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.

繁殖前线无处不在反应扩散系统，其不稳定性和与流的相互作用是很重要的现象。例如，在预混合组合中，这是我们的主要重点，火焰不稳定性和火焰流相互作用对组合设备设计师带来了重要的建模挑战；特别是，火焰不稳定性，尤其是当与声学结合在一起是混合物失败的主要原因，而火焰流相互作用在发动机性能中起着重要作用。尽管进行了广泛的研究，但我们对这些现象的理解仍然存在很大的差距，尤其是对于厚火焰。文献中有理论通常仅限于相对于问题的典型长度尺度（例如组合室的大小或流场通常湍流的尺度）较薄的火焰。对于许多在应用中，诸如限制在较小间隙和高纵横比的几何形状的繁殖的应用中，这种稀薄的理论对许多重要的问题不满足，这是小规模流对有效的繁殖速度和火焰建模对基于压缩的微型生成的领域的影响。为了扩展我们解决此类问题和其他问题的能力，我们打算以预混合的结合发展润滑理论，并将其应用于更好地了解火焰不稳定性和火焰流相互作用。该理论适用于将火焰厚度视为小于或与典型的长度尺度在横向横向火焰传播方向上的典型长度尺度的情况。我们的方法基于与PI开创性的“厚火不对称限制”相对应的方法，它的目的是揭示和利用G.I的三个第二个贡献之间的链接。 Taylor，A。Turing和G.Damköhler分别与通常称为Taylor分散，Turing不稳定和Damköhler的动荡组合假设相关。另一个主要部分是在开发的润滑理论框架内投资火焰不稳定性。我们将首先在厚的火焰不对称极限中得出这种理论的数学模型，尤其是泰勒分散，可变密度和化学反应。由于泰勒色散会改变质量和热量的有效扩散系数，从而控制A（图灵样）热 - 散热的火焰不稳定性，因此我们将研究泰勒 - 分散对使用分析衍生物和数值模拟的泰勒 - 分散对热降低不稳定性的影响。然后将解决强制连接下各种火焰不稳定性之间的耦合，专门采用了在火焰上最近和当前活动实验中使用的Hele-Shaw单元格配置。最后，将针对单向多尺度流和二维涡流流进行火焰流相互作用，并将尝试合成发现结果以得出改进的公式以获得有效的传播速度。最后一步是将调查扩展到新的方向，尤其是在外部组合遇到的反应扩散前线，例如通过检查泰勒色散触发图灵样不稳定性的能力。为了确保最大程度的影响，我们的发现将通过两种组合期刊和应用数学期刊的出版物传达给广泛的受众，并通过更广泛的重点以及科学会议和项目跨学科的研讨会在项目的第三年中组织。

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