CFD modelling of the powder segregation in multi-material laser directed energy deposition

International Journal of Thermal Sciences 198 (2024) 108885 Available online 8 January 2024 1290-0729/© 2024 The Authors. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). CFD modelling of the powder segregation in multi-material laser directed energy deposition Marta Ostolaza , Jon I˜ naki Arrizubieta * , Aitzol Lamikiz Department of Mechanical Engineering, University of the Basque Country (UPV/EHU), Plaza Ingeniero Torres Quevedo 1, 48013, Bilbao, Spain ARTICLE INFO Keywords: Multi-material Laser Directed Energy Deposition Powder segregation Continuous coaxial nozzle CFD modelling ABSTRACT One of the prevailing challenges in multi-material laser Directed Energy Deposition is the segregation of the constituents during the delivery of the feedstock into the melt pool. This phenomenon is of particular concern when metal-ceramic mixtures are involved, as the differences in the inertial properties of the powders are higher and segregation is aggravated. This issue affects the reliability of the process; indeed, powder segregation can influence the composition of the melt pool and, thus, that of the final part or coating. In this work, Computational Fluid Dynamics modelling is adopted to study this phenomenon and to explore strategies to overcome it. Firstly, a base multi-material CFD model is built. Secondly, a simplified algorithm is proposed to reduce the computational cost of simulating multiple scenarios. This model is first validated numerically against the base model. Then the simplified multi-material CFD model is experimentally validated. Thirdly, the developed tool is implemented to elaborate two strategies to minimise powder segregation in a Co-WC powder mixture. The first one is quite straightforward and little development is necessary to incorporate it to the industry. Conversely, the second one, though promising, needs further development and its practicality needs to be evaluated before being ready for industrial implementation. 1. Introduction Laser Directed Energy Deposition (L-DED) is currently one of the most industrially relevant metal Additive Manufacturing (AM) technologies [1]. The L-DED process is growing at a significant pace in the repair and remanufacturing sector [2]. Moreover, its popularity for coating deposition within the field of surface engineering is also increasing consistently [3]. As a result, the capabilities of L-DED for the production of wearand corrosion-resistant coatings have been intensively explored [4]. Indeed, the high intensity of the laser source results in a small and localised heat-affected zone, which minimises the distortion and damage to the base material in coating and repair applications [5]. Current industrial trends also point at multi-material AM as a highly promising field of research. Powder L-DED is the preferred AM technology for this purpose [6]. This is motivated by its unrivalled multi-material capability, which is achieved by the ability of L-DED to change the composition of the feedstock in-situ. To enable a precise multi-material production, the composition of the melt pool must be tightly controlled. This can be realised through multiple-hopper feeder solutions, which permit tuning the composition of the feedstock to be delivered into the melt pool [7]. Not only different alloys can be mixed to produce bimetallic structures or Functionally Graded Materials (FGM), but also metal-ceramic structures can be obtained. For instance, ceramic-reinforced Metal Matrix Composites (MMCs) have been proposed for increasing the wear resistance of highly demanded surfaces [8]. Emerging applications of MMC coatings include but are not limited to the aerospace, automotive, and tooling industries [9,10]. Although a promising field, multi-material L-DED is still far from being mature, and several challenges need to be addressed before being a robust and reliable technology. In addition to the challenges associated to the L-DED process itself, such as the metallurgical integrity or the control of the dimensional tolerances [11], additional issues arise as a result of the multi-material nature of the feedstock. Indeed, owing to the different inertial properties of the constituents, powder segregation may occur in the material feeding system. This concern was already raised in several review articles on multi-material AM [12,13]. They reported that such a segregation phenomenon could produce a large deviation from the expected composition in multi-material parts. This issue is substantially aggravated in the fabrication of ex-situ MMCs, considering that * Corresponding author. E-mail address: [email protected] (J.I. Arrizubieta). Contents lists available at ScienceDirect International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts https://doi.org/10.1016/j.ijthermalsci.2024.108885 Received 11 August 2023; Received in revised form 1 December 2023; Accepted 3 January 2024 International Journal of Thermal Sciences 198 (2024) 108885 2 the density of ceramic and metallic powders differs considerably. Indeed, if the dynamic behaviour of the constituent materials of the multi-material mixture is significantly different, the nozzle may distribute or concentrate the powder particles heterogeneously. This phenomenon is illustrated in Fig. 1. Nevertheless, this issue has not been systematically investigated in the literature, and the implications of mixing different materials need to be further explored. The behaviour of L-DED nozzles can be explored through experimental, analytical, or numerical approaches. Experimental characterisation methods typically rely on optical measurement principles [14]. Whilst suitable for the characterisation of existing nozzles, experimental approaches cannot address challenges involving the design of new systems. Moreover, understanding the effect of different factors on the powder concentrations is timeand resource-consuming if approached experimentally. Analytical models have also been employed to describe the behaviour of the powder nozzle in L-DED applications [15]. However, they provide an over-simplified solution to the problem, which lacks the flexibility required to guarantee an extended understanding of complex fluid-dynamic phenomena ruling the powder distribution. Conversely, numerical solutions have been widely explored to gain knowledge of how the L-DED nozzles behave. Indeed, Computational Fluid Dynamics (CFD) are a highly efficient tool to understand the phenomena involved in particle transportation and powder flow generation in L-DED. Driven by this need, many attempts to simulate the powder behaviour along L-DED nozzles can be found in the literature. Zhang et al. proposed a CFD model based on discrete phase modelling to describe the aerodynamic behaviour of a discrete coaxial nozzle [16]. Pan et al. employed a CFD model to describe the powder flow dynamics at different stages of the nozzle and to determine the region where the flow becomes fully developed [17]. Liu et al. also studied the powder distribution of continuous coaxial nozzles using CFD simulations and confirmed that the powder flow converged from an annular distribution at the exit of the nozzle into a Gaussian distribution at the focal plane [18]. Furthermore, CFD numerical models have been employed to investigate the influence of multiple factors on relevant features of the fluid flow. They have been used to compare the performance of different nozzles [19] or to evaluate the effect of the inclination of the nozzle on the catchment efficiency [20]. Other researchers focused on the influence of the substrate and the evaluation of the powder catchment efficiency for different substrate geometries [21]. Following this trend, numerical tools have been employed to study the influence of factors concerning the feedstock morphology, density, carrier and shielding gas flow rate, or nozzle design on the powder concentration. For instance, Fan et al. employed a CFD model in conjunction with statistical regression models to determine the correlation between several parameters and the powder stream in L-DED nozzles [22]. Zhou et al. also investigated the effect of powder characteristics on the L-DED nozzle behaviour and concluded that the particle size would substantially affect the powder distribution in the melt pool [23]. Interestingly enough, in a previous study, it was reported that the density, particle size, and particle morphology would affect the powder distribution and the stability of a discrete coaxial nozzle [24]. This was later confirmed by Gao et al. [25]. Nevertheless, all the literature mentioned so far focuses on single-material feedstock. The delivery of multi-material powder blends through L-DED nozzles is even more complex and is still at an early stage of research. On the one hand, the analysis of multi-material powder flows entails a higher degree of difficulty. On the other hand, there is an increased number of material combinations to be analysed, each of which is likely to have a different behaviour. The study of multi-material powder concentration was pioneered by Li et al., who put in evidence that powder segregation occurred in Cu–Al powder mixtures. After testing the effect of different parameters, they found that higher carrier gas rates would aggravate this problem [26]. Later on, they proposed a solution to mitigate powder separation, which consisted of the optimisation of the powder size of the constituents so that they would behave similarly [27]. Only one publication was found where the powder flow behaviour and powder segregation of ceramic-metallic powder mixtures was addressed. Indeed, Jiang et al. investigated the particle trajectories of TiC-Inconel 718 powder mixtures in off-axis nozzle configurations. They found that TiC particles developed a higher velocity, which resulted in a shorter focal distance and higher dispersion of the powder. As a consequence, a lower TiC content would be expected in the final deposited material [28]. As far as the behaviour of multi-material powder mixtures in L-DED nozzles is concerned, it remains a mostly unexplored field, especially in the case of ceramic-metallic powder mixtures. Although some insights have been provided on the powder flow behaviour of these mixtures, more comprehensive studies are required. For instance, the effect of the volumetric fraction of each constituent should be analysed. In addition, the behaviour of other nozzle configurations should be investigated, especially that of continuous coaxial nozzles due to their extended industrial use. Overall, further research is required to understand precisely how this issue affects the actual composition of multi-material parts fabricated by L-DED. This matter remains largely uninvestigated and the powder segregation in multi-material powder mixtures has not been studied in-depth yet. Driven by this need, in the present work, CFD modelling is proposed as a tool to investigate the behaviour of multi-material powder flows in L-DED continuous coaxial nozzles. To that end, a multi-material CFD model has been developed and validated. In addition, the effect of key parameters on the powder segregation has been investigated. Based on the existing literature, the novelty and contributions present in this research are to: (1) Develop a base multi-material CFD model to simulate metalceramic mixtures. (2) Propose a simplified algorithm to reduce the computational resources necessary to simulate metal-ceramic mixtures and validate it numerically against the base model. (3) Validate the simplified multi-material CFD model experimentally based on the composition of real parts produced by L-DED. (4) Provide two alternative approaches to address powder segregation issues and to increase the reliability of multi-material L-DED in terms of the control of the composition of the parts. 2. Methodology In this section, the procedure followed in the present research is depicted, see Fig. 2. First, a multi-material CFD model is developed. The Fig. 1. Powder segregation in the injection of multi-material powder mixtures with differing inertial properties. M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 3 basis of the model is detailed in section 3. Secondly, a superposition algorithm is proposed for the CFD simulation of multi-material powder mixtures, which is validated numerically against the base model (described in section 4.1) and experimentally (described in section 4.2). Lastly, two approaches for the correction of the powder segregation are evaluated, according to the proposal defined in section 5. The first approach anticipates the effect of the powder segregation on the composition of the melt pool and compensates it by adjusting the powder feeder. The second approach focuses on the optimisation of the diameter of the powder particles to minimise the powder segregation. 3. Basis of the base multi-material CFD model In this section, the multi-material CFD model developed is first introduced. The model is built within the ANSYS® Workbench environment and the Fluent module is employed to set the fluid dynamic model up, which is described hereafter. 3.1. Domain and mesh of the multi-material CFD model The aim of the present multi-material CFD model is to simulate the behaviour of metal-ceramic powder mixtures in the EHU-Coax continuous coaxial nozzle described in Ref. [29]. This nozzle was developed in-house and it comprises an inner and an outer cone, which delimit the confined region where the multiphase flow (carrier gas and powder feedstock) is transported, as shown in Fig. 3(a). The shielding gas flows via the coaxial hole, through which the laser beam is delivered too. The domain of the numerical model is referred to the volume filled by the fluid or, in this case, the multiphase flow. In the numerical problem object of this work, two regions of the domain can be distinguished, namely, the domain delimited by the geometry of the nozzle and the control domain where the unconfined multiphase flow is developed. In Fig. 3(b), both regions are shown. As far as the mesh is concerned, the complexity of the present problem lies in meshing the regions where flow through small gaps occurs, more specifically, in the confined flow region. Indeed, failure to generate a sufficiently fine mesh in those critical regions will result in inaccuracies during the resolution of the near-wall viscous effects. Therefore, a conservative approach has been adopted during the meshing procedure, which is the reason behind the high number of cells and nodes generated. In Fig. 4, the mesh employed during the simulations is shown. First order tetrahedral elements are employed for the mesh generation. Note that in the region of interest the mesh was refined to ensure the accuracy of the numerical results. A criterion generally employed to assess the quality of the mesh relies on the skewness of the elements, and values below 0.75 are commonly sought. In Table 1, statistical and quality data of the mesh are reported. 3.2. Material properties The multiphase flow comprises two phases, i.e. the solid phase and the fluid phase, which correspond to the powder feedstock and the shielding and carrier gas (both Argon), respectively. The material properties for the fluid phase are taken from the Fluent material database, being the density and the viscosity of the Argon 1.6228 kg m −3 and 914,684 kg m −1 s −1 , respectively. In contrast, the solid phase is constituted by inert particles of MetcoClad 6 Co-base alloy (referred to as M1) and MetcoClad 52001 tungsten carbide (referred to as M2). In order to completely define the inert particles, the density and morphology must be provided. Considering that the powder particles have been manufactured through gas atomisation, they are treated as fully spherical. As far as the particle size Fig. 2. Overview of the methodology of the present work. Fig. 3. (a) Internal components of the EHU-Coax continuous coaxial nozzle and (b) Volume domain of the CFD model. Fig. 4. Mesh of the CFD volume domain. M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 4 distribution is concerned, the Rosin-Rammler distribution is generally accepted. In Table 2, the properties of the MetcoClad 6 and 52001 powder particles are provided. 3.3. Model of the fluid flow: viscous formulation and boundary condition The viscous model selected for this problem is the kω SST RANS (Reynolds Averaged Navier-Stokes) model. In fact, this formulation is the most adequate for the present scenario: it offers an accurate nearwall resolution for mixed transitional and turbulent flows, whereas it behaves correctly in regions with adverse pressure gradients such as in the confined to free flow transition [29].With regard to the fluid flow, four boundary conditions are defined, see Table 3. At the shieldingand carrier-gas velocity inlets 1.504 m⋅s −1 and 9.022 m⋅s −1 velocity values are established, respectively, with a constant value and a perpendicular direction to the surface. They correspond to a 5 l⋅min −1 flow for the carrier gas and a 15 l⋅min −1 flow for the shielding gas. At the outlet a constant atmosphere pressure is considered, where a 0 Pa pressure is stablished. Lastly, at the walls in contact with the nozzle, a wall-type condition is defined, with a zero-velocity magnitude. The precise locations of each one of the boundary conditions are depicted in Fig. 5. 3.4. Model of the solid phase: discrete phase model formulation and boundary conditions The solid phase in the multiphase flow can be represented by inert particles and modelled through discrete phase modelling, due to the low volumetric fraction of the solid phase (<10 %). In addition, for very low particulate loadings, it can be assumed that solid particles do not influence the fluid flow. In the present research the Euler-Lagrange approach is considered, where the gas phase is considered as a continuous phase and modelled in an Eulerian scheme, whilst powder particles are treated as discrete phases and tracked individually through drag force balance analysis. In order to fully set the model up, the physical restrictions which rule the behaviour of the discrete phase need to be defined too. Due to the relative low particulate loading and high interspacing distance, the collisions between particles can be safely neglected and the only phenomenon to be modelled concerns the collisions between the particles and the walls of the internal cavities of the nozzle. The interaction between solid particles and solid walls is ruled by the restitution coefficient. The restitution coefficient accounts for the amount of kinetic energy recovered during the collision of a discrete phase particle and a wall, in other words, to which extent the collision is elastic. Typically, values in the range of 0.9–0.99 are employed [30]. In this case, and based on previous works [29], a 0.9 restitution coefficient is adopted between the powder particles and the internal nozzle walls. Lastly, the sources and sinks of the inert particles must be defined. The inert particles enter the CFD domain with the carrier gas, which drags the discrete phase in the direction of the fluid flow. Hence, eight injections of the discrete phase are defined, one per carrier gas inlet and material (red regions in Fig. 5). It is assumed that the particles are uniformly distributed throughout the inlet area and that they enter the system normally to the inlet. In addition, their velocity is assumed to be equal to that of the carrier gas. In terms of the particles leaving the system, an “escape” boundary condition is set to the outer faces of the control domain (BC3). This means that in case a particle “collides” with those regions, it automatically leaves the system. In this manner, the base model is fully defined and the only variables to be set are the mass flow rate of each constituent, according to the specific scenario to be simulated. Based on the characteristics of the multiphase flow, and with the aim of increasing the efficiency when simulating several scenarios with different input variables, a simplifying hypothesis based on the superposition algorithm is proposed and described hereafter. 4. Superposition algorithm for multi-material CFD model The low particulate loading and low Stokes number suggest that the discrete phase is going to have little influence on the fluid flow. Therefore, assuming that the particles are not going to interact with each other and that the fluid flow is not modified by the discrete phase in a significant manner, the individual contribution of each material could be calculated separately and added up to constitute the multi-material Table 1 Statistical and quality data of the mesh. No. Cells No. Faces No. Nodes Max. Skewness Av. Skewness 4,328,036 9,034,107 914,648 0.711 0.230 Table 2 Material properties of the solid phase. Material Density (kg⋅m −3 ) Rosin-Rammler distribution Min. diameter (m) Max. diameter (m) Mean diameter (m) MetcoClad 6 (M1) 8,440 4.5⋅10 −5 1.06⋅10 −4 8.022⋅10 −5 MetcoClad 52001 (M2) 15,630 4.5⋅10 −5 1.06⋅10 −4 8.084⋅10 −5 Table 3 Specifications of the boundary conditions for the fluid phase. Boundary condition Type Velocity magnitude (m⋅s −1 ) Gauge pressure (Pa) BC1 Velocity inlet 1.504 N/a BC2 Velocity inlet 9.022 N/a BC3 Pressure outlet N/a 0 BC4 Wall 0 N/a Fig. 5. Location of the boundary conditions for the fluid phase. M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 5 CFD model. In other words, the superposition principle could be applied. This superposition effect applies to the whole CFD domain, and it is mathematically described by equation (1), where DPM refers to the total discrete phase concentration in the location {x,y,z}of the domain and DPMi refers to the discrete phase of material i in the location {x,y,z} provided by the single-material CFD model. {DPM ({x,y,z})} = ∑ 2 i=1 {DPMi({x,y,z})} (1) in this manner, for the calculation of the multi-material DPM, singlematerial simulations are taken as reference, where the mass flow rate of the powder particles for the i material is ˙ mi0. For the calculation of DPMi({x,y,z}), it is assumed that the DPM in the single-material model will vary proportionally to the mass flow rate fed to the model. Therefore, the DPM at the location {x,y,z}for material i is recalculated for a specific mass flow rate ( ˙ mi) according to equation (2). {DPMi({x,y,z})}= {DPMi0({x,y,z}) }⋅ ˙mi ˙mi0 (2) where DPMi0({x,y,z})} refers to the discrete phase concentration in the location {x,y,z}obtained with the reference model, with the input set at ˙ m0 =5.5 g min −1 . 4.1. Procedure for the numerical validation of the superposition algorithm With the intent of numerically validating this hypothesis, the five scenarios shown in Table 4 are evaluated, where three different compositions of multi-material phase have been analysed. The performance of the simplified algorithm is assessed against that of the base multimaterial CFD model. In addition, considering that the validity of this superposition principle lies in the fluid flow not varying significantly for different compositions of the multi-material phase, the fluid velocity in the Z axis of scenarios 2 and 4 are compared to that of the reference, scenario 0. In Table 4, ˙ m1 and ˙ m2 correspond to the flow rate of M1 and M2, respectively. For this comparison, the discrete phase concentration or DPM along the Z axis is evaluated. Indeed, this variable determines the focal plane position (FPP), which will vary with the modification of the multimaterial powder composition. 4.2. Procedure for the experimental validation of the superposition algorithm With the intent of demonstrating the suitability of the simplified multi-material CFD model, its validity is assessed through experimental tests, which rely on the composition of the deposited material. To that end a Functionally Graded MMC sample was produced, where the nominal composition of the material fed varied according to Table 5. The experimental work is carried out in a 5-axis laser centre coupled with a 1 kW fibre laser and focused in a 1.8 mm diameter spot at the focal plane. The filler material is delivered by a Sulzer Metco Twin 10-C powder feeder, which allows to feed two different materials simultaneously, and focused in the melt pool by a coaxial continuous nozzle. In the present research, cobalt-based alloy Metcoclad 6 (M1) and tungsten carbide MetcoClad 52001 (M2) powders were employed. Both powders are gas-atomised and present a spherical shape with a size between 45 and 106 μ m, see Table 2 for further details. In the experimental validation test, a constant feed rate of 500 mm⋅min −1 was employed, whereas the laser power varies between 800 and 980 W as the amount of M2 increases. The employed mass rates of both filler materials, M1 and M2, are detailed in Table 5, which vary every two layers. The substrate shown in Fig. 6(a) is 70x70x15 mm 3 in size and the dimensions of the deposited geometry are of 50x20x5 mm 3 . As detailed in Table 5, the deposited geometry consists of 10 layers, in which the M1 and M2 compositions vary progressively, see Fig. 6(b). Prior to the LDED testing, the surface of the AISI 1045 steel substrate is ground and cleaned with acetone. Afterwards, and because of the high hardness of the M2 particles, the test piece was cut by wire electro-discharge machining (w-EDM). Three sections were prepared for compositional analysis in a scanning electron microscope (SEM) and the composition of each layer was measured by means of energy-dispersive X-ray spectroscopy (EDS). To that end, the Carl Zeiss EVO-40 scanning electron microscope (SEM) was employed. Area measurements per the scheme shown in Fig. 7 are carried out to estimate the actual composition of the deposited material. In total, two compositional measurements for each scenario are performed. The EDS measurements estimate the elemental composition of the material. Therefore, the composition of the powder mixture that gives place to such elemental composition needs to be derived based on the elemental composition of the constituent powders, namely the MetcoClad 6 (M1) and the MetcoClad 52001 (M2), which are shown in Table 6. In this case, the elemental Co and W contents are taken as the reference. All the Co of the multi-material mixture corresponds to the contribution of M1, which has a 60.5 % wt. Co. In contrast, both M1 and M2 contribute to the W content of the multi-material mixture. Indeed, M1 has a 4.0 % wt. W and M2 has a 95.78 % wt. W. Therefore, the composition of the multi-material mixture fed is estimated based on equation (3). M2wt.%=1 0.9578 (W%EDS −0.04 Co%EDS 0.605 )(3) where W%EDS and Co%EDS are the tungsten and cobalt contents given by the EDS analysis. Note that the term between brackets refers to the W Table 4 Scenarios simulated for the numerical validation. Scenario Ceramic wt. % ˙ m1 (g⋅min −1 ) ˙ m2 (g⋅min −1 ) 0 (Ref) 0 % 5.50 0.00 1 25 % 4.13 1.38 2 50 % 2.75 2.75 3 75 % 1.38 4.13 4 100 % 0.00 5.50 Table 5 Composition of the multilayer test for the experimental validation. Layer Ceramic wt. % ˙ m1 (g⋅min −1 ) ˙ m2 (g⋅min −1 ) 1–2 0 % 5.50 0.00 3–4 10 % 5.19 0.58 5–6 20 % 4.85 1.21 7–8 30 % 4.47 1.91 9–10 40 % 4.04 2.70 Fig. 6. Upper view of the manufactured validation component and a transversal cross-section, where the WC particles are revealed in a darker colour. M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 6 contributed by M2 and the term 0.04 Co%EDS 0.605 refers to the W contributed by M1. Such experimental value is compared to the numerical estimation, which is calculated through the procedure described subsequently. Considering that the sample for experimental validation was fabricated assuming an FPP of 15 mm, the DPM of each material at 15 mm from the nozzle exit is considered to contribute to the composition of a clad, see Fig. 8(a), which is calculated based on equations (1) and (2). In order to determine the composition of the powder mixture fed into the melt pool, the area corresponding to the melt pool needs to be defined. In addition, to provide a more accurate result, the geometry of the clad is also considered. Note that during the experimental work, the distance between the nozzle and the substrate was set to 15 mm before the fabrication of the multi-layer sample. The height of the deposited layers was assumed to be 0.5 mm, which was estimated based on single-layer experimental tests. Moreover, the volumetric rate of the powder stream provided by the feeder was kept constant to minimise the geometric variation of the height of subsequent layers. In the present research the CFD model does not consider the heat introduced by the laser into the substrate. In order to determine the shape of the melt pool created by the laser and therefore quantify the catchment efficiency of the L-DED process, the cross section of a clad is analysed under a microscope, see Fig. 8(b). This way, the region of the melt pool is discretised according to the morphology of the clad. Hence, the composition in each ring-shaped region is calculated and its impact on the total composition of the clad is weighted. Specific details on the geometric discretisation are given in Table 7. M2wt.%=∑ 15 j=1 nj⋅M2wt.%j,CFD model (4) As a result, and based on the proposed discretisation, the wt. % of the Fig. 7. (a) Regions where the EDS measurements were carried out within the multilayer sample for the experimental validation of the multi-material CFD model. White particles represent the M2 particles and (b) EDS results. Table 6 Chemical composition of the materials employed. Material Co Cr W Fe Ni Si C Mo M1 60.5. 28.00 4.00 3.00 3.00 1.50 1.00 1.00 M2 – – 95.78 0.19 – – 4.03 – Fig. 8. (a) Composition of the multi-material powder stream at the FPP and approximated morphology of the clad and (b) ring-shaped regions (from 1 to 15) employed to discretise the clad. Table 7 Ring-shaped geometric discretisation of the clad. Region, j Max. Ø (mm) Min. Ø (mm) Area (pixel) Total area (pixel) Weighting factor, n j (%) 1 0.1 0.0 0.683 7.467 9.14 2 0.2 0.1 0.651 8.72 3 0.3 0.2 0.642 8.60 4 0.4 0.3 0.640 8.57 5 0.5 0.4 0.626 8.38 6 0.6 0.5 0.601 8.05 7 0.7 0.6 0.556 7.44 8 0.8 0.7 0.537 7.19 9 0.9 0.8 0.496 6.64 10 1.0 0.9 0.488 6.53 11 1.1 1.0 0.407 5.45 12 1.2 1.1 0.383 5.13 13 1.3 1.2 0.290 3.88 14 1.4 1.3 0.273 3.66 15 1.5 1.4 0.196 2.62 M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 7 ceramic phase injected into the melt pool and subsequently solidified into the clad can be estimated according to equation (4), where M2wt.% is the weighted composition or ceramic phase content of the clad, nj is the weighting factor of region the j given in Table 7, and M2wt. %j,CFD model is the average ceramic content of the powder stream in the region j provided by the CFD model. To assess the validity of the proposed simplified multi-material model, the values obtained through equation (3) (experimental) and (4) (numerical), are compared for the scenarios contemplated in Table 4. 5. Strategies to overcome powder segregation Lastly, with the aid of the developed simplified multi-material CFD model, two approaches are proposed to overcome the challenge of powder segregation and to control the composition of the target multimaterial parts. The first approach is founded on the anticipation of the composition of the powder stream at the working plane, and the composition of the multi-material powder stream delivered by the powder feeder is tuned to achieve a specific powder composition in the melt pool. The second approach relies on tuning the granulometry of the ceramic phase so as to minimise powder segregation and to achieve a similar dynamic behaviour of the two materials. In the following sections the methodology proposed for each strategy is detailed. 5.1. Approach 1: Adjustment of the composition of the powder stream delivered by the feeder In order to overcome the challenge of tightly controlling the composition of the multi-material parts built, a transfer function is derived. This transfer function is calculated based on the simplified multi-material algorithm validated according to sections 4.1 and 4.2 and it correlates the composition of the powder stream entering the melt pool and the composition of the multi-material flow injected into the model, as shown in equation (5), where M2wt.% is the mass percentage of M2 (ceramic reinforcement phase) in the powder stream at the working plane and entering the melt pool, F is the transfer function, and M2in wt.% is the mass percentage of M2 in the powder stream entering the system through the discrete phase injections. M2wt.%=F[M2in wt.%](5) In order to derive the transfer function, several cases are tested with varying M2in wt.% (Table 8). The composition of the material entering the melt pool is calculated following the same method described in the previous section. Lastly, the transfer function is derived by seeking for the best fitting curve that correlates the input and the output of equation (5). 5.2. Approach 2: Optimisation of the granulometry of the ceramic phase (material 2) The second strategy proposed relies on minimising the powder segregation. In other words, it aims at modifying the diameter of the ceramic particles to make them follow the trajectories of the metallic particles closely. Four different scenarios are simulated to understand the effect of the size of the powder particles on their trajectories (Table 9x). The size of the metallic particles is kept constant to isolate this effect, and the same is done for the inputs of the CFD model in terms of gas inputs, etc. In addition, the composition of the multi-material powder stream injected into the model is fixed at 50 % wt. of M2, M2inwt.%=50. In order to lower the size of the ceramic particles in a systematic manner, the size of the actual reference particles is lowered proportionally employing a reduction factor (X) to the original PSD. In the studied problem, drag forces are going to dominate the path of discrete particles, therefore, adjusting the size of the discrete particles to make drag forces of both materials similar will most likely reduce powder segregation. Considering that the drag force in this case is proportional to ρ 2⋅d3, in Table 9 the ratio (R) between the drag forces acting on M1 and M2 are also depicted. The closer this ratio is to 1, the more similar the materials are, and the more similartheir drag behaviour. To quantify the powder segregation, the ratio between the ceramic content in powder stream fed to the model and entering the melt pool (Λ) is evaluated. In this way, it is possible to assess how similar the trajectories of the particles of each material are. The closer Λ is to 1, the greater the similarity between the materials in terms of dynamic behaviour and the lower the powder segregation. 6. Results and discussion In this section the results obtained are reported and discussed. Firstly, the simplifying hypothesis based on the superposition principle is numerically validated against the base model. Secondly, the simplified multi-material CFD model is validated against experimental data. Thirdly, two approaches are investigated to mitigate the effect of powder segregation on the composition of the fabricated part. 6.1. Numerical validation of the superposition algorithm In Fig. 9, the results obtained in the base multi-material CFD model for the scenarios considered in Table 4 are shown. In the overall view, the discrete phase concentration along the Z axis of all scenarios is comparatively shown. It is apparent that the powder mixtures behave differently according to the composition of the multi-material mixture or, in other words, the ceramic content. Indeed, powder mixtures with higher ceramic content, namely scenarios 2–4, exhibit a significantly higher peak of DPM at the FPP of M2. Conversely, this peak is lowered in favour of the DPM at the FPP of M1 as the ceramic content is diminished. Interestingly enough, it is apparent that powder segregation occurs and that powder particles of M1 (less dense) are going to concentrate at approximately 15.22 mm, while particles of M2 (denser) are going to concentrate more intensively at 13.65 mm. Based on the results obtained, which support the hypothesis of the trajectory of the particles being determined by the material and particle size, the utility of the superposition principle becomes apparent. With the aim of demonstrating the validity of the simplified algorithm proposed in section 4, two indicators are looked at. On the one hand, the discrete phase distribution along the Z axis is compared based on the data provided by the base multi-material CFD model and the Table 8 Cases studied to derive the transfer function. Case M2in wt.% ˙ m1 (g⋅min −1 ) ˙ m2 (g⋅min −1 ) 1 10 % 5.19 0.58 2 20 % 4.85 1.21 3 30 % 4.47 1.91 4 40 % 4.04 2.70 5 50 % 3.58 3.58 6 60 % 3.04 4.56 7 70 % 2.44 5.69 8 80 % 1.74 6.97 9 90 % 0.94 8.46 Table 9 Scenarios studied to adjust the granulometry of the powder. Scenario M2in wt.% ˙ m1 (g⋅min −1 ) ˙ m2 (g⋅min −1 ) X (−) R (−) 1 50 % 3.58 3.58 1.00 0.29 2 50 % 3.58 3.58 0.75 0.69 3 50 % 3.58 3.58 0.50 2.33 4 50 % 3.58 3.58 0.25 18.66 M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 8 simplified algorithm. On the other hand, the velocity of the fluid flow in scenarios 0, 2, and 4 is contrasted. In Fig. 10(a–c), the results corresponding to the numerical validation according to the DPM distribution along the z axis are shown. Data corresponding to the multi-material CFD model, the simplified algorithm, and the error are depicted. Results show that the simplified algorithm losses precision as the ceramic phase in the multi-material mixture increases. In Fig. 11, the evolution of the maximum error and the mean error in the region of interest (from 12 mm to 16 mm) is reported. This lack of fit with increasing M2 content is ascribed to the higher density of this material. Denser particles are more susceptible to influence the motion of the fluid phase. Nonetheless, the maximum error in the region of interest is kept below 6.5 % for all studied scenarios, and therefore, both calculation procedures, i.e. base and simplified models, are rendered equivalent. In terms of the motion of the fluid, a slight variation is observed in correlation with the composition of the powder mixture employed (Fig. 12). In the case of the heaviest material, i.e. M2, the fluid phase exhibits a slightly higher velocity in the region from 13.5 to 15 mm in the Z axis. In contrast, the results obtained with the 50 % multi-material mixture are precisely in between the data obtained for materials M1 and M2. The results obtained are in good agreement with the evolution of the error obtained. Namely, the more significant the modification of the motion of the fluid flow, the less accurate the superposition principle. Nonetheless, this lack of accuracy is reasonable, especially for 0–50 % wt. multi-material mixtures. As a result, the equivalence between the base and simplified model is ratified for the present applications. The simplified algorithm relies on the single-material CFD model to calculate Fig. 9. Discrete phase concentration along the Z axis for scenarios 0–4. In addition, a summary of all scenarios with a wider zoom is shown. FPP M1 and M2 indicate the focal plane position of materials 1 and 2 in single-material flows. Fig. 10. DPM in the z axis based on the multi-material CFD model and the simplified algorithm for the scenarios considered. Fig. 11. Evolution of the error of the simplified algorithm vs. the composition of the multi-material mixture. M. Ostolaza et al. International Journal of Thermal Sciences 198 (2024) 108885 9 the powder distribution of multi-material mixtures. Therefore, if the behaviour of mixtures with different compositional ratios is to be studied, the computational cost of the analysis is significantly reduced. As a matter of fact, running two simulations (one for each material) suffices to calculate all required scenarios, provided the inputs of the model regarding the fluid flow remain constant. 6.2. Experimental validation of the superposition algorithm Once the validity of the superposition assumption is numerically demonstrated, the CFD model is experimentally validated based on the composition of a multi-material FGM part produced by L-DED. Indeed, the powder segregation caused by the differing inertial properties of the constituents is likely to provoke a deviation of the real composition of deposited part from the targeted one. To that end, an experimental validation of the simplified algorithm is carried out following the scenarios contemplated in Table 5. Firstly, the composition of the multimaterial mixture at 15 mm from the nozzle exit is derived with the simplified algorithm. More specifically, the composition of the discrete phase with respect to the position on the X axis is studied. The results obtained are shown in Fig. 13(a). In Fig. 13(b) a more detailed view is provided with regard to the clad geometry. Dotted lines refer to the composition of the multi-material powder mixture at the inlets of the nozzle, while continuous lines refer to the ceramic content in the multimaterial powder stream at 15 mm from the exit of the nozzle. Based on the results obtained, and the weighting coefficients given in Table 7, the composition of the multi-material part is derived and compared to that measured through EDS. The results are shown in Table 10. The comparison between the numerical and the experimental data suggests that the simplified algorithm performs well, as it captures the deviation of the composition of the actual part with respect to the nominal composition. It must be highlighted, however, that the dilution of the layer below will affect the composition of the deposited layer. Hence, each layer n will be affected by the composition of the layer below n-1. In the present experiment, the dilution measured in a layer is roughly 15%, therefore, the composition of a layer depends mainly on the composition of the injected powder stream. In any case, if higher dilution values were reported due to the L-DED process parameters employed, it would introduce a greater error in the comparison between numerical and experimental results, as the CFD model does not account for the effect of dilution. This error is partially mitigated by taking the average of two subsequent layers per scenario. 6.3. Strategies to face powder segregation in multi-material L-DED Once agreed that the differing inertial properties affect the composition of the deposited multi-material clads due to powder segregation, Fig. 12. Velocity of the fluid phase. In the right-hand image, the velocity of the fluid phase in the XZ plane for scenarios 0 and 4 are shown. Fig. 13. (a) Composition of the multi-material powder stream at 15 mm from the exit of the nozzle and (b) a detail of the area of interest. Table 10 Results of the experimental validation of the simplified algorithm. Nominal composition, wt. % Numerical results, wt. % EDS measurements: Experimental results wt. % Error 10 8.71 8.40 ±2.66 4 % 20 17.54 17.04 ±1.21 3 % 30 26.66 25.16 ±3.97 6 % 40 36.19 33.82 ±0.37 7 % M. Ostolaza et al.