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.

Numerical simulation of 3D-microstructures in solidification processes based on the CAFE method

It was analyzed that the finite element-cellular automaton （CAFE） method was used to simulate 3D-microstructures in solidification processes. Based on this method, the 3D-microstructure of 9SMn28 free-cutting steel was simulated in solidification processes and the simulation results are consistent with the experimental ones. In addition, the effects of Gaussian distribution parameters were also studied. The simulation results show that the higher the mean undercooling, the larger the columnar dendrite zones, and the larger the maximum nucleation density, the smaller the size of grains. The larger the standard deviation, the less the number of minimum grains is. However, the uniformity degree decreases first, and then increases gradually.

Numerical Simulation of Solidification Process on Single Crystal Ni-Based Superalloy Investment Castings

Bridgman directional solidification of investment castings is a key technology for the production of reliable and highly efficient gas turbine blades. In this paper, a mathematical model for three-dimensional （3D） simulation of solidification process of single crystal investment castings was developed based on basic heat transfer equations. Complex heat radiation among the multiple blade castings and the furnace wall was considered in the model. Temperature distribution and temperature gradient in superalloy investment castings of single blade and multiple ones were investigated, respectively. The calculated cooling curves were compared with the experimental results and agreed well with the latter. It is indicated that the unsymmetrical temperature distribution and curved liquid-solid interface caused by the circle distribution of multiple turbine blades are probably main reasons why the stray grain and other casting defects occur in the turbine blade.

Study on Numerical Simulation of Mold Filling and Solidification Processes under Pressure Conditions

The mold filling and solidification simulation for the high pressure die casting (HPDC) and low pressure die casting (LPDC) processes were studied. A mathematical model considering the turbulent flow and heat transfer phenomenon during the HPDC process has been established and parallel computation technique was used for the mold filling simulation of the process. The laminar flow characteristics of the LPDC process were studied and a simplified model for the mold filling process of wheel castings has been developed. For the solidification simulation under pressure conditions, the cyclic characteristics and the complicated boundary conditions were considered and techniques to improve the computational efficiency are discussed. A new criterion for predicting shrinkage porosity of Al alloy under low pressure condition has been developed in the solidification simulation process.

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 ON NUMERICAL SIMULATION OF MOLD-FILLING AND SOLIDIFICATION PROCESSES OF SHAPED CASTING

The latest progress on the study of numerical simulation of mold filling and solidification process of shaped casting is reviewed. In mold filling process simulation of castings, the SOLA VOF algorithmis is improved in efficient free surface treatment and turbulence consideration, and parallel computational techniques are implemented to accelerate the fluid flow calculation time as well. Methods for predication of shrinkage defects of steel castings and S G. iron castings are developed based on the solidification simulation. In order to reduce the residual stress and deformation of castings, a combined FDM/FEM method is implemented for the modelling of stresses. Numerical models for the simulation of micro structure and prediction of mechanical properties of S G. iron are developed. The verifications and applications of the simulation software show that the models and techniques adopted in current research work are efficient and appropriate for the numerical simulation of shaped castings.

3-D Finite-Element Numerical Simulation of Centrifugal Induction Electrosalg Casting Solidification Process

A 3-D finite-element numerical simulation model of temperature field for CIESC casting solidification process was developed with the aid of ANSYS software and a series of corresponding experiments were made. The results showed that the good agreement was obtained between the numerical simulation and the experiments. Based on the numerical simulation results, the characteristics of temperature distribution in the castings during CIESC solidification process were analyzed and summarized. According to the G/R-1/2 method and numerical simulation results, there is no any shrinkage defect in the CIESC casting and structure or casting is fine and compact.

NUMERICAL SIMULATION OF FEEDSTOCK MELT FILLING IN A CYLINDRICAL CAVITY WITH SOLIDIFICATION IN POWDER INJECTION MOLDING

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COUPLED NUMERICAL SIMULATION OF STEEL FLOW AND SOLIDIFICATION IN SOFT-CONTACT BILLET MOLD

A coupled model including electromagnetic field, fluid dynamic, heat transfer and solidification, is developed and applied to the numerical simulation of steel flow and solidification in a 100mm × 100mm soft-contact mold. In this study, the 3D finite difference method and non-staggered grid system for fluid flow with body fitted coordinate were employed. Numerical results show that the electromagnetic force mainly affects the steel flow at upper part of mold, especially in the vicinity of meniscus. There exist upward flows covering the surfaces of the billet due to the concentration of electromagnetic force on the upper part of the billet. This flows join together and form a downward flow near the SEN, so a distinct circulating flow zone is formed at upper part of mold. After applying electromagnetic force, the steel velocity is improved and the temperature is raised. The strong stirring of electromagnetic force on liquid steel makes the kinetic energy on free surface increase. It is clearly seen that the solidification start point shifts downward in soft contact mold. As a result, the initial shell thickness gets thin and the initial solidification shell length is shortened.

NUMERICAL SIMULATION OF STRESS-STRAIN DISTRIBUTIONS FOR WELD METAL SOLIDIFICATION CRACKING IN STAINLESS STEEL

This paper analyzed the characteristics of welding solidification crack of stainless steels,and clearly re- vealed the the of the deformation in the molten - the pool and the solidification shrinkage on the stress - strain fields in the trail of molten - weld pool.Moreover, rheologic properties of the alloys in solid - liquid zone were also obtained by measuring the hading and unloading deform curves of the steels.As a result, a numerical model for simulation of stress - strain distributions of welding solidifi- cation crack was developed. On the basis of the model,the thesis simulated the driving force of solidifi- cation crack of stainless steels, that is, stress - strain fields in the trail of molten-weld pool with fi- nite element method.

Numerical simulation of mold-temperature-control solidification

A finite element method(FEM) for the numerical simulation of the columnar part of the mould-temperature-control solidification(MTCS) process was presented. The latent heat was taken into account and 3D transient heat transfer analysis was carried out by using the developed FEM software. The relative errors between the numerical and experimental data are less than 6%. Three MTCS cases were computed with this method. The first case only opens the cooling channels in the bottom of the mold. The second case individually controls the separate 7 groups of cooling channels by giving 7 control points. When the temperature of a control point reaches the preset value of 400℃, the corresponding channel will be opened. The third case opens all the cooling channels at the same time. The results indicate that in the second case, the solid-liquid interface keeps near-planar. The growth velocity of the solid-liquid interface is 0.3-0.4 mm/s, which is greater than 0.1-0.3 mm/s of the first case, performing better than the others. Thus the forming quality and efficiency part interior can be improved by mold-temperature-control and the numerical model is validated. The numerical simulation of MTCS can provide an available tool for the advanced investigation on the defect improvement and the crystal’s quality.

A METHOD OF AS-CAST CRACK PREDICTION BASED UPON NUMERICAL SIMULATION OF SOLIDIFICATION

Based on the numerical simulation of solidification of castings, a thermal stress formula and a thermal crack initiation criterion are established, which suggest that the cracks initiate at the two-thirds thickness of solidified layer from outside of castings. Cast steel wheels whose diameters are 800mm are employed to testify the positions of cracks through thermal ela- stic-plastic analyses and low magnifying structure observations conventionally. The results show that the numerical prediction of cracks coincides with the measured result, and the cracks do not necessarily follow where the defects such as shrinkage holes and porosities occur. It is also found that surface temperature control is an effective factor to avoid the crack formation.

NUMERICAL SIMULATION ON SOLIDIFICATION OF HORIZONTALLY CONTINUOUSLY CAST IRON BARS

The solidification process of a horizontally continuously cast gray iron bar of 4.6cm in diame- ter was modelled.The function describing the distribution of heat flux at the internal surface of graphite sleeve,which was equal to that on the surface of the iron bar,was inversely derived using numerical calculation from the temperature distribution in the sleeve measured in real production.By using the distribution of heat flux as a boundary condition on the surface of the iron bar,the numerical simulation on solidification of the iron bar taking longitudinal heat conduction into account was made.The profile of solidification front obtained from the numer- ical simulation was approximately coincident with that in real production.In addition,the quantitative relationships of the thickness of solidified shell at the exit of the mold to the main technological parameters,including the temperature of liquid iron at the entrance of the mold, the moving speed of the bar and the intensity of water cooling,were obtained from the numeri- cal simulation.

Numerical simulation of boundary heat flow effects on directional solidification microstructure of a binary alloy

The boundary heat flow has important significance for the microstructures of directional solidified binary alloy.Interface evolution of the directional solidified microstructure with different boundary heat flow was discussed.In this study, only one interface was allowed to have heat flow, and Neumann boundary conditions were imposed at the other three interfaces.From the calculated results, it was found that different boundary heat flows will result in different microstructures.When the boundary heat flow equals to 20 W·cm-2, the growth of longitudinal side branches is accelerated and the growth of transverse side branches is restrained, and meanwhile, there is dendritic remelting in the calculation domain.When the boundary heat flow equals to 40 W·cm-2, the growths of the transverse and longitudinal side branches compete with each other, and when the boundary heat flow equals to 100-200 W·cm-2, the growth of transverse side branches dominates absolutely.The temperature field of dendritic growth was analyzed and the relation between boundary heat flow and temperature field was also investigated.

Numerical Simulation of Transport Phenomena in Solidification of Multicomponent Ingot Using a Continuum Model

A continuum model proposed for dendrite solidification of multicomponent alloys, with any partial solid back diffusion, was used to numerically simulate the macroscopic solidification transport phenomena and macrosegregations in an upwards directionally solidified plain carbon steel ingot. The computational results of each macroscopic field of the physical variables involved in the solidification process at a middle solidification stage were presented.

Multi-physical fields distribution in billet during helical electromagnetic stirring:A numerical simulation research

Electromagnetic stirring is one of the widely applied techniques to modify the quality of casting billets.Different from conventional rotate stirring,the helical stirring is more professional in assisting multi-dimensional flow of molten metal and eliminating solidification defects.In this study,the single-winding helical stirring(SWHS)was introduced,offering advantages such as smaller volume and lower electromagnetic shielding compared to traditional helical stirring methods.Following a comprehensive numerical simulation,the stirring parameters of SWHS were adjusted to yoke inclination angle of 43°and frequency of 12 Hz.The higher electromagnetic force and flow velocity in drawing direction,as well as the lower temperature gradient induced by the SWHS,are positive factors for homogeneous solidification of billet.The experimental results on Al-8%Si alloy and 0.4%C-1.1%Mn steel demonstrate that compared to rotate stirring,the SWHS process can induce better billet quality and is more effective in accelerating the equiaxed expansion and reducing element segregation.The SWHS process can enhance the equiaxed ratio of the billet by 58.3%and reduce segregation degree of carbon element by 10.97%.Consequently,SWHS holds great promise as a potential approach for improving the quality of continuous casting billets.

Numerical Simulation and Parallel Computing of Acoustic Wave Equation in Isotropic-Heterogeneous Media

In this paper,we consider the numerical implementation of the 2D wave equation in isotropic-heterogeneous media.The stability analysis of the scheme using the von Neumann stability method has been studied.We conducted a study on modeling the propagation of acoustic waves in a heterogeneous medium and performed numerical simulations in various heterogeneous media at different time steps.Developed parallel code using Compute Unified Device Architecture(CUDA)technology and tested on domains of various sizes.Performance analysis showed that our parallel approach showed significant speedup compared to sequential code on the Central Processing Unit(CPU).The proposed parallel visualization simulator can be an important tool for numerous wave control systems in engineering practice.

Numerical simulation and processoptimization for producing large-sized castings

3-Dvelocity and temperature fields of mold filling and solidification processes of large-sized castingswere calculated,and the efficiency and accuracy of numerical calculation were studied.The mold filling andsolidification processes of large-sized stainless steel,iron and aluminum alloy castings were simulated by using ofnew scheme;their casting processes were optimized,and then applied to produce castings.

Experimental Study and Numerical Simulation of Directionally Solidified Turbine Blade Casting

The directional solidification process of turbine blade sample castings was investigated in the work. Variable withdrawal rates were used in one withdrawal process and compared with the other using uniform rate. A mathematical model for heat radiation transfer and microstructure simulation of directional solidification process was developed based on CA-FD method. The temperature distribution and microstructure w.ere simulated and compared with the experimental results. The stray grains were predicted and compared with the experimental results. The uneven temperature distribution of platform was the main reason of the formation of stray grains.

Study on Numerical Simulation of Mold Filling and Heat Transfer in Die Casting Process

A 3-D mathematical model considering turbulence phenomena has been established based on a computational fluid dynamics technique, so called 3-D SOLA-VOF (Solution Algorithm-Volume of Fluid), to simulate the fluid flow of mold filling process of die casting. In addition, the mathematical model for simulating the heat transfer in die casting process has also been established. The computation program has been developed by the authors with the finite difference method (FDM) recently. As verification, the mold filling process of a S-shaped die casting has been simulated and the simulation results coincide with that of the benchmark test. Finally, as a practical application, the gating design of a motorcycle component was modified by the mold filling simulation and the dies design of another motorcycle component was optimized by the heat transfer simulation. All the optimized designs were verified by the production practice.