-
摘要:
翼型结冰冰形的数值模拟预测通常比较复杂耗时,为了更加快速准确地预测冰形以减少计算资源消耗,建立了基于本征正交分解(POD)和Kriging模型的冰形快速预测方法。利用CFD数值模拟结果来构建样本空间,以飞行迎角为例详述了降阶模型的冰形预测的实现手段,并结合试验设计方法,完成了多参数的结冰冰形快速预测,同时研究了先进的Blind-Kriging模型的相关方法以及对于预测结果的改进。结果表明,降阶模型预测翼型结冰冰形与CFD数值模拟结果吻合较好,表明降阶模型可以快速、精确地应用于翼型结冰冰形预测。
-
关键词:
- 冰形预测 /
- 降阶模型 /
- 本征正交分解(POD) /
- Kriging模型 /
- Blind-Kriging模型
Abstract:The numerical simulation prediction of aero-icing ice shape is usually complicated and time-consuming. In order to predict ice shape more quickly and accurately and to reduce computational resource consumption, a quick ice shape prediction method based on proper orthogonal decomposition and Kriging model is proposed in this paper. Using a database of high-fidelity CFD numerical simulations to build sample space, in view of the change of attack angle, the procedure for predicting the ice shape by reduced order model is introduced. With the data sampling method of parameter space, multiparameter prediction of the ice shape is achieved. Meanwhile, the related methods of the advanced Blind-Kriging model and the improvement of the prediction results are studied. The result shows that the prediction results of the airfoil icing shape using the reduced order model agree well with the CFD numerical simulation results. The conclusion is made that the reduced order model is a quick and accurate approach for predicting the ice shapes of airfoil icing.
-
表 1 算例计算条件
Table 1. Calculation conditions of example
计算状态 数值 来流速度/(m·s-1) 100 液态水含量(LWC)/(g·m-3) 1 平均水滴直径(MVD)/μm 20 环境压力/Pa 101 325 结冰温度/K 263.15 结冰时间/s 360 表 2 快照矩阵特征值
Table 2. Eigenvalue of snapshot matrix
特征值序号 λx/10-6 λy/10-6 1 174 832 6 10 328.48 2 8.937 12 20.761 14 3 3.189 29 5.440 25 4 1.121 569 1.452 005 5 0.613 951 0.556 798 表 3 多参数样本选择范围
Table 3. Selection range for multiparameter sample
参数 最小值 最大值 飞行迎角/(°) 0 5 飞行速度/(m·s-1) 90 130 结冰温度/°F -22 +32 MVD/μm 15 40 高度/ft 0 22 000 表 4 验证算例计算条件
Table 4. Calculation conditions of verification example
算例状态 数值 飞行迎角/(°) 1.325 飞行速度/(m·s-1) 91.875 MVD/μm 25.5 高度/ft 12 031 结冰温度/°F 16 结冰时间/s 360 表 5 计算状态
Table 5. Calculation conditions
计算状态 数值 MVD/μm 20 环境压力/Pa 101 325 结冰温度/K 263.15 结冰时间/s 360 -
[1] 蒋天俊.结冰对飞机飞行性能影响的研究[D].南京: 南京航空航天大学, 2008. http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=D052562JIANG T J.Investigation of icing accretion influences on aircraft flight performance[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2008(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=D052562 [2] 姚若鹏.翼型的结冰数值模拟及相关控制研究[D].南京: 南京航空航天大学, 2012. http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=D280454YAO R P.The numerical simulation of ice accretion on airfoil and control research[D].Nanjing: Nanjing University of Aeronautics and Astronautics, 2012(in Chinese). http://www.wanfangdata.com.cn/details/detail.do?_type=degree&id=D280454 [3] 杨胜华.二维飞机结冰过程仿真[D].北京: 北京航空航天大学, 2010.YANG S H.Two-dimensional in-flight ice accretion simulation[D].Beijing: Beihang University, 2010(in Chinese). [4] 申晓斌, 郁嘉, 林贵平, 等.基于特征正交分解法的翼型结冰冰形快速预测[J].航空动力学报, 2013, 28(4):807-812. http://d.old.wanfangdata.com.cn/Periodical/hkdlxb201304012SHEN X B, YU J, LIN G P, et al.Fast prediction of ice shape based on proper orthogonal decomposition method[J].Journal of Aerospace Power, 2013, 28(4):807-812(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkdlxb201304012 [5] GALLIVAN K, GRIMME E, VAN DOOREN P.Pade approximation of large-scale dynamics systems with lanczos methods[C]//Proceedings of the 33rd IEEE Conference on Decision and Control.Piscataway, NJ: IEEE Press, 1994: 443-448. [6] CAMUSSI R, GUJ G.Orthonormal wavelet decomposition of turbulent flows:Intermittency and coherent structures[J].Journal of Fluid Mechanics, 1997, 348:177-199. doi: 10.1017/S0022112097006551 [7] AUBRY N, GUYONNET R, LIMA R.Spatio-temporal analysis of complex signals:Theory and applications[J].Journal of Statistical Physics, 1981, 64(3-4):683-739. http://d.old.wanfangdata.com.cn/OAPaper/oai_doaj-articles_03617a40a464dfac680a19bf9e3f0390 [8] HOLMES P, LUMLEY J L, BERKOOZ G.Turbulence, coherent structures, dynamical systems and symmetry[M].Cambridge:Cambridge University Press, 1996:68-100. [9] VOLKWEIN S.Proper orthogonal decomposition for nonlinear dynamical systems[EB/OL].Graz: University of Graz, 2005[2018-08-14] http://www.math.unikonstanz.de/numerik/personen/volkwein/PhDSchools/Volkwein_Part1.pdf. [10] NAKAKITA K, HABASHI W G, NADARAJAH S.Toward real-time aero-icing simulation using reduced order models[J].Journal of Aircraft, 2010, 47(1):96-115. doi: 10.2514/1.44077 [11] 葛宜元.试验设计方法与Design-Expert软件应用[M].哈尔滨:哈尔滨工业大学出版社, 2015:2-3.GE Y Y.Experimental design method and Design-Expert software application[M].Harbin:Harbin Institute of Technology Press, 2015:2-3(in Chinese). [12] 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, 1979, 21(2):239-245. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.1080/00401706.2000.10485979 [13] MORRIS M D, MITCHELL T J.Exploratory designs for computational experiments[J].Journal of Statistical Planning and Inference, 1995, 43(3):381-402. doi: 10.1016/0378-3758(94)00035-T [14] 丁鹏, 陶文诠.建立低阶模型的POD方法[J].工程热物理学报, 2009, 30(6):1019-1021. doi: 10.3321/j.issn:0253-231X.2009.06.032DING P, TAO W Q.Reduced order modeling with the proper orthogonal decomposition[J].Journal of Engineering Thermo Physics, 2009, 30(6):1019-1021(in Chinese). doi: 10.3321/j.issn:0253-231X.2009.06.032 [15] KERSCHEN G, GOLINVAL J, VAKAKIS A F, et al.The method of proper orthogonal de-composition for dynamical characterization and order reduction of mechanical sys-tems:An overview[J].Nonlinear Dynamics, 2005, 41(1-3):147-169. doi: 10.1007/s11071-005-2803-2 [16] SIROVICH L.Turbulence and the dynamics of coherent structures.Ⅰ-Coherent structures.Ⅱ-Symmetries and transformations.Ⅲ-Dynamics and scaling[J].Quarterly of Applied Mathematics, 1987, 45(3):561-571. doi: 10.1090/qam/1987-45-03 [17] KRIGE D G.A statistical approach to some basic mine valuation problems on the Witwatersrand[J].Journal of the Southern African Institute of Mining and Metallurgy, 1951, 52(6):119-139. http://cn.bing.com/academic/profile?id=e1a44ecdde7f607d72aaed1e53da62c9&encoded=0&v=paper_preview&mkt=zh-cn [18] 韩忠华.Kriging模型及代理优化算法研究进展[J].航空学报, 2016, 37(11):3197-3225. http://d.old.wanfangdata.com.cn/Periodical/hkxb201611001HAN Z H.Kriging surrogate model and its application to design optimization:A review of recent progress[J].Acta Aeronautica et Astronautica Sinica, 2016, 37(11):3197-3225(in Chinese). http://d.old.wanfangdata.com.cn/Periodical/hkxb201611001 [19] HÉLOÏSE B, FRANÇOIS M, WAGDI G H.FENSAP-ICE's three-dimensional in-flight ice accretion module:ICE3D[J].Journal of Aircraft, 2003, 40(2):239-247. doi: 10.2514/2.3113 [20] JEONG S, OBAYASHI S, YAMAMOTO K.Aerodynamic optimization design with kriging model[J].Transactions of the Japan Society for Aeronautical and Space Sciences, 2005, 48(161):161-168. doi: 10.2322/tjsass.48.161 [21] JECK R K.Icing Design Envelopes(14 CFR Parts 25 and 29, Appenddix C)Converted to a Distance-Based Format: DOT/FAA/AR-00/30[R].Washington, D.C.: FAA, 2002. [22] JOSEPH V R, HUNG Y, SUDJANTO A.Blind Kriging:A new method for developing metamodels[J].Journal of Mechanical Design, 2008, 130(3):350-353. doi: 10.1115-1.2829873/ [23] COUCKUYT I, FORRESTER A, GORISSEN D, et al.Blind Kriging:Implementation and performance analysis[J].Advances in Engineering Software, 2012, 49:1-13. doi: 10.1016/j.advengsoft.2012.03.002