The shadow of turbulence: algorithms and applications

湍流的阴影：算法与应用

• 批准号: EP/W001748/1
• 负责人: George Papadakis
• 金额: $ 66.14万
• 依托单位: Imperial College London
• 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: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW001748%2F1
• 关键词: shadow; turbulence; algorithms; applications

In many areas, ranging from aerodynamics to combustion and thermo-acoustics, design optimisation problems have been traditionally solved using a combination of steady Reynolds-Averaged-Navier-Stokes (RANS) solvers for flow prediction and adjoint methods for sensitivity analysis. However, when scale-resolving turbulent flow simulations are employed for flow prediction, existing adjoint algorithms diverge and therefore do not provide useful sensitivities. This is due to the chaotic nature of turbulence that produces exponentially diverging trajectories in phase space, a phenomenon popularly known as the `butterfly effect', which leads to unphysically large sensitivities. Trends in computing resources suggest that unsteady turbulent flow simulations will take an increasingly larger role in the future, gradually replacing RANS-based methods. This will improve the ability to predict unsteady phenomena in complex flows, but will leave a large gap in the design cycle, because existing adjoint methods for design and optimisation cannot be applied.At the start of the previous decade, however, a paradigm-shifting approach for sensitivity analysis suitable for chaotic dynamics was proposed, which is based on the Shadowing Lemma, a fundamental result of dynamical systems theory. Shadowing-based adjoint methods prevent the exponential divergence of trajectories and can therefore provide accurate and realistic sensitivities in chaotic systems. This advance holds the unique potential to transform the engineering design practice as well as to accelerate fundamental turbulence research. However, existing implementations developed for generic chaotic systems, scale very poorly with Reynolds numbers, preventing their application for practical engineering flows. In addition, turbulent flows governed by the Navier-Stokes equations often violate fundamental assumptions utilised to prove the convergence of current shadowing-based algorithms and the relevance of these advances to turbulent fluid systems at present remains questionable.The ambition of this project is to break these challenges and develop the next-generation of tools that will enable researchers and practitioners to tackle design problems using scale-resolving simulations for flow prediction and optimisation. To this end, the project will leverage the expertise and track record of the groups at Imperial College London and University of Southampton. We plan to develop new shadowing-based adjoint algorithms that exploit structural properties of turbulent flows and therefore scale to real-world problems. The combination of recently developed turbulence analysis tools that allow for a compact description of the underlying dynamics together with shadowing-based sensitivity analysis is largely unexplored, yet it carries the potential to provide paradigm-shifting advances.To demonstrate the potential of the newly developed tools, two optimisation problems in wall-bounded flows will be considered, namely flow reconstruction using data assimilation in transitional boundary layers and design of optimal heterogeneous compliant coatings for turbulent friction drag reduction in pressure-driven flows. These flows display a wide range of flow mechanisms and instabilities that are relevant to a variety of engineering applications. The expectation is that synthesising the insight obtained from these applications will pave the path to real-world design applications.

在许多领域，从空气动力学到燃烧和热声学，设计优化问题传统上是使用稳态雷诺平均纳维尔-斯托克斯（RANS）求解器进行流预测和伴随方法进行灵敏度分析的组合来解决的。然而，当尺度分辨湍流模拟用于流动预测时，现有的伴随算法发散，因此不提供有用的灵敏度。这是由于湍流的混沌性质，在相空间中产生指数发散的轨迹，这种现象通常被称为“蝴蝶效应”，导致非物理性的大灵敏度。计算资源的趋势表明，非定常湍流模拟将在未来发挥越来越大的作用，逐渐取代基于RANS的方法。这将提高预测复杂流动中非定常现象的能力，但会在设计周期中留下很大的空白，因为现有的设计和优化伴随方法无法应用，然而，在上一个十年的开始，提出了一种适用于混沌动力学的灵敏度分析的范式转换方法，该方法基于动力系统理论的基本结果Shadowing Lemma。基于阴影的伴随方法可以防止轨迹的指数发散，因此可以提供准确和现实的混沌系统的灵敏度。这一进展具有改变工程设计实践和加速基础湍流研究的独特潜力。然而，现有的实现开发的通用混沌系统，规模非常差的雷诺数，防止其应用于实际的工程流。此外，本发明还提供了一种方法，由Navier-Stokes方程控制的湍流流动经常违反用于证明当前基于阴影的算法收敛性的基本假设，并且这些进展与湍流系统的相关性目前仍然存在疑问。该项目的目标是打破这些挑战，并开发下一代工具，使研究人员和从业人员能够使用比例尺来解决设计问题。解决模拟的流量预测和优化。为此，该项目将利用伦敦帝国理工学院和南安普顿大学的专业知识和跟踪记录。我们计划开发新的基于阴影的伴随算法，利用湍流的结构特性，从而扩展到现实世界的问题。最近开发的湍流分析工具结合了基于阴影的敏感性分析，可以对基本动力学进行紧凑的描述，这在很大程度上是未开发的，但它有可能提供范式转变的进步。为了证明新开发的工具的潜力，将考虑壁面流动中的两个优化问题，即在过渡边界层中使用数据同化的流动重构和用于在压力驱动的流动中减少湍流摩擦阻力的最佳非均质顺应涂层的设计。这些流动显示了与各种工程应用相关的各种流动机制和不稳定性。我们的期望是，综合从这些应用程序中获得的见解将为现实世界的设计应用铺平道路。

项目成果

Sensitivity analysis of chaotic systems using a frequency-domain shadowing approach

使用频域阴影方法对混沌系统进行灵敏度分析

• DOI: 10.1016/j.jcp.2022.111757
• 发表时间: 2023
• 期刊: Journal of Computational Physics
• 影响因子: 4.1
• 作者: Kantarakias K

Sensitivity-enhanced generalized polynomial chaos for efficient uncertainty quantification

• DOI: 10.1016/j.jcp.2023.112377
• 发表时间: 2022-06
• 期刊: ArXiv
• 作者: Kyriakos D. Kantarakias;G. Papadakis

Flow Reconstruction Around a Surface-Mounted Prism from Sparse Velocity and/or Scalar Measurements Using a Combination of POD and a Data-Driven Estimator

结合使用 POD 和数据驱动估算器，通过稀疏速度和/或标量测量重建表面安装棱镜周围的流动

• DOI: 10.1007/s10494-023-00417-2
• 发表时间: 2023
• 期刊: Flow, Turbulence and Combustion
• 作者: Lu S