Numerical simulation on directional solidification and heat treatment processes of turbine blades

Study on turbine blades is crucial due to their critical role in ensuring the efficient and reliable operation of aircraft engines.Nickel-based single crystal superalloys are extensively used in the hot manufacturing of turbine blades due to their exceptional high-temperature mechanical properties.The hot manufacturing of single crystal blades involves directional solidification and heat treatment.Experimental manufacturing of these blades is time-consuming,capital-intensive,and often insufficient to meet industrial demands.Numerical simulation techniques have gained widespread acceptance in blade manufacturing research due to their low energy consumption,high efficiency,and rapid turnaround time.This article introduces the modeling and simulation of hot manufacturing in single crystal blades.The discussion outlines the prevalent mathematical models employed in numerical simulations related to blade hot manufacturing.It encapsulates the advancements in research concerning macro to micro-level numerical simulation techniques for directional solidification and heat treatment processes.Furthermore,potential future trajectories for the numerical simulation of single crystal blade hot manufacturing are also discussed.

Preparation, microstructure and dislocation of solar-grade multicrystalline silicon by directional solidification from metallurgical-grade silicon

A vacuum directional solidification with high temperature gradient was performed to prepare low cost solar-grade multicrystalline silicon （mc-Si） directly from metallurgical-grade mc-Si. The microstructure characteristic, grain size, boundary, solid-liquid growth interface, and dislocation structure under different growth conditions were studied. The results show that directionally solidified multicrystalline silicon rods with high density and orientation can be obtained when the solidification rate is below 60 μm/s. The grain size gradually decreases with increasing the solidification rate. The control of obtaining planar solid-liquid interface at high temperature gradient is effective to produce well-aligned columnar grains along the solidification direction. The growth step and twin boundaries are preferred to form in the microstructure due to the faceted growth characteristic of mc-Si. The dislocation distribution is inhomogeneous within crystals and the dislocation density increases with the increase of solidification rate. Furthermore, the crystal growth behavior and dislocation formation mechanism of mc-Si were discussed.

Effect of configuration on magnetic field in cold crucible using for continuous melting and directional solidification

To improve the power efficiency and optimize the configuration of cold crucible using for continuous melting and directional solidification （DS）, based on experimental verification, 3D finite element （FE） models with various configuration-elements were developed to investigate the magnetic field in cold crucible. Magnetic flux density （B） was measured and calculated under different configuration parameters. These parameters include the inner diameter （D2）, the slit width （d）, the thickness of crucible wall, the section shape of the slit and the shield ring. The results show that the magnetic flux density in z direction （Bz） both at the slit and at the midpoint of segment will increase with the decrease of D2 or with the increase of the width of the slit and the section area of wedge slit or removing the shield ring. In addition, there is a worst wall thickness that can induce the minimum Bz for a cold crucible with a certain outer diameter.

Effect of traveling magnetic field on dendrite growth of Pb-Sn alloy during directional solidification

The influence of melt convection on dendrite growth during the upward-directional solidification of Pb-33%Sn binary alloys was investigated.The melt convection was modulated by traveling magnetic field.When the direction of traveling magnetic field was changed from upward to downward,the primary dendrite spacing gradually increased,and the distribution peak of the primary dendrite spacing shifted to the field of narrower spacing.These result from the different intensities of melt convection,which are controlled by the traveling magnetic field.The effects of the traveling magnetic field on melt convection are similar to those of adjustment in the gravity level,thus,the primary dendrite spacing varies.When the intensity of the traveling magnetic field was 1 mT,and the drawing speed was 50 μm/s,the gravity acceleration reached 0.22g for the downward-traveling magnetic field and 3.07g for the upward-traveling magnetic field.

Directional solidification and characterization of NiAl-9Mo eutectic alloy

Ni-45.5Al-9Mo （mole fraction,%） alloy was directionally solidified with a constant temperature gradient （GL=334 K/cm） and growth rates ranging from 2 to 300 μm/s using a Bridgman type crystal growing facility with liquid metal cooling （LMC） technique. The effect of growth rate （v） on the solidified microstructures such as rod spacing （λ）, rod size （d） and rod volume fraction was experimentally investigated. Two types of the solidified interfaces, planar and cellular, were identified. On the condition of both planar and cellular eutectic microstructures, the relationships between λ, d and v were given as： λv1/2=5.90 μm·μm1/2·s1/2 and dv1/2=2.18μm·μm1/2·s1/2, respectively. It was observed that the volume fraction of Mo phase could be adjusted in a certain range. The variation of phase volume fraction was attributed to undercooling increase and the growth characteristics of the individual constituent phases during the eutectic growth.

Banding structure formation during directional solidification of Pb-Bi peritectic alloys

Directional solidification experiments on Pb-Bi peritectic alloys were carried out at very low growth rate （v=0.5 μm/s） and high temperature gradient （G=35 K/mm） in an improved Bridgman furnace. The banding structures were observed in both hypoperitectic and hyperperitectic compositions （Pb-xBi, x=26%, 28%, 30% and 34%）. Tree-like primary α phase in the center of the sample surrounded by the peritectic β phase matrix was also observed, resulting from the melt convection. The banding microstructure, however, is found to be transient after the tree-like structure and only the peritectic phase forms after a few bands. Composition variations in the banding structure are measured to determine the nucleation undercooling for both α and β phases. In a finite length sample, convection is shown to lead only to the transient formation of bands. In this transient banding regime, only a few bands with a variable width are formed, and this transient banding process can occur over a wide range of compositions inside the two-phase peritectic region.

Redistribution of iron during directional solidification of metallurgical-grade silicon at low growth rate

Redistribution of iron during directional solidification of metallurgical-grade silicon (MG-Si) was conducted at low growth rate. Concentrations of iron were examined by ICP-MS and figured in solid and liquid phases, at grain boundary and in growth direction. Concentrations are significantly different between solid and liquid phases. The thickness of the solute boundary layer is about 4 mm verified by mass balance law, and the effective distribution coefficient is 2.98×10?4. Iron element easily segregates at grain boundary at low growth rate. In growth direction, concentrations are almost constant until 86% ingot height, and they do not meet the Scheil equation completely, which is caused by the low growth rate. The effect of convection on the redistribution of iron was discussed in detail. Especially, the “dead zone” of convection plays an important role in the iron redistribution.

Interactions between γ-TiAl melt and Y_2O_3 ceramic material during directional solidification process

A γ-TiAl alloy with nominal composition of Ti-47%Al（molar fraction） was directionally solidified in an alumina mould with an Y2O3 protective coating.The effects of processing parameters（melting temperature and interaction time） on the metal-coating interface,microstructure and chemical composition of the alloy were evaluated.The result shows that the Y2O3 protective coating exhibits an effective barrier capability to avoid direct contact between the mould base material and the TiAl melt,although the Y2O3 coating is found to suffer some erosion and be slightly dissolved by the molten TiAl due to the coating-metal interactions.The directionally solidified alloys were contaminated with Y and O,and Y2O3 inclusions were dispersed in the metal matrix.The reason for this metal contamination is the Y2O3 coating dissolution by the TiAl melt.One mode of the interaction between Y2O3 and the TiAl melt is dissolution of yttrium and atomic oxygen in the melt by reaction Y2O3（s）=2Y（in TiAl melt）＋3O（in TiAl melt）.Both the extent of alloy contamination and the volume fractions of Y2O3 inclusions depend on the melting temperature and the interaction time.

Directional Solidification Assisted by Liquid Metal Cooling

An overview of the development and current status of the directional solidification process assisted by liquid metal cooling （LMC） has been presented in this paper. The driving force of the rapid development of the LMC process has been analyzed by considering the demands of （1） newer technologies that can provide higher thermal gradients for alleviated segregation in advanced alloy systems, and （2） better production yield of the large directionally solidified superalloy components. The brief history of the industrialization of the LMC process has been reviewed, followed by the discussion on the LMC parameters including selection of the cooling media, using of the dynamic baffle, and the influence of withdrawal rates and so on. The microstructure and mechanical properties of the traditional superalloys processed by LMC, as well as the new alloys particularly developed for LMC process were then described. Finally, future aspects concerning the LMC process have been summarized.

Numerical simulation of dendrite growth in Ni-based superalloy casting during directional solidification process

An understanding of dendrite growth is required in order to improve the properties of castings. For this reason, cellular automaton-finite difference(CA-FD) method was used to investigate the dendrite growth during directional solidification(DS)process. The solute diffusion model combined with macro temperature field model was established for predicting the dendrite growth behavior. Model validation was performed by the DS experiment, and the cooling curves and grain structures obtained by the experiment presented a reasonable agreement with the simulation results. The competitive growth of dendrites was also simulated by the proposed model, and the competitive behavior of dendrites with different misalignment angles was also discussed in detail.Subsequently, 3D dendrites growth was also investigated by experiment and simulation, and both were in good accordance. The influence on dendrites growth of initial nucleus was investigated by three simulation cases, and the results showed that the initial nuclei just had an effect on the initial growth stage of columnar dendrites, but had little influence on the final dendritic morphology and the primary dendrite arm spacing.

Study of ultrahigh-purity copper billets refined by vacuum melting and directional solidification

The purpose of this paper is to study large-sized copper billets refined with 5N ultrahigh purity after vacuum melting and directional solidifi-cation （VMDS）. The precise impurity analysis of copper billets was carried out with a glow discharge mass spectrometer （GDMS）. The re-sults demonstrate that the total concentration of twenty-two impurities is decreased by 63.1wt.%-66.5 wt.%. Ag, P, S, Na, Mg, Se, Zn, In and Bi are easy to be removed due to lgPimp - lgPCu 1.5, and they can be removed effectively under the vacuum condition of 1650-1700 K for 30 min. The electrical conductivity of 5N copper is higher than that of the raw material as the impurity concentrations decrease. The segrega-tion effect in directional solidification can be remarkable when the equilibrium distribution coefficient （k0） value is less than 0.65 due to the strong affinity of Cu for some metallic and non-metallic impurities.

Numerical calculation of flow field inside TiAl melt during rectangular cold crucible directional solidification

Numerical investigations on the flow field in Ti-Al melt during rectangular cold crucible directional solidification were carried out. Combined with the experimental results, 3-D finite element models for calculating flow field inside melting pool were established, the characteristics of the flow under different power parameters were further studied. Numerical calculation results show that there is a complex circular flow in the melt, a rapid horizontal flow exists on the solid/liquid interface and those flows confluence in the center of the melting pool. The flow velocity v increases with the increase of current intensity, but the flow patterns remain unchanged. When the current is 1000 A, the vmax reaches 4 mm/s and the flow on the interface achieves 3 mm/s. Flow patterns are quite different when the frequency changes from 10 kHz to 100 kHz, the mechanism of the frequency influence on the flow pattern is analyzed, and there is an optimum frequency for cold crucible directional solidification.

Progress on modeling and simulation of directional solidification of superalloy turbine blade casting

Directional solidified turbine blades of Ni-based superalloy are widely used as key parts of the gas turbine engines.The mechanical properties of the blade are greatly influenced by the final microstructure and the grain orientation determined directly by the grain selector geometry of the casting.In this paper,mathematical models were proposed for three dimensional simulation of the grain growth and microstructure evolution in directional solidification of turbine blade casting.Ray-tracing method was applied to calculate the temperature variation of the blade.Based on the thermo model of heat transfer,the competitive grain growth within the starter block and the spiral of the grain selector,the grain growth in the blade and the microstructure evolution were simulated via a modified Cellular Automaton method.Validation experiments were carried out,and the measured results were compared quantitatively with the predicted results.The simulated cooling curves and microstructures corresponded well with the experimental results.The proposed models could be used to predict the grain morphology and the competitive grain evolution during directional solidification.

Directional solidification of Ti-45Al-8Nb-(W,B,Y) alloy

Using a Bridgman vertical vacuum furnace,Ti-45Al-8Nb-（W,B,Y） （at.%） bars,which were prepared from a plasma arc melting （PAM） ingot,were directionally solidified at growth rates of 10,15,and 20 μm/s.Polysynthetic twinned （PST） crystal with an aligned lamellar microstructure was obtained at the growth rate of 15 μm/s because of high Nb addition.The principle of PST crystal growth and the effect of Nb element were discussed.The results of investigations on microstructure and micromechanical properties of the directionally solidified （DS） bars of Ti-45Al-8Nb-（W,B,Y） alloy are briefly summarized.

Phase field investigation on the initial planar instability with surface tension anisotropy during directional solidification of binary alloys

Phase field investigation reveals that the stability of the planar interface is related to the anisotropic intensity of surface tension and the misorientation of preferred crystallographic orientation with respect to the heat flow direction. The large anisotropic intensity may compete to determine the stability of the planar interface. The destabilizing effect or the stabilizing effect depends on the misorientation. Moreover, the interface morphology of initial instability is also affected by the surface tension anisotropy.

Fabrication of lotus-type porous Mg−Mn alloys by metal/gas eutectic unidirectional solidification

Lotus-type porous Mg–xMn(x=0,1,2 and 3 wt.%)alloys were fabricated by metal/gas eutectic unidirectional solidification(the Gasar process).The effects of Mn addition and the fabrication process on the porosity,pore diameter and microstructure of the porous Mg-Mn alloy were investigated.Mn addition improved the Mn precipitates and increased the porosity and pore diameter.With increasing hydrogen pressure from 0.1 to 0.6 MPa,the overall porosity of the Mg-2wt.%Mn ingot decreased from 55.3%to 38.4%,and the average pore diameter also decreased from 2465 to 312μm.Based on a theoretical model of the change in the porosity with the hydrogen pressure,the calculated results were in good agreement with the experimental results.It is shown that this technique is a promising method to fabricate Gasar Mg–Mn alloys with uniform and controllable pore structure.

In-situ observation of porosity formation during directional solidification of Al-Si casting alloys

In-situ observation of porosity formation during directional solidification of two Al-Si alloys (7%Si and 13%Si) was made by using of micro-focus X-ray imaging.In both alloys,small spherical pores initially form in the melt far away from the eutectic solid-liquid (S/L) interface and then grow and coagulate during solidification.Some pores can float and escape from the solidifying melt front at a relatively high velocity.At the end of solidification,the remaining pores maintain spherical morphology in the near eutectic alloy but become irregular in the hypoeutectic alloy.This is attributed to different solidification modes and aluminum dendrite interactions between the two alloys.The mechanism of the porosity formation is briefly discussed in this paper.

Influence of directional solidification variables on primary dendrite arm spacing of Ni-based superalloy DZ125

The primary dendrite morphology and spacing of DZ125 superalloy have been observed during directional solidification under high thermal gradient about 500 K/cm. The results reveal that the primary dendrite arm spacing decreases from 94 μm to 35.8 μm with the increase of directional solidification cooling rate from 2.525 K/s to 36.4 K/s. The regression equation of the primary dendrite arm spacings A, versus cooling rate is λ1=0.013（GV）-0.32. The predictions of Kurz/Fisher model and Hunt/Lu model accord reasonably well with the experimental data. The influence of directional solidification rate under variable thermal gradient on the primary dendrite arm spacing has also been investigated.

Solute redistribution and Rayleigh number in the mushy zone during directional solidification of Inconel 718

The interdendritic segregation along the mushy zone of directionally solidified superalloy Inconel 718 has been measured by scanning electron microscope (SEM) and energy dispersion analysis spectrometry (EDAX) techniques and the corresponding liquid composition profile was presented. The liquid density and Rayleigh number (Ra) profiles along the mushy zone were calculated as well. It was found that the liquid density difference increased from top to bottom in the mushy zone and there was no density inversion due to the segregation of Nb and Mo. However carbide formation in the freezing range and the preferred angle of the orientated dendrite array could prompt the fluid flow in the mushy zone although there was no liquid density inversion. The largest relative Rayleigh number appeared at 1,326 degrees C for Inconel 718 where the fluid flow most easily occurred.

Multiscale modelling and simulation of single crystal superalloy turbine blade casting during directional solidification process

As the key parts of an aero-engine,single crystal(SX)superalloy turbine blades have been the focus of much attention.However,casting defects often occur during the manufacturing process of the SX turbine blades.Modeling and simulation technology can help to optimize the manufacturing process of SX blades.Multiscale coupled models were proposed and used to simulate the physical phenomena occurring during the directional solidification(DS)process.Coupled with heat transfer(macroscale)and grain growth(meso-scale),3D dendritic grain growth was calculated to show the competitive grain growth at micro-scale.SX grain selection behavior was studied by the simulation and experiments.The results show that the geometrical structure and technical parameters had strong influences on the grain selection effectiveness.Based on the coupled models,heat transfer,grain growth and microstructure evolution of a complex hollow SX blade were simulated.Both the simulated and experimental results show that the stray grain occurred at the platform of the SX blade when a constant withdrawal rate was used in manufacturing process.In order to avoid the formation of the stray crystal,the multi-scale coupled models and the withdrawal rate optimized technique were applied to the same SX turbine blade.The modeling results indicated that the optimized variable withdrawal rate can achieve SX blade castings with no stray grains,which was also proved by the experiments.