The paper analyses the hydrodynamic instability of a flame propagating in the space between two parallel plates in the presence of gas flow. The linear analysis was performed in the framework of a two-dimensional model that describes the averaged gas flow in the space between the plates and the perturbations development of two-dimensional combustion wave. The model includes the parametric dependences of the flame front propagation velocity on its local curvature and on the combustible gas velocity averaged along the height of the channel. It is assumed that the viscous gas flow changes the surface area of the flame front and thereby affects the propagation velocity of the two-dimensional combustion wave. In the absence of the influence of the channel walls on the gas flow, the model transforms into the Darrieus–Landau model of flame hydrodynamic instability. The dependences of the instability growth rate on the wave vector of disturbances, the velocity of the unperturbed gas flow, the viscous friction coefficients and other parameters of the problem are obtained. It is shown that the viscous gas flow in the channel can lead, in some cases, to a significant increase in instability compared with a flame propagating in free space. In particular, the instability increment depends on the direction of the gas flow with respect direction of the flame propagation. In the case when the gas flow moves in the opposite direction to the direction of the flame propagation, the pulsating instability can appear.

中文翻译：

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气流存在下预混火焰在狭窄平面通道中传播的水动力不稳定性

该论文分析了在存在气流的情况下在两个平行板之间的空间中传播的火焰的流体动力学不稳定性。线性分析是在二维模型的框架内进行的，该模型描述了板之间空间中的平均气流和二维燃烧波的扰动发展。该模型包括火焰前沿传播速度对其局部曲率和沿通道高度平均的可燃气体速度的参数依赖性。假设粘性气流改变了火焰前沿的表面积，从而影响了二维燃烧波的传播速度。在没有通道壁对气流的影响的情况下，该模型转化为火焰流体动力学不稳定性的 Darrieus-Landau 模型。得到了不稳定增长率对扰动波矢量、未受扰动气流速度、粘性摩擦系数和问题其他参数的依赖关系。结果表明，与在自由空间中传播的火焰相比，通道中的粘性气流在某些情况下会导致不稳定性显着增加。特别地，不稳定性增量取决于相对于火焰传播方向的气体流动方向。在气体流动方向与火焰传播方向相反的情况下，会出现脉动不稳定性。得到未扰动气流的速度、粘性摩擦系数和问题的其他参数。结果表明，与在自由空间中传播的火焰相比，通道中的粘性气流在某些情况下会导致不稳定性显着增加。特别地，不稳定性增量取决于相对于火焰传播方向的气体流动方向。在气体流动方向与火焰传播方向相反的情况下，会出现脉动不稳定性。得到未扰动气流的速度、粘性摩擦系数和问题的其他参数。结果表明，与在自由空间中传播的火焰相比，通道中的粘性气流在某些情况下会导致不稳定性显着增加。特别地，不稳定性增量取决于相对于火焰传播方向的气体流动方向。当气流沿与火焰传播方向相反的方向运动时，就会出现脉动不稳定性。不稳定增量取决于相对于火焰传播方向的气体流动方向。在气体流动方向与火焰传播方向相反的情况下，会出现脉动不稳定性。不稳定增量取决于相对于火焰传播方向的气体流动方向。当气流沿与火焰传播方向相反的方向运动时，就会出现脉动不稳定性。