Impact of sulfur content on thermo-capillarity and melt pool dynamics in laser powder bed fusion of 316L powders

A three-dimensional numerical model is developed to investigate the influence of sulfur content on the transitions of thermo-capillarity and flow dynamics during laser powder bed fusion (LPBF) of 316L powders. The impacts of variations in sulfur contents on thermal behaviors involving heat transfer and solidification characteristics, thermo-capillarity transition, as well as the spatial and directional transitions in flow dynamics, are analyzed through mechanistic modeling techniques. It is observed that transient thermal behaviors, including melt pool profile, track morphology, and solidification processes, are significantly influenced by the contained sulfur concentration. High sulfur concentrations tend to result in finer microstructures and equiaxed grains. Through simulations, it is noted that the transition in the sign of temperature coefficient of surface tension (TCST) is more easily observable in low-sulfur level but disappears as the sulfur concentration is extremely low (0.0001%) With sulfur content increasing, a more homogenized velocity distribution is observed, accompanied with heightened flow complexity denoted by the emergence of additional branch flows and vortices. These findings offer valuable insights into the underlying physics of melt pool dynamics in the LPBF process and present a potential approach for process optimization.


Introduction
Laser powder bed fusion (LPBF), also known as selective laser melting (SLM), offers advantages over complex geometry, cost and time reduction, and manufacturing performance [1][2][3][4].It has drawn numerous interests from industry communities such as aerospace, automobile, and shipbuilding, etc.However, LPBF parts are also prone to be laden with process-induced defects and limited to widespread application.Arising from the printing process, defects can be classified as lack of fusion, gas-induced pores/voids, hot cracking and discontinuity [5][6][7][8][9], etc.Among many underlying causes, it is identified that unexpected melt pool dynamics is one of the major contributors to process resulted defects [10,11].For example, keyhole dynamics and nonhomogeneous mixing are not expected in LPBF.The laser-induced keyhole inside the melt pool is considered one of the key factors that result in the porosity in the final solidified melt pool for LPBF.The non-uniform dilution of alloy elements contributes to the formation of intermetallic compounds, which may induce the cracking of solidified parts.
The melt pool dynamics in LPBF are characterized by strong coupling between multiple scales and multiple physics, involving extreme physical phenomena such as rapid solidification (μs), ultra-high cooling rate (over 10 5 K/s), and high-temperature (over 3000 K) flow dynamics.High-resolution imaging devices and tools have been incorporated into experimental research on melt pool dynamics in metal additive manufacturing to obtain reliable online observations and perform quantitative analysis of the physical details of the morphology evolution, velocity field, powder spattering, etc [12][13][14][15].High-speed high-energy x-ray imaging in Argonne National Lab (ANL) [12], fast camera with high spatial and temporal resolution [13], optical pyrometer [14], and infrared thermography [15] have been well developed and demonstrated as efficient and strong imaging technologies to capture the extreme physics.Despite obtaining insightful knowledge from reliable observation through various advanced in situ imaging technologies, these methods are still limited in their ability to provide sufficient details on the melt pool dynamics due to the restrictions arising from imaging mechanisms based on optical and thermal theories and device capability.Furthermore, most of the groups interested in metal AM can hardly afford such cost-consuming research.
The rapid advancement of Computational Fluid Dynamics (CFD) technology and computer engineering has significantly facilitated the adoption of modeling and simulation approaches.These tools provide physicsinformed descriptions, thereby supporting the derivation of relationships between process, structure, and material properties in metal additive manufacturing [16,17].To gain insights into the laser-material interaction, heat transfer, phase change, powder behavior, flow dynamics, and the evolution of melted track morphology, as well as the solidification phenomenon within LPBF, extensive computational modeling works at the mesoscale, involving methods like the Finite Element Method (FEM) [18], Finite Volume Method (FVM) [19][20][21], and Discrete Element Method (DEM) [22,23], have been undertaken.Insights obtained from peer-reviewed publications have fundamentally elucidated the impacts of processing parameters through parametric studies and dimensional analyses [24].They have also contributed to revealing the formation mechanisms of underlying process-induced defects such as lack of fusion, porosity, and discontinuity.Furthermore, these studies have provided characterizations of the evolving morphology within the melt pool (including features such as the fusion line and gas/liquid interface) and the surface roughness of multi-track, multi-layer as-built components.
Materials used in metal additive manufacturing can be categorized into two groups based on their sulfur content: high-sulfur powders like 316L and Inconel 718, and low-sulfur powders including Ti6Al4V and AlSi10Mg.The increment of sulfur content can lead to significant transitions in melt pool dynamics.Particularly, the presence of sulfur in high-sulfur powders can induce a transition in the temperature coefficient of surface tension (TCST) under specific conditions [25].Furthermore, it can impact the thermo-capillary force, which serves as the primary driving force governing melt pool dynamics [26].Consequently, both the direction and magnitude of the melt pool's flow pattern can be substantially altered.The transition of TCST induced by sulfur and resulting changes in flow patterns have garnered significant attention in various laser manufacturing techniques of high-sulfur materials, such as laser welding of stainless steel [27], laser polishing of stainless steel [28], and laser direct energy deposition of Co-based powders [29].Particularly, great efforts have been denoted to explore the impact of surface-active elements involving sulfur, selenium, etc, on the melt pool dynamics by the welding community [30][31][32][33][34][35][36], both numerically and experimentally.Heiple et al [30] demonstrated that the addition of selenium to the molten pool increases the depth/width ratio for conduction mode welding but has little influence on melt pool dimensions for keyhole welding.This conclusion acts for gas tungsten arc (GTA), laser, and electron beam welds.Pitscheneder et al [31] concluded that the concentration of sulfur affects both the temporal evolution and the final shape of the melt pool only when the convective heat transfer is important, i.e., at high Peclet numbers.Moreover, numerical modeling further reveals the mechanism of sulfur-induced transitions of the sign of TSCT and the flow pattern inside the weld pool [32,33].Furthermore, the impact of sulfur-effect on flow instability and melt pool oscillation in GTA has been thoroughly studied by Ebrahimi et al [34][35][36].They found that the sulfur-effect on Marangoni convection enhances the flow instabilities for the internal flow and the reduction of sulfur content induces a contrary outward flow from the view of the melt pool surface, subsequently leading to a wide and shallow melt pool.These technologies share similar physics with LPBF.
The sulfur-induced transition of thermo-capillarity (TCST) and the resulting changes in melt pool dynamics have also drawn the attention of researchers who have interests in LPBF.A 3D thermal-fluid model was developed by Le et al [37] to reveal the effect of sulfur level on melt pool dynamics in LPBF.It is demonstrated that for stainless steel powders with a higher sulfur content, an inward Marangoni flow is prompted, which can increase the melt pool depth and reduce the porosity of the as-built part.In-situ direct observation of the melt pool dynamics for metal additive manufacturing was carried out by Aucott et al [38] through the high-energy synchrotron experiment, in which the transitions of flow dynamics are directly observed when the sign of temperature coefficient of surface tension is changed.Mathematical descriptions of TCST incorporated in proposed numerical models are expressed as a function of local sulfur content and temperature at the gas/liquid interface of the melt pool with references from [27][28][29][31][32][33][34][35][36][37].In these references, TCST is a variable and its transition from negative to positive or the inverse transition is considered.In contrast, it is simplified as a negative constant in references [16][17][18][19][20][21][22][23], where no consideration is given to sign transitions.
In a word, the utilization of a constant assumption is a dependable approach when low-sulfur powders are employed.However, this approach is not justifiable when simulating the melt pool dynamics for high-sulfur powders, such as 316L.In this situation, it is advisable to incorporate a functional description of the TCST.After conducting a thorough review of the existing literature , it can be inferred that the sulfur-induced transition of TCST and its consequent impact on flow pattern during LPBF of high-sulfur powders still have not been elucidated through high-fidelity, powder-scale multi-physics modeling.The lack of physical details about the powder-scale melt pool dynamics variations induced by sulfur-effect restricts the process adjustment aimed at microstructure refinement and property improvement for the real LPBF process.
To address this research gap, an enhanced powder-scale transient model that incorporates a surface tension sub-model is developed.The primary objective of this model is to explore the fundamental physical mechanisms underlying the sulfur-induced transition of thermo-capillarity and the resulting shifts in flow patterns during the LPBF of 316L powders.Considering the permissible maximum sulfur content in 316L and its globally recognized equivalent alloys, the current model is initially configured to investigate melt pool morphology and dimension through a systematic parametric examination of sulfur concentration.Subsequently, the numerical analysis to elucidate the sulfur-induced transition of TCST and its consequential impact on flow dynamics is performed.This work continuously explores the influence of sulfur concentration on the spatial and directional characteristics of melt pool dynamics.To this end, the mechanism that comprehensively describes the effects of sulfur on thermo-capillarity and flow dynamics across varying sulfur concentrations is proposed.The aim is to identify potential strategies for mitigating process-induced defects and enhancing the quality of as-built 316L components manufactured through LPBF.

Numerical procedure 2.1. Geometry and discretization
The size of 316L powders changes from 20 μm to 50 μm.A powder layer with a thickness of 50 μm is randomly generated and filled into the powder bed with the dimension of 1000 μm × 400 μm × 150 μm.The model geometry is uniformly discretized by tetrahedral cells with the size of 5 10 6 ´m with the mesh-sensitivity test in advance.

Powder-scale CFD model
An improved 3D transient powder-scale melt pool dynamics model incorporated with a surface tension submodel is proposed based on the software platform of FLOW-3D to simulate the sulfur-effect on thermocapillarity in LPBF of 316L powders.SIMPLE solver based on FVM is utilized for iteration with the maximum time step of s 10 .
The mathematical relation describing surface tension/TCST, local temperature, and sulfur content is obtained from [25].Volume of Fluid method (VOF) [39] is incorporated to construct the melt pool profile and track morphology, which can be expressed by: As described in equation (1), phase fraction F is calculated in each cell, while fluid velocity u is obtained from the solution of the momentum equation.Thus, the free surface of melt pool and melt track can be reconstructed in each iteration.

Thermo-physical properties
316L powders have garnered great attention in LPBF due to its strength, antioxidation properties, and corrosion resistance.The allowable content of suflur in 316L varies by global standards.It is 0.03% in US ASTM AISI and SAE, EU EN, and France ANFOR, while limited to 0.015% by China GB and England BS.Thermophysical properties of 316L powders and numerical constants for the current modelling are listed in table 1.

Boundary conditions
High-fidelity modelling depends on the accurate boundary conditions, and the detailed descriptions of energy aboundary and momentum bounday are given by followings.

Energy boundary
The energy boundary at gas/liquid surface of melt pool is given as: In equation (2), the first term at right hand denotes laser heat input, in which q is the laser incident angle relative to the gas/liquid interface, and r represents the distance to laser center.The reflectivity and the resultant absorption of laser energy are both assumed constant at the current work.The absorption is a variable and depend on laser characteristics, laser-ray incident angle, surface temperature, and base-material composition [42,43].The functional description is more realistic and can enhance the modelling accuracy.Based on the conclusion from Amin et al [43], the laser energy absorbed by melt pool is underestimated in the current modelling as the reflectivity is 0.7 and the resultant absorption is constant 0.3.As a result, the calculated peak temperature and melt pool dimensions are expected to be smaller than the real situation.
Moreover, the second term and third term denote the heat loss caused by heat convection and radiation, respectively.Heat transfer coefficient h c is strengthened by the shielding gas flow and determined with the reference from publications [29].The emissivity e at the current study comes from modelling experience for LPBF.Only the second and the third terms are included in the energy boundary for the other faces.

Momentum boundary
Momentum condition at gas/liquid surface of melt pool can be expressed as: The first and second term at right hand represent capillary force and thermal capillary force, respectively.pis the pressure.k is the gas/liquid surface curvature.The momentum boundary for the other boundaries of the model is no slip.

Assumptions
The current modeling is performed under some key assumptions.Flow dynamics are assumed to be Newtonian, laminar, and incompressible with the Boussinesq approximation.Particularly, fluid flow in the mushy zone is described by a porous flow based on the Carmen-Kozeny relation [44].Evaporation-induced heat loss and mass loss are not included because the LPBF process is in conduction mode under the current processing parameters.The thermal properties of 316L powders are considered a function of temperature but are sulfur independent.

Sub-model of surface tension
The mathematical relation of surface tension/TCST, local temperature, and sulfur content is derived from Sahoo et al [25].
In relations, R u is universal gas constant, s G is the surface excess at saturation, k l is the constant of segregation entropy, and H 0 D is the standard heat of absorption.Referencing the published literatures [25][26][27][28][29], s G is ´and H 0 ∆ is 1.88 10 KJ kmol 5 / -´in the current modeling.α s denotes the sulfur activity and is represented by the percentage of sulfur content.Consequently, both the surface tension and TCST are the function of local temperature and sulfur content.Different from the constant TCST with negative value when sulfur-effect is not considered, the TCST changes in every time step and the sign transition may occur in certain situations, e.g., the transition from positive to negative value or the inverse transition.In sulfur-free situation, the last term at right hand of equation ( 4) is not considered and the last two terms of equation ( 5) disappear, which results in the constant TCST with negative value.

Governing equations
Heat transfer, phase change, powder fusion, as well as fluid flow are all simulated in the proposed transient powder-scale model.The mass, momentum, and energy conservation of equations are all incorporated to describe melt pool dynamics, which could be respectively expressed as follows: In relations, u denotes the velocity vector, and g represents the gravitational acceleration vector.m is temperature-dependent dynamics viscosity and contributes to the construction of melt pool shape.For simplification, it is 100 Pa s • when the temperature is below liquidus and 6 10 Pa s 3 ´-• when temperature beyond liquidus.A mush is a numerical constant and set as 10 kg m s. 7 3 / • f l represents the liquid phase fraction, which is 0 below solidus (T s ) and 1 above liquidus (T , l ) and described by f l -when the temperature is between solidus and liquidus.M is a numerical constant and set as 10 −4 .A mush describes the mushy zone morphology and denotes the restriction for the porous flow, which has significant influence on the solid/liquid boundary [45].C p eq is the equivalent specific: ) representing the solidification interval and the melting temperature, respectively.In addition, is the specific enthalpy caused by phase change.

Results and discussion
Conduction mode is preferred in real LPBF manufacturing as the porosity in final solidified part is susceptible to keyhole mode.Consequently, most of the previous modelling works for LPBF focus on conduction mode.The differences in melt pool dynamics between sulfur free situation and 0.03% sulfur situation are thoroughly discussed and compared in our previsou publication [46].Some major conclusions are drawn from [46].The new flow pattern of combined outward-inward flow is observed because of the sulfur-induced transition of surface tension.The maximum velocity decreases in 0.03% sulfur situation because the sulfur-induced complex flow lowers the spatial gradient of temperature and decreases the driving force.Melt pool dynamics in 0.03% sulfur situation are more complex with more vortexes induced at transverse section and more branch flows and mixing positions of branch flow (MPBF) observed at longitudinal section.More detailed comparisons and discussion are presented in reference [46].
For the current work, the effects of sulfur content variations on thermal behavior, thermo-capillarity, and flow dynamics are analyzed and emphasized through a systematic parametric study.

Sulfur-effect on thermal behavior
As illustrated in figure 1(a), the proposed 3D model is discretized by unstructured tetrahedral mesh with a uniform size of m 5 10 .
To obtain a deeper understanding of the impact of sulfur on both melt pool morphology and, notably, melt pool dynamics, a systematic parametric study regarding sulfur content is conducted, utilizing the variables outlined in table 2. The selected study cases are thoughtfully structured to encompass a broad spectrum of sulfur content scenarios, involving the released standards for 316L stainless steel and equivalent alloys worldwide.Additionally, these cases in the current study serve as valuable reference points for other materials employed in metal additive manufacturing, such as Inconel 718.
The processing parameters are listed in table 1 and remained consistent across all six situations.Figure 2 illustrates the temperature field, melt pool, and melt track morphology at the stable stage for Sul-1, in which the sulfur content is extremely low.The color contour, along with the scale bar provided on the right side, represents the transient temperature field.Regions where the local temperature exceeds the liquidus temperature of 1808K are indicated in red.Consequently, the melt pool corresponding to the current printing time is colored red and highlighted by the black dotted ellipse, with the laser heat source located at its front part.The melt track, undergoing the melting and solidification process, is marked within the black dotted rectangle.As depicted, common process-induced defects observed in LPBF, such as balling, pores/voids, and discontinuities, are absent under the current processing conditions.This suggests that the employed parameters are well-suited for achieving a defect-free melt track in the LPBF of 316L powders, even with the significantly lower sulfur content found in Sul-1.The melt pool depicted in figure 2 is in a conduction mode, wherein energy from the laser heat source is absorbed by the upper layers of powders and subsequently conducted towards the lower powders and the substrate, thereby facilitating melt pool formation and dynamic evolution.Figure 3 illustrates the impact of sulfur content on the transient temperature distribution, melt pool profile, and melt track morphology for stable melt pool.The temperature field is represented by the color bar, and the melt pool profile is delineated by the black dotted rectangle.Melt pool length is indicated using white solid arrows.As the sulfur content increases, there is an initial rise followed by a subsequent decrease in melt pool length, with the maximum value occurring in the Sul-5 (0.015%).It is worth noting that melt pool duration correlates with melt pool length [47].Consequently, solidification parameters, such as cooling rate and morphology parameters, undergo changes, potentially resulting in transitions in grain size and morphology in accordance with metallurgical theory [48].Furthermore, as depicted in the longitudinal section, the surface roughness of the solidified track exhibits significant variation versus sulfur content, which greatly relies on the flow pattern inside the melt pool [49].
Figure 4 shows the melt pool profile and temperature field at the transverse section, as well as the 3D melt track, for all six cases.The location of the selected section is indicated by the black rectangle in the 3D sub-figure, with the scanning direction proceeding along the positive x-axis.As depicted, there is a notable variation in transverse melt pool morphology with changes in sulfur content.Subject to identical processing parameters, the peak temperature exhibits an initial increase followed by a decrease as sulfur content increases from Sul-1 to Sul-6.The melt pool depth, highlighted by black arrows and rectangle, initially drops, subsequently rise, with the sulfur content increasing.Moreover, the fluctuation of the free surface (gas/liquid interface), is considerably reduced in the situation with higher sulfur content.In summary, transient thermal behaviors, encompassing melt pool dimensions and melt track morphology, among others, are profoundly influenced by the sulfur content contained.Besides as illustrated in the transverse sections of figure 4, the heat effect zone (HAZ) presents a semi-circular shape for all the situations, which is the same as the distribution of the temperature isoline under heat conduction mode.Additionally, the distribution, and the area of HAZ change little from Sul-1 to Sul-6.It can be primarily concluded that the sulfur-induced transitions of heat transfer and fluid flow inside melt pool have no significant impact on the HAZ.
Figure 5 presents the 3D melt pool profile with the liquid fraction depicted by a color contour.In detail, values of one and zero represent the liquid and solid phases, respectively, while other values indicate the transition region between the two phases.To provide a clearer illustration, half of the melt pool is omitted along the y-axis direction, enabling a more detailed examination of the internal features within the melt pool.As sulfur content increases, the bottom of the melt pool, specifically the solid/liquid interface, undergoes significant changes.For instance, it exhibits a curved shape in Sul-1 and Sul-2 with low sulfur content but changes to a nearly flat interface in Sul-5 and Sul-6 when sulfur content is significantly elevated.What is more, this transition towards a smoother melt pool interface (solid/liquid interface) is not only observed in the longitudinal view but is also evident from three different perspectives as sulfur content increases.
Based on the transient thermal analysis of the melt pool [47], temperature gradient G and solidification rate R can be directly calculated from the developed model, subsequently the combined solidification parameters GR and G/R, in which GR is the cooling rate and G/R represents the morphology parameter.In accordance with metallurgical theory regarding the solidification process within the melt pool [48], GR determines the grain size of the solidified structure, and the grain morphology relies on the value of G/R.In specific, as GR increases, the solidified microstructure becomes finer.Planar, cellular, and equiaxed grains are prone to being observed with the drop of morphology parameter G/R.The temperature gradient, denoted as G, is perpendicular to the solidification front and can be expressed as G=||∇T||.On the other hand, the solidification rate, R, can be described by R V cos , q = • where V represents the heat source's movement speed, and q signifies the angle between the scanning direction and the normal direction to the solidification front.
To make an illustrative description of the effect of sulfur content on solidification rate R, a schematic showing the angle theta is plotted in figure 6. Evidently, 1 q is larger than , 2 q and consequently cos 1 q is smaller than cos , 2 q implying that solidification rate R for Sul-1 is smaller than that for Sul-2.Without the consideration of the change in temperature gradient G, the hypothesis that the cooling rate GR increases while morphology parameter G/R drops with the increment of sulfur content can be drawn from simulation results.Consequently, the solidified grain is expected to be finer and equiaxed grain is prone to occurring in high-sulfur situations.Notably, it should be emphasized that the above hypothesis is obtained based on the assumption that temperature gradient G is constant for different sulfur levels.However, the sulfur-induced transition of melt pool dynamics will reasonably lead to the change of temperature gradient G, and the combined parametersGR and G/R depend on both the temperature gradient G and solidification velocity R. Thus, the real effect of sulfurinduced transitions on solidified grains is much more complex and worth being numerically and experimentally researched in depth in future work.Here, the impact of sulfur element on solidification behavior in LPBF is emphasized and a potential approach is provided to control the printing process for microstructure refinement and property improvement.

Thermo-capillarity transition
Figure 7(a) to (f) depict the variations of surface tension and temperature coefficient of surface tension (TCST) concerning local temperature and sulfur content for all six cases.Surface tension acts as the most influential driving force governing flow dynamics for laser-induced melt pool [26].Notably, the sign transition of TCST can be induced when sulfur is contained in the printed powders.In the current simulation, the sulfur-induced effect on TCST is mathematically modelled, drawing from the description in reference [25].As presented in figure 7, TCST is illustrated by the blue dotted line.The transition of TCST from positive to negative occurs between Sul-2 and Sul-6, with Sul-1, characterized by the extremely low sulfur concentration, maintaining a negative TCST throughout.Consequently, the surface tension, denoted by the pink solid line, steadily decreases in Sul-1.Conversely, a two-stage pattern in surface tension, comprising an initial increase followed by a decrease, divided by the transition temperature T t (indicated by the black solid line), becomes evident as sulfur content increases from Sul-2 to Sul-6.T t rises with increasing sulfur content, changing from 1942 K for Sul-2 to 2590 K for Sul-6, signifying that the sign transition of TCST is prone to occurring in low-sulfur situations, but the TCST transition disappears as sulfur concentration reaches extremely low levels (Sul-1).Thus, there exists a sulfur concentration threshold, distinguishing between Sul-1 and Sul-2, that determines the occurrence of TCST sign transition.The direction of the flow pattern depends on the sign of TCST because surface tension is the dominant driving force in L-PBF [46].As depicted in figure 8, three distinct flow patterns correspond to the three TCST types.The fluid flow within the melt pool of Sul-1 is anticipated to align with the flow pattern illustrated in

Sulfur-effect on melt pool dynamics
The proposed 3D powder-scale model makes it possible to further discuss the impact of sulfur on melt pool dynamics, considering the variation in sulfur concentration.Figure 9 provides a depiction of the 3D velocity distribution across Sul-1 to Sul-6.As illustrated, the peak velocity occurs at front area and fluctuates around 5 m/s across these six scenarios.Sul-1 displays a noteworthy divergence in velocity distribution, characterized by a substantially higher velocity of 6.946 m/s.Conversely, as sulfur content increases, a more homogenous velocity distribution becomes evident in high-sulfur scenarios.For instance, in Sul-6, highlighted by the red dotted ellipse, the difference in velocity magnitude between the front and rear regions is relatively small.This contrasts with Sul-1, marked by the white dotted ellipse, where the velocity at the rear is less uniform.
To investigate the impact of sulfur on spatial and directional flow dynamics, fluid flow within the melt pool is analyzed by examining the flow dynamics in the longitudinal section, transverse section, and top view for all six scenarios.The spatial locations of the selected sections in the developed model are depicted in figure 10 for reference.In detail, the central section is chosen for the longitudinal view, while for the transverse section, the coordinate x = 0.55 mm is selected, with the laser starting at x = 0 mm.For the top  view, the plane defined by z = 0.1675 mm is utilized, while the bottom surface of the powder bed is established at z = 0 mm.
As depicted in figure 11, branch flows are indicated by white arrows with hollow heads, while vortexes are highlighted by white arrows with solid heads.Along the longitudinal section, there is a noticeable decline in peak velocity, coupled with an increase in flow complexity as sulfur content rises.In Sul-1, only two distinct branch flows are observed, whereas in high-sulfur scenarios (except for Sul-5), the flow pattern involving three branch flow or two branch flow together with one additional vortex is found.
Of particular interest is the observation of vortexes with opposite directions in Sul-2 and Sul-6, characterized by anticlockwise and clockwise rotations, respectively.These vortexes are both situated at the melt pool tail, where transient temperatures are lower due to the Gaussian distribution of the laser source.Referring to figure 7, the transition temperature of TCST in Sul-2 is 1942 K, whereas in Sul-6, T t is 2590 K.This suggests that the sign  Furthermore, it's worth noting that both forward and backward flows are observed in all six scenarios.This bidirectional flow is considered advantageous for promoting the homogeneous mixing of molten powders and the melted substrate [46].
Flow characteristics at the transverse section are depicted in figure 12, positioned near the center of the laser heat source, which corresponds to the high-temperature region within the melt pool.It's worth noting that the sign transition of TCST from positive to negative tends to occur when local temperatures are significantly higher, as illustrated in figure 7.In figure 12, an anticlockwise vortex is observed in Sul-1 and Sul-5 due to TCST (−), while no clockwise vortex is observed in any of the six scenarios.Furthermore, the branch flow exhibits a bottom-up direction consistently across Sul-1 to Sul-6, corresponding to the flow pattern described for TCST (-) in figure 8(a).
Figure 13 presents the flow dynamics from a top view (z = 0.1675 mm).A notable observation is the presence of a blank area, representing a lack of liquid material in the melt pool.This blank area is prominent in Sul-1 through Sul-4 but is not as evident in Sul-5 and Sul-6.In high-sulfur situations, it is expected that more powders will be melted and fill this blank area.Additionally, all the vortexes observed from the top view exhibit clockwise rotation.They are positioned at the tail region in Sul-1 and Sul-3, and at the head part in Sul-5 and Sul-6.The peak velocity at the top view exhibits fluctuations from Sul-1 to Sul-6, but an overall decreasing trend is still discernible, which is 4.76 m/s for Sul-1 but drops to 1.29 m/s for Sul-6.A combined frontward and backward branch flow is observed from Sul-1 to Sul-5 but is absent in Sul-6.This discrepancy can be attributed to the significantly larger melt pool depth observed in Sul-6 from the simulated longitudinal sections in figure 11.Consequently, the flow characteristics in figure 13 (f) primarily reflect the dynamics at the upper region of the melt pool, resulting in the formation of a main single branch flow at the selected section.Moreover, it's worth noting that fluid flow near the melt pool bottom for Sul-6 is likely to exhibit increased complexity.

Conclusion
A 3D powder-scale transient computational fluid dynamics model is proposed to analyze the sulfur-induced transitions of thermo-capillary and melt pool dynamics.The current study focuses on the impact of sulfur content present in 316L powders and equivalent materials used worldwide.Some fundamental conclusions can be summarized as follows.(1) As sulfur content increases, the peak temperature within melt pool initially rises, subsequently decreases, resulting in a substantial reduction in track surface fluctuations.The solid/liquid interface transforms from a curved shape in low-sulfur situations to near flat in high-sulfur situations.This transition is expected to result in the occurrences of finer solidified grains and equiaxed grains.
(2) The sign transition of TCST is more likely to occur in low-sulfur situations and the transition temperature increases from 1942 K for Sul-2 (0.001%) to 2590 K for Sul-6 (0.03%).However, it disappears when sulfur concentrations reach extremely low levels (Sul-1, 0.0001%).
(3) A more uniform velocity distribution with the decreasing of velocity magnitude is presented in high-sulfur situations.Additionally, flow complexity, characterized by a greater presence of branch flows and vortexes, is significantly elevated as sulfur content increases.
(4) In the longitudinal section, TCST (−) induces a bottom-up anticlockwise vortex at the rear in low-sulfur situations, while TCST (+) results in a top-down clockwise vortex at the tail in high-sulfur situations.In the transverse section, bottom-up branch flows are observed across the sulfur content range.For the top view, the blank area observed in low-sulfur scenarios disappears with increasing sulfur content.Engineering and Physical Sciences Research Council.Xinfeng Kan is grateful for the financial help from Jiangsu University (High-tech ship) Collaborative Innovation Center (1174872301-7).

Figure 1 .
Figure 1.(a) Mesh discretization and (b) Validation of the proposed model.The experiment observation of the melt pool in sub-figure (b) reprinted from [8], Copyright (2021), with permission from Elsevier.(The reader is referred to the web version of this article for a better understanding).

Figure 2 .
Figure 2. Temperature field, melt pool profile, and melt track morphology at the stable stage in Sul-1, corresponding to the physical time of 1100 μs.The temperature in Kelvin (K) is expressed by the color bar.(The reader is referred to the web version of this article for a better understanding).

Figure 3 .
Figure 3. Temperature field, melt pool profile, and melt track morphology at the top view and longitudinal section for different cases when melt pool is stable.(a) (g) Sul-1, (b) (h) Sul-2, (c) (i) Sul-3, (d) (j) Sul-4, (e) (k) Sul-5, (f) (l) Sul-6.The temperature in Kelvin (K) is expressed by the color bar.(The reader is referred to the web version of this article for a better understanding).

Figure 4 .
Figure 4. Temperature field with isolines, melt pool profile and melt track morphology at the transverse section for different cases when melt pool is stable.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.The temperature in Kelvin (K) is expressed by the color bar.(The reader is referred to the web version of this article for a better understanding).

Figure 5 .
Figure 5. 3D melt pool profile with liquid region labelled for different cases.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.Color contour represents the fraction of the liquid phase.(The reader is referred to the web version of this article for a better understanding).

Figure 6 .
Figure 6.Schematics illustrating the solidification behavior of Sul-1 and Sul-5.(a) Sul-1, (b) Sul-5.(The reader is referred to the web version of this article for a better understanding).

Figure 7 .
Figure 7. Plot of surface tension and temperature coefficient of surface tension (TCST) as the function of local temperature in Kelvin and sulfur content in percentage.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.(The reader is referred to the web version of this article for a better understanding).

figure 8 (
figure 8(a) due to its consistently negative TCST, and a singular inward flow, as shown in figure 8(b), will be formed due to the continuously positive TCST.In cases where coexistence of TCST (-) and TCST (+) remain, a combined inward-outward flow is desired, as presented in figure 8(c).

Figure 9 .
Figure 9. 3D velocity field for different cases.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.The color contour represents the magnitude of the velocity field (m/s) of the melt pool.(The reader is referred to the web version of this article for a better understanding).

Figure 10 .
Figure 10.Spatial positions of the selected sections in the developed model.(a) Central longitudinal section, (b) Transverse section x = 0.55 mm, (c) Top view z = 0.1675 mm.Corresponding to the printing time of 1.1 ms when the melt pool is in the quasi-steady stage.(The reader is referred to the web version of this article for a better understanding).

Figure 11 .
Figure 11.Spatial and directional flow characteristics at the central longitudinal section.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.The color contour represents the temperature field in Kelvin and the velocity field (m/s) is denoted by the black arrows.White arrows are used for the illustrations of the directions of branch flow and convection.(The reader is referred to the web version of this article for a better understanding).

Figure 12 .
Figure 12.Spatial and directional flow characteristics at transverse section.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.The color contour represents the temperature field in Kelvin and the velocity field (m/s) is denoted by the black arrows.White arrows are used for the illustrations of the directions of branch flow and convection.(The reader is referred to the web version of this article for a better understanding).

Figure 13 .
Figure 13.Spatial and directional flow characteristics at the top view section.(a) Sul-1, (b) Sul-2, (c) Sul-3, (d) Sul-4, (e) Sul-5, (f) Sul-6.The color contour represents the temperature field in Kelvin and the velocity field (m/s) is denoted by the black arrows.White arrows are used for the illustrations of the directions of branch flow and convection.(The reader is referred to the web version of this article for a better understanding).

Table 2 .
The distinct sulfur levels for parametric study and the corresponding occurrence of thermocapillarity transition.