mm, respectively. Since the contact parts of the three calculation domains are at the computing centre, the grid size is set to be 0.2 mm, and the partitioned grid is optimized. The mesh quality of the grids is set to 0.4 or above. The aspect ratio is set within 0–1, and the Jacobi matrix is set to 0.7 or above. The divided grid is shown in

The residual value of the FLUENT model is set as 0.001. The residual error is set to ensure that the relative difference of all equations in the adjacent time steps is within the specified range and to maintain the continuity of the gas-solid two-phase calculation. The simulation includes the continuity equation, momentum equation, _{2,} and the second phase is the particles. The inlets of powder flow and protective gas are set to velocity inlets, and the speed direction is perpendicular to the boundary. The velocities of carrier powder gas _{1} are 4 m/s and 1.5 m/s, respectively. The nozzle wall is set as the wall, and the nozzle outlet is the pressure outlet. Since the nozzle boundary is a free outlet, the pressure is set to 0 Pa. The exit boundary diameter of the calculation domain is 20 mm. The backflow turbulence intensity should not be set too large, so the backflow intensity in this manuscript is set to 0.5%. A phase-coupled SIMPLE algorithm is used. Spatial discretization is used in the discretization scheme. To ensure the convergence of the coupled model, a second-order upwind is selected.

Since the time step has a greater impact on the convergence of the DEM model than on the CFD model, the DEM time step is first determined in the coupled DEM-CFD model. The time step of the CFD model is an integer multiple of the time step of the DEM model. The calculation of the velocity and position information of the particles in the DEM model is a transient process. In the DEM model, it is assumed that the motion attributes of particles within a time step are unchanged. To improve the accuracy of the DEM model, the percentage of the Rayleigh time step is used to determine the time step of the model. The Rayleigh time step is the time required for the polarized wave generated by particle contact to pass through the hemisphere, which is shown in

where

To verify the rationality and reliability of the model, a powder transport verification experiment is performed. The powder feeding rate _{f} is 20 g/min. In the simulation, the particle size is set as 30 μm, and the specific parameters are shown in _{1} is the distance between the upper focal point of the powder flow and the nozzle outlet, which is the upper focal length; _{2} is the distance between the upper and lower focal points of the powder flow, which is the focal length; _{1} + _{2} is the lower focal length; _{3} is the laser defocusing amount; _{1} and _{2} are the diameter of the powder focal column and the spot diameter; and

Simulation parameter | Particle contact model | Gravity acceleration/^{2}) |
Particulate material | Particle Poisson’s ratio | Particle shear modulus/(N/m^{2}) |

Numerical value | Hertz-Mindlin (no slip) | −9.81 | Ni60A | 0.25 | 8 × 10^{9} |

Simulation parameter | Particle density/(kg/m^{3}) |
Geometry material | Geometry Poisson’s ratio | Geometry shear modulus/(N/m^{2}) |
Geometry density/(kg/m^{3}) |

Numerical value | 8000 | 45 steel | 0.36 | 7 × 10^{10} |
7800 |

Simulation parameter | Total particle generation rate/(g/min) | Particle incident velocity/(m/s) | Time Step/s | Data retention interval/s | Calculate the domain grid size |

Numerical value | 20 | 4 | 1 × 10^{−6} |
0.0005 | 4* |

The comparison between the simulated and experimental results is shown in

Data | Upper focus distance _{1}/mm |
Lower focal length _{1} + _{2}/mm |
Focus column length _{2}/mm |
Focus cylindrical diameter _{1}/(mm) |
---|---|---|---|---|

Experimental results | 16.0 | 20.0 | 4.0 | 2.5 |

Simulation results | 17.5 | 20.5 | 3.0 | 2.26 |

Accuracy | 90.6% | 97.5% | 75.0% | 90.4% |

The nozzle structure directly affects the trajectory of the powder flow and the agglomeration after being sprayed out. Based on the single factor method, the influences of the nozzle outlet width _{1} = 1.5 m/s, respectively. The powder feeding rate _{f} is 20 g/min. The angle between the nozzle wall and the horizontal plane is

Experiment number | Width of the nozzle outlet |
Inner and outer wall angle |
Angle of incidence |
---|---|---|---|

1 | 0.6, 1.0, 1.1, 1.3 | 10 | 90 |

2 | 1.0 | 8, 10, 11, 12 | 90 |

3 | 1.0 | 10 | 0, 30, 60, 90 |

To quantify the agglomeration of powder flow, the powder flow concentration per unit volume _{P}, as shown in

where _{P} is the volume occupied by powder particles per unit volume and _{f} is the volume occupied by air per unit volume. The greater the value of _{P} per unit volume of powder flow is, the better the powder flow agglomeration.

The angle between the inner and outer walls of nozzle

Experiment number | Width of nozzle outlet/mm | Simulation results | Experimental results | Accuracy | Simulation results | Experimental results | Accuracy |
---|---|---|---|---|---|---|---|

Upper focus distance _{1}/mm | Lower focal length _{1} + _{2}/mm |
||||||

1 | 16.5 | 16.0 | 96.88% | 18.5 | 17.8 | 96.07% | |

2 | 17.5 | 16.7 | 95.21% | 20.5 | 20.0 | 97.50% | |

3 | 18.5 | 18.0 | 97.22% | 21.9 | 21.5 | 98.14% | |

4 | 20.5 | 19.8 | 96.47% | 22.3 | 22.0 | 98.64% |

From the above simulation results, it can be seen that

Experiment number | Angle between inner and outer wall/° | Simulation results | Experimental results | Accuracy | Simulation results | Experimental results | Accuracy |
---|---|---|---|---|---|---|---|

Upper focus distance _{1}/mm | Lower focal length _{1} + _{2}/mm |
||||||

1 | 14.5 | 14.0 | 96.43% | 17.0 | 16.5 | 96.97% | |

2 | 17.3 | 16.8 | 97.02% | 20.5 | 20.0 | 97.50% | |

3 | 19.3 | 18.6 | 96.24% | 21.6 | 21.0 | 97.14% | |

4 | 20.3 | 19.6 | 96.43% | 23.3 | 22.8 | 97.81% |

_{1} of the powder coke column of the four nozzles with different _{1} becomes larger and the powder flow concentration per unit volume decreases. This is because the larger

It can be seen from the above simulation results that

Experiment number | Incident angle/° | Simulation results | Experimental results | Accuracy | Simulation results | Experimental results | Accuracy |
---|---|---|---|---|---|---|---|

Upper focus distance _{1}/mm | Lower focal length _{1} + _{2}/mm |
||||||

1 | 16.7 | 16.3 | 97.55% | 18.5 | 18.0 | 97.22% | |

2 | 9.5 | 9.0 | 94.44% | 16.0 | 15.8 | 98.73% | |

3 | 14.5 | 14.3 | 98.60% | 17.0 | 16.5 | 96.97% | |

4 | 17.5 | 16.8 | 95.83% | 20.5 | 20.0 | 97.50% |

From the above simulation results, it can be seen that

A smaller

The powder flow concentration per unit volume decreases as

When

This paper analyses the influence of three different structural parameters of the coaxial powder feeding nozzle on powder flow agglomeration from a single-factor point of view. Research on powder flow agglomeration under the coupling effect of various parameters has not been previously carried out. The powder flow agglomeration of the coaxial powder feeding nozzle under the combined action of different structural parameters needs further analysis. In addition, how to find the optimal structural parameters to effectively improve the powder utilization rate on the basis of the constructed laser coaxial powder feeding nozzle DEM-CFD gas-powder two-phase flow model needs further analysis. Therefore, based on the coupling of various parameters, the model has a certain generalization ability, and an optimization model of a laser coaxial powder feeding nozzle structure parameter with an optimal powder utilization rate as the main optimization goal will be the focus of future efforts.