Laser metal deposition (LMD) is a blown powder process which can be used for the additive manufacturing of large components or the generation of functional geometries on semifinished parts. In LMD, it is crucial that both the laser intensity and powder mass flow distribution within the process zone are precisely matched for a welding bead of predefined shape and a consistent layer quality. While there are many common tools for the characterization of laser intensity distributions, a deep understanding of powder propagation behavior is still missing. Therefore, the present work thoroughly characterizes the powder stream propagation behavior of a discrete coaxial nozzle with three angle-adjustable powder jets. A line laser is used to selectively illuminate individual layers horizontally to the nozzle, and the intensity of the illuminated powder is recorded with the aid of a CCD camera. An envelope of the powder distribution is then plotted from the individual layers, analogous to a caustic of a laser beam, and, thus, the powder stream is evaluated. A novel method is presented to compensate for the radial asymmetry of a discrete powder nozzle in the evaluation, thus making it comparable with continuous nozzles. The method is validated by characterizing the powder stream propagation behavior of a three-jet discrete nozzle. Influencing factors on the powder stream are the protective gas flow, the powder mass flow, the angle of the powder nozzles, and the interaction of the three powder jets. The investigations are supplemented by a point-particle large-eddy simulation of the particle-laden flow.

## I. INTRODUCTION

In the field of production technology, additive manufacturing is becoming increasingly important for the processing of metallic materials.^{1} It is used to produce prototypes, end products, and also various tools. The buildup rate for additively manufactured components is of particular importance. It is a characteristic value that can be used to evaluate productivity and, thus, economic efficiency. With the laser metal deposition (LMD) process, comparatively high buildup rates can be achieved, which are significantly higher than those in laser powder bed fusion (LPBF). However, the LMD process is not yet able to achieve the high geometric flexibility and resolution in printed components that is possible with the LPBF process.^{2} Most commonly used powder nozzle types for 3D-LMD are discrete nozzles, which have multiple powder streams, and continuous nozzles, which have a single stream from an annular gap.

The importance of the powder stream propagation in LMD has already been presented in many studies. A strong sensitivity of powder defocusing on build capabilities in LMD was presented by Zhu *et al*.^{3} and Zekovic *et al*.^{4} Prasad *et al*. showed that a powder stream that is well-focused to the melt pool does not only lead to a better catchment efficiency but can also lead to more precise geometrical features.^{5} The ideal position of the powder focus in respect to the melt pool for a high catchment efficiency can change with process parameters.^{6} Thus, for each requirement in weld bead width (e.g., filling and contour), a different nozzle with a predefined powder stream shape and powder focus may be used.

With a change in powder feed rate, the average speed of powder particles is almost constant, leading to the assumption that the volume fraction of particles in the powder flow is so small that an increase in powder leads to no effect in the trajectories of the particles in a four-jet nozzle.^{7} For this nozzle type, an increase in carrier gas flow rate leads to a higher divergence at the powder nozzle exit, as well as to an decrease of powder concentration.^{7–9} For a continuous nozzle, a change in powder mass flow rate shows no influence on the distance of the nozzle exit to the merging point of the powder stream.^{10} It is also stated that overall powder flow convergence increases in continuous nozzles with higher carrier gas flow rates due to a straighter particle trajectory and a suppressed diffusion of the powder distribution.^{11}

To gain more insight into the powder stream characteristics, different methods are utilized. The powder stream characterization can be carried out from different directions. Common is the observation from the side, resulting in a vertical view of the powder stream as a whole or a slice of it, depending on illumination. Another direction would be from above/below, resulting in images of horizontal slices of the powder stream, by means of illumination. When having a side view of the powder, the trace length of an illuminated particle captured with a fixed shutter speed can be used to calculate particle velocity.^{7,8,12} In high-speed recordings, particles can be tracked through multiple frames to calculate their velocity.^{13} Another approach in powder stream characterization is digital holographic particle image velocimetry,^{14} which has a rather complex experimental setup. A different characterization method was introduced by Mouchard *et al*. where simulations were used to reverse engineer the powder stream from blowing powder onto a test substrate.^{15}

A precise numerical simulation of laser metal deposition is beneficial in several aspects. Investigation of the LMD process using experiments requires a lot of expensive and technically difficult trials, while the computational fluid dynamics methods provide fast solutions with much lower cost. Numerical simulation of the LDM process allows us to isolatedly study the relevance of each control parameters and provides a full, three-dimensional set of variables over the entire parameter space. In addition, parameters can be derived from simulations which cannot be experimentally obtained. Numerical simulations based on the two-way coupling Eulerian–Lagrangian model have been intensively used in previous work to deepen the understanding of the relevant factors affecting the powder stream behavior.^{4,7,11} In this model, while the carrier gas flow is computed by solving the Navier–Stokes equations, the powder stream is calculated by solving the Lagrangian equation of the particle motion. To account for turbulence, almost all previous numerical simulations of the powder flow in LMD processes considered RANS model.^{8} Although there is a strict assumption associated with applying the turbulence models, that is the flow has to be fully turbulent, it sometimes occurs that the flow within the nozzles is laminar. In this work, we employ fully resolved large-eddy simulations to overcome this constraint and also to enhance fidelity of the results. In this approach, large energy-containing eddies are resolved and the small isotropic and homogeneous eddies are modeled.

For continuous gap nozzles, Ferreira *et al*. calculated the powder spot diameter by setting limits for an inner and external diameter at encompassing 1% and 86% of the maximal luminosity of the lightened particles.^{12} From these diameters at every standoff distance, a reconstruction of the powder stream caustic is presented. Liu *et al*. defined their powder diameter as the range in which 86.5% of all detected particles are, assuming that the powder at the stream waist has a gaussian distribution.^{16} Li *et al*. used 14% of the peak concentration of measured powder to calculate a powder spot diameter.^{13}

It was proposed to distinguish the powder stream below the nozzle tip into three zones: annular zone, consolidation zone, and dispersed zone^{10} or prewaist, waist, and dispersion region.^{9} A similar distinction into zones has been given by Liu *et al*. where the starting and ending point of the waist region are suggested.^{16} The waist region being the region where the powder stream has a gaussian distribution. Wen *et al*. proposed for a continuous nozzle that the beginning of the waist region is where the powder stream merges to one stream and the end to be where the powder concentration in the center decreases and the powder stream then begins to diverge.^{17}

In summary, it can be said that different methods for the characterization of powder streams have been presented, showing the growing interest in this research area. Most methods have been accompanied by simulations as well as simulation-only approaches to get a deeper understanding of the influencing factors on powder stream propagation. Some of these methods can also be used for a quality control of nozzles by giving quantifiable values, such as powder spot diameter and the working distance. For different nozzle types, these values can differ due to different stream propagations. A specific range in standoff distance to the nozzle will lead to a stable powder delivery and an accurate buildup geometry^{4,18} as well a good catchment efficiency if the laser spot size is also taken into consideration.^{19} This paper introduces a method to make the characteristics values such as the powder spot diameter and working distance applicable for different nozzle types by introducing an equivalent powder spot diameter, which is radially averaged. With this method, the influence of powder mass flow rate, shielding and carrier gas flow rates, as well as the inclination angle of the nozzles on the powder stream propagation are investigated.

## II. EXPERIMENTAL SETUP AND METHODS

### A. Experimental setup

The powder nozzle setup consists of three individually adjustable ceramic tubes (inner diameter = 1.7 mm) within a copper outer shell, usually used for lateral powder feeding. An Oerlikon Twin-150 powder feeder is used with AISI 316L powder. A stream of argon carrier gas will feed the powder to the process zone, where additional argon shielding gas meets the powder stream. To examine only a single horizontal layer of the powder stream, a line laser is used for illumination, as depicted in Fig. 1. The line laser has a wavelength of 650–655 nm, 10 mW of power, an opening angle of 20° and an approximate height of 150 *μ*m at the used distance. The laser is mounted onto a height adjustable table. A CCD camera (Allied Vision Mako G030C) is mounted lateral in regard to the nozzle on the same table as the line laser to ensure a consistent lighting of the powder.

The inclination angle of the three nozzles is varied between 23°, 39°, and 55° in respect to the vertical. The powder mass flow is raised in 3 g/min increments from 3 to 18 g/min. Shielding and carrier gas flow rates are varied between 5 and 15 l/min and 3 and 15 l/min, respectively.

### B. Data acquisition and analysis

The data processing procedure is depicted in Fig. 2. Videos are recorded with a set number of 100 frames. The exposure time varies. A mean image from these frames is calculated to compensate for fluctuations which may appear in the powder stream.^{20} An image which shows just the nozzle is subtracted from the image showing the nozzle and powder to eliminate the nozzle for future analysis. In order to obtain an undistorted image, a homography matrix is calculated for the transformation of the obtained images. The chessboard pattern which is used to generate the homography matrix also gives a conversion factor for pixels into millimeter. These transformed images can now be stacked and shown in false color to achieve an envelope of the powder distribution, similar to the caustic of a laser beam.

The powder stream should be characterized in all recorded standoff distances, even if the powder streams have not yet merged. To allow for later comparison to different layers or different nozzles, a radial-symmetrical representation of the powder distribution shall be calculated in each layer. A powder stream diameter can then be calculated in these standoff distances equivalent to diameters where the merged powder shows a gaussian distribution. This is achieved by setting the center of the powder stream and then evaluating the intensity of concentric circles around that center, see Fig. 3.

For each of the concentric circles, a mean intensity is calculated as well as a standard deviation. This standard deviation can then be used as a factor of how symmetrical to the center the powder stream is, as can be seen in Fig. 4 in two layers. The size of the powder spot is set to 14% of the measured maximum. This is similar to the D86 method used in laser beam measurements, which has also been suggested for powder by Li *et al.*^{13}

To detect the working distance of the nozzle, the proposed method is to take the standard deviation for the concentric circles into account. For each mean intensity on a single circle, a standard deviation is calculated, and this value is high when the powder streams have not merged. Dividing this standard deviation by the mean value gives the coefficient of variation for each circle. Then, the mean value of these coefficients is calculated within a proposed region of interest. This region of interest is set to be the smallest powder diameter of each parameter set. This way only the deviations within the smallest diameter are considered.

To analyze the interaction between powder streams, each of the three powder streams was recorded on its own. Two of the nozzles are not connected to the powder feeder. Both the powder mass flow rate and carrier gas flow rate are reduced by a factor of three to maintain the conditions of powder flow from all nozzles. Figure 5 shows the three streams, which are added up to form one powder envelope.

### C. Simulation

Simulations are used to supplement the experimental results and make additional parameters available, which cannot be measured in the experimental setup. We use the open-source software OpenFOAM to simulate the powder flow. In particular, we apply an Eulerian–Lagrangian approach, in which we solve the locally averaged Navier–Stokes equations for the gas phase and the Lagrangian equations of the motion for each particle. We use large-eddy simulation (LES) to deal with turbulence and take the gas–particle and particle–particle interactions into account. As the computational domain, we consider three round nozzles each of which has the diameter of 1.7 mm and the length of 100 mm attached to a large cylinder with diameter of 68 mm and length of 34 mm (see Fig. 6).

The governing equations for the gas phase are the conservation of mass and momentum expressed as

where the overbar indicates the LES filtering, $ui$ is the gas velocity, $xi$ is the position in the *i* direction, *t* is the time, $p\xaf$ is the modified filtered pressure divided by the constant gas density, $\nu $ is the gas kinematic viscosity, $\delta ij$ is the Kronecker delta, and $g=9.81m/s2$ is the gravitational acceleration. The variable $S\xafp$ describes the filtered particle–gas interaction forces per unit mass of the gas,^{21} and $\tau ij=uiuj\xaf\u2212u\xafiu\xafj$ is the subgrid-scale stress tensor, which we model via the dynamic subgrid-scale model based on the turbulent kinetic energy.^{22}

The governing equations for the motion of a particle are

where $xp$ and $up$ are the particle position and velocity, $\rho $ and $\rho p$ the gas and particle densities, and $CD$ is the drag coefficient given by Ref. 23. The variable *f* is the mass specific contact force on a particle by its adjacent particle or wall. We model this force using the soft-sphere approach.^{21} In addition, we adopt a stochastic approach in the soft-sphere model to consider the relevant effects of the wall roughness on particle–wall collisions. Details of this approach can be found in Ref. 24. Effects of the wall roughness on particle dynamics are characterized by the standard deviation of the roughness angle distribution.^{25,26} This parameter is a hybrid roughness parameter that combines the amplitude and spacing roughness parameters. In this work, we consider the standard deviation of the roughness angle distribution to be $6\xb0$^{27} and $\rho =1.78kgm\u22123$, $\nu =1.25\xd710\u22125m2s\u22121$, and $\rho p=7780kgm\u22123$.

## III. RESULTS

### A. Powder spot size

The powder mass flow rate was increased fivefold, while the resulting powder spot sizes stayed nearly the same for each angle of inclination, as can be seen in Fig. 7. A steeper angle of inclination leads to smaller powder spot sizes.

The increase of shielding gas from 5 to 15 l/min showed similar results. The powder spot size does not seem to change for each of the inclination angles. The steepest angle shows again the smallest radii (see Fig. 8).

Figure 9 shows that an increase in the carrier gas flow rate leads to a decrease in powder spot sizes for all inclination angles. Again, the steeper angles show smaller spot sizes.

The calculated radii for recorded standoff distances with varied carrier gas flow rate and for three inclination angles of the nozzles are shown in Fig. 10. It can be seen that a higher carrier gas flow (solid marks in Fig. 10) leads to smaller powder spot sizes in the waist region of the powder stream. If the powder nozzles have a flatter inclination angle (green and orange marks in Fig. 10), the waist region of the powder stream has a smaller standoff distance to the nozzle exits.

### B. Working distance

The mean coefficient of variation of the powder distribution for varied inclination angles is shown in Fig. 11. For all three variations, the coefficient starts at a higher value and then decreases almost linearly until it reaches a rather steady level. The steepest angle of inclination shows the smallest values of the mean coefficient of variation.

Figures 12(a)–12(c) show the whole powder distribution envelopes for the experiments depicted in Fig. 11, and in Figs. 12(d)–12(f) the theoretical start of working distance according to the steady region derived from the mean coefficient of variation.

### C. Interaction of powder streams

To analyze the effects of powder stream interaction in discrete nozzles, powder distributions were recorded with and without powder stream interaction. In Fig. 13(a), experimental results are shown with the three-nozzle setup. It can be seen that, if all nozzle exits are in use, the powder mass flow may vary between the exits. This imbalance gets weaker with an increase of standoff distance. Figure 13(b) shows the theoretical result obtained by superposition of the experimental results of single individual nozzles.

The resulting calculated powder diameters for both cases are depicted in Fig. 14. It can be seen that starting just above the waist of the powder stream at 13 mm the interacting powder stream has a larger powder diameter. This also continues after the waist region.

The mean coefficient of variation is also calculated for the interacting and noninteracting powder streams, see Fig. 15. Starting at 14 mm standoff distance, when the streams merge, the mean coefficient of variation starts to differ. The values for the stream without interaction are higher.

### D. Comparison between simulation and experimental results

We validate our simulations using the experimental results and then shortly discuss the particle concentration and the particle velocity profiles obtained from the simulations. For the sake of brevity, we conduct the simulations only for three cases with different carrier gas flow rates. In particular, we set the powder mass flow rate to 9 g/min, the shielding gas flow rate to 10 l/min, and the nozzle inclination angle at 23° and consider three carrier gas flow rates, i.e., 3, 9, and 15 l/min. Figure 16 compares the numerical simulation and experimental results for the smallest powder spot radius as well as the calculated radius with standoff distance. There is a high degree of consistency between the simulation and experimental results. In particular, we observe that the simulations capture the main features discussed before: (i) the smallest powder spot radius decreases with the carrier gas flow rate, (ii) the variation of the calculated radius with standoff distance exhibits a concave-shape profile, and (iii) the standoff distance, at which the powder spot radius is minimum, remains unchanged with the carrier gas flow rate. Despite the slight discrepancy between the results of the experiments and of the simulations, this comparison confirms that the employed point-particle LES code is capable of producing reliable results.

Figures 17(a) and 17(b) show the particle volume fraction at the symmetrical plane for two simulated cases. As expected, the particle concentration remarkably decreases with increasing the carrier gas flow rate. The reason is that the powder mass flow rate is constant between two cases, while the powder moves much faster in the case with the higher carrier gas flow rate [see Fig. 17(d)]. The particle concentration on the symmetry axis sharply increases at first but then declines with a smaller rate. The position of the maximum particle concentration appears to be approximately independent of the carrier gas flow rate, as shown in Fig. 17(c).

Figure 18 shows the particle volume fraction on the horizontal plane at 15 mm below the nozzle exit plane. Consistent with experimental results, we observe that the radial profiles of particle concentration are similar to the Gaussian distribution and that the powder spot size decreases with increasing the carrier gas flow rate. In addition, the radial profile of the particle velocity appears to be much flatter for the case with the smaller carrier gas flow rate.

## IV. DISCUSSION

The introduced method for the evaluation of powder distribution can be used for coaxial observation, but also for lateral observation, as presented here. An image transformation compensates for the angle of observation. Discrete nozzles show a radially asymmetrical powder distribution until the single streams merge. However, continuous nozzles can show radial asymmetry, as well, if part of the powder channel is blocked, for example. These radial asymmetries are compensated for by introducing an equivalent radial powder distribution. This is calculated by the mean intensity over concentric circles (Figs. 3 and 4). The normalized standard variation (coefficient of variation) is then used to find the working distance(s) (Fig. 11). Liu *et al*. [10] and Liu *et al*. [16], divided the powder stream in three regions. The mean coefficient of variation gives a strong indication of where the merging of the streams begins, thus the working distance should be where fluctuations for this value end. However, there is no detectable variation in this value which would indicate an end for the merging region, thus an end for the working distance. The powder streams after the working region are highly diffused, thus exhibiting no radial deviations in powder concentration.

The main influences on the calculated powder spot sizes are the inclination angle and the carrier gas flow of the powder. In this setup for angle-adjustable nozzles, the shielding gas nozzle has a comparably high distance to the nozzle exits, compared to conventional nozzles. This may explain why no direct influence from the shielding gas could be detected (Fig. 8). The powder mass flow rate also showed no significant influence on the powder spot size (Fig. 7). This is in agreement with the assumption of Tan *et al*. that the volume fraction of particles in the powder stream is so low that an increase in powder mass flow has no effect on particle trajectories.^{7} The increase in carrier gas flow leads to a smaller powder spot diameter for all investigated setups (Figs. 9 and 10). Consistent with this is the observation of Takemura *et al*. that particle trajectories are straighter for higher carrier gas flow rates.^{11} With less diffused powder, a higher convergence of powder flow is present. The biggest influence in these experiments had the inclination angle of the powder nozzles (Figs. 7–10). With a flatter angle, the meeting point of the streams has a much higher overlap than for steeper inclination angles.

The recording of the single powder streams on their own and subsequent superposition of the powder distribution envelopes allowed for an analysis of the impact the interaction of the powder streams has. It can be seen in Fig. 14 that before the streams start to merge the calculated diameters are nearly the same. At a standoff distance of around 13 mm, the diameter of the interacting powder streams gets larger than without the interaction. This is distinctive in the waist region of the powder distribution. It can be assumed that particles will collide since their trajectories are crossing. This would lead to a higher diffusion of particles and, thus, a larger powder spot size. Until 13.5 mm standoff distance, the mean coefficient of variation for both cases are almost the same. Subsequently, the interacting powder stream has the lower values. This can be explained by the proposed higher diffusion of powder as soon as the streams start merging. A higher diffusion of powder leads to a smaller deviation in powder concentration.

## V. CONCLUSION

For the first time, a method has been demonstrated that allows us to characterize the powder stream propagation behavior and compare powder jets from different nozzle types. Based on averaging the powder intensity over concentric circles in the measurements, an equivalent powder spot diameter can be calculated. One advantage of this is that the method is applicable for continuous, discrete, and even lateral nozzles. The mean coefficient of variation, which is introduced in this paper, is used to determine the beginning of the working distance of a discrete nozzle. This novel method was validated by examining the characteristics of the powder streams as well as the influence of powder stream interaction.

## ACKNOWLEDGMENTS

The work was supported by the North-German Supercomputing Alliance (HLRN). This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project No. 424886092 (adaptive powder nozzle for additive manufacturing processes).

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

### Author Contributions

**Annika Bohlen:** Formal analysis (equal); Investigation (equal); Visualization (equal); Writing – original draft (lead). **Thomas Seefeld:** Methodology (equal); Supervision (lead); Writing – review & editing (lead). **Armin Haghshenas:** Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Writing – original draft (supporting). **Rodion Groll:** Formal analysis (supporting); Funding acquisition (equal); Project administration (equal); Supervision (equal).

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