湍流燃烧机理和调控的活性子空间分析方法

高效、低排放等需求促使发动机燃烧趋于近极限燃烧组织，亟需在稳定可控燃烧方面取得突破。湍流燃烧机理复杂，影响湍流燃烧数值模拟预测的物理化学和初始/边界条件参数众多。但是在该高维映射关系中，预测目标量往往仅在输入参数空间中的少数方向上梯度显著，称之为活跃方向。当活跃方向与空间基的方向不一致时，采用传统的全局敏感性方法难以高效地分析出主控参数以及后续的湍流燃烧机理。而活性子方法可以通过梯度的协方差矩阵特征分解得到上述活跃方向。本文综述了活性子空间方法理论及在湍流燃烧模拟中的应用：即探究海量输入参数空间中的活跃方向，构造低维活性子空间和低维响应面，从而高效地量化模拟不确定性、表征主控物理过程，从而揭示湍流燃烧机理。最后，进一步探讨了基于活性子空间分析方法的湍流燃烧调控。

Active subspace methods for analysis and optimization of turbulent combustion

The demands for high efficiency and low emissions have driven the engines to near-limit combustion, leading to an urgent need for the development of innovative methods to analyze and modulate turbulent flames for stable combustion. There is a huge number of parameters affecting the flames. The quantity of predicted targets in turbulent flames varies primarily along a few directions in the space of input parameters. The classic global sensitivity measures to determine the most influential parameters perform poorly when the directions of variability are not aligned with the natural coordinates of the input space. We present the active subspace methods to first detect the directions of the strongest variability using evaluations of the gradient and subsequently exploit these directions to construct a response surface on a low-dimensional subspace-i.e., the active subspace of the inputs. With the active subspace methods, a theoretical framework has been formulated to efficiently quantify the uncertainty originating from the parameters of chemical kinetics and physical models for a more rigorous assessment of the predictability of simulations and to investigate the evolution of the key physiochemical processes in turbulent flames. The approach has recently been demonstrated for uncertainty quantification and flame stabilization analysis in turbulent flames and model combustion systems. In this work, the major findings are reviewed, with a discussion on future work for the analysis and modulation of turbulent flames with active subspace methods.