POD-BPNN prediction on the three-dimensional complex flow field of hypersonic waverider forebody/inlet
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摘要:
针对乘波前体-进气道三维构型，构建了基于本征正交分解（proper orthogonal decomposition, POD）和反向传播神经网络（back propagation neural network，BPNN）的流场快速预测模型，并对不同马赫数、攻角和反压下高超声速三维流场结构进行了快速预测研究。研究发现，快速预测模型能够准确预测样本空间内非样本工况的流场信息，对称面马赫数分布的预测误差小于0.5%、压力分布的预测误差小于3.8%、温度分布的预测误差小于1.1%。乘波体周围三维流场、壁面压力分布及主要性能参数的预测结果与CFD（computational fluid dynamics）计算结果高度一致。预测模型对样本空间外工况具备一定预测能力。流场数值模拟采用定常计算，而隔离段内激波串结构受到分离涡影响，具备非定常特性，预测模型在隔离段激波串区域存在较大的预测误差。
Abstract:A fast prediction model for the flow field was constructed based on proper orthogonal decomposition (POD) and back propagation neural network (BPNN) for a three-dimensional integrated waverider forebody-inlet. Moreover, the hypersonic three-dimensional flow fields were predicted under different Mach number, angle of attack and back pressure. The research showed that the prediction model can accurately predict the flow field of non-sample conditions in the sampling space. The errors of fast prediction model for the Mach number, pressure, and temperature were less than 0.5%, 3.8% and 1.1%, respectively. The predictive results of the flow field for the waverider forebody, pressure distribution and the main performance parameters were highly consistent with the CFD (computational fluid dynamics) results. The prediction model had certain prediction ability for the external working conditions of the sampling space. However, the flow field numerical simulation adopted steady calculation, while the shock string structure in the isolator was affected by the separated vortex and had unsteady characteristics, indicating a large prediction error in the shock string area of the isolator.
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图 5 验证算例模型网格及边界条件
Figure 5. Simulation domain grids and boundary conditions of validation example
图 8 压缩面沿程壁面压力分布对比图
Figure 8. Comparison of pressure distribution along the wall of the compression surface
图 13 在x= −300 mm截面马赫数分布对比图
Figure 13. Comparison of Mach number distribution atx= −300 mm
图 15 在x=328 mm截面马赫数分布对比图
Figure 15. Comparison of Mach number distribution at x=328 mm
图 16 乘波前体上壁面压力分布对比图
Figure 16. Comparison of pressure distributions on the upper surface of waverider forebody
图 17 进气道上壁面压力分布对比图
Figure 17. Comparison of pressure distributions on the upper surface of inlet
图 18 对称面马赫数分布对比图
Figure 18. Comparison of Mach number distribution on the plane of symmetry
图 19 对称面静压分布对比图
Figure 19. Comparison of static pressure distribution on the plane of symmetry
图 20 对称面静温分布对比图
Figure 20. Comparison of static temperature distribution on the plane of symmetry
图 22 隔离段沿流向纵向切面马赫数分布对比图
Figure 22. Comparison of Mach number distribution at sections of the isolation section along the flow direction
图 23 对称面马赫数分布对比图（样本空间外）
Figure 23. Comparison of Mach number distribution on the plane of symmetry （Outside the sample space）
表 1 设计点来流工况
Table 1. Flow conditions of design point
H0/km Ma p0/Pa T0/K ρ0/（kg/m3） 25 6 2549.2 221.6 0.04008 
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表 2 不同数量网格气动参数表
Table 2. Aerodynamic parameters of different grids
参数 网格数量/106 4.2 5.3 6.0 L/D 1.77 1.79 1.79 σth 0.641 0.676 0.675
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表 4 计算工况
Table 4. Computational conditions
序号 Ma A/（°） pb/p0 1 4.003 5.25 37.77 2 4.033 0.43 47.95 3 4.038 4.35 39.05 4 4.088 −3.39 40.70 5 4.118 −1.44 43.18 6 4.120 1.94 39.23 7 4.125 −2.49 45.93 8 4.135 −0.48 49.60 9 4.168 1.12 42.54 10 4.198 2.99 45.66 11 4.226 1.69 50.15 12 4.228 3.94 48.96 13 4.296 −1.42 51.80 14 4.323 −3.87 50.43 15 4.341 4.69 55.01 16 4.356 −2.94 49.05 17 4.383 −0.58 55.66 18 4.463 −2.64 57.86 19 4.473 5.51 55.93 20 4.476 2.01 54.65 21 4.536 4.71 62.54 22 4.568 −1.81 60.33 23 4.586 −3.91 62.81 24 4.613 2.73 57.40 25 4.621 −2.93 65.56 26 4.633 0.50 61.80 27 4.708 5.84 61.07 28 4.721 1.85 64.56 29 4.726 5.26 69.60 30 4.754 4.00 72.72 31 4.799 1.34 74.46 32 4.804 −2.09 65.20 33 4.834 −0.18 66.48 34 4.849 2.61 73.73 35 4.866 −1.17 67.77 36 4.894 5.01 78.22 37 4.966 −0.39 75.75 38 4.986 −1.32 76.39 39 4.994 −2.54 77.40 40 5.009 1.82 81.07 41 5.016 5.89 80.33 42 5.054 4.14 79.88 43 5.116 1.12 75.20 44 5.164 2.58 84.28 45 5.171 −1.27 83.73 46 5.176 0.22 77.40 47 5.209 −3.45 78.41 48 5.256 −2.39 87.22 49 5.271 −0.51 88.32 50 5.304 0.83 85.47 51 5.306 5.85 86.30 52 5.316 3.38 84.01 53 5.352 −3.04 94.65 54 5.364 4.43 94.92 55 5.367 2.43 92.35 56 5.394 −1.59 91.44 57 5.454 −0.82 97.49 58 5.472 5.07 88.59 59 5.489 3.31 95.20 60 5.492 2.33 101.80 61 5.502 0.12 90.33 62 5.509 −2.40 99.69 63 5.512 1.38 102.45 64 5.517 5.49 97.58 65 5.579 4.02 101.07 66 5.589 −3.59 95.11 67 5.597 1.79 93.82 68 5.617 0.52 98.41 69 5.639 −1.58 98.96 70 5.642 −3.13 104.37 71 5.654 5.03 106.02 72 5.699 −0.54 101.62 73 5.727 −2.07 109.51 74 5.732 1.09 108.13 75 5.742 2.09 105.84 76 5.754 −3.88 108.68 77 5.759 5.89 103.45 78 5.837 3.03 110.43 79 5.844 3.76 103.73 80 5.869 5.36 113.00 81 5.874 1.41 116.39 82 5.882 −1.03 107.40 83 5.899 4.33 111.80 84 5.912 0.39 112.63 85 5.914 3.59 119.23 86 5.927 −3.04 107.86 87 5.980 −0.52 116.02 88 5.997 −1.68 114.10
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表 5 对称面流场预测误差
Table 5. Flow field prediction error on the plane of symmetr
% 参数 工况 1 2 3 Ma 0.27 0.36 0.47 p/p0 3.11 2.46 3.71 T/T0 0.84 0.57 1.03
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表 6 主要性能参数预测结果
Table 6. Predicted results of main performance parameters
工况 $\dot m$/（kg/s） $ L/D $ $ {\sigma _{{\text{th}}}} $ CFD BPNN er/% CFD BPNN er/% CFD BPNN er/% 1 0.2793 0.2794 0.03 1.5715 1.5599 0.74 0.7629 0.7625 0.05 2 0.4730 0.4747 0.37 2.7272 2.7211 0.22 0.7015 0.7041 0.37 3 0.6525 0.6519 0.09 2.1671 2.1781 0.51 0.6631 0.6620 0.15
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