Investigation on the shape optimization of wide-envelop air-breathing hypersonic vehicle
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摘要: 针对吸气式宽包线高超声速飞行器的气动优化问题，基于任务要求建立了基于多点权重分配的气动外形优化模型，并采用“CFD+准一维流”方法开展了气动性能分析。为兼顾气动外形优化的效率与精度，通过改进现有的并行加点策略，发展了一套基于代理模型与梯度算法的分层优化框架，并采用函数算例对改进后的加点策略进行了验证。对吸气式高超声速飞行器的气动外形进行了分层优化，在满足各学科约束的情况下使飞行器在各个优化评估点处的气动性能均有所提升。Abstract: Aimed at the aerodynamic optimization problem of the wide-envelope air-breathing hypersonic vehicle, an aerodynamic shape optimization model based on multi-point weight distribution is established according to mission requirements. The aerodynamic performance analysis is based on "CFD+ quasi-one-dimensional flow" method. A set of layered optimization frameworks based on the proxy model and the gradient algorithm is developed by improving the existing parallel point addition strategy to consider both the efficiency and the accuracy during the aerodynamic shape optimization. A function calculation example is used to verify the improved point addition strategy. The aerodynamic shape of the air-breathing hypersonic vehicle is optimized in the current layered optimization framework. It shows that the vehicle's aerodynamic performances at all evaluation points are improved while meeting the constraints of various disciplines.
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图 1 基于翼身分解的分层优化思路
Figure 1. Multi-layer optimization idea based on wing body decomposition
图 4 z = 0面上飞行器纵向轮廓及截面位置
Figure 4. Longitudinal profile of the vehicle at z = 0 and the cross-section positions
图 5 飞行器机身截面轮廓和参数
Figure 5. Cross-section profile and parameters of the vehicle fuselage
图 11 G9算例各种自适应加点策略的收敛流程
Figure 11. Convergence process of various adaptive point addition strategies for the G9 case
图 12 基于离散伴随方法的优化流程图
Figure 12. Flow chart of the optimization process based on the discrete adjoint method
图 13 机身优化外形与基准外形对比
Figure 13. Comparison between the optimized and reference fuselage shapes
图 14 Ma = 5.5时机身对称面处的静压对比
Figure 14. Comparison of static pressure in the symmetry plane of the fuselage at Ma = 5.5
图 15 Ma = 5.5时机身对称面处的马赫数对比
Figure 15. Comparison of Mach number in the symmetry plane of the fuselage at Ma = 5.5
图 16 机翼基准外形与优化外形对比
Figure 16. Comparison between the baseline and the optimized shape of the wing
图 17 Ma = 5.5时机翼下表面的静压对比
Figure 17. Comparison of static pressure on the lower surface of the wing at Ma = 5.5
图 18 Ma = 5.5时机翼对称面处的马赫数对比
Figure 18. Comparison of Mach number in the symmetry plane of the wing at Ma = 5.5
图 19 Ma = 5.5时机翼半展长处上下表面压强对比
Figure 19. Comparison of pressure on the upper and lower surfaces of the wing at half-wingspan for Ma = 5.5
图 22 Ma = 5.5时两层优化结果在对称面处的静压对比
Figure 22. Comparison of static pressure in the symmetry plane for two-layer optimization at Ma = 5.5
图 23 Ma = 5.5时两层优化结果在对称面处的马赫数对比
Figure 23. Comparison of Mach number in the symmetry plane for two-layer optimization at Ma = 5.5
表 1 机身优化评估点权重系数
Table 1. Weight coefficients of the airframe optimization evaluation points
优化点 马赫数 权重系数 1 1.2 0.72 2 2.5 0.46 3 5.5 1.00 4 8.0 0.37 
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表 2 机翼优化评估点计算状态与权重
Table 2. Computational conditions and weights for the wing optimization evaluation points
优化点 马赫数 高度/km 迎角/(°) 权重系数 1 0.4 0 15 0.52 2 2.5 11.7 4 0.46 3 5.5 22.5 4 1.0 4 8.0 28 4 0.37
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表 3 机身约束变量及约束范围
Table 3. Airframe constraint variables and ranges
变量 取值范围 物理描述 ${\bar x_F}$ [0.65, 0.75] 静稳定性约束 ${\eta _{{\rm{body}}} }$ >0.28 飞行器机身的容积率 ${\sigma _{Ma = 1.2}}$ >0.945 总压恢复系数(Ma = 1.2) ${\sigma _{Ma = 2.5}}$ >0.78 总压恢复系数(Ma = 2.5) ${\sigma _{Ma = 5.5}}$ >0.38 总压恢复系数(Ma = 5.5) ${\sigma _{Ma = 8.0}}$ >0.18 总压恢复系数(Ma = 8.0) ${\varphi _{Ma = 1.2}}$ >0.3 Ma = 1.2时的流量系数 ${\varphi _{Ma = 2.5}}$ >0.45 Ma = 2.5时的流量系数 ${\varphi _{Ma = 5.5}}$ >0.9 Ma = 5.5时的流量系数 ${\varphi _{Ma = 8.0}}$ >0.98 Ma = 8.0时的流量系数 ${r_{{\rm{tip}}} }$ 10 mm 前缘半径
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表 4 机翼约束变量及约束范围
Table 4. Wing constraint variables and ranges
变量 取值范围 物理描述 ${C_{Lw} }_{,Ma = 0.4}$ >0.5 机翼升力系数(Ma = 0.4) ${\eta _{{\rm{wing}}} }$ >0.1 机翼容积率
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表 5 机身设计变量与范围
Table 5. Body design variables and ranges
变量 基准值 取值范围 物理描述 ${r_{{\rm{tip}}} }$/mm 10 [5,15] 飞行器前缘中点处半径 ${L_{{\rm{body}}} }$/mm 32000 [31000,33000] 飞行器机身长度 ${W_{{\rm{engine}}} }$/mm 5000 [4800,5200] 发动机宽度 ${\theta _{{\rm{exp}}} }$/(°) 15 [14,17] 上表面起始扩张角 ${H_{{\rm{body}}} }$/mm 4100 [4050,4200] 飞行器机身高度 $ n $ 0.2 [0.05,0.3] 飞行器头部形状参数 ${\theta }_{1,2,3,4}$/(°) 80 [75,85] 截面一、二、三、四底部
切线与水平面夹角$ {H_1} $/mm 1950 [1900,2000] 截面一控制点相对高度 $ {H_2} $/mm 2700 [2600,2750] 截面二控制点相对高度 $ {H_{3,4,5}} $/mm 3150 [3100,3250] 截面三、四、五控制点相对高度 ${L_{{\rm{nozzle}}} }$/mm 11000 [10000,12000] 尾喷管长度
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表 6 机翼设计变量与范围
Table 6. Wing design variables and ranges
参数 基准值 取值范围 ${\alpha _1}$/(°) 71 [70,75] ${\alpha _2}$/(°) 55 [50,60] ${\alpha _3}$/(°) 10 [5,15] ${C_1}$/mm 500 [400,600] ${C_2}$/mm 300 [200,400] ${L_1}$/mm 18000 [16000,20000] ${L_2}$/mm 5000 [4000,6000] $R$/mm 5000 [4500,6000] ${Z_w}$/mm 7000 [6000,8000] ${C_3}$/mm 250 [200,300] ${L_3}$/mm 2000 [1500,2500] ${H_{{\rm{cw}}} }$/mm 4000 [3000,5000]
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表 7 两种方法的梯度计算结果对比
Table 7. Comparison of the gradient calculation results between the two methods
控制参数 有限差分法 离散伴随法 相差百分比/% 上表面 下表面 上表面 下表面 上表面 下表面 a1 0.0373 0.0260 0.0378 0.0267 1.32 2.62 a2 0.0258 0.0169 0.0261 0.0172 1.15 1.74 a3 0.2224 0.0035 0.0227 0.0036 2.20 2.78 a4 0.0142 –0.0031 0.0143 –0.0030 0.70 3.33 a5 0.0101 –0.0070 0.0104 –0.0068 2.88 2.94 a6 0.0079 –0.0093 0.0080 –0.0090 1.25 3.33 a7 0.0047 –0.0118 0.0048 –0.0115 2.08 2.61
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表 8 G9函数优化结果及调用高精度模型次数对比
Table 8. Comparison of the G9 function optimization results and the times of calling high-precision models
自适应加点策略 优化结果 迭代调用高精度模型次数 最优理论解 680.63 EI单一加点法 722.79 200 混合加点法 681.60 600 Kriging信任法 695.49 600 多点EI加点法 683.04 600 改进的Kriging信任法 681.61 600 改进的多点EI加点法 680.98 600
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表 9 机身第一层优化结果
Table 9. First layer optimization results of the fuselage
参数符号 基准值 优化值 rtip/mm 10 10 Lbody/mm 32000 31101 Wengine/mm 5000 4853.3 θexp/(°) 15 14.01 Hbody/mm 4100 4087.8 n 0.2 0.07 H1/mm 1950 1931.4 θ3,4/(°) 80 83.8 H3,4,5/mm 3150 3203.3 Lnozzle/mm 11000 11821.6 ${\eta _{{\rm{body}}} }$ 0.282 0.2811 $ {\bar x_{F,Ma = 1.2}} $ 0.672 0.732 $ {\bar x_{F,Ma = 2.5}} $ 0.739 0.749 $ {\bar x_{F,Ma = 5.5}} $ 0.743 0.719 $ {\bar x_{F,Ma = 8.0}} $ 0.718 0.690 ${\sigma _{Ma = 1.2}}$ 0.947 0.947 ${\sigma _{Ma = 2.5}}$ 0.795 0.804 ${\sigma _{Ma = 5.5}}$ 0.384 0.390 ${\sigma _{Ma = 8.0}}$ 0.183 0.190 ${J_{{\rm{body}}} }$ 1.478 0.323
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表 10 机翼外形优化结果
Table 10. Wing shape optimization results
参数符号 基准值 优化值 ${\alpha _1}$/(°) 71 71.48 ${\alpha _2}$/(°) 55 50.85 ${\alpha _3}$/(°) 10 8.29 ${C_1}$/mm 500 405.5 ${C_2}$/mm 300 242.2 ${L_1}$/mm 18000 17588 ${L_2}$/mm 5000 5499 $R$/mm 5000 5231.3 ${Z_w}$/mm 7000 6710.5 ${C_3}$/mm 250 218.9 ${L_3}$/mm 2000 2388.3 ${H_{{\rm{cw}}} }$/mm 4000 3077.6 ${J_{{\rm{wing}}} }$ 2.312 0.971 ${C_{Dw,Ma = 0.4} }$ 0.144 0.135 ${C_{Dw,Ma = 2.5} }$ 0.00919 0.00654 ${C_{Dw,Ma = 5.5} }$ 0.00741 0.00616 ${C_{Dw,Ma = 8.0} }$ 0.00575 0.00478 ${C_{Lw,Ma = 0.4} }$ 0.5357 0.5038 ${\eta _{{\rm{wing}}} }$ 0.1106 0.1004
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表 11 翼身组合体优化前后参数对比
Table 11. Comparison of parameters before and after optimization of the wing body assembly
参数符号 优化前 优化后 设计变量 ${r_{{\rm{tip}}} }$/mm 10 10 ${L_{{\rm{body}}} }$/mm 31101 31078.3 ${W_{{\rm{engine}}} }$/mm 4853.3 4816.4 ${\theta _{{\rm{exp}}} }$/(°) 14.01 14 ${H_{{\rm{body}}} }$/mm 4087.8 4078.6 n 0.07 0.0683 $ {H_1} $/mm 1931.4 1924.3 $ {\theta _{3,4}} $/(°) 83.8 83.9 $ {H_{3,4,5}} $/mm 3203.3 3210.2 ${L_{{\rm{nozzle}}} }$/mm 11821.6 11836.8 ${\alpha _1}$/(°) 71.48 71.56 ${\alpha _2}$/(°) 50.85 51.22 ${\alpha _3}$/(°) 8.29 7.92 ${C_1}$/mm 405.5 401.6 ${C_2}$/mm 282.2 274.7 ${L_1}$/mm 17588 17462.8 ${L_2}$/mm 5499 5361.2 $R$/mm 5231.3 5334.5 ${Z_w}$/mm 6710.5 6642 ${C_3}$/mm 218.9 213.8 ${L_3}$/mm 2388.3 2452.1 ${H_{cw}}$/mm 3077.6 3080.6 $ {H_w} $/mm 600 521.4 ${L_w}$/mm 3500 3842 约束条件 $ {\bar x_{F,Ma = 1.2}} $ 0.709 0.723 $ {\bar x_{F,Ma = 2.5}} $ 0.676 0.681 $ {\bar x_{F,Ma = 5.5}} $ 0.711 0.704 $ {\bar x_{F,Ma = 8.0}} $ 0.727 0.721 ${\eta _{{\rm{body}}} }$ 0.2811 0.2812 ${\sigma _{Ma = 1.2}}$ 0.947 0.946 ${\sigma _{Ma = 2.5}}$ 0.804 0.802 ${\sigma _{Ma = 5.5}}$ 0.390 0.392 ${\sigma _{Ma = 8.0}}$ 0.190 0.192 ${\varphi _{Ma = 1.2}}$ 0.3052 0.3048 ${\varphi _{Ma = 2.5}}$ 0.460 0.460 ${\varphi _{Ma = 5.5}}$ 0.912 0.913 ${\varphi _{Ma = 8.0}}$ 0.998 0.999 ${\eta _{{\rm{wing}}} }$ 0.1004 0.10003 目标函数 ${C_{Lo, Ma = 0.4} }$ 0.7720 0.7649 ${C_{Do,Ma = 1.2} }$ 0.07202 0.07125 ${C_{ Do, Ma = 2.5} }$ 0.03688 0.03659 ${C_{Do, Ma = 5.5} }$ 0.004072 0.003864 ${C_{ Do, Ma = 8.0} }$ 0.006381 0.006179 ${J_{{\rm{com}}} }$ 0.362 0.291
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