-
摘要:
针对带捆绑火箭气动载荷分布受飞行状态及本身外形参数变化影响存在波动的现象,提出了依据多项式混沌理论对捆绑火箭气动载荷分布特征进行全局灵敏度分析及不确定性量化的方法,并以两助推构型火箭为例对所提方法进行验证。首先,提出了捆绑火箭气动载荷分布不确定性分析的方法,并给出仿真分析流程。其次,以两助推构型火箭为例对所提方法进行验证,建立火箭气动外形参数化模型,验证气动特性分析结果。最后,对该模型开展影响因素灵敏度分析及载荷分布不确定性分析,得到了不同因素的影响程度,以及气动轴力和法向力的不确定性分布形式,分析了流场流动情况及气动载荷波动的主要原因。分析结果为捆绑火箭气动载荷波动控制提供了一定参考,通过定量描述气动载荷分布不确定性,可以有效降低安全系数冗余,为开展精确结构设计提供依据。
Abstract:Aimed at the uncertainty of the aerodynamic load distribution of strap-on launch vehicles due to the uncertainty of flight status and shape parameters, a method based on the polynomial chaos theory to analyze the aerodynamic load distribution characteristics and quantify the uncertainty of the strap-on launch vehicle is proposed. A two-strap-on configuration was used as an example to verify the method. First, a method for uncertainty analysis of aerodynamic loads of the strap-on launch vehicles was proposed, and the simulation analysis process was given. Second, the method was verified by a two-strap-on configuration, the aerodynamic shape parametric model was established, and the aerodynamic characteristic analysis result was verified. Finally, the sensitivity analysis of influencing factors and the uncertainty analysis of load distribution were carried out, the influencing degree of different factors and the uncertainty distribution form of aerodynamic axial force and normal force were obtained according to the proposed method, and the flow mechanism was analyzed. The analysis results provide reference for the aerodynamic load control of strap-on launch vehicle. By describing the aerodynamic load uncertainty quantitatively, the safety factor redundancy can be reduced effectively and the basis of accurate structural design can be provided.
-
表 1 外形参数数值
Table 1. Values of shape parameters
参数 数值 参数 数值 θ1/(°) 17 d/m 1 θ2/(°) 14 L1/m 17.65 ϕ1/m 3.7 L2/m 21 ϕ2/m 2 L3/m 45.5 R1/m 0.66 L4/m 50 R2/m 0.22 表 2 不确定性分析结果
Table 2. Uncertainty analysis results
参数 峰值1 峰值2 峰值3 位置/m 3.862 3.862 33.83 均值/μ 51.02 362.1 391.5 标准差Δ/kN 5.560 22.91 42.23 不确定度/% 10.90 6.327 10.79 -
[1] 王锋. 运载火箭载荷计算及通用软件实现[D]. 长沙: 国防科学技术大学, 2001.WANG F. Calculation of launch vehicle load and software design[D]. Changsha: National University of Defense Technology, 2001(in Chinese). [2] WANG Y, YU X. Robust optimization of aerodynamic design using surrogate model[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2007, 24(3): 181-187. [3] BELLMAN R E, ZADEH L A. Decision-making in a fuzzy environment[J]. Management Science, 1970, 17(4): 141-164. doi: 10.1287/mnsc.17.4.B141 [4] FAES M. Interval methods for the identification and quantification of inhomogeneous uncertainty in finite element models[D]. Belgium: KU Leuven, 2017. [5] 宋鑫, 郑冠男, 杨国伟, 等. 几何不确定性区间分析及鲁棒气动优化设计[J]. 北京航空航天大学学报, 2019, 45(11): 2217-2227. doi: 10.13700/j.bh.1001-5965.2019.0077SONG X, ZHENG G N, YANG G W, et al. Interval analysis for geometric uncertainty and robust aerodynamic optimization design[J]. Journal of Beijing University of Aeronautics and Astronautics, 2019, 45(11): 2217-2227(in Chinese). doi: 10.13700/j.bh.1001-5965.2019.0077 [6] 邬晓敬, 张伟伟, 宋述芳, 等. 翼型跨声速气动特性的不确定性及全局灵敏度分析[J]. 力学学报, 2015, 47(4): 587-595. https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201504006.htmWU X J, ZHANG W W, SONG S F, et al. Uncertainty quantification and global sensitivity analysis of transonic aerodynamics about airfoil[J]. Chinese Journal of Theoretical and Applied Mechanics, 2015, 47(4): 587-595(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-LXXB201504006.htm [7] UEMATSU T, ASO S, TANI Y. Supersonic flight separation simulation for TSTO launch vehicles considering shock wave interaction reduction[C]//Proceedings of the AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition. Reston: AIAA, 2012. [8] 沈丹, 吴彦森, 岑拯. 芯级与助推器头部气动干扰流场数值模拟[J]. 导弹与航天运载技术, 2013(6): 42-46. https://www.cnki.com.cn/Article/CJFDTOTAL-DDYH201306015.htmSHEN D, WU Y S, CEN Z. Numerical simulation of aerodynamic interaction characteristics between the rocket and a booster's nosecone[J]. Missiles and Space Vehicles, 2013(6): 42-46(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-DDYH201306015.htm [9] STEFANOU G. The stochastic finite element method: Past, present and future[J]. Computer Methods in Applied Mechanics and Engineering, 2009, 198(9): 1031-1051. [10] SPANOS P D, GHANEM R. Stochastic finite element expansion for random media[J]. Journal of Engineering Mechanics, 1989, 115(5): 1035-1053. doi: 10.1061/(ASCE)0733-9399(1989)115:5(1035) [11] GHANEM R G, SPANOS P D. Stochastic finite elements: A spectral approach[M]. Berlin: Springer, 1992. [12] MOENS D, HANSS M. Non-probabilistic finite element analysis for parametric uncertainty treatment in applied mechanics: Recent advances[J]. Finite Elements in Analysis and Design, 2011, 47(1): 4-16. doi: 10.1016/j.finel.2010.07.010 [13] MLLER B, GRAF W, BEER M. Fuzzy structural analysis using alpha-level optimization[J]. Computational Mechanics, 2000, 26(6): 547-565. doi: 10.1007/s004660000204 [14] BETTIS B, HOSDER S, WINTER T. Efficient uncertainty quantification in multidisciplinary analysis of a reusable launch vehicle[C]//Proceedings of the 17th AIAA International Space Planes and Hypersonic Systems and Technologies Conference. Reston: AIAA, 2011. [15] HOSDER S, WALTERS R W, BALCH M. Point-collocation nonintrusive polynomial chaos method for stochastic computational fluid dynamics[J]. AIAA Journal, 2010, 48(12): 2721-2730. doi: 10.2514/1.39389 [16] 宋赋强, 阎超, 马宝峰, 等. 锥导乘波体构型的气动特性不确定度分析[J]. 航空学报, 2017, 39(2): 97-106. https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201802009.htmSONG F Q, YAN C, MA B F, et al. Uncertainty analysis of aerodynamic characteristics for cone-derived waverider configuration[J]. Acta Aeronautica et Astronautica Sinica, 2017, 39(2): 97-106(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HKXB201802009.htm [17] 肖思男, 吕震宙, 王薇. 不确定性结构全局灵敏度分析方法概述[J]. 中国科学: 物理学、力学、天文学, 2018, 48(1): 4-21. https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201801003.htmXIAO S N, LV Z Z, WANG W. A review of global sensitivity analysis for uncertainty structure[J]. Scientia Sinica Physica, Mechanica and Astronomica, 2018, 48(1): 4-21(in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-JGXK201801003.htm [18] XIAO S N, LU Z Z, XU L Y. A new effective screening design for structural sensitivity analysis of failure probability with the epistemic uncertainty[J]. Reliability Engineering and System Safety, 2016, 156(12): 1-14. [19] SOBOL'I M, KUCHERENKO S. Derivative based global sensitivity measures and their link with global sensitivity indices[J]. Mathematics and Computers in Simulation, 2016, 79(10): 3009-3017. [20] SOBOL'I M. Sensitivity analysis for non-linear mathematical models[J]. Mathematical Modeling and Computational Experiment, 1993, 1(1): 407-414. [21] SOBOL'I M. Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates[J]. Mathematics and Computers in Simulation, 2014, 55(1-3): 271-280. [22] QIAO L, HOMMA T. A new importance measure for sensitivity analysis[J]. Journal of Nuclear Science and Technology, 2010, 47(1): 53-61. doi: 10.1080/18811248.2010.9711927 [23] MANI M, NAGHIB-LAHOUTI A, NAZARINIA M. Experimental and numerical aerodynamic analysis of a satellite launch vehicle with strap-on boosters[J]. Aeronautical Journal, 2016, 108(1085): 379-386.