Research & Development

179

August 2008

Numerical simulation and process optimization for producing large-sized castings*Wang Junqing1, Sun Xun1, Guan Yang1, Wang Penghua1, Li Hailan1, Bai Limei2, Sun Xinzhi2

(1. Shenyang Research Institute of Foundry, Shenyang 110022, P. R. China; 2. Shenyang Gas Compressor Co. Ltd., Shenyang 110025,

P. R. China)

Abstract: 3-D velocity and temperature fi elds of mold fi lling and solidifi cation processes of large-sized castings were calculated, and the efficiency and accuracy of numerical calculation were studied. The mold filling and solidifi cation processes of large-sized stainless steel, iron and aluminum alloy castings were simulated by using of new scheme; their casting processes were optimized, and then applied to produce castings.

Key words: numerical simulation; mold fi lling; solidifi cation process; process optimization; stainless steel; alloyed iron and aluminum castings

CLC number: TP391.9 Document code: A Article ID: 1672-6421(2008)03-179-07

Since the 1960s there are 3 progressive periods for modeling and simulation of mold fi lling and solidifi cation processes

of castings. First, in 1988 3-D temperature fi elds were calculated successfully during solidifi cation of steel casting [1-4]. Second, in 1995 3-D velocity fields of metal flow in mold filling were calculated successfully by B. Sirrell of Birmingham University [5-9]. Third, since 1990 a new task to model and simulate the microstructure and morphology of crystal grains is underway. In order to calculate nucleation in a macroscopic mesh, undercooling at each microscopic cell and the random number of nuclei by Monte-Carlo method, the 3-D velocity, temperature and concentration fields in the meshes of casting should be computed. Some researchers tried to simulate 3-D microstructure of superalloy and ductile iron castings [10-14]. Meanwhile, foundry technicians are more interested in simulating mould filling, solidifi cation process of castings and optimizing the processing parameters to produce sound castings.

Since Re Number ≥ 2300 is the practical value in the

most of the mould filling processes, Lipinski, Yang and Sun considered the effects of turbulent fl ow on velocity and temperature fields, and solved more equations than those considered laminar flow only [15-17], but it needed quick and accurate calculating schemes of 3-D velocity and temperature fi elds. Powerful software was developed to increase effi ciency and assure accuracy of numerical calculation. 24 million tons of castings were manufactured annually in China, therefore, proper numerical simulations by using of appropriate software are needed eagerly in order to produce sound and large-sized castings effi ciently.

1 Modeling equationsWhen turbulent flow effects on processing parameters are taken into account and time averaged method is being used, the governing equations, including continuity, momentum, volume fraction, energy, turbulent kinetic energy, dissipate rate of turbulent kinetic energy equations, are as following:

Male, born in 1942, Ph.D, Chief Engineer. Research interests: numerical simulation of casting process, foundry metallurgy and engineering.Received: 2008-04-07; Accepted: 2008-06-10

*Wang Junqing

(1)

(2)

(3)

(4)

(5)

(6)

Some variables of the equations are calculated as following:

(7)

(8)

CHINA FOUNDRY Vol.5 No.3

180

(9)

(10)

(11)

(12)

(13)

(14)

(15)

Where: Ret – turbulence pulse Reynolds number;t – liquid density, kg/m3;xi, xj – coordinate, m;ui, uj – velocity, m/s;n – molecular dynamic viscosity, Pa·s;o – molecular kinematic viscosity, m2/s;nt – turbulent viscosity, Pa·s;ne, nT, nK, nf – generalized diffusion coeffi cient, Pa·s;t – time, s;gi – gravity acceleration, m/s2;T – temperature, K;p – pressure, N/m2;F – volume fraction, 0≤F≤1;qv – heat source term, kg·K/s·m3;K – turbulent kinetic energy, m2/s2;Pr – molecular Prandl number;f – dissipate rate of turbulent kinetic energy, m2/s3;G – the producing term of turbulent kinetic energy, Pa/s;coefficients: vT =0.9–1.0, vK =1.0, vf =1.3, C1 =1.44,

C2 =1.92, Cn = 0.09, f1 = 1.0Based on these equations, with appropriate initial and

boundary conditions, 3-D velocity and temperature fi elds can be calculated.

2 Program for the calculation and display of 3-D velocity and temperature fi elds

2.1 Pre-processing and post-processingPre-processing and post-processing programs were developed. It increases the enmeshment speed by 13 times by using new algorithm; for example, 1.93 million meshes can be generated in 5 seconds. The new program can read STL format fi le of casting solid geometry and is able to repair defects in STL fi le automatically; the inflow boundary condition can be set up and changed by mouse indicator; post-processing may show fi lling pattern, 3-D velocity vector variation, 3-D temperature distribution and result of ui, p and T on any section of the casting, and operation is quick and convenience. It is able to choose 19 different kinds of materials to represent different attribution of meshes during numerical calculation of mold fi lling and solidifi cation process of casting, which brings more practicality for engineering analysis [18].

2.2 Fluid fl ow and heat transfer calculation by high resolution MINMOD scheme

In this study, high resolution MINMOD mesh with 5 points was adopted to make the discretization of momentum and energy conservation equations on unequal size of meshes [19]; improved VOF method was used to deal with the evolution of free surface and SOLA technique was used to calculate the velocity of fl uid fl ow. Results showed that numerical accuracy was increased, as shown in Fig. 1, false diffusion and virtual physical phenomenon that generated from the numerical calculation were eliminated. The symmetrical distribution of temperature was reasonable during mold filling process of aluminum alloy plate casting.

Fig. 1 Mould fi lling simulation of plate casting by high resolution MINMOD scheme

3 Exploration for increasing effi ciency of numerical simulation

Since large portion of computing time was consumed in the simulation of velocity field during mold filling, so many efforts were devoted to increase the calculation efficiency. Velocity fi eld during mold fi lling was calculated by using of a new algorithm named predictor-two step corrector-VOF, which applied the implicit algorithm and large time step dt on calculation of velocity, pressure and temperature; and explicit algorithm with a small time step dt/n over the free surface range (n

is times cycles to get a new evolution of fl uid). Figure 2 showed the simulation results of Benchmark test by using of the new algorithm with Courant Number equal to 4, where C=u∆t/∆x. The simulated results were in agreement with the Benchmark test.

Figure 3 showed the velocity field simulation results of a plate casting with inflow velocity of 50 cm·s-1. Time cost for the whole simulation process was 392 min and 317 min, when Courant Number, C, equal to 4.0 and 8.0, respectively. Computing time can be shortened by 19% if Courant Number of 8.0 was used instead of 4.0. Although the adoption of a

Research & Development

181

August 2008

large Courant Number can lead to good simulation effi ciency and the general tendency of fl uid fl ow is similar, some obvious differences exist. The details can be found in Figs. 3 (b), (b') and (c), (c').

Therefore, a suitable Courant Number should be selected carefully in order to speed up the simulation without much lost of engineering accuracy.

(a) 0.52 s (b) 0.77 s (c) 1.01 s (d) 1.49 s (e) 1.74 s

Fig. 2 Mould fi lling simulation of the Benchmark test by predictor-two step corrector-VOF scheme with C=4

(a) 0.44 s, 10% (b) 1.73 s, 40% (c) 3.45 s, 80%

(a') 0.45 s, 10% (b') 1.73 s, 40% (c') 3.46 s, 80%

Fig. 3 Velocity fi elds of mould fi lling by predictor-two step corrector-VOF scheme for plate casting (a)-(c): C=4.0, (a')-(c'): C=8.0

(a) 0.44 s, 10% (b) 3.45 s, 80% Fig. 4 Temperature fi elds of mould fi lling for plate casting

Fig. 4 showed the temperature f i e l d s r e s u l t b y u s i n g o f predictor-two step corrector-VOF algorithm, and the Courant Number is 4.0; the temperature distribution is symmetrical and reasonable. New algorithm promotes calculation effi ciency a n d f a v o r s e n g i n e e r i n g application.

CHINA FOUNDRY Vol.5 No.3

182

4 Numerical simulation and process optimization of large-sized castings

4.1 Dual-phases stainless steel castingAim at producing dual-phases stainless steel impeller casting of 2,667 kg, numerical simulations for 3 different casting process techniques were carried out. Figure 5 showed the solid geometry of the impeller casting. Figure 6 showed the chill design and the solidified time field of casting process 1. Figure 7 showed the increased chill size to enlarge the cooling ability and the simulated result using casting process 2. In both technique 1 and technique 2, there are some isolated regions near blade bottoms or middle parts of the impeller casting, therefore shrinkage or porosity may be formed in the corresponded regions. This cannot meet the requirements of high strength and no defects in the connecting part of the blade root and the main body of the impeller, so techniques 1 and 2 were denied. Figure 8 showed the solid geometry and enmeshment of impeller casting with in-gate and risers, using casting technique 3, no any of chills, and enhancing feeding ability from inside of main body. Figure 9 showed the fl ow pattern, free surface evolution and temperature distribution during mold fi lling.

Fig. 5 Solid geometry of impeller casting

(a) Chill design (b) Solidifi ed time fi eld

Fig.6 Casting technique 1

(a) Chill design (b) Solidifi ed time fi eld

Fig. 7 Casting technique 2

(a) Solid geometry of casting with feeders (b) Enmeshment

Fig. 8 Casting technique 3

(a) 5.52 s, 25% (b) 16.55 s, 75% (c) 22.07 s, 100%

Fig. 9 Flow patterns and temperature fi elds during mould fi lling of impeller casting for casting technique 3

Research & Development

183

August 2008

Figure 10 showed the solidified t ime fields during solidification process. From these results it can be sure that liquid metal fi lls the mold cavity steadily. This solidifi cation process can meet the requirement of sequential solidifi cation,

4.2 Alloyed iron castingNumerical simulation of JT30-54 alloyed iron air compressor block casting with a weight of 7,665 kg was carried out to calculate temperature fields under 3 different casting processes. Two typical results for the casting technique 1 and 3 are shown in Figs. 12 and 13. For the casting technique 2, the simulated result was between the casting technique 1 and 3.

(a) 352 s (b) 1,996 s (c) 4,344 s

Fig.10 Solidifi ed time fi eld during solidifi cation process of impeller casting for casting technique 3

(b) Top view(a) Side view

Fig. 11 Impeller casting

and thus no shrinkage and porosity appear. Mold fi lling time was 22 s and solidifying time was 3.26 h, both of these times were suitable for foundry operation. Figure 11 showed the side and top views of the produced sound casting.

(a) Solid geometry (b) Riser and chills distribution (c) Defects prediction

Fig. 12 Numerical simulation and defect prediction under casting technique 1

Figure 12 shows the solid geometry, riser and chill positions in the mold, and also defect prediction of the casting under casting technique 1. As shown in Fig 12 (c), there exists a large range of isolated solidifi ed region in the middle part of casting.

Large area of shrinkage and porosity defects may be formed in this region. Leakage defect was detected when the produced casting was under pressurized testing. It demonstrated that the simulated results were reliable. Figure 13 shows the solid

CHINA FOUNDRY Vol.5 No.3

184

(a) Solid geometry (b) Riser and chills distribution (c) Defects prediction

Fig. 13 Numerical simulation and defect prediction under casting technique 3

geometry, riser position, chill distributions in the mold and also defect prediction of the casting under casting technique 3. Compared with those of casting technique 1, casting technique 3 enhanced the cooling ability by increasing both the quantity and size of the chills, and thus reduced the isolated volume signifi cantly. The isolated volume distributed separately and no linked porosity defects can be formed. The produced block

casting, as shown in Fig. 14, was machined and pressurized at 0.6 MPa, no leakage was detected. The casting satisfi ed the requirements in specifi cation.

4.3 Aluminum castingNumerical simulation of large thin walled ZL114A aluminum casting with a weight of 586 kg, pouring temperature of 710℃, mould temperature of 25℃ (no-bake furan resin bonded sand) and infl ow velocity 20–50 cm·s-1 was carried out to calculate velocity and temperature fields under 2 different casting processes by using of low pressure casting method. The solid geometry and enmeshment of aluminum casting with 15.03 million meshes are shown in Fig. 15 (a). There was a misrun defect if low infl ow velocity of 20 cm·s-1 was used, as shown in Fig. 15 (b). No misrun was appeared if infl ow velocity of 50 cm·s-1 was used, as shown in Fig. 15 (c), in this case the fi lling time was 44 s. Figures. 15 (d) and 15 (e) showed the temperature fields during solidification process in which the whole casting solidified in about 24 min. So final casting process parameters adopted were that the time of increasing pressure was 44 s, infl ow velocity at elevated liquid metal tube was 50 cm·s-1, holding pressure time was 24 min. By using these parameters, sound casting was produced, as shown in Fig. 15(f).

(a) Enmeshment of aluminum casting with 15.03 mil l ion meshes

(b) Misrun in mould filling with infl ow velocity 20 cm·s-1

(c) No misrun in mould fi lling with infl ow velocity 50 cm·s-1

Fig. 14 Block casting of an air compressor

Research & Development

185

August 2008

(d) Temperature fi eld at solidifi ed 20% (e) Temperature fi eld at solidifi ed 60%

Fig. 15 Numerical simulation of large thin walled aluminum casting by low pressure cast method

5 Conclusions (1) Time averaged governing equations,

include continuity, momentum, volume fraction, energy, turbulent kinetic energy, dissipate rate of turbulent kinetic energy equations were established. It is able to calculate the velocity and temperature fi elds for laminar and turbulent flow during mold fi lling and solidifi cation process.

(2) The developed computer program can read STL file, enmeshing solid geometry, displaying velocity vector, 3-D velocity and temperature fi elds, fi lling pattern, temperature distribution of mold fi lling and solidifi cation process.

(3) The numerical simulation can be used to predict the casting defects and to optimize the casting process parameters to produce large-sized sound stainless steel, alloyed iron and aluminum castings.

References[1] Morroen R E, Wilkes J O and Pehlke R D.

Numerical Simulation of Solidifi cation. Cast Metal Research, 1970(6): 184–192.

[2] Niyama E, et al. Predicting shrinkage in Large Steel Castings from Temperature Gradient Calculations. AFS, 1981(6 ):16–22.

[3] Zhang Yi and Wang Junqing. Numerical Simulation of Solidification Process of

[12] Lesoult G Catro M and Lacaze J. Physical Modeling of the Solidification of Spheroidal Graphite Irons: Revision of the coupled zone concept. Proceedings of Modeling Casting and Welding and Advanced Solidification Processes VIII, USA, 1998: 479.

[13] Catro M, et al. Prediction of the Solidifi cation Microstructure of Hypo- and Hyper-eutectic Spherical Graphite Cast Irons. Proceedings of Modeling Casting and Welding and Advanced Solidifi cation Processes VIII, USA, 1998: 487.

[14] Zhang Yutuo, Wang Junqing et al. Simulation the Dendritic Growth of Pure Material with the Phase Field Method. Foundry, 2003, 52(11): 1091–1095. (in Chinese)

[15] Lipinski D M, Schseter W and Flender E. Numerical Modeling of Filling Sequence and Solidifi cation of Castings. Proceedings of Modeling Casting, Welding and Advanced Solidification Processes VI, USA, 1993: 389–396.

[16] Yang Bingqian et al. Equivalent Laminar Model for 3-D Velocity Field of Turbulent Flow in Crystallizer of Continuous Casting. Journal of Xi’ an Jiaotong University, 1996, 30(4): 79–85.

[17] Sun Xun et al. Numerical Simulation of Mold Filling and Sol id i f icat ion Process for Permanent Mold Cast ing. Proceedings of Modeling Casting and Welding and Advanced Solidifi cation Processes IX, Aachen, Germany, 2000: 389–396.

[18] Guan Yang, et al. Research on Preprocessing and Processing of Mold Filling and Solidifi cation Process of Casing. Foundry, 2004, 53(11): 905–908. (in Chinese)

[19] Tao Wenquan. Recent Development of Numerical Heat Transfer. Beijing: Science Press, 2006. (in Chinese)

(f) Produced sound aluminum casting

Castings. Foundry, 1980(1): 10–16. (in Chinese)[4] Giamei A F and Abbaschian G J. Hammer Casting Simulation

– Round Rubin. Proceedings of Modeling Casting and Welding and Advanced Solidification Processes IV, Palm Coast, Florida, USA, 1988: 775–861.

[5] Stoehr R A. Simulation in the Design of Sand Casting. Proceedings of Modeling Casting and Welding Processes, Rindge, New Hampshire, USA, 1980: 3–18.

[6] Stoehr R A and Hwang W S. Modeling the Flow of Molten Metal Having a Free Surface during Entry into Molds. Proceedings of Modeling Casting and Welding II, USA, 1983: 47–58.

[7] Stoehr R A, Wang C, Hwang W S and Ingeslev P. Modeling the Filling of Complex Foundry Mould. Proceeding of Modeling Casting and Welding Processes III, Santebarbara, California, USA, 1986.

[8] Wang Junqing, Hansen S F and Hansen P N. 3-D Modeling and Simulation of Mould Filling Using PC’S. Proceedings of Modeling Casting and Welding Processes IV, Palm Coast, Florida, USA, 1988: 741–753.

[9] Sirrel B, Holliday M and Compbell J. The Benchmark Test 1995. Proceedings of Modeling Casting and Welding and Advanced Solidifi cation Processes VII, England, 1995: 915–933.

[10] Zhu P and Smith R W. Dynamic Simulation of Crystal Growth by Monte Carlo Method-I Model Description and Kinetics. Acta Metall. Mater., 1992, 40(4): 683–692.

[11] Li Dianzhong, Su Shifang, Xu Xuehua and Wang Junqing. Modeling of Microstructure Formation for Nickel Based Super Alloy Turbine Blade Casting. Proceedings of 61st World Foundry Congress, Beijing, China, 1995: 63–74.