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Modelling turbulence induced by hydrodynamic instability in differentially-rotating flow

模拟差动旋转流中由水动力不稳定性引起的湍流

基本信息

批准号：
EP/W019558/1
负责人：
Junho Park
金额：
$ 9.93万
依托单位：
Coventry University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2022
资助国家：
英国
起止时间：
2022 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FW019558%2F1
关键词：
Modelling turbulence induced hydrodynamic instability

项目摘要

Rotating fluid flow is ubiquitous in many naturally occurring and engineering systems and plays a crucial role. For instance, the turbulence of geophysical vortices in the oceans is responsible for the mixing of fluid momentum and scalars such as salinity or planktons. Rotating flow is also important in industrial processes to produce homogenised products by efficient turbulent mixing (e.g. glass or polymer manufacturing processes). Rotation profiles of fluid flow are often differential, i.e. the angular speed varies with radius from the rotation axis. Such differentially-rotating flow can become centrifugally unstable when an imbalance exists between the pressure gradient and centrifugal force, a situation arising when the angular momentum decreases with the radius. This centrifugal instability is very destructive and thus an important source of turbulence. Most of the studies on centrifugal instability have considered linear analyses in which perturbations that drive the instability are assumed to be small enough to neglect nonlinear terms in the governing equations. On the other hand, nonlinear development processes of the instability, such as saturation or laminar-turbulent transition, have not been thoroughly investigated. In particular, the nonlinear centrifugal instability is not fully understood under the combined effects of thermal diffusion and stratification. Fluid flow with heat transfer is a very common configuration in various natural and engineering systems, thus revealing the role of such thermal effects on turbulence can significantly contribute to our knowledge of multi-physical flow systems in physical sciences and engineering. This situation motivates the current research programme with two main objectives: (i) Investigate nonlinear development processes of the centrifugal instability under the effects of thermal diffusion and stratification, and; (ii) Develop a new turbulence model to apply to multi-physics simulations. In the first part of the programme, we will examine linear and nonlinear centrifugal instability of a famous rotating shear flow called Taylor-Couette (TC) flow, the flow between two concentric cylinders that rotate independently. We will first analyse linear centrifugal instability of the TC flow in thermally diffusive and stratified fluids using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) method. The linear analysis will reveal how the thermal effects affect the initial growth of small-amplitude perturbations and the WKBJ method will allow us to derive explicit mathematical expressions of the instability growth. Nonlinear instability will then be investigated by both direct numerical simulations and a semi-linear model. Such nonlinear analyses can demonstrate how nonlinear interactions between perturbations and base flow lead to the saturation or laminar-turbulent transition processes. The second part of the programme will focus on developing a new turbulence model. Results from linear and nonlinear stability analyses will be used to construct a turbulent viscosity to apply to multi-physics simulations. More specifically, we will apply the new model to the state-of-the-art code for stellar physics simulations of the evolution of rotating stars. The updated code will simulate the stellar evolution and produce results such as radial distributions of mass, angular momentum or chemicals in the stellar interior. The outcomes will be compared with those from other stellar evolution simulations and observations. By achieving the main objectives of the proposed research, we will advance our understanding of instability-induced turbulence and its role in the multi-physics processes of the evolution of star, as just one example. Such turbulence modelling will also be beneficial for researchers in other fields of physical sciences and engineering.

旋转流体流动在许多自然发生的和工程系统中普遍存在，并且起着至关重要的作用。例如，海洋中地球物理涡旋的湍流是造成流体动量和标量（如盐度或盐度）混合的原因。旋转流在工业过程中也很重要，可以通过有效的湍流混合生产均质产品（例如玻璃或聚合物制造过程）。流体流动的旋转轮廓通常是有差异的，即角速度随着距旋转轴的半径而变化。当压力梯度和离心力之间存在不平衡时，这种差动旋转流可能变得离心不稳定，当角动量随半径减小时出现这种情况。这种离心不稳定性具有很强的破坏性，因此是湍流的重要来源。大多数关于离心不稳定性的研究都考虑了线性分析，其中驱动不稳定性的扰动被假定为足够小，可以忽略控制方程中的非线性项。另一方面，不稳定性的非线性发展过程，如饱和或层流-湍流转变，还没有得到彻底的研究。特别是，在热扩散和分层的联合作用下，非线性离心不稳定性还没有完全理解。流体流动与传热是各种自然和工程系统中非常常见的结构，因此揭示这种热效应对湍流的作用可以显着有助于我们在物理科学和工程中的多物理流系统的知识。这种情况促使目前的研究计划有两个主要目标：（一）调查的非线性发展过程的离心不稳定的热扩散和分层的影响下，和（二）开发一个新的湍流模型，适用于多物理模拟。在该计划的第一部分中，我们将研究一个著名的旋转剪切流称为泰勒-库埃特（TC）流，两个独立旋转的同心圆柱之间的流动的线性和非线性离心不稳定性。我们将首先分析线性离心不稳定性的TC流在热扩散和分层流体使用Wentzel-Kramers-Brillouin-Jeffreys（WKBJ）方法。线性分析将揭示热效应如何影响小振幅扰动的初始增长，WKBJ方法将使我们能够导出不稳定性增长的显式数学表达式。非线性不稳定性，然后将调查直接数值模拟和半线性模型。这种非线性分析可以说明扰动和基流之间的非线性相互作用如何导致饱和或层流-湍流转变过程。该计划的第二部分将侧重于开发一个新的湍流模型。线性和非线性稳定性分析的结果将用于构建湍流粘度，以应用于多物理场模拟。更具体地说，我们将应用新模型的国家的最先进的代码恒星物理模拟旋转恒星的演化。更新后的代码将模拟恒星演化并产生恒星内部质量、角动量或化学物质的径向分布等结果。这些结果将与其他恒星演化模拟和观测结果进行比较。通过实现所提出的研究的主要目标，我们将推进我们的不稳定性引起的湍流及其在星星演化的多物理过程中的作用的理解，只是一个例子。这种湍流模型也将有利于物理科学和工程其他领域的研究人员。