论文标题
多分散粒子流动的广义稳定性理论。部分1。通道流
Generalized stability theory of polydisperse particle-laden flows. Part1. Channel flow
论文作者
论文摘要
我们提出了一种广泛的流体动力稳定性理论，用于在多分散粒子流中相互作用的颗粒。将分散的颗粒物添加到干净的流中可以稳定或破坏流动稳定，这取决于粒子的松弛时间尺度相对于载体流动时间尺度和颗粒载荷。为了研究多分散性和粒子相互作用对剪切流的流体动力稳定性的影响，我们通过结合线性稳定性分析和离散的欧拉分节式配方来提出一个新的数学框架，以描述流量和分散颗粒物。在此公式中，为分散相的每个尺寸截面编写了多动动量和传输方程，其中将相间和颗粒间质量和动量转移模拟为管理方程中的源项。通过线性化耦合方程来得出一个新的模态线性稳定性框架。使用这种方法，可以建模粒子流相互作用，例如多分散性，液滴汽化，凝结和聚结。该方法通过清洁和单分散颗粒流量的线性稳定性分析验证。我们表明，由于多分散性，载有颗粒的通道流的稳定性特征急剧变化。虽然相对较大的单分散颗粒倾向于稳定流量，但在低至中度的stokes数字中，添加非常小的质量分数的第二个尺寸段可能会大大提高生长速率，并且对于高雷诺数可能会破坏可能被认为是在Monodisperspesperse情况下被视为线性稳定的流量。这些发现可能适用于大量的流体力学应用，涉及含有颗粒的流量，例如大气流，环境流，医疗应用，推进和能量系统。
We present a generalized hydrodynamic stability theory for interacting particles in polydisperse particle-laden flows. The addition of dispersed particulate matter to a clean flow can either stabilize or destabilize the flow, depending on the particles' relaxation time-scale relative to the carrier flow time scales and the particle loading. To study the effects of polydispersity and particle interactions on the hydrodynamic stability of shear flows, we propose a new mathematical framework by combining a linear stability analysis and a discrete Eulerian sectional formulation to describe the flow and the dispersed particulate matter. In this formulation, multiple momentum and transport equations are written for each size-section of the dispersed phase, where interphase and inter-particle mass and momentum transfer are modelled as source terms in the governing equations. A new modal linear stability framework is derived by linearizing the coupled equations. Using this approach, particle-flow interactions, such as polydispersity, droplet vaporization, condensation, and coalescence, may be modelled. The method is validated with linear stability analyses of clean and monodisperse particle-laden flows. We show that the stability characteristics of a channel flow laden with particles drastically change due to polydispersity. While relatively large monodisperse particles tend to stabilize the flow, adding a second size section of a very small mass fraction of low-to-moderate Stokes number particles may significantly increase the growth rates, and for high-Reynolds numbers may destabilize flows that might have been regarded as linearly stable in the monodisperse case. These findings may apply to a vast number of fluid mechanics applications involving particle-laden flows such as atmospheric flows, environmental flows, medical applications, propulsion, and energy systems.
