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

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

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

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。

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.