Investigating the role of magnetic fields, instabilities and turbulence in fluid mixing

研究磁场、不稳定性和湍流在流体混合中的作用

• 批准号: 2606320
• 金额: --
• 依托单位: UNIVERSITY OF EXETER
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2021
• 资助国家: 英国
• 起止时间: 2021 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2606320
• 关键词: Investigating; role; magnetic; fields; instabilities

In hydrodynamic systems, a number of instabilities can grow from interface layers. These include two classic examples, the Rayleigh-Taylor instability, driven by gravity, and the Kelvin-Helmholtz instability, driven by shear flow. As these instabilities develop, non-linearities grow and a turbulent layer forms at the interface. A key characteristic of these layers is their growth in time which follows a self similar evolution (Zhou et al 2019).Analytically a similarity solution can be derived from the set of coupled PDEs that describe fluid motion, revealing the scaling with time for the expansion of the layer. These solutions can be extended to include further important physical complexities of the system, including modelling of density contrasts. This was performed by Hillier (2019) using a multi layer expansion which asymptotes to a model of the mean layer properties. Having a model of the mean layer properties allows important characteristics of the layer, including asymmetries and energy contained in the turbulent velocity field to be elucidated.The same linear instabilities that grow and develop the turbulent mixing layers in hydrodynamic systems also appear in magnetohydrodynamic (MHD) systems where magnetic fields and their dynamics couple with the flow. The non-linear MHD equations do permit similarity solutions, but there has only been limited work attempting to quantify how magnetic fields alter the mixing dynamics and with it the similarity solution. The key goal in this project is to develop similarity solutions in the MHD framework for interface turbulence mixing, benchmarking these solutions against 3D MHD simulations. This work can connect with turbulent mixing in industrial processes and astrophysical flows.

在流体动力系统中，许多不稳定性会从界面层产生。其中包括两个经典的例子，由重力驱动的瑞利-泰勒不稳定性和由剪切流驱动的开尔文-亥姆霍兹不稳定性。随着这些不稳定性的发展，非线性会增加，并在界面处形成湍流层。这些层的一个关键特征是它们随时间的增长，遵循自相似的演化（Zhou et al 2019）。通过分析，可以从描述流体运动的耦合偏微分方程组中导出相似解，从而揭示扩展随时间的缩放层的。这些解决方案可以扩展到包括系统的进一步重要的物理复杂性，包括密度对比建模。这是由 Hillier (2019) 使用多层展开来完成的，该多层展开渐近到平均层属性的模型。拥有平均层属性的模型可以阐明该层的重要特征，包括湍流速度场中包含的不对称性和能量。在流体动力系统中生长和发展湍流混合层的相同线性不稳定性也出现在磁流体动力学（MHD）中）磁场及其动力学与流动耦合的系统。非线性 MHD 方程确实允许相似解，但尝试量化磁场如何改变混合动力学及其相似解的工作非常有限。该项目的主要目标是在 MHD 框架中开发用于界面湍流混合的相似解决方案，并针对 3D MHD 模拟对这些解决方案进行基准测试。这项工作可以与工业过程和天体物理流中的湍流混合联系起来。