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脉冲激光辐照作用使得空间碎片产生能量吸收现象,在不同功率密度下,碎片表面出现熔化和气化,最后产生高速喷射的等离子体。当作用在空间碎片上的激光功率密度大于108 W/cm2时,空间碎片表面受热升温、熔化、气化,最终等离子体化形成辐照反喷羽流[14]。图 1为空间碎片在不同激光功率下的状态变化示意图。
从激光辐照空间碎片开始,空间碎片受热升温并未发生相变时,这一阶段可称为热传导阶段,这一阶段的初始条件为[15]:
$ T(t, z)=T_{\mathrm{a}}, (t=0) $
(1) 式中,Ta为环境温度, t为时间, z为空间。
边界条件为:
$ T(t, z)=T_{\mathrm{a}}, (z \rightarrow \infty) $
(2) $ -\left.\kappa \frac{\partial T(t, z)}{\partial z}\right|_{z=0}=\rho_s v_s\left(\Delta H+h_s+v_s{ }^2 / 2\right) $
(3) 式中,κ为热传导系数; ρsvs为空间碎片表面(z=0)处的质量流, ρs为碎片密度, vs为碎片表面蒸气粒子的速率; ΔH为气化焓;hs为空间碎片表面蒸气的质量焓;vs2/2为空间碎片表面蒸气的质量动能。
当激光功率达到一定的阈值后,开始发生气化进而等离子体化,其初始条件为:
$ \left\{\begin{array}{l} T(t, z)=T_{\mathrm{a}} \\ p=p_{\mathrm{a}} \\ n_{\mathrm{v}}=0 \\ v=0 \end{array}\right. $
(4) 式中,T为温度,p为压力,pa为初始环境压力, nv为蒸气数密度, v为初始速率。
在蒸气压力高于环境压力并发生非饱和气化的情况下,蒸气粒子在辐照表面的动态平衡将被打乱。离开的粒子数多于返回的,粒子间在多个平均自由程中互相撞击,然后再逐步趋于平衡,形成宏观状态均匀的蒸气流。所以在这个过程中辐照表面周围存在着极细的介质密度不连续区域,即蒸气粒子由动态不平衡到平衡的过渡带,称为克努森层[16]。其一端是凝聚态表面相界面,另一端为蒸气宏观流动起始边界(x=0)。该区域的功能与流体力学上间断面相似,阐述了激光气化过程中介质由凝聚态到气态剧烈变化过程。这个区的外部气化介质的流动可按连续介质处理。图 2为克努森层示意图,k为起始边界,s为空间碎片外表面。
由参考文献[17]可知,环境气体存在反压条件时,激光气化可使蒸气产生定常流动情况的初始边界条件:
$ \frac{T_k}{T_s}=\left[\sqrt{1+\pi\left(\frac{\gamma-1}{\gamma+1} \frac{m}{2}\right)^2}-\sqrt{\pi} \frac{\gamma-1}{\gamma+1} \frac{m}{2}\right]^2 $
(5) $ \begin{gathered} \frac{\rho_k}{\rho_s}=\sqrt{\frac{T_s}{T_k}}\left[\left(m^2+\frac{1}{2}\right) \exp \left(m^2\right) \operatorname{erfc}(m)-\frac{m}{\sqrt{\pi}}\right]+ \\ \frac{1}{2} \frac{T_s}{T_k}\left[1-\sqrt{\pi} \exp \left(m^2\right) \operatorname{erfc}(m)\right] \end{gathered} $
(6) $ \beta=\left[\left(2 m^2+1\right)-m \sqrt{\frac{\pi T_s}{T_k}}\right] \exp \left(m^2\right) \frac{\rho_s}{\rho_k} \sqrt{\frac{T_s}{T_k}} $
(7) $ m=v_k / \sqrt{2 R T_k} $
(8) 式中,Ts为碎片表面的温度;ρs为碎片表面的密度;Tk为羽流初始边界的温度;ρk为羽流初始边界的密度;γ为比热比;erfc(·)为余误差函数;β为相界面蒸气粒子数凝聚比;m为克努森层的质量;vk为羽流初始边界的速度;R为气体常数。
空间碎片主要由铝/铝合金构成,占比约为44%。空间碎片的几何形状有板状、块状、杆状、薄片状,但绝大部分为不规则形状[18]。下面选取薄片状的圆形铝合金碎片作为研究对象,分析纳秒脉冲激光辐照铝靶碎片过程中的动态响应特性。图 3为铝靶碎片在真空环境受激光辐照的示意图。
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对上述空间碎片模型需要进行材料参数设定。实验的铝靶碎片是人造卫星等人造飞行器的运载火箭碰撞的产物, 表 1中给出了该材料的基本物理参数。
表 1 铝靶碎片材料的基本物理参数
Table 1. Basic physical parameters of aluminium target debris
parameter name parameter values R/mm 20 density/(kg·m-3) 2700 heat capacity at constant pressure/(J·kg-1·K-1) 900 heat conductivity coefficient/(W·m-1·K-1) 0.2 elasticity modulus/Pa 7×1010 Poisson’s ratio 0.33 thermal expansion coefficient/K-1 2.3×105 完成材料设置后,需要对模型进行网格划分,由于本次实验会在微秒级时间内有千米级速度的变化,对网格划分有极高的要求。在2维模型中,三角形网格相比四边形网格能够更容易对研究对象进行拟合,有较高的适应性[19]。用有限元软件COMSOL可以很好地模拟激光辐照材料的实验[20]。脉冲激光与铝靶碎片相互作用,空间碎片表面产生的一系列剧变反应会在极短时间内完成,产生的等离子体以极高的速度脱离碎片表面, 这需要精细的网格模型才能更真实地描述脉冲激光与铝靶碎片之间的相互作用规律。本文作者在等离子体运动区域采用三角形网格,把网格的最大单元尺寸限制在1.2 mm内,最小的单元尺寸为0.1 mm,总共划分了26300个三角形单元和1024个四边形过渡单元。表 2中给出了网格划分参数。
表 2 网格划分参数
Table 2. Mesh division parameters
parameter name parameter values maximum unit size/m 0.0012 minimum unit size/m 0.0001 triangular units 26300 quadrilateral units 1024 side units 464 vertex units 8 相对于等离子体羽流的变化程度,铝靶碎片的变形可忽略不计。因此,采用较大尺寸的三角形网格对空间碎片模型进行划分,只需对边界进行四边形网格过渡化处理, 即可在不影响反应规律的情况下提高计算效率。图 4为脉冲激光辐照铝靶碎片的网格划分示意图。
纳秒脉冲激光辐照铝靶碎片动态响应的仿真研究
Numerical simulation of dynamic response for aluminum target debris irradiated by nanosecond pulse laser
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摘要: 为了研究纳秒脉冲激光与铝靶碎片的相互作用规律, 建立了纳秒脉冲激光辐照铝靶碎片的动态响应仿真模型, 采用COMSOL软件分析了不同作用时间和不同入射激光功率下的等离子体反喷羽流动力学特性, 得到了不同激光参数变化对脉冲激光辐照铝靶碎片产生等离子体反喷羽流的演化规律。结果表明, 相同脉冲激光功率作用下等离子体羽流反喷速度随作用时间的增加而增大; 相同脉冲激光时间作用下, 随着激光功率增加, 等离子体反喷羽流的最大速度也不断增大; 由于受等离子体屏蔽效应的影响, 反喷羽流速度在25 μs附近达到最大, 在700 kW时最大速率为1.87×104 m/s, 此时等离子体反喷羽流扩散半径增加了17 mm。该研究为纳秒脉冲激光辐照铝靶空间碎片降轨移除工程化应用提供了理论参考。Abstract: To study the interaction pattern of nanosecond pulse laser with aluminium debris, a dynamic response model of nanosecond pulse laser irradiation on aluminum debris was established, the dynamic characteristics of plasma expansion plumes under different action times and incident laser powers was investigated by COMSOL software, and the evolution rules of plasma expansion plumes generated by nanosecond pulse laser irradiating the debris were obtained with different laser parameters. The results show that the expansion velocity of plasma plumes increases with the increase of action times based on the same pulse laser power. At the same time, the maximum velocity of plasma expansion plumes increases with the increase of laser powers based on the same pulse laser time. According to the given conditions of this article, the maximum velocity of expansion plumes reached the maximum around 25 μs, and the maximum velocity at 700 kW is 1.87×104 m/s owing to the plasma shielding effect. At the moment, the diffusion radius of the plasma expansion plumes increases by 17 mm. The study provides a theoretical reference for the engineering application of nanosecond pulse laser irradiation of aluminium space debris de-orbiting removal.
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Key words:
- laser technique /
- plasma plume /
- numerical simulation /
- expansion velocity /
- space debris
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表 1 铝靶碎片材料的基本物理参数
Table 1. Basic physical parameters of aluminium target debris
parameter name parameter values R/mm 20 density/(kg·m-3) 2700 heat capacity at constant pressure/(J·kg-1·K-1) 900 heat conductivity coefficient/(W·m-1·K-1) 0.2 elasticity modulus/Pa 7×1010 Poisson’s ratio 0.33 thermal expansion coefficient/K-1 2.3×105 表 2 网格划分参数
Table 2. Mesh division parameters
parameter name parameter values maximum unit size/m 0.0012 minimum unit size/m 0.0001 triangular units 26300 quadrilateral units 1024 side units 464 vertex units 8 -
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