Fe-Bi-Mn三元合金多相相变-扩散体系中易切削相析出规律的数值研究

王哲, 王发展, 何银花, 王欣, 马姗, 王辉绵

NUMERICAL STUDY ON FREE-CUTTING PHASE PRECIPITATION BEHAVIOR IN Fe-Bi-Mn TERNARY ALLOY MULTIPHASE TRANSFORMATION- DIFFUSION SYSTEM

WANG Zhe, WANG Fazhan, HE Yinhua, WANG Xin, MA Shan, WANG Huimian

表1 守恒方程与传递速率方程[10,14,16]

Table 1 Conservative equations and transfer rate equations[10,14,16]

Name Equation Number Conservative equation Solid-liquid mass conservative ? ? t ( f s ρ s ) = M l s (1) ? ? t ( f l ρ l ) + ? ? ( f l ρ l u l ) = M s l (2) Liquid-gas mass conservative ? ? t ( f l ρ l ) + ? ? ( f l ρ l u l ) = M g l (3) ? ? t ( f g ρ g ) + ? ? ( f g ρ g u g ) = M l g (4) Solid-liquid momentum conservative ? ? t ( f l ρ l u l ) + ? ? ( f l ρ l u l ? u l ) = - f l ? p + ? ? τ l + f l ρ l g - U l s M - U l s D τ l = u l ( ? ? ( f l μ l ) + ( ? ? ( f l μ l ) ) T ) (5) Liquid-gas momentum conservative ? ? t ( f g ρ g u g ) + ? ? ( f g ρ g u g ? u g ) = - f g ? p + ? ? τ g + f g ρ g g - U g l M - U g l D τ g = u g ( ? ? ( f g μ g ) + ( ? ? ( f g μ g ) ) T ) (6) Solid-liquid species conservative ? ? t ( f s ρ s c s ) = C l s M (7) ? ? t ( f l ρ l c l ) + ? ? ( f l ρ l u l c l ) = C s l M (8) Liquid-gas species conservative ? ? t ( f l ρ l c l ) + ? ? ( f l ρ l u l c l ) = C g l M (9) ? ? t ( f g ρ g c g ) + ? ? ( f g ρ g u g c g ) = C l g M (10) Solid enthalpy conservative ? ? t ( f s ρ s h s ) = ? ? ( f s k s ? T s ) + Q s M + Q l s D h s = ∫ T r e f T s c p s d T + h s r e f (11) Liquid enthalpy conservative ? ? t ( f l ρ l h l ) + ? ? ( f l ρ l u l h l ) = ? ? ( f l k l ? T l ) + Q l M - Q l s D h l = ∫ T r e f T l c p l d T + h l r e f (12) Gas enthalpy conservative ? ? t ( f g ρ g h g ) + ? ? ( f g ρ g u g h g ) = ? ? ( f g k g ? T g ) + Q g M - Q g l D h g = ∫ T r e f T g c p g d T + h g r e f (13) Transfer rate equation Solid-liquid mass transfer rate M l s = v R l ? S l s ? ρ s (14) Liquid-gas mass transfer rate M g l = v R g ? S g l ? ρ l (15) Solid-liquid interface diffusion-phase transformation rate ν R l = d f s d t ? 1 S l s (16) Liquid-gas interface diffusion-phase transformation rate ν R g = d f l d t ? 1 S g l (17)