Prediction method of aero-heating of hypersonic vehicle bi-curvature leading edge based on machine learning
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摘要:
高超声速气动热预测技术是高超声速飞行器发展的关键技术之一，气动热环境的精准预测对飞行器热防护系统设计及气动布局优化具有重要意义。为快速获得高超声速飞行器表面的热流分布情况，缩短飞行器设计周期，基于具有广义可分离特性、可实现强非线性数据快速建模的多层分块(MBB)算法，提出一种针对高超声速飞行器双曲率前缘气动热分布的快速预测方法。通过数值计算获得双曲率前缘驻点区的气动热分布作为训练集数据，基于MBB算法提出预测热流分布的显式表达式，对表达式预测结果的统计分析显示，表达式预测值与测试集数据的偏差低于2%，这表明其具有较高的预测精度；将驻点区热流分布表达式进行外推，验证了机器学习公式在不同几何外形下的适用性。在双曲率前缘构型的防热设计及气动外形优化阶段，所提表达式可实现气动热环境的精准、快速预测。
Abstract:The prediction technology of hypersonic aero-heating is one of the key technologies for the development of high-speed vehicles. Creating an efficient method for predicting the hypersonic thermal conditions is highly important for designing thermal protection systems and optimizing aerodynamics. In order to obtain the heat flux distribution on the surface of hypersonic vehicles quickly and to shorten the vehicle design cycle, a fast prediction method for the aerothermal environment of the bi-curvature leading edge of hypersonic vehicles is proposed based on the multi-level block building (MBB) algorithm. The MBB algorithm is distinguished by its generalized separability, which enables it to efficiently represent highly nonlinear data. First, numerical simulations are conducted to obtain the database composed of the aero-heating data of the bi-curvature leading edges of the vehicles in the training set. Based on the MBB algorithm, an explicit expression for predicting the distributions of heat flux is given. The statistical analysis results demonstrate that the discrepancy between the estimated value and the observed value is below 2%, suggesting that the formula given in this study exhibits a high level of predictive precision. Further, an extrapolation of the formula is performed to verify its applicability for different geometric shapes. At the stage of thermal design and aerodynamic optimization of the bi-curvature leading edge configuration, the formulation proposed in this paper enables accurate and rapid prediction of the aerodynamic thermal environment.
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图 5 不同Ma和几何外形下的热流分布
Figure 5. Distributions of heat flux at different Ma and geometries
图 7 2%偏差带下公式与数值计算结果的对比
Figure 7. Comparison between formula under 2% deviation band and numerical results
图 8 驻点热流值及其导数值随R0的变化
Figure 8. The variations of stagnation heat flux and its derivative with the values of R0
表 1 数值模拟的参数设置
Table 1. Settings of parameters for numerical simulation
Ma r/mm R/mm R0 6，7，8，9，10 2 2，4，6，···，18，20 1，2，3，···，9，10 
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表 2 MBB算法热流分布公式
Table 2. Formula of heat flux distributions obtained by MBB algorithm
序号 q/qref R2 1 $ 0.803\;735-0.037\;163\;3 \ln ( {Ma})-0.128\;599 R_{0}^{-2}+0.398\;309 R_{0}^{-1}-0.645\;404 ({{\mathrm{sin}}}\theta )^{2} $ 0.99348017 2 $ 0.782\;952-0.014\;027\;4 {Ma}^{{2}/{3}}-0.128\;64 R_{0}^{-1}+0.398\;357 R_0^{-1}-0.645\;377(\sin \theta )^{ 2} $ 0.99309438 3 $ 0.743\;498-0.026\;448\;9 {Ma}^{{1}/{2}}+0.324\;038 R_{0}^{{2}/{3}}+0.012\;534\;3 R_{0}^{{1}/{3}}-0.641\;078 (\sin \theta )^{ 2} $ 0.99206282 4 $ 0.706\;337-0.004\;669\;15 {Ma}+0.324\;044 R_{2}^{{2}/{3}}+0.012\;532\;5 R_{0}^{{1}/{3}}-0.641\;065 (\sin \theta)^{2} $ 0.99174652
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