Brief Review of Recent Achievements in the Flamelet Manifold Selection and Probability Density Distribution for Flamelet Manifold Variables

Abstract The flamelet model is a commonly used tool for turbulent combustion simulations in the engineering field due to its computational efficiency and compatibility with complex chemical reaction mechanisms. Despite being widely used for decades, the flamelet model still faces challenges when applied to complex flame configurations, such as partially premixed flames, inhomogeneous inlets, supersonic combustion, or multiphase combustion. The principal challenges are posed by the uncertainty of the presumed shapes for probability density functions (PDFs) of the flamelet tabulation variables and the coupled process of turbulent diffusion and chemical reaction in turbulent combustion. Recent progress is reviewed from the viewpoint of the reaction manifold, with connections made to other combustion models, as well as the determination of joint (or conditional) PDFs for flamelet manifold parameters (e.g., progress variable, scalar dissipation rates, etc.). Promising improvements have been outlined in computational efficiency and the accuracy of predicted variable fields in simulating complex combustion systems (such as turbulent inhomogeneous combustion, combustion with multi-regime modes, and two-phase combustion). Advances in computational resources, direct numerical simulation data, artificial intelligence, stochastic simulation methods, and other dimension-reduction combustion models will contribute to the development of more accurate and efficient flamelet-like models for engineering applications.