Abstract: 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.

Key words: active subspace methods, turbulent combustion, parameter dimension reduction, controlling mechanism, uncertainty quantification