RESEARCH ON THE FLUTTER CHARACTERISTCIS OF AGARD445.6 SOLID WING CONSIDERING THE INITIAL ANGLE OF ATTACK BASED ON REDUCED ORDER MODEL
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摘要: 以AGARD445.6硬机翼为研究对象，发展了基于计算流体力学与模态叠加的并行流固耦合方法，计算该机翼在不同初始迎角、不同来流速度的气动弹性时域响应，结果表明：初始迎角小于7°时，该机翼颤振速度随着初始迎角增加而降低；初始迎角7°~10°，颤振速度随着迎角增大而增加。在10°迎角条件建立了基于径向基神经网络的非定常气动降阶模型，准确预测不同速度、减缩频率的非定常气动力，并使用时域龙格库塔法和频域VG法预测10°迎角的颤振特性；建立考虑初始迎角输入的非定常气动降阶模型，预测机翼不同初始迎角的颤振特性。基于降阶模型的初始迎角对颤振边界影响的机理分析表明：小迎角时，随着迎角的增加广义力系数幅值比增加，导致颤振速度的下降；迎角大于7°后展向涡改变了机翼表面压强分布，导致一扭广义力系数幅值比降低，从而增加该机翼颤振速度。Abstract: The AGARD445.6 solid wing is considered as the object of this study. The fluid-structure interaction method based on CFD and modal superposition is developed, and the aeroelastic responses at various angles of attack and velocities are calculated. Results indicate that with the increase of initial angle of attack, the flutter velocity decreases when the angle of attack is under 7°, and the flutter velocity increases when the angle of attack is between 7° and 10°. Then, at 10° angle of attack, the unsteady aerodynamic reduced order model based on radial basis function neural network is developed to predict the unsteady aerodynamic forces at different velocities and reduced frequencies. The flutter characteristics at 10° angle of attack are predicted using the time domain Runge-Kutta method and the frequency domain VG method. Then the unsteady aerodynamic reduced order model considering the input of initial angle is established to predict the flutter characteristics at different angles of attack. The analysis on the effect of initial angle on the flutter boundary shows that, at small angle, the increase of the generalized force coefficient amplitude ratio with the increase of the angle leads to the decrease of flutter velocity. When the initial angle is greater than 7°, the flow separation region expands, which changes the pressure distribution on the wing surface, leading to the decrease of the generalized force coefficient amplitude ratio of torsional mode, and hence results in the increase of flutter velocity.
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图 3 不同截面压强系数分布CFD与试验对比
Figure 3. Pressure coefficient at various sections by CFD and experiment
图 5 迎角10°90%展长处压强系数分布对比
Figure 5. The comparison result of pressure coefficient at 90% span and angle of 10°
图 6 0°迎角不同来流条件广义位移响应
Figure 6. Time responses of wing tip displacement at various velocities (angle of 0°)
图 7 计算状态点和颤振特性标准差误差棒
Figure 7. Calculation conditions and standard error bar of flutter boundary and frequency ratio
图 8 10°迎角不同来流条件广义位移时域响应
Figure 8. Aeroelastic responses at different reduced velocities (angle of 10°)
图 11 训练集、测试集包含的减缩频率、速度信息
Figure 11. Ranges of reduced frequencies and reduced velocities of training data set and test data set
图 14 V*=0.428，不同减缩频率k的AIC分量
Figure 14. AIC components at V*=0.428 and various reduced frequencies
图 15 k=0.4，不同速度V*的AIC分量
Figure 15. AIC components at k=0.4 and various reduced velocities
图 21 k=0.4，V*=0.443，不同迎角α的AIC分量
Figure 21. AIC components at k=0.4, V*=0.443 and various angles of attack
图 22 不同迎角ROM3颤振预测与流固耦合结果对比
Figure 22. Flutter prediction by ROM3 and CFD at various angles of attack
图 23 k=0.4，V*=0.443，不同迎角α下的广义力系数fij与广义位移dj的幅值比和相位差
Figure 23. Amplitude ratio and phase between general force coefficient and general displacement at k=0.4, V*=0.443 and various angles of attack by ROM3
图 24 机翼上表面压强云图和流线图
Figure 24. Pressure contour and streamline of the upper surface of the wing
图 25 不同迎角展向90%截面的δCp弦向分布
Figure 25. δCp distribution at 90% span section for different angles
图 27 通过式(14)积分得到90%展长截面的广义力系数
Figure 27. Generalized force coefficients at 90% span section is obtained by integrating equation (14)
表 1 迎角10°法向力系数Cn对比
Table 1. The comparison result of normal force coefficient Cn at angle of 10°
网格量 最大y+ 法向力系数Cn 误差/(%) 1.38×106 25 0.2320 0.3 2.34×106 6 0.2313 − 
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表 2 AGARD445.6软机翼前两阶模态频率
Table 2. Mode frequency of AGARD445.6 weakened wing
模态 一阶模态 二阶模态 频率/Hz 9.60 38.17
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表 3 试验与流固耦合计算结果对比
Table 3. Flutter results of CFD and experiment
试验结果颤振速度/(m/s) 流固耦合颤振速度/(m/s) 误差/(%) 172.46 171.4 0.61
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表 4 AGARD445.6硬机翼前两阶模态频率
Table 4. Mode frequency of AGARD445.6 solid wing
模态 一阶模态 二阶模态 频率/Hz 14.12 50.91
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表 5 ROM1和ROM2辨识误差
Table 5. Identification error of ROM1 and ROM2
广义力系数 f11 f21 f12 f22 ROM1 0.0160 0.0180 0.0352 0.0411 ROM2 0.0332 0.0335 0.0435 0.0547
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表 6 基于降阶模型的10°迎角颤振预测与流固耦合对比
Table 6. Flutter prediction by ROM and FSI, α = 10°
颤振特性 颤振边界 $V_{\rm f}^*$ 频率比 $\omega {}_{\rm f}/{\omega _\alpha }$ ROM1, RK法 0.487 0.74 ROM1, VG法 0.489 0.72 ROM2, RK法 0.472 0.77 ROM2, VG法 0.477 0.74 流固耦合 0.459-0.472 0.77~0.79
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表 7 ROM3辨识误差
Table 7. Identification error of ROM3
广义力系数 f11 f21 f12 f22 ROM3A 0.0228 0.0210 0.0181 0.0095 ROM3B 0.0283 0.0560 0.0222 0.0472
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