平板流内哈特曼边界层的稳定性分析

项目名称： 平板流内哈特曼边界层的稳定性分析

项目编号： No.11302076

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 董帅

作者单位： 华北电力大学（保定）

项目金额： 28万元

中文摘要： 平行平板内的流动稳定性及其随后发生的层流-湍流转捩过程，一直是流体力学研究中的中心问题和难题。当流体具有导电特性，且运行在垂直于流动方向的磁场环境中，上述问题会变得更加复杂。这一问题被称为哈特曼边界层的稳定性问题，近年来受到科学家和工程师的广泛关注。本研究课题拟采用非正则模态稳定性理论分析方法对平行平板流场内的流向条纹结构稳定性进行研究，获取最优次级扰动的空间分布形式和增长规律，以及流场在外界磁场作用下维持稳定的条件和相关临界参数。同时，申请人还将对激发层流-湍流转捩过程所需的最优非线性扰动，即最小扰动进行研究并获取其空间分布形式和变化规律。此外，申请人拟采用直接数值模拟方法对上述最优扰动激发的转捩过程中涉及到的层流-湍流边界问题开展动力学行为方面的研究，并获取相关流场结构。通过上述系统的研究，期望可以加深人们对哈特曼边界层内流动稳定性及层流-湍流转捩过程的认识和理解。

中文关键词： 哈特曼边界层；稳定性分析；非正则模态；最优扰动；磁场

英文摘要： The stability of channel flow between two parallel plates and the subsequent transition process have been the most important and central problems in fluid mechanics. It becomes more complex when the fluid is electrically conducting and working in the condition with magnetic field imposed externally in the wall-normal direction. In recent years, the so-called stability problem of Hartmann layer mentioned above, has received a lot of attention from scientists and engineers. In this project, the stability of streaks in the channel flow will be analyzed with nonmadal stability theory, and the optimal secondary perturbation in the linear framework will be solved. The effect of imposed magnetic field on the growth of optimal secondary perturbation will also be investigated and scaling laws of related parameters are expected to be obtained. Besides, the so-called minimal seed, or the nonlinear optimal perturbation with the smallest energy threshold triggering transition from laminar to turbulence state will be seeked in a furthur study. Taking the minimal seed as a starting point，the edge state between laminar and turbulence state in the presence of magnetic field will also be explored and the associated flow structures will be obtained and analyzed with direct numerical simulation method. The stability problem of Hart

英文关键词： Hartmann layer；stability analysis；non-modal ；optimal perturbation；magnetic field