Thermal-solutal-fluid flow of channel segregation during directional solidification of single-crystal nickel-based superalloys
Graphical abstract
Introduction
Single-crystal turbine blade is considered to be one of the most important components in the aerospace engines. During manufacture of the turbine blade by investment casting, freckle – set of equiaxed grains with no specific orientation distributed in chains – can be found commonly [1]. In the single crystal blade, the grain boundary has been removed to allow only one crystal grain to grow into the entire casting. The occurrence of freckle defect is detrimental to the integrity of the single crystal component in that the grain boundaries between the freckle equiaxed grains degrade the mechanical properties and reduce the stress-rupture life under high-temperature and high-pressure conditions [2,3].
Mechanisms of freckle formation have been reported widely in literature. Hellawell et al. [4,5] conducted visualization experiments, using a transparent NH4Cl-H2O system to study the formation of freckle during directional solidification. They observed well-developed chimneys and concluded that free fragments settled in the channels and grew into freckles. It should be noted that chimneys are solute enriched flow, and channel segregation is the uneven solute distribution in solidified metal. Laboratory X-ray radiography was used to observe the directional solidification of Ga-In alloys [6,7], and it was confirmed that the dendritic fragments caused by remelting tended to stay in the segregation channel. These findings explained why freckle was concentrated on the segregation channel of superalloy castings, and confirmed channel segregation was the essential condition for freckle formation. In a dendritic-scale simulation, Yuan and Lee (2012) [8] and Karagadde et al. (2014) [9] used the coupled cellular automaton and finite difference method to reveal the freckle initiation. They reported that the solute enrichment between dendrite arms caused by different dendritic growth rates was the origin of channel segregation formation.
Macroscopic mathematical model can also be used to predict freckle formation. Using the continuum mixture model established by Bennon and Incropera [10], Felicelli et al. [11,12] simulated heat transfer, species transfer and fluid flow, and predicted channel segregation on macro-scale. Based on the physics of Rayleigh-Bernard flow instabilities, Worster [13] attributed the formation of chimneys to the thermal-solutal convection, and proposed the Rayleigh number in the mushy zone as a criterion to estimate the possibility of freckle formation in castings. Beckermann et al. [14,15] developed a two-phase volume-averaged mathematical model to simulate the formation of freckles, and defined Rayleigh number as the function of thermal conductivity, viscosity, mean permeability of mushy zone, the height of mushy zone and the density difference between the top and bottom of the mushy zone. According to the simulation results and experimental data [16,17], they gave the critical Rayleigh number to predict freckles in superalloys CMSX-2 castings.
However, the Rayleigh number criterion could not work as well as expected in application, because the lateral heat flux in directional solidification was ignored, and researchers had to modify the critical Rayleigh number under specific conditions [18], [19], [20], [21]. Although the thermal conductivity of the shell mould used in nickel-based superalloys investment casting is poor, there is still a strong lateral heat flux during the withdrawal process [22]. In the study on the directional solidification of Ga-In alloys, Saad et al. [23] shown the significant impact of lateral temperature on channel formation. Additionally, the previous investigations on freckles in the other casting processes proved the sensitivity of freckles to the temperature field [24], [25], [26], [27], [28]. Furthermore, Ma et al. [29,30] also found that the freckles only appeared on the surface of the superalloy specimen during directional solidification process. On the scale of microstructure, Reinhart et al. [31] also observed the same specific distribution of channel in the in-situ and real-time X-radiography. This was completely different from the theoretical analysis that freckles tended to appear in the region with poor heat dissipation [1,32]. This was also different from the previous simulation results that channel segregation was formed in both centre and edge [12,14]. The understanding of specific distribution of freckles is crucial to the reduce or even eliminate the defect in superalloy castings, but obviously it has not been well explained yet.
In this work, we use the previously developed Eulerian two-phase model to simulate the three-dimensional channel segregation in the directional solidification of nickel-based superalloys CMSX-4. The lateral heat flux in Bridgman method is considered. The simulation result is validated by comparing the predicted channel segregation with the freckles observed in experimental results. The mechanism of the specific distribution of channel segregation is discussed, and the formation and disappearance of chimneys and channels are presented and rationalised. The sensitivity of channel segregation to cooling condition and geometric characteristics are also studied to further analyse the freckles in the actual manufacturing of nickel-based single-crystal superalloy turbine blade.
Section snippets
Thermal-chemical-fluid flow
To rationalise the thermal-chemical-fluid flow during directional solidification of single crystal superalloys, an Eulerian two-phase model adopted from Li et al. [26,33] is employed to describe the fluid flow, heat and mass transfer during the process. The governing equations, source terms and auxiliary equations are listed in Table 1.
Two phases of liquid metal and solid dendrite trunks are defined in this model. The dendrite trunks are approximated to be immobile staggered cylinders extending
Simulation parameters
The benchmark cylinder specimen with a diameter of 20 mm and a height of 30 mm is used in our simulation. The previous investigations [25,26,41,42] have shown the mesh sensitivity of channel segregation and concluded that the grid size should be comparable to the primary dendritic arm spacing to capture the details of channel segregation. Thus, the average grid size in the simulation is set to 500 µm, which is equal to the primary dendrite arm spacing, so as to accurately capture the details of
Verification of the model
Ma et al. [29,30] found that the freckle only appeared on the surface of the superalloy specimen during directional solidification process. To the best of our knowledge, no model has, thus far, predicted the surface channel segregation. The predicted channels in the previous simulation results are mainly distributed in the centre [12,14]. In our simulation result, channel segregation is only formed on the surface of specimen, extending from bottom to top, as shown in Fig. 2c. The distribution
Stabilization of channel segregation and disappearance of chimneys
The segregation distribution along one of the channels during solidification process is shown in Fig. 6, which demonstrates the development of channel segregation. Once a channel is formed, solute is further rejected into the channel, resulting in an increase in the segregation index [57,58]. Due to the further solute enrichment, the local solidification procedure is further delayed. The solute concentration gradient along casting direction drives strong upward flow with enriched solute,
Conclusions
In the present work, we employ a three-dimensional Eulerian two-phase model to investigation the channel segregation of superalloys in directional solidification. The distribution and morphology of predicted channel segregation are in good agreement with experimental observations. The main conclusions are summarised as follows:
- 1.
The heat flux on the lateral wall produces significant perturbation on the thermal-solutal convection of liquid metal in the directional solidification. Under the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work is sponsored by National Natural Science Foundation of China (nos. 52074182 and 91860121) and the Joint Funds of the National Natural Science Foundation of China (no. U1660203) and National Science and Technology Major Project (2017-Ⅶ-0008-0102).
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