The present study examines, in presence of thermal expansion effects, the existence of the multiplicity of solutions previously reported within the context of diffusive-thermal modeling in [15], for lean premixed flames with low Lewis number (Le < 1) propagating in narrow circular adiabatic channels subject to a Poiseuille flow. For this, direct numerical simulations have been carried out within the framework of variable-density Navier–Stokes equations and zero-Mach-number approximation. The simulations, conducted for both axisymmetric and three-dimensional cylindrical geometries, confirm the coexistence of multiple steady flame structures for a given flow rate. They show that axisymmetric flames concave towards the upstream are more unstable to three-dimensional perturbations than convex (toward the upstream) flames. This result evinces earlier findings obtained from stability analysis. The non-axisymmetry property of the flame is also found to push back the critical flashback limits at larger flow rate when compared to those predicted under the assumption of flame axisymmetry.

本研究在存在热膨胀效应的情况下，检查了先前在[15]中的扩散热模型的背景下报道的解决方案的存在性，该解决方案是针对低Lewis值的稀薄预混火焰（Le <1）在受Poiseuille流动影响的狭窄圆形绝热通道中传播。为此，已经在变密度Navier–Stokes方程和零马赫数近似的框架内进行了直接数值模拟。针对轴对称和三维圆柱几何体进行的模拟，确认了在给定流量下多个稳定火焰结构的共存。他们表明，向上游凹入的轴对称火焰在三维扰动方面比凸向（朝上游）火焰更不稳定。该结果表明从稳定性分析获得了较早的发现。当与在假设火焰轴对称的情况下预测的极限相比时，还发现火焰的非轴对称特性以较大的流速将临界闪回极限推回了极限。