Advanced Instability Methods (AIM) Network

在许多科学和工业情况下，预测流动中的微小扰动是会增长(不稳定流)还是会衰减(稳定流)是很重要的。稳定性理论的工业应用包括：喷墨打印机中喷嘴的破碎；燃烧室中的大规模混合；燃气轮机中的热声振荡；风力涡轮机的耦合模式颤振以及制药应用中的小通道混合。传统的方法是将扰动分解成在两个空间维度上正常(即正交)的模式，并分别研究每个模式的增长。然而，这往往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(Re)数(即在所有速度下)都是稳定的。然而，在现实中，流动在Re~2000处变得湍流，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，在第三个空间维度上，模式是非正态的(即非正交的)。这意味着它们可以相互补充能量，不应分开考虑。这种不正常的行为往往会在科学家和工程师最感兴趣的中间时间导致强劲的瞬时增长。例如，在管流中，非正态分析预测，在Re~2000处，微小扰动将迅速发展为沿流方向的条纹，这与实验证据一致。在过去的十年里，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，非正态是他们所分析的简单流动的瞬变行为的根本原因。这一网络的目的是在更复杂的流动中加速开发，特别是那些与工业相关的流动。传统的稳定性分析目前应用于许多工业场合，对于简单的流动，可能会漏掉一些最重要的行为。非常规分析不仅更准确，还可以预测流动中对产生预期结果最有影响的区域，如良好的混合。在开发过程中，这些信息将使工程师能够从最终结果向后设计，而不是通过反复试验来进行“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能够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需要常规分析就足够的情况。为此，我们会检讨雷克管内的正则流动，例如喷流/尾流、管流、边界层和热声振荡，并加快进行一些工业个案研究。为此，我们会与学术界和工业界合作，建立一个跨学科的国际网络。技术目标将需要广泛的专门知识：数学，以保持对规范流动的理解；数值，以执行从简单流动到复杂流动时所需的高阶计算；实验，以收集证据目录，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明确，该网络将扩展到更广泛的行业社区。目前，有几个团体在这一领域开展工作，但在这个相对年轻的领域，它们之间几乎没有正式的互动。该网络将建立在英国在流动不稳定方面的传统优势之上，并纳入来自印度的合作伙伴，印度最近在非正常分析方面进行了一些杰出的工作。该网络将从一个非常重要的海外合作伙伴(来自法国巴黎理工大学的彼得·施密德)开始，并在两年的创业期内扩展到国际上。

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.