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气流环境下激光辐照材料是一个复杂的多物理场强耦合物理过程,存在气流换热、热-力耦合等多种物理效应,激光加载的能量、气流流动引起对流换热导致的能量损失以及材料烧蚀导致能量交换将共同决定靶材内部温度的分布,需要建立相应的物理模型[19-21]。对于激光加载和能量耦合过程,鉴于不透明金属材料对激光吸收深度小,通常约10 nm量级,计算中激光加载能量作为面热源处理,在材料区域内,热传导方程的数学描述为:
$ \rho c \frac{\partial T}{\partial t}=\nabla \cdot(\kappa \nabla T)+Q_{\mathrm{r}} $
(1) 式中:ρ为壳材料密度;c为壳材料比热容;T为材料温度;t为时间;$\nabla $为矢量微分算符;κ为材料导热系数;Qr为材料相变和氧化反应热源项。
激光加载区域边界条件为:
$ \left(\kappa \frac{\partial T}{\partial z}\right)+q_{\mathrm{c}}+q_{\mathrm{r}}=q_1 $
(2) 式中:z为靶厚度;qc为对流换热热流;qr为辐射换热热流;ql为材料表面吸收的激光热流。
加载对流边界换热热流可表示为:
$ q_{\mathrm{c}}=h_{\mathrm{c}}\left(T-T_0\right) $
(3) 式中:hc对流换热系数;T0为表面气流温度。
辐射换热热流为:
$ q_{\mathrm{r}}=\sigma \varepsilon\left(T^4-T_0{ }^4\right) $
(4) 式中:σ为Stefan-Boltzmann常数;ε为表面发射率。
假定靶温度1000 K,辐射换热热流功率密度约1 W/cm2量级,相对于对流和加载激光功率密度较小,计算中可忽略。激光辐照下金属表面高温物质脱落,激光束直接辐照下一层材料,使得辐照热效应增强。为了模拟这种熔蚀效应,将受激光辐照的最外层未剥离表面定义为熔迹面。热软化物质剥离采用温度准则判据,即达到某高温状态热软化材料被气流剥离[19, 21]。采用“单元生死法”计算边界的移动和热传导,当某一离散单元的温度超过熔化温度或气化温度,定义该单元不再参与计算,对应加载边界施加到新的单元上,整个过程不可逆。
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通过计算结果与实验结果比较校验计算模型,模型校验用算例参数和数据编号见表 1。表中自然对流下实验结果case 1和case 2参数引自参考文献[16]。自然对流下激光辐照实验靶板温升模拟结果见图 1a,亚声速气流条件下实验的模拟结果见图 1b。图中,R为到靶板中心点距离。模拟计算的case 1和shot 1靶背面不同位置温升与实验结果符合较好,计算结果显示靶板未发生熔穿,靶板升温和辐照结束后自然冷却过程均与实验结果一致;实验测得的case 2和shot 2靶板熔穿时间Δt分别为6.5 s和6.0 s,采用计算铝板靶背面中心点温升获得靶板熔穿时间,模型计算的case 2和shot 2的熔穿时间分别为7.0 s和5.6 s,计算结果与实验结基本一致。通过温升曲线和熔穿时间比较,新建模型可较好地模拟激光辐照靶板的温度和熔穿过程。
表 1 模型校验用算例参数
Table 1. Parameters of simulation case for model verification
number power density/(W·cm-2) irradiation time/s material material dimension/mm flow velocity/(m·s-1) case 1 1190 10 LY12 $ \varnothing$30×2 0 case 2 1190 10 LY12 $ \varnothing$30×1 0 shot 1 800 10 LY12 100×100×3 120 shot 2 1400 10 LY12 100×100×3 120
气流与激光联合作用铝合金板热响应研究
Study on thermal response of aluminum alloy plate subjected to airflow and laser irradiation
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摘要: 为了获得激光加工等应用中气流环境激光辐照材料的热响应特性和熔穿规律,采用面热源近似和不定常热传导分析方法构建了包括热传导、对流换热、熔化烧蚀等主要机制的物理模型,并通过实验校核后进行了气流环境激光辐照铝合金热学响应定量评估,获得气流环境不同激光功率密度下铝合金靶板温升和烧蚀熔穿规律。结果表明,相同靶参数下,熔穿时间随着激光功率密度增加而急剧减小,并且熔穿时间变化规律与热平衡积分方法气化烧蚀模型结果一致;不同条件下熔穿时间显示,在激光功率密度较小(500 W/cm2附近)时,气流引起对流换热因素对激光烧蚀熔穿影响较大,而在激光功率密度较高(1500 W/cm2以上)时,气流引起对流换热因素对激光烧蚀熔穿影响较小。建立的气流条件下激光辐照热响应模型与实际物理过程更接近,计算获得的熔穿规律为激光辐照模型合理简化提供了定量的参考依据。Abstract: In order to obtain the thermal response and melting through characteristics of materials irradiated by high energy laser with airflow environment in field of laser processing and other applications, a physical model considering the mechanisms of heat conduction, convective heat transfer, melting and ablation was constructed by using the approximation of plane heat source and unsteady method. The model was validated by experiments and was used for evaluating quantitatively the thermal responses of material. Then, the temperature rise and penetration law of aluminum alloy plates subjected to different laser power density in airflow were obtained. The results indicate that the melting through time decreases sharply with the increase of laser power density under the same target parameters. And the calculated melting through time is consistent with the results by using the gasification ablation model of thermal balance integration method in the literature. The analysis of perforation time under different conditions shows that the airflow factor has a significant influence on laser ablation melting through when the laser power density is small (approximately around 500 W/cm2). When the laser power density is large (above 1500 W/cm2), the effect of airflow through convective heat transfer is insignificant. In addition, the physical model considered in calculation is close to the actual physical process. Above calculation results and analytical understanding provide a quantitative basis for simplifying reasonably the laser ablation models.
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Key words:
- laser technique /
- laser irradiation /
- airflow /
- thermal response /
- laser ablation
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表 1 模型校验用算例参数
Table 1. Parameters of simulation case for model verification
number power density/(W·cm-2) irradiation time/s material material dimension/mm flow velocity/(m·s-1) case 1 1190 10 LY12 $ \varnothing$30×2 0 case 2 1190 10 LY12 $ \varnothing$30×1 0 shot 1 800 10 LY12 100×100×3 120 shot 2 1400 10 LY12 100×100×3 120 -
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