Experimental and Numerical Investigation on the Formation Mechanism of Freckle Defects in a Novel Third-Generation Nickel-Based Single Crystal Superalloy Turbine Blade

Abstract

This paper investigates the formation mechanism and key influencing factors of freckle defects that arise during the directional solidification of a novel third-generation nickel-based single crystal superalloy turbine blade. A combined experimental and multi-physics numerical simulation approach was adopted. The results indicate that freckle formation primarily originates from solutal convection, which subsequently triggers a cascade of processes, including the development of convection-induced segregation channels, flow-driven dendrite fragmentation, and the migration and aggregation of dendrite fragments. The severity of freckling is closely dependent on both the casting’s position within the furnace and its local geometric characteristics. Castings located in regions with poorer heating conditions exhibit lower temperature gradients and slower solidification rates, significantly increasing their susceptibility to freckle formation. Similarly, on a given casting, the side subjected to less favorable heating is more prone to freckle initiation. The freckle number varies non-monotonically along the blade height, increasing from 3 to a maximum of 16, with a temporary decrease near the platform and a final reduction near the top. This trend is mainly attributed to thickness-dependent channel segregation, as well as freckle propagation into the interior and coalescence at higher positions. This study provides a crucial theoretical basis for understanding the formation mechanism of freckle defects in nickel-based single crystal superalloys and offers valuable guidance for optimizing blade manufacturing processes, reducing solidification defects, and enhancing blade quality and service performance.

1. Introduction

Nickel-based single crystal superalloys are the core materials for manufacturing turbine blades in advanced aeroengines and heavy-duty gas turbines, and their temperature capability directly determines the power and efficiency of the engines [1,2]. With the continuous increase in thrust-to-weight ratio requirements in the aviation industry, the turbine inlet temperature has exceeded 1650 °C, posing extremely stringent challenges to the high-temperature performance of these alloys. Third-generation nickel-based single crystal superalloys have significantly enhanced high-temperature strength and creep resistance through the addition of high levels of refractory elements (e.g., 3–6 wt.% Re and 5–8 wt.% W). However, this increased alloying also intensifies the tendency for macrosegregation during solidification, leading to a variety of solidification defects, among which freckle defects are a typical example [3,4].

During the directional solidification process for manufacturing single crystal blades, freckle defects represent a typical and detrimental macroscopic solidification defect. These defects are typically distributed in chains along the gravity direction, consisting of strings of fine equiaxed grains and often accompanied by localized eutectic enrichment [5,6,7,8,9]. The presence of freckles compromises the single crystal integrity of the casting, significantly degrading the high-temperature mechanical properties and fatigue life of the blade. Since such defects cannot be eliminated by subsequent heat treatment, they frequently lead to high rejection rates of blades, making them a critical bottleneck restricting the yield improvement of high-performance single crystal blades.

Since the 1970s, freckle defects have received systematic attention. Copley et al. [10,11,12] were the first to systematically describe their morphology and characteristics. Subsequently, numerous studies have explored their formation mechanism using industrial superalloys [13,14,15] or model alloys (e.g., Pb-Sn, Pb-Sb [16], and NH₄Cl–H₂O [17]). It is widely accepted that freckles originate from thermo-solutal convection within the mushy zone: the interdendritic liquid, enriched with low-density solute elements such as Al and Ti, undergoes density inversion, triggering upward flow that washes away and remelts dendrite arms, ultimately leading to the formation of equiaxed grain chains [18]. It was reported that higher cooling rates and temperature gradients are generally conducive to suppressing freckle defects [19,20]; however, this simple rule is not universally applicable to all castings [21]. In recent years, Ma et al. [14,22,23] have systematically revealed through experiments the influence of turbine blade geometry on freckle formation, proposing various mechanisms such as the “edge effect,” “shadow effect,” “step effect,” “curvature effect,” and “crystal orientation effect.” However, in actual blades, because multiple effects often intertwine and coexist, identifying the dominant mechanism remains challenging.

With the advancement of numerical simulation techniques, researchers have begun to explore the formation mechanism of freckles in depth from the perspective of multi-physics and multiphases coupling. Beckermann et al. [24,25] established a macroscopic transport model considering thermo-solutal convection, proposed a Rayleigh number-based criterion for freckle formation, and achieved effective prediction of freckle distribution in castings with simple geometries. However, for actual turbine blades with complex internal cavity structures, traditional models still struggle to achieve accurate predictions. This difficulty stems from the fact that the blade geometry significantly perturbs the temperature and solute fields at the solidification front, inducing local heat flux anomalies and solute enrichment, which in turn affect defect initiation and evolution. Although some models that directly resolve dendrite morphology at the microscale [26,27] can effectively reveal the initiation mechanism of freckles, their computational cost is extremely high. The lattice Boltzmann method (LBM) has been widely adopted to investigate the solidification behavior of superalloys [28,29]. It enables high-resolution simulation of dendritic morphology and solidification phenomena at the microscale, offering an intuitive representation of channel segregation formation. However, applying LBM to full-scale castings remains computationally prohibitive due to its substantial computational cost. With current computational capabilities, simulating engineering-scale castings using this approach continues to pose significant challenges. They are only applicable to locally simplified geometric regions and have difficulty coupling global thermal factors such as radiation and shading within the Bridgman furnace, making them unsuitable for full-blade simulations at an engineering scale. Recent studies indicate that solidification models based on the volume-averaged method are more promising for such problems [30,31]. By averaging microscopic phenomena, this method achieves effective coupling with macroscopic transport processes and has demonstrated good capability and computational efficiency in predicting freckle initiation and evolution [32,33].

In industrial production, turbine blades are typically cast in clusters by arranging multiple blades into a circular mold assembly within a Bridgman furnace. Due to the significant shading effect inside the furnace, considerable temperature differences arise among blades positioned at different orientations, with measured variations reaching approximately 20 K [34]. Experimental observations indicate that regions of the blade facing away from the heat source are more susceptible to freckle formation, whereas areas facing the heating zone remain nearly free of such defects [34]. Furthermore, the ceramic cores used to form the internal cavities of hollow blades further increase the complexity of the thermal and flow fields during solidification [35,36,37].

The present study investigates the formation characteristics of freckle defects during the directional solidification of a novel third-generation nickel-based single-crystal superalloy turbine blade under industrial casting conditions. Casting experiments were conducted in a Bridgman furnace, and the freckles in the as-solidified blades were systematically characterized, with particular emphasis on the freckle morphology and the grain structures in the vicinity of the freckles. The freckling tendency of turbine blades located at different positions within the furnace was compared to evaluate the influence of thermal–flow conditions on defect formation. In addition, a correlation analysis between local solidification conditions and freckle formation was performed using the Rayleigh number criterion. Finally, based on the solidification process characteristics obtained from the digital twin simulation framework previously developed by the authors [30,38], the freckle formation mechanism is discussed by considering the interaction between interdendritic flow and solidification behavior.

2. Experimental and Numerical Methods

2.1. Casting Preparation and Characterization

This study investigates a novel third-generation nickel-based single crystal superalloy, and its nominal chemical composition is presented in

Table 1. Chemical composition of the investigated superalloy (in wt.%).

Element	Al	Co	Cr	Fe	Hf	Mo	Nb	Re	Ta	Ti	W	Ni
Content	5.69	5.97	3.39	0.21	0.03	0.41	0.10	4.89	8.07	0.15	6.52	Base

. Single crystal turbine blades were fabricated using the spiral grain selector method in a directional solidification furnace. The freckle defects formed in the as-cast microstructure of the blades were characterized and analyzed.

The molds were fabricated using alumina-based ceramic shells, with each shell assembly containing nine castings of varying geometries and/or orientations. Casting and directional solidification were carried out in a VIM-IC/DS/SC Bridgman vacuum directional solidification furnace manufactured by ALD, which features precise temperature control. The configuration of the hot zone and the spatial arrangement of the shell assembly are shown in Figure 1a. The geometries of the castings examined in this study are presented in Figure 1b,c: (b) the geometry and dimensions of the blade, and (c) the surface morphology of an as-cast single-crystal turbine blade. The specific process steps are as follows: Prior to pouring, the ceramic shell was transferred to the furnace’s preheating chamber and preheated to a holding temperature precisely controlled at 1723 ± 5 K. After the alloy charge was completely melted, the melt was poured into the preheated ceramic shell at the same temperature of 1723 ± 5 K. Following the pouring, the shell assembly was withdrawn from the hot zone (1723 ± 5 K) into the cold zone (353 ± 2 K) at a rate of 1.5 mm/min to trigger the directional solidification process.

After the directional solidification process, the mold assembly was removed from the furnace, and the shell was eliminated. The casting system was removed using a precision cutting machine. To examine the single crystal integrity and freckle defects, the castings were first subjected to macro-etching using an etchant with a composition of CuSO₄:HCl:H₂O = 4 g:10 mL:20 mL. Freckle defects and other grain defects were identified and marked through this macro-etching method. Subsequently, cross-sectional samples were sectioned from the blade airfoil using a wire electrical discharge machine. These samples were sequentially mounted, ground, polished, and chemically etched using the same etchant formulation. The microstructure was observed using an MM-400 optical microscope. A schematic diagram of the casting gating system model and the investigated castings are shown in Figure 1.

2.2. Numerical Calculation Model and Method

2.2.1. Temperature Field Calculation

Figure 1a shows the full-scale geometric model of the gating system within the Bridgman furnace. Although the nine castings vary in shape and orientation, they are arranged in a centrosymmetric pattern. Accordingly, a 1/9 symmetry model was adopted for temperature field simulation of the investigated casting to reduce computational cost, as depicted in Figure 2a. The system comprises an upper heating zone and a lower cooling zone separated by an insulating baffle. The ceramic shell mold rests on a water-cooled copper chill plate, with a ceramic core embedded to form the internal cavity of the turbine blade. Directional solidification is accomplished by withdrawing the mold assembly downward at a constant rate.

Temperature field simulation was performed using the commercial software ProCAST 2019.0. The geometric models of the turbine blade, ceramic core, and ceramic shell are shown in Figure 2b,c, respectively. In the model, the relative lifting motion of the furnace body was used to simulate the dynamic displacement between the shell and the furnace. The calculated temperature field data will serve as the initial and boundary conditions for the subsequent flow-solidification coupling analysis using the ANSYS Fluent 17.1 software.

2.2.2. Flow-Solidification Coupling Calculation

To describe the solidification process in the casting, a numerical framework based on a multiphase volume-averaged solidification model was employed, and the thermal field transfer scheme is illustrated in Figure 3. To couple the furnace-scale thermal field with the local solidification behavior of the turbine blade, a global–local digital twin strategy previously developed was adopted [38]. In the first step, the global temperature field of the Bridgman furnace, including the casting system, was calculated using ProCAST. In the second step, the flow and solidification processes inside the turbine blade were simulated using the multiphase volume-averaged solidification model. The temperature history on the blade surface obtained from the ProCAST simulation was then mapped onto the local model to provide thermal boundary conditions. The method for transferring thermal data between the two simulations is illustrated in Figure 3c–e. Temperature histories were extracted from predefined locations on the blade surface in the ProCAST model (blue points) and expressed as fitted temperature–time functions. In the local solidification model, temperatures at the centroids of computational cells (red points) were obtained by bilinear interpolation from the surrounding surface data points. The interpolated temperature histories were subsequently implemented through a user-defined function as thermal boundary conditions for the flow–solidification calculations. To verify the ProCAST–FLUENT thermal coupling, a calibration calculation without melt flow was performed. The temperature profiles and solidification-front shape obtained in FLUENT reproduced the original ProCAST results closely, confirming that the thermal mapping procedure introduced only negligible interpolation error under the present spatial discretization [38].

Owing to the high computational cost of fluid-flow simulations, only Casting B was considered in the coupled flow–solidification calculations. The computational domain of the volume-averaged solidification model was restricted to the blade body region (Figure 3b). The governing equations include the conservation of mass, momentum, energy, and solute for the multiphase system, enabling the simulation of melt convection, permeability evolution within the mushy zone, and thermo-solutal convection during solidification. Further details of the model formulation are provided in Ref. [38].

In this framework, the liquid melt and the solid phase representing columnar dendrites are treated as interpenetrating continua, and the local liquid fraction, solid fraction, temperature, solute concentration, and melt velocity are obtained by solving coupled mass, momentum, species, and enthalpy conservation equations. Columnar dendrite growth was described using a simplified cylindrical morphology, and the tip-front kinetics were tracked with the LGK model [38]. Local equilibrium was assumed at the solid–liquid interface, while the mushy zone was treated as a porous medium governed by Darcy flow. Thermo-solutal buoyancy was introduced through the Boussinesq approximation, whereas solidification shrinkage was neglected. The alloy melt was treated as an incompressible fluid with constant density and viscosity. To balance computational cost and accuracy, the multicomponent superalloy was approximated as an equivalent binary alloy system to represent its solidification behavior. Regions susceptible to freckle formation were evaluated using the solute enrichment index. The key material properties and processing parameters used in the simulations are summarized in

Table 2. Material properties and processing parameters [38].

Properties/parameters	Symbol	Units	Values
Thermophysical
Specific heat of the alloy	cp,l; cp,s	J·Kg−1·K−1	500.0
Latent heat	Δhf	J·Kg−1	2.4 × 105
Liquid diffusion coefficient	D1	m2·s−1	3.6 × 10−9
Liquid thermal conductivity	k1	W·m−1·K−1	33.5
Solid thermal conductivity	ks	W·m−1·K−1	24.6
Thermal expansion coefficient	βT	K−1	−1.16 × 10−4
Solutal expansion coefficient	β c	wt.%−1	−0.228
Density	ρ	Kg·m−3	7646.0
Viscosity	μ1	Kg·m−1·s−1	4.9 × 10−3
Thermodynamic
Eutectic temperature	Teut	K	1627.0
Liquidus slope	m	K (wt.%)−1	−1.145
Equilibrium partition coefficient	k	-	0.57
Primary dendritic arm spacing	λ1	µm	500.0
Melting point of the solvent	Tf	K	1728.0
Others
Initial concentration	${\overline{C}}_0$	wt.%	35.09
Initial temperature	T0	K	1773.0
Withdrawal velocity	v	mm/min	3.0

[38]. A full mesh-independence study has not yet been performed because the blade thickness is only about 1.5 mm, and further mesh refinement would greatly increase the computational cost. In this study, a minimum mesh size of 0.2 mm and a time step of 0.01 s were used. Since the simulation results agree well with the experimental observations, the current mesh size and time step are considered acceptable for the present analysis.

3. Experimental Results and Analysis of Freckle Defects

3.1. Macroscopic Characteristics of Freckles in Castings at Different Furnace Positions

Two nickel-based superalloy turbine blade castings (designated as Casting A and Casting B), prepared under identical conditions with consistent dimensions, were selected as the research objects. Their positioning within the furnace is illustrated in Figure 2. Casting A, positioned adjacent to the heating element, was defined as the hot zone casting; Casting B, positioned away from the heat source, was defined as the cold zone casting.

To elucidate the macroscopic distribution characteristics of freckle defects on the outer surfaces of the two castings, a visual inspection method was employed to qualitatively document the distribution locations, morphological features, size ranges, and number density of the defects. The specific procedure was as follows: after etching, the entire surface of the casting was observed under natural light conditions. The positions of freckle defects visible to the naked eye were marked, and their macroscopic distribution patterns and aggregation tendencies were systematically recorded. This provided foundational data to subsequent analysis of defect formation causes.

3.1.1. Distribution of Freckles on the Outer Surface of Casting A

Figure 4 illustrates the macroscopic distribution of freckles on the outer surface of Casting A. Detailed observations revealed that freckle defects were present exclusively on the convex side (Figure 4a,b), while no freckle defects were observed on the concave side (Figure 4c). Figure 4d presents a schematic diagram of the freckle distribution on the convex side. Following a previous work of the authors [30], freckles were distinguished from segregation channels by the presence of stray grains. A segregation channel is defined as a freckle only when spurious grains are present; otherwise, it is termed a quasi-freckle. Regions marked by orange lines represent segregation channels, appearing as continuous traces with uniform coloration, where abundant eutectic aggregates were observed under metallographic microscopy. Regions marked in red represent stray grains, appearing as dotted or patchy discoloration in the form of intermittent traces, which constitute the core manifestation of freckle defects. For ease of description, as depicted in Figure 4d, the three freckle traces on the convex side were designated as Freckle-I, Freckle-II, and Freckle-III.

Freckle-I originated at the bottom of the turbine blade, with its trace line predominantly consisting of segregation channels (marked by orange lines). After extending above the platform, stray grains (marked by red lines) appeared within the segregation channels, indicating the transformation into freckle defects in this region. Along the solidification direction, Freckle-I shows a clear incubation stage and subsequently develops within eutectic-enriched segregation channels, indicating a strong correlation between freckle formation and eutectic segregation. Unlike Freckle-I, both Freckle-II and Freckle-III formed directly in the fir-tree root region without an obvious incubation stage of segregation channels, presenting predominantly as stray grains in the form of dotted or patchy discoloration.

3.1.2. Distribution of Freckles on the Outer Surface of Casting B

Figure 5 illustrates the macroscopic characteristics of freckle defects on the outer surface of Casting B. Observations reveal that freckle defects on this blade are also exclusively distributed on the convex side (Figure 5a,b), with no defects observed on the concave side (Figure 5c). For ease of description, the seven freckle traces on the convex side are sequentially designated as Freckle-I through Freckle-VII, as shown in Figure 5d, where orange lines indicate segregation channels and red lines indicate stray grains.

Freckle-I disappears from the blade surface after extending only a short distance, with some of its internal stray grains subsequently evolving into coarse misoriented dendrites (i.e., sliver defects). Freckle-II originates near the bottom of the turbine blade. In the lower airfoil region, it appears as segregation channels (orange lines). As solidification proceeds upward, these channels gradually evolve into freckles containing stray grains in the middle and upper airfoil regions, appearing as dotted or patchy discoloration. This transition is attributed to the increasing flow intensity within the segregation channel. In the lower blade region, the relatively small thickness results in weak interdendritic flow, and the defect mainly appears as segregation channels. With increasing blade thickness along the solidification direction, the flow intensity increases, enhancing dendrite arm remelting and fragmentation and promoting the formation of misoriented grains within the channel. Consequently, Freckle-I, III, and IV form directly in the upper part of the airfoil region without developing a long segregation-channel tail.

Furthermore, Freckle-II, III, and IV, located on the airfoil, disappear from the surface when extending near the platform, with no freckle defects observed in the platform region. Notably, as the blade cross-section exhibits a pattern of “contraction-expansion-recontraction” along the solidification height, the distribution of freckle defects correspondingly presents a characteristic of “appearance-disappearance-reappearance.” This phenomenon is consistent with findings from our previous studies [14], namely that freckle defects do not appear immediately after cross-section expansion but gradually emerge after a brief incubation period.

3.2. Metallographic Analysis of Typical Freckle Defect Regions in Casting B

Based on the preceding observations of the macroscopic distribution characteristics of freckle defects on Casting B. Three typical regions were selected for metallographic analysis: the segregation channel region of Freckle-II, the transition region between the segregation channel and stray grains, and the initiation region of Freckle-V above the platform.

3.2.1. Metallographic Characteristics of the Segregation Channel Region of Freckle-II

An Olympus GX71 metallographic microscope was employed to observe the microstructure of specimens after grinding, polishing, and etching. The analysis focused on the microscopic morphology, grain structure, eutectic aggregation characteristics, and precipitated phase distribution within the defect regions, aiming to reveal the microstructural differences between the defect regions and the matrix.

The sampling location for the segregation channel region of Freckle-II on Casting B is shown in Figure 6a, and the corresponding metallographic structure of the cross-section A-A is presented in Figure 6b. Figure 6c,d show the locally enlarged structures of the regions marked by the blue and red boxes in Figure 6b, respectively. As shown in Figure 6b–d, significant asymmetric microstructural characteristics are observed on the blade cross-section: the outer surface of the convex side exhibits a continuous and densely distributed eutectic layer, indicating solute enrichment during solidification; in contrast, the inner surface of the suction side shows relatively depleted eutectic structures, with the area fraction of interdendritic eutectic regions being significantly lower than that on the outer surface. Further partitioning of the inner and outer sides in Figure 6d was performed, where the inner surface region of the convex side was marked as A and the outer surface region of the convex side was marked as B. The eutectic content in the two regions was measured using Image Pro Plus 6.0 software, and the area fraction of the eutectic structure was determined to be 19.67% in region A and 32.26% in region B. Furthermore, no distinct grain boundaries are observed between the segregation channel of Freckle-II and the surrounding matrix.

The aforementioned microstructural differences between the convex side and the concave side indicate that the formation of segregation channels is closely related to the asymmetric heating conditions during solidification. The convex side, facing the cold zone, experiences a slower solidification rate, allowing sufficient solute enrichment and the formation of a continuous eutectic layer. In contrast, the concave side, facing the hot zone, undergoes faster solidification with more complete solute diffusion, resulting in a relatively depleted eutectic layer. Essentially, the segregation channel is a eutectic concentration zone formed by solute enrichment, and its unique microstructure lays the compositional foundation for the subsequent nucleation and evolution of stray grains.

3.2.2. Transition from Segregation Channel to Stray Grains in Freckle-II

The sampling positions for the transition region between the segregation channel and stray grains of Freckle-II on Casting B are shown in Figure 7a,b, and the corresponding metallographic structure of the longitudinal section is presented in Figure 7c. Analysis of Figure 7c reveals significant microstructural characteristics on the blade longitudinal section: the lower region adjacent to the segregation channel retains a substantial amount of eutectic-rich structure; after transitioning toward the upper part of the airfoil, isolated fine stray grains gradually form and progressively increase in the amount of stray grains with the increasing height, with clearly visible grain boundaries. This microstructural transformation confirms the incubation and formation process of freckle defects, namely the stepwise evolution mechanism from solute segregation accumulation forming eutectic channels to eutectic convection disrupting dendrites and evolving into stray grains.

3.2.3. Metallographic Characteristics of the Freckle-VI Region

The metallographic structure of the Freckle-VI region on Casting B is shown in Figure 8. Located above the platform, this region represents the direct initiation site of freckle defects. In contrast to the segregation channel and transition region of Freckle-II, its microscopic morphology exhibits significant differences: the entire region lacks distinct incubation characteristics of segregation channels, with defects primarily characterized by isolated stray grains. Regarding the distribution and evolution of stray grains, this region displays a pronounced longitudinal variation. The bottom of the initiation zone is dominated by fine, irregularly dispersed stray grains appearing as dotted patterns. As the solidification height increases, the stray grains gradually coarsen, evolving into large blocky grains in the upper part of the region, with clearly visible grain boundaries. This evolutionary sequence indicates that the formation of Freckle-VI also undergoes a dynamic process from onset to further development, albeit without experiencing an obvious segregation channel incubation stage.

The above characteristics indicate that the formation mechanism of Freckle-VI differs from that of Freckle-II. Its initiation is primarily associated with flow disturbances caused by the abrupt cross-sectional change above the platform. Due to the relatively weak local solute segregation, the conditions for forming a continuous eutectic layer are not met, consequently exhibiting a microstructure dominated by stray grains.

4. Solidification Simulation and Freckle Formation Analysis

4.1. Correlation Analysis Between Solidification Process Characteristics and Freckle Formation

4.1.1. Criteria for Freckle Formation

Since the formation of freckle defects originates from the flow behavior of the interdendritic liquid, researchers have also attempted to reveal their formation mechanism by establishing fluid dynamics models [39]. Within this research framework, the Rayleigh number (Ra) and its variants are commonly employed to characterize the stability of interdendritic liquid flow within the mushy zone [24,40,41,42]. For instance, the Rayleigh number criterion proposed by Auburtin et al. [40] is expressed as:

$$Ra={\displaystyle \frac{\Delta \rho }{{\rho }_0}}{\displaystyle \frac{gKh}{\alpha \nu }}$$

(1)

where ρ₀ is the initial density (Kg/m³); Δρ is the density variation (Kg/m³); g is the gravitational acceleration (m/s²); h is the mushy zone width (m); α is the thermal diffusivity (m²/s); ν is the kinematic viscosity (m²/s); and K is the average permeability (m²).

The average permeability K is calculated using the following expression [43]:

$$K=3.75\times {10}^{-4}{f}_{\mathrm{L}}^2{\lambda }_1^2$$

(2)

where f_L is the liquid fraction, and λ₁ is the primary dendrite arm spacing (μm).

The primary dendrite arm spacing is related to the solidification conditions and can be calculated by the following equation [43]:

$${\lambda }_1=C\times {G_{\mathrm{T}}}^{-m}{V}^{-n}$$

(3)

where G_T is the temperature gradient (K/mm), V is the solidification rate (μm/s), and C, m, n are material constants related to the alloy composition, all greater than 0. For example, Guo et al. [44] determined the relevant constants for the DD8 alloy through experiments as: C = 1114.5, m = 0.52, n = 0.12.

The aforementioned Rayleigh number essentially represents the ratio of the driving force for upward liquid flow to the resistance within the mushy zone. When Ra in a certain region exceeds the critical value Ra* during solidification, it can be determined that freckle defects will initiate at that location. This critical value can be determined through theoretical calculations or experimental measurements.

4.1.2. Analysis of Freckle Formation Mechanism in Castings at Different Furnace Positions

Third-generation nickel-based single crystal superalloys contain high concentrations of refractory elements such as Re and W, exhibiting severe microsegregation behavior during solidification: high-melting-point, high-atomic-weight elements like Re and W tend to segregate to the dendrite cores, while low-density, eutectic-forming elements such as Al and Ta preferentially enrich in the interdendritic liquid [3]. This pronounced elemental segregation leads to two critical consequences: first, the interdendritic liquid becomes enriched with low-density elements (Al, Ta), resulting in density inversion that provides the driving force for thermosolutal convection; second, the solidification interval (the temperature difference between liquidus and solidus) increases significantly, forming a wide mushy zone that provides the spatial conditions for convection and dendrite fragmentation.

Macroscopic observations indicate that freckle defects on the convex side outer surface of Casting B (cold zone casting) are significantly more severe than those of Casting A (hot zone casting) in terms of distribution range, number density, and morphological complexity. This difference arises from the distinct temperature fields and solidification conditions experienced by the two castings due to their different positions within the furnace.

Figure 9 presents the calculated solidification progression of the castings at t = 4500 s. It can be seen that at the same moment, Casting B (cold zone) exhibits faster solidification progression and a wider mushy zone, whereas Casting A (hot zone) shows slower solidification progression and a narrower mushy zone. Figure 10 shows the calculated temperature gradient distribution within the blade castings during solidification when the casting temperature drops to T = 1396.37 °C (solid fraction f_s = 50%). At the same solidification height, the temperature gradient of Casting A is approximately twice that of Casting B.

According to the Rayleigh number model formula (1), a larger mushy zone width h leads to a larger Rayleigh number Ra, resulting in a higher susceptibility to freckle defects. Furthermore, based on the primary dendrite arm spacing formula (3), a smaller temperature gradient G_T results in a larger primary dendrite arm spacing λ₁, which in turn increases the average permeability K (see formula (2)), thereby further elevating the Ra value. Consequently, Casting B exhibits a significantly larger Rayleigh number than Casting A due to its wider mushy zone and smaller temperature gradient, which fundamentally accounts for the markedly greater severity of freckle defects in Casting B compared to Casting A.

4.1.3. Analysis of Freckle Defect Distribution Differences Between the Concave Side and Convex Side of the Same Casting

Macroscopic observations indicate significant differences in freckle defect distribution on different sides of the same casting. Taking Casting B as an example, the convex side exhibits severe freckle defects characterized by wide distribution range, high number density, and diverse morphologies, while the concave side surface remains clean, with virtually no freckle defects or obvious segregation traces. This difference originates from the distinctly different temperature fields and solidification conditions experienced by different sides of the casting within the furnace.

Figure 11 presents the simulated solidification progression of Casting B at t = 4500 s. It can be observed that at the same moment, the convex side, being adjacent to the cold zone, exhibits faster solidification progression and a wider mushy zone, whereas the concave side, situated close to the hot zone and receiving intense thermal radiation from the heating wall, shows slower solidification progression and a narrower mushy zone. Figure 12 displays the calculated temperature gradient distribution during solidification when the casting temperature drops to T = 1396.37 °C (solid fraction f_s = 50%). At the same solidification height, the temperature gradient on the concave side is larger than that on the convex side.

According to the Rayleigh number model formula (1) and the primary dendrite arm spacing formula (3), the convex side, characterized by a wider mushy zone and a smaller temperature gradient, exhibits a significantly larger Rayleigh number than the concave side. Furthermore, a portion of the solute from the concave side can migrate to the convex side through convection, further reducing its own segregation tendency. Consequently, the concave side surface remains largely free of freckle defects and segregation channels, while the convex side shows a substantially higher severity of freckle defects. In summary, the pronounced difference in freckle defect distribution between the convex side and concave side of Casting B results from the coupled effects of temperature field and solidification behavior under asymmetric heating conditions.

4.2. The Formation Mechanism of Freckle Defects and Model Validation

4.2.1. Formation Mechanism of Freckles

During directional solidification, light solute elements are rejected at the solid–liquid interface, leading to progressive enrichment of solute in the interdendritic liquid within the mushy zone. As solidification proceeds, the solute concentration of the interdendritic liquid increases with the depth of the mushy zone, resulting in a density inversion in which the lower part of the mushy zone contains lighter liquid. This density instability induces thermo-solutal convection and promotes the formation of channel segregation [38]. As shown in Figure 13a, the low-density solute-enriched liquid rises within the mushy zone and develops into segregation channels. The upward flow continuously entrains surrounding solute-rich interdendritic liquid into the channel, thereby sustaining and intensifying the channel flow. When the flow intensity becomes sufficiently strong, the higher-order dendrite arms near the channel are remelted and fragmented, leading to the formation of stray grains [30]. After complete solidification, freckles appear macroscopically as regions of local eutectic enrichment accompanied by dispersed misoriented stray grains.

The calculated freckle distribution is presented in Figure 13b. Multiple freckles are predicted on the convex side of the blade, and their severity increases toward the upper part of the airfoil, which agrees well with the experimental observations shown in Figure 5. To further analyze the spatial evolution of freckles, three horizontal sections located below the platform, within the platform, and above the platform were examined. As illustrated in Figure 13b, the segregation channels formed below the platform penetrate through the platform region and immediately develop into freckles above it. This simulation result explains the experimental observations in Figure 5 and Figure 8, where freckles are observed below the platform, disappear on the platform surface, and reappear immediately above the platform. These results indicate that freckle formation is a continuous process governed by the coupled effects of interdendritic flow and solute transport during solidification.

Figure 14 presents a comparison between the simulated and experimental results of freckle defect distribution on different regions of the outer surface of Casting B. As shown in Figure 14a, for the convex side of the turbine blade, although the simulation did not exactly replicate every individual segregation channel marked as Freckles I–VII, it successfully captured the overall distribution trend of the freckle defects. Figure 14b,c illustrate the comparison of freckle distribution on the right and left sides of the fir-tree root, respectively. The simulation results accurately reproduced the number and positions of the freckles observed in the experiments. In summary, the simulation and experimental results are in good agreement.

On the concave side, the freckle defects predicted by the simulation were not observed experimentally. This discrepancy may result from the combined effects of numerical and experimental factors. As discussed in Section 4.1.3, the solidification front on the convex side is a preferential site for freckle initiation. However, the neglect of liquid flow in the ProCAST thermal calculation may overestimate the mushy zone height on the concave side, thereby affecting the accuracy of defect prediction.

In addition, during the actual directional solidification process, the ceramic core is prone to eccentricity, leading to uneven wall thickness distribution of the blade. If the ceramic core shifts slightly toward the concave side, the local wall thickness on the convex side becomes slightly greater than that on the concave side. Such geometric deviation may further enhance the melt flow intensity in the convex side region, consequently influencing the actual distribution of freckle defects.

4.2.2. Comparison of Simulated and Experimental Freckles Distribution on the Cross-Section

Figure 15 presents a comparison between the simulated and experimental results of freckle defect distribution on the casting cross-section near the platform. As shown in Figure 15b, for the turbine blade cross-section, although the simulation did not exactly replicate every individual segregation channel, it successfully captured the overall distribution trend of the freckle defects.

Furthermore, as shown in Figure 15b, freckle defects are observed not only on the outer surface of the convex side (Surface B2) but also on the inner surface of the concave side (Surface A2). This finding differs from the observations in previous sections, where freckle defects were found to be distributed only on the outer surface of the casting. It is worth noting that both the simulation and experimental results confirm the presence of freckle defects on the inner surface of the concave side, demonstrating good agreement between the two.

Referring to the analysis method in Section 4.1.3, a comparison of the solidification progress between the outer surface (Surface A1) and the inner surface (Surface A2) of the concave side reveals that at the same solidification moment, the mushy zone height on Surface A2 is larger than that on Surface A1; at the same height position, the temperature gradient on Surface A2 is smaller than that on Surface A1. According to the Rayleigh number model (Equation (1)) and the primary dendrite arm spacing formula (Equation (3)), a wider mushy zone and a smaller temperature gradient result in a larger Rayleigh number, indicating a higher susceptibility to freckle formation. Therefore, Surface A2 is more prone to freckle defects than Surface A1, which mechanistically explains the appearance of freckle defects on the inner surface of the concave side. This finding is consistent with the results reported in the literature [45] and holds significant guiding importance for optimizing the directional solidification process of third-generation nickel-based single crystal superalloys.

A quantitative analysis of the number of freckles was made and the results are shown in Figure 16. The calculated results show a trend that is in good agreement with the experimental results. Along the height of the single-crystal blade, the number of freckles in the airfoil region shows a gradual increase. At lower heights, only 3 freckles are observed, while their number increases to 10 with increasing height. This is mainly due to the increasing local thickness of the blade, which facilitates interdendritic flow and promotes the formation and development of channel segregations (freckles). In the transition region near the platform, the freckle number exhibits a temporary decrease. This is because some of the freckles that have already developed in the lower airfoil region grow into the interior of the casting (see Figure 13b), resulting in a reduced number of freckles observed on blade surface. Above the platform region, the freckle number increases again. The larger cross-sectional thickness is more favorable for freckle formation. Additionally, some freckles that have already developed in the lower regions extend through the platform into the interior of the casting and reappear on the observed cross-section, particularly after entering the section contraction zone. The number of freckles increases to a maximum of 16 at this location. Near the top of the blade, the freckle number decreases, while their size increases. This is due to the coalescence of smaller freckles into larger ones, leading to fewer but wider freckles.

Given the good consistency between the present simulation results and experimental observations, the adopted simplification is considered reasonable. However, as indicated in our previous studies on ternary alloys [46], an accurate description of the solidification process requires proper evaluation of the solidification path by accounting for multicomponent phase equilibria and growth kinetics. Further improvement will be done by directly resolving the solidification path in superalloys.

As shown in Figure 14, some experimentally observed freckles were not numerically predicted. The discrepancy may be related to several simplifications in the present model. The current mesh resolution may still be insufficient to fully capture the local flow and solidification details in the thin blade section. In addition, some material properties were treated as constants, and the multicomponent Ni-based superalloy was simplified as an equivalent binary alloy. These simplifications may reduce the quantitative accuracy of the predicted segregation behavior and freckle formation.

5. Conclusions

(1) The formation mechanism of freckle defects during the directional solidification of a third-generation nickel-based single crystal superalloy turbine blade has been elucidated. Freckle formation originates from severe microsegregation caused by high concentrations of refractory elements (Re, W, Ta, etc.), which induces density inversion in the interdendritic liquid and the development of a wide mushy zone. Under the influence of thermo-solutal convection, dendrites undergo fragmentation and aggregate into equiaxed grain chains, ultimately evolving into surface chain-like freckle defects.

(2) The critical role of casting position in determining freckle defect distribution has been clarified. Casting B, positioned farther from the heat source, exhibits a substantially larger Rayleigh number than Casting A (located closer to the heat source), due to its lower temperature gradient and wider mushy zone. Consequently, freckle defects in Casting B are significantly more severe in terms of distribution range, number density, and morphological complexity. The strong agreement between simulation results and experimental observations confirms the decisive influence of thermal field and solidification conditions on freckle formation.

(3) The underlying causes of the asymmetric freckle distribution on opposite sides of the same casting have been identified. The suction side, being farther from the heat source, is characterized by a wider mushy zone and a smaller temperature gradient, resulting in a Rayleigh number substantially higher than that of the pressure side. This explains the severe freckling observed on the suction side, while the pressure side, benefiting from its proximity to the heat source, remains virtually defect-free.

(4) The accuracy and reliability of the volume-averaged multiphase solidification model for predicting freckle defects have been validated. The simulation successfully captures the overall distribution trend of freckle defects on both the outer surface and cross-section of Casting B, achieving good consistency with experimental results. Notably, both simulation and experiments confirm the presence of freckle defects not only on the outer surface of the suction side but also on the inner surface of the pressure side. This finding broadens the current understanding of freckle distribution patterns and is consistent with results reported in the literature. Quantitative analysis of freckle number along the blade height further demonstrates good agreement between simulation and experiment, with the model capturing the non-monotonic variation trend, including the temporary decrease near the platform and the final reduction near the top.

(5) The susceptibility to freckle formation varies with blade geometry and is influenced by both thickness-dependent channel segregation and the migration and coalescence of freckles. In the airfoil region, freckle formation exhibits a gradual increase with increasing local thickness, requiring an incubation stage involving segregation channels. Near the platform, a temporary decrease in freckle number is observed due to the inward growth of existing freckles. In contrast, the fir-tree root region exhibits severe freckle defects, characterized by a high number of freckles and direct formation without a segregation channel incubation stage. This is attributed to the fir-tree root being a thick-walled section located in the upper part of the casting, where both the temperature gradient and solidification rate are low. Near the blade top, freckle number decreases while freckle size increases due to coalescence.

(6) The established “global-local” two-step digital twin strategy has successfully enabled cross-scale coupling calculations between macroscopic thermal fields and microstructural evolution. This provides a feasible technical pathway for the digital manufacturing of turbine blades and offers significant guidance for optimizing directional solidification processes and achieving active defect control. Future work will focus on improving quantitative accuracy by incorporating multicomponent phase equilibria and growth kinetics to more accurately resolve the solidification path.