A framework is proposed to investigate the behavior of LES flame surface density models for simple academic cases, here the development of a statistically one-dimensional flame in an homogenous and isotropic turbulence, by comparison with a prescribed reference solution. First, a set of zero-dimensional equations is derived to reproduce a fractal flame surface evolving from an initially planar shape up to equilibrium. Then, a balance equation including a sub-grid scale contribution is solved to mimic the evolution of the overall resolved flame surface in an actual large eddy simulation.

Non-dynamic and dynamic versions of an algebraic sub-grid scale flame surface wrinkling factor model are investigated. The non-dynamic model overestimates the total flame surface in early stages of the flame development while under (respectively over) estimation of unresolved surfaces are partly compensated by larger (respectively lower) resolved surfaces. Moreover, model parameters strongly affect flame response times possibly compromising the prediction of combustion instabilities. Results are improved using a dynamic flame surface wrinkling factor model.

The generality of conclusions are limited by the enforcement of the reference solution but the proposed approach is well-suited to qualitative investigations of sub-grid scale models at negligible computational costs, to support direct numerical simulation studies or to help in analyzing LES results. It also suggests new possible closures for future developments.

提出了一个框架来研究 LES 火焰表面密度模型在简单学术案例中的行为，这里是通过与规定的参考解决方案进行比较，在均匀和各向同性湍流中统计一维火焰的发展。首先，推导出一组零维方程来再现分形火焰表面，从最初的平面形状演变为平衡状态。然后，求解包含子网格尺度贡献的平衡方程，以模拟实际大涡模拟中整体解析火焰表面的演变。

研究了代数子网格尺度火焰表面起皱因子模型的非动态和动态版本。非动态模型在火焰发展的早期高估了总火焰表面，而对未解析表面的低估（分别高估）被较大（分别较低）的解析表面部分补偿。此外，模型参数强烈影响火焰响应时间，可能会影响燃烧不稳定性的预测。使用动态火焰表面起皱因子模型改进了结果。

结论的一般性受到参考解决方案的执行的限制，但所提出的方法非常适合以可忽略的计算成本对亚网格比例模型进行定性研究，以支持直接数值模拟研究或帮助分析 LES 结果。它还为未来的发展提出了新的可能关闭。