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摘要:
针对碳化材料烧蚀性能参数测量难度大的问题，对基于优化算法的烧蚀性能参数辨识方法进行了研究。根据一维连续模型描述碳化烧蚀材料的内部热响应情况，与公开试验数据进行对比验证，各测量点计算误差均小于15%。采用基函数表征法对材料碳化前后的比热容和导热率进行表征，基函数选取为切比雪夫多项式。根据PICA材料的温度测试试验数据，对材料的热解动力学参数和基函数的待定系数采用遗传算法进行辨识，将辨识得到的材料烧蚀性能参数代入一维连续模型中进行计算，与验证工况下的试验数据进行比对，计算得到的温度曲线平均相对误差小于10%。
Abstract:In response to the difficulty in measuring the ablation performance parameters of thermal protection materials, this paper studies the identification method of ablation performance parameters based on optimization algorithms. The one-dimensional continuous model is used to describe the internal thermal response of carbonization ablation thermal protective materials. Compared with the public experimental data, the calculation error of each measurement point is less than 15%. The basis function characterisation approach uses the Chebyshev polynomial as the basis function to characterize the material’s specific heat capacity and thermal conductivity both before and after carbonization. According to the temperature test experimental data of PICA materials in the public literature, the pyrolysis kinetic parameters of the materials and the undetermined coefficients of the basis function are identified by genetic algorithm, and the parameter identification results are substituted into the one-dimensional continuous model for calculation. Compared with the experimental data in the public literature, the average relative error of the temperature curves under the two verification conditions is less than 10%.
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图 4 碳化烧蚀材料沿壁厚方向温度分布
Figure 4. Temperature distribution of carbonized ablation material along wall thickness direction
图 5 不同位置处材料热响应数值仿真与试验结果对比
Figure 5. Comparison between numerical simulation and experimental results of thermal response of materials at different positions
表 1 材料性能及初始条件
Table 1. Material properties and initial conditions
材料性能 数值 ${\rho _{\rm{v}}}$/(kg·m−3) 1 810 ${\rho _{\rm{c}}}$/(kg·m−3) 1440 ${\lambda_{\rm{v}}}$/($ {\text{W}} \cdot {{\text{m}}^{ - 1}} \cdot ^\circ {{\text{C}}^{ - 1}} $) $0.804 + 2.76 \times {10^{ - 4}}T$ ${\lambda_{\rm{c}}}$/($ {\text{W}} \cdot {{\text{m}}^{ - 1}} \cdot ^\circ {{\text{C}}^{ - 1}} $) $ \begin{array}{*{20}{c}} \begin{gathered} 0.955 + 8.42 \times {10^{ - 4}}T - 4.07 \times {10^{ - 6}}{T^2} + 5.32 \times {10^{ - 9}}{T^3} \\ \end{gathered} \end{array} $ $ {C_{\rm{v}}} $/(${\text{kJ}} \cdot {\text{k}}{{\text{g}}^{ - 1}} \cdot ^\circ {{\text{C}}^{ - 1}}$) $ 1.089 + 1.09 \times {10^{ - 3}}T $ ${C_{\rm{c}}}$/(${\text{kJ}} \cdot {\text{k}}{{\text{g}}^{ - 1}} \cdot ^\circ {{\text{C}}^{ - 1}}$) $ 0.87 + 1.02 \times {10^{ - 3}}T $ ${C_{\rm{pg}}}$/(${\text{kJ}} \cdot {\text{k}}{{\text{g}}^{ - 1}} \cdot ^\circ {{\text{C}}^{ - 1}}$) 9.63 $\varepsilon $ 0.9 $\sigma $/(${\text{W}} \cdot {{\text{m}}^{ - 2}} \cdot {{\text{K}}^{ - 4}}$) $5.73 \times {10^{ - 8}}$ ${T_0}$/${\text{K}}$ 300 $E$/(${\text{kJ}}\cdot {\mathrm{kmol}}^{-1}$) $2.60 \times {10^5}$ $A$/${{\text{s}}^{ - 1}}$ $1.98 \times {10^{29}}$(剩余率≥0.91)，$8.16 \times {10^{18}}$(剩余率＜0.91) $m$ 17.33(剩余率≥0.91)，6.3(剩余率≥0.91) 
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表 2 最终时刻不同位置温度对比
Table 2. Temperature comparison of different positions at the final moment
位置/mm 温度/K 相对误差/% 试验值 仿真值 1 1264.8 1295.6 2.44 5 1095.4 1188.4 8.49 10 938.54 1020.6 8.74 29 521.37 594.39 14.00
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表 3 试验条件及编号
Table 3. Experimental conditions and numbers
编号 热流密度/
$\left({\text{W}}\cdot\left( {{{\text{m}}^2} \cdot {\text{s}}} \right)^{-1}\right)$持续
时间/s材料
厚度/cm测量
位置/cm1 5.68×106 11 15.24 1.08 2 5.68×106 11 15.24 1.93 3 1.90×107 17 20.32 3.77 4 9.66×106 22 10.16 2.56
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