In order to solve the problem of poor powder flow convergence effect of the four-channel coaxial powder feeding nozzle for laser cladding, the structural parameters of the four-channel coaxial powder feeding nozzle were simulated and optimized. First, a two-dimensional structure diagram of the nozzle was established, and the influence of the nozzle structural parameters on the powder convergence morphology was analyzed using a theoretical model; then, based on the gas-solid two-phase flow theory, the structural parameters of the laser cladding four-channel nozzle were simulated and analyzed using finite element simulation software, and the variation law of the powder flow parameters under different structural parameters and the distribution law of the external flow field concentration were explored, and a reasonable range of structural parameters was obtained; finally, a powder feeding test was carried out on the nozzle after parameter optimization, and the test results were compared and verified with the simulation results. The research results show that: when the nozzle powder tube inclination angle increases, the focal length increases, and the powder concentration increases rapidly and then stabilizes, and the inclination angle is suitable between 60° and 75°; when the inner diameter of the nozzle powder tube increases, the powder concentration and focal length increase first and then decrease, and the powder spot diameter decreases first and then increases, and the inner diameter is suitable at about 1.5 mm; when the spacing at the nozzle powder tube outlet increases, the focal length increases, and the spacing is suitable at about 12 mm; when the inner diameter of the nozzle incident tube increases, the powder feeding speed increases, and the powder concentration decreases, and the inner diameter of the incident tube should be matched with the conveying tube as much as possible; when the nozzle outer protective gas inclination angle is 35°~65°, the protective gas acts at the powder flow convergence. The test results verify the accuracy of the model, the powder spot diameter is 2.2 mm, the powder focal length is 16.1 mm, and the powder convergence effect is good. This model can provide a reference for improving the nozzle powder feeding effect. Keywords: Additive manufacturing technology; Powder flow convergence effect; Coaxial powder feeding nozzle; Numerical simulation; Structural parameters; Powder flow

Laser cladding technology is an additive manufacturing technology that has emerged in recent years. This technology can be used to repair complex parts with high processing costs or improve the surface performance of workpieces, thereby effectively reducing production and manufacturing costs [1-2].

In the laser cladding process, powder delivery is an important factor. Good powder delivery can provide a stable and high-quality cladding layer. As an important component of powder delivery, the nozzle directly affects the convergence state of powder particles. Among them, the coaxial powder feeding nozzle is the most widely used in this technology. Coaxial powder feeding nozzles are divided into ring type and multi-channel type.

The powder flow formed by the ring type has better convergence and smaller powder spots, but the powder chamber is easy to clog and the powder utilization rate is low. The three-channel and four-channel nozzles are the current mainstream multi-channel coaxial powder feeding nozzles. Compared with the ring type, the multi-channel coaxial powder feeding nozzle has a simple structure. The multi-channel powder tube can set a variety of powder feeding ratios. At the same time, the powder focus is far away from the substrate surface, which can adapt to substrates with more complex surface morphology and is not easy to cause powder blockage [3-4]. In the coaxial powder feeding laser cladding technology, the powder spot diameter, powder spot focal length, powder concentration, and the uniformity and stability of the powder flow are the key parameters affecting the quality of the cladding layer. The powder feeding nozzle, as a key component that determines these parameters, has received extensive attention from domestic and foreign scholars. Among them, the influence of the nozzle’s structural parameters on the above parameters is particularly significant. In order to obtain better cladding forming quality, the various structural parameters of the coaxial powder feeding nozzle must be reasonably optimized. At present, domestic and foreign scholars have conducted extensive research on the powder feeding process of the laser cladding nozzle and the powder convergence of the nozzle’s external flow field based on the gas-solid two-phase flow theory. ARRIZUBIETA J I et al. [5] conducted numerical simulations on parameters such as powder concentration, powder feeding speed, and powder utilization, and changed the internal structure of the coaxial nozzle to improve the uniformity of powder delivery; however, this study only analyzed the powder distribution when the nozzle worked in the vertical direction. Duan Jiawei [6] used simulation software to simulate the relationship between nozzle structural parameters and powder feeding effect, and designed a powder feeding nozzle with double-sided powder feeding and flow channel contraction, which improved the powder utilization rate; however, during the powder feeding process, the gas-solid two-phase flow model and parameter settings did not fully match the actual situation and needed further optimization. Liu Jie [7] conducted simulation optimization design on the structure of a ring nozzle, determined the reasonable range of structural parameters, and used the optimized nozzle to conduct powder feeding experiments, effectively improving the working performance of the original nozzle; however, the actual processing nozzle was printed with photosensitive resin (instead of metal manufacturing), which has certain limitations. Guo Chenguang et al. [8] conducted a three-dimensional powder feeding nozzle gas-powder flow field simulation analysis based on the characterization parameters such as the powder flow distribution concentration on the central axis and the powder flow distribution concentration per unit distance, and obtained the influence of the powder feeding process parameters on the powder flow distribution; however, they did not analyze the influence of each factor on the powder spot diameter. GRIGORYANTS A G et al. [9] established a mathematical model for powder spray convergence, determined the optimal geometric parameters of the nozzle, and used simulation software to verify and determine the optimal parameters of powder particle size and carrier gas flow; however, they did not consider the influence of the interaction between the parameters on convergence. Yan Ruifeng et al. [10] used three-dimensional modeling simulation and image processing software to study the influence of the process parameters of the coaxial powder feeding nozzle on the powder flow and flat-top laser coupling effect, and obtained a reasonable powder disk rotation speed and carrier gas flow rate; however, they did not consider the influence of the nozzle design optimization on the powder flow field. SACHIN A et al. [11] studied the effect of nozzle inclination on powder flow dynamics and powder capture efficiency and found that the inclined nozzle would lead to asymmetry and deflection of the powder jet, and the powder capture efficiency would decrease rapidly with the increase of nozzle inclination; however, the improvement measures proposed lacked practical verification. Yang Guang et al. [12] obtained the gas pressure parameters to improve the problem of poor nozzle powder convergence by simulating the effect of different air curtain pressures on powder flow; however, the above study only focused on three different pressure conditions and did not explore a wider range of gas pressure. GAO Xiang et al. [13] used the discrete element method to simulate the interaction between powder particles and gas flow and evaluated the effect of nozzle geometry on powder flow behavior in laser cladding; however, it did not consider the effect of channel diameter in the geometry on powder capture rate. At present, scholars have mainly studied the process parameters of coaxial powder feeding or the structural parameters of annular nozzles, but less research has been conducted on the influence of various structural parameters of multi-channel nozzles on the powder convergence of the external flow field. The author establishes a two-dimensional structural model of a four-channel coaxial powder feeding nozzle, establishes the geometric relationship between the powder tube inclination angle, powder tube inner diameter, powder tube radius, incident tube radius, and external protective gas inclination angle and focal length, focal depth, and focal radius; based on the gas-solid two-phase flow principle, a three-dimensional four-channel powder flow channel numerical model is established to analyze the influence of various structural parameters on the powder flow field convergence outside the nozzle, in order to establish a theoretical research foundation for the optimization design of multi-channel coaxial powder feeding nozzles and further improve the morphology quality of the cladding layer.

1 Four-channel nozzle numerical model

As a key component in the laser cladding system, the four-channel nozzle usually forms the entire laser cladding system together with the laser, powder feeding device, etc.
During the cladding process, the laser is transmitted and focused through an optical system (such as a reflector, focusing mirror, etc.) to form a light spot of a certain shape and diameter; at the same time, the powder feeding device evenly and stably delivers the metal powder to the four powder feeding channels of the nozzle at a certain speed and flow rate; at the nozzle outlet, the laser beam and the powder flow almost simultaneously reach the cladding area, and the metal powder is rapidly melted under the influence of the high-energy laser beam and metallurgically combined with the substrate to form a cladding layer.

1.1 Establishment of the geometric model of the four-channel powder feeding nozzle

The four-channel powder feeding nozzle is one of the key components of laser cladding.

The nozzle’s powder tube inclination angle, powder tube inner diameter and other structural parameters directly affect the powder convergence, powder spot diameter, powder focal length, uniformity and other parameters.

In order to study the relationship between the nozzle’s geometric size parameters and the powder flow convergence, the author proposed a series of hypotheses [14-15] for the movement process of powder particles and established a two-dimensional structural model of the powder feeding nozzle.
The assumptions are as follows: 1) The powder velocity is consistent with the carrier gas velocity, and the speed and direction of the gas powder ejection along the nozzle powder tube at the outlet remain constant; 2) The collision between particles and the divergence of the protective gas outside the nozzle are not considered; 3) Under the rectification of the carrier gas and the nozzle structure, the powder is evenly dispersed when ejected; 4) The powder particles are uniformly spherical with a diameter of 80 μm. The two-dimensional structure of the coaxial nozzle is shown in Figure 1. It can be seen from Figure 1 that: under the premise of ignoring the collision effect, the powder should move along the inclination direction of the powder tube, and after the nozzle rectification, it will continue to move along the powder tube outlet direction, and finally form a powder flow convergence (theoretically converge into a cylindrical area). However, smaller powder particles will have fluid-like properties, which makes the powder divergent after ejection and deviate from the motion trajectory, and the diameter of the convergence area increases, thereby affecting the quality of laser cladding. Based on the relationship between each structural parameter and the powder focal length, focal depth and focal radius, the author deduced the powder flow convergence influence function:
See (1)-(4) in the figure

Where: f1, f2 are the upper focal length and lower focal length of the powder flow convergence focus;
r4, r5 are the projections of the powder delivery channel outlet radius 1/2d1 in the x-axis and y-axis directions; r is the distance from the center point of the powder tube outlet to the center axis of the nozzle; α is the angle between the powder tube and the x-axis;
d1 is the inner diameter of the powder tube outlet; γ is the powder flow divergence angle.
The focal depth h between the upper and lower focal lengths of the powder flow convergence is: (5)

The radii r2 and r3 of the powder flow convergence focus are: (6), (7)

The external protective gas inclination angle β should be within an appropriate range to act on the powder flow convergence area, that is: (8), (9)

In multi-channel coaxial powder delivery, when the carrier gas flow rate and powder delivery amount remain unchanged, the difference in the coaxial nozzle structural parameters will change the focal length and powder spot diameter, thereby affecting the powder flow convergence.

1.2 Continuous phase control equation
The simulation of the powder convergence motion process in the external flow field of the coaxial nozzle belongs to the complex problem of gas-solid two-phase flow. The model solved in the simulation process is usually the Euler model and the discrete phase model. Among them, the Euler model regards discrete particles as pseudo-flow, so when calculating, both the particle phase and the gas phase are treated as continuous phases to reduce the amount of calculation and calculation time.

Since the particle phase accounts for a relatively low proportion of the two-phase mixture (generally 10%~12%), the discrete phase model does not have fluid characteristics and the influence of the interaction can be ignored. Therefore, the powder-carrying gas flow can be regarded as the continuous phase and the powder particles as the discrete phase [16-17]. In the laser cladding process, since the volume ratio of the powder particles (316L iron powder) under the action of the carrier gas (nitrogen) is less than 10%, the author uses the discrete phase model to simulate and analyze the flow field outside the nozzle. To facilitate the simulation calculation, the author makes the following assumptions in the calculation [18]: 1) The influence of laser energy and other heat sources on the movement of gas-solid two-phase flow is not considered; 2) The carrier gas flow rate and the powder particles enter the velocity calculation domain with the same initial velocity; 3) Only the gravity and additional mass force of the continuous phase and the discrete phase are considered; 4) The powder flow field is a stable and uniform flow field and does not change with time. In the discrete phase model, the gas is an incompressible gas. Therefore, the author ignores the thermal effects between powder particles, and based on the Navier–Stokes (N–S) equation and the Reynolds average time method, the continuous phase model is modeled, and combined with the realizable k-ε turbulence model (the model was proposed by SHIH TH et al. [19]), the corrected equation of the dissipation rate is accurately derived, making it superior to the standard model in terms of jet, channel and boundary layer flow. The basic control equations of turbulence include the continuity equation and the momentum equation. Among them, the turbulent kinetic energy k equation and the dissipation rate ε equation are as follows: (10)-(12)

Where: μ is the laminar dynamic viscosity; μ1 is the eddy viscosity, which is usually calculated by k and ε and an empirical constant Cμ. Unlike other k-ε models, Cμ is not a constant, but a function of laminar strain and curl; Gk is the turbulent kinetic energy generated by the laminar velocity gradient; Gb is the turbulent kinetic energy generated by the buoyancy; YM is the fluctuation caused by excessive diffusion in compressible turbulence; ρ is the compressed gas density; k is the fluid dynamic viscosity; ε is the turbulent dissipation rate; C1 is an empirical constant; the constant C3ε determines the degree to which ε is affected by buoyancy; v is the flow velocity; σk, σε are the turbulent Planck numbers corresponding to the turbulent kinetic energy k and the dissipation rate ε.

Where: subscripts i and j are time-averaged continuity equations expressed in tensor indices; Sk and Sε are user-defined; the values ​​of C1ε, C2, σk, σε are optimized as model constants and are defined as C1ε=1.44, C2=1.9, σk =1.0, σε =1.2.

1.3 Calculation equations for discrete phase particles
In Fluent simulation, the trajectory of discrete powder particles is described by the Lagrangian method. Ignoring the volume proportion of particles in the powder flow, the governing differential equation for the force balance of particles is: (13)
Where: up is the velocity of the powder particles; gx is the gravitational acceleration in the x direction; FD is the unit mass drag on the particles; Fx is the additional force, including thermophoretic force and Saffman lift, etc. The calculation process only considers the particle’s own weight and apparent mass force.

2 Numerical simulation experiment

The author established a three-dimensional flow channel model of a laser cladding four-channel powder feeding nozzle in SolidWorks.
The flow channel calculation model of the nozzle is shown in Figure 2.

In Figure 2 (a), the three-dimensional model of the nozzle is composed of the inner protective gas channel, the powder feeding channel and the outer protective gas channel from the inside to the outside. Among them, the powder feeding channel consists of two sections of pipes, and the inner diameters of the front section incident pipe and the rear section conveying pipe are different.
In order to obtain relatively accurate simulation results, the cylindrical area in Figure 2 is an air domain that is much larger than the calculation domain; the entrances of each channel are velocity entrances, named as the inner protection entrance, powder feeding entrance, and outer protection entrance respectively; the air domain is set as the outlet and all are pressure outlets; the walls of each channel are uniformly named as the wall surface, and then the elastic recovery coefficient, the incident velocity of each channel, the solver and other parameters are set to simulate and analyze the various structural parameters.
Since the author mainly studies the single factor influence of each structural parameter on the powder convergence of the external flow field, the other parameters should be unified when solving the calculation domain. Among them, the powder feeding amount is 15 g/min, the inner protective gas speed is 3 m/s, the powder carrier gas speed is 5 m/s, and the outer protective gas speed is 7 m/s. In Figure 2 (b), the author uses Fluent-mashing to mesh the model, encrypts the powder flow convergence area, and uses Poly-hexcore to mesh it.

3 Experimental results analysis

3.1 Effect of nozzle powder tube inclination on convergence

The author uniformly sets the inner diameter of the powder tube to 1.5 mm and the spacing at the powder tube outlet to 6 mm.

The powder convergence concentration of the axial and radial plane outer flow field of the nozzle with different powder tube inclination angles is shown in Figure 3.

In Figure 3, as the nozzle powder tube inclination angle increases, the powder focal length increases, the powder convergence is more concentrated, and the powder spot shape is more regular.
The reason for this phenomenon is that due to the influence of the structure, a larger inclination angle makes the powder flow converge far away from the nozzle outlet, and the convergence focus is farther from the nozzle outlet; a smaller inclination angle causes the powder flow to converge near the nozzle, and the powder flow is sprayed at a larger angle, which increases the dispersion between powder particles, and the diffusion effect makes the powder spot shape irregular; while a larger inclination angle allows the powder flow to converge after forming a stable flow state, reducing the divergence of powder particles, making the powder spot shape more regular, and the convergence concentration higher.
Under the same conditions, the powder concentration distribution of different nozzle powder tube inclination angles along the central axis Y direction is shown in Figure 4.

It can be seen from Figure 4 that as the nozzle powder tube inclination angle increases, the powder focal length increases, and the powder concentration rises first and then stabilizes.
This is because the smaller inclination angle causes the powder to scatter severely at the nozzle outlet, and at a larger powder flow injection angle, the powder particles are more affected by gravity and airflow, which intensifies the powder scattering, resulting in low powder concentration. The powder convergence area is easily affected by the protective gas, further reducing the concentration; at the same time, the scattered powder may splash and block the nozzle, which is not conducive to the powder feeding experiment, so the inclination angle should not be too small.
As the inclination angle increases, the powder flow gradually stabilizes, and the powder convergence concentration also increases accordingly. However, when the inclination angle is too large, the concentration growth slows down, and when the inclination angle is 75°, due to the large focal length of the powder, the powder stiffness is insufficient due to the increase in the effect of gravity, causing the powder concentration to fluctuate when it starts to converge, so the inclination angle should not be too large.
In summary, the appropriate powder tube inclination angle is between 60° and 75°.

3.2 Influence of the inner diameter of the nozzle powder tube on convergence
The author uniformly sets the nozzle powder tube inclination angle to 65° and the spacing at the nozzle powder tube outlet to 6 mm.
The distribution of powder concentration along the Y direction of the central axis of the nozzle with different powder tube inner diameters is shown in Figure 5. It can be seen from Figure 5 that the inner diameter of the nozzle powder tube has a significant effect on powder convergence. As the inner diameter of the powder tube increases, the powder concentration and powder focal length both show a trend of increasing first and then decreasing. When the inner diameter of the powder tube is 0.5 mm, the concentration is almost 0, because the flow resistance of the powder in the powder tube is too large, resulting in powder blockage; when the inner diameter of the powder tube is 1 mm, the powder begins to converge but the concentration fluctuates greatly. Because the flow resistance in the powder tube is still large, some powder cannot be effectively used, so there is still blockage in the powder tube. At the same time, the powder diverges severely after being sprayed from the nozzle, resulting in poor powder flow convergence effect, so the powder concentration distribution fluctuates greatly; when the inner diameter of the powder tube is 1.5 mm, the powder concentration curve is approximately Gaussian distribution, the powder forms a stable powder flow, and the concentration increases rapidly to 22.9 kg/m3 after convergence, and then rapidly decreases to 0 kg/m3, almost without the influence of powder divergence; when the inner diameter of the powder tube is 2 mm ~2.5 mm, the powder concentration decreases. This phenomenon occurs because the tube diameter is too wide, which makes the distribution range of powder particles in the powder tube space wide, resulting in insufficient gas stiffness and difficulty in forming a highly concentrated powder flow. Therefore, the diameter of the sprayed powder flow beam becomes larger and the dispersion is high, resulting in a decrease in concentration. The powder focal length increases first and then decreases with the increase of the inner diameter. When the inner diameter is small, the powder is severely blocked. When the inner diameter is large, the powder flow diameter increases, the convergence position is advanced, and the focal length decreases. Under the same conditions, the powder convergence of different nozzle powder tube inner diameters along the convergence plane X direction is shown in Figure 6. It can be seen from Figure 6 that when the inner diameter is 0.5 mm, due to severe powder blockage, the powder flow fails to converge to form an effective powder spot. As the inner diameter of the nozzle powder tube increases, the powder spot diameter decreases first and then increases. When the inner diameter is 1 mm, the powder still fails to form a stable powder flow, and the powder is scattered, resulting in irregular powder spots with large diameters; when the inner diameter is 1.5 mm, the powder flow is stable, so the powder spot diameter is close to the inner diameter of the powder tube; when the inner diameter is 2 mm ~ 2.5 mm, the convergent powder spot diameter increases due to insufficient gas stiffness and the increase in the diameter of the powder flow beam.
In summary, under the premise of ensuring that the powder is not blocked and sprayed stably, in order to obtain a smaller powder spot diameter, the smallest possible inner diameter should be selected, that is, the inner diameter is about 1.5 mm.

3.3 Effect of the spacing at the nozzle powder tube outlet on convergence
The author uniformly sets the nozzle powder tube inclination angle to 65° and the nozzle powder tube inner diameter to 1.5 mm.
Under the same conditions, the powder concentration distribution along the central axis Y direction and along the convergence plane X direction of the nozzle powder tube outlet spacing is shown in Figure 7.

As shown in Figure 7, the distance between the nozzle and the powder tube outlet has a significant effect on the powder focal length. As the distance between the powder tube outlet increases, the powder focal length increases, the concentration slowly decreases, and the powder spot size remains almost unchanged. The reason for this phenomenon is that due to the influence of structural parameters, the distance between the powder tube outlet increases, resulting in a large initial width of the powder flow, which requires a longer distance to converge, and the focal length increases accordingly; at the same time, since the powder needs a longer distance to converge after being ejected from the nozzle, it is more susceptible to gravity and air resistance, resulting in insufficient gas stiffness, which reduces the amount of powder carried and reduces the powder concentration; but it does not affect the powder aggregation performance, so the powder spot size is stable. In order to avoid high temperature burning of the nozzle, when the distance between the powder tube outlet is about 12 mm, the powder focal length is more appropriate if the structural design allows. 3.4 Influence of the inner diameter of the nozzle incident tube on convergence
The author uniformly sets the inner diameter of the nozzle delivery tube to 1.5 mm, the inner diameter of the nozzle incident tube to 2 mm, and the carrier gas velocity to 5 m/s. The velocity vector distribution of the nozzle single powder tube along the axial plane is shown in Figure 8.

It can be seen from Figure 8 that: when the inner diameter of the nozzle incident tube is smaller than the inner diameter of the nozzle delivery tube, the powder delivery speed will decay to about 1.78m/s due to the increase in space; when the inner diameter of the nozzle incident tube is equal to the inner diameter of the nozzle delivery tube, the powder delivery speed remains almost unchanged; when the inner diameter of the nozzle incident tube is larger than the inner diameter of the nozzle delivery tube, the powder delivery speed increases sharply due to the narrowing of the delivery space. Therefore, the larger the inner diameter of the nozzle incident tube, the greater the powder delivery speed.
Under the same conditions, the powder concentration distribution of different nozzle incident tube inner diameters along the central axis Y direction and the convergence plane X direction is shown in Figure 9.

It can be seen from Figure 9 that: when the inner diameter of the nozzle incident tube is equal to the inner diameter of the conveying tube, the powder concentration is the highest, and the powder spot concentration is more evenly distributed along the central axis; if the inner diameter of the nozzle incident tube is smaller than the inner diameter of the nozzle conveying tube, the gas stiffness will be insufficient due to the reduced powder feeding speed, causing serious powder dispersion. Therefore, there are obvious fluctuations when the powder converges, and the powder concentration is unevenly distributed; if the inner diameter of the nozzle incident tube is larger than the inner diameter of the nozzle conveying tube, the powder feeding speed is too large, which will cause the number of powder particles ejected per unit time to increase, the distribution range is too wide, and the powder concentration will decrease or even fail to form an effective powder spot. In summary, in order to maintain a good powder feeding effect, the inner diameter of the incident tube should be matched with the conveying tube as much as possible. 3.5 Influence of the inclination angle of the nozzle outer protective gas on convergence The author uniformly sets the nozzle powder tube inclination angle to 65°, the nozzle powder tube inner diameter to 1.5 mm, the nozzle incident tube inner diameter to 2 mm, and the nozzle powder tube outlet spacing to 6 mm. The powder convergence concentration of the external flow field in the axial and radial planes of the nozzle with different external protective gas inclination angles is shown in Figure 10.

As shown in Figure 10, the effect of the nozzle external protective gas inclination angle on the size of the powder spot diameter and the focal position is not obvious. When the inclination angle is 35°, the powder flow is subjected to a certain tangential velocity by the external protective gas flow, resulting in a tighter powder flow of powder particles to converge toward the center, but the divergence will cause the powder spot shape to be irregular; when the inclination angle is 50°, the powder is evenly distributed at the convergence point and the powder spot shape is regular; when the inclination angle is 65°, the powder flow diverges, which is similar to the case without external protective gas, with little difference.
Under the same conditions, the powder concentration distribution along the Y direction of the central axis of the nozzle with different external protective gas inclination angles is shown in Figure 11.

As shown in Figure 11, when the inclination angle is 35°, the external shielding gas mainly acts on the upper part of the powder flow convergence area, and its rectifying effect causes the powder to converge to the center and increase the powder concentration; when the inclination angle is 50°, the gas almost completely acts on the powder flow convergence, and the powder particles at the powder convergence are more evenly distributed, while the concentration at the focus is lower than that without external shielding gas; when the inclination angle is 65°, the external shielding gas flow is parallel to the powder-carrying gas flow, and has little effect on the convergence area, so the powder concentration curve is not much different from that without external shielding gas.
In summary, the inclination angle of the nozzle external shielding gas should be between 35° and 65°, which can make the powder concentration change little, and the distribution in the convergence area more uniform and the shape more regular.

3.6 Parameter optimization and experimental verification
According to the influence of the above structural parameters on the convergence of powder flow, the author optimizes the nozzle and designs and manufactures the actual object.
The laser cladding system and the actual nozzle are shown in Figure 12.

In Figure 12, the laser cladding system used in the experiment consists of ABB2600, Chuangxin MFSC 3000X series fiber laser, cooler and powder feeder; the nozzle is made of copper with good thermal conductivity. According to the simulation results, the author selects reasonable structural parameters to optimize the nozzle structure. The optimized nozzle structural parameters are shown in Table 1. Under the same powder feeding amount, carrier gas speed, shielding gas speed and other conditions, the author installed the optimized coaxial powder feeding nozzle on the laser cladding system, carried out powder feeding experiments, and compared the experimental results with the simulation results to verify the reliability of the model. The comparison between the experimental results and the simulation results is shown in Figure 13. It can be seen from Figure 13 that the powder in each channel is stable, there is no obvious divergence phenomenon, and the powder convergence is good, and the powder utilization rate is high; at the same time, the simulation and experimental results of the powder spot diameter and powder focal length have errors of 10% and 1.9% respectively, both of which do not exceed 10%. This shows that the simulation results fit well with the test results; the simulation results of this model have high accuracy, and the model has high reference value for flow field simulation.

4 Conclusion
The author established a two-dimensional structural model of a four-channel laser cladding coaxial powder feeding nozzle, and established the geometric relationship between various structural parameters and focal length, focal depth, and powder spot diameter; based on the principle of gas-solid two-phase flow, a three-dimensional flow channel model of a four-channel powder feeding nozzle was established, and the effects of various structural parameters on the convergence of powder in the nozzle flow field were studied; the optimized nozzle was tested on a prototype to verify the accuracy of the simulation results.
The research conclusions are as follows:
1) When the nozzle powder tube inclination angle increases, the powder focal length increases, and the powder concentration increases first and then stabilizes. When the powder tube inclination angle is 60°~75°, the powder flow is stable and the powder can be gathered in a safe position; when the nozzle external protective gas inclination angle is too small, the powder convergence and divergence will be serious, and when it is too large, the external protective gas flow will not act on the powder convergence area; when the nozzle external protective gas inclination angle is 35°~65°, the external protective gas flow acts on the convergence area, the powder concentration distribution is more uniform, and the powder spot shape is more regular;
2) When the nozzle powder tube inner diameter increases, the powder focal length increases first and then decreases, and the powder concentration also tends to increase first and then decrease. Under the premise of ensuring that the powder is not blocked and can be sprayed stably, in order to obtain a smaller powder spot diameter, the inner diameter of the nozzle powder tube should be as small as possible. The appropriate nozzle powder tube inner diameter is about 1.5 mm; at the same time, the powder delivery speed will increase with the increase of the inner diameter of the nozzle incident tube. In order to maintain a good powder delivery effect, the inner diameter of the incident tube should be matched with the conveying tube as much as possible; 3) The spacing at the nozzle powder tube outlet mainly affects the powder focal position. The nozzle powder tube outlet spacing is in direct proportion to the powder focal length. The larger the powder tube outlet spacing, the larger the powder focal length. When the powder tube outlet spacing is about 12 mm, the powder focal length is appropriate; the optimized four-channel nozzle powder spot diameter is 2.2 mm, the powder focal length is 16.1 mm, the powder flow does not have obvious divergence, the powder convergence is good, and the powder utilization rate is high. In subsequent research, the author will conduct multi-objective optimization research on the influence of various structural parameters, and establish a regression model of structural parameters and powder flow convergence characteristics, in order to obtain an ideal combination of structural parameters.