2.3　Simulation results

2.3.1　Distribution of the flow field

In this study，a convergent Reynolds average turbulent flow field using ANSYS FLUENT 16.0 with the renormalization group k-ε turbulent model is obtained. The flow field at 2.3 s is acquired to obtain its characteristics because the flow field becomes stable at this time point. Six horizontal （X-Y） planes are selected to project the flow-field distribution，and these horizontal planes are at perpendicular distances of 8，18，28，180，280 and 380 mm （along the Z direction） from the workbench. To clear present the flow characteristics of the flow field above the workbench，it chooses an observing window with the same size as the workbench. Flow field distribution on planes at different distance from the workbench shows in Fig. 2-5.Fig. 2-5（a） shows the velocity vector diagram of the plane 8 mm above the workbench. The velocity in the middle plane reaches 1.9 m/s and gradually reduces on both sides. The velocity reduces to 0.1 m/s around the outlet，and the flow pattern is almost uniform from Inlet1 to the outlet. Fig. 2-5（b） and Fig. 2-5（c） show maximum velocities of 1.4 and 1.2 m/s，respectively，each of which is concentrated at the center of its planes because of the structure of Inlet1. The entire distribution of the flow fields on the three observation planes is similar to a laminar flow pattern，and there is no backflow or turbulent flow. This indicates that the structure of the chamber is very reasonable and can ensure the stability of gas flow above the workbench.

However，Fig. 2-5（d），Fig. 2-5（e），and Fig. 2-5（f） show a very different and disorder distribution of the flow filed. It is obvious that the flow velocities at these heights are small since these three planes are far away from the Inlet1. But the flow velocity at the plane with a height of 380 mm is larger compared to those with heights of 180 and 280 mm，since the Inlet2 is located at height of 446 mm.

To better display and analyze the flow field in the chamber，three vertical planes across points A1-C1'，A2-C2'，and A3-C3' are used to project the flow-field distribution，as shown in Fig. 2-6. Although several cyclonic flows exist in the middle of the chamber，the flow field is relatively stable in the area above the workbench up to a height of 30 mm. Above this uniform flow area，the flow field becomes turbulent，blowing the smoke and particles along disorderly trajectories. In particular，the cross-section shown in Fig. 2-6（b） intersects with the inlet pipe. The maximum flow velocity，which is in the pipe branches，greatly exceeds the flow velocity around the outlet. The structure at the branch causes the flow to take a nearly 90° turn. Consequently，the flow becomes turbulent，and its velocity changes abruptly，reaching as high as 9.8 m/s.

In conclusion，placing the product to be printed at the center of the workbench improves the final quality because a uniform high-velocity flow can blow away by-products such as spatter particles.

2.3.2　Distribution of the temperature field

The laser scans the area above the workbench and heats the metallic powders to very high temperatures to melt them. As the diameter of the laser spot is only 200 μm，only the area around the laser scanning path （Zone 1） can be analyzed in Fig. 2-7 and Fig. 2-8. Considering that large temperature fluctuations may exist at the beginning and end of the scanning process，the temperature fields at 0.045，0.145，0.245，0.345，and 0.445 s are analyzed. As shown in Fig. 2-7，the point with the highest temperature is always close to the head region of the heating zone，and there is a long tail created by the residual heat. In Fig. 2-7（a），under a laser power of 100 W，the highest temperatures in the heating areas at the five time points are 2738，2790，2938，2831，and 2706 K，respectively. The deviation is only 232 K，which is less than 8% of the average observation temperature，indicating that the temperature is almost stable during the scanning process.Temperature fluctuation may occur because of a small degree of non-uniformity in the distribution of the flow field above the workbench （Fig. 2-5 and Fig. 2-6）.Furthermore，although there is a significant increase in temperature in the laser heating regions，most areas along the scanning path remain at the initial environmental temperature after the laser moves away because metal workbench conducts heat rapidly. Owing to the rapid loss of heat caused by heat transfer，radiation，and convection，the high temperature is confined to a small area.Similar characteristics in the temperature distributions for a laser power of 200 W are presented in Fig. 2-7（b）.

Fig. 2-8 shows the laser induced velocity disturbance inside the chamber. The height of the observation window is 1.6 mm，and the velocity disturbance is minimal，although the degree of velocity disturbance increases as the laser power is increased from 100 to 200 W. The reason can be that the laser spot is too small，in the order of micrometers. Therefore，the laser induced velocity disturbance inside the L-PBF printer can be ignored.

2.3.3　Distribution of spatter particles

To study the distribution of the spatter particles，it defines two planes: Plane1 and Plane2，as shown in Fig. 2-9. It also defines five injection directions （IDs） and hypothesizes that all the spatter particles are injected at the same initial velocity along each direction. One ID is upright，and the others （in planes 1 and 2） are at an angle of 45° with respect to the workbench. To simplify the calculation，it only simulates the injection of 100 particles per direction，and the diameter of a particle is chosen to be 50 μm ［25］. Furthermore，the initial particle velocities are set as 5 and 10 m/s. Heeling et al. ［26］ found that the initial particle velocity could reach 7.5 m/s or higher during the L-PBF process. It develops a movable particle-injection model using a self-developed UDF DEFINE_DPM_INJECTION_INIT in which the particles are injected along five directions at a velocity of 5 or 10 m/s with the injection location being moved with the laser spot. It simulates the particle trajectory using the Lagrangian tracking method in the DPM ［17］.

In the DPM，particle tracking in the flow field is stochastic，and particle-particle interactions are negligible because the discrete phase （particles） is sufficiently dilute. The UDF DEFINE_DPM_BC is used to specify user-defined boundary conditions with the trapping criterion for particles and is executed whenever a particle touched a wall inside the L-PBF printer.

Fig. 2-10 shows the final distribution of the spatter particles when the laser power is 100 W. Fig. 2-10（a） shows that when the initial velocity of the particles is 5 m/s，the particles are almost linearly distributed along the flow direction because their initial velocity of 5 m/s is not sufficient for an escape from the gas flow，and some are blown into the outlet.

Fig. 2-10（b） shows the final distribution when the initial velocity of the particles is 10 m/s. The distribution of the particles along ID4 and ID5 is relatively similar to that shown in Fig. 2-10（a）. However，the particles along ID1，ID2，and ID3 are disturbed to some degree. In particular，the particles along ID1 can reach the upper cyclonic flows in the chamber，and being irregularly deposited on the workbench and the bottom of the chamber. They are blown into the outlet as well.

Fig. 2-11 shows particle deposition at different locations when the laser power is 100 W. When the initial velocity is 5 m/s，most of the particles along ID1 and ID5（55% and 59%，respectively） are deposited on the workbench，which has a negative impact on the quality of the printed products. Conversely，none of the particles along ID4 are deposited on the workbench because their initial velocity vector is consistent with the gas flow and their travel distance is much farther away from the workbench.When the initial velocity is increased to 10 m/s，the number of particles along ID1 and ID5 that are deposited on the workbench increased to 82% and 70%，respectively. However，the number of particles along ID2 deposits on the workbench reduced from 50% to 35% because of the disorderly gas flow. And 13% of the particles are deposited in the outlet as well，which is unavailable when the initial velocity is 5 m/s. Moreover，the number of particles along ID3 and ID4 deposits on the workbench do not change significantly. In summary，most of the particles blown toward the outlet are those injected along flow direction （ID4），and a large percentage of the other particles are deposited inside the printer chamber and on the workbench.

Fig. 2-12 and Fig. 2-13 show the final particle distribution when the laser power is 200 W. The overall characteristics of the particle distribution are similar to the characteristics at a laser power of 100 W. Overall，most of injected particles finally deposits on the workbench.

It will degrade the part quality and specially，cause interface problems since the AM is a layer-by-layer printing process. Because this work simplifies the particle movement by ignoring the particle-particle and particle-wall interactions，above phenomena will be more serious in actual manufacturing process.

It provides a serious challenge to optimize the chamber structure and ventilation system of the printer. The possible approaches for controlling the particle deposition can be the magnetic control of injected particles，or adsorption of the injected particles by negative pressure pipe，which will be studied in our future work.