SCIENCE CHINA Technological Sciences • RESEARCH PAPER •
December 2011 Vol.54 No.12: 3191–3202 doi: 10.1007/s11431-011-4607-6
Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades ZHANG Hang, XU QingYan*, TANG Ning, PAN Dong & LIU BaiCheng Key Laboratory for Advanced Materials Processing Technology, Ministry of Education, Department of Mechanical Engineering, Tsinghua University, Beijing 100084, China Received August 24, 2011; accepted September 26, 2011; published online November 5, 2011
Directional solidified (DS) turbine blades are widely used in advanced gas turbine engine. The size and orientation of columnar grains have great influence on the high temperature property and performance of the turbine blade. Numerical simulation of the directional solidification process is an effective way to investigate the grain’s growth and morphology, and hence to optimize the process. In this paper, a mathematical model was presented to study the directional solidified microstructures at different withdrawal rates. Ray-tracing method was applied to calculate the temperature variation of the blade. By using a Modified Cellular Automation (MCA) method and a simple linear interpolation method, the mushy zone and the microstructure evolution were studied in detail. Experimental validations were carried out at different withdrawal rates. The calculated cooling curves and microstructure agreed well with those experimental. It is indicated that the withdrawal rate affects the temperature distribution and growth rate of the grain directly, which determines the final size and morphology of the columnar grain. A moderate withdrawal rate can lead to high quality DS turbine blades for industrial application. directional solidified (DS) turbine blade, Cellular Automation (CA), numerical modeling and simulation Citation:
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Zhang H, Xu Q Y, Tang N, et al. Numerical simulation of microstructure evolution during directional solidification process in directional solidified (DS) turbine blades. Sci China Tech Sci, 2011, 54: 31913202, doi: 10.1007/s11431-011-4607-6
Introduction
Gas turbine blade, as a key part used in aeronautical industry or energy industry, is mainly manufactured by Bridgman process currently. The controlling parameters of the Bridgman solidification process, such as withdrawal rate, temperature gradient, pouring temperature and so on, influence the size and morphology of columnar grains and the property and performance of the final casting. The withdrawal rate, which affects temperature distribution and determines the formation of casting defects and the final properties, has drawn more attentions of factory and laboratory [1–6]. Too *Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2011
high withdrawal rate would cause extremely concave solid-liquid (S/L) interface, which leads to declining grains, transverse grains or other defects, whereas too low withdrawal rate would bring coarsened grain, crack in the shell, or other defects and thus low productivity. Both numerical methods [7–14] and experimental methods [15–18] are used to learn more about the Bridgman process in the past few decades. Many kinds of numerical methods and models are proposed to simulate the process of Bridgman directional solidification process and microstructure of columnar grains in blade castings. In this work, a heat transfer model was built to simulate the temperature distribution during the solidification process, and a coupling technique between macro & micro modeling tech.scichina.com
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was proposed to decrease huge calculation amount and make the microstructure simulation of the whole blade feasible. Adding the discrete treatment technology and optimizing the algorithm, the solidification process of hollow turbine blade was modeled firstly. A Modified Cellular Automation (MCA) method based on Cellular Automation (CA) was referred to simulating the microstructure actually and visually. Validation experiments were carried out at different withdrawal rates. The simulated microstructure results agreed well with the results of validation experiments. Using the numerical method, details of temperature field, mushy zone distribution and microstructure morphology could be obtained, and the process of the solidification could be observed. By the simulation and experiment investigation, a too low withdrawal rate could cause coarse grains and low productivity, but a too high withdrawal rate will cause declining and unstable growth. A moderate withdrawal rate was proposed for real production finally.
2 Mathematical models 2.1 The simplified model of directional solidification process It is important to focus on the manufacturing process from pouring of the high temperature liquid metal to the end of the solidification. The Bridgman furnace as seen in Figure 1 can be simplified into five parts: heating zone, baffler, cooling zone, chill and withdrawal unit. A group of mold shells are fixed on the chill. As the temperature is high enough, the liquid metal is poured into the mold and kept for minutes. Then withdrawal unit starts at a certain speed. A temperature gradient is formed by the baffler, and the S/L interface advances around the location of the baffler. The withdrawal unit continues to move until the mold is drawn entirely into the cooling zone and the metal finishes solidification.
Figure 1 The simplified physical model of the directional solidification process in 2D.
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2.2
Heat transfer equation
The calculation of temperature field is the basis in the simulation. The energy conservation equation is described as follows:
c
2T 2T 2T T 2 2 2 t y z x
f S QR , L t
(1)
where T is the temperature, t is the time, is the density, L is the latent heat, c is the specific heat, is the heat conductivity; x, y and z are the coordinates; fS is the solid fraction, QR is the energy exchange by heat radiation. 2.3 Coupling technique for the calculation of macro heat transfer and microstructure evolution Compared with the calculation of macro temperature distribution, the microstructure simulation needs extremely fine elements. If we adopt the identical element size to couple and calculate macro temperature distribution and microstructure formation, it means huge elements amount and enormous calculation time. This coupling macroµ scale technique was proposed by Xu and Pan [19], et al. In this paper, macro-grids for temperature calculation and micro-grids for microstructure calculation were nested together; and the maro time step of temperature calculation was divided into several time spans to calculate the microstructure in calculation circle. This nesting technology of macro and micro calculations by time steps compromises the calculation scale and calculation time (seen Figure 2). In simulating process, macro temperature distribution is calculated based on the macro-grids and macro time step at
Figure 2
Sketch-map of coupling macro and micro calculations.
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first. Then temperatures of micro-grids can be obtained by the interpolation method. The releasing of latent heat of the superalloy will heat up micro zones of the dendrite grains’ tips and leads to an uneven temperature distribution, which needs an amendment of the temperature distribution. Meanwhile, micro temperature gradient distribution must coincide with that of macro one. So the linear interpolation method was designed as shown in Figure 3. For a micro cell (l, m, n) in the macro grid (x, y, z), the micro cell’s temperature can be calculated as Txl,,ym, ,zn Tx , y , z Gx l x G y m y Gz n z.
(2)
And Gx, Gy, Gz can be gotten by: Tx , y , z Tx 1, y , z / x Gx Tx 1, y , z Tx , y , z / x
0 x
Tx , y , z Tx , y 1, z / y Gy Tx , y 1, z Tx , y , z / y
0 m y y 2 , y 2 m y y ;
(4)
Tx , y , z Tx , y , z 1 / z Gz Tx , y , z 1 Tx , y , z / z
0 n z z 2 , z 2 n z z .
(5)
l x x 2 , 2 l x x ;
(3)
In eqs. (2)–(5), Tx,y,z is the temperature in the centre of the macro grid (x, y, z); Txl,,ym, ,zn is the temperature of the micro cell (l, m, n) in the macro grid (x, y, z ); x, y and z are the lengths of the micro cell in x, y and z directions, respectively; x, y and z are the lengths of the macro grid in x, y and z directions, respectively. After the calculation of micro cell temperature, the nucleation and grain growth of the microstructure can be calculated, and the latent heat is obtained by the following
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equation:
Q L f sVmic .
(6)
The macro-grid’s temperature will be modified by temperature recovery method [23] In this way the bidirectional coupling of micro and macro calculations at one macro temperature step is done successfully. Then macro temperature and microstructure could be calculated gradually until the end of solidification of the whole casting. 2.4
MCA method
The CA method has been used to simulate microstructure and grain competition for many years. The numerical model is discrete, and then there will be a great amount of cells. Each cell has some parameters to describe its state (such as temperature, concentration, growth direction, and so on). Figure 4(a) shows that the basic evolvement of the liquid cells are captured in the two prior growth directions [01] and [10]. In Figure 4(b), the liquid cells are captured in prior growth directions [01] and [10], and the cells in the direction which is vertical to the prior growth directions also are captured. These two capturing rules are the basic process of CA method, which describe the gains’ growth and coarsening. However, some special cells (added cells in [01] and [10] directions shown in Figure 4(b)) should be captured in this step to modify the grains directions and keep the [01] and [10] directions as the prior growth direction. This treatment is named MCA method, and it releases the reliance of e CA to the discrete grids. The numerical results of grains’ morphology agreed well with those of experiments by the MCA method. This method is well adopted in the simulation of microstructures [19, 20]. 2.5
Competitive growth of columnar dendritic grains
The competitive growth of dendritic grains influences the size and morphology of the final microstructure of the blade. The mechanism of the competitive growth of dendritic grains is clearly shown in Figure 5. The tips of the grains grow at a speed which has close relationship with the undercooling in the melt. Assume that grain tips grow at a same uniform undercooling. So the grains advance at a same speed named vn. If there is a grain whose preferential growth orientation has a degree with the direction of heat flux, the growth rate of this grain is just as eq. (7) at the direction of heat flux. v vn cos .
Figure 3 Sketch-map of linear interpolation method.
(7)
The angles between the preferential growth orientation and heat flow direction are different. Grains with bigger angles grow slower than those with smaller ones, as seen in eq. (7). As the growth is continuous, grains with smaller angles
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Figure 4
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Explanation of MCA method in 2D gridding. (a) Basic growth; (b) modified process of add some special cells.
and eliminated. The grains with smaller angles can grow faster and advance smoothly.
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Figure 5 Principle of the competitive growth of columnar drains.
have enough time and space to develop their secondary and tertiary dendritic arms. These developed dendritic arms may block the normal growth of grains with bigger deviation. Finally, these kinds of grains with bigger angles are stopped
Experiments
Modern advanced gas turbine blades have hollow structure, thin wall and complex shape. Figure 6 shows 3D shape of a turbine blade in this research. The blade can be divided into four parts, just as seen in Figures 6(a) and 6(b): starter block, blade body, platform and tenon. Among these four parts, the blade body has a very complex shape, what is more, it has a hollow structure, and its thinnest wall is only about 0.8 mm. The thinnest place of the platform is 1.0 mm. The tenon is also hollow. This means some complicated problems in the solidification process. In order to verify and validate the numerical modeling, experiments were carried out and the microstructure of the casting was observed. Figure 6(c) shows the distribution of six turbine blades on the chill plate.
Figure 6 3D geometry and distribution pattern of turbine blades on the chill plate. (a) 3D model of the blade (back side); (b) 3D model of the blade (basin side); (c) distribution of turbine blades on the chill plate.
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Ni-based superalloy DZ125 [21] was used to produce the turbine blade in the experiments. The nominal chemical composition of DZ125 is shown in Table 1. The validation experiments were carried out at three different withdrawal rates named Vl (low rate, which is above 3 mm min1), Vm (middle rate, which is between 3 mm min1 and 12 mm min1) and Vh (high rate, which is below 12 mm min1), respectively. The other controlling parameters of these experiments were kept unchanged, such as a uniform pouring temperature (which was high above 1500°C), a fixed electricity power, a stable circular cooling water volume, and so on. In each experiment, there were six blades fixed on the chill plate and manufactured at each time. After the directional solidification, the shell was broken out and blade was cut out and eroded. Then the microstructures could be observed and compared with the calculated results.
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Results and discussion
Corresponding to the validation experiments, the numerical calculation chose the same processing parameters to simulate the directional process at three withdrawal rates above, Vl, Vm and Vh. The temperature distribution, mush zone distribution and microstructure of the whole blade were shown and described below. 4.1 The 3D model after finite difference dividing treatment In this work, the Cellular Automation-Finite Difference (CA-FD) method was adopted to simulate the directional solidification process. The finite difference mesh generation treatment is the based work for the whole calculation. The 3D models with meshed grids are shown in Figure 7. Several cross sections of the blades after finite difference dividing are magnified in Figures 8(a)–8(c).
Figure 7
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Table 1 ( wt.%)
4.2
The nominal chemical composition of superalloy DZ125 [21]
C
Cr
Co
W
Mo
0.1
8.9
10
7
2
Al
Ti
Ta
Hf
Ni
5.2
0.9
3.8
1.5
balance
The calculated temperature distribution
According to the numerical simulation results, the temperature changing with time is shown in Figures 9, 10, 11 (where HZ, CZ and Bf represent heating zone, cooling zone and baffler respectively). In this research, we choose to analyze the temperature distribution on the basin side of the blade. When the withdrawal rate is low (Vl), the temperature of the blade’s part above the baffler appears higher on the left side which is close to the center of the furnace (as shown in Figure 9), but lower on the right side near the furnace wall. However, the temperature of the blade’s part that below the baffler is almost even at Vl. As the withdrawal rate is middle (Vm), the temperature distribution is similar to that of the low rate, but slopes of the temperature isothermal lines become larger. When the solid fractions at different withdrawal rates are of the same values, the location of baffler at Vm is higher than that at Vl. When the withdrawal rate increases to high rate (Vh), the temperature distribution is very different from that at low or middle rate. Firstly, the isothermal lines of temperature appear uneven and unstable. Furthermore, they showed obviously concave in the cooling zone. Secondly, according to the temperature value, the S/L interface is below the baffler and deep into the cooling zone, which is critically harmful to keeping a stable growth of the columnar grains as shown in Figure 11. 4.3
The calculated mushy zone
The mushy zone is defined as the zone where temperature is below the liquidus and above the solidus, which is from
Turbine blade and mold shell after finite difference mesh generating. (a) Blade (back side); (b) blade (basin side); (c) mold shell.
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Figure 8 Horizontal cross sections of the turbine blade after finite difference mesh generating. (a) Middle section of the tenon; (b) top section of the blade body; (c) bottom section of the blade body.
1295°C to 1375°C for the alloy used in the experiments [21]. Figures 12, 13 and 14 show the mushy zone variation with the solid fraction increasing at different withdrawal rates. Several solid fractions, 40%, 50%, 60% and 80% were chosen to show the changing tendency of mushy zone for Vl group and Vh group. For the middle withdrawal rate (Vm)
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group, there are more solid fractions (20%, 40%, 45%, 50%, 55%, 60%, 65% and 80%) to describe the mushy zone changing gradually. The mushy zone at Vl has some characteristics. Firstly, the length of this mushy zone is narrower and more horizontal compared with those at other withdrawal rates, and it becomes wider and wider with the solid fraction increasing gradually. When the withdrawal rate is low, there is enough time for heat transfer in the blade casting, so the temperature gradient near the baffler turns to be high and the length of the mushy zone becomes narrow and horizontal. As the withdrawal process is going on, the main way by which the heat is dissipated changes from heat conduction through z coordinate to heat radiation toward the surrounded cooling zone. In ordinary directional solidification process, the efficiency of heat radiating is far lower than that of conducting, therefore there is no enough time to dissipate heat as the heat transferring and the width of the mushy zone appears enlarged near the end of the solidification. Secondly, the location of the mushy zone is above the baffler’s upper edge. This is because the growth rate of columnar grains is faster than the withdrawal rate. Then the S/L interface develops faster than the movement of baffler. Then the location of baffler becomes lower than the S/L interface gradually, as
Figure 9 Temperature distribution during the solidification at Vl (basin side). (a) fs =40%, t =2 min; (b) fs =50%, t =11 min; (c) fs =60%, t =19 min; (d) fs =80%, t =24 min.
Figure 10 Temperature distribution during the solidification at Vm (basin side). (a) fs =40%, t =2 min; (b) fs =50%, t =8 min; (c) fs =60%, t =12 min; (d) fs =80%, t =16 min.
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Figure 11 Temperature distribution during the solidification at Vh (basin side). (a) fs =40%, t =2 min; (b) fs =50%, t =7 min; (c) fs =60%, t =10 min; (d) fs =80%, t =1 2min.
Figure 12 Mushy zone distribution during the solidification at Vl (basin side). (a) fs =40%, t =2 min; (b) fs =50%, t =11 min; (c) fs =60%, t =19 min; (d) fs =80%, t =24 min.
Figure 13 Mushy zone distribution during the solidification at Vm (basin side). (a) fs =20%, t =1 min; (b) fs =40%, t =2 min; (c) fs =45%, t =5 min; (d) fs =50%, t =8 min; (e) fs =55%, t =11 min; (f) fs =60%, t =12 min; (g) fs =65%, t =13 min; (h) fs =80%, t =16 min.
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Figure 14 Mushy zone distribution during the solidification at Vh (basin side). (a) fs =40%, t =2 min; (b) fs =50%, t =7 min; (c) fs =60%, t =10 min; (d) fs = 80%, t =12 min.
seen in Figures 12(a)–12(c). However this situation tends to form coarsened grains. In Figure 13 the mushy zone advances at different solid fractions in detail at Vm. The length of the mushy zone turns to be slight wider than that at Vl but narrower than that at Vh. The changing tendency of the mushy zone being wider with solid fraction increasing is still similar to that of the Vl group, but the shape of mushy zone is little concave and slight declining. The location of the mushy zone is just in the position of the baffler, as seen in Figure 13. This location is what industries and laboratories want, since it leads to erect, parallel and stable colum-
nar grains. The simulation results change very much at Vh, and the length of mushy zone is enlarged, especially near the end of solidification. The shape of mushy zone turns to be extremely concave and unstable, which may cause converging grains and stray grains. 4.4
Microstructure simulation and validation
Figures 15, 16 and 17 describe the grain growths in the turbine blade casting during solidification. In these figures, different grey scales represent different columnar grains,
Figure 15 Simulation result of microstructure size and morphology during the solidification at Vl. (a) fs =20%, t =1 min; (b) fs =40%, t =2 min; (c) fs = 45%, t =5 min; (d) fs =50%, t =11 min; (e) fs =55%, t =16 min; (f) fs =60%, t =19 min; (g) fs =65%, t =20 min; (h) fs =100%, t =29 min.
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Figure 16 Simulation result of microstructure size and morphology during the solidification at Vm. (a) fs =20%, t =1 min; (b) fs =40%, t =2 min; (c) fs =45%, t =5 min; (d) fs =50%, t =8 min; (e) fs =55%, t =11 min; (f) fs =60%, t =12 min; (g) fs =65%, t =13 min; (h) fs =100%, t =19 min.
Figure 17 Simulation result of microstructure size and morphology during the solidification at Vh. (a) fs =20%, t =1 min; (b) fs =40%, t =2 min; (c) fs = 45%, t =4 min; (d) fs =50%, t =7 min;(e) fs =55%, t =9 min; (f) fs =60%, t =10 min; (g) fs =65%, t =11 min; (h) fs =100%, t =15 min.
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and the liquid metal is set to be achromatic in order to present the morphology and location of the microstructure clearly. According to the simulation results, the grain growing processes are similar at different rates. The nucleation takes place at the bottom of the starter block, and after that these tiny nuclei grow in the opposite direction of the heat flow. These grains have the 001 crystal directions pointing to all directions, but only those whose 001 preferential growth orientation best aligned with that of heat flow could get the fastest growth rate. As the best-aligned grains continually grow and become coarse, the grains which were not well aligned with respect to the maximum gradient of the temperature field would grow at a much slower speed and may be restrained and submerged. Finally at the top of the starter block, there are numbers of developed columnar grains with 001 crystal orientation parallel to z coordinate axis, which advance to the body of the blade. The columnar grains selected in the starter block grow steadily into the body of blade. Because two edges of the blade body cool faster, the grains in these places will incline. Some grains will transversely grow and coarsen, so the widths of grains on the sides of the body are wider than those in the centre. When some grains’ tips arrive at the platform zone, the second arms of these columnar grains may appear transverse developments and the ternary arms will grow from the second arms. They become coarse gradually and take up the whole platform. Sometimes the stray grains maybe nucleate and grow from the corner of the platform at this period. The grains at the center of the body directly develop through platform towards the tenon zone, and keep coarsening, and finally take up the tenon zone. As the withdrawal rate increases, the fronts of the microstructures become more and more uneven. When the rate is low, the S/L interface is horizontal. While the rate rises to middle value, the S/L interface turns to be higher on one side and lower on the other side showing a declining shape. As the withdrawal rate is up to high rate, the S/L interface becomes concave, that is higher on the edges side and lower in the center, and will lead to the incline growths of grains on the edge sides and the transverse coarsening of grains. However it is prone to form the defects, such as large-angle crystal and coarsening grains. 4.5 Comparison of simulation results with experimental The validation experiments were carried out in this work. After the solidification and removing the shell, three groups of specimens were prepared. The surfaces of the blade castings were eroded, and then the morphology of the microstructure was observed. The morphology of microstructure by simulation was compared with that by experiments, as shown in Figures 18 and 19. The simulation results agreed well with the experimental. Widths of columnar grains, an-
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gles of grains to z coordinate axis and identification of different grains in different zones in the simulation were all in accordance with those of experiments. The simulation results in Figures 18(a)–18(c) show that on the back side of the blade the widths of columnar grains are small and the angles of the grains to z coordinate axis are tiny, which are proved by the validation experiments, as shown in Figure 18 (d)–18(f). Both the simulations and experiments show that the widths and the angles of columnar grains increase as the withdrawal rate increases to high rate. Figure 19 shows the simulation and experiment results on the basin side of the blade. When the withdrawal rate is low, the angles of the grains to z coordinate axis are small, but the grains on the edge sides show coarsening and declining growth in some degree as seen in Figure 19(a). The results presented in Figure 19(d)–19(f) also appear the obviously coarsening grains on the right side (the leading edge of the blade). That is, there are also the coarsening grains on the basin side of the blade casting. Meanwhile, at the middle withdrawal rate as seen in Figures 18(b), 18(e), 19(b), and 19(e), both the simulation results and the experiment results can verify that the angles of the grains to z coordinate axis are small and the widths of columnar grains are approximately even, and the microstructure is better for the real turbine blade. From both the simulation and experiments, it can be seen that the columnar grains of the basin side of the blade show deflective growth seriously on the right side (the leading edge) if the withdrawal rate is too high, and most of the columnar grains lean to one side of the blade. For the DS process of the superalloy turbine blade casting, the withdrawal rate greatly influences the grain growth. A lower or higher rate will cause abnormal columnar grains, which coincides with that of Elliot et al. [22]. In the real production in aeronautical industry, it is necessary to adopt a higher withdrawal rate to improve the productivity. But too high withdrawal rate will lead to the declining grains and instable growth, and the property of the microstructure will be hard to control. However, low withdrawal rate not only decreases the productivity but also causes coarsened grains and uneven sizes of different columnar grains. In total, choosing a proper value of withdrawal rate may get better microstructure for the DS turbine blades.
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Conclusions
(1) The 3D macro heat transfer model and microstructure model were coupled together to simulate the microstructure evolution in the DS turbine blades during directional solidification process. The temperature distribution and the microstructure morphology of the blade at different withdrawal rates were predicted. (2) The validation experiments were performed at low, middle and high withdrawal rates which were the same with the simulation parameters. The size and morphology of
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Figure 18 Comparison of the simulated microstructure with the experimental (back side). (a)(d) Low withdrawal rate; (b)(e) middle withdrawal rate; (c)(f) high withdrawal rate; (a)(b)(c) simulation results; (d)(e)(f) experimental results.
Figure 19 Comparison of microstructure by simulation and experiment (basin side). (a)(d) Low withdrawal rate; (b)(e) middle withdrawal rate; (c)(f) high withdrawal rate; (a)(b)(c) simulation results; (d)(e)(f) experiment results.
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microstructure were obtained by numerical calculation and experiments. The competitive growth and evolution of the columnar grains were confirmed by experiments and analyzed by the simulation further. (3) It is proved by the simulation and experiments that the withdrawal rate significantly influences the microstructure evolution of the DS turbine blade casting. Either too low or too high rate is bad for the ideal microstructure, and a moderate withdrawal rate makes it more possible to obtain better microstructure and higher productivity.
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This work was supported by the National Basic Research Program of China (Grant Nos. 2005CB724105, 2011CB706801), National Natural Science Foundation of China (Grant No. 10477010), National High Technology Research and Development Program of China (Grant No. 2007AA04Z141) and Important National Science & Technology Specific Projects (Grant Nos. 2009ZX04006-041, 2011ZX04014-052). 1
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