非定常气动载荷场融合建模方法探索及验证

丁轩鹤; 粟华; 龚春林; 王子一; 杨予成

doi:10.13224/j.cnki.jasp.20230416

非定常气动载荷场融合建模方法探索及验证

doi: 10.13224/j.cnki.jasp.20230416

丁轩鹤^1,,
粟华^{1, 2},
龚春林^{1, 2,*, ,},
王子一¹,
杨予成¹

1.
西北工业大学航天学院，西安 710072
2.
西北工业大学航天学院陕西省空天飞行器设计重点实验室，西安 710072

基金项目: 基础科研计划（JCKY2020204B016）

详细信息

作者简介:
丁轩鹤（1998-），男，博士生，主要从事飞行器总体设计研究

通讯作者:
龚春林（1980-），男，教授，博士，主要从事飞行器总体设计研究。E-mail：leonwood@nwpu.edu.cn

中图分类号: V211.3
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- 被引次数: 0
出版历程
- 收稿日期: 2023-06-25
- 网络出版日期: 2025-06-19

Exploration and verification of unsteady aerodynamic load field fusion modeling method

DING Xuanhe^1
,,
SU Hua^{1, 2},
GONG Chunlin^{1, 2,*
, ,},
WANG Ziyi¹,
YANG Yucheng¹

1.
School of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China
2.
Shannxi Aerospace Flight Vehicle Design Key Laboratory，School of Astronautics，Northwestern Polytechnical University，Xi’an 710072，China

摘要

摘要:
飞行器虚拟飞行试验涉及气动、结构等众多高精度学科模型的多物理场仿真，准确快速的非定常气动载荷场计算是其关键制约因素。目前基于计算流体力学的非定常气动力计算成本十分昂贵，为了提升高精度非定常气动载荷场的计算效率并保证计算精度，基于Co-Kriging模型和POD场量降阶，提出一种基于多源数据融合的高效非定常气动载荷场预测方法。以4%厚度圆弧翼为测试对象，通过综合当地活塞理论计算得到的低精度载荷数据和计算流体动力学得到的高精度仿真数据构建非定常气动载荷场，分析了不同飞行工况下非定常气动载荷和颤振边界，结果表明：提出的基于数据融合的非定常气动载荷场预测方法，在内插时表面载荷预测精度不低于99.41%，在外插时表面载荷预测精度不低于83.32%，颤振分析结果误差不超过0.637%，计算效率提升了285.89倍。
- 数据融合 /
- Co-Kriging模型 /
- 降阶模型 /
- 虚拟飞行试验 /
- 非定常气动力 /
- 颤振
Abstract:
The virtual flight test of aircraft involves multi-physical field simulation of many high-precision discipline models such as aerodynamics and structure. Accurate and fast unsteady aerodynamic load field calculation is the key constraint. At present, the calculation cost of unsteady aerodynamics based on computational fluid dynamics is very expensive. In order to improve the calculation efficiency of high-precision unsteady aerodynamic load field and ensure the calculation accuracy, an efficient unsteady aerodynamic load field prediction method based on multi-source data fusion with Co-Kriging model and POD field reduction was proposed. Taking the 4% thickness arc wing as the test object, the unsteady aerodynamic load field was constructed by integrating the low-precision load data calculated by the local flow piston theory and the high-precision simulation data obtained by computational fluid dynamics. The unsteady aerodynamic load and flutter boundary under different flight conditions were analyzed. The results showed that the proposed unsteady aerodynamic load field prediction method based on data fusion had a surface load prediction accuracy of no less than 99.41% in case of interpolation, a surface load prediction accuracy of no less than 83.32% in case of extrapolation, and a flutter analysis result error of no more than 0.637%. The computational efficiency was improved by 285.89 times.
- data fusion /
- Co-Kriging model /
- reduced order model /
- virtual flight test /
- unsteady aerodynamic /
- flutter

HTML

图 1 融合模型建模流程图

Figure 1. Fusion model modeling flow chart

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图 2 4%厚度圆弧翼数值仿真的计算网格

Figure 2. Calculation grid for numerical simulation of 4% thickness circular arc wing

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图 3 高低精度数据前6阶模态

Figure 3. First 6th order modal coefficients for high and low precision data

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图 4 $ t=0.037\;\mathrm{s} $时翼型表面压力分布和计算误差

Figure 4. Airfoil surface pressure distribution and calculation error at t = 0.037 s

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图 5 $ t=0.178\;\mathrm{s} $时翼型表面压力分布和计算误差

Figure 5. Airfoil surface pressure distribution and calculation error at t = 0.178 s

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图 6 升力系数随时间变化情况和计算误差

Figure 6. Variation of lift coefficient with time and calculation error

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图 7 阻力系数随时间变化情况和计算误差

Figure 7. Variation of drag coefficient with time and calculation error

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图 8 不同初始攻角下升力系数误差

Figure 8. Lift coefficient error at different initial angles of attack

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图 9 不同初始攻角下阻力系数误差

Figure 9. Drag coefficient error at different initial angles of attack

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图 10 不同攻角变化率下升力系数误差

Figure 10. Lift coefficient error at different attack change rate

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图 11 不同攻角变化率下阻力系数误差

Figure 11. Drag coefficient error at different attack change rate

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图 12 $ t=0.041\;\mathrm{s} $时翼型表面压力分布

Figure 12. Airfoil surface pressure distribution at t=0.041 s

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图 13 平动条件下升阻力系数随时间变化情况

Figure 13. Time variation of lift drag coefficient under translational conditions

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图 14 平动条件下升阻力系数计算误差

Figure 14. Calculation error of lift drag coefficient under translational conditions

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图 15 平动条件下升阻力系数随时间变化情况

Figure 15. Time variation of lift drag coefficient under translational conditions

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图 16 平动条件下升阻力系数计算误差

Figure 16. Calculation error of lift drag coefficient under translational conditions

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图 17 $ Ma=4 $，$ {\alpha }_{0}={5}^{\circ } $，$ {V}_{{\mathrm{f}}}^{\mathrm{*}}\approx 1.28 $时3种非定常气动力求解方法下的时域仿真

Figure 17. Time domain simulation of three non-constant aerodynamic solution methods for $Ma = 4$, ${\alpha _0} = {5{\text{°}} }$,$V_{\text{f}}^* \approx 1.28$

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表 1 不同阶数高低精度数据重构误差

Table 1. Reconstruction error of high and low precision data of different orders

阶数	重构类型	方均根误差	最大相对误差/%
前5阶	高精度数据	46.7551	1.08
前5阶	低精度数据	67.5477	2.14
前6阶	高精度数据	11.0356	0.56
前6阶	低精度数据	61.4382	2.08
前10阶	高精度数据	11.0093	0.31
前10阶	低精度数据	54.5775	2.08

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表 2 预测模型和当地活塞理论升阻力系数预测误差

Table 2. Prediction model and local piston theory lift drag coefficient prediction error

模型	升力系数预测误差/10⁻⁸	阻力系数预测误差/10⁻¹⁰
融合模型	1.2064	2.1893
当地活塞理论	82.906	4.0217

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表 3 平动条件下融合模型内插和当地活塞理论升阻力系数预测误差

Table 3. Prediction model internal interpolation and local piston theory lift drag coefficient prediction error under translational conditions

模型	升力系数预测误差/10⁻⁴	阻力系数预测误差/10⁻⁵
融合模型	3.7999	4.8674
当地活塞理论	24.012	33.112

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表 4 平动条件下融合模型外插和当地活塞理论升阻力系数预测误差

Table 4. Prediction model extrapolation interpolation and local piston theory lift drag coefficient prediction error under translational conditions

模型	升力系数预测误差/10⁻⁴	阻力系数预测误差/10⁻⁵
融合模型	3.4583	5.5291
当地活塞理论	7.9865	11.478

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参考文献(25)

[1]	LIU Mengnan, FANG Shuiliang, DONG Huiyue, et al. Review of digital twin about concepts, technologies, and industrial applications[J]. Journal of Manufacturing Systems, 2021, 58: 346-361. doi: 10.1016/j.jmsy.2020.06.017
[2]	MAGILL J C, CATALDI P, MORENCY J R, et al. Demonstration of a wire suspension for wind-tunnel virtual flight testing[J]. Journal of Spacecraft and Rockets, 2009, 46(3): 624-633. doi: 10.2514/1.39188
[3]	黄宇, 阎超, 席柯, 等. 基于数值虚拟飞行技术的飞行器动态特性分析[J]. 航空学报, 2016, 37(8): 2525-2538. HUANG Yu, YAN Chao, XI Ke, et al. Analysis of flying vehicle’s dynamic characteristics based on numerical virtual flight technology[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(8): 2525-2538. (in Chinese HUANG Yu, YAN Chao, XI Ke, et al. Analysis of flying vehicle’s dynamic characteristics based on numerical virtual flight technology[J]. Acta Aeronautica et Astronautica Sinica, 2016, 37(8): 2525-2538. (in Chinese)
[4]	季卫栋, 王江峰, 樊孝峰, 等. 高超声速流场与结构温度场一体化计算方法[J]. 航空动力学报, 2016, 31(1): 153-160. JI Weidong, WANG Jiangfeng, FAN Xiaofeng, et al. Algorithms for hypersonic fluid-structural-thermal integrated[J]. Journal of Aerospace Power, 2016, 31(1): 153-160. (in Chinese JI Weidong, WANG Jiangfeng, FAN Xiaofeng, et al. Algorithms for hypersonic fluid-structural-thermal integrated[J]. Journal of Aerospace Power, 2016, 31(1): 153-160. (in Chinese)
[5]	衣春轮, 刘燕斌, 曹瑞, 等. 基于代理模型的高超声速飞行器外形参数优化[J]. 航空动力学报, 2019, 34(11): 2354-2365. YI Chunlun, LIU Yanbin, CAO Rui, et al. Shape parameters optimization of hypersonic vehicle based on surrogate model[J]. Journal of Aerospace Power, 2019, 34(11): 2354-2365. (in Chinese YI Chunlun, LIU Yanbin, CAO Rui, et al. Shape parameters optimization of hypersonic vehicle based on surrogate model[J]. Journal of Aerospace Power, 2019, 34(11): 2354-2365. (in Chinese)
[6]	王子一, 粟华, 龚春林, 等. 数字孪生机翼损伤模式快速识别与监测方法[J]. 航空动力学报, 2024, 39(6): 20220395. WANG Ziyi, SU Hua, GONG Chunlin, et al. Rapid identification and monitoring of digital twin wings damage patterns[J]. Journal of Aerospace Power, 2024, 39(6): 20220395. (in Chinese WANG Ziyi, SU Hua, GONG Chunlin, et al. Rapid identification and monitoring of digital twin wings damage patterns[J]. Journal of Aerospace Power, 2024, 39(6): 20220395. (in Chinese)
[7]	张文杰, 王国新, 朱悉铭, 等. 基于数字孪生的航天电推进器优化设计方法[J]. 宇航学报, 2022, 43(4): 518-527. ZHANG Wenjie, WANG Guoxin, ZHU Ximing, et al. Digital twin-based optimization design method for aerospace electric thruster[J]. Journal of Astronautics, 2022, 43(4): 518-527. (in Chinese ZHANG Wenjie, WANG Guoxin, ZHU Ximing, et al. Digital twin-based optimization design method for aerospace electric thruster[J]. Journal of Astronautics, 2022, 43(4): 518-527. (in Chinese)
[8]	ASHLEY H, ZARTARIAN G. Piston theory-a new aerodynamic tool for the aeroelastician[J]. Journal of the Aeronautical Sciences, 1956, 23(12): 1109-1118. doi: 10.2514/8.3740
[9]	黄礼耀, 陈奎林, 卢叔全. 跨声速偶极子网格法的改进和在颤振计算中的应用[J]. 空气动力学学报, 1998, 16(3): 379-385. HUANG Liyao, CHEN Kuilin, LU Shuquan. The improvement of transonic doublet lattice method and the application to flutter calculation[J]. Acta Aerodynamica Sinica, 1998, 16(3): 379-385. (in Chinese HUANG Liyao, CHEN Kuilin, LU Shuquan. The improvement of transonic doublet lattice method and the application to flutter calculation[J]. Acta Aerodynamica Sinica, 1998, 16(3): 379-385. (in Chinese)
[10]	YAN Cheng, YIN Zeyong, SHEN Xiuli, et al. Surrogate-based optimization with improved support vector regression for non-circular vent hole on aero-engine turbine disk[J]. Aerospace Science and Technology, 2020, 96: 105332. doi: 10.1016/j.ast.2019.105332
[11]	LIU Haitao, ONG Y S, CAI Jianfei, et al. Cope with diverse data structures in multi-fidelity modeling: a Gaussian process method[J]. Engineering Applications of Artificial Intelligence, 2018, 67: 211-225. doi: 10.1016/j.engappai.2017.10.008
[12]	QIU Zhan, WANG Fuxin. On aeroelastic response of an airfoil under dynamic stall using time delay neural network[J]. Aerospace Systems, 2018, 1(2): 87-97. doi: 10.1007/s42401-018-0010-3
[13]	CHANG K J, HAFTKA R T, GILES G L, et al. Sensitivity-based scaling for approximating structural response[J]. Journal of Aircraft, 1993, 30(2): 283-288. doi: 10.2514/3.48278
[14]	CHOI S, ALONSO J J, KROO I M, et al. Multifidelity design optimization of low-boom supersonic jets[J]. Journal of Aircraft, 2008, 45(1): 106-118. doi: 10.2514/1.28948
[15]	LEIFSSON L, KOZIEL S, JONSSON E. Wing aerodynamic shape optimization by space mapping[J]. Advances in Intelligent Systems and Computing, 2014, 256: 319-332.
[16]	BANDLER J W, BIERNACKI R M, CHEN Shaohua, et al. Space mapping technique for electromagnetic optimization[J]. IEEE Transactions on Microwave Theory and Techniques, 1994, 42(12): 2536-2544. doi: 10.1109/22.339794
[17]	BANDLER J W, ISMAIL M A, RAYAS-SANCHEZ J E, et al. Neuromodeling of microwave circuits exploiting space-mapping technology[J]. IEEE Transactions on Microwave Theory and Techniques, 1999, 47(12): 2417-2427. doi: 10.1109/22.808989
[18]	JIA Z G, WANG R Q, HU D Y, et al. Application of fluid-solid couple on multidisciplinary optimization design for turbine blade[J]. Acta Aeronautica et Astronautica Sinica, 2013, 1(12): 106-117.
[19]	KENNEDY M. Predicting the output from a complex computer code when fast approximations are available[J]. Biometrika, 2000, 87(1): 1-13. doi: 10.1093/biomet/87.1.1
[20]	FORRESTER A I J, SÓBESTER A, KEANE A J. Multi-fidelity optimization via surrogate modelling[J]. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2007, 463(2088): 3251-3269. doi: 10.1098/rspa.2007.1900
[21]	HAN Zhonghua, ZIMMERMANN, GÖRTZ S. Alternative cokriging method for variable-fidelity surrogate modeling[J]. AIAA Journal, 2012, 50(5): 1205-1210. doi: 10.2514/1.J051243
[22]	HAN Zhonghua, GÖRTZ S. Hierarchical Kriging model for variable-fidelity surrogate modeling[J]. AIAA Journal, 2012, 50(9): 1885-1896. doi: 10.2514/1.J051354
[23]	HAN Zhonghua, XU Chenzhou, ZHANG Liang, et al. Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids[J]. Chinese Journal of Aeronautics, 2020, 33(1): 31-47. doi: 10.1016/j.cja.2019.05.001
[24]	FEENY B F, KAPPAGANTU R. On the physical interpretation of proper orthogonal modes in vibrations[J]. Journal of Sound and Vibration, 1998, 211(4): 607-616. doi: 10.1006/jsvi.1997.1386
[25]	张伟伟, 叶正寅. 基于当地流活塞理论的气动弹性计算方法研究[J]. 力学学报, 2005, 37(5): 632-639. ZHANG Weiwei, YE Zhengyin. Numerical method of aeroelasticity based on local piston theory[J]. Acta Mechanica Sinica, 2005, 37(5): 632-639. (in Chinese ZHANG Weiwei, YE Zhengyin. Numerical method of aeroelasticity based on local piston theory[J]. Acta Mechanica Sinica, 2005, 37(5): 632-639. (in Chinese)