A multi-fidelity aerodynamic modeling method of aerospace vehicles with shape configuration independent was proposed based on Gaussian process regression model, in order to satisfy the demand of full speed domain and large airspace of aerospace vehicle in the preliminary design stage. The traditional engineering estimation method and computational fluid dynamics (CFD) numerical simulation method were treated as the data sources of low-fidelity and high-fidelity aerodynamic characteristics, respectively. Specifically, a fast estimation model for aerodynamics of aerospace vehicles was established by using the panel method in the enigineering estimation method. Then, high-fidelity aerodynamic performance of aerospace vehicles was achieved based on the three-dimensional compressible Euler equations in the CFD numerical simulation. Moreover, the developed multi-fidelity aerodynamic modeling method was validated by the dual-parameter problems of FTB. The prediction accuracy and stability of the developed multi-fidelity aerodynamic model were better than that of the single-fidelity surrogate model with the same number of high-fidelity data points through comparison and analysis. Meanwhile, the relative error of prediction was less than 1%. The multi-fidelity aerodynamic model was used as the source of aerodynamic data for the reentry problem of the aerospace vehicle, and the influence of single fidelity and multi-fidelity modeling methods on the simulation of re-entry trajectory was compared and analyzed. Results show that the proposed multi-fidelity aerodynamic model can fast provide a high accurate aerodynamic data required from trajectory simulation.
Ting-wei JI,Xu ZHA,Fang-fang XIE,Yu-si WU,Xin-shuai ZHANG,Yi-yang JIANG,Chang-ping DU,Yao ZHENG. Multi-fidelity aerodynamic modeling method of aerospace vehicles based on Gaussian process regression. Journal of ZheJiang University (Engineering Science), 2023, 57(11): 2314-2324.
Fig.2Calculation fidelity versus cost distribution for high fidelity and low fidelity model
Fig.3Density model of atmosphere between 0 and 70 km
Fig.4Three views of FTB model
Fig.5Comparison of calculation results of lift and drag coefficients
气动系数
$ {\bar \varepsilon _{{\rm{en}}}} $
$ {\bar \varepsilon _{{\rm{CFD}}}} $
$ \eta $/%
Cl
0.02763
0.02222
3.53
Cd
0.01203
0.00411
9.56
Tab.1Comparison of average errors of solving aerodynamic coefficients by two methods
方法
Ns
CPU配置
NC
t
CFD数值模拟
1997434
Intel(R) Xeon(R) Platinum 8175M CPU @ 2.50 GHz
45
1.79 h
基于工程估算的 快速预测方法
5912
Intel(R) Core(TM) i5-8400 CPU @ 2.80 GHz
1
0.58 s
Tab.2Comparison of calculation cost of solving aerodynamic coefficients by two method
Fig.6Process of multi-fidelity aerodynamic modeling
Fig.7Correlation between high-fidelity samples and multi-fidelity predicted values for lift coefficient under different numbers of high-fidelity samples
Fig.8Error cloud figure of multi-fidelity model for lift coefficient
Fig.9Correlation between data of test set and multi-fidelity predicted values for lift coefficient under different numbers of high-fidelity samples
Tab.4Variance of squared error for multi-fidelity model of lift coefficient
Fig.10Cloud figure of multi-fidelity modeling results for lift and drag coefficients
Fig.11Process of reentry trajectory simulation
Fig.12Curve of reentry characteristic and comparison of errors based on single-fidelity and multi-fidelity aerodynamic models
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