基于稀疏网格配置方法的超燃冲压发动机高维不确定性量化

doi:10.13675/j.cnki.tjjs.190809

推进技术 ›› 2021, Vol. 42 ›› Issue (6): 1201-1212.DOI: 10.13675/j.cnki.tjjs.190809

• 总体与系统 • 下一篇

基于稀疏网格配置方法的超燃冲压发动机高维不确定性量化

高嘉豪，何淼生，刘成诚，张斌，刘洪

上海交通大学航空航天学院高超声速创新技术研究实验室，上海 200240

出版日期:2021-06-15 发布日期:2021-08-15
作者简介:高嘉豪，硕士生，研究领域为高超声速空气动力学。E-mail：chickenwest@sjtu.edu.cn
基金资助:
国家自然科学基金（51906146；91741113）。

High Dimensional Uncertainty Quantification in Scramjet Performance Analysis Using Sparse Grid Collocation Methods

Hypersonic Innovation Technology Research Laboratory，College of Aeronautics and Astronautics， Shanghai Jiaotong University，Shanghai 200240，China

Online:2021-06-15 Published:2021-08-15

摘要/Abstract

摘要： 为了定量地研究随机不确定性对超燃冲压发动机性能评估及优化设计可能带来的影响及其规律特征，基于高斯过程描述发动机工作状态及来流环境等控制参数随机误差，建立由自由来流条件、进气道压缩系统以及燃烧加热等构成的发动机输入边界不确定性表征。耦合全局敏感度分析、稀疏网格技术、概率配置方法及等压燃烧热力学分析模型，提出了面向超燃冲压发动机高维不确定性量化方法，研究量化了上述随机不确定性输入对典型超燃冲压发动机性能的影响及其不确定性传递特征。结果表明：马赫数6.0巡航条件下，发动机的比冲对进气道的压缩过程最为敏感，占比达到65%~70%，而对燃烧加热的敏感性最低，进气道压缩系统的初始压缩激波以及来流马赫数对于整个超燃冲压发动机的比推力敏感性要显著高于其他输入因素；随着燃烧室入口马赫数由2.0增大到3.0，单一因素存在5%不确定性导致的发动机比冲性能评估的不确定度由最小的5.5%快速放大到约7.63%，系统朝着不稳定的方向发展，多种随机不确定性共同作用下的发动机性能不确定性传递存在一定的耦合效应；高速进气道正常工作需要处理的空气动能与外部注入的燃料热能之比随飞行马赫数增加呈现近似2次方指数型增长，从能量流视角开展进一步的分析研究，将有助于深度理解超燃冲压发动机性能不确定性的传递行为。

关键词: 超燃冲压发动机;高维不确定性量化;随机配置方法;敏感度分析;热力循环模型

Abstract: In order to quantitatively study the possible impact of stochastic uncertainty on the performance evaluation and optimization design of the scramjet engine， based on the Gaussian process， the stochastic errors of control parameters such as the engine operating conditions and the freestream flow parameters has been described in this paper， and the uncertainty of the engine’s input boundary consisting of freestream flow conditions， the intake initial compression system， and combustion heating has been established. Coupled with global sensitivity analysis， sparse grid technology， probabilistic collocation method， and isobaric combustion thermodynamic analysis model， a high-dimensional uncertainty quantification method for the scramjet is proposed， and the transfer characteristics of the above stochastic uncertainties input as well as their impact on scramjet performance are quantified for typical scramjet. The results show that the specific impulse of the engine is most sensitive to the compression process of the intake， accounting for 65% to 70%， and the least sensitive to combustion heating under a cruise condition of Mach 6.0， and the uncertainties coming from the initial compression shock and incoming Mach number of the high Mach number inlet compression system are significantly higher than the other input factors for the specific thrust sensitivity of the entire scramjet. As the combustor entrance Mach number increased from 2.0 to 3.0， the uncertainty of the specific impulse performance evaluation of the engine induced by a single factor of 5% will quickly increase from a minimum of 5.5% to 7.63%， indicating an unstable developing direction， and there is a certain coupling effect in the transmission of engine performance uncertainty under the combination of multiple stochastic uncertainties. The ratio of the kinetic energy of the air that needs to be processed to the high-speed intake to the heat energy of the externally injected fuel exhibits an exponential growth of approximately square power as the freestream Mach number increases， further analysis and research utilizing an energy and exergy analysis tool will be very helpful for a deeper understanding on the transfer behavior of the performance uncertainty of the scramjet engine.

Key words: Scramjet engine;High-dimensional uncertainty quantification;Stochastic collocation method;Sensitivity analysis;Thermodynamic analysis model

高嘉豪，何淼生，刘成诚，张斌，刘洪. 基于稀疏网格配置方法的超燃冲压发动机高维不确定性量化[J]. 推进技术, 2021, 42(6): 1201-1212.

GAO Jia-hao, HE Miao-sheng, LIU Cheng-cheng, ZHANG Bin, LIU Hong. High Dimensional Uncertainty Quantification in Scramjet Performance Analysis Using Sparse Grid Collocation Methods[J]. Journal of Propulsion Technology, 2021, 42(6): 1201-1212.

参考文献

[1] Heiser W， Pratt D， Daley D， et al. Hypersonic AirBreathing Propulsion［M］. Washington DC： AIAA Education Series， 1994.
[2] Huan X， Safta C， Sargsyan K， et al. Global Sensitivity Analysis and Quantification of Model Error for Large Eddy Simulation in Scramjet Design［R］. AIAA 2017-1089.
[3] Roux J A. Parametric Ideal Scramjet Cycle Analysis［J］. Journal of Thermophysics and Heat Transfer， 2011， 25（4）： 581-585.
[4] Roux J A， Choi J， Shakya N. Parametric Scramjet Cycle Analysis for Nonideal Mass Flow Rate［J］. Journal of Thermophysics and Heat Transfer， 2014， 28（1）： 166-171.
[5] Roux J A， Tiruveedula L S. Constant Velocity Combustion Parametric Ideal Scramjet Cycle Analysis［J］. Journal of Thermophysics and Heat Transfer， 2016， 30（3）： 698-704.
[6] Yang Q， Chang J， Bao W. Thermodynamic Analysis on Specific Thrust of the Hydrocarbon Fueled Scramjet［J］. Energy， 2014， 76： 552-558.
[7] Zhang D， Yang S， Zhang S， et al. Thermodynamic Analysis on Optimum Performance of Scramjet Engine at High Mach Numbers［J］. Energy， 2015， 90： 1046-1054.
[8] Smart M K， Hass N E， Paull A. Flight Data Analysis of the HyShot Ⅱ Scramjet Flight Experiment［J］. AIAA Journal， 2006， 44（10）： 2366-2375.
[9] Constantine P G， Emory M， Larsson J， et al. Exploiting Active Subspaces to Quantify Uncertainty in the Numerical Simulation of the HyShot II Scramjet［J］. Journal of Computational Physics， 2015， 302： 1-20.
[10] Gardner A D， Hannemann K， Pauli A， et al. Ground Testing of the HyShot Supersonic Combustion Flight Experiment in HEG［M］. Berlin： Springer， 2005.
[11] Ekoto I W， Bowersox R D W， Beutner T， et al. Supersonic Boundary Layers with Periodic Surface Roughness［J］. AIAA Journal， 2008， 46（2）： 486-497.
[12] Liu H， Yan C， Zhao Y， et al. Uncertainty and Sensitivity Analysis of Flow Parameters on Aerodynamics of a Hypersonic Inlet［J］. Acta Astronautica， 2018， 151： 703-716.
[13] Iman R L， Helton J C. An Investigation of Uncertainty and Sensitivity Analysis Techniques for Computer Models［J］. Risk Analysis， 1988， 8（1）： 71-90.
[14] Xiu D， Karniadakis G E. The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations［J］. SIAM Journal on Scientific Computing， 2002， 24（2）： 619-644.
[15] Xiu D， Hesthaven J S. High-Order Collocation Methods for Differential Equations with Random Inputs［J］. SIAM Journal on Scientific Computing， 2005， 27（3）： 1118-1139.
[16] Witteveen J， Duraisamy K， Iaccarino G. Uncertainty Quantification and Error Estimation in Scramjet Simulation［R］. AIAA 2011-2283.
[17] Wang Q， Duraisamy K， Alonso J J， et al. Risk Assessment of Scramjet Unstart Using Adjoint-based Sampling Methods［J］. AIAA Journal， 2012， 50（3）： 581-592.
[18] Crow A J. Computational Uncertainty Quantification of Thermal Radiation in Supersonic Combustion Chambers［D］. Michigan： The University of Michigan， 2013.
[19] Jackson K， Gruber M， Barhorst T. The HIFiRE Flight 2 Experiment： An Overview and Status Update［R］. AIAA 2009-5029.
[20] Jackson K， Gruber M， Buccellato S. HIFiRE Flight 2 Overview and Status Update 2011［R］. AIAA 2011-2202.
[21] Gianluca G， Eldred M S， Iaccarino G. A Multifidelity Multilevel Monte Carlo Method for Uncertainty Propagation in Aerospace Applications［R］. AIAA 2017-1951.
[22] 张旭，王利，林言中，等. 超燃冲压发动机总体化性能分析［J］. 推进技术， 2014， 35（2）： 157-165.
[23] Champion KSW. Middle Atmosphere Density Data and Comparison with Models［J］. Advances in Space Research， 1990， 10（6）： 17-26.
[24] 张伟，王小永，于剑，等. 来流导致的高超声速气动热不确定度量化分析［J］. 北京航空航天大学学报， 2017， 303（5）： 211-218.
[25] 颜勇，祝培源，宋立明，等. 基于非平稳高斯过程的叶栅加工误差不确定性量化［J］. 推进技术， 2017（8）： 92-100.
[26] Villadsen J， Michelsen M L. Solution of Differential Equation Models by Polynomial Approximation［M］. New Jersey： Prentice-Hall， 1978.
[27] 汤涛，周涛. 不确定性量化的高精度数值方法和理论［J］. 中国科学：数学， 2015， 45（7）： 891-928.
[28] Chen H， Li L Y， Liu C C， et al. Uncertainty Quantification of the Surface Properties in Hypersonic Rarefied Cylinder Flows［C］. Glasgow： 31st International Symposium on Rarefied Gas Dynamics， 2018.
[29] 刘成诚，李林颖，余彬，等. 来流速度不确定度对超声速混合层流场特性影响研究［C］. 北京：第十八届全国激波与激波管学术会议， 2018.
[30] 陈浩，林震，刘成诚，等. 基于直接模拟蒙特卡洛方法的真空羽流不确定量化研究［J］. 推进技术， 2020， 41（1）： 73-84.
[31] Smolyak S A. Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions［J］. Reports of the Academy of Sciences of the USSR， 1963， 4： 240-243.
[32] Nobile F， Tempone R， Webster C. A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data［J］. SIAM Journal on Numerical Analysis， 2008， 46： 2309-2345.
[33] Nobile F， Tempone R， Webster C. An Anisotropic Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data［J］. SIAM Journal on Numerical Analysis， 2008， 46： 2411-2442.
[34] Michael K S. How Much Compression Should a Scramjet Inlet Do？［J］. AIAA Journal， 2006， 50（3）： 610-619.
[35] Cao R F， Chang J T， Tang J F， et al. Study on Combustion Mode Transition of Hydrogen Fueled Dual-Mode Scramjet Engine Based on Thermodynamic Cycle Analysis［J］. International Journal of Hydrogen Energy， 2014， 39： 21251-21258.

基于稀疏网格配置方法的超燃冲压发动机高维不确定性量化

High Dimensional Uncertainty Quantification in Scramjet Performance Analysis Using Sparse Grid Collocation Methods

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 0

编辑推荐

Metrics

本文评价