Advanced Instability Methods (AIM) Network

在许多科学和工业情况下，预测流动中的小扰动是增长（不稳定流动）还是衰减（稳定流动）是很重要的。稳定性理论的工业应用包括：喷墨打印机中喷墨的破裂；燃烧室内的大规模混合；燃气轮机热声振荡研究风力涡轮机的耦合模态颤振和制药用小通道的混合。传统的方法是将扰动分解为两个空间维度上的正态（即正交）模态，并分别研究每个模态的生长。然而，这通常会给出不准确的结果。作为一个简单的例子，该技术预测管道中的流动在所有雷诺数（即所有速度）下都是稳定的。然而，在实际中，在Re ~ 2000时，流动变得紊流，这取决于外部噪声和管道的粗糙度。这种差异的产生是因为，在第三空间维度中，模态是非正态的（即非正交的）。这意味着它们可以相互提供能量，不应该单独考虑。这种不正常的行为通常会在中间时间引起强烈的瞬态增长，这是科学家和工程师最感兴趣的。例如，在管道流动中，非正态分析预测，在Re ~ 2000，微小的扰动将迅速发展成流向的条纹，这与实验证据一致。在过去的十年中，应用数学界对非正态稳定性分析的兴趣激增。人们普遍认为，非正态性是他们所分析的简单流动的瞬态行为的根本原因。这个网络的目的是加速在较复杂的流动中开发，特别是与工业有关的流动。传统的稳定性分析目前应用于许多工业情况，对于简单的流动，可能会遗漏一些最重要的行为。非正态分析不仅更准确，而且还能预测流中对产生理想结果（如良好混合）影响最大的区域。随着开发，这些信息将允许工程师从最终结果“向后”设计，而不是通过试验和错误“向前”设计。我们的长期愿景是，下一代计算流体动力学工具将包含可以执行非正常稳定性分析的模块。一个重要的目标是区分需要非正态分析的情况和常规分析足够的情况。我们将通过回顾典型流动，如射流/尾迹，管道流动，边界层和Rijke管中的热声振荡，以及通过加快一些工业案例研究的工作来做到这一点。为了实现这一目标，我们将与学术和工业合作伙伴建立一个多学科的国际网络。技术目标将需要广泛的专业知识：数学，以保持对规范流程的理解；数值，执行高阶计算，这将是必要的，当从简单到复杂的流动；实验，收集证据目录，以证明该技术何时比正常模式分析更相关。随着适用范围变得更加清晰，该网络将扩展到更广泛的工业社区。目前，有几个小组正在这个领域工作，但在这个相对年轻的领域，他们之间很少有正式的互动。该网络将以英国在流量不稳定性方面的传统优势为基础，并吸纳来自印度的合作伙伴，印度最近在非常态分析方面做了一些杰出的工作。该网络将从一个非常重要的海外合作伙伴（来自法国巴黎综合理工学院的Peter Schmid）开始，并在两年的启动期间向国际扩展。

In many scientific and industrial situations, it is important to predict whether a small perturbation in a flow will grow (unstable flow) or decay (stable flow). Industrial applications of stability theory include: the break-up of the jet in an ink-jet printer; large scale mixing in a combustion chamber; thermo-acoustic oscillation in a gas turbine; coupled mode flutter of a wind turbine and mixing in small channels for pharmaceutical applications. The conventional technique is to decompose the perturbation into modes that are normal (i.e. orthogonal) in two spatial dimensions and to study the growth of each mode separately. This, however, often gives inaccurate results. As a simple example, this technique predicts that the flow in a pipe will be stable at all Reynolds (Re) numbers (i.e. at all velocities). In reality, however, the flow becomes turbulent at Re ~ 2000, depending on external noise and the pipe's roughness.This discrepancy arises because, in the third spatial dimension, the modes are non-normal (i.e. non-orthogonal). This means that they can feed energy into each other and should not be considered separately. This non-normal behaviour often causes strong transient growth at the intermediate times that are of most interest to scientists and engineers. For instance, in pipe flow, a non-normal analysis predicts that tiny perturbations will rapidly develop into stream-wise streaks at Re ~ 2000, agreeing with experimental evidence. In the last decade, there has been a surge of interest in non-normal stability analysis within the applied maths community. It is widely thought that non-normality is the root cause of the transient behaviour of the simple flows they have analysed. The aim of this network is to accelerate its exploitation in more complex flows, particularly those with industrial relevance. Conventional stability analyses are currently applied to many industrial situations and, as for simple flows, could miss some of the most significant behaviour.Non-normal analyses, as well as being more accurate, also predict the regions of a flow that are most influential in creating a desired result, such as good mixing. With development, this information will allow engineers to design 'backwards' from an end result, rather than 'forwards' by trial and error. Our long term vision is that the next generation of Computational Fluid Dynamics tools will contain modules that can perform non-normal stability analysis. An important goal is to distinguish between the situations in which a non-normal analysis is required and those in which a conventional analysis is sufficient. We will do this both by reviewing the canonical flows, such as jets/wakes, pipe flow, boundary layers and thermo-acoustic oscillations in a Rijke tube, and by accelerating work on a number of industrial case studies.To achieve this, we will create a multi-disciplinary international network with both academic and industrial partners. The technical goals will require a broad range of expertise: mathematical, to retain the understanding developed for the canonical flows; numerical, to perform the high order computations that will be necessary when moving from simple to complicated flows; experimental, to assemble a catalogue of evidence that will demonstrate when the technique is more relevant than normal mode analysis. The network will expand to a broader industrial community as the ranges of applicability becomes clearer. Currently, several groups are working in this area but, in this relatively young field, there is little formal interaction between them. The network will build on the UK's traditional strength in flow instability and incorporate partners from India, where there has recently been some outstanding work in non-normal analysis. The network will start with one very significant overseas partner (Peter Schmid from Ecole Polytechnique, France) and expand internationally during the two year start-up period.