The reaction progress variable is a crucial concept in the advanced flamelet combustion models. As a controlling variable, a well-defined progress variable must consider the essential features of the combustion process. It is usually a heuristically defined linear combination of some major chemical species mass fractions. However, such a simple definition could lead to inaccurate results for the fuel-rich reactive mixtures or complicated fuels, due to the vast number of chemical species in the combustion process. In this paper, a new method for generating a reaction progress variable is proposed through solving a constrained optimisation problem. The proposed method uses a genetic algorithm with new constraints. The major new constraint is the minimisation of the inverse of a progress variable-based Damköhler number in addition to the minimisation of the gradients of a collection of chemical species concentrations, as used in the previous methods. Hence, this scheme increases the Damköhler number defined based on the progress variable. The applicability and performance of the current optimised progress variable are evaluated for ethanol–air partially premixed flames in an axisymmetric two-dimensional counterflow burner and a two-dimensional plugged flow triple-flame burner. The effects of the number of chemical species included in the progress variable and the flow field strain rate on a partially premixed ethanol–air flame prediction are investigated. Results indicate that including the progress variable Damköhler number in the determination of the progress variable has a considerable effect on the accuracy of Flamelet Generated Manifold (FGM) model prediction of fuel-rich and lean reactive mixtures, especially at higher strain rates. Also, it is shown that the inclusion of the critical chemical species for ignition and fuel decomposition processes, such as CH₃O₂, CH₃CHO, sC₂H₄OH, HO₂, H and H₂O₂, in the definition of progress variable has a significant effect on the accuracy of the ethanol–air flame predictions.

反应进程变量是先进小火焰燃烧模型中的一个关键概念。作为控制变量，定义明确的进度变量必须考虑燃烧过程的基本特征。它通常是一些主要化学物质质量分数的启发式定义的线性组合。然而，由于燃烧过程中有大量化学物质，这种简单的定义可能会导致富含燃料的反应混合物或复杂燃料的结果不准确。本文提出了一种通过求解约束优化问题来生成反应进程变量的新方法。所提出的方法使用具有新约束的遗传算法。主要的新约束是最小化基于进度变量的 Damköhler 数的倒数，以及最小化化学物种浓度集合的梯度，如先前方法中使用的那样。因此，该方案增加了基于进度变量定义的 Damköhler 数。在轴对称二维逆流燃烧器和二维塞流三火焰燃烧器中，评估了当前优化的进度变量对乙醇-空气部分预混火焰的适用性和性能。研究了进展变量中包含的化学物质数量和流场应变率对部分预混乙醇-空气火焰预测的影响。结果表明，在确定进度变量时包括进度变量 Damköhler 数对富燃料和稀反应混合物的火焰生成歧管 (FGM) 模型预测的准确性有相当大的影响，尤其是在较高应变率下。此外，还表明包含用于点火和燃料分解过程的关键化学物质，例如 CH₃ O ₂、CH ₃ CHO、sC ₂ H ₄ OH、HO ₂、H 和H ₂ O ₂，​​在定义进度变量时对乙醇-空气火焰预测的准确性有显着影响。