30 論文鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 速度論に基づく真空浸炭炉のマルチステップシミュレーション Multi-step Simulation of Vacuum-carburizing Reactor based on

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1 30 論文鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 速度論に基づく真空浸炭炉のマルチステップシミュレーション Multi-step Simulation of Vacuum-carburizing Reactor based on Kinetics Approach Soichiro Makino, Masahide Inagaki, Hideaki Ikehata, Koji Tanaka, Hiroyuki Inoue and Koji Inagaki Synopsis : A novel and efficient simulation technique for the purpose of optimization of vacuum-carburizing process was proposed. This method consists of three steps: calculation of gas convection and diffusion, calculation of only gas diffusion, and calculation of carbon diffusion in steel. The first step provides the gas convection velocity that is employed in the second step. Adsorption rate of carbon on the steel surface is obtained in the second step, and carbon concentration in the steel is calculated in the third step based on the adsorption rate of carbon. Experiments were conducted to verify the proposed method in both laboratory- and industrial-scale reactors. Comparison of the computational predictions to the experimental data revealed that the proposed technique enabled accurate prediction of the adsorption rate of carbon on the steel surface at various temperature conditions, the amount of carburized carbon at each operating time, and the profile of carbon concentration in the steel; in other words, the carburized depth. In addition, the calculation of the industrial-scale reactor, whose simulation model consisted of approximately seven million computational meshes, was completed within about two days. Therefore, the proposed simulation technique could be used to control and optimize the process in industrial vacuum-carburizing reactors. Key words: vacuum-carburizing; numerical simulation; computational fluid dynamics; acetylene; carbon diffusion. 1. 諸言 1 3 Khan 4 Yada and Watanabe 5 Computational Fluid Dynamics 1 1 mm m 10 m 5 10 m 10 m 6 cm m J-STAGE ReceivedonJul.4,2018;AcceptedonAug.31,2018;J-STAGEAdvancepublished onoct.19, ToyotaCentralR&DLaboratories,Inc.,41-1YokomichiNagakute,Aichi ToyotaCentralR&DLaboratories,Inc.,nowDaidoUniversity 3 ToyotaMotorCorporation Correspondingauthor: makino@mosk.tytlabs.co.jp DOI: 30

2 31 2. マルチステップ計算法の提案 Fig.1 Step 1 Step 2 Step 3 Step 1 Step 2 U in τc L g g L g /U in τc g D g L g2 / D g π U in 10 1 U in Step 1 Step 2 Step 2 Step 3 τd g τ s d 2 D g L s K 1300 K 3000 Pa Step 2 Step 3 3. シミュレーション手法 Step 1 Step 2 Step Step Navier-Stokes Fig. 1. Schematic overview of the multi-step simulation for the vacuum-carburizing reactor. 31

3 32 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 3 σ ij i j i (1,1) i j T ** 12 ρ kg/m 3 t s u m/s j x m x j 1 x x 2 y x 3 z n w' kg/ m 3 s s w mol/ m 2 s s p Pa η Pa s Y i D m 2 i /s P 0 Pa R J/ mol K T K M kg/mol j C 2 H 2 H 2 w s η i Chapman-Enskog 7 7 σ i Lennard-Jones (2,2) i T * 8 k B J/K Boltzmann ε J i Lennard-Jones η η i X i Lennard-Jones ε ij i j , Morita 10,11 Yada and Watanabe 5 15 * 16 k m/s C s C2H2 mol/m 3 w s w s k s A E J/mol Step 2 Step 2 Step 1 U j 32

4 w' s Step 1 16 w s D i Step Step 3 Step 3 γ ξ 20 1 Step 2 Step 1 Step Y Csat Step 1 Step 3 Step 2 Step 3 1 ρ A Y C D C D C Wells 実験方法 2 Fig.3 18 mm 50 mm SCr mm 100% C 2 H 2 62mL/min 1223 K 1273 K 1323 K 1373 K 300 Pa C 2 H 2 24 ξ 0 Y Csat Y C Y Csat w s Neumann Y C Y Csat Y Csat Dirichlet ξ Y C ,14 Y Csat 1.35mass% Y C0 0.2mass% 3 4 シミュレーション手順 Fig.2 Step Step Fig. 2. Computational flow-chart of the multi-step simulation. 33

34 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 5 4 1373 K 11 Fig.4 130 mm SCr420 28 Fig.4 x-y Fig.

6L/min 1 1223 K 1200 Pa 240 C 2 H 2 EPMA ElectronProbe Micro Analyzer JXA-8200 25 mm Fig.5 5.

Illustration of the industrial reactor for vacuumcarburizing. Fig. 5.

5 34 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No K 11 Fig mm SCr Fig.4 x-y Fig.5 A B 18 mm 50 mm SCr % C 2 H 2 Fig mm 5 x x y y z C 2 H 2 3L/min 0.6L/min K 1200 Pa 240 C 2 H 2 EPMA ElectronProbe Micro Analyzer JXA mm Fig.5 5. シミュレーション条件 Fig. 3. Illustration of the test reactor for vacuum-carburizing. 0.5mm Fig. 4. Illustration of the industrial reactor for vacuumcarburizing. Fig. 5. Illustration of the location of test pieces for EPMA. The circles which are indicated by A and B are the test pieces and the arrow in the test piece indicates EPMA line. 34

35 Step 2 Step 1 Step 3 Fig.6 1 mm 680 3 Fig.6 x-y Fig.6 z Fig.4 1 Step 1 Step 2 Step 3 Fig.5 50 mm y Step 3 in-house Step 1 Step 2 15 Step 3 Step 3 7.8 m 17 28 29 Fig.7 5 5 Fig.

6 35 Step 2 Step 1 Step 3 Fig.6 1 mm Fig.6 x-y Fig.6 z Fig.4 1 Step 1 Step 2 Step 3 Fig.5 50 mm y Step 3 in-house Step 1 Step 2 15 Step 3 Step m Fig Fig.7 C 2 H 浸炭量の時間変化 Fig K 6. 結果および考察 6 1 表面反応モデルの提案 Fig. 7. Comparison of the computational prediction to the experimental data for adsorption rate of carbon as a function of temperature. Fig. 6. Computational domain and grid of the industrial reactor. Note that the view direction is opposite to that in Fig.4 in terms of z direction. Fig. 8. Comparison of the computational prediction to the experimental data for amount of carburized carbon as a function of operating time. 35

36 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 40 6 3 団体処理用試験炉における炭素濃度分布 Fig.9 y x-z C 2 H 2 C 2 H 2 C 2 H 2 C 2 H 2 A B Fig.10 EPMA A B A Fig.9 C 2 H 2 B Fig.

7 36 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No 団体処理用試験炉における炭素濃度分布 Fig.9 y x-z C 2 H 2 C 2 H 2 C 2 H 2 C 2 H 2 A B Fig.10 EPMA A B A Fig.9 C 2 H 2 B Fig.11 A 10 B シミュレーション時間 CPU Xeon X7560 Nehalem/8core/2.27GHz 4 128GB Step 1 24 Step Fig. 10. Comparison of the computational predictions to the experimental data for carbon concentration profiles in the steel. Fig. 9. Distributions of mass fraction of C 2 H 2 (colors), and adsorption rate of carbon on the surface of workpieces (mono color). Additionally, some velocity vectors of the gas are plotted. Fig. 11. Amounts of carburized carbon at positions A and B as a function of operating time. 36

8 Step 結論 C 2 H 2 2 文 1) M.Sugiyama:Netsu Shori (J. Jpn. Soc. Heat Treat.), 37(1997),154. 2) N.Okumura:Netsu Shori (J. Jpn. Soc. Heat Treat.), 49(2009),257. 3) P.Kula, R.Pietrasik and K.Dybowski: J. Mater. Process. Technol., (2005),876. 4) R.U.Khan,S.Bajohr,D.Buchholz,R.Reimert,H.D.Minh,K.Norinaga, V.M.Janardhanan, S.Tischer and O.Deutschmann: J. Anal. Appl. Pyrolysis, 81(2008),148. 5) K.YadaandO.Watanabe:Comput. Fluids, 79(2013),65. 6) T.Kajishima and K.Taira: Computational Fluid Dynamics, Springer InternationalPublishingAG,Switzerland,(2017),56. 7 ) 6 (1999),99. 8) C.R.Wilke:Chem. Eng. Progress, 46(1950),95. 9) R.B.Bird, W.E.Stewart and E.N.Lightfoot: Transport Phenomena, JohnWiley&Sons,NewYork,(1960), ) T.MoritaandT.Hanyuda:Tetsu-to-Hagané, 92(2006), ) T.Morita,K.InoueandT.Hanyuda:Denki Seiko (Electr. Furn. Steel), 77(2006),5. 12) C.Wells,W.BatzandR.F.Mehl:Trans. Am. Inst. Min. Metall. Eng., 188(1950), ) H.Ikehata, K.Tanaka, H.Takamiya and H.Mizuno: Tetsu-to-Hagané, 97(2011), ) K.Tanaka, H.Ikehata, H.Takamiya and H.Mizuno: Tetsu-to-Hagané, 97(2011), ) S.Makino,M.Inagaki,K.Nakashima,T.KozawaandN.Horinouichi:J. Cryst. Growth, 454(2016),156. 献 37

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30 論 文 鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 速度論に基づく真空浸炭炉のマルチステップシミュレーション Multi-step Simulation of Vacuum-carburizing Reactor based on

30 論文鉄と鋼 Tetsu-to-Hagané Vol. 105 (2019) No. 1 速度論に基づく真空浸炭炉のマルチステップシミュレーション Multi-step Simulation of Vacuum-carburizing Reactor based on