Bychkov V V, Kovalev K A, Liberman M A
Department of Plasma Physics, Umea University, S-901 87 Umea, Sweden.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1999 Sep;60(3):2897-911. doi: 10.1103/physreve.60.2897.
A time-dependent nonlinear equation for a nonstationary curved flame front of an arbitrary expansion coefficient is derived under the assumptions of a small but finite flame thickness and weak nonlinearity. On the basis of the derived equation, stability of two-dimensional curved stationary flames propagating in tubes with ideally adiabatic and slip walls is studied. The stability analysis shows that curved stationary flames become unstable for sufficiently wide tubes. The obtained stability limits are in a good agreement with the results of numerical simulations of flame dynamics and with semiqualitative stability analysis of curved stationary flames. Possible outcomes of the obtained instability at the nonlinear stage are discussed. The instability may result in extra wrinkles at a flame front close to the stability limits and in self-turbulization of the flame far from the limits. The self-turbulization can also be interpreted as a fractal structure. The fractal dimension of a flame front and velocity of a self-turbulized flame are evaluated.
在火焰厚度小但有限且非线性较弱的假设下，推导了具有任意膨胀系数的非定常弯曲火焰前沿的含时非线性方程。基于所推导的方程，研究了在具有理想绝热壁和滑移壁的管道中传播的二维弯曲定常火焰的稳定性。稳定性分析表明，对于足够宽的管道，弯曲定常火焰会变得不稳定。所得到的稳定性极限与火焰动力学数值模拟结果以及弯曲定常火焰的半定性稳定性分析结果吻合良好。讨论了在非线性阶段所得到的不稳定性可能产生的结果。这种不稳定性可能导致在接近稳定性极限的火焰前沿出现额外的褶皱，并导致远离极限处的火焰自湍流。自湍流也可解释为一种分形结构。评估了火焰前沿的分形维数和自湍流火焰的速度。
