Numerical simulation and measurement of two-dimensional thermal diffusion length under continuous heat loading
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摘要: 热扩散系数是大能量、高功率激光系统中光学元件的重要参数，关系到元件的抗激光损伤性能，但现有热扩散系数测量方法在多维热传导情况下的测量结果误差较大，且热扩散长度是热扩散系数测量的基础，因此采用有限元法仿真了热源连续加热下的二维热传导并总结了热扩散长度与热扩散系数及加热时间之间的关系规律，据此提出了热源连续加热下测量二维热扩散长度的模型与方法。首先采用有限元分析建立模型仿真了一维热传导情况下的热扩散长度与热扩散系数的关系式并与数值解析表达式比较，二者符合较好，验证了使用连续热源与热扩散长度求解热扩散系数的可行性；之后扩展到二维热扩散情况，并讨论了热损失、样品厚度和热源加载时间对结果的影响；最后给出了实际测量方案，并给出提升测量精度措施。该工作为方便准确地测量材料或元件的热扩散长度提供思路，对制备高功率、大能量激光系统元件具有重要意义。Abstract: Thermal diffusion coefficient is an important parameter of optical components in high-energy and high-power laser systems, and it is related to the laser damage resistance of components. However, the measurement error of the existing thermal diffusion coefficient measurement methods is large under the condition of multi-dimensional thermal conduction. As thermal diffusion length is the basis of thermal diffusion coefficient measurement, our study used the finite element method to simulate the two-dimensional heat conduction under continuous heating of heat source, and summarized the relationship between thermal diffusion length, thermal diffusion coefficient and heating time. On this basis, it proposed a model and method for measuring two-dimensional thermal diffusion length under continuous heating of heat source. Firstly, finite element analysis was used to establish a model to simulate the relationship between thermal diffusion length and thermal diffusion coefficient in one-dimensional heat conduction, and the two models were compared with numerical analytical expressions. The feasibility of using continuous heat source and thermal diffusion length to solve the thermal diffusion coefficient was verified. The effects of heat loss, sample thickness and heat source loading time on the results were discussed. Finally, the practical measurement scheme and measures to improve the measurement accuracy were put forward. This study provides a way to measure the thermal diffusion length of materials or components conveniently and accurately, and is of great significance for fabrication of high power and high energy laser system components.
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图 1 一维热绝缘仿真模型示意图
Figure 1. Schematic of the 1D thermal diffusion model under the continuous heat source
图 2 加载时间为10 s、热扩散系数为80 mm2/s时，无热损失的温度分布和表面温度场分布，以及不同热扩散系数下相应的LC和相对偏差δ1D
Figure 2. Loading time is 10 s, temperature distribution without heat loss and surface temperature field distribution when TDC is 80 mm2/s, and corresponding LC and corresponding relative deviation δ1D under different TDCs
图 3 考虑表面对流传热的一维热扩散模型示意图和热扩散系数为80 mm2/s、加载时间10 s时，不同厚度下温升沿x方向变化曲线
Figure 3. Schematic diagram of 1D thermal diffusion model considering surface convective heat transfer and when the TDC is 80 mm2/s and the loading time is 10 s, the temperature rise along the x direction under different thicknesses
图 4 当h=10 W/(m2·K)时，不同热源加载时间下一维热扩散模型的相对偏差结果
Figure 4. Relative deviation results of the 1D thermal diffusion model under different heat source loading times when h = 10 W/(m2·K)
图 5 半径为100 μm的连续热源作用下二维热扩散模型示意图
Figure 5. Schematic of the 2D thermal diffusion model under the continuous heat source with a radius of 100 μm
图 6 连续热源半径为100 μm、热扩散系数为100 mm2/s、加载时间为20 s时，绝热条件下的表面温度分布和图(a)所示虚线框区域的等温线图，以及温度从热源边缘沿径向上升和LC-2D随加载时间的变化
Figure 6. With a continuous heat source of radius 100 μm, TDC of 100 mm2/s, and loading time of 20 s, surface temperature distribution under thermal insulation, isotherm plots of the dashed box area in Fig.(a) and temperature rise along the radial direction from the edge of the heat source and variation of LC-2D with loading time
图 7 热扩散系数为100 mm2/s时，LC-2D与热源加载时间的拟合结果和A和α的拟合结果
Figure 7. Fitting result of LC-2D and heat source loading time when the TDC is 100 mm2/s, and coefficients A and α
图 8 不同热源加载时间下二维热扩散模型模拟的相对偏差结果
Figure 8. Relative deviation results of the 2D thermal diffusion model simulation under different heat source loading times
图 9 当h=10 W/(m2 K)时，半径为100 μm的连续热源的二维热扩散模型示意图和当热扩散系数为100 mm2/s，加载时间为20 s时，不同厚度下热源边缘沿径向的温升
Figure 9. Schematic of the 2D thermal diffusion model with a continuous heat source of a radius of 100 μm when h=10 W/(m2·K), and temperature rise along the radial direction from the edge of the heat source under different thicknesses when the TDC is 100 mm2/s and loading time is 20 s
图 10 当h=10 W/(m2·K)时，不同热源加载时间下二维热扩散模型的相对偏差结果
Figure 10. Relative deviation results of the 2D thermal diffusion model under different heat source loading times when h=10 W/(m2·K)
表 1 一维热扩散仿真参数
Table 1. 1D thermal diffusion model simulation parameters
model length/mm model thickness/mm heat source power
density/(W·cm−2)thermal diffusion
coefficient/(mm2·s−1)heat source loading
time/s500 0.5 200 1～200 0～10 
下载: 导出CSV
表 2 热扩散系数在 1～200 mm2/s内的拟合参数A和B
Table 2. Fitting results of A and B when the TDC ranges from 1～200 mm2/s
TDC/(mm2·s−1) A B 1 0.49 0.34 9 1.04 0.33 20 1.36 0.32 40 1.72 0.32 60 1.97 0.32 80 2.15 0.32 100 2.32 0.32 120 2.46 0.32 140 2.59 0.32 160 2.70 0.32 180 2.81 0.32 200 2.90 0.32
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