We explore numerically the morphological patterns of thermo-diffusive instabilities in combustion fronts with a continuum fuel source, within a range of Lewis numbers and ignition temperatures, focusing on the cellular regime. For this purpose, we generalize the model of Brailovsky et al. to include distinct process kinetics and reactant heterogeneity. The generalized model is derived analytically and validated with other established models in the limit of infinite Lewis number for zero-order and first-order kinetics. Cellular and dendritic instabilities are found at low Lewis numbers thanks to a dynamic adaptive mesh refinement technique that reduces finite size effects, which can affect or even preclude the emergence of these patterns. This technique also allows achieving very large computational domains, enabling the study of system-size effects. Our numerical linear stability analysis is consistent with the analytical results of Brailovsky et al. The distinct types of dynamics found in the vicinity of the critical Lewis number, ranging from steady-state cells to continued tip-splitting and cell-merging, are well described within the framework of thermo-diffusive instabilities and are consistent with previous numerical studies. These types of dynamics are classified as "quasi-linear" and characterized by low amplitude cells and may follow the mode selection mechanism and growth prescribed by the linear theory. Below this range of Lewis number, highly non-linear effects become prominent and large amplitude, complex cellular and {\it{seaweed}} dendritic morphologies emerge.
Non-linear simulations of combustion instabilities with a quasi-1D Navier-Stokes code
由于稀薄预混燃烧系统比非预混系统更容易受到燃烧不稳定性的影响，因此对能够以高精度预测燃烧不稳定性的发生的改进的数值设计工具的需求日益增加。燃烧不稳定性中固有的非线性可能是至关重要的，我们在这里提出了一种方法，其中一维Navier-Stokes方程和标量输运方程求解的几何形状的变截面。重点是附着火焰，并为此目的，一个新的唯象模型的不稳定的热释放从火焰前锋介绍。在附着火焰法（AFM）中，热释放发生在火焰的整个长度上。根据Ditaranto和Hals [Combustion and Flame，146，493-512（2006）]对氧燃料火焰中的热声不稳定性的实验研究的结果，验证了使用AFM方法的非线性代码。数值模拟结果与实验测量结果一致，准确地再现了共振声压模式的频率和振幅。
Flame-wall interaction of thermodiffusively unstable hydrogen/air flames -- Part II: Parametric variations of equivalence ratio, temperature, and pressure
Acoustic radiation of thermodiffusively unstable turbulent lean premixed hydrogen-air flames
Polytechnic University of Bari（巴里理工大学）；CERFACS（法国燃烧研究与交流中心）；Institut de Mécanique des Fluides de Toulouse, IMFT, Université de Toulouse, CNRS（图卢兹大学CNRS图卢兹流体力学研究所）
Assessment of turbulent fire dynamics and combustion instabilities using a flamelet model
University of Science and Technology of China（中国科学技术大学）；State Key Laboratory of Fire Science（火灾科学国家重点实验室）；University of Wuppertal（乌珀塔尔大学）；Technical University of Darmstadt（达姆施塔特工业大学）
Synergy of turbulence and thermo-diffusive effects on the intermittent boundary-layer flashback of swirling flames
State Key Laboratory for Turbulence and Complex Systems, College of Engineering, Peking University（北京大学工学院湍流与复杂系统国家重点实验室）；HEDPS-CAPT, Peking University（北京大学高能量密度物理研究所）
