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焊接技术在国内工业领域具有较好应用和发展前景[1-3]. 激光焊接在激光加工制造中发挥着巨大的作用. 与钨极氩弧焊、熔化极气体保护焊等相比，激光焊接具有能量密度高、热影响区小、焊接速度高等优点[4-5].
在激光焊接过程中，表面张力对熔池流动行为有一定程度的影响. 熔池中不同位置的表面张力的数值不同，这是因为表面张力与温度有直接关系，温度越高表面张力的值越低[6]. 在焊接试验中，添加氧等活性元素可增大熔深[7]. 一些学者基于FLUENT软件研究了表面张力对TIG焊接过程熔池的影响[8-9]，发现氧含量对Marangoni流力的影响较大，进而影响焊缝的熔深和熔宽. 庞盛永[10]对表面张力分别为0.2, 0.6和1.0 N/m时的匙孔、熔池行为进行了研究，发现表面张力较小时匙孔的最大深度和最小深度均最大，匙孔表面受到的表面张力越小，匙孔越不容易闭合. 李俐群等人[11]研究了表面张力作用下的熔池流动行为，发现表面张力温度系数为负值时熔池表面以匙孔为中心由内向外流动，表面张力温度系数为正值时，熔池表面为由外向内流动.
铝合金具有较高的热导率、线膨胀系数以及较低的熔点. 激光焊接铝合金时易产生气孔、咬边等焊接缺陷[12-13].
基于以上分析，文中通过FLUENT19.0软件建立激光焊接热-流耦合模型，研究不同表面张力温度系数(为负值)对激光焊接熔池行为的影响规律.
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通过FLUENT19.0软件对激光自熔焊熔池行为进行数值模拟. 激光焊接模型的控制方程为[14]
连续性控制方程
$$ \frac{\partial \rho}{\partial {t}} + \frac{\partial(\rho u)}{\partial {x}} + \frac{\partial(\rho v)}{\partial {y}} + \frac{\partial(\rho w)}{\partial {\textit{z}}}=0 $$ (1) 动量守恒方程，x方向为
$$ \frac{{\partial \left( {\rho {{u}}} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {{uu}}} \right)}}{{\partial x}} - \frac{{\partial \left( {\rho {{u}}{{{u}}_{{0}}}} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho uv} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho {{uw}}} \right)}}{{\partial {\textit{z}}}} = $$ $$- \frac{{\partial P}}{{\partial x}}+\frac{\partial }{{\partial x}}\left( {\mu \frac{{\partial u}}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {\mu \frac{{\partial u}}{{\partial y}}} \right) + \frac{\partial }{{\partial {\textit{z}}}}\left( {\mu \frac{{\partial u}}{{\partial {\textit{z}}}}} \right) + {S_{\text{u}}} $$ (2) y方向为
$$ \frac{{\partial \left( {\rho {{v}}} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {{vu}}} \right)}}{{\partial x}} - \frac{{\partial \left( {\rho {{v}}{{{u}}_{{0}}}} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho {{vv}}} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho {{vw}}} \right)}}{{\partial {\textit{z}}}} = $$ $$ - \frac{{\partial P}}{{\partial y}} +\frac{\partial }{{\partial x}}\left( {\mu \frac{{\partial v}}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {\mu \frac{{\partial v}}{{\partial y}}} \right) + \frac{\partial }{{\partial {\textit{z}}}}\left( {\mu \frac{{\partial v}}{{\partial {\textit{z}}}}} \right) + {S_{\rm{v}}} $$ (3) z方向为
$$ \frac{{\partial \left( {\rho {{w}}} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho {{wu}}} \right)}}{{\partial x}} - \frac{{\partial \left( {\rho {{w}}{{{u}}_{{0}}}} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho {{wv}}} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho {{ww}}} \right)}}{{\partial {\textit{z}}}} = $$ $$ - \frac{{\partial P}}{{\partial {\textit{z}}}}+\frac{\partial }{{\partial x}}\left( {\mu \frac{{\partial w}}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {\mu \frac{{\partial w}}{{\partial y}}} \right) + \frac{\partial }{{\partial {\textit{z}}}}\left( {\mu \frac{{\partial w}}{{\partial {\textit{z}}}}} \right) + {S_{\text{w}}} $$ (4) 能量守恒方程为
$$ \frac{{\partial \left( {\rho H} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho uH} \right)}}{{\partial x}} - \frac{{\partial \left( {\rho {u_0}H} \right)}}{{\partial x}} + \frac{{\partial \left( {\rho vH} \right)}}{{\partial y}} + \frac{{\partial \left( {\rho wH} \right)}}{{\partial {\textit{z}}}} = $$ $$ \frac{\partial }{{\partial x}}\left( {k\frac{{\partial T}}{{\partial x}}} \right) + \frac{\partial }{{\partial y}}\left( {k\frac{{\partial T}}{{\partial y}}} \right) + \frac{\partial }{{\partial {\textit{z}}}}\left( {k\frac{{\partial T}}{{\partial {\textit{z}}}}} \right) + {S_{\rm{E}}} $$ (5) 式中：u, v, w分别为沿x, y, z方向的速度；P为压力；
$ {u_0} $ 为焊接速度；Su, Sv, Sw分别为动量方程沿x, y, z方向的源项；H0为混合焓；SE为能量方程的源项；$ \rho $ 为母材的密度；$ T $ 为温度；t为焊接时间；$ k $ 为母材导热系数；$ \mu $ 为液态流体的动力粘度.模型计算的工艺参数为：激光功率2 800 W，焊接速度为3.0 m/min. 激光束热源模型公式为
$$ {q_{{\rm{laser}}}} = \frac{{9{\alpha _{{\rm{abs}}}}Q}}{{{\text{π}} R_0^2{H_0}\left( {1 - {e^3}} \right)}}\exp \left[ {\frac{{ - 9\left( {{x^2} + {y^2}} \right)}}{{R_0^2\log \left( {{H_0}/{\textit{z}}} \right)}}} \right] $$ (6) 式中：Q为激光束的能量；αabs为相应的系数；H0为激光热源高度；R0为激光有效半径. 数学模型中添加的反冲压力、表面张力、浮力见文献[15].
为提高计算的精确度，软件中设置的时间步长为1 × 10−5. 焊接工件的材料为6056铝合金，其热物理性能参数如表1所示.
表 1 6056铝合金热物理性能参数
Table 1. Thermophysical property parameters of 6056 aluminum alloy
固相密度
${\rho _{\rm{s}}}$/（kg·m−3）液相密度
${\rho _{\rm{l}}}$/（kg·m−3）固相线温度
${T_{\rm{s}}}$/K液相线温度
${T_{\rm{L}}}$/K气相线温度
${T_{\rm{v}}}$/K熔化潜热
${L_{\rm{m}}}$/（J·kg−1）蒸发潜热
${L_{\rm{v}}}$/（J·kg−1）热膨胀系数
${\beta _{\rm{k}}}$/$ {{\rm{K}}^{ - 1}} $传热系数
${h_{\rm{c}}}$/（${\rm{W} } \cdot { {\rm{K} }^{ - 1} } \cdot { {\rm{m} }^{ - 2} }$）发射率
$ \varepsilon $环境温度
${T_{{\rm{ref}}} }$/K2 700 2 590 860 917 2 740 3.87 × 105 1.08 × 107 1.92 × 105 15 0.08 300 -
为分析表面张力温度系数为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)对熔池流场的影响，分别截取熔池纵截面和熔池横截面，沿匙孔中心截取获得熔池横截面. 熔池纵截面和熔池横截面示意图如图1所示.
图 1 熔池纵截面和横截面截取示意图
Figure 1. Schematic diagram of longitudinal and cross sections of molten pool
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图2 ~ 图4分别为表面张力温度系数为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)的不同时间步熔池纵截面流场. 可以发现，随着表面张力温度系数的减小，熔池后方顺时针流动漩涡的趋势逐渐减弱，甚至消失，这主要是因为随着表面张力温度系数的减小，Marangoni作用力增强造成的. 而且随着表面张力温度系数的减小，焊接飞溅的数量增多. 分析认为，激光入射到焊接工件，激光作用区域的材料熔化、蒸发形成匙孔，在蒸发反冲压力、表面张力、浮力等力的作用下，熔池表面产生凸起. 凸起的液态金属脱离熔池形成飞溅需要满足下式[16]，即
图 2 激光自熔焊纵截面熔池流场(−2.5 × 10−4 N/(m·K))
Figure 2. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −2.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 3 激光自熔焊纵截面熔池流场(−3.5 × 10−4 N/(m·K))
Figure 3. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −3.5 × 10−4N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 4 激光自熔焊纵截面熔池流场(−4.9 × 10−4 N/(m·K))
Figure 4. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −4.9 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
$$ \rho_{{\rm{m}}} v_{{\rm{m}}}^{2}>\frac{2 \delta}{r} $$ (7) 式中：δ为表面张力；r为熔池表面凸起金属的半径；ρm为熔池金属密度；vm为熔池表面凸起金属的流动速度.
当焊接过程处于稳定状态时，匙孔内壁的反冲压力pr与熔池表面凸起金属流动速度为
$$ p_{{\rm{r}}}=\frac{\rho_{{\rm{m}}} v_{{\rm{m}}}^{2}}{2} $$ (8) 由公式(7)和公式(8)可得到
$$ p_{{\rm{r}}}>\frac{\delta}{r} $$ (9) 随着表面张力系数的减小，熔池相同位置的表面张力减小，因此与表面张力温度系数为−2.5 × 10−4, −3.5 × 10−4 N/(m·K)相比，表面张力温度系数为−4.9 × 10−4 N/(m·K)的熔池更容易产生焊接飞溅(图4).
图2 ~ 图4的熔池表面均出现了由匙孔开口向熔池边缘流动的趋势，这主要是Marangoni作用力引起的. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)时，匙孔底部出现了闭合，产生了焊接气泡(图2c)，而当表面张力温度系数为−3.5 × 10−4, −4.9 × 10−4 N/(m·K)时，匙孔底部未产生焊接气泡.
对表面张力温度系数分别为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)的不同时间步熔池长度进行统计，如图5所示(图中虚线为熔池长度的平均值). 由图可知，随着表面张力温度系数的减小，熔池长度逐渐增加. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池长度平均值为3.28 mm；当表面张力温度系数为−3.5 × 10−4 N/(m·K)，熔池长度平均值为3.73 mm；当表面张力温度系数为−4.9 × 10−4 N/(m·K)，熔池长度平均值为4.14 mm.
图 5 不同时间步的熔池长度尺寸
Figure 5. Length of molten pool at different time steps
对表面张力温度系数分别为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)的不同时间步熔池流体最大流动速度进行统计，如图6所示(图中虚线为熔池流体最大流动速度的平均值). 由图可知，随着表面张力温度系数的减小，熔池流体最大流动速度逐渐增大. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池流体最大流动速度的平均值为2.89 m/s；当表面张力温度系数为−3.5 × 10−4N/(m·K)，熔池流体最大流动速度的平均值为3.53 m/s；当表面张力温度系数为−4.9 × 10−4N/(m·K)，熔池流体最大流动速度的平均值为4.09 m/s.
图 6 不同时间步的熔池流体最大流动速度
Figure 6. Maximum flow velocity of melt in molten pool at different time steps
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图7 ~ 图9分别为表面张力温度系数为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)的不同时间步熔池横截面流场(左侧为熔池流场方向，右侧为熔池流线). 可以发现，随着表面张力温度系数的减小，由熔池边缘指向匙孔的流动趋势变强，这主要是由于表面张力温度系数的变小，Marangoni作用力增强造成的.
图 7 激光自熔焊纵截面熔池流场(−2.5 × 10−4 N/(m·K))
Figure 7. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −2.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 8 激光自熔焊纵截面熔池流场(−3.5 × 10−4 N/(m·K))
Figure 8. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −3.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 9 激光自熔焊纵截面熔池流场(−4.9 × 10−4 N/(m·K))
Figure 9. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −4.9 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
对表面张力温度系数分别为−2.5 × 10−4, −3.5 × 10−4, −4.9 × 10−4 N/(m·K)的不同时间步熔池横截面面积进行统计，如图10所示(图中虚线为熔池面积的平均值). 由图可知，随着表面张力温度系数的减小，熔池横截面的面积逐渐减小. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池面积的平均值为4.52 mm2；当表面张力温度系数为−3.5 × 10−4 N/(m·K)，熔池面积的平均值为4.03 mm2；当表面张力温度系数为−4.9 × 10−4 N/(m·K)，熔池面积的平均值为3.28 mm2.
图 10 不同时间步的熔池面积尺寸
Figure 10. Area of molten pool at different time steps
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为验证数值模拟模型的正确性，采用型号为
$ {\text{camrecord 5000}} \times {\text{2}} $ 的高速摄像机对激光焊接过程进行实时监测，并采用辅助光源对熔池区域进行照亮. 试验参数与数值模拟参数相同(表面张力温度系数为−3.5 × 10−4 N/(m·K))，图11为高速摄像机拍摄的熔池图像与数值模拟熔池图像的对比验证. 通过对比发现，高速摄像机拍摄的熔池图像与数值模拟熔池图像的轮廓基本一致.
图 11 试验熔池图像与数值模拟熔池图像
Figure 11. Weld pool images obtained by experiment and numerical simulation
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(1) 随着表面张力温度系数的减小，熔池后方顺时针流动漩涡的趋势逐渐减弱，甚至消失. 而且随着表面张力温度系数的减小，焊接飞溅的数量增多.
(2) 随着表面张力温度系数的变小，纵截面熔池长度逐渐增加. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池长度平均值为3.28 mm；当表面张力温度系数为−3.5 × 10−4 N/(m·K)，熔池长度平均值为3.73 mm；当表面张力温度系数为−4.9 × 10−4 N/(m·K)，熔池长度平均值为4.14 mm.
(3) 随着表面张力温度系数的减小，纵截面熔池流体最大流动速度逐渐增大. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池流体最大流动速度的平均值为2.89 m/s；当表面张力温度系数为−3.5 × 10−4 N/(m·K)，熔池流体最大流动速度的平均值为3.53 m/s；当表面张力温度系数为−4.9 × 10−4 N/(m·K)，熔池流体最大流动速度的平均值为4.09 m/s.
(4) 随着表面张力温度系数的减小，熔池横截面的面积逐渐减小. 当表面张力温度系数为−2.5 × 10−4 N/(m·K)，熔池面积的平均值为4.52 mm2；当表面张力温度系数为−3.5 × 10−4N/(m·K)，熔池面积的平均值为4.03 mm2；当表面张力温度系数为−4.9 × 10−4 N/(m·K)，熔池面积的平均值为3.28 mm2.
Effect of surface tension on molten pool and keyhole during laser welding
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摘要: 基于FLUENT19.0软件，建立了激光焊接热-流耦合模型，对比分析了不同表面张力温度系数(为负值)对熔池流场的影响. 结果表明，随着表面张力温度系数的减小，熔池后方顺时针漩涡的流动趋势逐渐减弱，甚至消失，而且焊接飞溅的数量增多. 纵截面熔池长度逐渐增加，纵截面熔池流体最大流动速度逐渐增大，熔池横截面的面积逐渐减小.当表面张力温度系数为−2.5 × 10−4 N/(m·K)时，熔池长度平均值为3.28 mm、熔池流体最大流动速度的平均值为2.89 m/s、熔池横截面面积的平均值为4.52 mm2；当表面张力温度系数为−3.5 × 10−4 N/(m·K)时，熔池长度平均值为3.73 mm、熔池流体最大流动速度的平均值为3.53 m/s、熔池横截面面积的平均值为4.03 mm2；当表面张力温度系数为−4.9 × 10−4 N/(m·K)时，熔池长度平均值为4.14 mm、熔池流体最大流动速度的平均值为4.09 m/s、熔池横截面面积的平均值为3.28 mm2.Abstract: Based on fluent 19.0 software, the heat flow coupling model of laser welding was established, and the effects of different surface tension temperature coefficients (negative values) on the flow field of molten pool were compared and analyzed. The results showed that with the decrease of surface tension temperature coefficient, the trend of clockwise flow vortex behind the molten pool gradually weakened or even disappeared, and the amount of welding spatter increased. With the decrease of surface tension temperature coefficient, the length of longitudinal section molten pool gradually increased, the maximum flow velocity of longitudinal section molten pool gradually increased, and the cross-sectional area of molten pool gradually decreased. When the temperature coefficient of surface tension was -2.5 × 10-4 N/(m·K), the average length of molten pool was 3.28 mm, the average maximum flow velocity of molten pool fluid was 2.89 m/s, and the average cross-sectional area of molten pool was 4.52 mm2. When the temperature coefficient of surface tension was -3.5 × 10-4 N/(m·K), the average length of molten pool was 3.73 mm, the average maximum flow velocity of molten pool fluid was 3.53 m/s, and the average cross-sectional area of molten pool was 4.03 mm2. When the temperature coefficient of surface tension was -4.9 × 10-4 N/(m·K), the average length of molten pool was 4.14 mm, the average maximum flow velocity of molten pool fluid was 4.09 m/s, and the average cross-sectional area of molten pool was 3.28 mm2.
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Key words:
- laser welding /
- surface tension /
- molten pool /
- keyhole
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图 1 熔池纵截面和横截面截取示意图
Figure 1. Schematic diagram of longitudinal and cross sections of molten pool
图 2 激光自熔焊纵截面熔池流场(−2.5 × 10−4 N/(m·K))
Figure 2. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −2.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 3 激光自熔焊纵截面熔池流场(−3.5 × 10−4 N/(m·K))
Figure 3. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −3.5 × 10−4N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 4 激光自熔焊纵截面熔池流场(−4.9 × 10−4 N/(m·K))
Figure 4. Flow field of longitudinal section molten pool in autogenous laser welding: surface tension temperature coefficient was −4.9 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 6 不同时间步的熔池流体最大流动速度
Figure 6. Maximum flow velocity of melt in molten pool at different time steps
图 7 激光自熔焊纵截面熔池流场(−2.5 × 10−4 N/(m·K))
Figure 7. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −2.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 8 激光自熔焊纵截面熔池流场(−3.5 × 10−4 N/(m·K))
Figure 8. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −3.5 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 9 激光自熔焊纵截面熔池流场(−4.9 × 10−4 N/(m·K))
Figure 9. The longitudinal section flow field of the molten pool in autogenous laser welding: surface tension temperature coefficient was −4.9 × 10−4 N/(m·K). (a) step 2100; (b) step 2300; (c) step 2600; (d) step 2900
图 11 试验熔池图像与数值模拟熔池图像
Figure 11. Weld pool images obtained by experiment and numerical simulation
表 1 6056铝合金热物理性能参数
Table 1. Thermophysical property parameters of 6056 aluminum alloy
固相密度 ${\rho _{\rm{s}}}$ /（kg·m−3）液相密度 ${\rho _{\rm{l}}}$ /（kg·m−3）固相线温度 ${T_{\rm{s}}}$ /K液相线温度 ${T_{\rm{L}}}$ /K气相线温度 ${T_{\rm{v}}}$ /K熔化潜热 ${L_{\rm{m}}}$ /（J·kg−1）蒸发潜热 ${L_{\rm{v}}}$ /（J·kg−1）热膨胀系数 ${\beta _{\rm{k}}}$ /$ {{\rm{K}}^{ - 1}} $ 传热系数 ${h_{\rm{c}}}$ /（${\rm{W} } \cdot { {\rm{K} }^{ - 1} } \cdot { {\rm{m} }^{ - 2} }$ ）发射率
$ \varepsilon $ 环境温度 ${T_{{\rm{ref}}} }$ /K2 700 2 590 860 917 2 740 3.87 × 105 1.08 × 107 1.92 × 105 15 0.08 300 
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