图 1  增材制造中的液体熔池凝固

Fig. 1.  Solidification of the molten pool during additive manufacturing.

图 2  不同流速下, 逆临界形态数$ {\cal{M}}_{\mathrm{c}}^{ - 1} $随泰勒数$ {T_{\mathrm{a}}} $的变化曲线, 所用参数取值为$ \beta = 1 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 1 $, $ \varGamma $ = 0.02

Fig. 2.  Function of inverse critical morphological number $ {\cal{M}}_{\mathrm{c}}^{ - 1} $ with Taylor number $ {T_{\mathrm{a}}} $ under different flow velocities, with the parameter values set to $ \beta = 1 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 1 $ and $ \varGamma $ = 0.02.

图 3  不同泰勒数$ {T_{\mathrm{a}}} $下, 逆临界形态数$ {\cal{M}}_{\mathrm{c}}^{ - 1} $随$ {v^{ - 1}} $变化的函数关系, 所用参数取值为$ \beta = 1 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 1 $, $ \varGamma $ = 0.06

Fig. 3.  Functional relationship of the inverse critical morphological number $ {\cal{M}}_{\mathrm{c}}^{ - 1} $ with $ {v^{ - 1}} $ under different Taylor numbers $ {T_{\mathrm{a}}} $, with the parameter values set to $ \beta = 1 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 1 $ and $ \varGamma $ = 0.06.

图 4  不同泰勒数$ {T_{\mathrm{a}}} $下, 逆临界形态数$ {\cal{M}}_{\mathrm{c}}^{ - 1} $随表面能$ \varGamma $变化的函数关系, 所用参数取值为$ v = 100 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 0.5 $, $ \beta $ = 0.01

Fig. 4.  Functional relationship of the inverse critical morphological number $ {\cal{M}}_{\mathrm{c}}^{ - 1} $ with surface energy $ \varGamma $ under different Taylor numbers $ {T_{\mathrm{a}}} $, with the parameter values set to $ v = 100 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}} = 0.5 $ and $ \beta $ = 0.01.

图 5  平面$ (\alpha {\cal{V}}, {{\cal{M}}^{ - 1}}{\cal{V}}) $上的中性稳定性曲线, 所用参数取值为$ {a_2} = 0 $, $ \beta/v = 0.01 $, $ {k_{\mathrm{E}}} = 0.5 $, $ {\cal{R}}$ = 1

Fig. 5.  Neutral stability curve on plane $ (\alpha {\cal{V}}, {{\cal{M}}^{ - 1}}{\cal{V}}) $, with the parameter values set to $ {a_2} = 0 $, $ \beta/v = 0.01 $, $ {k_{\mathrm{E}}} = 0.5 $ and $ {\cal{R}}$ = 1.

图 6  当泰勒数$ {T_{\mathrm{a}}} = 10 $时, 不同流速$ {\cal{V}} $下的中性稳定性曲线, 所用参数取值为$ {a_2} = 0 $, $ \beta = 0.01 $, $ {k_{\mathrm{E}}} = 0.5 $, $ \varGamma = $$ 0.001 $, $ {\cal{R}}$ = 1

Fig. 6.  Neutral stability curves under different flow velocities $ {\cal{V}} $ at a Taylor number of $ {T_{\mathrm{a}}} = 10 $ with the parameter values set to $ {a_2} = 0 $, $ \beta = 0.01 $, $ {k_{\mathrm{E}}} = 0.5 $, $ \varGamma = 0.001 $ and $ {\cal{R}}$ = 1.

图 7  当泰勒数$ {T_{\mathrm{a}}} = 10 $时, 熔池内瞬时扰动浓度场与速度场分布图, 所用参数取值为$ {a_1} = 1.6 $, $ {a_2} = 0 $, $ {\cal{R}}$ = 1. 图中彩色背景表示扰动浓度场, 白色箭头表示扰动速度矢量场

Fig. 7.  Instantaneous distributions of the perturbation concentration field and velocity field in the melt pool at a Taylor number of $ {T_{\mathrm{a}}} = 10 $, with parameter values set to $ {a_1} = 1.6 $, $ {a_2} = 0 $ and $ {\cal{R}} = 1 $. The colored background represents the perturbation concentration field, while the white arrows indicate the perturbation velocity vector field.