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CAFE simulation of normalized mixture concentration for: a Case 1, b Case 2, c Case 3, d Case 4 and e Case 5. The equivalent solutal expansion coefficient for each case is given.
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Evolution of grain structure and formation of freckle defects were simulated in directionally solidified nickel-based superalloy casting with abrupt contraction in cross-section area. A two-dimensional (2D) Cellular Automaton (CA) – Finite Element (FE) model was presented. The transport of liquid momentum, heat and solute mass at macroscopic scale,...
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... plumes. The distribution of segregated pockets is not continuous. The birth and death of segregated pockets are mainly controlled by the local convection patterns. In both Figs. 4 and 5, we can suggest that different convection cells above the mush dominate at different times. Thus, the stabilizing solutal plume flow cannot be established. Fig. 3 is examined again. For all cases, freckles are observed to form at the horizontal and vertical edges of the casting and are relatively straight and continuous in all cases except in Case 5. For example, in Case 4, solutal channels close to the vertical edges of the part with wideness 20 mm develop from bottom to top and the width is ...
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... is examined again. For all cases, freckles are observed to form at the horizontal and vertical edges of the casting and are relatively straight and continuous in all cases except in Case 5. For example, in Case 4, solutal channels close to the vertical edges of the part with wideness 20 mm develop from bottom to top and the width is about 630 μm (Fig. 3(d)). According to the wall effect [7], an abrupt contraction in cross section introduces surfaces that provide relatively high permeability for freckling convection in comparison to neighbouring dendritic network. As shown in Fig. 5, when solidification front proceeds into the parts with wideness of 20 mm and 5 mm, upward flow along the ...
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A theoretical and computational study analysing the initiation of yield-stress fluids percolation in porous media is presented. Yield-stress fluid flows through porous media are complicated due to the non-linear rheological behaviour of this type of fluids, rendering the conventional Darcy type approach invalid. A critical pressure gradient must be...
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... The equivalent solute concentration was calculated using Eq. (3) [39,40] ...
... (4) Multicomponent system. The current multicomponent superalloy was treated as a pseudo-binary alloy [39,40]. On the basis of the good agreement between the simulation results and the experimental observations of the current work and other works [22,39,40], this simplification seems to be acceptable. ...
... The current multicomponent superalloy was treated as a pseudo-binary alloy [39,40]. On the basis of the good agreement between the simulation results and the experimental observations of the current work and other works [22,39,40], this simplification seems to be acceptable. Referring to our previous work on the ternary alloy [45,46], the solidification path should be calculated properly by considering the multicomponent phase diagram, growth kinetics and the flow-induced macrosegregation. ...
Single-crystal superalloy turbine blades (TBs) fabricated using directional solidification are key components of aeroengines and gas turbines. Owing to thermal–solutal convection during solidification, such components are susceptible to flow-induced defects such as freckles and/or eutectic accumulation. The formation mechanisms of the above defects are well understood, but reliable theories or empirical laws are unavailable to guide the engineering production process as the thermal–solutal convection is sensitive to the alloy, Bridgeman furnace design, shape and internal structure of the TB, withdrawal parameters, etc. This study proposes a novel method to ‘digitally twin’ the directional solidification of the TB, i.e. to utilise a physically based numerical model to quantitatively simulate the solidification process, including freckle formation and eutectic accumulation. It includes two simulations: one for the global thermal field in the Bridgeman furnace, including the casting system, and the other for the flow and solidification within the casting component. The former is modelled using ProCAST, the latter is modelled using a volume-average-based multiphase solidification model, and both are coupled. To verify the digital twin concept, an actual industrial TB with slight geometrical modification (removal of the fins while maintaining the inner surface profile) was cast in a Bridgman furnace, and the as-solidified TB was inspected for freckles. An excellent agreement between the simulation and experimental results was obtained. Typically, an actual TB features a complex inner structure (fins) that connects the front and back blades with an average wall thickness of 1.5 mm. A fresh simulation was performed for the TB with inner fins. It was observed that the inner fins of the TB along with other process conditions, such as the shadowing effect of the furnace, play an important role in freckle formation. This study demonstrates the necessity of the digital twin in future TB production.
... ey are the casting method and the various casting techniques used, and the casting parameters and conditions used for casting. Directional solidification (DS) refers to the process of ensuring that grains grow in a single Table 2. Simulation studies: any study in which simulations were performed in order to reproduce or simulate different casting features, grain structures, skin formation, like the progression of S/L interface, shape of liquidus isotherm, etc. [2,8,36,37,41,42,54,56,[60][61][62][63][64][65][66][67][68] 2 Prediction studies: any study in which various methods were used for predicting the features of the cast specimens like pore size, freckle formation, grain structure, grain size, and fatigue life [9,17,20,28,37,41,43,58,69] 3 Conventional investment casting (Bridgman furnace): any study that focuses on the conventional casting process where a Bridgman furnace is used [16,[44][45][46]70] 4 LMC process: any study in which LMC process was used or was talked about in depth [1,30,35,36,71] Advances in Materials Science and Engineering 3 HRS process: any study in which HRS process was used or was talked about in depth [8,30,36,71] 6 ...
... Vacuum condition: any study that talked in depth about the effects of using vacuum conditions during casting procedure [26] 24 Effect of alloying elements: any study that talks about the effects of different alloying elements and how varying their contents can affect the final product [7,40,42,55,59,73,76,77,82,83,90] Advances in Materials Science and Engineering 5 Freckles: any study that talks about the formation of freckles, the harm they do, and how freckling can be avoided [5, 8, 26-28, 35, 42, 85, 90-93] 26 ...
... Grain selection: any study that talks in depth about the grain selection/competitive growth process that takes place when selecting a single grain while producing SX components [4,6,36,49,56,62,85,95,97] 33 Geometric effect: any study that talks about how the geometry or dimensions of the components, the mould, or the cores affect the properties of the final product [4,5,8,31,42,79,80,93] 6 Advances in Materials Science and Engineering Ceramic mould/core constituents: any study that deals with the effects the composition and type of constituents of the ceramic slurry used in making the mould and cores have on the final product [56,66,87] 35 ...
In this review article, research papers related to recent developments in Ni-superalloy technologies have been reviewed in order to provide an insight into recent achievements and the potential for further study, research, and development in this field. In this paper, studies on various aspects of Ni-based superalloys are reviewed, such as production methods, which include widely used casting methods, as well as unconventional alternative procedures, novel techniques, or simulation and prediction of certain alloy casting properties. Reviewing was done by categorising the papers into 4 major categories: manufacturing of Ni-based superalloys, effects of alloying elements, physical and mechanical properties of Ni-based superalloys, and defects in Ni-based superalloys. The process used to make Ni-superalloy parts can have a huge impact on the production process efficiency, the final product’s quality and properties, and the defects formed in it. Investment casting is one of the most common methods for making Ni-superalloy parts. Manufacturing covers studies on various casting methods used to make Ni-based superalloy components, novel techniques and methods developed to improve casting procedures to produce better products, and alternative manufacturing methods like AM and HIP processing. Similar to production process, the role of alloying elements is also very important. Even minor changes in their compositions can cause significant changes in the final product. Simultaneously, these alloying elements appear to be more efficient in the development of new methods to control product quality, suppress defect formation, and improve material properties such as the creep and fatigue. As a result, the effects of various alloying elements used in castings of Ni-based superalloys are thoroughly examined. A material’s properties are its most important components. They assist the industrialist in selecting or developing a material based on the needs of the application/use. With this in mind, many researchers have conducted extensive research on physical and mechanical properties, as well as how to improve them. Fatigue life, stress rupture, creep properties, impact ductility, strain response, stress relaxation behaviour, and so on are some of the most important physical and mechanical properties of Ni-superalloys. This article thoroughly reviews various studies on these properties, how and by what factors they are affected, and how they can be improved. Another important factor to consider when making Ni-superalloy castings is defect formation, which can affect the properties of the final product. Freckle defects, hot tears, porosities, and slivers are some of the major defects that occur in Ni-superalloys during the casting process. This article also reviews in detail about these defects, how they form, and how they affect the final product. These defects were found to have a significant influence on a variety of properties, such as creep, fatigue behaviour, and fracture mechanism. Topics and areas such as reinforcement of Ni-superalloys with the help of CNCs and 3D printing of Ni-superalloys that can provide scope for potential future research are highlighted based on the above-reviewed papers.
... 10 The CMSX-4 nickel-based superalloy is used in this work. The thermophysical properties of CMSX-4 are listed in Table 2, and the nominal composition and phase-diagram parameters are listed in Table 3 [43,44], the primary dendrite arm spacing is set to 500μm, and the secondary dendrite arm spacing is 100μm [45,46]. All the boundaries of the computational domain are no-slip boundaries. ...
Channel segregation-known as freckle-is one of the most complex defects which severely limit mechanical properties of investment cast single-crystal turbine blades. The freckle phenomenon is induced by the thermal-solutal-fluid flow instability during solidification process; it is therefore important to gain better understanding of the fluid flow, heat transfer and species transport during the investment casting process. In this work, a three-dimensional Eulerian two-phase model is developed to investigate chimney behaviours and the evolution of channel segregation in the directional solidification of nickel-based single crystal superalloy CMSX-4. The results reveal that the channels are merely distributed on the surface of ingot backed up with targeted experiments, and the morphology of the predicted channel segregation is also consistent with the observed freckle chains. By ignoring lateral heat flux, deviation in the prediction of channel segregation using Rayleigh number criterion is anticipated, because not all the chimneys can be developed into channel segregation under the significant perturbation. In the mushy zone, the perturbation of the melt convection from the horizontal direction to the casting direction leads to the extinction of existing chimneys, thereby exacerbating channel segregation. Once the stable channel segregation is formed, it will be developed steadily under further solute enrichment caused by thermal-solutal convection. Channel segregations is difficult to develop continuously in the centre of the representative rod, while channels near the lateral walls are more likely to develop stable flow along the casting direction. It is suggested that the weaker lateral heat flux can suppress the formation of channel segregation, providing an effective process design criterion for the freckle mitigation during the single crystal casting.
... Guo [10] and Sung [11] respectively reported the effect of grid spacing on the simulation results of freckle formation in leadtin alloy and nickel-based superalloy, and also proposed a more reasonable grid spacing in the numerical calculation. Sun et al. [12] simulated the formation of freckles during directional solidification of nickel-based superalloy castings under the condition of cross-section shrinkage. The results show that cross-section shrinkage leads to the increase of local permeability in the mushy zone, which promotes the formation of freckles. ...
... In addition, the equilibrium partition coefficient of solutes in solidification system can be obtained from eq. (12). In this way, the updated equation of solid fraction in the solidification system of multi-component alloys are as eq. ...
In order to investigate the solute distribution and freckles formation during directional solidification of superalloy ingots, a mathematical model with coupled solution of flow field, solute and temperature distribution was developed. Meanwhile, the reliability of this model was verified by the experimental and simulation results in relevant literatures. The three-dimensional directional solidification process of Ni-5.8wt%Al-15.2wt%Ta superalloy ingot was simulated, and then the dynamic growth of solute enrichment channels was demonstrated inside the ingot. Freckles formation under different cooling rates was studied, and the local segregation degree inside the ingot was obtained innovatively after solidification. The results show that the number of freckles formed at the top gradually decreases, and so do the degree of solute enrichment at these freckles with the increase of cooling rate. Moreover, the relative and volume-averaged segregation ratio is defined to describe the segregation degree inside the ingot. The span of relative segregation ratio for positive segregation is wider than that for negative segregation, but it accounts for less of total volume. As the cooling rate increases from 0.1 K/s to 1.0 K/s, the proportion of weak segregation (-20%~20%) increases significantly from 26% to 41%, so that the segregation degree is weakened in general. By analyzing the freckles formation and segregation degree inside the ingot, the numerical simulation results can provide a theoretical basis for optimizing the actual production process to suppress the freckle defects.
... It is now fully coupled with momentum, mass and energy transportation in liquid, solid and mushy zones [148,149]. Models derived from CA approaches such as Cellular Automata Finite Difference (CAFD) have simulated the evolution of dendritic morphology during alloy solidification in the presence of melt convection [150][151][152], stray grain formation [153,154], multiscale modelling [155], geometry-related grain boundary formation [156], freckle formation [157] and multi-component systems [158,159]. However, a major challenge with this method is the substantial anisotropic influence of the underlying grid on the simulation results [160]. ...
... The grid anisotropy superposes the physical anisotropy and therefore impedes the interpretation of the simulated microstructure; currently restricting CA simulation to a qualitative representation of dendritic solidification. dendritic morphology during alloy solidification in the presence of melt convection [150][151][152], stray grain formation [153,154], multiscale modelling [155], geometry-related grain boundary formation [156], freckle formation [157] and multi-component systems [158,159]. However, a major challenge with this method is the substantial anisotropic influence of the underlying grid on the simulation results [160]. ...
The primary spacing is intrinsically linked with the mechanical behavior of directionally solidified materials. Because of this relationship, a significant amount of solidification work is reported in the literature, which relates the primary spacing to the process variables. This review provides a comprehensive chronological narrative on the development of the directional dendritic growth problem over the past 85 years. A key focus within this review is detailing the relationship between key solidification parameters, the operating point of the dendrite tip, and the primary spacing. This review critiques the current state of directional dendritic growth and primary spacing modelling, briefly discusses dendritic growth computational and experimental research, and suggests areas for future investigation.
The freckle is a typical surface defect formed during the directional solidification of SC (single crystal) components of Ni-based superalloys. It generally appears as a long and narrow trail of equiaxed grains aligned roughly parallel to the direction of gravity, which breaks the integrity. Once appears, the freckle can never be avoided by further treatment. With the turbine blade requirements increasing, the state-of-the-art methods include adding more refractory elements into Ni-based SC superalloys, and the design of blades with a more complex geometric shape make the freckle defects grow easier at the special surface zones. This leads to a significant challenge in controlling grain defect formation in SC blades and vanes for freckles. The current consensus to freckle formation is described as the Rayleigh-Taylor instability (RTI) flow that occurred in the interdendritic zone. During solidification, the compositional segregation (CS) occurred as soon as the solid interface forwarding led to the density changes between the interdendritic melting phases and the residual liquids. For nickel-based superalloys, the enrichment of low-density solutes like Al, and Ti at the interdendritic zone will make the liquid lighter. However, the widely used Ra model can’t correctly match the freckle tendency of the components with complex shapes (called geometrical effects of freckles), especially for blades. Recent reports indicate that the freckles occur at the preferred positions in the casting. In this work, a novel model is designed to quantitatively discuss the geometrical effects on freckle formation and to combine existing Ra number models with solidification models to enable freckle predictions at a smaller scale. The proceeding of this work can make the design of complex blades easier.
A freckle is a grain defect frequently found in Ni-based single-crystal (SC) superalloy castings resulting in a high scrap rate. A precise prediction of the defect before production is of great importance, especially for the complex-shaped blades and vanes. Without reckoning geometrical effects, the state-of-the-art Rayleigh number (Ra) model fails to accurately forecast the freckle formation positions. In this study, a novel Ra-based mathematical model was proposed. It not only shortened the calculation period and eliminated the physically meaningless at the singularity of the existing model, but also quantified the geometrical effects. Using the model, the Ra at every position of SC castings was calculated, which can be used to evaluate the freckling tendency of the whole casting and locate the specific positions of the freckling risk zone. A freckle-free approximate critical Rayleigh number about 1.5 was determined. A highly consistent and accurate prediction of this model was validated by comparing it with the experiments using complex-shaped SC castings, which suggests its great prospects for industrial application.
The interface heat transfer coefficient (IHTC) at the different casting/shell mold interfaces during the vacuum investment casting process was investigated by measuring the temperatures of K4169 superalloy melt and mold shell during the preheating, transferring, pouring, and solidification processes. The inverse model of ProCAST was used to calculate the interface heat transfer coefficient (IHTC) based on the temperature measurement results. The inverse calculation results show that the heat transfer between the shell mold and the outside air changes from natural convection to forced convection during the transfer process, but the heat transfer between the shell mold and the inside air is consistently natural convection heat transfer. Then, the convective heat transfer coefficient gradually decreases to 0.1 W/m2·K with the vacuum increases and is finally converted to radiation heat transfer at a vacuum of 10-3 Pa. In the early stages of solidification, the IHTC between the shell mold and the casting can reach 16,000 W/m2·K due to the close contact and the large temperature difference between them, and with the thermal expansion of the shell mold and cooling contraction of the casting, the formation of the gap leads to the interfacial heat transfer coefficient gradually stabilizing at 100–200 W/m2·K. The experimental validation results show that the IHTC has a great influence on the accuracy of the prediction of the location and shape of shrinkage porosities in the vacuum investment castings.
A cellular automaton (CA)-finite element (FE) model was implemented for multi-scale modelling of micro-segregation, mesoscopic grain structure and macroscopic segregation during direct chill (DC) casting of industrial billets or slabs. The macroscopic transport of mass, momentum, energy and solutes is solved on an FE grid, while the mesoscopic grain structure governed by nucleation, growth kinetics and grain evolution was calculated on a CA grid. The solidification path was determined using a modified micro-segregation model for multi-component aluminium alloys. An Euler representation was used for pre-processing and post-processing, and a Lagrangian representation was used for expanding the calculation domain and for resolving the CAFE model. By simulating a DC casting experiment of the 2024 aluminium alloy, a typical grain structure was reproduced, and the composition map showed a reasonable deviation. This model was applied to an industrial-scale DC cast slab of an Al-3.5Cu-1.5Mg (wt. %) alloy, and three simulations with different nucleation undercoolings were performed for a grain-unrefined slab, a grain-refined slab and an equilibrium solidified slab, respectively. The slabs tended to solidify at equilibrium with the decreasing nucleation undercooling. The earlier release of latent heat yielded a smaller liquid undercooling region ahead of the solidification front, and a finer grain structure. A typical grain structure with coarse equiaxial grains at the centre and fine columnar grains near the bottom surface as well as sidewall was observed for the grain-unrefined slab. By contrast, the grain structure of the grain-refined slab was fully equiaxial. Furthermore, the grain structure, temperature field, melt flow and macro-segregation were quantitatively investigated.
