非均匀含尘通道流的不稳定性机制
Mechanism of instability in non-uniform dusty channel flow
AI总结：
本文研究压力驱动非均匀含尘通道流的不稳定性机制，发现临界层与颗粒浓度变化重叠时产生新的重叠模式，推导临界层平衡方程揭示其物理机制，还分析了密度比和重力等因素的影响。
摘要：
压力驱动通道流中的颗粒通常呈非均匀分布。非均匀颗粒负载会产生两种低雷诺数不稳定性模式，这在洁净流体的泊肃叶流中不存在，本文将阐明其机制。研究观察到两类截然不同的行为：当主导扰动的临界层与颗粒浓度变化重叠时，会产生新的不稳定性，我们称之为重叠模式；但当这些层分离时，仅出现传统的托尔明-施利希廷不稳定性模式。我们沿洁净流体经典分析的思路，推导了该流动中主导的临界层平衡方程，揭示了临界层内的浓度变化如何引发两种颗粒驱动的不稳定性。由于这些变化，扰动动能的产生在性质和程度上都发生了显著改变。令人惊讶的是，尽管两种重叠模式的本征结构对称性和指数增长区域完全不同，但它们的能量收支几乎相同，这凸显了临界层内变化的相关性。研究表明壁面层并不重要。我们推导了包含完整方程中在流场某处占主导地位的所有项的最小复合理论，并证明它包含了关键物理机制。当颗粒相对于流体无限致密时，体积分数可忽略不计；但对于有限密度比，颗粒体积分数会形成有效粘度分布，在当前流动中表现为均匀稳定作用。本文忽略了重力，未来将对其进行研究；稳定性算子的非正态性导致的扰动瞬态增长也将是研究方向，以探索向湍流过渡的机制。
英文摘要：
Particles in pressure-driven channel flow are often inhomogeneously distributed. Two modes of low-Reynolds number instability, absent in Poiseuille flow of clean fluid, are created by inhomogeneous particle loading, and their mechanism is worked out here. Two distinct classes of behaviour are seen: when the critical layer of the dominant perturbation overlaps with variations in particle concentration, the new instabilities arise, which we term overlap modes. But when the layers are distinct, only the traditional Tollmien-Schlichting mode of instability occurs. We derive the dominant critical layer balance equations in this flow along the lines done classically for clean fluid. These reveal how concentration variations within the critical layer cause two the particle-driven instabilities. As a result of these variations, disturbance kinetic energy production is qualitatively and majorly altered. Surprisingly the two overlap modes, though completely different in the symmetry of the eigenstructure and regime of exponential growth, show practically identical energy budgets, highlighting the relevance of variations within the critical layer. The wall layer is shown to be unimportant. We derive a minimal composite theory comprising all terms in the complete equation which are dominant somewhere in the flow, and show that it contains the essential physics. When particles are infinitely dense relative to the fluid, the volume fraction is negligible. But for finite density ratios, the volume fraction of particles causes a profile of effective viscosity. This is shown to be uniformly stabilizing in the present flow. Gravity is neglected here, and will be important to study in future. So will transient growth of perturbations due to non-normality of the stability operator, in a quest for the mechanism of transition to turbulence.
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