Aerodynamic pressure field reconstruction from sparse points using data assimilation method
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摘要: 风洞实验中获取模型高精度压力分布至关重要，但现有测量方法仍然存在一些缺陷。为获得风洞模型的全域压力分布，本文通过集合变换卡尔曼滤波（ETKF）对风洞实验的稀疏实测数据和数值计算数据进行同化，实现了基于模型物面有限测点的全空间流场高精度重构。分别使用二维翼型RAE 2822和NACA 0012进行实验验证，RAE 2822的压力稀疏重构结果比线性理论修正更加接近实测结果，此效果在激波位置体现得尤其明显，压力系数的预测误差降低了约3%，使用ETKF修正后的迎角及马赫数集合均值计算得到的机翼升力系数和力矩系数与实验值的误差均小于1%；NACA 0012实验面向风洞测量的全场感知应用，探讨了基于少量测点进行压力重构的可行性。实验结果表明：采用机翼物面6个测点重构的压力系数，相对误差可达2.42%，且同化效果与数据点位置密切相关。Abstract: In wind tunnel experiments, the high-precision pressure distribution of models is highly required, but existing measurement methods still have certain shortcomings. In order to obtain the global pressure distribution of the wind tunnel model, this paper assimilated the sparse measured data and numerical calculation data of the wind tunnel experiment by Ensemble Transform Kalman Filter (ETKF), and realized the high-precision reconstruction of the full-space flow field based on the finite measurement points of the model surface. Two-dimensional airfoil RAE 2822 and NACA 0012 were used for experimental verification. Sparse reconstruction of pressure results of RAE 2822 is more consistent with the measured results than the linear theory correction. This effect is especially evident at the shock wave position, and the prediction error of the pressure coefficient is reduced by about 3%. The lift coefficient and moment coefficient of the wing calculated by using the modified ETKF set mean of attack angle and Mach number are less than 1% error from the experimental values. Experiment of NACA 0012 is oriented to the full-field sensing application of wind tunnel experiments and explore the feasibility of pressure reconstruction based on a small number of measurement points. The experimental results show that the relative error of pressure coefficients reconstructed using six measurement points on the wing object surface can be reduced to 2.42%, and the comparison results show that the assimilation effect is highly dependent on the data point locations.
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图 3 集合成员迎角在ETKF同化前后的分布
Figure 3. Distribution of ensemble angel of attack before and after ETKF assimilation
图 4 集合成员马赫数在ETKF前后的分布
Figure 4. Distribution of ensemble Mach number before and after ETKF assimilation
图 5 集合的迎角及马赫数均值随迭代过程的变化
Figure 5. Mean of angle of attack and Mach number changes with iterations
图 7 ETKF同化后的压力系数曲线与线性理论修正曲线对比
Figure 7. Comparison of the pressure coefficient curve after assimilation of ETKF with the linear theory correction
图 11 NACA 0012的ETKF同化结果与实验值的对比
Figure 11. Comparison of ETKF assimilation results with experimental values in NACA 0012
表 1 RAE 2822 网格质量及节点数量
Table 1. Quality and node number of RAE 2822 mesh
单元质量最小值 网格节点数量 第一层网格高度/m 值 0.9441 77429 4.2 × 10−6 
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表 2 ETKF前后集合成员迎角、马赫数的均值及方差
Table 2. Mean and variance of ensemble angle of attack and Mach number before and after ETKF
迎角 马赫数 初始均值 2.310° 0.729 ETKF后均值 2.434° 0.7328 初始方差 3.192 × 10−2 2.770 × 10−4 ETKF后方差 1.039 × 10−3 2.770 × 10−7
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表 3 RAE 2822 case 6边界条件
Table 3. Boundary condition of RAE 2822 case 6
迎角/(°) 马赫数 雷诺数 原始条件 2.92 0.725 6.5 × 106 线性理论 2.31 0.729 6.5 × 106 ETKF 2.43 0.733 6.5 × 106
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表 4 ETKF同化和线性理论修正后CL和Cm、激波位置Cp平均相对误差与实验值的对比
Table 4. Comparison of CL, Cm and Cp average relative error near the shock wave position between ETKF, linear theory and experiment
Cp平均相对误差 CL CL误差 Cm Cm误差 实验值 — 0.7430 — −0.0950 — ETKF 5.741% 0.7379 0.67% −0.0941 0.95% 线性理论 8.881% 0.7120 4.17% −0.0918 3.37%
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表 5 NACA0012 网格质量及节点数量
Table 5. Quality and node number of NACA 0012 mesh
最小单元 节点数量 第一层网格高度/m 值 0.8818 32050 1.0 × 10−5
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表 6 4组实验的压力测点序号及迭代次数
Table 6. The number of pressure measuring points and iteration times of 4 groups of experiments
使用的压力测点序号 迭代次数 同化实验1 1，2，3，4，5，6 3 同化实验2 7，8，9，10，11，12 3 同化实验3 1，5，9，13，17，21 3 同化实验4 1～44（所有测点） 4
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表 7 4组实验ETKF后的迎角、马赫数及压力系数平均相对误差
Table 7. Angle of attack, Mach number and pressure coefficient average relative error after ETKF in 4 groups of experiments
迎角/(°) 马赫数 压力系数平均相对误差 同化实验1 3.3932 0.3884 2.42% 同化实验2 3.7286 0.3937 5.74% 同化实验3 3.5340 0.3928 3.77% 同化实验4 3.4159 0.3131 1.05% 未同化实验 4.0208 0.4022 8.72%
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[1] TEDUKA N, KAMEDA M, ASAI K, et al. Adsorptive pressure-sensitive coatings for unsteady flow measurements[J]. Transactions of the Japan Society of Mechanical Engineers, Series B, 2002, 68(669): 1391–1399. doi: 10.1299/kikaib.68.1391 [2] 李峰, 王洪博. 风洞分布测压试验校准技术发展现状[J]. 计测技术, 2020, 40(1): 1–7. doi: 10.11823/j.issn.1674-5795.2020.01.01LI F, WANG H B. Overview of calibration technology for wind tunnel distribution pressure test[J]. Metrology & Measurement Technology, 2020, 40(1): 1–7. doi: 10.11823/j.issn.1674-5795.2020.01.01 [3] XIONG W N, ZHU C, GUO D L, et al. Bio-inspired, intelligent flexible sensing skin for multifunctional flying perception[J]. Nano Energy, 2021, 90: 106550. doi: 10.1016/j.nanoen.2021.106550 [4] 郭栋梁, 侯超, 朱臣, 等. 飞行器表面气动载荷的柔性智能蒙皮多参量测量[J]. 实验流体力学, 2022, 36(2): 146–154. doi: 10.11729/syltlx20210115GUO D L, HOU C, ZHU C, et al. Multi-parameter measurement of aerodynamic load via flexible sensing skin[J]. Journal of Experiments in Fluid Mechanics, 2022, 36(2): 146–154. doi: 10.11729/syltlx20210115 [5] VAMSI KRISHNA C, WANG M Y, HEMATI M S, et al. Reconstructing the time evolution of wall-bounded turbulent flows from non-time-resolved PIV measurements[J]. Physical Review Fluids, 2020, 5(5): 054604. doi: 10.1103/physrevfluids.5.054604 [6] CALLAHAM J L, MAEDA K, BRUNTON S L. Robust flow reconstruction from limited measurements via sparse representation[J]. Physical Review Fluids, 2019, 4(10): 103907. doi: 10.1103/physrevfluids.4.103907 [7] SUN L, WANG J X. Physics-constrained Bayesian neural network for fluid flow reconstruction with sparse and noisy data[J]. Theoretical and Applied Mechanics Letters, 2020, 10(3): 161–169. doi: 10.1016/j.taml.2020.01.031 [8] 李静, 张伟伟. 基于Gappy POD的流场数据填补方法[J]. 气体物理, 2020, 5(4): 1–10. doi: 10.19527/j.cnki.2096-1642.0791LI J, ZHANG W W. Gappy proper orthogonal decomposition for flow data reconstruction[J]. Physics of Gases, 2020, 5(4): 1–10. doi: 10.19527/j.cnki.2096-1642.0791 [9] 周铸, 黄江涛, 黄勇, 等. CFD技术在航空工程领域的应用、挑战与发展[J]. 航空学报, 2017, 38(3): 020891. doi: 10.7527/S1000-6893.2016.0311ZHOU Z, HUANG J T, HUANG Y, et al. CFD technology in aeronautic engineering field: applications, challenges and development[J]. Acta Aeronautica et Astronautica Sinica, 2017, 38(3): 020891. doi: 10.7527/S1000-6893.2016.0311 [10] GARNER H C, ROGERS E W, ACUM W E, et al. Subsonic wind tunnel wall corrections[R]. AD0657092, 1966. [11] CARRASSI A, BOCQUET M, BERTINO L, et al. Data assimilation in the geosciences: an overview of methods, issues, and perspectives[J]. WIREs Climate Change, 2018, 9(5): e535. doi: 10.1002/wcc.535 [12] CHANDRAMOULI P, MEMIN E, HEITZ D. 4D large scale variational data assimilation of a turbulent flow with a dynamics error model[J]. Journal of Computational Physics, 2020, 412: 109446. doi: 10.1016/j.jcp.2020.109446 [13] BELLIGOLI Z, DWIGHT R, EITELBERG G. Assessment of a data assimilation technique for wind tunnel wall interference corrections[C]//Proc of the AIAA Scitech 2019 Forum. 2019: 0939. doi: 10.2514/6.2019-0939 [14] LI Q, LI R Y, JI K F, et al. Kalman filter and its application[C]//Proc of the 2015 8th International Conference on Intelligent Networks and Intelligent Systems (ICINIS). 2016: 74-77. doi: 10.1109/ICINIS.2015.35 [15] NERGER L, JANJIĆ T, SCHRÖTER J, et al. A unification of ensemble square root Kalman filters[J]. Monthly Weather Review, 2012, 140(7): 2335–2345. doi: 10.1175/mwr-d-11-00102.1 [16] BISHOP C H, ETHERTON B J, MAJUMDAR S J. Adaptive sampling with the ensemble transform Kalman filter. Part I: theoretical aspects[J]. Monthly Weather Review, 2001, 129(3): 420–436. doi:10.1175/1520-0493(2001)129<0420:aswtet>2.0.co;2 [17] LE PROVOST M, ELDREDGE J D. Ensemble Kalman filter for vortex models of disturbed aerodynamic flows[J]. Physical Review Fluids, 2021, 6(5): 050506. doi: 10.1103/physrevfluids.6.050506 [18] KATO H, YOSHIZAWA A, UENO G, et al. A data assimilation methodology for reconstructing turbulent flows around aircraft[J]. Journal of Computational Physics, 2015, 283: 559–581. doi: 10.1016/j.jcp.2014.12.013 [19] LI T X, HE C X, WEN X, et al. Data assimilation of rotor flow at hovering state using ensemble Kalman filter[J]. Journal of Visualization, 2023: 1–25. doi: 10.1007/s12650-022-00906-y [20] MCKAY M D, BECKMAN R J, CONOVER W J. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code[J]. Technometrics, 2000, 42(1): 55–61. doi: 10.1080/00401706.2000.10485979 [21] HAASE W, BRADSMA F, ELSHOLZ E, et al. EUROVAL-An European initiative on validation of CFD codes[M]. Wiesbaden: Springer Fachmedien Wiesbaden, 1993, 42: 123-184. doi: 10.1007/978-3-663-14131-0. [22] COOK P H, MCDONALD M A, FIRMIN M C P. Aerofoil RAE 2822: pressure distributions, and boundary layer and wake measurements[C]//Proc of the AGARD Report AR. 1979. [23] LADSON C L, HILL A S, JOHNSON W G. Pressure distributions from high Reynolds number transonic tests of an NACA 0012 airfoil in the Langley 0.3-meter transonic cryogenic tunnel[R]. NASA-TM-100526, 1987. -
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