Taylor dispersion, Turing instability and a lubrication theory for flames

泰勒色散、图灵不稳定性和火焰润滑理论

• 批准号: EP/V004840/1
• 负责人: Joel Daou
• 金额: $ 46.71万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Research Grant
• 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=EP%2FV004840%2F1
• 关键词: Taylor; dispersion; Turing; instability; lubrication

Propagating fronts are ubiquitous in reaction-diffusion systems and their instabilities and interactions with flows are phenomena of high practical importance. For example, in premixed combustion, which is our main focus, flame instabilities and flame-flow interactions pose important modelling challenges for the designers of combustion devices; in particular, flame instabilities, especially when coupled with acoustics are a major reason for combustor failure, and flame-flow interactions play an important role in engine performance.Despite extensive investigations, there are still huge gaps in our understanding of these phenomena especially for thick flames. Theories available in the literature are generally restricted to flames that are thin relative to the length scales typical of the problems such as the size of the combustion chamber or the scales of the flow field which is often turbulent. Such thin-flame theories are not satisfactory for many problems which are important in applications such as the propagation of flames confined to geometries with small gaps and high aspect ratios, the effect of small scale flows on the effective propagation speed and flame modelling in the developing field of combustion-based micropower generation. To extend our ability to address such problems and others, we intend to develop a lubrication theory in premixed combustion and apply it to better understand flame instabilities and flame-flow interactions. The theory is applicable in situations where the flame thickness may be considered smaller than, or comparable with, a typical length scale in a direction transverse to flame propagation. Our approach, based on a methodology corresponding to the 'thick flame asymptotic limit' pioneered by the PI, is original as it aims to unveil and exploit the links between three seminal contributions by G.I. Taylor, A. Turing and G. Damköhler associated respectively with what are commonly known as Taylor dispersion, Turing instability, and Damköhler's hypotheses of turbulent combustion.One major part of the project is to tackle challenging questions from turbulent combustion (such as the mechanism of the so-called bending effect), when these questions are formulated for laminar flames. Another major part is the investigation of flame instabilities in the framework of the lubrication theory being developed. We shall begin by deriving the mathematical models of such theory in the thick flame asymptotic limit, accounting in particular for Taylor dispersion, variable density and chemical reactions. Since Taylor dispersion modifies the effective diffusion coefficients of mass and heat which in turn control a (Turing-like) thermo-diffusive flame instability, we shall investigate the effect of Taylor-dispersion on the thermo-diffusive instability using analytical derivations and numerical simulations. The coupling between various flame instabilities under forced convection will then be addressed, adopting specifically the Hele-Shaw cell configuration used in recent and currently active experiments on flames. Finally the flame-flow interactions will be addressed for unidirectional multi-scale flows and two-dimensional vortical flows, and attempts will be made to synthesize the findings to derive improved formulas for the effective propagation speed. The final step is to extend the investigations in new directions, in particular to reaction-diffusion fronts encountered outside combustion, e.g. by examining the ability of Taylor dispersion to trigger Turing-like instabilities for such fronts. In order to ensure maximum impact, our findings will be communicated to a wide audience via publications in both combustion journals and applied mathematics journals with broader focus, as well as via scientific meetings and an inter-disciplinary workshop to be organised in the third year of the project.

传播前沿在反应扩散系统中无处不在，它们的不稳定性和与流动的相互作用是具有高度实际重要性的现象，例如，在我们主要关注的预混合燃烧中，火焰不稳定性和火焰流相互作用给设计者带来了重要的建模挑战。燃烧装置的稳定性；特别是，火焰不稳定性，特别是与声学相结合时，是燃烧器故障的主要原因，而火焰流相互作用在发动机性能中起着重要作用。我们对这些现象的理解仍然存在巨大差距，尤其是对于厚火焰，文献中提供的理论通常仅限于相对于燃烧室尺寸或流动规模等典型问题的长度尺度而言较薄的火焰。这种薄火焰理论对于许多在应用中很重要的问题并不令人满意，例如限制在小间隙和高纵横比的几何形状中的火焰传播、小规模流动对有效传播速度的影响。和为了扩展我们解决此类问题和其他问题的能力，我们打算开发预混合燃烧中的润滑理论，并将其应用于更好地理解火焰不稳定性和发展火焰流相互作用。适用于火焰厚度小于或等于火焰传播横向方向上的典型长度尺度的情况。我们的方法基于与由PI 是原创的，因为它旨在揭示和利用 G.I. Taylor、A. Turing 和 G. Damköhler 的三个开创性贡献之间的联系，这些贡献分别与通常所说的泰勒色散、图灵不稳定性和 Damköhler 的湍流燃烧假设相关。该项目的主要部分是解决湍流燃烧的挑战性问题（例如所谓的弯曲效应的机制），这些问题是针对层流火焰制定的。主要部分是在正在开发的润滑理论框架中研究火焰不稳定性，我们将首先推导厚火焰渐近极限的数学模型，特别是考虑泰勒色散、变密度和化学反应。泰勒色散修改了质量和热量的有效扩散系数，进而控制（类图灵）热扩散火焰不稳定性，我们将使用以下方法研究泰勒色散对热扩散不稳定性的影响然后将解决强制对流下各种火焰不稳定性之间的耦合，特别采用最近和当前活跃的火焰实验中使用的 Hele-Shaw 单元配置，最后将解决单向多方向火焰流相互作用。 -尺度流和二维涡流，并尝试综合这些发现，得出有效传播速度的改进公式。最后一步是将研究扩展到新的方向，特别是反应扩散前沿。外部燃烧，例如通过检查泰勒色散触发此类前沿的图灵不稳定性的能力，为了确保最大的影响，我们的研究结果将通过燃烧期刊和应用数学期刊上的出版物传达给更广泛的受众。 ，以及通过在项目第三年组织的科学会议和跨学科研讨会。

项目成果

Effects of curvature on triple flame propagation in fuel-oxidizer counterflow

• DOI: 10.1016/j.combustflame.2022.112353
• 发表时间: 2022-11
• 期刊: Combustion and Flame
• 影响因子: 4.4
• 作者: Shumeng Xie;Dehai Yu;J. Daou;Zheng Chen

Stability of diffusion flames under shear flow: Taylor dispersion and the formation of flame streets

• DOI: 10.1016/j.combustflame.2023.113003
• 发表时间: 2023-11
• 期刊: Combustion and Flame
• 影响因子: 4.4
• 作者: Prabakaran Rajamanickam;Aiden Kelly;J. Daou

Diffusive-thermal instabilities of a planar premixed flame aligned with a shear flow

与剪切流对齐的平面预混火焰的扩散热不稳定性

• DOI: 10.1080/13647830.2023.2254734
• 发表时间: 2023
• 期刊: Combustion Theory and Modelling
• 影响因子: 1.3
• 作者: Daou J

Flame stability under flow-induced anisotropic diffusion and heat loss

流动引起的各向异性扩散和热损失下的火焰稳定性

• DOI: 10.1016/j.combustflame.2022.112588
• 发表时间: 2023
• 期刊: Combustion and Flame
• 影响因子: 4.4
• 作者: Daou J

A thick reaction zone model for premixed flames in two-dimensional channels

二维通道中预混火焰的厚反应区模型

• DOI: 10.1080/13647830.2023.2174046
• 发表时间: 2023
• 期刊: Combustion Theory and Modelling
• 影响因子: 1.3
• 作者: Rajamanickam P